%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW373+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 18:08:42 EDT 2024 % Result : Theorem 191.28s 191.39s % Output : CNFRefutation 191.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.13 % Problem : SWW373+1 : TPTP v8.2.0. Released v5.2.0. % 0.09/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n013.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Jun 19 09:23:54 EDT 2024 % 0.13/0.34 % CPUTime : % 0.62/0.63 start to proof:theBenchmark % 191.04/191.23 %------------------------------------------- % 191.04/191.23 % File :CSE---1.7 % 191.04/191.23 % Problem :theBenchmark % 191.04/191.23 % Transform :cnf % 191.04/191.23 % Format :tptp:raw % 191.04/191.23 % Command :java -jar mcs_scs.jar %d %s % 191.04/191.23 % 191.04/191.23 % Result :Theorem 171.580000s % 191.04/191.23 % Output :CNFRefutation 171.580000s % 191.04/191.23 %------------------------------------------- % 191.04/191.24 %------------------------------------------------------------------------------ % 191.04/191.24 % File : SWW373+1 : TPTP v8.2.0. Released v5.2.0. % 191.04/191.24 % Domain : Software Verification % 191.04/191.24 % Problem : Hoare's Logic with Procedures 435529, 5000 axioms selected % 191.04/191.24 % Version : Especial. % 191.04/191.24 % English : % 191.04/191.24 % 191.04/191.24 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 191.04/191.24 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 191.04/191.24 % Source : [Bla11] % 191.04/191.24 % Names : hoare_435529.5000.p [Bla11] % 191.04/191.24 % 191.04/191.24 % Status : ContradictoryAxioms % 191.04/191.24 % Rating : 0.81 v8.2.0, 0.78 v8.1.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.83 v7.0.0, 0.87 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, 1.00 v5.2.0 % 191.04/191.24 % Syntax : Number of formulae : 5250 (1739 unt; 0 def) % 191.04/191.24 % Number of atoms : 12616 (4519 equ) % 191.04/191.24 % Maximal formula atoms : 13 ( 2 avg) % 191.04/191.24 % Number of connectives : 8383 (1017 ~; 154 |; 719 &) % 191.04/191.24 % ( 891 <=>;5602 =>; 0 <=; 0 <~>) % 191.04/191.24 % Maximal formula depth : 22 ( 6 avg) % 191.04/191.24 % Maximal term depth : 19 ( 2 avg) % 191.04/191.24 % Number of predicates : 148 ( 147 usr; 2 prp; 0-7 aty) % 191.04/191.24 % Number of functors : 392 ( 392 usr; 56 con; 0-7 aty) % 191.04/191.24 % Number of variables : 16677 (16533 !; 144 ?) % 191.04/191.24 % SPC : FOF_CAX_RFO_SEQ % 191.04/191.24 % 191.04/191.24 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 191.04/191.24 % 2011-03-01 12:47:30 % 191.04/191.24 %------------------------------------------------------------------------------ % 191.04/191.24 %----Relevant facts (4986) % 191.04/191.24 fof(fact_ext,axiom, % 191.04/191.24 ! [V_g_2,V_f_2] : % 191.04/191.24 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 191.04/191.24 => V_f_2 = V_g_2 ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_empty,axiom, % 191.04/191.24 ! [V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 191.04/191.24 % 191.04/191.24 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 191.04/191.24 ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 191.04/191.24 % 191.04/191.24 fof(fact_cut,axiom, % 191.04/191.24 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 191.04/191.24 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 191.04/191.24 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_G_H_2) % 191.04/191.24 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_hoare__derivs_Oinsert,axiom, % 191.04/191.24 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 191.04/191.24 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.04/191.24 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 191.04/191.24 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_derivs__insertD,axiom, % 191.04/191.24 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 191.04/191.24 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) % 191.04/191.24 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.04/191.24 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_insertE,axiom, % 191.04/191.24 ! [V_A_2,V_b_2,V_a_2,T_a] : % 191.04/191.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 191.04/191.24 => ( V_a_2 != V_b_2 % 191.04/191.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_insertCI,axiom, % 191.04/191.24 ! [V_b_2,V_B_2,V_a_2,T_a] : % 191.04/191.24 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 191.04/191.24 => V_a_2 = V_b_2 ) % 191.04/191.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_emptyE,axiom, % 191.04/191.24 ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.24 % 191.04/191.24 fof(fact_singleton__iff,axiom, % 191.04/191.24 ! [V_a_2,V_b_2,T_a] : % 191.04/191.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 191.04/191.24 <=> V_b_2 = V_a_2 ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_singletonE,axiom, % 191.04/191.24 ! [V_a_2,V_b_2,T_a] : % 191.04/191.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 191.04/191.24 => V_b_2 = V_a_2 ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_MGT__BodyN,axiom, % 191.04/191.24 ! [V_G_2,V_pn_2] : % 191.04/191.24 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 191.04/191.24 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_MGF__lemma1,axiom, % 191.04/191.24 ! [V_ca_2,V_G_2] : % 191.04/191.24 ( c_Hoare__Mirabelle_Ostate__not__singleton % 191.04/191.24 => ( ! [B_x] : % 191.04/191.24 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 191.04/191.24 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) % 191.04/191.24 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 191.04/191.24 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_equalityCE,axiom, % 191.04/191.24 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 191.04/191.24 ( V_A_2 = V_B_2 % 191.04/191.24 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.24 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 191.04/191.24 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_empty__not__insert,axiom, % 191.04/191.24 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 191.04/191.24 % 191.04/191.24 fof(fact_insert__not__empty,axiom, % 191.04/191.24 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.24 % 191.04/191.24 fof(fact_doubleton__eq__iff,axiom, % 191.04/191.24 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.04/191.24 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.24 <=> ( ( V_a_2 = V_ca_2 % 191.04/191.24 & V_b_2 = V_d_2 ) % 191.04/191.24 | ( V_a_2 = V_d_2 % 191.04/191.24 & V_b_2 = V_ca_2 ) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_singleton__inject,axiom, % 191.04/191.24 ! [V_b_2,V_a_2,T_a] : % 191.04/191.24 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.24 => V_a_2 = V_b_2 ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_eq__mem__trans,axiom, % 191.04/191.24 ! [V_A_2,T_a,V_b_2,V_a_2] : % 191.04/191.24 ( V_a_2 = V_b_2 % 191.04/191.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 191.04/191.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_eqelem__imp__iff,axiom, % 191.04/191.24 ! [V_A_2,T_a,V_y_2,V_x_2] : % 191.04/191.24 ( V_x_2 = V_y_2 % 191.04/191.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.24 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_eqset__imp__iff,axiom, % 191.04/191.24 ! [V_x_2,T_a,V_B_2,V_A_2] : % 191.04/191.24 ( V_A_2 = V_B_2 % 191.04/191.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.24 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_mem__def,axiom, % 191.04/191.24 ! [V_A_2,V_x_2,T_a] : % 191.04/191.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.24 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_insert__code,axiom, % 191.04/191.24 ! [V_x_2,V_A_2,V_y_2,T_a] : % 191.04/191.24 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 191.04/191.24 <=> ( V_y_2 = V_x_2 % 191.04/191.24 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 191.04/191.24 % 191.04/191.24 fof(fact_insert__commute,axiom, % 191.04/191.25 ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) ). % 191.04/191.25 % 191.04/191.25 fof(fact_insert__absorb2,axiom, % 191.04/191.25 ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) ). % 191.04/191.25 % 191.04/191.25 fof(fact_equals0D,axiom, % 191.04/191.25 ! [V_a_2,T_a,V_A_2] : % 191.04/191.25 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.25 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_empty__iff,axiom, % 191.04/191.25 ! [V_ca_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.25 % 191.04/191.25 fof(fact_ex__in__conv,axiom, % 191.04/191.25 ! [V_A_2,T_a] : % 191.04/191.25 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.25 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_all__not__in__conv,axiom, % 191.04/191.25 ! [V_A_2,T_a] : % 191.04/191.25 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.25 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_insert__absorb,axiom, % 191.04/191.25 ! [V_A_2,V_a_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.25 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_insertI2,axiom, % 191.04/191.25 ! [V_b_2,V_B_2,V_a_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 191.04/191.25 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_insert__ident,axiom, % 191.04/191.25 ! [V_B_2,V_A_2,V_x_2,T_a] : % 191.04/191.25 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.25 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 191.04/191.25 => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2) % 191.04/191.25 <=> V_A_2 = V_B_2 ) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_insert__iff,axiom, % 191.04/191.25 ! [V_A_2,V_b_2,V_a_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 191.04/191.25 <=> ( V_a_2 = V_b_2 % 191.04/191.25 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_insertI1,axiom, % 191.04/191.25 ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 191.04/191.25 % 191.04/191.25 fof(fact_the__elem__eq,axiom, % 191.04/191.25 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ). % 191.04/191.25 % 191.04/191.25 fof(fact_BodyN,axiom, % 191.04/191.25 ! [V_G_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 191.04/191.25 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.04/191.25 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_weak__Body,axiom, % 191.04/191.25 ! [V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] : % 191.04/191.25 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.04/191.25 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_bot__apply,axiom, % 191.04/191.25 ! [V_x_2,T_b,T_a] : % 191.04/191.25 ( class_Orderings_Obot(T_a) % 191.04/191.25 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_com_Osimps_I6_J,axiom, % 191.04/191.25 ! [V_pname_H_2,V_pname_2] : % 191.04/191.25 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 191.04/191.25 <=> V_pname_2 = V_pname_H_2 ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_MGF__complete,axiom, % 191.04/191.25 ! [V_Q_2,V_P_2,V_ca_2] : % 191.04/191.25 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 191.04/191.25 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 191.04/191.25 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_eq__mem,axiom, % 191.04/191.25 ! [V_y_2,V_x_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 191.04/191.25 <=> V_x_2 = V_y_2 ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_evalc_OBody,axiom, % 191.04/191.25 ! [V_s1,V_s0,V_pn] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 191.04/191.25 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_evalc__elim__cases_I6_J,axiom, % 191.04/191.25 ! [V_s1,V_s,V_P] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 191.04/191.25 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_WT__bodiesD,axiom, % 191.04/191.25 ! [V_b,V_pn] : % 191.04/191.25 ( c_Com_OWT__bodies % 191.04/191.25 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 191.04/191.25 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_vimage__singleton__eq,axiom, % 191.04/191.25 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 191.04/191.25 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_hoare__sound,axiom, % 191.04/191.25 ! [V_ts_2,V_G_2,T_a] : % 191.04/191.25 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 191.04/191.25 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_vimageI,axiom, % 191.04/191.25 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 191.04/191.25 ( hAPP(V_f_2,V_a_2) = V_b_2 % 191.04/191.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 191.04/191.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_vimage__code,axiom, % 191.04/191.25 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 191.04/191.25 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_com__det,axiom, % 191.04/191.25 ! [V_u,V_t,V_s,V_c] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 191.04/191.25 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 191.04/191.25 => V_u = V_t ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_triple_Oinject,axiom, % 191.04/191.25 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 191.04/191.25 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 191.04/191.25 <=> ( V_fun1_2 = V_fun1_H_2 % 191.04/191.25 & V_com_2 = V_com_H_2 % 191.04/191.25 & V_fun2_2 = V_fun2_H_2 ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_vimage__eq,axiom, % 191.04/191.25 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 191.04/191.25 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_vimageD,axiom, % 191.04/191.25 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 191.04/191.25 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_vimageI2,axiom, % 191.04/191.25 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 191.04/191.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_vimage__empty,axiom, % 191.04/191.25 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.25 % 191.04/191.25 fof(fact_WT_Oequations_I7_J,axiom, % 191.04/191.25 ! [V_a_2] : % 191.04/191.25 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 191.04/191.25 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_evalc_Oequations_I9_J,axiom, % 191.04/191.25 ! [V_a3_2,V_a2_2,V_a1_2] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 191.04/191.25 <=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_insert__dom,axiom, % 191.04/191.25 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 191.04/191.25 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 191.04/191.25 => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_domI,axiom, % 191.04/191.25 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 191.04/191.25 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 191.04/191.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_WTs__elim__cases_I7_J,axiom, % 191.04/191.25 ! [V_P] : % 191.04/191.25 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 191.04/191.25 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_the_Osimps,axiom, % 191.04/191.25 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 191.04/191.25 % 191.04/191.25 fof(fact_triple_Osimps_I2_J,axiom, % 191.04/191.25 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 191.04/191.25 % 191.04/191.25 fof(fact_triple_Orecs,axiom, % 191.04/191.25 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 191.04/191.25 % 191.04/191.25 fof(fact_hoare__derivs_OSkip,axiom, % 191.04/191.25 ! [V_P_2,V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 191.04/191.25 % 191.04/191.25 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 191.04/191.25 ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 191.04/191.25 % 191.04/191.25 fof(fact_conseq2,axiom, % 191.04/191.25 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_G_2,T_a] : % 191.04/191.25 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.04/191.25 => ( ! [B_Z,B_s] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 191.04/191.25 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 191.04/191.25 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_conseq1,axiom, % 191.04/191.25 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_G_2,T_a] : % 191.04/191.25 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.04/191.25 => ( ! [B_Z,B_s] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 191.04/191.25 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 191.04/191.25 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_Comp,axiom, % 191.04/191.25 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_G_2,T_a] : % 191.04/191.25 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.04/191.25 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.04/191.25 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 191.04/191.25 ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 191.04/191.25 % 191.04/191.25 fof(fact_evalc_OSemi,axiom, % 191.04/191.25 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 191.04/191.25 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 191.04/191.25 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_evalc_OSkip,axiom, % 191.04/191.25 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 191.04/191.25 % 191.04/191.25 fof(fact_evalc__elim__cases_I1_J,axiom, % 191.04/191.25 ! [V_t,V_s] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 191.04/191.25 => V_t = V_s ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_WTs__elim__cases_I4_J,axiom, % 191.04/191.25 ! [V_c2,V_c1] : % 191.04/191.25 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 191.04/191.25 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 191.04/191.25 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_com_Osimps_I3_J,axiom, % 191.04/191.25 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 191.04/191.25 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 191.04/191.25 <=> ( V_com1_2 = V_com1_H_2 % 191.04/191.25 & V_com2_2 = V_com2_H_2 ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_com_Osimps_I13_J,axiom, % 191.04/191.25 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 191.04/191.25 % 191.04/191.25 fof(fact_com_Osimps_I12_J,axiom, % 191.04/191.25 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 191.04/191.25 % 191.04/191.25 fof(fact_evalc_Oequations_I4_J,axiom, % 191.04/191.25 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 191.04/191.25 <=> ? [B_s1] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 191.04/191.25 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_WT_OSemi,axiom, % 191.04/191.25 ! [V_c1,V_c0] : % 191.04/191.25 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 191.04/191.25 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 191.04/191.25 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_WT_Oequations_I4_J,axiom, % 191.04/191.25 ! [V_a2_2,V_a1_2] : % 191.04/191.25 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 191.04/191.25 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 191.04/191.25 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_com_Osimps_I48_J,axiom, % 191.04/191.25 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 191.04/191.25 % 191.04/191.25 fof(fact_com_Osimps_I49_J,axiom, % 191.04/191.25 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 191.04/191.25 % 191.04/191.25 fof(fact_evalc_Oequations_I1_J,axiom, % 191.04/191.25 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 191.04/191.25 % 191.04/191.25 fof(fact_WT_Oequations_I1_J,axiom, % 191.04/191.25 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 191.04/191.25 % 191.04/191.25 fof(fact_com_Osimps_I19_J,axiom, % 191.04/191.25 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 191.04/191.25 % 191.04/191.25 fof(fact_com_Osimps_I18_J,axiom, % 191.04/191.25 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 191.04/191.25 % 191.04/191.25 fof(fact_WT_OSkip,axiom, % 191.04/191.25 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 191.04/191.25 % 191.04/191.25 fof(fact_elem__set,axiom, % 191.04/191.25 ! [V_xo_2,V_x_2,T_a] : % 191.04/191.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 191.04/191.25 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 191.04/191.25 % 191.04/191.25 fof(fact_option_Oinject,axiom, % 191.04/191.26 ! [V_a_H_2,V_a_2,T_a] : % 191.04/191.26 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 191.04/191.26 <=> V_a_2 = V_a_H_2 ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_option_Orecs_I2_J,axiom, % 191.04/191.26 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_option_Osimps_I5_J,axiom, % 191.04/191.26 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_ranI,axiom, % 191.04/191.26 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 191.04/191.26 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 191.04/191.26 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_is__none__code_I2_J,axiom, % 191.04/191.26 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_domD,axiom, % 191.04/191.26 ! [V_m_2,T_b,V_a_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 191.04/191.26 => ? [B_b] : hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),B_b) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_evalc__elim__cases_I4_J,axiom, % 191.04/191.26 ! [V_t,V_s,V_c2,V_c1] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 191.04/191.26 => ~ ! [B_s1] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 191.04/191.26 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite__dom__body,axiom, % 191.04/191.26 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 191.04/191.26 % 191.04/191.26 fof(fact_vimageE,axiom, % 191.04/191.26 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 191.04/191.26 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_WT_OBody,axiom, % 191.04/191.26 ! [V_pn] : % 191.04/191.26 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 191.04/191.26 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_ospec,axiom, % 191.04/191.26 ! [V_x_2,V_P_2,V_A_2,T_a] : % 191.04/191.26 ( ! [B_x] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Option_Oset(T_a,V_A_2))) % 191.04/191.26 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.04/191.26 => ( V_A_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 191.04/191.26 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_WTs__elim__cases_I8_J,axiom, % 191.04/191.26 ! [V_a_2,V_P_2,V_X_2] : % 191.04/191.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2))) % 191.04/191.26 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_vimage__insert,axiom, % 191.04/191.26 ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup1E,axiom, % 191.04/191.26 ! [V_x_2,V_B_2,V_A_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 191.04/191.26 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 191.04/191.26 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup1CI,axiom, % 191.04/191.26 ! [T_a,V_A_2,V_x_2,V_B_2] : % 191.04/191.26 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 191.04/191.26 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 191.04/191.26 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_UnE,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.26 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_UnCI,axiom, % 191.04/191.26 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 191.04/191.26 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 191.04/191.26 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) % 191.04/191.26 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_is__none__code_I1_J,axiom, % 191.04/191.26 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_is__none__def,axiom, % 191.04/191.26 ! [V_x_2,T_a] : % 191.04/191.26 ( c_Option_Ois__none(T_a,V_x_2) % 191.04/191.26 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_option_Orecs_I1_J,axiom, % 191.04/191.26 ! [V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 191.04/191.26 % 191.04/191.26 fof(fact_option_Osimps_I4_J,axiom, % 191.04/191.26 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__absorb,axiom, % 191.04/191.26 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__commute,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__left__absorb,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__left__commute,axiom, % 191.04/191.26 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__assoc,axiom, % 191.04/191.26 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_bex__Un,axiom, % 191.04/191.26 ! [V_P_2,V_B_2,V_A_2,T_a] : % 191.04/191.26 ( ? [B_x] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.26 & hBOOL(hAPP(V_P_2,B_x)) ) % 191.04/191.26 <=> ( ? [B_x] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.26 & hBOOL(hAPP(V_P_2,B_x)) ) % 191.04/191.26 | ? [B_x] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 191.04/191.26 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_ball__Un,axiom, % 191.04/191.26 ! [V_P_2,V_B_2,V_A_2,T_a] : % 191.04/191.26 ( ! [B_x] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.26 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.04/191.26 <=> ( ! [B_x] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.26 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.04/191.26 & ! [B_x] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 191.04/191.26 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_com_Osimps_I7_J,axiom, % 191.04/191.26 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 191.04/191.26 ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) % 191.04/191.26 <=> ( V_vname_2 = V_vname_H_2 % 191.04/191.26 & V_pname_2 = V_pname_H_2 % 191.04/191.26 & V_fun_2 = V_fun_H_2 ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup1I1,axiom, % 191.04/191.26 ! [V_B_2,T_a,V_x_2,V_A_2] : % 191.04/191.26 ( hBOOL(hAPP(V_A_2,V_x_2)) % 191.04/191.26 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup1I2,axiom, % 191.04/191.26 ! [V_A_2,T_a,V_x_2,V_B_2] : % 191.04/191.26 ( hBOOL(hAPP(V_B_2,V_x_2)) % 191.04/191.26 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__iff,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.26 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.26 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_UnI1,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.26 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_UnI2,axiom, % 191.04/191.26 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 191.04/191.26 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__empty__left,axiom, % 191.04/191.26 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__empty__right,axiom, % 191.04/191.26 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__empty,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,T_a] : % 191.04/191.26 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.26 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.26 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__insert__right,axiom, % 191.04/191.26 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_Un__insert__left,axiom, % 191.04/191.26 ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_not__None__eq,axiom, % 191.04/191.26 ! [T_a,V_x_2] : % 191.04/191.26 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 191.04/191.26 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_not__Some__eq,axiom, % 191.04/191.26 ! [T_a,V_x_2] : % 191.04/191.26 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 191.04/191.26 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_option_Osimps_I3_J,axiom, % 191.04/191.26 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 191.04/191.26 % 191.04/191.26 fof(fact_option_Osimps_I2_J,axiom, % 191.04/191.26 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 191.04/191.26 % 191.04/191.26 fof(fact_vimage__Un,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_com_Osimps_I62_J,axiom, % 191.04/191.26 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_com_Osimps_I63_J,axiom, % 191.04/191.26 ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_com_Osimps_I50_J,axiom, % 191.04/191.26 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_com_Osimps_I51_J,axiom, % 191.04/191.26 ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_com_Osimps_I20_J,axiom, % 191.04/191.26 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_com_Osimps_I21_J,axiom, % 191.04/191.26 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 191.04/191.26 % 191.04/191.26 fof(fact_insert__is__Un,axiom, % 191.04/191.26 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2) ). % 191.04/191.26 % 191.04/191.26 fof(fact_domIff,axiom, % 191.04/191.26 ! [V_m_2,T_b,V_a_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 191.04/191.26 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 191.04/191.26 ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.26 % 191.04/191.26 fof(fact_set__empty__eq,axiom, % 191.04/191.26 ! [V_xo_2,T_a] : % 191.04/191.26 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.26 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_WT_Oequations_I8_J,axiom, % 191.04/191.26 ! [V_a3_2,V_a1_2,V_a2_2] : % 191.04/191.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 191.04/191.26 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_WT_OCall,axiom, % 191.04/191.26 ! [V_a_2,V_X_2,V_pn_2] : % 191.04/191.26 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2))) % 191.04/191.26 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite_OinsertI,axiom, % 191.04/191.26 ! [V_a_2,V_A_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.26 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite_OemptyI,axiom, % 191.04/191.26 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__apply,axiom, % 191.04/191.26 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 191.04/191.26 ( class_Lattices_Olattice(T_a) % 191.04/191.26 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite__UnI,axiom, % 191.04/191.26 ! [V_G_2,V_F_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) % 191.04/191.26 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_G_2))) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite__Un,axiom, % 191.04/191.26 ! [V_G_2,V_F_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_G_2))) % 191.04/191.26 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.26 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite__insert,axiom, % 191.04/191.26 ! [V_A_2,V_a_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 191.04/191.26 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__bot__left,axiom, % 191.04/191.26 ! [V_x,T_a] : % 191.04/191.26 ( class_Lattices_Obounded__lattice__bot(T_a) % 191.04/191.26 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__bot__right,axiom, % 191.04/191.26 ! [V_x,T_a] : % 191.04/191.26 ( class_Lattices_Obounded__lattice__bot(T_a) % 191.04/191.26 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__eq__bot__iff,axiom, % 191.04/191.26 ! [V_y_2,V_x_2,T_a] : % 191.04/191.26 ( class_Lattices_Obounded__lattice__bot(T_a) % 191.04/191.26 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 191.04/191.26 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 191.04/191.26 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite_Oequations_I1_J,axiom, % 191.04/191.26 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.26 % 191.04/191.26 fof(fact_map__comp__None__iff,axiom, % 191.04/191.26 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 191.04/191.26 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 191.04/191.26 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 191.04/191.26 | ? [B_k_H] : % 191.04/191.26 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 191.04/191.26 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_map__comp__simps_I1_J,axiom, % 191.04/191.26 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 191.04/191.26 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 191.04/191.26 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_map__comp__Some__iff,axiom, % 191.04/191.26 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 191.04/191.26 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) % 191.04/191.26 <=> ? [B_k_H] : % 191.04/191.26 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 191.04/191.26 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_map__comp__simps_I2_J,axiom, % 191.04/191.26 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 191.04/191.26 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 191.04/191.26 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite,axiom, % 191.04/191.26 ! [V_A_2,T_a] : % 191.04/191.26 ( class_Finite__Set_Ofinite(T_a) % 191.04/191.26 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite__code,axiom, % 191.04/191.26 ! [V_A_2,T_a] : % 191.04/191.26 ( class_Finite__Set_Ofinite(T_a) % 191.04/191.26 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup_Oidem,axiom, % 191.04/191.26 ! [V_a,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__idem,axiom, % 191.04/191.26 ! [V_x,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup_Ocommute,axiom, % 191.04/191.26 ! [V_b,V_a,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => 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) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_inf__sup__aci_I5_J,axiom, % 191.04/191.26 ! [V_y,V_x,T_a] : % 191.04/191.26 ( class_Lattices_Olattice(T_a) % 191.04/191.26 => 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) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__commute,axiom, % 191.04/191.26 ! [V_y,V_x,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => 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) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup_Oleft__idem,axiom, % 191.04/191.26 ! [V_b,V_a,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => 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) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_inf__sup__aci_I8_J,axiom, % 191.04/191.26 ! [V_y,V_x,T_a] : % 191.04/191.26 ( class_Lattices_Olattice(T_a) % 191.04/191.26 => 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) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__left__idem,axiom, % 191.04/191.26 ! [V_y,V_x,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => 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) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup_Oleft__commute,axiom, % 191.04/191.26 ! [V_c,V_a,V_b,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => 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)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_inf__sup__aci_I7_J,axiom, % 191.04/191.26 ! [V_z,V_y,V_x,T_a] : % 191.04/191.26 ( class_Lattices_Olattice(T_a) % 191.04/191.26 => 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)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__left__commute,axiom, % 191.04/191.26 ! [V_z,V_y,V_x,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => 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)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup_Oassoc,axiom, % 191.04/191.26 ! [V_c,V_b,V_a,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => 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)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_inf__sup__aci_I6_J,axiom, % 191.04/191.26 ! [V_z,V_y,V_x,T_a] : % 191.04/191.26 ( class_Lattices_Olattice(T_a) % 191.04/191.26 => 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)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_sup__assoc,axiom, % 191.04/191.26 ! [V_z,V_y,V_x,T_a] : % 191.04/191.26 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.26 => 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)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_folding__one_Oinsert,axiom, % 191.04/191.26 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.26 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.26 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_folding__one__idem_Ounion__idem,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.26 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.26 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.26 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 191.04/191.26 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.26 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.26 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_folding__image__simple_Oinsert,axiom, % 191.04/191.26 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.26 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 191.04/191.26 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 191.04/191.26 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.26 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.04/191.26 => 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)) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 191.04/191.26 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.26 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.26 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_finite__induct,axiom, % 191.04/191.26 ! [V_P_2,V_F_2,T_a] : % 191.04/191.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.26 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.26 => ( ! [B_x,B_F] : % 191.04/191.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 191.04/191.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 191.04/191.26 => ( hBOOL(hAPP(V_P_2,B_F)) % 191.04/191.26 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 191.04/191.26 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 191.04/191.26 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.26 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 191.04/191.26 => 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) ) ) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_ran__map__upd,axiom, % 191.04/191.26 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 191.04/191.26 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 191.04/191.26 => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ) ). % 191.04/191.26 % 191.04/191.26 fof(fact_folding__one__idem_Oin__idem,axiom, % 191.04/191.26 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.26 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 191.04/191.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.26 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oinsert,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one__idem_Oidem,axiom, % 191.04/191.27 ! [V_x_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 191.04/191.27 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__image__simple__idem_Oidem,axiom, % 191.04/191.27 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.27 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_map__upd__eqD1,axiom, % 191.04/191.27 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 191.04/191.27 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) % 191.04/191.27 => V_x_2 = V_y_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_map__upd__triv,axiom, % 191.04/191.27 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 191.04/191.27 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 191.04/191.27 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_map__upd__Some__unfold,axiom, % 191.04/191.27 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 191.04/191.27 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 191.04/191.27 <=> ( ( V_x_2 = V_a_2 % 191.04/191.27 & V_b_2 = V_y_2 ) % 191.04/191.27 | ( V_x_2 != V_a_2 % 191.04/191.27 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Osingleton,axiom, % 191.04/191.27 ! [V_x_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__image__simple_Oempty,axiom, % 191.04/191.27 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.27 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oin__idem,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oinsert__idem,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Ounion__idem,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.27 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oidem,axiom, % 191.04/191.27 ! [V_x,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one_Osingleton,axiom, % 191.04/191.27 ! [V_x_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.27 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__triv,axiom, % 191.04/191.27 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oclosed,axiom, % 191.04/191.27 ! [V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.04/191.27 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one_Oclosed,axiom, % 191.04/191.27 ! [V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.04/191.27 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oremove,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 191.04/191.27 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_dom__fun__upd,axiom, % 191.04/191.27 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 191.04/191.27 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 191.04/191.27 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) % 191.04/191.27 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 191.04/191.27 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one_Oremove,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 191.04/191.27 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__image__simple_Oremove,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.27 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Ounion__inter,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.27 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oinsert__remove,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 191.04/191.27 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_x_2),V_A_2) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf1E,axiom, % 191.04/191.27 ! [V_x_2,V_B_2,V_A_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 191.04/191.27 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 191.04/191.27 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf1I,axiom, % 191.04/191.27 ! [T_a,V_B_2,V_x_2,V_A_2] : % 191.04/191.27 ( hBOOL(hAPP(V_A_2,V_x_2)) % 191.04/191.27 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 191.04/191.27 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_IntE,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.27 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_IntI,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 191.04/191.27 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_DiffE,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.27 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_DiffI,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 191.04/191.27 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_finite__Int,axiom, % 191.04/191.27 ! [V_G_2,V_F_2,T_a] : % 191.04/191.27 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.27 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) % 191.04/191.27 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_G_2))) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_finite__Diff,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Inf__fin_Oidem,axiom, % 191.04/191.27 ! [V_x,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf1D2,axiom, % 191.04/191.27 ! [V_x_2,V_B_2,V_A_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 191.04/191.27 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf1D1,axiom, % 191.04/191.27 ! [V_x_2,V_B_2,V_A_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 191.04/191.27 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__Int2,axiom, % 191.04/191.27 ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__Int__distrib2,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__assoc,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__Diff,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__idemp,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__Int__distrib,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__left__commute,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__left__absorb,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__commute,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__absorb,axiom, % 191.04/191.27 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__apply,axiom, % 191.04/191.27 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_minus__apply,axiom, % 191.04/191.27 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 191.04/191.27 ( class_Groups_Ominus(T_a) % 191.04/191.27 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__assoc,axiom, % 191.04/191.27 ! [V_z,V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__sup__aci_I2_J,axiom, % 191.04/191.27 ! [V_z,V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf_Oassoc,axiom, % 191.04/191.27 ! [V_c,V_b,V_a,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__left__commute,axiom, % 191.04/191.27 ! [V_z,V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__sup__aci_I3_J,axiom, % 191.04/191.27 ! [V_z,V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf_Oleft__commute,axiom, % 191.04/191.27 ! [V_c,V_a,V_b,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__left__idem,axiom, % 191.04/191.27 ! [V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => 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) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__sup__aci_I4_J,axiom, % 191.04/191.27 ! [V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => 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) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf_Oleft__idem,axiom, % 191.04/191.27 ! [V_b,V_a,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => 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) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__commute,axiom, % 191.04/191.27 ! [V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => 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) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__sup__aci_I1_J,axiom, % 191.04/191.27 ! [V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => 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) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf_Ocommute,axiom, % 191.04/191.27 ! [V_b,V_a,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => 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) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__idem,axiom, % 191.04/191.27 ! [V_x,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf_Oidem,axiom, % 191.04/191.27 ! [V_a,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__disjoint,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__triv,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Un__Diff__Int,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__Un,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__Int,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fold__inf__insert,axiom, % 191.04/191.27 ! [V_a_2,V_b_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__bot__right,axiom, % 191.04/191.27 ! [V_x,T_a] : % 191.04/191.27 ( class_Lattices_Obounded__lattice__bot(T_a) % 191.04/191.27 => 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) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__bot__left,axiom, % 191.04/191.27 ! [V_x,T_a] : % 191.04/191.27 ( class_Lattices_Obounded__lattice__bot(T_a) % 191.04/191.27 => 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) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__sup__absorb,axiom, % 191.04/191.27 ! [V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => 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 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_sup__inf__absorb,axiom, % 191.04/191.27 ! [V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => 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 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__sup__distrib1,axiom, % 191.04/191.27 ! [V_z,V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Odistrib__lattice(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_sup__inf__distrib1,axiom, % 191.04/191.27 ! [V_z,V_y,V_x,T_a] : % 191.04/191.27 ( class_Lattices_Odistrib__lattice(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__sup__distrib2,axiom, % 191.04/191.27 ! [V_x,V_z,V_y,T_a] : % 191.04/191.27 ( class_Lattices_Odistrib__lattice(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_sup__inf__distrib2,axiom, % 191.04/191.27 ! [V_x,V_z,V_y,T_a] : % 191.04/191.27 ( class_Lattices_Odistrib__lattice(T_a) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_DiffD2,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_DiffD1,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__iff,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.27 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_IntD2,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_IntD1,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__iff,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.27 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fold__empty,axiom, % 191.04/191.27 ! [V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__cancel,axiom, % 191.04/191.27 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__empty,axiom, % 191.04/191.27 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 191.04/191.27 % 191.04/191.27 fof(fact_empty__Diff,axiom, % 191.04/191.27 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_finite__Diff2,axiom, % 191.04/191.27 ! [V_A_2,V_B_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.27 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_disjoint__iff__not__equal,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 <=> ! [B_x] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.27 => ! [B_xa] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 191.04/191.27 => B_x != B_xa ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__empty__right,axiom, % 191.04/191.27 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__empty__left,axiom, % 191.04/191.27 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_insert__inter__insert,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Un__Diff,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Un__Diff__cancel2,axiom, % 191.04/191.27 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Un__Diff__cancel,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Un__Int__crazy,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Un__Int__distrib2,axiom, % 191.04/191.27 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__Un__distrib2,axiom, % 191.04/191.27 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Un__Int__distrib,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__Un__distrib,axiom, % 191.04/191.27 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_vimage__Diff,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_vimage__Int,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_insert__Diff1,axiom, % 191.04/191.27 ! [V_A_2,V_B_2,V_x_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 191.04/191.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_insert__Diff__if,axiom, % 191.04/191.27 ! [V_A_2,V_B_2,V_x_2,T_a] : % 191.04/191.27 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 191.04/191.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) % 191.04/191.27 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 191.04/191.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_insert__Diff__single,axiom, % 191.04/191.27 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__insert2,axiom, % 191.04/191.27 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__insert,axiom, % 191.04/191.27 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.27 % 191.04/191.27 fof(fact_finite__Diff__insert,axiom, % 191.04/191.27 ! [V_B_2,V_a_2,V_A_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)))) % 191.04/191.27 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__insert__left__if1,axiom, % 191.04/191.27 ! [V_B_2,V_C_2,V_a_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__insert__right__if1,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_a_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__insert__left__if0,axiom, % 191.04/191.27 ! [V_B_2,V_C_2,V_a_2,T_a] : % 191.04/191.27 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__insert__right__if0,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_a_2,T_a] : % 191.04/191.27 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__insert__left,axiom, % 191.04/191.27 ! [V_B_2,V_C_2,V_a_2,T_a] : % 191.04/191.27 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 191.04/191.27 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Int__insert__right,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_a_2,T_a] : % 191.04/191.27 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 191.04/191.27 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_insert__Diff,axiom, % 191.04/191.27 ! [V_A_2,V_a_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Diff__insert__absorb,axiom, % 191.04/191.27 ! [V_A_2,V_x_2,T_a] : % 191.04/191.27 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_union__fold__insert,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),V_B_2),V_A_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fold__sup__insert,axiom, % 191.04/191.27 ! [V_a_2,V_b_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2)) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_inf__Sup__absorb,axiom, % 191.04/191.27 ! [V_a_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_dom__minus,axiom, % 191.04/191.27 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 191.04/191.27 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 191.04/191.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 191.04/191.27 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_a_2),V_A_2) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__image__simple_Ounion__inter,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.04/191.27 => 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)) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__idem__iff,axiom, % 191.04/191.27 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 191.04/191.27 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__upd,axiom, % 191.04/191.27 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__same,axiom, % 191.04/191.27 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__apply,axiom, % 191.04/191.27 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 191.04/191.27 ( ( V_z_2 = V_x_2 % 191.04/191.27 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) % 191.04/191.27 & ( V_z_2 != V_x_2 % 191.04/191.27 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__twist,axiom, % 191.04/191.27 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] : % 191.04/191.27 ( V_a_2 != V_ca_2 % 191.04/191.27 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_ca_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_ca_2),V_d_2)),V_a_2),V_b_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__other,axiom, % 191.04/191.27 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 191.04/191.27 ( V_z_2 != V_x_2 % 191.04/191.27 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__idem,axiom, % 191.04/191.27 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 191.04/191.27 ( hAPP(V_f_2,V_x_2) = V_y_2 % 191.04/191.27 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 191.04/191.27 ! [V_a_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_a_2),V_A_2) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one_Oeq__fold_H,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_x_2),V_A_2) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.27 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one_Oinsert__remove,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 191.04/191.27 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one_Ounion__inter,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.27 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__one_Ounion__disjoint,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.27 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.04/191.27 => ( 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)) % 191.04/191.27 => 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)) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__left__comm_Ofold__rec,axiom, % 191.04/191.27 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 191.04/191.27 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__None__restrict,axiom, % 191.04/191.27 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 191.04/191.27 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 191.04/191.27 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) % 191.04/191.27 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 191.04/191.27 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Inf__fin_Oremove,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 191.04/191.27 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 191.04/191.27 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__left__comm_Ofold__insert,axiom, % 191.04/191.27 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__upd__restrict__conv,axiom, % 191.04/191.27 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 191.04/191.27 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_restrict__fun__upd,axiom, % 191.04/191.27 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 191.04/191.27 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 191.04/191.27 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) % 191.04/191.27 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 191.04/191.27 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_finite__empty__induct,axiom, % 191.04/191.27 ! [V_P_2,V_A_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 191.04/191.27 => ( ! [B_a,B_A] : % 191.04/191.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 191.04/191.27 => ( hBOOL(hAPP(V_P_2,B_A)) % 191.04/191.27 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) % 191.04/191.27 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_x_2),V_A_2) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Inf__fin_Ounion__inter,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.27 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 191.04/191.27 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.27 => 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)) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_restrict__in,axiom, % 191.04/191.27 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 191.04/191.27 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_restrict__restrict,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Inf__fin_Osingleton,axiom, % 191.04/191.27 ! [V_x_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_restrict__out,axiom, % 191.04/191.27 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 191.04/191.27 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_restrict__map__insert,axiom, % 191.04/191.27 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ). % 191.04/191.27 % 191.04/191.27 fof(fact_dom__restrict,axiom, % 191.04/191.27 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ). % 191.04/191.27 % 191.04/191.27 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 191.04/191.27 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.27 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_sup__Inf__absorb,axiom, % 191.04/191.27 ! [V_a_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Inf__fin_Oin__idem,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.27 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Inf__fin_Oinsert__idem,axiom, % 191.04/191.27 ! [V_x_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ). % 191.04/191.27 % 191.04/191.27 fof(fact_Inf__fin_Ounion__idem,axiom, % 191.04/191.27 ! [V_B_2,V_A_2,T_a] : % 191.04/191.27 ( class_Lattices_Olattice(T_a) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.27 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 191.04/191.28 ! [V_a_2,V_A_2,T_a] : % 191.04/191.28 ( class_Lattices_Olattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_a_2),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__upd__restrict,axiom, % 191.04/191.28 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__fin_Oinsert,axiom, % 191.04/191.28 ! [V_x_2,V_A_2,T_a] : % 191.04/191.28 ( class_Lattices_Olattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__fin_Oinsert__remove,axiom, % 191.04/191.28 ! [V_x_2,V_A_2,T_a] : % 191.04/191.28 ( class_Lattices_Olattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 191.04/191.28 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : % 191.04/191.28 ( class_Lattices_Olattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__fin_Oclosed,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( class_Lattices_Olattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_ran__restrictD,axiom, % 191.04/191.28 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2)))) % 191.04/191.28 => ? [B_x] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.04/191.28 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Sup__fold__sup,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),c_Orderings_Obot__class_Obot(T_a)),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.04/191.28 => ( ! [B_x] : % 191.04/191.28 ( 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))) % 191.04/191.28 => hAPP(V_g_2,B_x) = V_z_2 ) % 191.04/191.28 => 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)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 191.04/191.28 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 191.04/191.28 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__diff1,axiom, % 191.04/191.28 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Oab__group__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 191.04/191.28 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__diff1__ring,axiom, % 191.04/191.28 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Rings_Oring(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_restrict__upd__same,axiom, % 191.04/191.28 ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_restrict__complement__singleton__eq,axiom, % 191.04/191.28 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_ComplI,axiom, % 191.04/191.28 ! [V_A_2,V_ca_2,T_a] : % 191.04/191.28 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 191.04/191.28 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__eq__Compl__iff,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : % 191.04/191.28 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2) % 191.04/191.28 <=> V_A_2 = V_B_2 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_double__complement,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 191.04/191.28 % 191.04/191.28 fof(fact_compl__eq__compl__iff,axiom, % 191.04/191.28 ! [V_y_2,V_x_2,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 191.04/191.28 <=> V_x_2 = V_y_2 ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_uminus__apply,axiom, % 191.04/191.28 ! [V_x_2,V_A_2,T_b,T_a] : % 191.04/191.28 ( class_Groups_Ouminus(T_a) % 191.04/191.28 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_double__compl,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_ComplE,axiom, % 191.04/191.28 ! [V_A_2,V_ca_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 191.04/191.28 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_ComplD,axiom, % 191.04/191.28 ! [V_A_2,V_ca_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 191.04/191.28 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__iff,axiom, % 191.04/191.28 ! [V_A_2,V_ca_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 191.04/191.28 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__UnionD,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_vimage__Compl,axiom, % 191.04/191.28 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm__idem__insert,axiom, % 191.04/191.28 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inf__compl__bot,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_compl__inf__bot,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__eq,axiom, % 191.04/191.28 ! [V_y,V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_compl__sup,axiom, % 191.04/191.28 ! [V_y,V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_compl__inf,axiom, % 191.04/191.28 ! [V_y,V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm__idem__sup,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.28 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm__idem__inf,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.28 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__disjoint,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__disjoint2,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__Un,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__Int,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__Diff__eq,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Diff__Compl,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Diff__eq,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__diff1__nat,axiom, % 191.04/191.28 ! [V_f_2,V_A_2,V_a_2,T_a] : % 191.04/191.28 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 191.04/191.28 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_sup__Sup__fold__sup,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_B_2),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Sup__fin__Sup,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Sup__binary,axiom, % 191.04/191.28 ! [V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Sup__insert,axiom, % 191.04/191.28 ! [V_A_2,V_a_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Sup__singleton,axiom, % 191.04/191.28 ! [V_a_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Sup__empty,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_UnionI,axiom, % 191.04/191.28 ! [V_A_2,V_C_2,V_X_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Union__disjoint,axiom, % 191.04/191.28 ! [V_A_2,V_C_2,T_a] : % 191.04/191.28 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 <=> ! [B_x] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 191.04/191.28 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__diff__eq,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Oab__group__add(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum_Oremove,axiom, % 191.04/191.28 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__diff1_H,axiom, % 191.04/191.28 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_compl__unique,axiom, % 191.04/191.28 ! [V_y,V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 191.04/191.28 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_UNIV__I,axiom, % 191.04/191.28 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Sup__UNIV,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Union__UNIV,axiom, % 191.04/191.28 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__fun__UNIVD2,axiom, % 191.04/191.28 ! [T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__right__imp__eq,axiom, % 191.04/191.28 ! [V_c,V_a,V_b,T_a] : % 191.04/191.28 ( class_Groups_Ocancel__semigroup__add(T_a) % 191.04/191.28 => ( 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) % 191.04/191.28 => V_b = V_c ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__imp__eq,axiom, % 191.04/191.28 ! [V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 191.04/191.28 => ( 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) % 191.04/191.28 => V_b = V_c ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__left__imp__eq,axiom, % 191.04/191.28 ! [V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ocancel__semigroup__add(T_a) % 191.04/191.28 => ( 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) % 191.04/191.28 => V_b = V_c ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__right__cancel,axiom, % 191.04/191.28 ! [V_ca_2,V_a_2,V_b_2,T_a] : % 191.04/191.28 ( class_Groups_Ocancel__semigroup__add(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2) % 191.04/191.28 <=> V_b_2 = V_ca_2 ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__left__cancel,axiom, % 191.04/191.28 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Groups_Ocancel__semigroup__add(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2) % 191.04/191.28 <=> V_b_2 = V_ca_2 ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 191.04/191.28 ! [V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Oab__semigroup__add(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_top__apply,axiom, % 191.04/191.28 ! [V_x_2,T_b,T_a] : % 191.04/191.28 ( class_Orderings_Otop(T_a) % 191.04/191.28 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__option__UNIV,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))) % 191.04/191.28 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__Plus__UNIV__iff,axiom, % 191.04/191.28 ! [T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))) % 191.04/191.28 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.28 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__Prod__UNIV,axiom, % 191.04/191.28 ! [T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__diff__cancel,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => 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 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__add__cancel,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => 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 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__add__cancel,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => 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 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__minus__cancel,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => 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 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__add,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__add__distrib,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Oab__group__add(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_UNIV__not__empty,axiom, % 191.04/191.28 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__UNIV,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Finite__Set_Ofinite(T_a) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Un__UNIV__left,axiom, % 191.04/191.28 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Un__UNIV__right,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Int__UNIV__left,axiom, % 191.04/191.28 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 191.04/191.28 % 191.04/191.28 fof(fact_Int__UNIV__right,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 191.04/191.28 % 191.04/191.28 fof(fact_vimage__UNIV,axiom, % 191.04/191.28 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__minus__eq__add,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_ab__diff__minus,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Oab__group__add(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__def,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_sup__top__right,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Obounded__lattice__top(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_sup__top__left,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Obounded__lattice__top(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inf__top__left,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Obounded__lattice__top(T_a) % 191.04/191.28 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inf__top__right,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Obounded__lattice__top(T_a) % 191.04/191.28 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inf__eq__top__iff,axiom, % 191.04/191.28 ! [V_y_2,V_x_2,T_a] : % 191.04/191.28 ( class_Lattices_Obounded__lattice__top(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 191.04/191.28 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 191.04/191.28 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Diff__UNIV,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__empty__eq,axiom, % 191.04/191.28 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__UNIV__eq,axiom, % 191.04/191.28 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__compl,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 191.04/191.28 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__partition,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__partition2,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Compl__eq__Diff__UNIV,axiom, % 191.04/191.28 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2) ). % 191.04/191.28 % 191.04/191.28 fof(fact_compl__top__eq,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_compl__bot__eq,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_sup__compl__top,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_compl__sup__top,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__Un__nat,axiom, % 191.04/191.28 ! [V_f_2,V_B_2,V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Union__empty,axiom, % 191.04/191.28 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__eq__diff__eq,axiom, % 191.04/191.28 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Groups_Oab__group__add(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 191.04/191.28 => ( V_a_2 = V_b_2 % 191.04/191.28 <=> V_ca_2 = V_d_2 ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_neg__equal__iff__equal,axiom, % 191.04/191.28 ! [V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 191.04/191.28 <=> V_a_2 = V_b_2 ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__equation__iff,axiom, % 191.04/191.28 ! [V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 191.04/191.28 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_equation__minus__iff,axiom, % 191.04/191.28 ! [V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 191.04/191.28 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__minus,axiom, % 191.04/191.28 ! [V_a,T_a] : % 191.04/191.28 ( class_Groups_Ogroup__add(T_a) % 191.04/191.28 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Union__insert,axiom, % 191.04/191.28 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Union__Un__distrib,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Un__eq__Union,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__insert,axiom, % 191.04/191.28 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_F_2)) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum_Oinsert,axiom, % 191.04/191.28 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__Un__Int,axiom, % 191.04/191.28 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.28 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum_Oinsert__remove,axiom, % 191.04/191.28 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__Un__disjoint,axiom, % 191.04/191.28 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.28 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setsum__Un,axiom, % 191.04/191.28 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Oab__group__add(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 191.04/191.28 ! [V_y,V_x,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__ring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__Union,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 191.04/191.28 => ( ! [B_M] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__fold__inf,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),c_Orderings_Otop__class_Otop(T_a)),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_insert__partition,axiom, % 191.04/191.28 ! [V_F_2,V_x_2,T_a] : % 191.04/191.28 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 191.04/191.28 => ( ! [B_x] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) % 191.04/191.28 => ! [B_xa] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) % 191.04/191.28 => ( B_x != B_xa % 191.04/191.28 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 191.04/191.28 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_UnionE,axiom, % 191.04/191.28 ! [V_C_2,V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 191.04/191.28 => ~ ! [B_X] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 191.04/191.28 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__upd__left,axiom, % 191.04/191.28 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 191.04/191.28 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 191.04/191.28 => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 191.04/191.28 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2) % 191.04/191.28 => c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Diff1__fold__graph,axiom, % 191.04/191.28 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2)) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__upd__image,axiom, % 191.04/191.28 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 191.04/191.28 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) % 191.04/191.28 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__monoid__big_Oinfinite,axiom, % 191.04/191.28 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 191.04/191.28 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.28 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__Inter,axiom, % 191.04/191.28 ! [V_M_2,T_a] : % 191.04/191.28 ( ? [B_x] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 191.04/191.28 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_top1I,axiom, % 191.04/191.28 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_image__eqI,axiom, % 191.04/191.28 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 191.04/191.28 ( V_b_2 = hAPP(V_f_2,V_x_2) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_InterE,axiom, % 191.04/191.28 ! [V_X_2,V_C_2,V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_InterD,axiom, % 191.04/191.28 ! [V_X_2,V_C_2,V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__imageI,axiom, % 191.04/191.28 ! [V_h_2,T_b,V_F_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inter__empty,axiom, % 191.04/191.28 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__assoc,axiom, % 191.04/191.28 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2) ). % 191.04/191.28 % 191.04/191.28 fof(fact_rev__image__eqI,axiom, % 191.04/191.28 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_imageI,axiom, % 191.04/191.28 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_image__iff,axiom, % 191.04/191.28 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 191.04/191.28 <=> ? [B_x] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.04/191.28 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_range__eqI,axiom, % 191.04/191.28 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 191.04/191.28 ( V_b_2 = hAPP(V_f_2,V_x_2) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_rangeI,axiom, % 191.04/191.28 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_image__is__empty,axiom, % 191.04/191.28 ! [V_A_2,V_f_2,T_a,T_b] : % 191.04/191.28 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_image__empty,axiom, % 191.04/191.28 ! [V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_empty__is__image,axiom, % 191.04/191.28 ! [V_A_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) % 191.04/191.28 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_image__insert,axiom, % 191.04/191.28 ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_image__Un,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 191.04/191.28 ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 191.04/191.28 ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2) ). % 191.04/191.28 % 191.04/191.28 fof(fact_surj__image__vimage__eq,axiom, % 191.04/191.28 ! [V_A_2,V_f_2,T_a,T_b] : % 191.04/191.28 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inter__UNIV,axiom, % 191.04/191.28 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Int__eq__Inter,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inter__insert,axiom, % 191.04/191.28 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inter__Un__distrib,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_empty__fold__graphE,axiom, % 191.04/191.28 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) % 191.04/191.28 => V_x_2 = V_z_2 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph_OemptyI,axiom, % 191.04/191.28 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph_Oequations_I1_J,axiom, % 191.04/191.28 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph__imp__finite,axiom, % 191.04/191.28 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__None,axiom, % 191.04/191.28 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 191.04/191.28 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 191.04/191.28 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 191.04/191.28 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__find__right,axiom, % 191.04/191.28 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 191.04/191.28 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 191.04/191.28 => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__UNIV,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 191.04/191.28 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 191.04/191.28 => V_y_2 = V_x_2 ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_insert__image,axiom, % 191.04/191.28 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__vimageD,axiom, % 191.04/191.28 ! [V_F_2,V_h_2,T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 191.04/191.28 => ( hAPP(c_Set_Oimage(T_a,T_b,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_image__vimage__eq,axiom, % 191.04/191.28 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_UNIV__option__conv,axiom, % 191.04/191.28 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__range__updI,axiom, % 191.04/191.28 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph_OinsertI,axiom, % 191.04/191.28 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 191.04/191.28 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 191.04/191.28 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 191.04/191.28 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 191.04/191.28 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 191.04/191.28 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 191.04/191.28 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 191.04/191.28 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 191.04/191.28 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 191.04/191.28 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__SomeD,axiom, % 191.04/191.28 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 191.04/191.28 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 191.04/191.28 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 191.04/191.28 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 191.04/191.28 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__Some__iff,axiom, % 191.04/191.28 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 191.04/191.28 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 191.04/191.28 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 191.04/191.28 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 191.04/191.28 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_dom__map__add,axiom, % 191.04/191.28 ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__upd,axiom, % 191.04/191.28 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm_Ofold__equality,axiom, % 191.04/191.28 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 191.04/191.28 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__singleton,axiom, % 191.04/191.28 ! [V_a_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__empty,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_image__map__upd,axiom, % 191.04/191.28 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 191.04/191.28 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__insert,axiom, % 191.04/191.28 ! [V_A_2,V_a_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 191.04/191.28 ! [V_c,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 191.04/191.28 ! [V_d,V_c,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 191.04/191.28 ! [V_d,V_c,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 191.04/191.28 ! [V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 191.04/191.28 ! [V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 191.04/191.28 ! [V_d,V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_map__add__comm,axiom, % 191.04/191.28 ! [V_m2_2,V_m1_2,T_b,T_a] : % 191.04/191.28 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 191.04/191.28 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__binary,axiom, % 191.04/191.28 ! [V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inf__Inf__fold__inf,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__fin__Inf,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold1Set_Ointros,axiom, % 191.04/191.28 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 191.04/191.28 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => ? [B_y_H] : % 191.04/191.28 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 191.04/191.28 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__add__inverse2,axiom, % 191.04/191.28 ! [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 ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__add__inverse,axiom, % 191.04/191.28 ! [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 ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__diff__left,axiom, % 191.04/191.28 ! [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)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__cancel,axiom, % 191.04/191.28 ! [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) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__cancel2,axiom, % 191.04/191.28 ! [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) ). % 191.04/191.28 % 191.04/191.28 fof(fact_iso__tuple__UNIV__I,axiom, % 191.04/191.28 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 191.04/191.28 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 191.04/191.28 ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 191.04/191.28 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 191.04/191.28 | ? [B_x,B_y] : % 191.04/191.28 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 191.04/191.28 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 191.04/191.28 & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Inf__fin_Ohom__commute,axiom, % 191.04/191.28 ! [V_N_2,V_h_2,T_a] : % 191.04/191.28 ( class_Lattices_Olattice(T_a) % 191.04/191.28 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.04/191.28 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_empty__fold1SetE,axiom, % 191.04/191.28 ! [V_x_2,V_f_2,T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold1Set__nonempty,axiom, % 191.04/191.28 ! [V_x_2,V_A_2,V_f_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 191.04/191.28 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_nat__add__commute,axiom, % 191.04/191.28 ! [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) ). % 191.04/191.28 % 191.04/191.28 fof(fact_nat__add__left__commute,axiom, % 191.04/191.28 ! [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)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_nat__add__assoc,axiom, % 191.04/191.28 ! [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)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_nat__add__left__cancel,axiom, % 191.04/191.28 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.28 ( 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) % 191.04/191.28 <=> V_m_2 = V_n_2 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_nat__add__right__cancel,axiom, % 191.04/191.28 ! [V_n_2,V_k_2,V_m_2] : % 191.04/191.28 ( 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) % 191.04/191.28 <=> V_m_2 = V_n_2 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__commute,axiom, % 191.04/191.28 ! [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) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold1Set__sing,axiom, % 191.04/191.28 ! [V_b_2,V_a_2,V_f_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_b_2)) % 191.04/191.28 <=> V_a_2 = V_b_2 ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_Sup__fin_Ohom__commute,axiom, % 191.04/191.28 ! [V_N_2,V_h_2,T_a] : % 191.04/191.28 ( class_Lattices_Olattice(T_a) % 191.04/191.28 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.04/191.28 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold1Set_Oequations,axiom, % 191.04/191.28 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2)) % 191.04/191.28 <=> ? [B_a,B_A] : % 191.04/191.28 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 191.04/191.28 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 191.04/191.28 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_insert__fold1SetE,axiom, % 191.04/191.28 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2)) % 191.04/191.28 => ~ ! [B_a,B_A] : % 191.04/191.28 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_folding__one__idem_Ohom__commute,axiom, % 191.04/191.28 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 191.04/191.28 => ( ! [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)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.04/191.28 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 191.04/191.28 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_v_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => ~ ! [B_y] : % 191.04/191.28 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 191.04/191.28 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__range__map__of__map__add,axiom, % 191.04/191.28 ! [V_l_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),c_Map_Omap__add(T_b,T_a,V_f_2,hAPP(c_Map_Omap__of(T_b,T_a),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__map__freshness,axiom, % 191.04/191.28 ! [V_f_2,T_b,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 191.04/191.28 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.28 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph__permute__diff,axiom, % 191.04/191.28 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 191.04/191.28 ( class_Groups_Oab__semigroup__mult(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_x_2)) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_InterI,axiom, % 191.04/191.28 ! [V_A_2,V_C_2,T_a] : % 191.04/191.28 ( ! [B_X] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 191.04/191.28 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 191.04/191.28 ! [V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Groups_Oab__semigroup__mult(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_mult__left__idem,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_mult__idem,axiom, % 191.04/191.28 ! [V_x,T_a] : % 191.04/191.28 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.04/191.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_times_Oidem,axiom, % 191.04/191.28 ! [V_a,T_a] : % 191.04/191.28 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.04/191.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 191.04/191.28 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 191.04/191.28 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 191.04/191.28 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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))) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 191.04/191.28 ! [V_rx,V_ly,V_lx,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 191.04/191.28 ! [V_rx,V_ly,V_lx,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 191.04/191.28 ! [V_ry,V_rx,V_lx,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 191.04/191.28 ! [V_ry,V_rx,V_lx,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 191.04/191.28 ! [V_z,V_y,V_x,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_crossproduct__noteq,axiom, % 191.04/191.28 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 191.04/191.28 => ( ( V_a_2 != V_b_2 % 191.04/191.28 & V_ca_2 != V_d_2 ) % 191.04/191.28 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 191.04/191.28 ! [V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 191.04/191.28 ! [V_b,V_m,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_crossproduct__eq,axiom, % 191.04/191.28 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 191.04/191.28 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) % 191.04/191.28 <=> ( V_w_2 = V_x_2 % 191.04/191.28 | V_y_2 = V_z_2 ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__mult__distrib,axiom, % 191.04/191.28 ! [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)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_add__mult__distrib2,axiom, % 191.04/191.28 ! [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)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__mult__distrib2,axiom, % 191.04/191.28 ! [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)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_diff__mult__distrib,axiom, % 191.04/191.28 ! [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)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Groups_Oab__semigroup__mult(T_a) % 191.04/191.28 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fun__left__comm__idem,axiom, % 191.04/191.28 ! [T_a] : % 191.04/191.28 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.04/191.28 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__dom__map__of,axiom, % 191.04/191.28 ! [V_l_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_l_2)))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold__graph__insert__swap,axiom, % 191.04/191.28 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 191.04/191.28 ( class_Groups_Oab__semigroup__mult(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_y_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 191.04/191.28 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2))) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_finite__range__map__of,axiom, % 191.04/191.28 ! [V_xys_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_eq__add__iff2,axiom, % 191.04/191.28 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 191.04/191.28 ( class_Rings_Oring(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 191.04/191.28 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_eq__add__iff1,axiom, % 191.04/191.28 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 191.04/191.28 ( class_Rings_Oring(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 191.04/191.28 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__mult__right,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Oring(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__mult__left,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Oring(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__mult__commute,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Oring(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_minus__mult__minus,axiom, % 191.04/191.28 ! [V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Oring(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_square__eq__iff,axiom, % 191.04/191.28 ! [V_b_2,V_a_2,T_a] : % 191.04/191.28 ( class_Rings_Oidom(T_a) % 191.04/191.28 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) % 191.04/191.28 <=> ( V_a_2 = V_b_2 % 191.04/191.28 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_comm__semiring__class_Odistrib,axiom, % 191.04/191.28 ! [V_c,V_b,V_a,T_a] : % 191.04/191.28 ( class_Rings_Ocomm__semiring(T_a) % 191.04/191.28 => 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)) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_combine__common__factor,axiom, % 191.04/191.28 ! [V_c,V_b,V_e,V_a,T_a] : % 191.04/191.28 ( class_Rings_Osemiring(T_a) % 191.04/191.28 => 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) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_nat__mult__assoc,axiom, % 191.04/191.28 ! [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)) ). % 191.04/191.28 % 191.04/191.28 fof(fact_nat__mult__commute,axiom, % 191.04/191.28 ! [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) ). % 191.04/191.28 % 191.04/191.28 fof(fact_left__add__mult__distrib,axiom, % 191.04/191.28 ! [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) ). % 191.04/191.28 % 191.04/191.28 fof(fact_body__def,axiom, % 191.04/191.28 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold1__eq__fold,axiom, % 191.04/191.28 ! [V_a_2,V_A_2,T_a] : % 191.04/191.28 ( class_Groups_Oab__semigroup__mult(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.28 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold1__Un,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : % 191.04/191.28 ( class_Groups_Oab__semigroup__mult(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold1__insert,axiom, % 191.04/191.28 ! [V_x_2,V_A_2,T_a] : % 191.04/191.28 ( class_Groups_Oab__semigroup__mult(T_a) % 191.04/191.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_setprod_Oremove,axiom, % 191.04/191.28 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 191.04/191.28 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.28 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_card__Un__disjoint,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.28 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.28 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_fold1__eq__fold__idem,axiom, % 191.04/191.28 ! [V_a_2,V_A_2,T_a] : % 191.04/191.28 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.04/191.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inj__on__Un,axiom, % 191.04/191.28 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.28 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.28 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 191.04/191.28 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inj__on__empty,axiom, % 191.04/191.28 ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inj__uminus,axiom, % 191.04/191.28 ! [V_A_2,T_a] : % 191.04/191.28 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.28 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_card__image,axiom, % 191.04/191.28 ! [V_A_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.28 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inj__on__def,axiom, % 191.04/191.28 ! [V_A_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.28 <=> ! [B_x] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.28 => ! [B_xa] : % 191.04/191.28 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 191.04/191.28 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 191.04/191.28 => B_x = B_xa ) ) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_eq__card__imp__inj__on,axiom, % 191.04/191.28 ! [V_f_2,T_b,V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) % 191.04/191.28 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inj__on__iff__eq__card,axiom, % 191.04/191.28 ! [V_f_2,T_b,V_A_2,T_a] : % 191.04/191.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.28 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.28 <=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 191.04/191.28 % 191.04/191.28 fof(fact_inj__onD,axiom, % 191.04/191.28 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.28 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.28 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 191.04/191.28 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 191.04/191.29 => V_x_2 = V_y_2 ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__iff,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 191.04/191.29 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 191.04/191.29 <=> V_x_2 = V_y_2 ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__contraD,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.29 => ( V_x_2 != V_y_2 % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 191.04/191.29 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__eq,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 191.04/191.29 <=> V_x_2 = V_y_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_injD,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 191.04/191.29 => V_x_2 = V_y_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__Int,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.29 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 191.04/191.29 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__diff,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.29 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__Some,axiom, % 191.04/191.29 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2) ). % 191.04/191.29 % 191.04/191.29 fof(fact_finite__imageD,axiom, % 191.04/191.29 ! [V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 191.04/191.29 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 191.04/191.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__image__eq__iff,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 191.04/191.29 <=> V_A_2 = V_B_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__Un__image__eq__iff,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.29 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 191.04/191.29 <=> V_A_2 = V_B_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 191.04/191.29 ! [V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.29 => ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__map__add__dom,axiom, % 191.04/191.29 ! [V_m_H_2,V_m_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2)) % 191.04/191.29 <=> c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold1__singleton__def,axiom, % 191.04/191.29 ! [V_a_2,V_f_2,T_a,V_g_2] : % 191.04/191.29 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 191.04/191.29 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold1__singleton,axiom, % 191.04/191.29 ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__image__mem__iff,axiom, % 191.04/191.29 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_range__ex1__eq,axiom, % 191.04/191.29 ! [V_b_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) % 191.04/191.29 <=> ? [B_x] : % 191.04/191.29 ( V_b_2 = hAPP(V_f_2,B_x) % 191.04/191.29 & ! [B_y] : % 191.04/191.29 ( V_b_2 = hAPP(V_f_2,B_y) % 191.04/191.29 => B_y = B_x ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_finite__UNIV__surj__inj,axiom, % 191.04/191.29 ! [V_f_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.29 => ( hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_finite__UNIV__inj__surj,axiom, % 191.04/191.29 ! [V_f_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.29 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_image__Int,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_image__set__diff,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_folding__one_Oeq__fold,axiom, % 191.04/191.29 ! [V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.29 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__fun__updI,axiom, % 191.04/191.29 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 191.04/191.29 => c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_finite__vimageI,axiom, % 191.04/191.29 ! [V_h_2,T_b,V_F_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.29 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 191.04/191.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__vimage__image__eq,axiom, % 191.04/191.29 ! [V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.04/191.29 => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod__insert,axiom, % 191.04/191.29 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_Oinsert,axiom, % 191.04/191.29 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod__Un__Int,axiom, % 191.04/191.29 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_Ounion__inter,axiom, % 191.04/191.29 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Sup__fin_OF__eq,axiom, % 191.04/191.29 ! [V_A_2,T_a] : % 191.04/191.29 ( class_Lattices_Olattice(T_a) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_A_2) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Inf__fin_OF__eq,axiom, % 191.04/191.29 ! [V_A_2,T_a] : % 191.04/191.29 ( class_Lattices_Olattice(T_a) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card_Ounion__inter,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__Un__Int,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__Diff__subset__Int,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_Oinsert__remove,axiom, % 191.04/191.29 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod__Un__disjoint,axiom, % 191.04/191.29 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_Ounion__disjoint,axiom, % 191.04/191.29 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__insert,axiom, % 191.04/191.29 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 191.04/191.29 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.04/191.29 & ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold1__insert__idem,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.04/191.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold1__Un2,axiom, % 191.04/191.29 ! [V_B_2,V_A_2,T_a] : % 191.04/191.29 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_semilattice__big_OF__eq,axiom, % 191.04/191.29 ! [V_A_2,V_F_2,V_f_2,T_a] : % 191.04/191.29 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold1__in,axiom, % 191.04/191.29 ! [V_A_2,T_a] : % 191.04/191.29 ( class_Groups_Oab__semigroup__mult(T_a) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),V_A_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__Diff__singleton__if,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 191.04/191.29 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__Diff__singleton,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card_Oremove,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_hom__fold1__commute,axiom, % 191.04/191.29 ! [V_N_2,V_h_2,T_a] : % 191.04/191.29 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.04/191.29 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.04/191.29 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card_Oinsert__remove,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__Diff__insert,axiom, % 191.04/191.29 ! [V_B_2,V_a_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__Diff2__less,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__UNIV__unit,axiom, % 191.04/191.29 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) ). % 191.04/191.29 % 191.04/191.29 fof(fact_order__less__irrefl,axiom, % 191.04/191.29 ! [V_x,T_a] : % 191.04/191.29 ( class_Orderings_Opreorder(T_a) % 191.04/191.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_linorder__neq__iff,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,T_a] : % 191.04/191.29 ( class_Orderings_Olinorder(T_a) % 191.04/191.29 => ( V_x_2 != V_y_2 % 191.04/191.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__less__iff__gr__or__eq,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,T_a] : % 191.04/191.29 ( class_Orderings_Olinorder(T_a) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 191.04/191.29 | V_x_2 = V_y_2 ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_linorder__less__linear,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Olinorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 | V_x = V_y % 191.04/191.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_linorder__antisym__conv3,axiom, % 191.04/191.29 ! [V_x_2,V_y_2,T_a] : % 191.04/191.29 ( class_Orderings_Olinorder(T_a) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.29 <=> V_x_2 = V_y_2 ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_linorder__neqE,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Olinorder(T_a) % 191.04/191.29 => ( V_x != V_y % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__imp__neq,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Oorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => V_x != V_y ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_order__less__not__sym,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Opreorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_order__less__imp__not__less,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Opreorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_order__less__imp__not__eq,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Oorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => V_x != V_y ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_order__less__imp__not__eq2,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Oorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => V_y != V_x ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_order__less__asym_H,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Orderings_Opreorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_xt1_I9_J,axiom, % 191.04/191.29 ! [V_a,V_b,T_a] : % 191.04/191.29 ( class_Orderings_Oorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 191.04/191.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_ord__eq__less__trans,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Orderings_Oord(T_a) % 191.04/191.29 => ( V_a = V_b % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_xt1_I1_J,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Orderings_Oorder(T_a) % 191.04/191.29 => ( V_a = V_b % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_ord__less__eq__trans,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Orderings_Oord(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.29 => ( V_b = V_c % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_xt1_I2_J,axiom, % 191.04/191.29 ! [V_c,V_a,V_b,T_a] : % 191.04/191.29 ( class_Orderings_Oorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 191.04/191.29 => ( V_b = V_c % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_order__less__trans,axiom, % 191.04/191.29 ! [V_z,V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Opreorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_xt1_I10_J,axiom, % 191.04/191.29 ! [V_z,V_x,V_y,T_a] : % 191.04/191.29 ( class_Orderings_Oorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_order__less__asym,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Opreorder(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_linorder__cases,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Orderings_Olinorder(T_a) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => ( V_x != V_y % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_one__reorient,axiom, % 191.04/191.29 ! [V_x_2,T_a] : % 191.04/191.29 ( class_Groups_Oone(T_a) % 191.04/191.29 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 191.04/191.29 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__not__refl,axiom, % 191.04/191.29 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat__neq__iff,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( V_m_2 != V_n_2 % 191.04/191.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.04/191.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_linorder__neqE__nat,axiom, % 191.04/191.29 ! [V_y,V_x] : % 191.04/191.29 ( V_x != V_y % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__irrefl__nat,axiom, % 191.04/191.29 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__not__refl2,axiom, % 191.04/191.29 ! [V_m,V_n] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 191.04/191.29 => V_m != V_n ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__not__refl3,axiom, % 191.04/191.29 ! [V_t,V_s] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 191.04/191.29 => V_s != V_t ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat__less__cases,axiom, % 191.04/191.29 ! [V_P_2,V_n_2,V_m_2] : % 191.04/191.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 191.04/191.29 => ( ( V_m_2 = V_n_2 % 191.04/191.29 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 191.04/191.29 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 191.04/191.29 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_linorder__neqE__linordered__idom,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.29 => ( V_x != V_y % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__add__one,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semidom(T_a) % 191.04/191.29 => 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)))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__1__mult,axiom, % 191.04/191.29 ! [V_n,V_m,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semidom(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__1__left,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Omonoid__mult(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__1,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__1__right,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Omonoid__mult(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult_Ocomm__neutral,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__less__imp__less__left,axiom, % 191.04/191.29 ! [V_b,V_a,V_c,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.04/191.29 => ( 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))) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__less__imp__less__right,axiom, % 191.04/191.29 ! [V_b,V_c,V_a,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.04/191.29 => ( 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))) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__strict__mono,axiom, % 191.04/191.29 ! [V_d,V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__strict__left__mono,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.29 => 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))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__strict__right__mono,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.29 => 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))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__less__cancel__left,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__less__cancel__right,axiom, % 191.04/191.29 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__eq__diff__less,axiom, % 191.04/191.29 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.29 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__supI2,axiom, % 191.04/191.29 ! [V_a,V_b,V_x,T_a] : % 191.04/191.29 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 191.04/191.29 => 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))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__supI1,axiom, % 191.04/191.29 ! [V_b,V_a,V_x,T_a] : % 191.04/191.29 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 191.04/191.29 => 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))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__infI1,axiom, % 191.04/191.29 ! [V_b,V_x,V_a,T_a] : % 191.04/191.29 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 191.04/191.29 => 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)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__infI2,axiom, % 191.04/191.29 ! [V_a,V_x,V_b,T_a] : % 191.04/191.29 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 191.04/191.29 => 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)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_neg__less__iff__less,axiom, % 191.04/191.29 ! [V_a_2,V_b_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_minus__less__iff,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__minus__iff,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod__eq__1__iff,axiom, % 191.04/191.29 ! [V_f_2,V_F_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.29 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 191.04/191.29 <=> ! [B_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 191.04/191.29 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__add__less1,axiom, % 191.04/191.29 ! [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)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__add__less2,axiom, % 191.04/191.29 ! [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)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat__add__left__cancel__less,axiom, % 191.04/191.29 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.29 ( 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))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_trans__less__add1,axiom, % 191.04/191.29 ! [V_m,V_j,V_i] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.04/191.29 => 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))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_trans__less__add2,axiom, % 191.04/191.29 ! [V_m,V_j,V_i] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.04/191.29 => 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))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__less__mono1,axiom, % 191.04/191.29 ! [V_k,V_j,V_i] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.04/191.29 => 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))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__less__mono,axiom, % 191.04/191.29 ! [V_l,V_k,V_j,V_i] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 191.04/191.29 => 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))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__add__eq__less,axiom, % 191.04/191.29 ! [V_n,V_m,V_l,V_k] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 191.04/191.29 => ( 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) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__lessD1,axiom, % 191.04/191.29 ! [V_k,V_j,V_i] : % 191.04/191.29 ( 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)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__less__mono2,axiom, % 191.04/191.29 ! [V_l,V_n,V_m] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 191.04/191.29 => 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))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__imp__diff__less,axiom, % 191.04/191.29 ! [V_n,V_k,V_j] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 191.04/191.29 => 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)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat__mult__eq__1__iff,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 191.04/191.29 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 191.04/191.29 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat__mult__1__right,axiom, % 191.04/191.29 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat__1__eq__mult__iff,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 191.04/191.29 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 191.04/191.29 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat__mult__1,axiom, % 191.04/191.29 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__Sup__iff,axiom, % 191.04/191.29 ! [V_S_2,V_a_2,T_a] : % 191.04/191.29 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.29 & class_Orderings_Olinorder(T_a) ) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 191.04/191.29 <=> ? [B_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 191.04/191.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Inf__less__iff,axiom, % 191.04/191.29 ! [V_a_2,V_S_2,T_a] : % 191.04/191.29 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.29 & class_Orderings_Olinorder(T_a) ) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 191.04/191.29 <=> ? [B_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 191.04/191.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 191.04/191.29 ! [V_m,V_a,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 191.04/191.29 ! [V_a,V_m,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 191.04/191.29 ! [V_m,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_square__eq__1__iff,axiom, % 191.04/191.29 ! [V_x_2,T_a] : % 191.04/191.29 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 191.04/191.29 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 191.04/191.29 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 191.04/191.29 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 191.04/191.29 ! [V_x,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__ring__1(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_Oempty,axiom, % 191.04/191.29 ! [V_g_2,T_b,T_a] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_a) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod__empty,axiom, % 191.04/191.29 ! [V_f_2,T_b,T_a] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_a) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod__infinite,axiom, % 191.04/191.29 ! [V_f_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_Oinfinite,axiom, % 191.04/191.29 ! [V_g_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__diff__inverse,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.04/191.29 => 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 ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__diff__conv,axiom, % 191.04/191.29 ! [V_k_2,V_j_2,V_i_2] : % 191.04/191.29 ( 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))) % 191.04/191.29 <=> 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)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__add__iff1,axiom, % 191.04/191.29 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 191.04/191.29 ( class_Rings_Oordered__ring(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__add__iff2,axiom, % 191.04/191.29 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 191.04/191.29 ( class_Rings_Oordered__ring(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_pigeonhole,axiom, % 191.04/191.29 ! [V_A_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 191.04/191.29 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card_Oinsert,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__Diff1__less,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_Ounion__inter__neutral,axiom, % 191.04/191.29 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => ( ! [B_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.29 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod__Un__one,axiom, % 191.04/191.29 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 191.04/191.29 => ( ! [B_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 191.04/191.29 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_termination__basic__simps_I1_J,axiom, % 191.04/191.29 ! [V_z,V_y,V_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 191.04/191.29 => 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))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_termination__basic__simps_I2_J,axiom, % 191.04/191.29 ! [V_y,V_z,V_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 191.04/191.29 => 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))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold__Un__disjoint,axiom, % 191.04/191.29 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setsum__strict__mono,axiom, % 191.04/191.29 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.29 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.29 => ( ! [B_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2))) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__Suc__Diff1,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__Inter,axiom, % 191.04/191.29 ! [V_f_2,T_b,T_a,V_S_2] : % 191.04/191.29 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 191.04/191.29 => ( ! [B_A] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 191.04/191.29 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 191.04/191.29 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold__image__Un__Int,axiom, % 191.04/191.29 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__mono,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_lessI,axiom, % 191.04/191.29 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__Suc,axiom, % 191.04/191.29 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__inject,axiom, % 191.04/191.29 ! [V_y,V_x] : % 191.04/191.29 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 191.04/191.29 => V_x = V_y ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat_Oinject,axiom, % 191.04/191.29 ! [V_nat_H_2,V_nat_2] : % 191.04/191.29 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 191.04/191.29 <=> V_nat_2 = V_nat_H_2 ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__n__not__n,axiom, % 191.04/191.29 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 191.04/191.29 % 191.04/191.29 fof(fact_n__not__Suc__n,axiom, % 191.04/191.29 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 191.04/191.29 % 191.04/191.29 fof(fact_psubsetD,axiom, % 191.04/191.29 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__psubset__empty,axiom, % 191.04/191.29 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__less__SucD,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__lessD,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__SucE,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.04/191.29 => V_m = V_n ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__trans__Suc,axiom, % 191.04/191.29 ! [V_k,V_j,V_i] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__lessI,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.04/191.29 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__SucI,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__antisym,axiom, % 191.04/191.29 ! [V_m,V_n] : % 191.04/191.29 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 191.04/191.29 => V_m = V_n ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__less__less__Suc__eq,axiom, % 191.04/191.29 ! [V_m_2,V_n_2] : % 191.04/191.29 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 191.04/191.29 <=> V_n_2 = V_m_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__less__eq,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( 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))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__Suc__eq,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 191.04/191.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.04/191.29 | V_m_2 = V_n_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__less__eq,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__Suc__shift,axiom, % 191.04/191.29 ! [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)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__Suc,axiom, % 191.04/191.29 ! [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)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__Suc__right,axiom, % 191.04/191.29 ! [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)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__Suc__Suc,axiom, % 191.04/191.29 ! [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) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__diff__diff,axiom, % 191.04/191.29 ! [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) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__mult__cancel1,axiom, % 191.04/191.29 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.29 ( 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) % 191.04/191.29 <=> V_m_2 = V_n_2 ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold__image__empty,axiom, % 191.04/191.29 ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__iff__Suc__add,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.04/191.29 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__add__Suc2,axiom, % 191.04/191.29 ! [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)))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__add__Suc1,axiom, % 191.04/191.29 ! [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)))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__less__Suc,axiom, % 191.04/191.29 ! [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))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__mult__less__cancel1,axiom, % 191.04/191.29 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.29 ( 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))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__Suc,axiom, % 191.04/191.29 ! [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)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__Suc__right,axiom, % 191.04/191.29 ! [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)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_inj__on__strict__subset,axiom, % 191.04/191.29 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__Suc__1,axiom, % 191.04/191.29 ! [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 ). % 191.04/191.29 % 191.04/191.29 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 191.04/191.29 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.29 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_psubset__card__mono,axiom, % 191.04/191.29 ! [V_A_2,V_B_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__monoid__big_OF__eq,axiom, % 191.04/191.29 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 191.04/191.29 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 191.04/191.29 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.29 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) % 191.04/191.29 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.04/191.29 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__insert__disjoint,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__insert__if,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) % 191.04/191.29 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold__image__insert,axiom, % 191.04/191.29 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Oab__semigroup__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.29 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_OF__eq,axiom, % 191.04/191.29 ! [V_g_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) % 191.04/191.29 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_setprod_Oeq__fold,axiom, % 191.04/191.29 ! [V_g_2,V_A_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_card__insert,axiom, % 191.04/191.29 ! [V_x_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.29 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__Suc__eq__diff__pred,axiom, % 191.04/191.29 ! [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) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__eq__plus1__left,axiom, % 191.04/191.29 ! [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) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__eq__plus1,axiom, % 191.04/191.29 ! [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)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Body__triple__valid__Suc,axiom, % 191.04/191.29 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 191.04/191.29 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) % 191.04/191.29 <=> c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_fold__image__Un__one,axiom, % 191.04/191.29 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.04/191.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 191.04/191.29 => ( ! [B_x] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 191.04/191.29 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 191.04/191.29 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_T_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_evaln_OBody,axiom, % 191.04/191.29 ! [V_s1,V_n,V_s0,V_pn] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_n),V_s1)) % 191.04/191.29 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),hAPP(c_Nat_OSuc,V_n)),V_s1)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_finite__fun__UNIVD1,axiom, % 191.04/191.29 ! [T_b,T_a] : % 191.04/191.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) % 191.04/191.29 => ( hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 191.04/191.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__zeroE,axiom, % 191.04/191.29 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_evaln_OSemi,axiom, % 191.04/191.29 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_evaln_OSkip,axiom, % 191.04/191.29 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_evaln__elim__cases_I1_J,axiom, % 191.04/191.29 ! [V_t,V_n,V_s] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 191.04/191.29 => V_t = V_s ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_zero__less__Suc,axiom, % 191.04/191.29 ! [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))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_psubset__trans,axiom, % 191.04/191.29 ! [V_C_2,V_B_2,V_A_2,T_a] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_zero__reorient,axiom, % 191.04/191.29 ! [V_x_2,T_a] : % 191.04/191.29 ( class_Groups_Ozero(T_a) % 191.04/191.29 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 191.04/191.29 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_bot__nat__def,axiom, % 191.04/191.29 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.29 % 191.04/191.29 fof(fact_triple__valid__def2,axiom, % 191.04/191.29 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] : % 191.04/191.29 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)) % 191.04/191.29 <=> ! [B_Z,B_s] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 191.04/191.29 => ! [B_s_H] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H)) % 191.04/191.29 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_evaln__Suc,axiom, % 191.04/191.29 ! [V_s_H,V_n,V_s,V_c] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 191.04/191.29 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add_Ocomm__neutral,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__add(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__0__right,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Omonoid__add(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_double__zero__sym,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.29 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 191.04/191.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__0,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Ocomm__monoid__add(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__0__left,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Omonoid__add(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__0__iff,axiom, % 191.04/191.29 ! [V_a_2,V_b_2,T_a] : % 191.04/191.29 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 191.04/191.29 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 191.04/191.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_divisors__zero,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Ono__zero__divisors(T_a) % 191.04/191.29 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_no__zero__divisors,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Ono__zero__divisors(T_a) % 191.04/191.29 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__eq__0__iff,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,T_a] : % 191.04/191.29 ( class_Rings_Oring__no__zero__divisors(T_a) % 191.04/191.29 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__zero__right,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Omult__zero(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__zero__left,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Omult__zero(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Ocomm__semiring__1(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_right__minus__eq,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 <=> V_a_2 = V_b_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_eq__iff__diff__eq__0,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Oab__group__add(T_a) % 191.04/191.29 => ( V_a_2 = V_b_2 % 191.04/191.29 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__self,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__0__right,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_one__neq__zero,axiom, % 191.04/191.29 ! [T_a] : % 191.04/191.29 ( class_Rings_Ozero__neq__one(T_a) % 191.04/191.29 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_zero__neq__one,axiom, % 191.04/191.29 ! [T_a] : % 191.04/191.29 ( class_Rings_Ozero__neq__one(T_a) % 191.04/191.29 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_neg__equal__zero,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.29 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 191.04/191.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_neg__equal__0__iff__equal,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_equal__neg__zero,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.29 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 191.04/191.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_neg__0__equal__iff__equal,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 191.04/191.29 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_minus__zero,axiom, % 191.04/191.29 ! [T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_evaln__evalc,axiom, % 191.04/191.29 ! [V_t,V_n,V_s,V_c] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_eval__eq,axiom, % 191.04/191.29 ! [V_t_2,V_s_2,V_ca_2] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2)) % 191.04/191.29 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Zero__not__Suc,axiom, % 191.04/191.29 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat_Osimps_I2_J,axiom, % 191.04/191.29 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__not__Zero,axiom, % 191.04/191.29 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat_Osimps_I3_J,axiom, % 191.04/191.29 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Zero__neq__Suc,axiom, % 191.04/191.29 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Suc__neq__Zero,axiom, % 191.04/191.29 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__less0,axiom, % 191.04/191.29 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_neq0__conv,axiom, % 191.04/191.29 ! [V_n_2] : % 191.04/191.29 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__nat__zero__code,axiom, % 191.04/191.29 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.04/191.29 % 191.04/191.29 fof(fact_gr__implies__not0,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.04/191.29 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_gr0I,axiom, % 191.04/191.29 ! [V_n] : % 191.04/191.29 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_plus__nat_Oadd__0,axiom, % 191.04/191.29 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 191.04/191.29 % 191.04/191.29 fof(fact_Nat_Oadd__0__right,axiom, % 191.04/191.29 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__is__0,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__eq__self__zero,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 191.04/191.29 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diffs0__imp__equal,axiom, % 191.04/191.29 ! [V_n,V_m] : % 191.04/191.29 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 => V_m = V_n ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__self__eq__0,axiom, % 191.04/191.29 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.29 % 191.04/191.29 fof(fact_minus__nat_Odiff__0,axiom, % 191.04/191.29 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 191.04/191.29 % 191.04/191.29 fof(fact_diff__0__eq__0,axiom, % 191.04/191.29 ! [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) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__cancel2,axiom, % 191.04/191.29 ! [V_n_2,V_k_2,V_m_2] : % 191.04/191.29 ( 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) % 191.04/191.29 <=> ( V_m_2 = V_n_2 % 191.04/191.29 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__cancel1,axiom, % 191.04/191.29 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.29 ( 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) % 191.04/191.29 <=> ( V_m_2 = V_n_2 % 191.04/191.29 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__is__0,axiom, % 191.04/191.29 ! [V_n_2,V_m_2] : % 191.04/191.29 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__0__right,axiom, % 191.04/191.29 ! [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) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__0,axiom, % 191.04/191.29 ! [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) ). % 191.04/191.29 % 191.04/191.29 fof(fact_nat__mult__eq__cancel__disj,axiom, % 191.04/191.29 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.29 ( 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) % 191.04/191.29 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.29 | V_m_2 = V_n_2 ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_evaln_Oequations_I4_J,axiom, % 191.04/191.29 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2)) % 191.04/191.29 <=> ? [B_s1] : % 191.04/191.29 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 191.04/191.29 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_evaln_Oequations_I1_J,axiom, % 191.04/191.29 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_sum__squares__eq__zero__iff,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_Body__triple__valid__0,axiom, % 191.04/191.29 ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ). % 191.04/191.29 % 191.04/191.29 fof(fact_triple__valid__Suc,axiom, % 191.04/191.29 ! [V_t,V_n,T_a] : % 191.04/191.29 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 191.04/191.29 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_sum__squares__gt__zero__iff,axiom, % 191.04/191.29 ! [V_y_2,V_x_2,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) % 191.04/191.29 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__sum__squares__lt__zero,axiom, % 191.04/191.29 ! [V_y,V_x,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring(T_a) % 191.04/191.29 => ~ 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))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__neg__neg,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__pos__pos,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_pos__add__strict,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semidom(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__strict__left__mono__neg,axiom, % 191.04/191.29 ! [V_c,V_a,V_b,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__strict__right__mono__neg,axiom, % 191.04/191.29 ! [V_c,V_a,V_b,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_comm__mult__strict__left__mono,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__strict__left__mono,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__strict__right__mono,axiom, % 191.04/191.29 ! [V_c,V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__neg__neg,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__neg__pos,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__less__cancel__left__neg,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_zero__less__mult__pos2,axiom, % 191.04/191.29 ! [V_a,V_b,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.04/191.29 => ( 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))) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_zero__less__mult__pos,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.04/191.29 => ( 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))) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__pos__neg2,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__pos__neg,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__pos__pos,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.04/191.29 => 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))) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__less__cancel__left__pos,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__less__cancel__left__disj,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 191.04/191.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 191.04/191.29 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_mult__less__cancel__right__disj,axiom, % 191.04/191.29 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring__strict(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))) % 191.04/191.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 191.04/191.29 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__square__less__zero,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__ring(T_a) % 191.04/191.29 => ~ 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))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__iff__diff__less__0,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_add__scale__eq__noteq,axiom, % 191.04/191.29 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 191.04/191.29 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 191.04/191.29 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.29 => ( ( V_a = V_b % 191.04/191.29 & V_c != V_d ) % 191.04/191.29 => 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)) ) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_not__one__less__zero,axiom, % 191.04/191.29 ! [T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semidom(T_a) % 191.04/191.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_zero__less__one,axiom, % 191.04/191.29 ! [T_a] : % 191.04/191.29 ( class_Rings_Olinordered__semidom(T_a) % 191.04/191.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_neg__less__nonneg,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_neg__less__0__iff__less,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_neg__0__less__iff__less,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_less__minus__self__iff,axiom, % 191.04/191.29 ! [V_a_2,T_a] : % 191.04/191.29 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 191.04/191.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_right__minus,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_eq__neg__iff__add__eq__0,axiom, % 191.04/191.29 ! [V_b_2,V_a_2,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 191.04/191.29 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_left__minus,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_ab__left__minus,axiom, % 191.04/191.29 ! [V_a,T_a] : % 191.04/191.29 ( class_Groups_Oab__group__add(T_a) % 191.04/191.29 => 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) ) ). % 191.04/191.29 % 191.04/191.29 fof(fact_minus__unique,axiom, % 191.04/191.29 ! [V_b,V_a,T_a] : % 191.04/191.29 ( class_Groups_Ogroup__add(T_a) % 191.04/191.30 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_diff__0,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Groups_Ogroup__add(T_a) % 191.04/191.30 => 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) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum__empty,axiom, % 191.04/191.30 ! [V_f_2,T_b,T_a] : % 191.04/191.30 ( class_Groups_Ocomm__monoid__add(T_a) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum_Oempty,axiom, % 191.04/191.30 ! [V_g_2,T_b,T_a] : % 191.04/191.30 ( class_Groups_Ocomm__monoid__add(T_a) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum__infinite,axiom, % 191.04/191.30 ! [V_f_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.30 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum_Oinfinite,axiom, % 191.04/191.30 ! [V_g_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.30 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setprod__zero__iff,axiom, % 191.04/191.30 ! [V_f_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( ( class_Rings_Ocomm__semiring__1(T_b) % 191.04/191.30 & class_Rings_Ono__zero__divisors(T_b) ) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) % 191.04/191.30 <=> ? [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.30 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setprod__zero,axiom, % 191.04/191.30 ! [V_f_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( class_Rings_Ocomm__semiring__1(T_b) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( ? [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.30 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_less__Suc__eq__0__disj,axiom, % 191.04/191.30 ! [V_n_2,V_m_2] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 191.04/191.30 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 | ? [B_j] : % 191.04/191.30 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_less__Suc0,axiom, % 191.04/191.30 ! [V_n_2] : % 191.04/191.30 ( 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)))) % 191.04/191.30 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_gr0__conv__Suc,axiom, % 191.04/191.30 ! [V_n_2] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 191.04/191.30 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_one__is__add,axiom, % 191.04/191.30 ! [V_n_2,V_m_2] : % 191.04/191.30 ( 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) % 191.04/191.30 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 191.04/191.30 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.04/191.30 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__is__1,axiom, % 191.04/191.30 ! [V_n_2,V_m_2] : % 191.04/191.30 ( 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)) % 191.04/191.30 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 191.04/191.30 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.04/191.30 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__gr__0,axiom, % 191.04/191.30 ! [V_n_2,V_m_2] : % 191.04/191.30 ( 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))) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 191.04/191.30 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card_Oempty,axiom, % 191.04/191.30 ! [T_a] : hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card__infinite,axiom, % 191.04/191.30 ! [V_A_2,T_a] : % 191.04/191.30 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__eq__1__iff,axiom, % 191.04/191.30 ! [V_n_2,V_m_2] : % 191.04/191.30 ( 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)) % 191.04/191.30 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 191.04/191.30 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_diff__less,axiom, % 191.04/191.30 ! [V_m,V_n] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 191.04/191.30 => 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)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_zero__less__diff,axiom, % 191.04/191.30 ! [V_m_2,V_n_2] : % 191.04/191.30 ( 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))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nat__mult__eq__cancel1,axiom, % 191.04/191.30 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 191.04/191.30 => ( 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) % 191.04/191.30 <=> V_m_2 = V_n_2 ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nat__mult__less__cancel1,axiom, % 191.04/191.30 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 191.04/191.30 => ( 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))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nat__0__less__mult__iff,axiom, % 191.04/191.30 ! [V_n_2,V_m_2] : % 191.04/191.30 ( 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))) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__less__cancel1,axiom, % 191.04/191.30 ! [V_n_2,V_m_2,V_k_2] : % 191.04/191.30 ( 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))) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__less__cancel2,axiom, % 191.04/191.30 ! [V_n_2,V_k_2,V_m_2] : % 191.04/191.30 ( 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))) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__less__mono1,axiom, % 191.04/191.30 ! [V_k,V_j,V_i] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__less__mono2,axiom, % 191.04/191.30 ! [V_k,V_j,V_i] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_diff__add__0,axiom, % 191.04/191.30 ! [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) ). % 191.04/191.30 % 191.04/191.30 fof(fact_One__nat__def,axiom, % 191.04/191.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__eq__self__implies__10,axiom, % 191.04/191.30 ! [V_n,V_m] : % 191.04/191.30 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 191.04/191.30 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 191.04/191.30 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum__eq__0__iff,axiom, % 191.04/191.30 ! [V_f_2,V_F_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.04/191.30 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 <=> ! [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 191.04/191.30 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Suc__pred_H,axiom, % 191.04/191.30 ! [V_n] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.04/191.30 => 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))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__eq__if,axiom, % 191.04/191.30 ! [V_n,V_m] : % 191.04/191.30 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 191.04/191.30 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 => 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)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__eq__if,axiom, % 191.04/191.30 ! [V_n,V_m] : % 191.04/191.30 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.04/191.30 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 => 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)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_zero__less__two,axiom, % 191.04/191.30 ! [T_a] : % 191.04/191.30 ( class_Rings_Olinordered__semidom(T_a) % 191.04/191.30 => 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)))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card__eq__0__iff,axiom, % 191.04/191.30 ! [V_A_2,T_a] : % 191.04/191.30 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.30 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card__ge__0__finite,axiom, % 191.04/191.30 ! [V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 191.04/191.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_diff__Suc__less,axiom, % 191.04/191.30 ! [V_i,V_n] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Suc__pred,axiom, % 191.04/191.30 ! [V_n] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.04/191.30 => 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 ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_n__less__m__mult__n,axiom, % 191.04/191.30 ! [V_m,V_n] : % 191.04/191.30 ( 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)) % 191.04/191.30 => ( 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)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_n__less__n__mult__m,axiom, % 191.04/191.30 ! [V_m,V_n] : % 191.04/191.30 ( 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)) % 191.04/191.30 => ( 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)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_one__less__mult,axiom, % 191.04/191.30 ! [V_m,V_n] : % 191.04/191.30 ( 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)) % 191.04/191.30 => ( 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)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nat__diff__split__asm,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,V_P_2] : % 191.04/191.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 191.04/191.30 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 191.04/191.30 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 191.04/191.30 | ? [B_d] : % 191.04/191.30 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 191.04/191.30 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nat__diff__split,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,V_P_2] : % 191.04/191.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 191.04/191.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 191.04/191.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 191.04/191.30 & ! [B_d] : % 191.04/191.30 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 191.04/191.30 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum__eq__Suc0__iff,axiom, % 191.04/191.30 ! [V_f_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 191.04/191.30 <=> ? [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.30 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 191.04/191.30 & ! [B_xa] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 191.04/191.30 => ( B_x != B_xa % 191.04/191.30 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum__eq__1__iff,axiom, % 191.04/191.30 ! [V_f_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 191.04/191.30 <=> ? [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.30 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 191.04/191.30 & ! [B_xa] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 191.04/191.30 => ( B_x != B_xa % 191.04/191.30 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setprod__pos__nat__iff,axiom, % 191.04/191.30 ! [V_f_2,V_S_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_S_2))) % 191.04/191.30 <=> ! [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card__gt__0__iff,axiom, % 191.04/191.30 ! [V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 191.04/191.30 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_finite__UNIV__card__ge__0,axiom, % 191.04/191.30 ! [T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum_OF__eq,axiom, % 191.04/191.30 ! [V_g_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.30 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum_Oeq__fold,axiom, % 191.04/191.30 ! [V_g_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Suc__diff__1,axiom, % 191.04/191.30 ! [V_n] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.04/191.30 => 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 ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_evaln_Oequations_I9_J,axiom, % 191.04/191.30 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2)) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2),V_a4_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_triple_Osize_I1_J,axiom, % 191.04/191.30 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_even__less__0__iff,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_triple_Osize_I2_J,axiom, % 191.04/191.30 ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_evaln__elim__cases_I6_J,axiom, % 191.04/191.30 ! [V_s1,V_n,V_s,V_P] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1)) % 191.04/191.30 => ~ ! [B_n] : % 191.04/191.30 ( V_n = hAPP(c_Nat_OSuc,B_n) % 191.04/191.30 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),B_n),V_s1)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card_Ounion__inter__neutral,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.30 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.30 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.04/191.30 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum_Ounion__inter__neutral,axiom, % 191.04/191.30 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.30 => ( ! [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.30 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setsum__Un__zero,axiom, % 191.04/191.30 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 191.04/191.30 ( class_Groups_Ocomm__monoid__add(T_b) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 191.04/191.30 => ( ! [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 191.04/191.30 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card__Suc__eq,axiom, % 191.04/191.30 ! [V_k_2,V_A_2,T_a] : % 191.04/191.30 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 191.04/191.30 <=> ? [B_b,B_B] : % 191.04/191.30 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 191.04/191.30 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 191.04/191.30 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 191.04/191.30 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.04/191.30 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_double__eq__0__iff,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.30 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_option_Osize_I2_J,axiom, % 191.04/191.30 ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__odd__less__0,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_com_Osize_I4_J,axiom, % 191.04/191.30 ! [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))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card__Plus__conv__if,axiom, % 191.04/191.30 ! [V_B_2,T_b,V_A_2,T_a] : % 191.04/191.30 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 191.04/191.30 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) % 191.04/191.30 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 191.04/191.30 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_com_Osize_I12_J,axiom, % 191.04/191.30 ! [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))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setprod__diff1,axiom, % 191.04/191.30 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( class_Fields_Ofield(T_b) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 191.04/191.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__neg,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__1__neg,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__sgn,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => 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) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__zero__left,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => 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) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__zero,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 191.04/191.30 => 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) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__divide__distrib,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_times__divide__eq__right,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => 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) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_diff__divide__distrib,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__1,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_minus__divide__left,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => 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) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn0,axiom, % 191.04/191.30 ! [T_a] : % 191.04/191.30 ( class_Groups_Osgn__if(T_a) % 191.04/191.30 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__0__0,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__times,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_eq__divide__imp,axiom, % 191.04/191.30 ! [V_b,V_a,V_c,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 191.04/191.30 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__eq__imp,axiom, % 191.04/191.30 ! [V_a,V_b,V_c,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 191.04/191.30 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nonzero__divide__eq__eq,axiom, % 191.04/191.30 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 191.04/191.30 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nonzero__eq__divide__eq,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 191.04/191.30 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__self__if,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 191.04/191.30 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 191.04/191.30 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__self,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_right__inverse__eq,axiom, % 191.04/191.30 ! [V_a_2,V_b_2,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 191.04/191.30 <=> V_a_2 = V_b_2 ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nonzero__minus__divide__right,axiom, % 191.04/191.30 ! [V_a,V_b,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nonzero__minus__divide__divide,axiom, % 191.04/191.30 ! [V_a,V_b,T_a] : % 191.04/191.30 ( class_Rings_Odivision__ring(T_a) % 191.04/191.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__0,axiom, % 191.04/191.30 ! [T_a] : % 191.04/191.30 ( class_Rings_Oring__1(T_a) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__add,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Oring__1(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__mult,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Oring__1(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__diff,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Oring__1(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__1,axiom, % 191.04/191.30 ! [T_a] : % 191.04/191.30 ( class_Rings_Oring__1(T_a) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__minus,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Oring__1(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__less,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__greater,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_option_Osize_I1_J,axiom, % 191.04/191.30 ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_com_Osize_I15_J,axiom, % 191.04/191.30 ! [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) ). % 191.04/191.30 % 191.04/191.30 fof(fact_com_Osize_I16_J,axiom, % 191.04/191.30 ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_com_Osize_I7_J,axiom, % 191.04/191.30 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_com_Osize_I9_J,axiom, % 191.04/191.30 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_com_Osize_I8_J,axiom, % 191.04/191.30 ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_com_Osize_I1_J,axiom, % 191.04/191.30 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__double__eq__0__iff,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Int_Oring__char__0(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_finite__PlusD_I2_J,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_b,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 191.04/191.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_finite__PlusD_I1_J,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_b,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 191.04/191.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_finite__Plus,axiom, % 191.04/191.30 ! [V_B_2,T_b,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_finite__Plus__iff,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_b,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 191.04/191.30 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__1__pos,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__pos,axiom, % 191.04/191.30 ! [V_a,T_a] : % 191.04/191.30 ( class_Rings_Olinordered__idom(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.30 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_card__Plus,axiom, % 191.04/191.30 ! [V_B_2,T_b,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.04/191.30 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Ints__odd__nonzero,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Int_Oring__char__0(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 191.04/191.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sgn__if,axiom, % 191.04/191.30 ! [V_x,T_a] : % 191.04/191.30 ( class_Groups_Osgn__if(T_a) % 191.04/191.30 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 191.04/191.30 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.04/191.30 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.04/191.30 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_UNIV__Plus__UNIV,axiom, % 191.04/191.30 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ). % 191.04/191.30 % 191.04/191.30 fof(fact_gt__half__sum,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.30 => 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)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_less__half__sum,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.30 => 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))))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_diff__divide__eq__iff,axiom, % 191.04/191.30 ! [V_y,V_x,V_z,T_a] : % 191.04/191.30 ( class_Fields_Ofield(T_a) % 191.04/191.30 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__diff__eq__iff,axiom, % 191.04/191.30 ! [V_y,V_x,V_z,T_a] : % 191.04/191.30 ( class_Fields_Ofield(T_a) % 191.04/191.30 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_diff__frac__eq,axiom, % 191.04/191.30 ! [V_w,V_x,V_z,V_y,T_a] : % 191.04/191.30 ( class_Fields_Ofield(T_a) % 191.04/191.30 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__frac__eq,axiom, % 191.04/191.30 ! [V_w,V_x,V_z,V_y,T_a] : % 191.04/191.30 ( class_Fields_Ofield(T_a) % 191.04/191.30 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__add__eq__iff,axiom, % 191.04/191.30 ! [V_y,V_x,V_z,T_a] : % 191.04/191.30 ( class_Fields_Ofield(T_a) % 191.04/191.30 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_times__divide__times__eq,axiom, % 191.04/191.30 ! [V_w,V_z,V_y,V_x,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_minus__divide__divide,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => 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) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_minus__divide__right,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Plus__eq__empty__conv,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_b,T_a] : % 191.04/191.30 ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) % 191.04/191.30 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.04/191.30 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_zero__less__divide__iff,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 191.04/191.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 191.04/191.30 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__less__0__iff,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 191.04/191.30 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__pos__pos,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__pos__neg,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__neg__pos,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__neg__neg,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__strict__right__mono,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__strict__right__mono__neg,axiom, % 191.04/191.30 ! [V_c,V_a,V_b,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_eq__divide__eq,axiom, % 191.04/191.30 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 191.04/191.30 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) % 191.04/191.30 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__eq__eq,axiom, % 191.04/191.30 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 191.04/191.30 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) % 191.04/191.30 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__divide__mult__cancel__right,axiom, % 191.04/191.30 ! [V_b,V_a,V_c,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__divide__mult__cancel__left,axiom, % 191.04/191.30 ! [V_b,V_a,V_c,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_frac__eq__eq,axiom, % 191.04/191.30 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 191.04/191.30 ( class_Fields_Ofield(T_a) % 191.04/191.30 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2) % 191.04/191.30 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_less__divide__eq,axiom, % 191.04/191.30 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 191.04/191.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.30 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__less__eq,axiom, % 191.04/191.30 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 191.04/191.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.30 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_pos__less__divide__eq,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_pos__divide__less__eq,axiom, % 191.04/191.30 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__imp__div__pos__less,axiom, % 191.04/191.30 ! [V_z,V_x,V_y,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.04/191.30 => ( 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))) % 191.04/191.30 => 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)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__imp__less__div__pos,axiom, % 191.04/191.30 ! [V_x,V_z,V_y,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.04/191.30 => ( 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)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_neg__less__divide__eq,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_neg__divide__less__eq,axiom, % 191.04/191.30 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__strict__left__mono,axiom, % 191.04/191.30 ! [V_c,V_a,V_b,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.30 => ( 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))) % 191.04/191.30 => 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))) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_divide__strict__left__mono__neg,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Fields_Olinordered__field(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => ( 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))) % 191.04/191.30 => 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))) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__num__frac,axiom, % 191.04/191.30 ! [V_x,V_z,V_y,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__divide__eq__iff,axiom, % 191.04/191.30 ! [V_y,V_x,V_z,T_a] : % 191.04/191.30 ( class_Fields_Ofield(T_a) % 191.04/191.30 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__frac__num,axiom, % 191.04/191.30 ! [V_z,V_x,V_y,T_a] : % 191.04/191.30 ( class_Fields_Ofield__inverse__zero(T_a) % 191.04/191.30 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 => 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) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nat_Osize_I2_J,axiom, % 191.04/191.30 ! [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))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setprod__Un,axiom, % 191.04/191.30 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 191.04/191.30 ( class_Fields_Ofield(T_b) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.30 => ( ! [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.04/191.30 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 191.04/191.30 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nat_Osize_I4_J,axiom, % 191.04/191.30 ! [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))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_option_Osize_I4_J,axiom, % 191.04/191.30 ! [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) ). % 191.04/191.30 % 191.04/191.30 fof(fact_option_Osize_I3_J,axiom, % 191.04/191.30 ! [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) ). % 191.04/191.30 % 191.04/191.30 fof(fact_setprod__pos__nat,axiom, % 191.04/191.30 ! [V_f_2,V_S_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.04/191.30 => ( ! [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 191.04/191.30 => 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))) ) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_psubset__insert__iff,axiom, % 191.04/191.30 ! [V_B_2,V_x_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 191.04/191.30 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 191.04/191.30 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 191.04/191.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__refl,axiom, % 191.04/191.30 ! [V_x,T_a] : % 191.04/191.30 ( class_Orderings_Opreorder(T_a) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_equalityI,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.04/191.30 => V_A_2 = V_B_2 ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subsetD,axiom, % 191.04/191.30 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_empty__subsetI,axiom, % 191.04/191.30 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Inter__anti__mono,axiom, % 191.04/191.30 ! [V_A_2,V_B_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__refl,axiom, % 191.04/191.30 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 191.04/191.30 % 191.04/191.30 fof(fact_set__eq__subset,axiom, % 191.04/191.30 ! [T_a,V_B_2,V_A_2] : % 191.04/191.30 ( V_A_2 = V_B_2 % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_equalityD1,axiom, % 191.04/191.30 ! [T_a,V_B_2,V_A_2] : % 191.04/191.30 ( V_A_2 = V_B_2 % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_equalityD2,axiom, % 191.04/191.30 ! [T_a,V_B_2,V_A_2] : % 191.04/191.30 ( V_A_2 = V_B_2 % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__trans,axiom, % 191.04/191.30 ! [V_C_2,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_equalityE,axiom, % 191.04/191.30 ! [T_a,V_B_2,V_A_2] : % 191.04/191.30 ( V_A_2 = V_B_2 % 191.04/191.30 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__fun__def,axiom, % 191.04/191.30 ! [V_g_2,V_f_2,T_a,T_b] : % 191.04/191.30 ( class_Orderings_Oord(T_b) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.04/191.30 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_linorder__linear,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__eq__iff,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( V_x_2 = V_y_2 % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_rev__predicate1D,axiom, % 191.04/191.30 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 191.04/191.30 ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 191.04/191.30 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__eq__refl,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Opreorder(T_a) % 191.04/191.30 => ( V_x = V_y % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__funD,axiom, % 191.04/191.30 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 191.04/191.30 ( class_Orderings_Oord(T_b) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__antisym__conv,axiom, % 191.04/191.30 ! [V_x_2,V_y_2,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> V_x_2 = V_y_2 ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_predicate1D,axiom, % 191.04/191.30 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 191.04/191.30 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.04/191.30 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_ord__eq__le__trans,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Orderings_Oord(T_a) % 191.04/191.30 => ( V_a = V_b % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_xt1_I3_J,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( V_a = V_b % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_ord__le__eq__trans,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Orderings_Oord(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => ( V_b = V_c % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_xt1_I4_J,axiom, % 191.04/191.30 ! [V_c,V_a,V_b,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 191.04/191.30 => ( V_b = V_c % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__antisym,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => V_x = V_y ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__trans,axiom, % 191.04/191.30 ! [V_z,V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Opreorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_xt1_I5_J,axiom, % 191.04/191.30 ! [V_x,V_y,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => V_x = V_y ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_xt1_I6_J,axiom, % 191.04/191.30 ! [V_z,V_x,V_y,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__funE,axiom, % 191.04/191.30 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 191.04/191.30 ( class_Orderings_Oord(T_b) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_linorder__le__cases,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Union__mono,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_nat__size,axiom, % 191.04/191.30 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 191.04/191.30 % 191.04/191.30 fof(fact_linorder__not__less,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_linorder__not__le,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_linorder__le__less__linear,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__less__le,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 & V_x_2 != V_y_2 ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_less__le__not__le,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Orderings_Opreorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__le__less,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.30 | V_x_2 = V_y_2 ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_leI,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_not__leE,axiom, % 191.04/191.30 ! [V_x,V_y,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_linorder__antisym__conv1,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> V_x_2 = V_y_2 ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__neq__le__trans,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( V_a != V_b % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_xt1_I12_J,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( V_a != V_b % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_leD,axiom, % 191.04/191.30 ! [V_x,V_y,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__less__imp__le,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Opreorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_linorder__antisym__conv2,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Orderings_Olinorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> V_x_2 = V_y_2 ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__le__imp__less__or__eq,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.30 | V_x = V_y ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__le__neq__trans,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => ( V_a != V_b % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_xt1_I11_J,axiom, % 191.04/191.30 ! [V_a,V_b,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 191.04/191.30 => ( V_a != V_b % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__less__le__trans,axiom, % 191.04/191.30 ! [V_z,V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Opreorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_xt1_I7_J,axiom, % 191.04/191.30 ! [V_z,V_x,V_y,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_order__le__less__trans,axiom, % 191.04/191.30 ! [V_z,V_y,V_x,T_a] : % 191.04/191.30 ( class_Orderings_Opreorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_xt1_I8_J,axiom, % 191.04/191.30 ! [V_z,V_x,V_y,T_a] : % 191.04/191.30 ( class_Orderings_Oorder(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_in__mono,axiom, % 191.04/191.30 ! [V_x_2,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_set__rev__mp,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,V_x_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_set__mp,axiom, % 191.04/191.30 ! [V_x_2,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__le__imp__le__left,axiom, % 191.04/191.30 ! [V_b,V_a,V_c,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.04/191.30 => ( 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))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__le__imp__le__right,axiom, % 191.04/191.30 ! [V_b,V_c,V_a,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.04/191.30 => ( 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))) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__mono,axiom, % 191.04/191.30 ! [V_d,V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__left__mono,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__right__mono,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__le__cancel__left,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__le__cancel__right,axiom, % 191.04/191.30 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_bot__least,axiom, % 191.04/191.30 ! [V_x,T_a] : % 191.04/191.30 ( class_Orderings_Obot(T_a) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_diff__eq__diff__less__eq,axiom, % 191.04/191.30 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.30 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__empty,axiom, % 191.04/191.30 ! [V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.04/191.30 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__supE,axiom, % 191.04/191.30 ! [V_x,V_b,V_a,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( 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)) % 191.04/191.30 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 191.04/191.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sup__mono,axiom, % 191.04/191.30 ! [V_d,V_b,V_c,V_a,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sup__least,axiom, % 191.04/191.30 ! [V_z,V_x,V_y,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 191.04/191.30 => 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)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__supI,axiom, % 191.04/191.30 ! [V_b,V_x,V_a,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 191.04/191.30 => 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)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sup__absorb1,axiom, % 191.04/191.30 ! [V_x,V_y,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sup__absorb2,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__supI2,axiom, % 191.04/191.30 ! [V_a,V_b,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__supI1,axiom, % 191.04/191.30 ! [V_b,V_a,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__sup__iff,axiom, % 191.04/191.30 ! [V_z_2,V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)),V_z_2)) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__iff__sup,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sup__ge2,axiom, % 191.04/191.30 ! [V_x,V_y,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => 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))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__sup__ord_I4_J,axiom, % 191.04/191.30 ! [V_x,V_y,T_a] : % 191.04/191.30 ( class_Lattices_Olattice(T_a) % 191.04/191.30 => 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))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_sup__ge1,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__sup(T_a) % 191.04/191.30 => 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))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__sup__ord_I3_J,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Olattice(T_a) % 191.04/191.30 => 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))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_finite__subset,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_rev__finite__subset,axiom, % 191.04/191.30 ! [V_A_2,V_B_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__sup__ord_I1_J,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Olattice(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__le1,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__sup__ord_I2_J,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Olattice(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__le2,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => 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)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__iff__inf,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__inf__iff,axiom, % 191.04/191.30 ! [V_z_2,V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2))) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__infI1,axiom, % 191.04/191.30 ! [V_b,V_x,V_a,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 191.04/191.30 => 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)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__infI2,axiom, % 191.04/191.30 ! [V_a,V_x,V_b,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 191.04/191.30 => 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)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__absorb1,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__absorb2,axiom, % 191.04/191.30 ! [V_x,V_y,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.04/191.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__infI,axiom, % 191.04/191.30 ! [V_b,V_a,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__greatest,axiom, % 191.04/191.30 ! [V_z,V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_inf__mono,axiom, % 191.04/191.30 ! [V_d,V_b,V_c,V_a,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__infE,axiom, % 191.04/191.30 ! [V_b,V_a,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Osemilattice__inf(T_a) % 191.04/191.30 => ( 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))) % 191.04/191.30 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 191.04/191.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_top__greatest,axiom, % 191.04/191.30 ! [V_x,T_a] : % 191.04/191.30 ( class_Orderings_Otop(T_a) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__insertI,axiom, % 191.04/191.30 ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__insertI2,axiom, % 191.04/191.30 ! [V_b_2,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_insert__mono,axiom, % 191.04/191.30 ! [V_a_2,V_D_2,V_C_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__imp__neg__le,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_neg__le__iff__le,axiom, % 191.04/191.30 ! [V_a_2,V_b_2,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_minus__le__iff,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__minus__iff,axiom, % 191.04/191.30 ! [V_b_2,V_a_2,T_a] : % 191.04/191.30 ( class_Groups_Oordered__ab__group__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_compl__le__compl__iff,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_compl__mono,axiom, % 191.04/191.30 ! [V_y,V_x,T_a] : % 191.04/191.30 ( class_Lattices_Oboolean__algebra(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__image__iff,axiom, % 191.04/191.30 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 191.04/191.30 <=> ? [B_AA] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 191.04/191.30 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_image__mono,axiom, % 191.04/191.30 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__UNIV,axiom, % 191.04/191.30 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Un__upper1,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Un__upper2,axiom, % 191.04/191.30 ! [V_A_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__Un__eq,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Un__absorb1,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Un__absorb2,axiom, % 191.04/191.30 ! [V_A_2,V_B_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Un__least,axiom, % 191.04/191.30 ! [V_B_2,V_C_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Un__mono,axiom, % 191.04/191.30 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Int__lower1,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Int__lower2,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Int__absorb2,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Int__absorb1,axiom, % 191.04/191.30 ! [V_A_2,V_B_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.04/191.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Int__greatest,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,V_C_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Int__mono,axiom, % 191.04/191.30 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Diff__subset,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Diff__mono,axiom, % 191.04/191.30 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_double__diff,axiom, % 191.04/191.30 ! [V_C_2,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.04/191.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__inj__on,axiom, % 191.04/191.30 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 191.04/191.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Sup__le__iff,axiom, % 191.04/191.30 ! [V_b_2,V_A_2,T_a] : % 191.04/191.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2)) % 191.04/191.30 <=> ! [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_less__fun__def,axiom, % 191.04/191.30 ! [V_g_2,V_f_2,T_a,T_b] : % 191.04/191.30 ( class_Orderings_Oord(T_b) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.04/191.30 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Compl__subset__Compl__iff,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_Compl__anti__mono,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_asm,axiom, % 191.04/191.30 ! [V_G_2,V_ts_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_G_2)) % 191.04/191.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_weaken,axiom, % 191.04/191.30 ! [V_ts_2,V_ts_H_2,V_G_2,T_a] : % 191.04/191.30 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_H_2) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 191.04/191.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_thin,axiom, % 191.04/191.30 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 191.04/191.30 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_G_2)) % 191.04/191.30 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_le__Inf__iff,axiom, % 191.04/191.30 ! [V_A_2,V_b_2,T_a] : % 191.04/191.30 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))) % 191.04/191.30 <=> ! [B_x] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_vimage__mono,axiom, % 191.04/191.30 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_psubset__eq,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 & V_A_2 != V_B_2 ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__iff__psubset__eq,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 | V_A_2 = V_B_2 ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_psubset__imp__subset,axiom, % 191.04/191.30 ! [V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_psubset__subset__trans,axiom, % 191.04/191.30 ! [V_C_2,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_subset__psubset__trans,axiom, % 191.04/191.30 ! [V_C_2,V_B_2,V_A_2,T_a] : % 191.04/191.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.04/191.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__nonpos__nonpos,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__increasing2,axiom, % 191.04/191.30 ! [V_a,V_b,V_c,T_a] : % 191.04/191.30 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__increasing,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__nonneg__eq__0__iff,axiom, % 191.04/191.30 ! [V_y_2,V_x_2,T_a] : % 191.04/191.30 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 191.04/191.30 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.04/191.30 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_add__nonneg__nonneg,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 191.04/191.30 ! [V_a_2,T_a] : % 191.04/191.30 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 191.04/191.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_split__mult__neg__le,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__cancel__semiring(T_a) % 191.04/191.30 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 191.04/191.30 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_split__mult__pos__le,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__ring(T_a) % 191.04/191.30 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 191.04/191.30 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 191.04/191.30 => 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))) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__mono,axiom, % 191.04/191.30 ! [V_d,V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__semiring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.30 => 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))) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__mono_H,axiom, % 191.04/191.30 ! [V_d,V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__semiring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.30 => 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))) ) ) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__left__mono__neg,axiom, % 191.04/191.30 ! [V_c,V_a,V_b,T_a] : % 191.04/191.30 ( class_Rings_Oordered__ring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__right__mono__neg,axiom, % 191.04/191.30 ! [V_c,V_a,V_b,T_a] : % 191.04/191.30 ( class_Rings_Oordered__ring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_comm__mult__left__mono,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__comm__semiring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__left__mono,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__semiring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__right__mono,axiom, % 191.04/191.30 ! [V_c,V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__semiring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__nonpos__nonpos,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__ring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => 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))) ) ) ) ). % 191.04/191.30 % 191.04/191.30 fof(fact_mult__nonpos__nonneg,axiom, % 191.04/191.30 ! [V_b,V_a,T_a] : % 191.04/191.30 ( class_Rings_Oordered__cancel__semiring(T_a) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.04/191.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__nonneg__nonpos2,axiom, % 191.28/191.31 ! [V_b,V_a,T_a] : % 191.28/191.31 ( class_Rings_Oordered__cancel__semiring(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__nonneg__nonpos,axiom, % 191.28/191.31 ! [V_b,V_a,T_a] : % 191.28/191.31 ( class_Rings_Oordered__cancel__semiring(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__nonneg__nonneg,axiom, % 191.28/191.31 ! [V_b,V_a,T_a] : % 191.28/191.31 ( class_Rings_Oordered__cancel__semiring(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__0__iff,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__ring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 191.28/191.31 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_zero__le__mult__iff,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__ring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 191.28/191.31 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_zero__le__square,axiom, % 191.28/191.31 ! [V_a,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__ring(T_a) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__le__less__mono,axiom, % 191.28/191.31 ! [V_d,V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__less__le__mono,axiom, % 191.28/191.31 ! [V_d,V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__iff__diff__le__0,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,T_a] : % 191.28/191.31 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_not__one__le__zero,axiom, % 191.28/191.31 ! [T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.31 => ~ 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_zero__le__one,axiom, % 191.28/191.31 ! [T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_minus__le__self__iff,axiom, % 191.28/191.31 ! [V_a_2,T_a] : % 191.28/191.31 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_neg__le__0__iff__le,axiom, % 191.28/191.31 ! [V_a_2,T_a] : % 191.28/191.31 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__minus__self__iff,axiom, % 191.28/191.31 ! [V_a_2,T_a] : % 191.28/191.31 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_neg__0__le__iff__le,axiom, % 191.28/191.31 ! [V_a_2,T_a] : % 191.28/191.31 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_insert__subset,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_x_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2)) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_subset__insert,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_x_2,T_a] : % 191.28/191.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_distrib__sup__le,axiom, % 191.28/191.31 ! [V_z,V_y,V_x,T_a] : % 191.28/191.31 ( class_Lattices_Olattice(T_a) % 191.28/191.31 => 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)))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_distrib__inf__le,axiom, % 191.28/191.31 ! [V_z,V_y,V_x,T_a] : % 191.28/191.31 ( class_Lattices_Olattice(T_a) % 191.28/191.31 => 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)))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_subset__singletonD,axiom, % 191.28/191.31 ! [V_x_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 191.28/191.31 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__right__mono__neg,axiom, % 191.28/191.31 ! [V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__right__mono,axiom, % 191.28/191.31 ! [V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__le__0__iff,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 191.28/191.31 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_zero__le__divide__iff,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 191.28/191.31 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_finite__surj,axiom, % 191.28/191.31 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 191.28/191.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_image__Int__subset,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Sup__upper,axiom, % 191.28/191.31 ! [V_A_2,V_x_2,T_a] : % 191.28/191.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Un__Int__assoc__eq,axiom, % 191.28/191.31 ! [V_C_2,V_B_2,V_A_2,T_a] : % 191.28/191.31 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_image__diff__subset,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Diff__subset__conv,axiom, % 191.28/191.31 ! [V_C_2,V_B_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Diff__partition,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Inf__lower,axiom, % 191.28/191.31 ! [V_A_2,V_x_2,T_a] : % 191.28/191.31 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_subset__Compl__self__eq,axiom, % 191.28/191.31 ! [V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 191.28/191.31 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_image__vimage__subset,axiom, % 191.28/191.31 ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Union__Int__subset,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Union__upper,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Inter__Un__subset,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Inter__lower,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => 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) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat_Osize_I3_J,axiom, % 191.28/191.31 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) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__nonpos__neg,axiom, % 191.28/191.31 ! [V_b,V_a,T_a] : % 191.28/191.31 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__neg__nonpos,axiom, % 191.28/191.31 ! [V_b,V_a,T_a] : % 191.28/191.31 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__strict__increasing2,axiom, % 191.28/191.31 ! [V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__strict__increasing,axiom, % 191.28/191.31 ! [V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__nonneg__pos,axiom, % 191.28/191.31 ! [V_b,V_a,T_a] : % 191.28/191.31 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__pos__nonneg,axiom, % 191.28/191.31 ! [V_b,V_a,T_a] : % 191.28/191.31 ( class_Groups_Oordered__comm__monoid__add(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__left__le__imp__le,axiom, % 191.28/191.31 ! [V_b,V_a,V_c,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.28/191.31 => ( 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))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__right__le__imp__le,axiom, % 191.28/191.31 ! [V_b,V_c,V_a,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.28/191.31 => ( 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))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__less__imp__less__left,axiom, % 191.28/191.31 ! [V_b,V_a,V_c,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.28/191.31 => ( 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))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__left__less__imp__less,axiom, % 191.28/191.31 ! [V_b,V_a,V_c,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring(T_a) % 191.28/191.31 => ( 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))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__less__imp__less__right,axiom, % 191.28/191.31 ! [V_b,V_c,V_a,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.28/191.31 => ( 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))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__right__less__imp__less,axiom, % 191.28/191.31 ! [V_b,V_c,V_a,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring(T_a) % 191.28/191.31 => ( 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))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__less__imp__less,axiom, % 191.28/191.31 ! [V_d,V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => 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))) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__less__le__imp__less,axiom, % 191.28/191.31 ! [V_d,V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => 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))) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__strict__mono_H,axiom, % 191.28/191.31 ! [V_d,V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => 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))) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__strict__mono,axiom, % 191.28/191.31 ! [V_d,V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => 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))) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__cancel__left__neg,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__ring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__cancel__left__pos,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__ring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_sum__squares__le__zero__iff,axiom, % 191.28/191.31 ! [V_y_2,V_x_2,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__ring__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_sum__squares__ge__zero,axiom, % 191.28/191.31 ! [V_y,V_x,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__ring(T_a) % 191.28/191.31 => 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)))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__left__le__one__le,axiom, % 191.28/191.31 ! [V_y,V_x,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.31 => 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)) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__right__le__one__le,axiom, % 191.28/191.31 ! [V_y,V_x,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.31 => 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)) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__add__iff1,axiom, % 191.28/191.31 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 191.28/191.31 ( class_Rings_Oordered__ring(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__add__iff2,axiom, % 191.28/191.31 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 191.28/191.31 ( class_Rings_Oordered__ring(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__nonpos__neg,axiom, % 191.28/191.31 ! [V_y,V_x,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__nonpos__pos,axiom, % 191.28/191.31 ! [V_y,V_x,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_frac__le,axiom, % 191.28/191.31 ! [V_z,V_w,V_y,V_x,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 191.28/191.31 => 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))) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_frac__less,axiom, % 191.28/191.31 ! [V_z,V_w,V_y,V_x,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 191.28/191.31 => 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))) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_frac__less2,axiom, % 191.28/191.31 ! [V_z,V_w,V_y,V_x,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 191.28/191.31 => 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))) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__nonneg__neg,axiom, % 191.28/191.31 ! [V_y,V_x,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__nonneg__pos,axiom, % 191.28/191.31 ! [V_y,V_x,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_inj__on__iff__surj,axiom, % 191.28/191.31 ! [V_A_H_2,T_b,T_a,V_A_2] : % 191.28/191.31 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 => ( ? [B_f] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2)) ) % 191.28/191.31 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_finite__surj__inj,axiom, % 191.28/191.31 ! [V_f_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2))) % 191.28/191.31 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_endo__inj__surj,axiom, % 191.28/191.31 ! [V_f_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)),V_A_2)) % 191.28/191.31 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 191.28/191.31 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_inj__image__subset__iff,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_inj__on__image__Int,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.28/191.31 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_inj__on__image__set__diff,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 191.28/191.31 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_disjoint__eq__subset__Compl,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,T_a] : % 191.28/191.31 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_surj__Compl__image__subset,axiom, % 191.28/191.31 ! [V_A_2,V_f_2,T_a,T_b] : % 191.28/191.31 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_vimage__subsetD,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 191.28/191.31 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_folding__one__idem_Osubset__idem,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 191.28/191.31 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => 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) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat_Osize_I1_J,axiom, % 191.28/191.31 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.31 % 191.28/191.31 fof(fact_convex__bound__le,axiom, % 191.28/191.31 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__1(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 191.28/191.31 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 191.28/191.31 => 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)) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__left__mono__neg,axiom, % 191.28/191.31 ! [V_c,V_b,V_a,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => ( 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))) % 191.28/191.31 => 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))) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__left__mono,axiom, % 191.28/191.31 ! [V_c,V_a,V_b,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 191.28/191.31 => ( 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))) % 191.28/191.31 => 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))) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_neg__divide__le__eq,axiom, % 191.28/191.31 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_neg__le__divide__eq,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__imp__le__div__pos,axiom, % 191.28/191.31 ! [V_x,V_z,V_y,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.31 => ( 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)) % 191.28/191.31 => 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))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__imp__div__pos__le,axiom, % 191.28/191.31 ! [V_z,V_x,V_y,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.31 => ( 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))) % 191.28/191.31 => 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)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_pos__divide__le__eq,axiom, % 191.28/191.31 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_pos__le__divide__eq,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__le__eq,axiom, % 191.28/191.31 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__divide__eq,axiom, % 191.28/191.31 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_subset__insert__iff,axiom, % 191.28/191.31 ! [V_B_2,V_x_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__single__insert,axiom, % 191.28/191.31 ! [V_B_2,V_x_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_sup__le__fold__sup,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Osemilattice__sup(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_fold__inf__le__inf,axiom, % 191.28/191.31 ! [V_b_2,V_a_2,V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Osemilattice__inf(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setsum__diff,axiom, % 191.28/191.31 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 191.28/191.31 ( class_Groups_Oab__group__add(T_b) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_fold1__belowI,axiom, % 191.28/191.31 ! [V_a_2,V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Osemilattice__inf(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)),V_a_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__bij__eq,axiom, % 191.28/191.31 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2)) % 191.28/191.31 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),V_B_2)),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.28/191.31 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_below__fold1__iff,axiom, % 191.28/191.31 ! [V_x_2,V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Osemilattice__inf(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2))) % 191.28/191.31 <=> ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__Diff__subset,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Sup__fin_Osubset__idem,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Olattice(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Inf__fin_Osubset__idem,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Olattice(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_inj__image__Compl__subset,axiom, % 191.28/191.31 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_vimage__subsetI,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),V_A_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__psubset,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setsum__diff__nat,axiom, % 191.28/191.31 ! [V_f_2,V_A_2,V_B_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Inf__le__Sup,axiom, % 191.28/191.31 ! [V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Olattice(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_convex__bound__lt,axiom, % 191.28/191.31 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 191.28/191.31 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 191.28/191.31 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 191.28/191.31 => 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)) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setsum__mono2,axiom, % 191.28/191.31 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 191.28/191.31 ( class_Groups_Oordered__comm__monoid__add(T_b) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.31 => ( ! [B_b] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setsum__mono3,axiom, % 191.28/191.31 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 191.28/191.31 ( ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.31 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_the__inv__into__into,axiom, % 191.28/191.31 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setprod__mono__one__left,axiom, % 191.28/191.31 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 191.28/191.31 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 191.28/191.31 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 191.28/191.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setprod__mono__one__right,axiom, % 191.28/191.31 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 191.28/191.31 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 191.28/191.31 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 191.28/191.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setsum__mono__zero__left,axiom, % 191.28/191.31 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 191.28/191.31 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 191.28/191.31 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 191.28/191.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setsum__mono__zero__right,axiom, % 191.28/191.31 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 191.28/191.31 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 191.28/191.31 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 191.28/191.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le0,axiom, % 191.28/191.31 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__0__eq,axiom, % 191.28/191.31 ! [V_n_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 191.28/191.31 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 191.28/191.31 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Suc__leD,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__SucE,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 191.28/191.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__SucI,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Suc__le__mono,axiom, % 191.28/191.31 ! [V_m_2,V_n_2] : % 191.28/191.31 ( 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))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__Suc__eq,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.31 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_not__less__eq__eq,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Suc__n__not__le__n,axiom, % 191.28/191.31 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 191.28/191.31 % 191.28/191.31 fof(fact_termination__basic__simps_I5_J,axiom, % 191.28/191.31 ! [V_y,V_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__or__eq__imp__le,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 | V_m = V_n ) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__neq__implies__less,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => ( V_m != V_n % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__imp__le__nat,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__eq__less__or__eq,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.31 | V_m_2 = V_n_2 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__less__le,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.31 & V_m_2 != V_n_2 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_termination__basic__simps_I4_J,axiom, % 191.28/191.31 ! [V_y,V_z,V_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_termination__basic__simps_I3_J,axiom, % 191.28/191.31 ! [V_z,V_y,V_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__leE,axiom, % 191.28/191.31 ! [V_n,V_k,V_m] : % 191.28/191.31 ( 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)) % 191.28/191.31 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__leD1,axiom, % 191.28/191.31 ! [V_n,V_k,V_m] : % 191.28/191.31 ( 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)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__leD2,axiom, % 191.28/191.31 ! [V_n,V_k,V_m] : % 191.28/191.31 ( 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)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__le__mono,axiom, % 191.28/191.31 ! [V_l,V_k,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 191.28/191.31 => 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))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__le__mono1,axiom, % 191.28/191.31 ! [V_k,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_trans__le__add2,axiom, % 191.28/191.31 ! [V_m,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_trans__le__add1,axiom, % 191.28/191.31 ! [V_m,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__add__left__cancel__le,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_k_2] : % 191.28/191.31 ( 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))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__iff__add,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.31 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__add1,axiom, % 191.28/191.31 ! [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))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__add2,axiom, % 191.28/191.31 ! [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))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__le__self,axiom, % 191.28/191.31 ! [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)) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__le__mono2,axiom, % 191.28/191.31 ! [V_l,V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__le__mono,axiom, % 191.28/191.31 ! [V_l,V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__diff__cancel,axiom, % 191.28/191.31 ! [V_n,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 191.28/191.31 => 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 ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_eq__diff__iff,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_k_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 191.28/191.31 => ( 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) % 191.28/191.31 <=> V_m_2 = V_n_2 ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Nat_Odiff__diff__eq,axiom, % 191.28/191.31 ! [V_n,V_m,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 191.28/191.31 => 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) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__diff__iff,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_k_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 191.28/191.31 => ( 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))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__square,axiom, % 191.28/191.31 ! [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))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__cube,axiom, % 191.28/191.31 ! [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)))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__mono1,axiom, % 191.28/191.31 ! [V_k,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__mono2,axiom, % 191.28/191.31 ! [V_k,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__mono,axiom, % 191.28/191.31 ! [V_l,V_k,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 191.28/191.31 => 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))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evaln__nonstrict,axiom, % 191.28/191.31 ! [V_m,V_t,V_n,V_s,V_c] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.31 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__eq__Suc__le,axiom, % 191.28/191.31 ! [V_m_2,V_n_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__Suc__eq__le,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Suc__le__eq,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__imp__less__Suc,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Suc__leI,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__less__Suc__eq,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 191.28/191.31 <=> V_n_2 = V_m_2 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Suc__le__lessD,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__is__0__eq,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__is__0__eq_H,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Suc__diff__le,axiom, % 191.28/191.31 ! [V_m,V_n] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Suc__mult__le__cancel1,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_k_2] : % 191.28/191.31 ( 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))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__less__mono,axiom, % 191.28/191.31 ! [V_c,V_b,V_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 191.28/191.31 => 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))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__diff__iff,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_k_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 191.28/191.31 => ( 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))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__diff__right,axiom, % 191.28/191.31 ! [V_i,V_j,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__diff__conv,axiom, % 191.28/191.31 ! [V_i_2,V_k_2,V_j_2] : % 191.28/191.31 ( 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)) % 191.28/191.31 <=> 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__add__diff,axiom, % 191.28/191.31 ! [V_m,V_n,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__add__diff__inverse,axiom, % 191.28/191.31 ! [V_m,V_n] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.31 => 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 ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__diff__assoc,axiom, % 191.28/191.31 ! [V_i,V_j,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__diff__conv2,axiom, % 191.28/191.31 ! [V_i_2,V_j_2,V_k_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 191.28/191.31 => ( 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))) % 191.28/191.31 <=> 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)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__add__diff__inverse2,axiom, % 191.28/191.31 ! [V_m,V_n] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.31 => 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 ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__imp__diff__is__add,axiom, % 191.28/191.31 ! [V_k_2,V_j_2,V_i_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 191.28/191.31 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 191.28/191.31 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__add__assoc,axiom, % 191.28/191.31 ! [V_i,V_j,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__diff__assoc2,axiom, % 191.28/191.31 ! [V_i,V_j,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__add__assoc2,axiom, % 191.28/191.31 ! [V_i,V_j,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__insert__le,axiom, % 191.28/191.31 ! [V_x_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_one__le__mult__iff,axiom, % 191.28/191.31 ! [V_n_2,V_m_2] : % 191.28/191.31 ( 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))) % 191.28/191.31 <=> ( 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)) % 191.28/191.31 & 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)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__cancel2,axiom, % 191.28/191.31 ! [V_n_2,V_k_2,V_m_2] : % 191.28/191.31 ( 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))) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__le__cancel1,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_k_2] : % 191.28/191.31 ( 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))) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__mult__le__cancel1,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_k_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 191.28/191.31 => ( 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))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__mono,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__seteq,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 191.28/191.31 => V_A_2 = V_B_2 ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__image__le,axiom, % 191.28/191.31 ! [V_f_2,T_b,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__Suc__diff__eq2,axiom, % 191.28/191.31 ! [V_m,V_j,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__Suc__diff__eq1,axiom, % 191.28/191.31 ! [V_m,V_j,V_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__le__add__iff1,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 191.28/191.31 => ( 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))) % 191.28/191.31 <=> 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)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__diff__add__eq1,axiom, % 191.28/191.31 ! [V_n,V_m,V_u,V_i,V_j] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__eq__add__iff1,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 191.28/191.31 => ( 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) % 191.28/191.31 <=> 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 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__le__add__iff2,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 191.28/191.31 => ( 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))) % 191.28/191.31 <=> 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))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__diff__add__eq2,axiom, % 191.28/191.31 ! [V_n,V_m,V_u,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__eq__add__iff2,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 191.28/191.31 => ( 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) % 191.28/191.31 <=> 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) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_the__inv__into__f__f,axiom, % 191.28/191.31 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.31 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_the__inv__into__f__eq,axiom, % 191.28/191.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.31 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_the__inv__f__f,axiom, % 191.28/191.31 ! [V_x_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.31 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_the__inv__into__onto,axiom, % 191.28/191.31 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_inj__on__the__inv__into,axiom, % 191.28/191.31 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__less__add__iff2,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 191.28/191.31 => ( 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))) % 191.28/191.31 <=> 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))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__less__add__iff1,axiom, % 191.28/191.31 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 191.28/191.31 => ( 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))) % 191.28/191.31 <=> 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)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__card__le__card__Diff,axiom, % 191.28/191.31 ! [V_A_2,V_B_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_f__the__inv__into__f,axiom, % 191.28/191.31 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 191.28/191.31 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__Diff1__le,axiom, % 191.28/191.31 ! [V_x_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__inj__on__le,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2)) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_inj__on__iff__card__le,axiom, % 191.28/191.31 ! [V_B_2,T_b,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.28/191.31 => ( ? [B_f] : % 191.28/191.31 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2)) ) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Powp__mono,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_a,V_A_2)),c_Predicate_OPowp(T_a,V_B_2))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_finite__subset__induct,axiom, % 191.28/191.31 ! [V_P_2,V_A_2,V_F_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 191.28/191.31 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.28/191.31 => ( ! [B_a,B_F] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 191.28/191.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 191.28/191.31 => ( hBOOL(hAPP(V_P_2,B_F)) % 191.28/191.31 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 191.28/191.31 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_field__le__mult__one__interval,axiom, % 191.28/191.31 ! [V_y,V_x,T_a] : % 191.28/191.31 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 => ( ! [B_z] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.31 => 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)) ) ) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Inter__subset,axiom, % 191.28/191.31 ! [V_B_2,V_A_2,T_a] : % 191.28/191.31 ( ! [B_X] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 191.28/191.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setsum__SucD,axiom, % 191.28/191.31 ! [V_n_2,V_A_2,V_f_2,T_a] : % 191.28/191.31 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) % 191.28/191.31 => ? [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.31 & 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))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 191.28/191.31 ! [V_N_2] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 191.28/191.31 <=> ? [B_m] : % 191.28/191.31 ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__refl,axiom, % 191.28/191.31 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 191.28/191.31 % 191.28/191.31 fof(fact_nat__le__linear,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_eq__imp__le,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( V_m = V_n % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__trans,axiom, % 191.28/191.31 ! [V_k,V_j,V_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__antisym,axiom, % 191.28/191.31 ! [V_n,V_m] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.31 => V_m = V_n ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_finite__nat__set__iff__bounded,axiom, % 191.28/191.31 ! [V_N_2] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 191.28/191.31 <=> ? [B_m] : % 191.28/191.31 ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ord_OatMost__iff,axiom, % 191.28/191.31 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ord_OatLeast__iff,axiom, % 191.28/191.31 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ord_OlessThan__iff,axiom, % 191.28/191.31 ! [V_k_2,V_less_2,V_i_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ord_OgreaterThan__iff,axiom, % 191.28/191.31 ! [V_k_2,V_less_2,V_i_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ord_OatLeastAtMost__iff,axiom, % 191.28/191.31 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2))) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 191.28/191.31 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_infinite__UNIV__nat,axiom, % 191.28/191.31 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 191.28/191.31 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ord_OatLeastLessThan__iff,axiom, % 191.28/191.31 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 191.28/191.31 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_ex__least__nat__less,axiom, % 191.28/191.31 ! [V_n_2,V_P_2] : % 191.28/191.31 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 191.28/191.31 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 191.28/191.31 => ? [B_k] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 191.28/191.31 & ! [B_i] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 191.28/191.31 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 191.28/191.31 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card__partition,axiom, % 191.28/191.31 ! [V_k_2,V_C_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 191.28/191.31 => ( ! [B_c] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 191.28/191.31 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 191.28/191.31 => ( ! [B_c1] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 191.28/191.31 => ! [B_c2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 191.28/191.31 => ( B_c1 != B_c2 % 191.28/191.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 191.28/191.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osize_I5_J,axiom, % 191.28/191.31 ! [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))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osize_I13_J,axiom, % 191.28/191.31 ! [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))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evaln_OIfFalse,axiom, % 191.28/191.31 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 191.28/191.31 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evaln_OIfTrue,axiom, % 191.28/191.31 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 191.28/191.31 ( hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evaln__elim__cases_I5_J,axiom, % 191.28/191.31 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_n_2),V_t_2)) % 191.28/191.31 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.31 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 191.28/191.31 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.31 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evalc__elim__cases_I5_J,axiom, % 191.28/191.31 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2)) % 191.28/191.31 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.31 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 191.28/191.31 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.31 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evalc_OIfTrue,axiom, % 191.28/191.31 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 191.28/191.31 ( hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evalc_OIfFalse,axiom, % 191.28/191.31 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 191.28/191.31 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_WTs__elim__cases_I5_J,axiom, % 191.28/191.31 ! [V_c2_2,V_c1_2,V_b_2] : % 191.28/191.31 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 191.28/191.31 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 191.28/191.31 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I4_J,axiom, % 191.28/191.31 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 191.28/191.31 ( 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) % 191.28/191.31 <=> ( V_fun_2 = V_fun_H_2 % 191.28/191.31 & V_com1_2 = V_com1_H_2 % 191.28/191.31 & V_com2_2 = V_com2_H_2 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evaln_Oequations_I5_J,axiom, % 191.28/191.31 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2)),V_a2_2),V_a4_2),V_a5_2)) % 191.28/191.31 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 191.28/191.31 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evaln_Oequations_I6_J,axiom, % 191.28/191.31 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2)),V_a2_2),V_a4_2),V_a5_2)) % 191.28/191.31 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 191.28/191.31 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evalc_Oequations_I6_J,axiom, % 191.28/191.31 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2)) % 191.28/191.31 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 191.28/191.31 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_evalc_Oequations_I5_J,axiom, % 191.28/191.31 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2)) % 191.28/191.31 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 191.28/191.31 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.31 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I55_J,axiom, % 191.28/191.31 ! [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) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I54_J,axiom, % 191.28/191.31 ! [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) ). % 191.28/191.31 % 191.28/191.31 fof(fact_WT_Oequations_I5_J,axiom, % 191.28/191.31 ! [V_a2_2,V_a1_2,V_a3_2] : % 191.28/191.31 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 191.28/191.31 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 191.28/191.31 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_WT_OIf,axiom, % 191.28/191.31 ! [V_b_2,V_c1_2,V_c0_2] : % 191.28/191.31 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 191.28/191.31 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 191.28/191.31 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I57_J,axiom, % 191.28/191.31 ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I56_J,axiom, % 191.28/191.31 ! [V_fun_H_2,V_pname_H_2,V_vname_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_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I44_J,axiom, % 191.28/191.31 ! [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) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I45_J,axiom, % 191.28/191.31 ! [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) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I14_J,axiom, % 191.28/191.31 ! [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) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osimps_I15_J,axiom, % 191.28/191.31 ! [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 ). % 191.28/191.31 % 191.28/191.31 fof(fact_fold__image__1,axiom, % 191.28/191.31 ! [V_f_2,V_S_2,T_a,T_b] : % 191.28/191.31 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 191.28/191.31 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 191.28/191.31 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_card_Oneutral,axiom, % 191.28/191.31 ! [V_A_2,T_a] : % 191.28/191.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.31 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.28/191.31 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_fold__image__cong,axiom, % 191.28/191.31 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 191.28/191.31 ( class_Groups_Oab__semigroup__mult(T_b) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.31 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 191.28/191.31 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_inf__le__fold__inf,axiom, % 191.28/191.31 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Osemilattice__inf(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_ca_2),V_A_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_fold__sup__le__sup,axiom, % 191.28/191.31 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 191.28/191.31 ( class_Lattices_Osemilattice__sup(T_a) % 191.28/191.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_ca_2))) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_expand__Suc,axiom, % 191.28/191.31 ! [V_v] : % 191.28/191.31 ( 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))) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_eq__number__of,axiom, % 191.28/191.31 ! [V_y_2,V_x_2,T_a] : % 191.28/191.31 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.31 & class_Int_Oring__char__0(T_a) ) % 191.28/191.31 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 191.28/191.31 <=> V_x_2 = V_y_2 ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_number__of__reorient,axiom, % 191.28/191.31 ! [V_x_2,V_w_2,T_a] : % 191.28/191.31 ( class_Int_Onumber(T_a) % 191.28/191.31 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 191.28/191.31 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__number__of,axiom, % 191.28/191.31 ! [V_y_2,V_x_2,T_a] : % 191.28/191.31 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.31 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__number__of,axiom, % 191.28/191.31 ! [V_y_2,V_x_2,T_a] : % 191.28/191.31 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.31 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__number__of__left,axiom, % 191.28/191.31 ! [V_z,V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__number__of__eq,axiom, % 191.28/191.31 ! [V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_number__of__add,axiom, % 191.28/191.31 ! [V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_number__of__mult,axiom, % 191.28/191.31 ! [V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_arith__simps_I32_J,axiom, % 191.28/191.31 ! [V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_mult__number__of__left,axiom, % 191.28/191.31 ! [V_z,V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_diff__number__of__eq,axiom, % 191.28/191.31 ! [V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_number__of__diff,axiom, % 191.28/191.31 ! [V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_number__of__minus,axiom, % 191.28/191.31 ! [V_w,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_arith__simps_I30_J,axiom, % 191.28/191.31 ! [V_w,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__number__of__eq__not__less,axiom, % 191.28/191.31 ! [V_w_2,V_v_2,T_a] : % 191.28/191.31 ( ( class_Int_Onumber(T_a) % 191.28/191.31 & class_Orderings_Olinorder(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_right__distrib__number__of,axiom, % 191.28/191.31 ! [V_c,V_b,V_v,T_b] : % 191.28/191.31 ( ( class_Int_Onumber(T_b) % 191.28/191.31 & class_Rings_Osemiring(T_b) ) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_left__distrib__number__of,axiom, % 191.28/191.31 ! [V_v,V_b,V_a,T_b] : % 191.28/191.31 ( ( class_Int_Onumber(T_b) % 191.28/191.31 & class_Rings_Osemiring(T_b) ) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__number__of__diff1,axiom, % 191.28/191.31 ! [V_c,V_w,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_add__number__of__diff2,axiom, % 191.28/191.31 ! [V_w,V_c,V_v,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_left__diff__distrib__number__of,axiom, % 191.28/191.31 ! [V_v,V_b,V_a,T_b] : % 191.28/191.31 ( ( class_Int_Onumber(T_b) % 191.28/191.31 & class_Rings_Oring(T_b) ) % 191.28/191.31 => 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))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_right__diff__distrib__number__of,axiom, % 191.28/191.31 ! [V_c,V_b,V_v,T_b] : % 191.28/191.31 ( ( class_Int_Onumber(T_b) % 191.28/191.31 & class_Rings_Oring(T_b) ) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_minus__number__of__mult,axiom, % 191.28/191.31 ! [V_z,V_w,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_Ints__number__of,axiom, % 191.28/191.31 ! [V_w_2,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__eq__eq__number__of1,axiom, % 191.28/191.31 ! [V_a_2,V_w_2,V_b_2,T_a] : % 191.28/191.31 ( ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_a_2 % 191.28/191.31 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) % 191.28/191.31 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__eq__eq__number__of,axiom, % 191.28/191.31 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 191.28/191.31 ( ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) % 191.28/191.31 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) ) % 191.28/191.31 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_eq__divide__eq__number__of,axiom, % 191.28/191.31 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 191.28/191.31 ( ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 191.28/191.31 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) = V_b_2 ) % 191.28/191.31 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_eq__divide__eq__number__of1,axiom, % 191.28/191.31 ! [V_w_2,V_b_2,V_a_2,T_a] : % 191.28/191.31 ( ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) % 191.28/191.31 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_b_2 ) % 191.28/191.31 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.31 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__divide__eq__number__of1,axiom, % 191.28/191.31 ! [V_w_2,V_b_2,V_a_2,T_a] : % 191.28/191.31 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__divide__eq__number__of,axiom, % 191.28/191.31 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 191.28/191.31 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__less__eq__number__of,axiom, % 191.28/191.31 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 191.28/191.31 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__less__eq__number__of1,axiom, % 191.28/191.31 ! [V_a_2,V_w_2,V_b_2,T_a] : % 191.28/191.31 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__le__eq__number__of1,axiom, % 191.28/191.31 ! [V_a_2,V_w_2,V_b_2,T_a] : % 191.28/191.31 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_divide__le__eq__number__of,axiom, % 191.28/191.31 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 191.28/191.31 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__divide__eq__number__of,axiom, % 191.28/191.31 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 191.28/191.31 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_le__divide__eq__number__of1,axiom, % 191.28/191.31 ! [V_w_2,V_b_2,V_a_2,T_a] : % 191.28/191.31 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.31 & class_Int_Onumber(T_a) ) % 191.28/191.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) % 191.28/191.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 191.28/191.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 191.28/191.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osize_I3_J,axiom, % 191.28/191.31 ! [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))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_com_Osize_I11_J,axiom, % 191.28/191.31 ! [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))) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setsum__reindex__cong,axiom, % 191.28/191.31 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 191.28/191.31 ( class_Groups_Ocomm__monoid__add(T_c) % 191.28/191.31 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.31 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 191.28/191.31 => ( ! [B_a] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 191.28/191.31 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 191.28/191.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_number__of__pred,axiom, % 191.28/191.31 ! [V_w,T_a] : % 191.28/191.31 ( class_Int_Onumber__ring(T_a) % 191.28/191.31 => 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)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setprod__pos,axiom, % 191.28/191.31 ! [V_f_2,V_A_2,T_a,T_b] : % 191.28/191.31 ( class_Rings_Olinordered__semidom(T_b) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_setprod__nonneg,axiom, % 191.28/191.31 ! [V_f_2,V_A_2,T_a,T_b] : % 191.28/191.31 ( class_Rings_Olinordered__semidom(T_b) % 191.28/191.31 => ( ! [B_x] : % 191.28/191.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 191.28/191.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_WTs__elim__cases_I3_J,axiom, % 191.28/191.31 ! [V_ca_2,V_a_2,V_Y_2] : % 191.28/191.31 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) % 191.28/191.31 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 191.28/191.31 % 191.28/191.31 fof(fact_less__eq__number__of__int__code,axiom, % 191.28/191.31 ! [V_l_2,V_k_2] : % 191.28/191.31 ( 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))) % 191.28/191.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_minus__numeral__code_I6_J,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_plus__numeral__code_I9_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_minus__numeral__code_I5_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_times__numeral__code_I5_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__number__of__int__code,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zsgn__def,axiom, % 191.28/191.32 ! [V_i] : % 191.28/191.32 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.32 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 191.28/191.32 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 191.28/191.32 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 191.28/191.32 => 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)) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_pos__zmult__eq__1__iff,axiom, % 191.28/191.32 ! [V_n_2,V_m_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 191.28/191.32 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 191.28/191.32 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 191.28/191.32 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__zless__mono2,axiom, % 191.28/191.32 ! [V_k,V_j,V_i] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 191.28/191.32 => 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))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__bin__lemma,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 191.28/191.32 <=> 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__0__less__1,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zless__linear,axiom, % 191.28/191.32 ! [V_y,V_x] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 191.28/191.32 | V_x = V_y % 191.28/191.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zless__add1__eq,axiom, % 191.28/191.32 ! [V_z_2,V_w_2] : % 191.28/191.32 ( 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)))) % 191.28/191.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 191.28/191.32 | V_w_2 = V_z_2 ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_odd__less__0,axiom, % 191.28/191.32 ! [V_z_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__strict__right__mono,axiom, % 191.28/191.32 ! [V_k,V_j,V_i] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_odd__nonzero,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__zminus__inverse2,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__0__right,axiom, % 191.28/191.32 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__0,axiom, % 191.28/191.32 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 191.28/191.32 % 191.28/191.32 fof(fact_zminus__0,axiom, % 191.28/191.32 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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__zminus,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiff__zmult__distrib,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiff__zmult__distrib2,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__commute,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__assoc,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__zmult__distrib2,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__zmult__distrib,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zminus__zminus,axiom, % 191.28/191.32 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__commute,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__left__commute,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__assoc,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zminus__zadd__distrib,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__int__def__symmetric,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__int__def,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__1,axiom, % 191.28/191.32 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__1__right,axiom, % 191.28/191.32 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 191.28/191.32 % 191.28/191.32 fof(fact_pred__def,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I2_J,axiom, % 191.28/191.32 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 191.28/191.32 ( 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) % 191.28/191.32 <=> ( V_loc_2 = V_loc_H_2 % 191.28/191.32 & V_fun_2 = V_fun_H_2 % 191.28/191.32 & V_com_2 = V_com_H_2 ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__left__mono,axiom, % 191.28/191.32 ! [V_k,V_j,V_i] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zle__antisym,axiom, % 191.28/191.32 ! [V_w,V_z] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 191.28/191.32 => V_z = V_w ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zle__trans,axiom, % 191.28/191.32 ! [V_k,V_j,V_i] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zle__linear,axiom, % 191.28/191.32 ! [V_w,V_z] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 191.28/191.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zle__refl,axiom, % 191.28/191.32 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zle__diff1__eq,axiom, % 191.28/191.32 ! [V_z_2,V_w_2] : % 191.28/191.32 ( 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)))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__one__le__iff__zero__less,axiom, % 191.28/191.32 ! [V_z_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_le__iff__pred__less,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zless__le,axiom, % 191.28/191.32 ! [V_w_2,V_z_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 191.28/191.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 191.28/191.32 & V_z_2 != V_w_2 ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zle__add1__eq__le,axiom, % 191.28/191.32 ! [V_z_2,V_w_2] : % 191.28/191.32 ( 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)))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add1__zle__eq,axiom, % 191.28/191.32 ! [V_z_2,V_w_2] : % 191.28/191.32 ( 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)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_le__imp__0__less,axiom, % 191.28/191.32 ! [V_z] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zless__imp__add1__zle,axiom, % 191.28/191.32 ! [V_z,V_w] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__zless__mono,axiom, % 191.28/191.32 ! [V_z,V_z_H,V_w,V_w_H] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 191.28/191.32 => 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))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I41_J,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I40_J,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_WT_Oequations_I3_J,axiom, % 191.28/191.32 ! [V_a1_2,V_a3_2,V_a2_2] : % 191.28/191.32 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 191.28/191.32 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_WT_OLocal,axiom, % 191.28/191.32 ! [V_a_2,V_Y_2,V_ca_2] : % 191.28/191.32 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 191.28/191.32 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I37_J,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I36_J,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I43_J,axiom, % 191.28/191.32 ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I42_J,axiom, % 191.28/191.32 ! [V_fun_H_2,V_pname_H_2,V_vname_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_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I35_J,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I34_J,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I10_J,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_com_Osimps_I11_J,axiom, % 191.28/191.32 ! [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 ). % 191.28/191.32 % 191.28/191.32 fof(fact_self__quotient__aux2,axiom, % 191.28/191.32 ! [V_q,V_r,V_a] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.32 => ( 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)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_self__quotient__aux1,axiom, % 191.28/191.32 ! [V_q,V_r,V_a] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.32 => ( 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)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_q__pos__lemma,axiom, % 191.28/191.32 ! [V_r_H,V_q_H,V_b_H] : % 191.28/191.32 ( 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))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_q__neg__lemma,axiom, % 191.28/191.32 ! [V_r_H,V_q_H,V_b_H] : % 191.28/191.32 ( 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))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_unique__quotient__lemma,axiom, % 191.28/191.32 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 191.28/191.32 ( 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))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiv__mono2__lemma,axiom, % 191.28/191.32 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 191.28/191.32 ( 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) % 191.28/191.32 => ( 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))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_number__of__is__id,axiom, % 191.28/191.32 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__0__neq__1,axiom, % 191.28/191.32 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiv__mono2__neg__lemma,axiom, % 191.28/191.32 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 191.28/191.32 ( 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) % 191.28/191.32 => ( 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))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_unique__quotient__lemma__neg,axiom, % 191.28/191.32 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 191.28/191.32 ( 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))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 191.28/191.32 ! [V_y,V_x] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.32 => 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))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 191.28/191.32 ! [V_y,V_x] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.32 => 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))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__number__of__diff__1,axiom, % 191.28/191.32 ! [V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__number__of__lemma,axiom, % 191.28/191.32 ! [V_v,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ( ( 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))) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ 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))) % 191.28/191.32 => 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) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_negative__zle,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_negative__zless,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 191.28/191.32 ! [V_A_2] : % 191.28/191.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 191.28/191.32 <=> 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__eq__iff,axiom, % 191.28/191.32 ! [V_n_2,V_m_2,T_a] : % 191.28/191.32 ( class_Nat_Osemiring__char__0(T_a) % 191.28/191.32 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) % 191.28/191.32 <=> V_m_2 = V_n_2 ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Pls__def,axiom, % 191.28/191.32 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I19_J,axiom, % 191.28/191.32 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I2_J,axiom, % 191.28/191.32 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__Pls,axiom, % 191.28/191.32 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__Pls__right,axiom, % 191.28/191.32 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__Pls,axiom, % 191.28/191.32 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__bin__simps_I1_J,axiom, % 191.28/191.32 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 191.28/191.32 % 191.28/191.32 fof(fact_minus__Pls,axiom, % 191.28/191.32 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 191.28/191.32 % 191.28/191.32 fof(fact_inj__int,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 191.28/191.32 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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 191.28/191.32 ! [V_P_2] : % 191.28/191.32 ( ! [B_x] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 191.28/191.32 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.32 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 191.28/191.32 ! [V_P_2] : % 191.28/191.32 ( ? [B_x] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 191.28/191.32 & hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.32 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 191.28/191.32 ! [V_y_2,V_x_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 191.28/191.32 ! [V_y_2,V_x_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 191.28/191.32 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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__0,axiom, % 191.28/191.32 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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__eq__0__conv,axiom, % 191.28/191.32 ! [V_n_2] : % 191.28/191.32 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.32 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zero__zle__int,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__less__0__conv,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zless__int,axiom, % 191.28/191.32 ! [V_n_2,V_m_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zle__int,axiom, % 191.28/191.32 ! [V_n_2,V_m_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__int__left,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zadd__int,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zle__iff__zadd,axiom, % 191.28/191.32 ! [V_z_2,V_w_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 191.28/191.32 <=> ? [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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zero__le__imp__of__nat,axiom, % 191.28/191.32 ! [V_m,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__0__le__iff,axiom, % 191.28/191.32 ! [V_n,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_negative__eq__positive,axiom, % 191.28/191.32 ! [V_m_2,V_n_2] : % 191.28/191.32 ( 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) % 191.28/191.32 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.32 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__less__0__iff,axiom, % 191.28/191.32 ! [V_m,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.32 => ~ 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_number__of__Pls,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_semiring__norm_I112_J,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__int__zless__negative,axiom, % 191.28/191.32 ! [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)))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__int,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__mult,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__numeral__0__right,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__numeral__0,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__0,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__less__iff,axiom, % 191.28/191.32 ! [V_n_2,V_m_2,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__imp__of__nat__less,axiom, % 191.28/191.32 ! [V_n,V_m,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.32 => 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))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__less__imp__less,axiom, % 191.28/191.32 ! [V_n,V_m,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.32 => ( 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))) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__1,axiom, % 191.28/191.32 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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__le__iff,axiom, % 191.28/191.32 ! [V_n_2,V_m_2,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__add,axiom, % 191.28/191.32 ! [V_n,V_m,T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_bin__less__0__simps_I1_J,axiom, % 191.28/191.32 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__number__of__Pls,axiom, % 191.28/191.32 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.32 % 191.28/191.32 fof(fact_semiring__norm_I113_J,axiom, % 191.28/191.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__mult,axiom, % 191.28/191.32 ! [V_n,V_m,T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zero__is__num__zero,axiom, % 191.28/191.32 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__1,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Ints__of__nat,axiom, % 191.28/191.32 ! [V_n_2,T_a] : % 191.28/191.32 ( class_Rings_Oring__1(T_a) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_inj__of__nat,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Nat_Osemiring__char__0(T_a) % 191.28/191.32 => c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__le__0__conv,axiom, % 191.28/191.32 ! [V_n_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__Suc0__eq__1,axiom, % 191.28/191.32 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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zless__iff__Suc__zadd,axiom, % 191.28/191.32 ! [V_z_2,V_w_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 191.28/191.32 <=> ? [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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__zle__neg,axiom, % 191.28/191.32 ! [V_m_2,V_n_2] : % 191.28/191.32 ( 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)))) % 191.28/191.32 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.32 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__Suc,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_negative__zle__0,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiff__int,axiom, % 191.28/191.32 ! [V_m,V_n] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__Suc,axiom, % 191.28/191.32 ! [V_m,T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_divide__Numeral0,axiom, % 191.28/191.32 ! [V_x,T_a] : % 191.28/191.32 ( ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.32 & class_Int_Onumber__ring(T_a) ) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_eq__0__number__of,axiom, % 191.28/191.32 ! [V_v_2] : % 191.28/191.32 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_eq__number__of__0,axiom, % 191.28/191.32 ! [V_v_2] : % 191.28/191.32 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__nat__number__of,axiom, % 191.28/191.32 ! [V_v_H_2,V_v_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 191.28/191.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__diff,axiom, % 191.28/191.32 ! [V_m,V_n,T_a] : % 191.28/191.32 ( class_Rings_Oring__1(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_le__nat__number__of,axiom, % 191.28/191.32 ! [V_v_H_2,V_v_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zero__less__int__conv,axiom, % 191.28/191.32 ! [V_n_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__zless__mono2__lemma,axiom, % 191.28/191.32 ! [V_k,V_j,V_i] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 191.28/191.32 => 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))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__zle__0__negative,axiom, % 191.28/191.32 ! [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))))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_negative__zless__0,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_le__special_I1_J,axiom, % 191.28/191.32 ! [V_y_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_le__special_I3_J,axiom, % 191.28/191.32 ! [V_x_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__special_I3_J,axiom, % 191.28/191.32 ! [V_x_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__special_I1_J,axiom, % 191.28/191.32 ! [V_y_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__0__less__iff,axiom, % 191.28/191.32 ! [V_n_2,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__0__number__of,axiom, % 191.28/191.32 ! [V_v_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__nat__number__of,axiom, % 191.28/191.32 ! [V_v_H,V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 191.28/191.32 => 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)) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__number__of__mult__left,axiom, % 191.28/191.32 ! [V_k,V_v_H,V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__nat__number__of,axiom, % 191.28/191.32 ! [V_v_H,V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Suc__diff__number__of,axiom, % 191.28/191.32 ! [V_m,V_v] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiff__int__split,axiom, % 191.28/191.32 ! [V_y_2,V_x_2,V_P_2] : % 191.28/191.32 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) % 191.28/191.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 191.28/191.32 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) % 191.28/191.32 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 191.28/191.32 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_number__of2,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_eq__special_I1_J,axiom, % 191.28/191.32 ! [V_y_2,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 191.28/191.32 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_eq__special_I3_J,axiom, % 191.28/191.32 ! [V_x_2,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.32 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__number__of__add__1,axiom, % 191.28/191.32 ! [V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__1__add__number__of,axiom, % 191.28/191.32 ! [V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__int__eq,axiom, % 191.28/191.32 ! [V_n_2,V_m_2] : % 191.28/191.32 ( 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) % 191.28/191.32 <=> V_m_2 = V_n_2 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 191.28/191.32 ! [V_y_2,V_x_2] : % 191.28/191.32 ( 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) % 191.28/191.32 <=> V_x_2 = V_y_2 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 191.28/191.32 ! [V_B_2,V_A_2] : % 191.28/191.32 ( V_A_2 = V_B_2 % 191.28/191.32 <=> 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 191.28/191.32 ! [V_A_2,V_x_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 191.28/191.32 <=> 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 191.28/191.32 ! [V_B_2,V_A_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.32 <=> 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 191.28/191.32 ! [V_B_2,V_A_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.32 <=> 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_infinite__UNIV__int,axiom, % 191.28/191.32 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_iszero__0,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_iszero__def,axiom, % 191.28/191.32 ! [V_z_2,T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => ( c_Int_Oiszero(T_a,V_z_2) % 191.28/191.32 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__iszero__1,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_succ__pred,axiom, % 191.28/191.32 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 191.28/191.32 % 191.28/191.32 fof(fact_succ__def,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_iszero__Numeral0,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_number__of__succ,axiom, % 191.28/191.32 ! [V_k,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_eq__number__of__eq,axiom, % 191.28/191.32 ! [V_y_2,V_x_2,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 191.28/191.32 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Suc__nat__number__of__add,axiom, % 191.28/191.32 ! [V_n,V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => 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) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_setsum__bounded,axiom, % 191.28/191.32 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 191.28/191.32 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 191.28/191.32 & class_Rings_Osemiring__1(T_b) ) % 191.28/191.32 => ( ! [B_i] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))),V_K_2))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nats__number__of,axiom, % 191.28/191.32 ! [V_w_2,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_tsub__def,axiom, % 191.28/191.32 ! [V_x,V_y] : % 191.28/191.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 191.28/191.32 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 191.28/191.32 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_decr__mult__lemma,axiom, % 191.28/191.32 ! [V_k_2,V_P_2,V_d_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 191.28/191.32 => ( ! [B_x] : % 191.28/191.32 ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.32 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 191.28/191.32 => ! [B_x] : % 191.28/191.32 ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.32 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__neg__0,axiom, % 191.28/191.32 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__neg__int,axiom, % 191.28/191.32 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__neg__1,axiom, % 191.28/191.32 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__neg__eq__ge__0,axiom, % 191.28/191.32 ! [V_x_2] : % 191.28/191.32 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_neg__def,axiom, % 191.28/191.32 ! [V_Z_2] : % 191.28/191.32 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__neg__number__of__Pls,axiom, % 191.28/191.32 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_neg__imp__number__of__eq__0,axiom, % 191.28/191.32 ! [V_v] : % 191.28/191.32 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nats__0,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_neg__zminus__int,axiom, % 191.28/191.32 ! [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))))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nats__add,axiom, % 191.28/191.32 ! [V_b_2,V_a_2,T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nats__mult,axiom, % 191.28/191.32 ! [V_b_2,V_a_2,T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nats__1,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__in__Nats,axiom, % 191.28/191.32 ! [V_n_2,T_a] : % 191.28/191.32 ( class_Rings_Osemiring__1(T_a) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_eq__nat__number__of,axiom, % 191.28/191.32 ! [V_v_H_2,V_v_2] : % 191.28/191.32 ( 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) % 191.28/191.32 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 191.28/191.32 => 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))) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 191.28/191.32 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 191.28/191.32 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 191.28/191.32 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__number__of__add__left,axiom, % 191.28/191.32 ! [V_k,V_v_H,V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 191.28/191.32 => 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) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_int__nat__number__of,axiom, % 191.28/191.32 ! [V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => 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) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 191.28/191.32 ! [V_y,V_x] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.32 => 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))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_neg__number__of__pred__iff__0,axiom, % 191.28/191.32 ! [V_v_2] : % 191.28/191.32 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 191.28/191.32 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_tsub__eq,axiom, % 191.28/191.32 ! [V_x,V_y] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 191.28/191.32 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_of__nat__number__of__eq,axiom, % 191.28/191.32 ! [V_v,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => 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) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => 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) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Suc__nat__number__of,axiom, % 191.28/191.32 ! [V_v] : % 191.28/191.32 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_negD,axiom, % 191.28/191.32 ! [V_x] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.32 => ? [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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_incr__mult__lemma,axiom, % 191.28/191.32 ! [V_k_2,V_P_2,V_d_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 191.28/191.32 => ( ! [B_x] : % 191.28/191.32 ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.32 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 191.28/191.32 => ! [B_x] : % 191.28/191.32 ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.32 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zero__less__imp__eq__int,axiom, % 191.28/191.32 ! [V_k] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 191.28/191.32 => ? [B_n] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 191.28/191.32 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_eq__special_I2_J,axiom, % 191.28/191.32 ! [V_y_2,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 191.28/191.32 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_eq__special_I4_J,axiom, % 191.28/191.32 ! [V_x_2,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 191.28/191.32 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I51_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 191.28/191.32 <=> V_k_2 = V_l_2 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I34_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__eq__int__code_I16_J,axiom, % 191.28/191.32 ! [V_k2_2,V_k1_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__int__code_I16_J,axiom, % 191.28/191.32 ! [V_k2_2,V_k1_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I17_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I46_J,axiom, % 191.28/191.32 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I39_J,axiom, % 191.28/191.32 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 191.28/191.32 % 191.28/191.32 fof(fact_bin__less__0__simps_I4_J,axiom, % 191.28/191.32 ! [V_w_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I22_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I12_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Bit1__def,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_neg__number__of__Bit1,axiom, % 191.28/191.32 ! [V_w_2] : % 191.28/191.32 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 191.28/191.32 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_minus__Bit1,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_iszero__number__of__Bit1,axiom, % 191.28/191.32 ! [V_w,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Int_Oring__char__0(T_a) ) % 191.28/191.32 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_succ__Pls,axiom, % 191.28/191.32 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 191.28/191.32 % 191.28/191.32 fof(fact_number__of__Bit1,axiom, % 191.28/191.32 ! [V_w,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__numeral__1__right,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__numeral__1,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_semiring__norm_I110_J,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_numeral__1__eq__1,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I5_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I29_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_divide__Numeral1,axiom, % 191.28/191.32 ! [V_x,T_a] : % 191.28/191.32 ( ( class_Fields_Ofield(T_a) % 191.28/191.32 & class_Int_Onumber__ring(T_a) ) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_divide__numeral__1,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( ( class_Fields_Ofield(T_a) % 191.28/191.32 & class_Int_Onumber__ring(T_a) ) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_one__is__num__one,axiom, % 191.28/191.32 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__numeral__1__eq__1,axiom, % 191.28/191.32 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Numeral1__eq1__nat,axiom, % 191.28/191.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_not__iszero__Numeral1,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_numeral__3__eq__3,axiom, % 191.28/191.32 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)))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_numeral__1__eq__Suc__0,axiom, % 191.28/191.32 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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 191.28/191.32 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))))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Suc3__eq__add__3,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 191.28/191.32 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)))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_le__special_I2_J,axiom, % 191.28/191.32 ! [V_y_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_le__special_I4_J,axiom, % 191.28/191.32 ! [V_x_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__special_I4_J,axiom, % 191.28/191.32 ! [V_x_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__special_I2_J,axiom, % 191.28/191.32 ! [V_y_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__special_I3_J,axiom, % 191.28/191.32 ! [V_v,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__special_I2_J,axiom, % 191.28/191.32 ! [V_w,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Suc__diff__eq__diff__pred,axiom, % 191.28/191.32 ! [V_m,V_n] : % 191.28/191.32 ( 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)) % 191.28/191.32 => 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)))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__special_I1_J,axiom, % 191.28/191.32 ! [V_w,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__special_I2_J,axiom, % 191.28/191.32 ! [V_v,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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)))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_one__code__numeral__code,axiom, % 191.28/191.32 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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__2__cases,axiom, % 191.28/191.32 ! [V_n] : % 191.28/191.32 ( 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))))) % 191.28/191.32 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.32 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_decr__lemma,axiom, % 191.28/191.32 ! [V_z,V_x,V_d] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_incr__lemma,axiom, % 191.28/191.32 ! [V_x,V_z,V_d] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 191.28/191.32 => 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)))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_half__gt__zero__iff,axiom, % 191.28/191.32 ! [V_r_2,T_a] : % 191.28/191.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.32 & class_Int_Onumber__ring(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__of__nat,axiom, % 191.28/191.32 ! [V_n,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__eq__0,axiom, % 191.28/191.32 ! [V_a_2,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.32 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__zero,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__add__abs,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__mult__self,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__mult,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__minus__commute,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__one,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_code__numeral__zero__minus__one,axiom, % 191.28/191.32 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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I48_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 191.28/191.32 <=> V_k_2 = V_l_2 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__idempotent,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__minus__cancel,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__ge__self,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__le__D1,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__divide,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__eq__int__code_I13_J,axiom, % 191.28/191.32 ! [V_k2_2,V_k1_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I31_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I14_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__int__code_I13_J,axiom, % 191.28/191.32 ! [V_k2_2,V_k1_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__int__eq,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Bit0__Pls,axiom, % 191.28/191.32 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I38_J,axiom, % 191.28/191.32 ! [V_l_2] : % 191.28/191.32 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 191.28/191.32 <=> c_Int_OPls = V_l_2 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I44_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 191.28/191.32 <=> V_k_2 = c_Int_OPls ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I49_J,axiom, % 191.28/191.32 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I50_J,axiom, % 191.28/191.32 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Bit0__def,axiom, % 191.28/191.32 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__Bit0__Bit0,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__Bit0,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__bin__simps_I7_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_minus__Bit0,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__ge__zero,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__le__zero__iff,axiom, % 191.28/191.32 ! [V_a_2,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.32 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__of__nonneg,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__not__less__zero,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ~ 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zero__less__abs__iff,axiom, % 191.28/191.32 ! [V_a_2,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2))) % 191.28/191.32 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__of__pos,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__triangle__ineq,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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)))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__mult__less,axiom, % 191.28/191.32 ! [V_d,V_b,V_c,V_a,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 191.28/191.32 => 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))) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__triangle__ineq3,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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)))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__triangle__ineq2,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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)))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__triangle__ineq2__sym,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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)))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__le__D2,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__leI,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 191.28/191.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__le__iff,axiom, % 191.28/191.32 ! [V_b_2,V_a_2,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 191.28/191.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 191.28/191.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__ge__minus__self,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__less__iff,axiom, % 191.28/191.32 ! [V_b_2,V_a_2,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 191.28/191.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 191.28/191.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nonzero__abs__divide,axiom, % 191.28/191.32 ! [V_a,V_b,T_a] : % 191.28/191.32 ( class_Fields_Olinordered__field(T_a) % 191.28/191.32 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_bin__less__0__simps_I3_J,axiom, % 191.28/191.32 ! [V_w_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I21_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I27_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__eq__int__code_I14_J,axiom, % 191.28/191.32 ! [V_k2_2,V_k1_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I32_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I10_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I4_J,axiom, % 191.28/191.32 ! [V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I16_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__int__code_I15_J,axiom, % 191.28/191.32 ! [V_k2_2,V_k1_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__zmult__eq__1,axiom, % 191.28/191.32 ! [V_n,V_m] : % 191.28/191.32 ( 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) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__Bit1__Bit0,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__Bit0__Bit1,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__bin__simps_I3_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__bin__simps_I9_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__bin__simps_I10_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__sgn__abs,axiom, % 191.28/191.32 ! [V_x,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__sgn,axiom, % 191.28/191.32 ! [V_k,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_neg__number__of__Bit0,axiom, % 191.28/191.32 ! [V_w_2] : % 191.28/191.32 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 191.28/191.32 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_pred__Bit0,axiom, % 191.28/191.32 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_pred__Bit1,axiom, % 191.28/191.32 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 191.28/191.32 % 191.28/191.32 fof(fact_iszero__number__of__Bit0,axiom, % 191.28/191.32 ! [V_w_2,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Int_Oring__char__0(T_a) ) % 191.28/191.32 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 191.28/191.32 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_succ__Bit1,axiom, % 191.28/191.32 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_succ__Bit0,axiom, % 191.28/191.32 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__eq__mult,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Rings_Oordered__ring__abs(T_a) % 191.28/191.32 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 191.28/191.32 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__mult__pos,axiom, % 191.28/191.32 ! [V_y,V_x,T_a] : % 191.28/191.32 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__diff__triangle__ineq,axiom, % 191.28/191.32 ! [V_d,V_c,V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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))))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__triangle__ineq4,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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)))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__of__nonpos,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__minus__le__zero,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__of__neg,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__if,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Groups_Oabs__if(T_a) % 191.28/191.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__div__pos,axiom, % 191.28/191.32 ! [V_x,V_y,T_a] : % 191.28/191.32 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_number__of__Bit0,axiom, % 191.28/191.32 ! [V_w,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zabs__less__one__iff,axiom, % 191.28/191.32 ! [V_z_2] : % 191.28/191.32 ( 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))) % 191.28/191.32 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zabs__def,axiom, % 191.28/191.32 ! [V_i] : % 191.28/191.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 191.28/191.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.32 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I15_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__int__code_I14_J,axiom, % 191.28/191.32 ! [V_k2_2,V_k1_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_rel__simps_I33_J,axiom, % 191.28/191.32 ! [V_l_2,V_k_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_less__eq__int__code_I15_J,axiom, % 191.28/191.32 ! [V_k2_2,V_k1_2] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 191.28/191.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_card__UNIV__bool,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__Bit1,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_diff__bin__simps_I8_J,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__Bit1__Bit1,axiom, % 191.28/191.32 ! [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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zero__code__numeral__code,axiom, % 191.28/191.32 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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_abs__number__of,axiom, % 191.28/191.32 ! [V_x,T_a] : % 191.28/191.32 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.32 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.32 => ( ( 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))) % 191.28/191.32 => 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)) ) % 191.28/191.32 & ( ~ 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))) % 191.28/191.32 => 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) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_double__number__of__Bit0,axiom, % 191.28/191.32 ! [V_w,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_number__of1,axiom, % 191.28/191.32 ! [V_n] : % 191.28/191.32 ( 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))) % 191.28/191.32 => ( 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)))) % 191.28/191.32 & 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)))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__2,axiom, % 191.28/191.32 ! [V_z,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mult__2__right,axiom, % 191.28/191.32 ! [V_z,T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_one__add__one__is__two,axiom, % 191.28/191.32 ! [T_a] : % 191.28/191.32 ( class_Int_Onumber__ring(T_a) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_numeral__2__eq__2,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_semiring__norm_I115_J,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 191.28/191.32 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))))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__2__eq__Suc_H,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_add__2__eq__Suc,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__mult__2,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__mult__2__right,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 191.28/191.32 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)))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_nat__1__add__1,axiom, % 191.28/191.32 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))) ). % 191.28/191.32 % 191.28/191.32 fof(fact_half__gt__zero,axiom, % 191.28/191.32 ! [V_r,T_a] : % 191.28/191.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 191.28/191.32 & class_Int_Onumber__ring(T_a) ) % 191.28/191.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 191.28/191.32 => 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)))))) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmod__number__of__Bit1,axiom, % 191.28/191.32 ! [V_v,V_w] : % 191.28/191.32 ( ( 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))) % 191.28/191.32 => 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)) ) % 191.28/191.32 & ( ~ 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))) % 191.28/191.32 => 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)) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_neg__zmod__mult__2,axiom, % 191.28/191.32 ! [V_b,V_a] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.32 => 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)) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_pos__zmod__mult__2,axiom, % 191.28/191.32 ! [V_b,V_a] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.32 => 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))) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_pos__zdiv__mult__2,axiom, % 191.28/191.32 ! [V_b,V_a] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_neg__zdiv__mult__2,axiom, % 191.28/191.32 ! [V_b,V_a] : % 191.28/191.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmod__self,axiom, % 191.28/191.32 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmod__zero,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__self,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__by__0,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__0,axiom, % 191.28/191.32 ! [V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmod__zdiv__trivial,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__div__trivial,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_DIVISION__BY__ZERO,axiom, % 191.28/191.32 ! [V_a] : % 191.28/191.32 ( 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) % 191.28/191.32 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__mod__trivial,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_div__mod__equality,axiom, % 191.28/191.32 ! [V_c,V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_div__mod__equality2,axiom, % 191.28/191.32 ! [V_c,V_a,V_b,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__div__equality,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__div__equality2,axiom, % 191.28/191.32 ! [V_a,V_b,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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 ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmult__div__cancel,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmod__zdiv__equality_H,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zmod__zdiv__equality,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiv__zmult1__eq,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiv__zmod__equality,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiv__zmod__equality2,axiom, % 191.28/191.32 ! [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) ). % 191.28/191.32 % 191.28/191.32 fof(fact_zdiv__zadd1__eq,axiom, % 191.28/191.32 ! [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)) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__minus__cong,axiom, % 191.28/191.32 ! [V_a_H,V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Oring__div(T_a) % 191.28/191.32 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 191.28/191.32 => 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) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__minus__eq,axiom, % 191.28/191.32 ! [V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Oring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__diff__cong,axiom, % 191.28/191.32 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 191.28/191.32 ( class_Divides_Oring__div(T_a) % 191.28/191.32 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 191.28/191.32 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 191.28/191.32 => 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) ) ) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__diff__eq,axiom, % 191.28/191.32 ! [V_c,V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Oring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__diff__left__eq,axiom, % 191.28/191.32 ! [V_c,V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Oring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__diff__right__eq,axiom, % 191.28/191.32 ! [V_c,V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Oring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__mult__right__eq,axiom, % 191.28/191.32 ! [V_c,V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__mult__left__eq,axiom, % 191.28/191.32 ! [V_c,V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.32 => 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) ) ). % 191.28/191.32 % 191.28/191.32 fof(fact_mod__mult__eq,axiom, % 191.28/191.32 ! [V_c,V_b,V_a,T_a] : % 191.28/191.32 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__mult1,axiom, % 191.28/191.33 ! [V_b,V_a,V_c,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__mult2,axiom, % 191.28/191.33 ! [V_b,V_c,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__simps_I4_J,axiom, % 191.28/191.33 ! [V_b,V_c,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__cong,axiom, % 191.28/191.33 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 191.28/191.33 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 191.28/191.33 => 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) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__add__cong,axiom, % 191.28/191.33 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 191.28/191.33 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 191.28/191.33 => 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) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__simps_I1_J,axiom, % 191.28/191.33 ! [V_b,V_c,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__simps_I2_J,axiom, % 191.28/191.33 ! [V_c,V_b,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__add__eq,axiom, % 191.28/191.33 ! [V_c,V_b,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__add__left__eq,axiom, % 191.28/191.33 ! [V_c,V_b,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__add__right__eq,axiom, % 191.28/191.33 ! [V_c,V_b,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__add__self1,axiom, % 191.28/191.33 ! [V_a,V_b,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__add__self2,axiom, % 191.28/191.33 ! [V_b,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__zero,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__zminus__zminus,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__zminus2,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__simps_I3_J,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__zmult1__eq,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiff__zmod__right,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiff__zmod__left,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zminus__zmod,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__zminus__zminus,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__zminus2,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__0,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__by__0,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__by__1,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__self2__is__0,axiom, % 191.28/191.33 ! [V_b,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__self1__is__0,axiom, % 191.28/191.33 ! [V_a,V_b,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__zmult2__eq,axiom, % 191.28/191.33 ! [V_b,V_a,V_c] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__self2,axiom, % 191.28/191.33 ! [V_c,V_b,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__self1,axiom, % 191.28/191.33 ! [V_b,V_c,V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__by__1,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__zminus1__eq__if,axiom, % 191.28/191.33 ! [V_a,V_b] : % 191.28/191.33 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => 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)) ) % 191.28/191.33 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => 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)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__zminus2__eq__if,axiom, % 191.28/191.33 ! [V_a,V_b] : % 191.28/191.33 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => 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)) ) % 191.28/191.33 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => 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)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 191.28/191.33 ! [V_a_2,V_b_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 191.28/191.33 ! [V_a_2,V_b_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__neg__pos__less0,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__self,axiom, % 191.28/191.33 ! [V_a] : % 191.28/191.33 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__le__nonneg__dividend,axiom, % 191.28/191.33 ! [V_k,V_m] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_pos__mod__bound,axiom, % 191.28/191.33 ! [V_a,V_b] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_neg__mod__bound,axiom, % 191.28/191.33 ! [V_a,V_b] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__number__of__Bit0,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__eq__0__iff,axiom, % 191.28/191.33 ! [V_d_2,V_m_2] : % 191.28/191.33 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__zminus1__not__zero,axiom, % 191.28/191.33 ! [V_l,V_k] : % 191.28/191.33 ( 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) % 191.28/191.33 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__zminus2__not__zero,axiom, % 191.28/191.33 ! [V_l,V_k] : % 191.28/191.33 ( 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) % 191.28/191.33 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__mult1__if,axiom, % 191.28/191.33 ! [V_b,V_a,V_c,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__self2__is__id,axiom, % 191.28/191.33 ! [V_a,V_b,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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 ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__self1__is__id,axiom, % 191.28/191.33 ! [V_a,V_b,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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 ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__mult2,axiom, % 191.28/191.33 ! [V_b,V_a,V_c,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__mult1,axiom, % 191.28/191.33 ! [V_b,V_a,V_c,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__self,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__neg__lemma,axiom, % 191.28/191.33 ! [V_n_2,V_P_2,V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 191.28/191.33 <=> ! [B_i,B_j] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 & 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) ) % 191.28/191.33 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__pos__lemma,axiom, % 191.28/191.33 ! [V_n_2,V_P_2,V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 191.28/191.33 <=> ! [B_i,B_j] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 191.28/191.33 & 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) ) % 191.28/191.33 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__mono1__neg,axiom, % 191.28/191.33 ! [V_b,V_a_H,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__mono1,axiom, % 191.28/191.33 ! [V_b,V_a_H,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__neg__neg__trivial,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 191.28/191.33 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__mono2__neg,axiom, % 191.28/191.33 ! [V_b,V_b_H,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__nonpos__pos__le0,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 191.28/191.33 ! [V_a_2,V_b_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__pos__pos__trivial,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 191.28/191.33 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__nonneg__neg__le0,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__mono2,axiom, % 191.28/191.33 ! [V_b,V_b_H,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 191.28/191.33 ! [V_b_2,V_a_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 191.28/191.33 ! [V_i_2,V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 191.28/191.33 ! [V_a_2,V_b_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__eq__0__iff,axiom, % 191.28/191.33 ! [V_k_2,V_i_2] : % 191.28/191.33 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 191.28/191.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_int__div__less__self,axiom, % 191.28/191.33 ! [V_k,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__zmult2__eq,axiom, % 191.28/191.33 ! [V_b,V_a,V_c] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__neg__neg__trivial,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 191.28/191.33 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_neg__mod__conj,axiom, % 191.28/191.33 ! [V_a,V_b] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ( 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))) % 191.28/191.33 & 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_neg__mod__sign,axiom, % 191.28/191.33 ! [V_a,V_b] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__pos__pos__trivial,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 191.28/191.33 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_pos__mod__conj,axiom, % 191.28/191.33 ! [V_a,V_b] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.33 => ( 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))) % 191.28/191.33 & 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_pos__mod__sign,axiom, % 191.28/191.33 ! [V_a,V_b] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__zminus2__eq__if,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => 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) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__zminus1__eq__if,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__self2,axiom, % 191.28/191.33 ! [V_c,V_a,V_b,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__self1,axiom, % 191.28/191.33 ! [V_c,V_a,V_b,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__add__self2,axiom, % 191.28/191.33 ! [V_a,V_b,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__add__self1,axiom, % 191.28/191.33 ! [V_a,V_b,T_a] : % 191.28/191.33 ( class_Divides_Osemiring__div(T_a) % 191.28/191.33 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__pos__neg__trivial,axiom, % 191.28/191.33 ! [V_b,V_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.33 => ( 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))) % 191.28/191.33 => 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) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_divmod__int__rel__div__eq,axiom, % 191.28/191.33 ! [V_r_1,V_y,V_b_1,V_a_1] : % 191.28/191.33 ( 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) % 191.28/191.33 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 191.28/191.33 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__zdiv,axiom, % 191.28/191.33 ! [V_k_2,V_n_2,V_P_2] : % 191.28/191.33 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 191.28/191.33 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.33 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 191.28/191.33 => ! [B_i] : % 191.28/191.33 ( ? [B_j] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 191.28/191.33 & 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) ) % 191.28/191.33 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 191.28/191.33 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ! [B_i] : % 191.28/191.33 ( ? [B_j] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 & 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) ) % 191.28/191.33 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_divmod__int__rel__mod__eq,axiom, % 191.28/191.33 ! [V_y,V_q_1,V_b_1,V_a_1] : % 191.28/191.33 ( 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) % 191.28/191.33 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 191.28/191.33 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmult2__lemma__aux2,axiom, % 191.28/191.33 ! [V_q,V_r,V_b,V_c] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmult2__lemma__aux1,axiom, % 191.28/191.33 ! [V_q,V_r,V_b,V_c] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmult2__lemma__aux4,axiom, % 191.28/191.33 ! [V_q,V_b,V_r,V_c] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmult2__lemma__aux3,axiom, % 191.28/191.33 ! [V_q,V_b,V_r,V_c] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__zmod,axiom, % 191.28/191.33 ! [V_k_2,V_n_2,V_P_2] : % 191.28/191.33 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 191.28/191.33 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 191.28/191.33 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 191.28/191.33 => ! [B_i,B_j] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 191.28/191.33 & 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) ) % 191.28/191.33 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 191.28/191.33 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => ! [B_i,B_j] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 & 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) ) % 191.28/191.33 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__number__of__Bit0,axiom, % 191.28/191.33 ! [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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__number__of__Bit1,axiom, % 191.28/191.33 ! [V_v,V_w] : % 191.28/191.33 ( ( 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))) % 191.28/191.33 => 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)) ) % 191.28/191.33 & ( ~ 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))) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__of__aux__code,axiom, % 191.28/191.33 ! [V_n,V_i] : % 191.28/191.33 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.33 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 191.28/191.33 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_z3div__def,axiom, % 191.28/191.33 ! [V_k,V_l] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 191.28/191.33 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_z3mod__def,axiom, % 191.28/191.33 ! [V_k,V_l] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 191.28/191.33 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_of__nat__double,axiom, % 191.28/191.33 ! [V_x,T_a] : % 191.28/191.33 ( class_Rings_Osemiring__1(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__minus1__odd,axiom, % 191.28/191.33 ! [V_n,T_a] : % 191.28/191.33 ( class_Rings_Oring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult2__eq,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__less,axiom, % 191.28/191.33 ! [V_n,V_m] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__power__eq,axiom, % 191.28/191.33 ! [V_n,V_z] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 191.28/191.33 ! [V_n,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult2__eq,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult1__eq,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mod__equality_H,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mult__div__cancel,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Divides_Omod__div__equality_H,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__add1__eq,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__le__mono,axiom, % 191.28/191.33 ! [V_k,V_n,V_m] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__le__dividend,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__less__eq__dividend,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__distrib,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__distrib2,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__int,axiom, % 191.28/191.33 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 191.28/191.33 ! [V_q,V_p,V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zpower__zpower,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 191.28/191.33 ! [V_q,V_y,V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_int__power,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zpower__int,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 191.28/191.33 ! [V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zpower__zmod,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__nat__number__of,axiom, % 191.28/191.33 ! [V_n,V_v] : % 191.28/191.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__nat__number__of__number__of,axiom, % 191.28/191.33 ! [V_w,V_v] : % 191.28/191.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.33 => 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)) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__div__distrib,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__mod__distrib,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__1,axiom, % 191.28/191.33 ! [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 ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__less,axiom, % 191.28/191.33 ! [V_n,V_m] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__mult__div__cancel__disj,axiom, % 191.28/191.33 ! [V_n,V_m,V_k] : % 191.28/191.33 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => 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) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 191.28/191.33 ! [V_q,V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 191.28/191.33 ! [V_q,V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 191.28/191.33 ! [V_q,V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 191.28/191.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__0,axiom, % 191.28/191.33 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__1,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__Suc,axiom, % 191.28/191.33 ! [V_n,V_m] : % 191.28/191.33 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 191.28/191.33 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.28/191.33 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__less__divisor,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 191.28/191.33 ! [V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 191.28/191.33 ! [V_q,V_p,V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 191.28/191.33 ! [V_y_2,V_x_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 191.28/191.33 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 191.28/191.33 <=> V_x_2 = V_y_2 ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_all__nat,axiom, % 191.28/191.33 ! [V_P_2] : % 191.28/191.33 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 191.28/191.33 <=> ! [B_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 191.28/191.33 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_ex__nat,axiom, % 191.28/191.33 ! [V_P_2] : % 191.28/191.33 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 191.28/191.33 <=> ? [B_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 191.28/191.33 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_eq__nat__nat__iff,axiom, % 191.28/191.33 ! [V_z_H_2,V_z_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 191.28/191.33 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 191.28/191.33 <=> V_z_2 = V_z_H_2 ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__eq__0__iff,axiom, % 191.28/191.33 ! [V_d_2,V_m_2] : % 191.28/191.33 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 191.28/191.33 ! [V_n,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__if,axiom, % 191.28/191.33 ! [V_n,V_m] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => 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) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__geq,axiom, % 191.28/191.33 ! [V_n,V_m] : % 191.28/191.33 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__self3,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_le__mod__geq,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zdiv__int,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__number__of,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__number__of__def,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zpower__zadd__distrib,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 191.28/191.33 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zmod__int,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_neg__nat,axiom, % 191.28/191.33 ! [V_z] : % 191.28/191.33 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 191.28/191.33 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_not__neg__nat,axiom, % 191.28/191.33 ! [V_z] : % 191.28/191.33 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 191.28/191.33 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Ints__power,axiom, % 191.28/191.33 ! [V_n_2,V_a_2,T_a] : % 191.28/191.33 ( class_Rings_Oring__1(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__int__nat__set__return__embed,axiom, % 191.28/191.33 ! [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 ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 191.28/191.33 ! [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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 191.28/191.33 ! [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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__nat__number__of,axiom, % 191.28/191.33 ! [V_v_H,V_v] : % 191.28/191.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__nat__number__of,axiom, % 191.28/191.33 ! [V_v_H,V_v] : % 191.28/191.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 191.28/191.33 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 191.28/191.33 => 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))) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_one__div__nat__number__of,axiom, % 191.28/191.33 ! [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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 191.28/191.33 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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__le__mono2,axiom, % 191.28/191.33 ! [V_k,V_n,V_m] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__mult__div__cancel1,axiom, % 191.28/191.33 ! [V_n,V_m,V_k] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__self1__is__m,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => 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 ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__mult__self__is__m,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => 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 ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__less__dividend,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__0__iff,axiom, % 191.28/191.33 ! [V_i_2] : % 191.28/191.33 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__le__0,axiom, % 191.28/191.33 ! [V_z] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zless__nat__conj,axiom, % 191.28/191.33 ! [V_z_2,V_w_2] : % 191.28/191.33 ( 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))) % 191.28/191.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__mono__iff,axiom, % 191.28/191.33 ! [V_w_2,V_z_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__le__divisor,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 191.28/191.33 ! [V_y_2,V_x_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__1,axiom, % 191.28/191.33 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__mult__self4,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_int__nat__eq,axiom, % 191.28/191.33 ! [V_z] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.33 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.33 => 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) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_int__eq__iff,axiom, % 191.28/191.33 ! [V_z_2,V_m_2] : % 191.28/191.33 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 191.28/191.33 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 191.28/191.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__0__le,axiom, % 191.28/191.33 ! [V_z] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.33 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zless__nat__eq__int__zless,axiom, % 191.28/191.33 ! [V_z_2,V_m_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 191.28/191.33 <=> 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__zminus__int,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__le__zpower__abs,axiom, % 191.28/191.33 ! [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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__abs__mult__distrib,axiom, % 191.28/191.33 ! [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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_one__mod__nat__number__of,axiom, % 191.28/191.33 ! [V_v_H] : % 191.28/191.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 191.28/191.33 => 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)) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__geq,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__if,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.33 => 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)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__div,axiom, % 191.28/191.33 ! [V_k_2,V_n_2,V_P_2] : % 191.28/191.33 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 191.28/191.33 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 191.28/191.33 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => ! [B_i,B_j] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 191.28/191.33 => ( 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) % 191.28/191.33 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__less__nat__eq,axiom, % 191.28/191.33 ! [V_z_2] : % 191.28/191.33 ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 191.28/191.33 ! [V_y_2,V_x_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__less__eq__zless,axiom, % 191.28/191.33 ! [V_z_2,V_w_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__eq__iff,axiom, % 191.28/191.33 ! [V_m_2,V_w_2] : % 191.28/191.33 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 191.28/191.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 191.28/191.33 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 191.28/191.33 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__eq__iff2,axiom, % 191.28/191.33 ! [V_w_2,V_m_2] : % 191.28/191.33 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 191.28/191.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 191.28/191.33 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 191.28/191.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 191.28/191.33 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__le__eq__zle,axiom, % 191.28/191.33 ! [V_z_2,V_w_2] : % 191.28/191.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 191.28/191.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 191.28/191.33 => ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__nat,axiom, % 191.28/191.33 ! [V_i_2,V_P_2] : % 191.28/191.33 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 191.28/191.33 <=> ( ! [B_n] : % 191.28/191.33 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 191.28/191.33 => hBOOL(hAPP(V_P_2,B_n)) ) % 191.28/191.33 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__lemma,axiom, % 191.28/191.33 ! [V_q,V_b,V_r,V_c] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__mod,axiom, % 191.28/191.33 ! [V_k_2,V_n_2,V_P_2] : % 191.28/191.33 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 191.28/191.33 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 191.28/191.33 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => ! [B_i,B_j] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 191.28/191.33 => ( 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) % 191.28/191.33 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__add__distrib,axiom, % 191.28/191.33 ! [V_z_H,V_z] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power3__eq__cube,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_int__eq__iff__number__of,axiom, % 191.28/191.33 ! [V_v_2,V_m_2] : % 191.28/191.33 ( 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) % 191.28/191.33 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 191.28/191.33 & 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__mult__distrib,axiom, % 191.28/191.33 ! [V_z_H,V_z] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__diff__distrib,axiom, % 191.28/191.33 ! [V_z,V_z_H] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Suc__times__mod__eq,axiom, % 191.28/191.33 ! [V_m,V_k] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 191.28/191.33 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)))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__eq__if,axiom, % 191.28/191.33 ! [V_p,V_m] : % 191.28/191.33 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 191.28/191.33 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => 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)))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__less__zpower__abs__iff,axiom, % 191.28/191.33 ! [V_n_2,V_x_2] : % 191.28/191.33 ( 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))) % 191.28/191.33 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.33 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 191.28/191.33 ! [V_y,V_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_le__div__geq,axiom, % 191.28/191.33 ! [V_m,V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__div_H,axiom, % 191.28/191.33 ! [V_n_2,V_m_2,V_P_2] : % 191.28/191.33 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 191.28/191.33 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 191.28/191.33 | ? [B_q] : % 191.28/191.33 ( 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)) % 191.28/191.33 & 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)))) % 191.28/191.33 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_split__div__lemma,axiom, % 191.28/191.33 ! [V_m_2,V_q_2,V_n_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 191.28/191.33 => ( ( 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)) % 191.28/191.33 & 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)))) ) % 191.28/191.33 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Suc__div__eq__add3__div,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__Suc__eq__div__add3,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div2__Suc__Suc,axiom, % 191.28/191.33 ! [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))))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_add__self__div__2,axiom, % 191.28/191.33 ! [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 ). % 191.28/191.33 % 191.28/191.33 fof(fact_one__less__nat__eq,axiom, % 191.28/191.33 ! [V_z_2] : % 191.28/191.33 ( 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))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__less__iff,axiom, % 191.28/191.33 ! [V_m_2,V_w_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 191.28/191.33 <=> 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 191.28/191.33 ! [V_z] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Suc__mod__eq__add3__mod,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod__Suc__eq__mod__add3,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__eq__power2,axiom, % 191.28/191.33 ! [V_a_2,T_a] : % 191.28/191.33 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 191.28/191.33 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__power2,axiom, % 191.28/191.33 ! [T_a] : % 191.28/191.33 ( class_Rings_Osemiring__1(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 191.28/191.33 ! [V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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)))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__eq__square,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod2__Suc__Suc,axiom, % 191.28/191.33 ! [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)))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_one__power2,axiom, % 191.28/191.33 ! [T_a] : % 191.28/191.33 ( class_Rings_Osemiring__1(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 191.28/191.33 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)))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__minus,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Rings_Oring__1(T_a) % 191.28/191.33 => 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)))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__mult__distrib__neg,axiom, % 191.28/191.33 ! [V_z_H,V_z] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__even__eq,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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)))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__abs,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => 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)))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_abs__power2,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => 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)))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__eq__imp__eq,axiom, % 191.28/191.33 ! [V_y,V_x,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( 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)))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.33 => V_x = V_y ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__le__imp__le,axiom, % 191.28/191.33 ! [V_y,V_x,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( 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)))))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__le__power2,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => 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)))))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__less__power2,axiom, % 191.28/191.33 ! [V_a_2,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 191.28/191.33 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__less__0,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => ~ 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_sum__power2__eq__zero__iff,axiom, % 191.28/191.33 ! [V_y_2,V_x_2,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__2,axiom, % 191.28/191.33 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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__eq__square__number__of,axiom, % 191.28/191.33 ! [V_w,T_b] : % 191.28/191.33 ( ( class_Groups_Omonoid__mult(T_b) % 191.28/191.33 & class_Int_Onumber(T_b) ) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__eq__1__iff,axiom, % 191.28/191.33 ! [V_a_2,T_a] : % 191.28/191.33 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 191.28/191.33 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) % 191.28/191.33 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 191.28/191.33 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 191.28/191.33 ! [V_n,V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__minus__even,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Oring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_div__2__gt__zero,axiom, % 191.28/191.33 ! [V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 191.28/191.33 => 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)))))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__less__imp__less,axiom, % 191.28/191.33 ! [V_y,V_x,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( 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)))))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_sum__power2__le__zero__iff,axiom, % 191.28/191.33 ! [V_y_2,V_x_2,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.33 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_sum__power2__ge__zero,axiom, % 191.28/191.33 ! [V_y,V_x,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => 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))))))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_sum__power2__gt__zero__iff,axiom, % 191.28/191.33 ! [V_y_2,V_x_2,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 191.28/191.33 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_not__sum__power2__lt__zero,axiom, % 191.28/191.33 ! [V_y,V_x,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => ~ 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__sum,axiom, % 191.28/191.33 ! [V_y,V_x,T_a] : % 191.28/191.33 ( class_Int_Onumber__ring(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__le__even__power_H,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => 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)))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__odd__eq,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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))))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 191.28/191.33 ! [V_n,V_x,T_a] : % 191.28/191.33 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mod2__gr__0,axiom, % 191.28/191.33 ! [V_m_2] : % 191.28/191.33 ( 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)))))) % 191.28/191.33 <=> 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__minus1__even,axiom, % 191.28/191.33 ! [V_n,T_a] : % 191.28/191.33 ( class_Rings_Oring__1(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_int__power__div__base,axiom, % 191.28/191.33 ! [V_k,V_m] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 191.28/191.33 => 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)))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Suc__n__div__2__gt__zero,axiom, % 191.28/191.33 ! [V_n] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => 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)))))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power2__diff,axiom, % 191.28/191.33 ! [V_y,V_x,T_a] : % 191.28/191.33 ( class_Int_Onumber__ring(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_odd__0__le__power__imp__0__le,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => ( 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))))) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_odd__power__less__zero,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_int__of__code,axiom, % 191.28/191.33 ! [V_k] : % 191.28/191.33 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.33 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 191.28/191.33 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.33 => ( ( 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) % 191.28/191.33 => 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)))))) ) % 191.28/191.33 & ( 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) % 191.28/191.33 => 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)) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__strict__mono,axiom, % 191.28/191.33 ! [V_n,V_b,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => 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))) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__diff,axiom, % 191.28/191.33 ! [V_m,V_n,V_a,T_a] : % 191.28/191.33 ( class_Fields_Ofield(T_a) % 191.28/191.33 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.33 => 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)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_one__less__power,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__increasing__iff,axiom, % 191.28/191.33 ! [V_y_2,V_x_2,V_b_2,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_field__power__not__zero,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 191.28/191.33 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 191.28/191.33 ! [V_m_2,V_x_2] : % 191.28/191.33 ( 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)) % 191.28/191.33 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__Suc__0,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__zero__less__power__iff,axiom, % 191.28/191.33 ! [V_n_2,V_x_2] : % 191.28/191.33 ( 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))) % 191.28/191.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 191.28/191.33 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__power__less__imp__less,axiom, % 191.28/191.33 ! [V_n,V_m,V_i] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 191.28/191.33 => ( 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))) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__mult__distrib,axiom, % 191.28/191.33 ! [V_n,V_b,V_a,T_a] : % 191.28/191.33 ( class_Groups_Ocomm__monoid__mult(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__commutes,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__one,axiom, % 191.28/191.33 ! [V_n,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_of__nat__power,axiom, % 191.28/191.33 ! [V_n,V_m,T_a] : % 191.28/191.33 ( class_Rings_Osemiring__1(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__mult,axiom, % 191.28/191.33 ! [V_n,V_m,V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__divide,axiom, % 191.28/191.33 ! [V_n,V_b,V_a,T_a] : % 191.28/191.33 ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__abs,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__one__right,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__le__power,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__mono,axiom, % 191.28/191.33 ! [V_n,V_b,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__less__power,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__eq__0__iff,axiom, % 191.28/191.33 ! [V_n_2,V_a_2,T_a] : % 191.28/191.33 ( ( class_Power_Opower(T_a) % 191.28/191.33 & class_Rings_Omult__zero(T_a) % 191.28/191.33 & class_Rings_Ono__zero__divisors(T_a) % 191.28/191.33 & class_Rings_Ozero__neq__one(T_a) ) % 191.28/191.33 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_one__le__power,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__0__Suc,axiom, % 191.28/191.33 ! [V_n,T_a] : % 191.28/191.33 ( ( class_Power_Opower(T_a) % 191.28/191.33 & class_Rings_Osemiring__0(T_a) ) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__inject__exp,axiom, % 191.28/191.33 ! [V_n_2,V_m_2,V_a_2,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 191.28/191.33 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) % 191.28/191.33 <=> V_m_2 = V_n_2 ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__Suc,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Power_Opower(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__Suc2,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__one__le__power,axiom, % 191.28/191.33 ! [V_n,V_i] : % 191.28/191.33 ( 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)) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__0,axiom, % 191.28/191.33 ! [V_a,T_a] : % 191.28/191.33 ( class_Power_Opower(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__add,axiom, % 191.28/191.33 ! [V_n,V_m,V_a,T_a] : % 191.28/191.33 ( class_Groups_Omonoid__mult(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nonzero__power__divide,axiom, % 191.28/191.33 ! [V_n,V_a,V_b,T_a] : % 191.28/191.33 ( class_Fields_Ofield(T_a) % 191.28/191.33 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__one__over,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_abs__power__minus,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__less__imp__less__base,axiom, % 191.28/191.33 ! [V_b,V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( 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))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__inject__base,axiom, % 191.28/191.33 ! [V_b,V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( 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)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.33 => V_a = V_b ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__le__imp__le__base,axiom, % 191.28/191.33 ! [V_b,V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( 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)))) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__gt1__lemma,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => 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)))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__less__power__Suc,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => 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)))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__0__left,axiom, % 191.28/191.33 ! [V_n,T_a] : % 191.28/191.33 ( ( class_Power_Opower(T_a) % 191.28/191.33 & class_Rings_Osemiring__0(T_a) ) % 191.28/191.33 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => 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) ) % 191.28/191.33 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.33 => 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) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__gt1,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => 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)))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__strict__increasing__iff,axiom, % 191.28/191.33 ! [V_y_2,V_x_2,V_b_2,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__less__imp__less__exp,axiom, % 191.28/191.33 ! [V_n,V_m,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => ( 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))) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__strict__increasing,axiom, % 191.28/191.33 ! [V_a,V_N,V_n,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_zero__le__power__abs,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.33 => 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))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__increasing,axiom, % 191.28/191.33 ! [V_a,V_N,V_n,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__minus,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Oring__1(T_a) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__Suc__less,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__eq__imp__eq__base,axiom, % 191.28/191.33 ! [V_b,V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( 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) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.33 => V_a = V_b ) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__Suc__less__one,axiom, % 191.28/191.33 ! [V_n,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.33 => 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__strict__decreasing,axiom, % 191.28/191.33 ! [V_a,V_N,V_n,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.33 => 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))) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__decreasing,axiom, % 191.28/191.33 ! [V_a,V_N,V_n,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 191.28/191.33 => 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))) ) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__le__imp__le__exp,axiom, % 191.28/191.33 ! [V_n,V_m,V_a,T_a] : % 191.28/191.33 ( class_Rings_Olinordered__semidom(T_a) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 191.28/191.33 => ( 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))) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__aux__def,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 191.28/191.33 ! [V_B_2,V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 191.28/191.33 ! [V_B_2,V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.33 => 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__morphism__nat__int,axiom, % 191.28/191.33 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))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 191.28/191.33 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 191.28/191.33 ! [V_B_2,V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 191.28/191.33 ! [V_B_2,V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.33 => 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)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nat__set__def,axiom, % 191.28/191.33 ! [V_S_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_S_2) % 191.28/191.33 <=> ! [B_x] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 191.28/191.33 ! [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)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 191.28/191.33 ! [V_B_2,V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.33 => ( V_A_2 = V_B_2 % 191.28/191.33 <=> 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) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 191.28/191.33 ! [V_x_2,V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__nat__int__set__return__embed,axiom, % 191.28/191.33 ! [V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => 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 ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 191.28/191.33 ! [V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 191.28/191.33 <=> 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))) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 191.28/191.33 ! [V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => 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)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 191.28/191.33 ! [V_B_2,V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.33 <=> 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 191.28/191.33 ! [V_B_2,V_A_2] : % 191.28/191.33 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.33 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.33 <=> 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))) ) ) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_card__Pow,axiom, % 191.28/191.33 ! [V_A_2,T_a] : % 191.28/191.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.33 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__power__power,axiom, % 191.28/191.33 ! [T_a] : % 191.28/191.33 ( class_Power_Opower(T_a) % 191.28/191.33 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__m1__odd,axiom, % 191.28/191.33 ! [V_n,T_a] : % 191.28/191.33 ( class_Int_Onumber__ring(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_power__m1__even,axiom, % 191.28/191.33 ! [V_n,T_a] : % 191.28/191.33 ( class_Int_Onumber__ring(T_a) % 191.28/191.33 => 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) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_PowI,axiom, % 191.28/191.33 ! [V_B_2,V_A_2,T_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I42_J,axiom, % 191.28/191.33 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I45_J,axiom, % 191.28/191.33 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 191.28/191.33 % 191.28/191.33 fof(fact_Bit1__Min,axiom, % 191.28/191.33 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I43_J,axiom, % 191.28/191.33 ! [V_l_2] : % 191.28/191.33 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 191.28/191.33 <=> c_Int_OMin = V_l_2 ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I47_J,axiom, % 191.28/191.33 ! [V_k_2] : % 191.28/191.33 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 191.28/191.33 <=> V_k_2 = c_Int_OMin ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I40_J,axiom, % 191.28/191.33 c_Int_OMin != c_Int_OPls ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I37_J,axiom, % 191.28/191.33 c_Int_OPls != c_Int_OMin ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I7_J,axiom, % 191.28/191.33 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I24_J,axiom, % 191.28/191.33 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Cantors__paradox,axiom, % 191.28/191.33 ! [V_A_2,T_a] : % 191.28/191.33 ~ ? [B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_a),V_A_2) ). % 191.28/191.33 % 191.28/191.33 fof(fact_image__Pow__surj,axiom, % 191.28/191.33 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 191.28/191.33 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 191.28/191.33 => hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Pow__top,axiom, % 191.28/191.33 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Union__Pow__eq,axiom, % 191.28/191.33 ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2 ). % 191.28/191.33 % 191.28/191.33 fof(fact_Pow__not__empty,axiom, % 191.28/191.33 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_bin__less__0__simps_I2_J,axiom, % 191.28/191.33 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I20_J,axiom, % 191.28/191.33 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I23_J,axiom, % 191.28/191.33 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I26_J,axiom, % 191.28/191.33 ! [V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I30_J,axiom, % 191.28/191.33 ! [V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I6_J,axiom, % 191.28/191.33 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I3_J,axiom, % 191.28/191.33 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I13_J,axiom, % 191.28/191.33 ! [V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I9_J,axiom, % 191.28/191.33 ! [V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I28_J,axiom, % 191.28/191.33 ! [V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_rel__simps_I8_J,axiom, % 191.28/191.33 ! [V_k_2] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_eq__number__of__Pls__Min,axiom, % 191.28/191.33 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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Int_OMin__def,axiom, % 191.28/191.33 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 191.28/191.33 % 191.28/191.33 fof(fact_mult__Min,axiom, % 191.28/191.33 ! [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) ). % 191.28/191.33 % 191.28/191.33 fof(fact_neg__number__of__Min,axiom, % 191.28/191.33 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_pred__Pls,axiom, % 191.28/191.33 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 191.28/191.33 % 191.28/191.33 fof(fact_add__Min__right,axiom, % 191.28/191.33 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 191.28/191.33 % 191.28/191.33 fof(fact_add__Min,axiom, % 191.28/191.33 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 191.28/191.33 % 191.28/191.33 fof(fact_pred__Min,axiom, % 191.28/191.33 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 191.28/191.33 % 191.28/191.33 fof(fact_nonzero__number__of__Min,axiom, % 191.28/191.33 ! [T_a] : % 191.28/191.33 ( class_Int_Onumber__ring(T_a) % 191.28/191.33 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_succ__Min,axiom, % 191.28/191.33 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 191.28/191.33 % 191.28/191.33 fof(fact_diff__bin__simps_I2_J,axiom, % 191.28/191.33 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Pow__bottom,axiom, % 191.28/191.33 ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))) ). % 191.28/191.33 % 191.28/191.33 fof(fact_Pow__iff,axiom, % 191.28/191.33 ! [V_B_2,V_A_2,T_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 191.28/191.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.28/191.33 % 191.28/191.33 fof(fact_PowD,axiom, % 191.28/191.33 ! [V_B_2,V_A_2,T_a] : % 191.28/191.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 191.28/191.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.28/191.33 % 191.28/191.34 fof(fact_Pow__mono,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__Pow__iff,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 191.28/191.34 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_mult__minus1__right,axiom, % 191.28/191.34 ! [V_z,T_a] : % 191.28/191.34 ( class_Int_Onumber__ring(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_mult__minus1,axiom, % 191.28/191.34 ! [V_z,T_a] : % 191.28/191.34 ( class_Int_Onumber__ring(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_subset__Pow__Union,axiom, % 191.28/191.34 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_arith__simps_I31_J,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Int_Onumber__ring(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_number__of__Min,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Int_Onumber__ring(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_abs__minus__one,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.34 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_divide__minus1,axiom, % 191.28/191.34 ! [V_x,T_a] : % 191.28/191.34 ( ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.34 & class_Int_Onumber__ring(T_a) ) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_rel__simps_I11_J,axiom, % 191.28/191.34 ! [V_k_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_rel__simps_I25_J,axiom, % 191.28/191.34 ! [V_k_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_zmod__minus1__right,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_diff__bin__simps_I4_J,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_minus__Min,axiom, % 191.28/191.34 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 191.28/191.34 % 191.28/191.34 fof(fact_zmult__eq__1__iff,axiom, % 191.28/191.34 ! [V_n_2,V_m_2] : % 191.28/191.34 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 191.28/191.34 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 191.28/191.34 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 191.28/191.34 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 191.28/191.34 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 191.28/191.34 ! [V_n,V_m] : % 191.28/191.34 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 191.28/191.34 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 191.28/191.34 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_diff__bin__simps_I5_J,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_diff__bin__simps_I6_J,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_power_Opower_Opower__0,axiom, % 191.28/191.34 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 191.28/191.34 % 191.28/191.34 fof(fact_power_Opower_Opower__Suc,axiom, % 191.28/191.34 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Pow__insert,axiom, % 191.28/191.34 ! [V_A_2,V_a_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_a),V_a_2)),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Pow__UNIV,axiom, % 191.28/191.34 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_zdiv__minus1__right,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Pow__Int__eq,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__Pow__mono,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_minus1__divide,axiom, % 191.28/191.34 ! [V_x,T_a] : % 191.28/191.34 ( ( class_Fields_Ofield__inverse__zero(T_a) % 191.28/191.34 & class_Int_Onumber__ring(T_a) ) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_abs__power__minus__one,axiom, % 191.28/191.34 ! [V_n,T_a] : % 191.28/191.34 ( ( class_Int_Onumber__ring(T_a) % 191.28/191.34 & class_Rings_Olinordered__idom(T_a) ) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_div__eq__minus1,axiom, % 191.28/191.34 ! [V_b] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Pow__empty,axiom, % 191.28/191.34 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Un__Pow__subset,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_div__pos__neg__trivial,axiom, % 191.28/191.34 ! [V_b,V_a] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.34 => ( 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))) % 191.28/191.34 => 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) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_zmod__minus1,axiom, % 191.28/191.34 ! [V_b] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 191.28/191.34 ! [V_A_2,V_x_2] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x_2) % 191.28/191.34 => ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 191.28/191.34 <=> 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))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Osize_I1_J,axiom, % 191.28/191.34 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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__greaterThanLessThan__int,axiom, % 191.28/191.34 ! [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)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__of__nat,axiom, % 191.28/191.34 ! [V_k,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.34 => 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)))) ) % 191.28/191.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.34 => 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)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__greaterThanLessThan__int,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_number__of__eq,axiom, % 191.28/191.34 ! [V_k,T_a] : % 191.28/191.34 ( class_Int_Onumber__ring(T_a) % 191.28/191.34 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_int__number__of__def,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__int__eq,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__eq__iff,axiom, % 191.28/191.34 ! [V_z_2,V_w_2,T_a] : % 191.28/191.34 ( class_Int_Oring__char__0(T_a) % 191.28/191.34 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 191.28/191.34 <=> V_w_2 = V_z_2 ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 191.28/191.34 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 191.28/191.34 ! [V_y,V_x] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x) % 191.28/191.34 => ( c_Nat__Transfer_Ois__nat(V_y) % 191.28/191.34 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 191.28/191.34 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 191.28/191.34 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 191.28/191.34 ! [V_y,V_x] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x) % 191.28/191.34 => ( c_Nat__Transfer_Ois__nat(V_y) % 191.28/191.34 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 191.28/191.34 ! [V_y,V_x] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x) % 191.28/191.34 => ( c_Nat__Transfer_Ois__nat(V_y) % 191.28/191.34 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 191.28/191.34 ! [V_y,V_x] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x) % 191.28/191.34 => ( c_Nat__Transfer_Ois__nat(V_y) % 191.28/191.34 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 191.28/191.34 ! [V_n,V_x] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x) % 191.28/191.34 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 191.28/191.34 ! [V_y,V_x] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x) % 191.28/191.34 => ( c_Nat__Transfer_Ois__nat(V_y) % 191.28/191.34 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__0,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__0__eq__iff,axiom, % 191.28/191.34 ! [V_z_2,T_a] : % 191.28/191.34 ( class_Int_Oring__char__0(T_a) % 191.28/191.34 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 191.28/191.34 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__eq__0__iff,axiom, % 191.28/191.34 ! [V_z_2,T_a] : % 191.28/191.34 ( class_Int_Oring__char__0(T_a) % 191.28/191.34 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.34 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__le__iff,axiom, % 191.28/191.34 ! [V_z_2,V_w_2,T_a] : % 191.28/191.34 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__less__iff,axiom, % 191.28/191.34 ! [V_z_2,V_w_2,T_a] : % 191.28/191.34 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__add,axiom, % 191.28/191.34 ! [V_z,V_w,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__number__of__eq,axiom, % 191.28/191.34 ! [V_v,T_a] : % 191.28/191.34 ( class_Int_Onumber__ring(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__mult,axiom, % 191.28/191.34 ! [V_z,V_w,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__1,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__diff,axiom, % 191.28/191.34 ! [V_z,V_w,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__of__nat__eq,axiom, % 191.28/191.34 ! [V_n,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__minus,axiom, % 191.28/191.34 ! [V_z,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Ints__of__int,axiom, % 191.28/191.34 ! [V_z_2,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__power,axiom, % 191.28/191.34 ! [V_n,V_z,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_is__nat__def,axiom, % 191.28/191.34 ! [V_x_2] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x_2) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThanLessThan__empty,axiom, % 191.28/191.34 ! [V_k_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 191.28/191.34 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__uminus__greaterThanLessThan,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 191.28/191.34 ! [V_x_2,V_A_2] : % 191.28/191.34 ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 191.28/191.34 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__m1,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Int_Onumber__ring(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 191.28/191.34 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__le__0__iff,axiom, % 191.28/191.34 ! [V_z_2,T_a] : % 191.28/191.34 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__0__le__iff,axiom, % 191.28/191.34 ! [V_z_2,T_a] : % 191.28/191.34 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__less__0__iff,axiom, % 191.28/191.34 ! [V_z_2,T_a] : % 191.28/191.34 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__int__0__less__iff,axiom, % 191.28/191.34 ! [V_z_2,T_a] : % 191.28/191.34 ( class_Rings_Olinordered__idom(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_of__nat__nat,axiom, % 191.28/191.34 ! [V_z,T_a] : % 191.28/191.34 ( class_Rings_Oring__1(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 191.28/191.34 => 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) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 191.28/191.34 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Osize_I2_J,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I4_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nitpick_Oint__lcm__def,axiom, % 191.28/191.34 ! [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)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Osize_I3_J,axiom, % 191.28/191.34 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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__greaterThanAtMost,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__greaterThanLessThan,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__greaterThanAtMost__int,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Oinject,axiom, % 191.28/191.34 ! [V_code__numeral_H_2,V_code__numeral_2] : % 191.28/191.34 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 191.28/191.34 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Osimps_I2_J,axiom, % 191.28/191.34 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Osimps_I3_J,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThanAtMost__empty,axiom, % 191.28/191.34 ! [V_k_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 191.28/191.34 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThanAtMost__empty__iff,axiom, % 191.28/191.34 ! [V_l_2,V_k_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 191.28/191.34 ! [V_l_2,V_k_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) % 191.28/191.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I20_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I14_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__greaterThanAtMost,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Osize_I4_J,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I10_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Suc__code__numeral__minus__one,axiom, % 191.28/191.34 ! [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 ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__greaterThanLessThan,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__greaterThanAtMost__int,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I16_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nitpick_Onat__lcm__def,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I19_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I3_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I5_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__atLeastLessThan,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__atLeastAtMost,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__atLeastAtMost__int,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__atLeastLessThan__int,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I15_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I21_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__eq__iff,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 191.28/191.34 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 191.28/191.34 <=> ( V_a_2 = V_ca_2 % 191.28/191.34 & V_b_2 = V_d_2 ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 191.28/191.34 => V_a_2 = V_ca_2 ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 191.28/191.34 => V_b_2 = V_d_2 ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__Suc__atLeastAtMost,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__Suc__atLeastLessThan,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__add__nat__ivl,axiom, % 191.28/191.34 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 191.28/191.34 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 191.28/191.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__diff__nat__ivl,axiom, % 191.28/191.34 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 191.28/191.34 ( class_Groups_Oab__group__add(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 191.28/191.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 191.28/191.34 ! [V_k_2,V_f_2] : % 191.28/191.34 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 191.28/191.34 ! [V_n_2,V_m_2] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_m_2) % 191.28/191.34 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 191.28/191.34 => 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))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastAtMostSuc__conv,axiom, % 191.28/191.34 ! [V_n_2,V_m_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan0,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__singleton,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I6_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__atLeastLessThan,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 191.28/191.34 ! [V_y_2,V_x_2] : % 191.28/191.34 ( c_Nat__Transfer_Ois__nat(V_x_2) % 191.28/191.34 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I18_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastatMost__empty__iff,axiom, % 191.28/191.34 ! [V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastatMost__empty__iff2,axiom, % 191.28/191.34 ! [V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) % 191.28/191.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastatMost__empty,axiom, % 191.28/191.34 ! [V_a_2,V_b_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 191.28/191.34 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastatMost__subset__iff,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2))) % 191.28/191.34 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 191.28/191.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__empty,axiom, % 191.28/191.34 ! [V_a_2,V_b_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 191.28/191.34 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastAtMost__singleton,axiom, % 191.28/191.34 ! [V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastAtMost__singleton__iff,axiom, % 191.28/191.34 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.34 <=> ( V_a_2 = V_b_2 % 191.28/191.34 & V_b_2 = V_ca_2 ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastAtMost__singleton_H,axiom, % 191.28/191.34 ! [V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( V_a_2 = V_b_2 % 191.28/191.34 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__empty__iff2,axiom, % 191.28/191.34 ! [V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) % 191.28/191.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__empty__iff,axiom, % 191.28/191.34 ! [V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__subset__iff,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2))) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 191.28/191.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I17_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__uminus__atLeastAtMost,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__diff,axiom, % 191.28/191.34 ! [V_m_2,V_n_2,V_i_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 191.28/191.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2),V_m_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I11_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 191.28/191.34 ! [V_k_2,V_f_2,T_a] : % 191.28/191.34 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.34 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__head__upt__Suc,axiom, % 191.28/191.34 ! [V_f_2,V_n_2,V_m_2,T_a] : % 191.28/191.34 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__head__Suc,axiom, % 191.28/191.34 ! [V_f_2,V_n_2,V_m_2,T_a] : % 191.28/191.34 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 191.28/191.34 ! [V_y_2,V_x_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 191.28/191.34 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThanSuc,axiom, % 191.28/191.34 ! [V_n_2,V_m_2] : % 191.28/191.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.34 => 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)) ) % 191.28/191.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.34 => 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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__atLeastAtMost,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastatMost__psubset__iff,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2))) % 191.28/191.34 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 191.28/191.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 191.28/191.34 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2)) % 191.28/191.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastLessThan__add__Un,axiom, % 191.28/191.34 ! [V_k_2,V_j_2,V_i_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 191.28/191.34 => 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))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I22_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__op__ivl__Suc,axiom, % 191.28/191.34 ! [V_f_2,V_m_2,V_n_2,T_a] : % 191.28/191.34 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 191.28/191.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I16_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I13_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I12_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_subset__card__intvl__is__intvl,axiom, % 191.28/191.34 ! [V_k_2,V_A_2] : % 191.28/191.34 ( 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))))) % 191.28/191.34 => 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))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I9_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__uminus__atLeastLessThan,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__uminus__greaterThanAtMost,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__cl__ivl__Suc,axiom, % 191.28/191.34 ! [V_f_2,V_m_2,V_n_2,T_a] : % 191.28/191.34 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 191.28/191.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__atLeastZeroLessThan__int,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__atLeastLessThan__int,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__ub__add__nat,axiom, % 191.28/191.34 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 191.28/191.34 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.34 => ( 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)))) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_simp__from__to,axiom, % 191.28/191.34 ! [V_i_2,V_j_2] : % 191.28/191.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 191.28/191.34 => 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)) ) % 191.28/191.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 191.28/191.34 => 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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I15_J,axiom, % 191.28/191.34 ! [V_u_2,V_m_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_nat__gcd_Osimps,axiom, % 191.28/191.34 ! [V_x,V_y] : % 191.28/191.34 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.34 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 191.28/191.34 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.34 => 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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__atLeastAtMost__int,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Nitpick_Oint__gcd__def,axiom, % 191.28/191.34 ! [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)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_aset_I6_J,axiom, % 191.28/191.34 ! [V_A_2,V_t_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ( 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)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 191.28/191.34 => 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)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_bset_I8_J,axiom, % 191.28/191.34 ! [V_B_2,V_t_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ( 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)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 191.28/191.34 => 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))) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_bset_I3_J,axiom, % 191.28/191.34 ! [V_B_2,V_t_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ( 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)) % 191.28/191.34 => ( ! [B_x] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xa] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 191.28/191.34 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 191.28/191.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_all__nat__less,axiom, % 191.28/191.34 ! [V_P_2,V_n_2] : % 191.28/191.34 ( ! [B_m] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 191.28/191.34 => hBOOL(hAPP(V_P_2,B_m)) ) % 191.28/191.34 <=> ! [B_x] : % 191.28/191.34 ( 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))) % 191.28/191.34 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ex__nat__less,axiom, % 191.28/191.34 ! [V_P_2,V_n_2] : % 191.28/191.34 ( ? [B_m] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 191.28/191.34 & hBOOL(hAPP(V_P_2,B_m)) ) % 191.28/191.34 <=> ? [B_x] : % 191.28/191.34 ( 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))) % 191.28/191.34 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_all__nat__less__eq,axiom, % 191.28/191.34 ! [V_P_2,V_n_2] : % 191.28/191.34 ( ! [B_m] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 191.28/191.34 => hBOOL(hAPP(V_P_2,B_m)) ) % 191.28/191.34 <=> ! [B_x] : % 191.28/191.34 ( 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))) % 191.28/191.34 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ex__nat__less__eq,axiom, % 191.28/191.34 ! [V_P_2,V_n_2] : % 191.28/191.34 ( ? [B_m] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 191.28/191.34 & hBOOL(hAPP(V_P_2,B_m)) ) % 191.28/191.34 <=> ? [B_x] : % 191.28/191.34 ( 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))) % 191.28/191.34 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_aset_I3_J,axiom, % 191.28/191.34 ! [V_A_2,V_t_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ( 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)) % 191.28/191.34 => ( ! [B_x] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xa] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 191.28/191.34 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 191.28/191.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_aset_I5_J,axiom, % 191.28/191.34 ! [V_A_2,V_t_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 191.28/191.34 => 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)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_bset_I7_J,axiom, % 191.28/191.34 ! [V_B_2,V_t_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 191.28/191.34 => 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))) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_bset_I4_J,axiom, % 191.28/191.34 ! [V_B_2,V_t_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( B_x != V_t_2 % 191.28/191.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_aset_I4_J,axiom, % 191.28/191.34 ! [V_A_2,V_t_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( B_x != V_t_2 % 191.28/191.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_bset_I6_J,axiom, % 191.28/191.34 ! [V_t_2,V_B_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 191.28/191.34 => 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)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_aset_I8_J,axiom, % 191.28/191.34 ! [V_t_2,V_A_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 191.28/191.34 => 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))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_periodic__finite__ex,axiom, % 191.28/191.34 ! [V_P_2,V_d_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 191.28/191.34 => ( ! [B_x,B_k] : % 191.28/191.34 ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.34 <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) ) % 191.28/191.34 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 191.28/191.34 <=> ? [B_x] : % 191.28/191.34 ( 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))) % 191.28/191.34 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_aset_I7_J,axiom, % 191.28/191.34 ! [V_t_2,V_A_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 191.28/191.34 => 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))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_bset_I5_J,axiom, % 191.28/191.34 ! [V_t_2,V_B_2,V_D_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 191.28/191.34 => ! [B_x] : % 191.28/191.34 ( ! [B_xa] : % 191.28/191.34 ( 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))) % 191.28/191.34 => ! [B_xb] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 191.28/191.34 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 191.28/191.34 => 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)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__atLeastZeroLessThan__int,axiom, % 191.28/191.34 ! [V_u_2] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 191.28/191.34 => 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))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__lessThan,axiom, % 191.28/191.34 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_finite__atMost,axiom, % 191.28/191.34 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_lessThan__Suc__atMost,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_lessThan__eq__iff,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 191.28/191.34 <=> V_x_2 = V_y_2 ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atMost__eq__iff,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 191.28/191.34 <=> V_x_2 = V_y_2 ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__lessThan,axiom, % 191.28/191.34 ! [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 ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I2_J,axiom, % 191.28/191.34 ! [V_u_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I10_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I7_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeast0LessThan,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_lessThan__0,axiom, % 191.28/191.34 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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeast0AtMost,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_lessThan__Suc,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_card__atMost,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atMost__Suc,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atMost__iff,axiom, % 191.28/191.34 ! [V_k_2,V_i_2,T_a] : % 191.28/191.34 ( class_Orderings_Oord(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_lessThan__iff,axiom, % 191.28/191.34 ! [V_k_2,V_i_2,T_a] : % 191.28/191.34 ( class_Orderings_Oord(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atMost__subset__iff,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_lessThan__subset__iff,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_lessThan__strict__subset__iff,axiom, % 191.28/191.34 ! [V_n_2,V_m_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atMost__0,axiom, % 191.28/191.34 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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_single__Diff__lessThan,axiom, % 191.28/191.34 ! [V_k_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I8_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I4_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I2_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I9_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I3_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I1_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 191.28/191.34 ! [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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThan__0,axiom, % 191.28/191.34 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))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atMost__Int__atLeast,axiom, % 191.28/191.34 ! [V_n_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Osimps_I5_J,axiom, % 191.28/191.34 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ). % 191.28/191.34 % 191.28/191.34 fof(fact_int__val__lemma,axiom, % 191.28/191.34 ! [V_k_2,V_f_2,V_n_2] : % 191.28/191.34 ( ! [B_i] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 191.28/191.34 => 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))) ) % 191.28/191.34 => ( 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)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 191.28/191.34 => ? [B_i] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 191.28/191.34 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeast__eq__iff,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 191.28/191.34 <=> V_x_2 = V_y_2 ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThan__eq__iff,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 191.28/191.34 <=> V_x_2 = V_y_2 ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeast__Suc__greaterThan,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I1_J,axiom, % 191.28/191.34 ! [V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I13_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I12_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeast__iff,axiom, % 191.28/191.34 ! [V_k_2,V_i_2,T_a] : % 191.28/191.34 ( class_Orderings_Oord(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeast__subset__iff,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeast__0,axiom, % 191.28/191.34 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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThan__iff,axiom, % 191.28/191.34 ! [V_k_2,V_i_2,T_a] : % 191.28/191.34 ( class_Orderings_Oord(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThan__subset__iff,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2))) % 191.28/191.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Compl__lessThan,axiom, % 191.28/191.34 ! [V_k_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Compl__atLeast,axiom, % 191.28/191.34 ! [V_k_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Compl__greaterThan,axiom, % 191.28/191.34 ! [V_k_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Compl__atMost,axiom, % 191.28/191.34 ! [V_k_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I14_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I8_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I6_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__uminus__atMost,axiom, % 191.28/191.34 ! [V_x_2,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__uminus__atLeast,axiom, % 191.28/191.34 ! [V_x_2,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_atLeast__Suc,axiom, % 191.28/191.34 ! [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)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I7_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__un_I11_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__uminus__greaterThan,axiom, % 191.28/191.34 ! [V_x_2,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_image__uminus__lessThan,axiom, % 191.28/191.34 ! [V_x_2,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_ivl__disj__int_I5_J,axiom, % 191.28/191.34 ! [V_u_2,V_l_2,T_a] : % 191.28/191.34 ( class_Orderings_Oorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_greaterThan__Suc,axiom, % 191.28/191.34 ! [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)))) ). % 191.28/191.34 % 191.28/191.34 fof(fact_code__numeral_Osimps_I4_J,axiom, % 191.28/191.34 ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 191.28/191.34 % 191.28/191.34 fof(fact_nat0__intermed__int__val,axiom, % 191.28/191.34 ! [V_k_2,V_f_2,V_n_2] : % 191.28/191.34 ( ! [B_i] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 191.28/191.34 => 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))) ) % 191.28/191.34 => ( 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)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 191.28/191.34 => ? [B_i] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 191.28/191.34 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_nat__mod__eq__lemma,axiom, % 191.28/191.34 ! [V_y,V_n,V_x] : % 191.28/191.34 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 191.28/191.34 => ? [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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_mod__induct__0,axiom, % 191.28/191.34 ! [V_i_2,V_P_2,V_p_2] : % 191.28/191.34 ( ! [B_i] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 191.28/191.34 => ( hBOOL(hAPP(V_P_2,B_i)) % 191.28/191.34 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 191.28/191.34 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 191.28/191.34 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_setsum__ivl__cong,axiom, % 191.28/191.34 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] : % 191.28/191.34 ( ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.34 & class_Orderings_Oord(T_a) ) % 191.28/191.34 => ( V_a_2 = V_ca_2 % 191.28/191.34 => ( V_b_2 = V_d_2 % 191.28/191.34 => ( ! [B_x] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 191.28/191.34 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 191.28/191.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_nat__intermed__int__val,axiom, % 191.28/191.34 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 191.28/191.34 ( ! [B_i] : % 191.28/191.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 191.28/191.34 => 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))) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 191.28/191.34 => ? [B_i] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 191.28/191.34 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_log_Osimps,axiom, % 191.28/191.34 ! [V_i,V_b] : % 191.28/191.34 ( ( ( 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))) % 191.28/191.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 191.28/191.34 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 191.28/191.34 & ( ~ ( 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))) % 191.28/191.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 191.28/191.34 => 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))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_mod__div__decomp,axiom, % 191.28/191.34 ! [V_b,V_a,T_a] : % 191.28/191.34 ( class_Divides_Osemiring__div(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_bool_Osize_I1_J,axiom, % 191.28/191.34 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.34 % 191.28/191.34 fof(fact_bool_Osize_I2_J,axiom, % 191.28/191.34 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.34 % 191.28/191.34 fof(fact_minus__shift__def,axiom, % 191.28/191.34 ! [V_r,V_l,V_k] : % 191.28/191.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 191.28/191.34 => 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) ) % 191.28/191.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 191.28/191.34 => 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) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_inc__shift__def,axiom, % 191.28/191.34 ! [V_k,V_v] : % 191.28/191.34 ( ( V_v = V_k % 191.28/191.34 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 191.28/191.34 & ( V_v != V_k % 191.28/191.34 => 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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_fold1__antimono,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_field__le__epsilon,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Fields_Olinordered__field(T_a) % 191.28/191.34 => ( ! [B_e] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) ) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__add__distrib__left,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__less__iff__disj,axiom, % 191.28/191.34 ! [V_z_2,V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 191.28/191.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 191.28/191.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__less__iff__conj,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,V_z_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2))) % 191.28/191.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oless__infI2,axiom, % 191.28/191.34 ! [V_a,V_x,V_b,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 191.28/191.34 => 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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oless__infI1,axiom, % 191.28/191.34 ! [V_b,V_x,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 191.28/191.34 => 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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__le1,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__le2,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__iff__inf,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.28/191.34 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__inf__iff,axiom, % 191.28/191.34 ! [V_z_2,V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2))) % 191.28/191.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__infI1,axiom, % 191.28/191.34 ! [V_b,V_x,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 191.28/191.34 => 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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__infI2,axiom, % 191.28/191.34 ! [V_a,V_x,V_b,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 191.28/191.34 => 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)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__absorb1,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__absorb2,axiom, % 191.28/191.34 ! [V_x,V_y,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__infI,axiom, % 191.28/191.34 ! [V_b,V_a,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 191.28/191.34 => 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))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__greatest,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 191.28/191.34 => 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))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__mono,axiom, % 191.28/191.34 ! [V_d,V_b,V_c,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 191.28/191.34 => 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))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__infE,axiom, % 191.28/191.34 ! [V_b,V_a,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( 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))) % 191.28/191.34 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 191.28/191.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__le__iff__disj,axiom, % 191.28/191.34 ! [V_z_2,V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 191.28/191.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 191.28/191.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__Suc__Suc,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Oidem,axiom, % 191.28/191.34 ! [V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__assoc,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf_Oassoc,axiom, % 191.28/191.34 ! [V_c,V_b,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__left__commute,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 191.28/191.34 ! [V_c,V_a,V_b,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__left__idem,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 191.28/191.34 ! [V_b,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__commute,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf_Ocommute,axiom, % 191.28/191.34 ! [V_b,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf_Oidem,axiom, % 191.28/191.34 ! [V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__0R,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__0L,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_inf__min,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( ( class_Lattices_Osemilattice__inf(T_a) % 191.28/191.34 & class_Orderings_Olinorder(T_a) ) % 191.28/191.34 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__diff__distrib__left,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__diff,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__number__of,axiom, % 191.28/191.34 ! [V_v,V_u,T_b] : % 191.28/191.34 ( ( class_Int_Onumber(T_b) % 191.28/191.34 & class_Orderings_Oord(T_b) ) % 191.28/191.34 => ( ( 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))) % 191.28/191.34 => 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) ) % 191.28/191.34 & ( ~ 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))) % 191.28/191.34 => 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) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ofold__inf__insert,axiom, % 191.28/191.34 ! [V_a_2,V_b_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Int__atLeastAtMostL1,axiom, % 191.28/191.34 ! [V_d_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Int__atLeastAtMostR1,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 191.28/191.34 ! [V_b_2,V_a_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),V_b_2))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ofold1__belowI,axiom, % 191.28/191.34 ! [V_a_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_a_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_fold1__below__iff,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) % 191.28/191.34 <=> ? [B_x] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Obelow__fold1__iff,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) % 191.28/191.34 <=> ! [B_x] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_fold1__strict__below__iff,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) % 191.28/191.34 <=> ? [B_x] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_strict__below__fold1__iff,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) % 191.28/191.34 <=> ! [B_x] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__ord__min,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Orderings_Oord(T_a) % 191.28/191.34 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Oremove,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 191.28/191.34 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Oremove,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 191.28/191.34 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Oeq__fold_H,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_inf__nat__def,axiom, % 191.28/191.34 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Osingleton,axiom, % 191.28/191.34 ! [V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min__le,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_x_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 191.28/191.34 ! [V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min__in,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Oin__idem,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_OF__eq,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min__antimono,axiom, % 191.28/191.34 ! [V_N_2,V_M_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 191.28/191.34 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_M_2))) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 191.28/191.34 ! [V_a_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min__insert,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Osubset__idem,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min__Un,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Oeq__fold__idem_H,axiom, % 191.28/191.34 ! [V_a_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 191.28/191.34 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Oinsert,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Oinsert__remove,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 191.28/191.34 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Ounion__disjoint,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Ounion__inter,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),V_A_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Oclosed,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 191.28/191.34 ! [V_N_2,V_h_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.28/191.34 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min_Ohom__commute,axiom, % 191.28/191.34 ! [V_N_2,V_h_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.28/191.34 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_minus__Min__eq__Max,axiom, % 191.28/191.34 ! [V_S_2,T_a] : % 191.28/191.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.34 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_minus__Max__eq__Min,axiom, % 191.28/191.34 ! [V_S_2,T_a] : % 191.28/191.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.34 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 191.28/191.34 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ! [B_x] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_ca_2),V_A_2))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Min__eqI,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ! [B_y] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Osingleton,axiom, % 191.28/191.34 ! [V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max__ge,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max__in,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max__mono,axiom, % 191.28/191.34 ! [V_N_2,V_M_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 191.28/191.34 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2))) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Oremove,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 191.28/191.34 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max__eqI,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ! [B_y] : % 191.28/191.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Oeq__fold_H,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Ounion__disjoint,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 191.28/191.34 ! [V_x,V_z,V_y,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__inf__distrib2,axiom, % 191.28/191.34 ! [V_x,V_z,V_y,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__inf__distrib1,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__sup__absorb,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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 ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__inf__absorb,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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 ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_max__add__distrib__left,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oless__supI1,axiom, % 191.28/191.34 ! [V_b,V_a,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 191.28/191.34 => 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))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oless__supI2,axiom, % 191.28/191.34 ! [V_a,V_b,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 191.28/191.34 => 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))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_less__max__iff__disj,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,V_z_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 191.28/191.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 191.28/191.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_max__less__iff__conj,axiom, % 191.28/191.34 ! [V_z_2,V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 191.28/191.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_le__maxI1,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_le__maxI2,axiom, % 191.28/191.34 ! [V_x,V_y,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__iff__sup,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.28/191.34 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__sup__iff,axiom, % 191.28/191.34 ! [V_z_2,V_y_2,V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 191.28/191.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 191.28/191.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__supI1,axiom, % 191.28/191.34 ! [V_b,V_a,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 191.28/191.34 => 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))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__supI2,axiom, % 191.28/191.34 ! [V_a,V_b,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 191.28/191.34 => 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))) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__absorb2,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__absorb1,axiom, % 191.28/191.34 ! [V_x,V_y,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__supI,axiom, % 191.28/191.34 ! [V_b,V_x,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 191.28/191.34 => 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)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__least,axiom, % 191.28/191.34 ! [V_z,V_x,V_y,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 191.28/191.34 => 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)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__mono,axiom, % 191.28/191.34 ! [V_d,V_b,V_c,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 191.28/191.34 => 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))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ole__supE,axiom, % 191.28/191.34 ! [V_x,V_b,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( 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)) % 191.28/191.34 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 191.28/191.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_le__max__iff__disj,axiom, % 191.28/191.34 ! [V_y_2,V_x_2,V_z_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 191.28/191.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 191.28/191.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_max__Suc__Suc,axiom, % 191.28/191.34 ! [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)) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Oidem,axiom, % 191.28/191.34 ! [V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__assoc,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup_Oassoc,axiom, % 191.28/191.34 ! [V_c,V_b,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__left__commute,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup_Oleft__commute,axiom, % 191.28/191.34 ! [V_c,V_a,V_b,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__left__idem,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup_Oleft__idem,axiom, % 191.28/191.34 ! [V_b,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__commute,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup_Ocommute,axiom, % 191.28/191.34 ! [V_b,V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup_Oidem,axiom, % 191.28/191.34 ! [V_a,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_max__0R,axiom, % 191.28/191.34 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 191.28/191.34 % 191.28/191.34 fof(fact_max__0L,axiom, % 191.28/191.34 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 191.28/191.34 % 191.28/191.34 fof(fact_sup__max,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( ( class_Lattices_Osemilattice__sup(T_a) % 191.28/191.34 & class_Orderings_Olinorder(T_a) ) % 191.28/191.34 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_max__diff__distrib__left,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Groups_Oordered__ab__group__add(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_max__number__of,axiom, % 191.28/191.34 ! [V_v,V_u,T_b] : % 191.28/191.34 ( ( class_Int_Onumber(T_b) % 191.28/191.34 & class_Orderings_Oord(T_b) ) % 191.28/191.34 => ( ( 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))) % 191.28/191.34 => 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) ) % 191.28/191.34 & ( ~ 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))) % 191.28/191.34 => 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) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Odistrib__inf__le,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Odistrib__sup__le,axiom, % 191.28/191.34 ! [V_z,V_y,V_x,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => 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)))) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_minus__min__eq__max,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_minus__max__eq__min,axiom, % 191.28/191.34 ! [V_y,V_x,T_a] : % 191.28/191.34 ( class_Groups_Olinordered__ab__group__add(T_a) % 191.28/191.34 => 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)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_nat__minus__add__max,axiom, % 191.28/191.34 ! [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) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Ofold__sup__insert,axiom, % 191.28/191.34 ! [V_a_2,V_b_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2)) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Oin__idem,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Int__atLeastAtMost,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Int__atLeastLessThan,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Int__greaterThanAtMost,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Int__greaterThanLessThan,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Int__atLeastAtMostL2,axiom, % 191.28/191.34 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_b_2) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Int__atLeastAtMostR2,axiom, % 191.28/191.34 ! [V_d_2,V_ca_2,V_a_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_d_2) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_OF__eq,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__le__fold__sup,axiom, % 191.28/191.34 ! [V_b_2,V_a_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max__insert,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Osubset__idem,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Osup__Inf__absorb,axiom, % 191.28/191.34 ! [V_a_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = V_a_2 ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max__Un,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Oeq__fold__idem_H,axiom, % 191.28/191.34 ! [V_a_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Oinsert,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Oinsert__remove,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 191.28/191.34 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Ounion__inter,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.34 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_max__ord__max,axiom, % 191.28/191.34 ! [T_a] : % 191.28/191.34 ( class_Orderings_Oord(T_a) % 191.28/191.34 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_Max_Oclosed,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OInf__le__Sup,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OSup__fin_Oremove,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 191.28/191.34 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_sup__nat__def,axiom, % 191.28/191.34 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 191.28/191.34 ! [V_x_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 191.28/191.34 ! [V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 191.28/191.34 ! [V_x_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 191.28/191.34 ! [V_B_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ) ). % 191.28/191.34 % 191.28/191.34 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 191.28/191.34 ! [V_a_2,V_A_2,T_a] : % 191.28/191.34 ( class_Orderings_Olinorder(T_a) % 191.28/191.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = V_a_2 ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 191.28/191.35 ! [V_a_2,V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 191.28/191.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.35 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 191.28/191.35 ! [V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),V_A_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 191.28/191.35 ! [V_N_2,V_h_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.28/191.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Max_Ohom__commute,axiom, % 191.28/191.35 ! [V_N_2,V_h_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.28/191.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 191.28/191.35 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( ! [B_x] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_ca_2))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osize_I6_J,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osize_I14_J,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_evaln_OWhileFalse,axiom, % 191.28/191.35 ! [V_n_2,V_ca_2,V_s_2,V_b_2] : % 191.28/191.35 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_n_2),V_s_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_evaln_OWhileTrue,axiom, % 191.28/191.35 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] : % 191.28/191.35 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_n_2),V_s2_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_evalc_OWhileTrue,axiom, % 191.28/191.35 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] : % 191.28/191.35 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_evalc_OWhileFalse,axiom, % 191.28/191.35 ! [V_ca_2,V_s_2,V_b_2] : % 191.28/191.35 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_WTs__elim__cases_I6_J,axiom, % 191.28/191.35 ! [V_ca_2,V_b_2] : % 191.28/191.35 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) % 191.28/191.35 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I52_J,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I53_J,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I47_J,axiom, % 191.28/191.35 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I46_J,axiom, % 191.28/191.35 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I61_J,axiom, % 191.28/191.35 ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I60_J,axiom, % 191.28/191.35 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I38_J,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I39_J,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I17_J,axiom, % 191.28/191.35 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I16_J,axiom, % 191.28/191.35 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_While,axiom, % 191.28/191.35 ! [V_b_2,V_ca_2] : % 191.28/191.35 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 191.28/191.35 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_WT_Oequations_I6_J,axiom, % 191.28/191.35 ! [V_a1_2,V_a2_2] : % 191.28/191.35 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 191.28/191.35 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I58_J,axiom, % 191.28/191.35 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I59_J,axiom, % 191.28/191.35 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_com_Osimps_I5_J,axiom, % 191.28/191.35 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 191.28/191.35 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 191.28/191.35 <=> ( V_fun_2 = V_fun_H_2 % 191.28/191.35 & V_com_2 = V_com_H_2 ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_evalc_Oequations_I7_J,axiom, % 191.28/191.35 ! [V_a2_2,V_a3_2,V_a1_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 191.28/191.35 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.35 => ? [B_s1] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 191.28/191.35 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_evalc_Oequations_I8_J,axiom, % 191.28/191.35 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 191.28/191.35 <=> ( ( V_a5_2 = V_a2_2 % 191.28/191.35 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 191.28/191.35 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.35 & ? [B_s1] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 191.28/191.35 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_evaln_Oequations_I8_J,axiom, % 191.28/191.35 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2)) % 191.28/191.35 <=> ( ( V_a6_2 = V_a2_2 % 191.28/191.35 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 191.28/191.35 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.35 & ? [B_s1] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 191.28/191.35 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_evaln_Oequations_I7_J,axiom, % 191.28/191.35 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2)) % 191.28/191.35 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 191.28/191.35 => ? [B_s1] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 191.28/191.35 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_subtract__code__numeral__def,axiom, % 191.28/191.35 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.35 % 191.28/191.35 fof(fact_minus__code__numeral__code,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pair__box_Osize_I1_J,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_b,T_a] : c_Nitpick_Opair__box_Opair__box__size(T_a,T_b,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pair__box_Oinject,axiom, % 191.28/191.35 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.35 ( c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a_H_2,V_b_H_2) % 191.28/191.35 <=> ( V_a_2 = V_a_H_2 % 191.28/191.35 & V_b_2 = V_b_H_2 ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pair__box_Osize_I2_J,axiom, % 191.28/191.35 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pair__box_Osimps_I2_J,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__case(T_b,T_c,T_a,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pair__box_Orecs,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__rec(T_b,T_c,T_a,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_arith__series__int,axiom, % 191.28/191.35 ! [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)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 191.28/191.35 ! [V_w] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( 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)))) % 191.28/191.35 => 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))) ) % 191.28/191.35 & ( ~ 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)))) % 191.28/191.35 => 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)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fold__image__reindex,axiom, % 191.28/191.35 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 191.28/191.35 ( class_Groups_Oab__semigroup__mult(T_c) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 191.28/191.35 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__abs,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__abs__ge__zero,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__add__atLeastAtMost,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_ran__empty,axiom, % 191.28/191.35 ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_of__nat__setprod,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 191.28/191.35 & class_Rings_Osemiring__1(T_a) ) % 191.28/191.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 191.28/191.35 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 191.28/191.35 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__addf,axiom, % 191.28/191.35 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum_Odistrib,axiom, % 191.28/191.35 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Oplus__class_Oplus(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_h_2),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__number__of__Bit0,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inj__on__add__nat,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pred__subset__eq,axiom, % 191.28/191.35 ! [V_S_2,V_R_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pred__subset__eq2,axiom, % 191.28/191.35 ! [V_S_2,V_R_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2))) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_less__eq__Suc__le__raw,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_restrict__map__to__empty,axiom, % 191.28/191.35 ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__dividef,axiom, % 191.28/191.35 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Fields_Ofield__inverse__zero(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod_Odistrib,axiom, % 191.28/191.35 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_h_2),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__1,axiom, % 191.28/191.35 ! [V_A_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Oone__class_Oone(T_a))),V_A_2) = c_Groups_Oone__class_Oone(T_a) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_bot__empty__eq,axiom, % 191.28/191.35 ! [V_x_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_bot__fun__def,axiom, % 191.28/191.35 ! [V_x_2,T_b,T_a] : % 191.28/191.35 ( class_Orderings_Obot(T_a) % 191.28/191.35 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pred__equals__eq2,axiom, % 191.28/191.35 ! [V_S_2,V_R_2,T_b,T_a] : % 191.28/191.35 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) % 191.28/191.35 <=> V_R_2 = V_S_2 ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pred__equals__eq,axiom, % 191.28/191.35 ! [V_S_2,V_R_2,T_a] : % 191.28/191.35 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) % 191.28/191.35 <=> V_R_2 = V_S_2 ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_bot__empty__eq2,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__Compl__def,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Ouminus(T_a) % 191.28/191.35 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__timesf,axiom, % 191.28/191.35 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 191.28/191.35 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 191.28/191.35 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_o__eq__dest__lhs,axiom, % 191.28/191.35 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 191.28/191.35 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2 % 191.28/191.35 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_K__record__comp,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,V_ca_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ). % 191.28/191.35 % 191.28/191.35 fof(fact_o__eq__elim,axiom, % 191.28/191.35 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 191.28/191.35 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_ca_2),V_d_2) % 191.28/191.35 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_o__eq__dest,axiom, % 191.28/191.35 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 191.28/191.35 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_ca_2),V_d_2) % 191.28/191.35 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_o__apply,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_o__assoc,axiom, % 191.28/191.35 ! [V_h_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_h_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_o__def,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_vimage__ident,axiom, % 191.28/191.35 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__upd__def,axiom, % 191.28/191.35 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 191.28/191.35 ( ( V_x_2 = V_a_2 % 191.28/191.35 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 ) % 191.28/191.35 & ( V_x_2 != V_a_2 % 191.28/191.35 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 191.28/191.35 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.28/191.35 => c_Finite__Set_Ofun__left__comm(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_comp__cong,axiom, % 191.28/191.35 ! [T_e,T_d,T_c,T_a,T_b,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 191.28/191.35 ( 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)) % 191.28/191.35 => hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_restrict__map__empty,axiom, % 191.28/191.35 ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fold__image__def,axiom, % 191.28/191.35 ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_map__add__def,axiom, % 191.28/191.35 ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_map__add__empty,axiom, % 191.28/191.35 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2 ). % 191.28/191.35 % 191.28/191.35 fof(fact_empty__map__add,axiom, % 191.28/191.35 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2 ). % 191.28/191.35 % 191.28/191.35 fof(fact_empty__upd__none,axiom, % 191.28/191.35 ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inj__on__id2,axiom, % 191.28/191.35 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inj__on__imageI2,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 191.28/191.35 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_H_2),V_f_2),V_A_2) % 191.28/191.35 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_vimage__compose,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,V_g_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_a,T_c,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_g_2),V_x_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__upd__comp,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_c),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_map__comp__empty_I2_J,axiom, % 191.28/191.35 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a) ). % 191.28/191.35 % 191.28/191.35 fof(fact_map__comp__empty_I1_J,axiom, % 191.28/191.35 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 191.28/191.35 % 191.28/191.35 fof(fact_map__comp__def,axiom, % 191.28/191.35 ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_int__setprod,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inj__fun,axiom, % 191.28/191.35 ! [T_c,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.35 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_abs__setprod,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Fields_Olinordered__field(T_a) % 191.28/191.35 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_restrict__map__def,axiom, % 191.28/191.35 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.35 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.35 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_dom__const,axiom, % 191.28/191.35 ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_dom__empty,axiom, % 191.28/191.35 ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_dom__eq__empty__conv,axiom, % 191.28/191.35 ! [V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_of__int__setprod,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 191.28/191.35 & class_Rings_Oring__1(T_a) ) % 191.28/191.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_a] : % 191.28/191.35 ( ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 & class_Groups_Ocomm__monoid__mult(T_a) ) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_card__eq__setsum,axiom, % 191.28/191.35 ! [V_A_2,T_a] : hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_map__upd__nonempty,axiom, % 191.28/191.35 ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_of__int__setsum,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Rings_Oring__1(T_a) % 191.28/191.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_of__nat__setsum,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Rings_Osemiring__1(T_a) % 191.28/191.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inj__singleton,axiom, % 191.28/191.35 ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_abs__setsum__abs,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.35 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__0,axiom, % 191.28/191.35 ! [V_A_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_int__setsum,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__commute,axiom, % 191.28/191.35 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_a),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))),V_A_2)),V_B_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__divide__distrib,axiom, % 191.28/191.35 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Fields_Ofield(T_a) % 191.28/191.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Rings_Oinverse__class_Odivide(T_a)),V_f_2)),V_r_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__negf,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Oab__group__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__right__distrib,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 191.28/191.35 ( class_Rings_Osemiring__0(T_a) % 191.28/191.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2)),V_f_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__left__distrib,axiom, % 191.28/191.35 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Rings_Osemiring__0(T_a) % 191.28/191.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_r_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__product,axiom, % 191.28/191.35 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Rings_Osemiring__0(T_a) % 191.28/191.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_finite__range__imageI,axiom, % 191.28/191.35 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 191.28/191.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__constant__conv,axiom, % 191.28/191.35 ! [V_ca_2,T_b,T_a,V_A_2] : % 191.28/191.35 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.35 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_range__composition,axiom, % 191.28/191.35 ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__image,axiom, % 191.28/191.35 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2)),V_A_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__ident,axiom, % 191.28/191.35 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__compose,axiom, % 191.28/191.35 ! [V_r_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_a,T_b,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_r_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 191.28/191.35 ! [V_n_2,V_m_2,V_f_2,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 191.28/191.35 ! [V_n_2,V_m_2,V_f_2,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__subtractf,axiom, % 191.28/191.35 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Oab__group__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__diff__def,axiom, % 191.28/191.35 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.35 ( class_Groups_Ominus(T_a) % 191.28/191.35 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inf__Int__eq2,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inf__Int__eq,axiom, % 191.28/191.35 ! [V_x_2,V_S_2,V_R_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inf__fun__def,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Lattices_Olattice(T_a) % 191.28/191.35 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__add__atLeastLessThan,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_sup__Un__eq,axiom, % 191.28/191.35 ! [V_x_2,V_S_2,V_R_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_sup__Un__eq2,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_sup__fun__def,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( class_Lattices_Olattice(T_a) % 191.28/191.35 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__delta_H,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__delta,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__constant,axiom, % 191.28/191.35 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.35 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__delta_H,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__delta,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_vimage__const,axiom, % 191.28/191.35 ! [T_b,V_A_2,V_ca_2,T_a] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.28/191.35 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.28/191.35 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__constant,axiom, % 191.28/191.35 ! [V_A_2,V_y_2,T_b,T_a] : % 191.28/191.35 ( class_Rings_Osemiring__1(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_power__number__of__even,axiom, % 191.28/191.35 ! [V_w_2,V_z_2,T_a] : % 191.28/191.35 ( class_Int_Onumber__ring(T_a) % 191.28/191.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fold__image__distrib,axiom, % 191.28/191.35 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_b)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_MGT__def,axiom, % 191.28/191.35 ! [V_ca_2] : c_Hoare__Mirabelle_OMGT(V_ca_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_ca_2),c_Natural_Oevalc(V_ca_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_dual__max,axiom, % 191.28/191.35 ! [T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_dual__min,axiom, % 191.28/191.35 ! [T_a] : % 191.28/191.35 ( class_Orderings_Olinorder(T_a) % 191.28/191.35 => c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__constant,axiom, % 191.28/191.35 ! [V_y_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_COMBK(T_b,T_a),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_zpower__number__of__even,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_comp__surj,axiom, % 191.28/191.35 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 191.28/191.35 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => ( hAPP(c_Set_Oimage(T_a,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 191.28/191.35 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_a,T_c,T_b,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__lessThan__Suc,axiom, % 191.28/191.35 ! [V_n_2,V_f_2,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inj__on__imageI,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 191.28/191.35 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2),V_A_2) % 191.28/191.35 => c_Fun_Oinj__on(T_c,T_b,V_g_2,hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_comp__inj__on,axiom, % 191.28/191.35 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.35 => ( c_Fun_Oinj__on(T_b,T_c,V_g_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) % 191.28/191.35 => c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_comp__inj__on__iff,axiom, % 191.28/191.35 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.35 => ( c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) % 191.28/191.35 <=> c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inj__comp,axiom, % 191.28/191.35 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.35 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 191.28/191.35 => c_Fun_Oinj__on(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__atMost__Suc,axiom, % 191.28/191.35 ! [V_n_2,V_f_2,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_a] : % 191.28/191.35 ( ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 & class_Groups_Ocomm__monoid__mult(T_a) ) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__add__int__atLeastLessThan,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 191.28/191.35 ! [V_f_2,V_A_2,T_a] : % 191.28/191.35 ( ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 & class_Groups_Ocomm__monoid__mult(T_a) ) % 191.28/191.35 => ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Powp__Pow__eq,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__restrict__set,axiom, % 191.28/191.35 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__eq__fold__image,axiom, % 191.28/191.35 ! [V_f_2,T_b,V_A_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_b,tc_HOL_Obool),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_power__number__of__even__number__of,axiom, % 191.28/191.35 ! [V_w_2,V_v_2,T_a] : % 191.28/191.35 ( class_Int_Onumber__ring(T_a) % 191.28/191.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_card_Oeq__fold__g,axiom, % 191.28/191.35 ! [V_A_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_card__def,axiom, % 191.28/191.35 ! [V_A_2,T_a] : % 191.28/191.35 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fun__left__comm__idem__remove,axiom, % 191.28/191.35 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_vimage__if,axiom, % 191.28/191.35 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 191.28/191.35 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 191.28/191.35 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 191.28/191.35 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 191.28/191.35 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_diff__nat__eq__if,axiom, % 191.28/191.35 ! [V_z_2,V_z_H_2] : % 191.28/191.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 191.28/191.35 => 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) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg__div__mod,axiom, % 191.28/191.35 ! [V_l,V_k] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg__minus1,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 191.28/191.35 ! [V_f_2,V_A_2,T_a] : % 191.28/191.35 ( ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 & class_Groups_Ocomm__monoid__mult(T_a) ) % 191.28/191.35 => ( c_Nat__Transfer_Onat__set(V_A_2) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_LoopF,axiom, % 191.28/191.35 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_adjust__eq,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_hoare__derivs_OBody,axiom, % 191.28/191.35 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__head,axiom, % 191.28/191.35 ! [V_P_2,V_n_2,V_m_2,T_a] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_minus__fold__remove,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2),V_A_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Body__sound__lemma,axiom, % 191.28/191.35 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_dom__eq__singleton__conv,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.35 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__reindex,axiom, % 191.28/191.35 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_c) % 191.28/191.35 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_eq__number__of__Suc,axiom, % 191.28/191.35 ! [V_n_2,V_v_2] : % 191.28/191.35 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 191.28/191.35 <=> 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))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Suc__eq__number__of,axiom, % 191.28/191.35 ! [V_v_2,V_n_2] : % 191.28/191.35 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 191.28/191.35 <=> 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))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__reindex__cong,axiom, % 191.28/191.35 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_c) % 191.28/191.35 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.35 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 191.28/191.35 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__reindex,axiom, % 191.28/191.35 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_c) % 191.28/191.35 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__number__of__Bit1,axiom, % 191.28/191.35 ! [V_w_2] : % 191.28/191.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 191.28/191.35 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 191.28/191.35 => 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)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_geometric__sum,axiom, % 191.28/191.35 ! [V_n_2,V_x_2,T_a] : % 191.28/191.35 ( class_Fields_Ofield(T_a) % 191.28/191.35 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x_2),c_Groups_Oone__class_Oone(T_a))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_gauss__sum,axiom, % 191.28/191.35 ! [V_n_2,T_a] : % 191.28/191.35 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Groups_Oone__class_Oone(T_a))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__natinterval__difff,axiom, % 191.28/191.35 ! [V_f_2,V_n_2,V_m_2,T_a] : % 191.28/191.35 ( class_Groups_Oab__group__add(T_a) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_less__Suc__number__of,axiom, % 191.28/191.35 ! [V_v_2,V_n_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 <=> 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))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_less__number__of__Suc,axiom, % 191.28/191.35 ! [V_n_2,V_v_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 <=> 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)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_le__number__of__Suc,axiom, % 191.28/191.35 ! [V_n_2,V_v_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 <=> 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)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_le__Suc__number__of,axiom, % 191.28/191.35 ! [V_v_2,V_n_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 <=> 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))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_max__number__of__Suc,axiom, % 191.28/191.35 ! [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)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_max__Suc__number__of,axiom, % 191.28/191.35 ! [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)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_power__number__of__odd,axiom, % 191.28/191.35 ! [V_z_2,V_w_2,T_a] : % 191.28/191.35 ( class_Int_Onumber__ring(T_a) % 191.28/191.35 => ( ( 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))) % 191.28/191.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(T_a))) ) % 191.28/191.35 & ( ~ 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))) % 191.28/191.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod__gen__delta,axiom, % 191.28/191.35 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ca_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 191.28/191.35 ! [V_x_2,V_y_2,V_ca_2] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 191.28/191.35 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 191.28/191.35 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 191.28/191.35 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum_Oreindex,axiom, % 191.28/191.35 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_zpower__number__of__odd,axiom, % 191.28/191.35 ! [V_z_2,V_w_2] : % 191.28/191.35 ( ( 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))) % 191.28/191.35 => 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))) ) % 191.28/191.35 & ( ~ 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))) % 191.28/191.35 => 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) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setprod_Oreindex,axiom, % 191.28/191.35 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_arith__series__general,axiom, % 191.28/191.35 ! [V_n_2,V_d_2,V_a_2,T_a] : % 191.28/191.35 ( class_Rings_Ocomm__semiring__1(T_a) % 191.28/191.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg_Osimps,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( ( ( 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))) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ ( 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))) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => 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))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__number__of__Suc,axiom, % 191.28/191.35 ! [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)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__Suc__number__of,axiom, % 191.28/191.35 ! [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)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_arith__series__nat,axiom, % 191.28/191.35 ! [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)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_the__inv__into__comp,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)) % 191.28/191.35 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)))) % 191.28/191.35 => hAPP(c_Fun_Othe__inv__into(T_c,T_b,V_A_2,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Fun_Othe__inv__into(T_c,T_a,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_a,T_b,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_power__number__of__odd__number__of,axiom, % 191.28/191.35 ! [V_v_2,V_w_2,T_a] : % 191.28/191.35 ( class_Int_Onumber__ring(T_a) % 191.28/191.35 => ( ( 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))) % 191.28/191.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(T_a))) ) % 191.28/191.35 & ( ~ 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))) % 191.28/191.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg__eqn,axiom, % 191.28/191.35 ! [V_a,V_b] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => ( ( 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))) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ 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))) % 191.28/191.35 => 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))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg__eqn__number__of,axiom, % 191.28/191.35 ! [V_w,V_v] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( 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)))) % 191.28/191.35 => 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))) ) % 191.28/191.35 & ( ~ 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)))) % 191.28/191.35 => 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)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Body1,axiom, % 191.28/191.35 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_diff__nat__number__of,axiom, % 191.28/191.35 ! [V_v_2,V_v_H_2] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 191.28/191.35 => 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) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_norm__frac_Osimps,axiom, % 191.28/191.35 ! [V_a_2,V_b_2] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 191.28/191.35 => 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))) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__case__add__eq__if,axiom, % 191.28/191.35 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 191.28/191.35 ! [V_w] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( 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))) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ 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))) % 191.28/191.35 => 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)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_sup2CI,axiom, % 191.28/191.35 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 191.28/191.35 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_sup2E,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 191.28/191.35 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inf2E,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 191.28/191.35 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 191.28/191.35 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inf2I,axiom, % 191.28/191.35 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_bot2E,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,T_b,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_sup2I2,axiom, % 191.28/191.35 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_sup2I1,axiom, % 191.28/191.35 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inf2D2,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inf2D1,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_less__by__empty,axiom, % 191.28/191.35 ! [V_B_2,T_a,V_A_2] : % 191.28/191.35 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_predicate2D,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_rev__predicate2D,axiom, % 191.28/191.35 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__case__0,axiom, % 191.28/191.35 ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__case__Suc,axiom, % 191.28/191.35 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg__0,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_max__Suc1,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_max__Suc2,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 191.28/191.35 ! [V_n_2,V_m_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 191.28/191.35 <=> 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)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_diff__Suc,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__Suc1,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_min__Suc2,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg__div__mod,axiom, % 191.28/191.35 ! [V_l,V_k] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__case__number__of,axiom, % 191.28/191.35 ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg__eqn__number__of,axiom, % 191.28/191.35 ! [V_w,V_v] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( 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))) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ 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))) % 191.28/191.35 => 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)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg__eqn,axiom, % 191.28/191.35 ! [V_a,V_b] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 191.28/191.35 => 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) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 191.28/191.35 => 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))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg_Osimps,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => 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) ) % 191.28/191.35 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => 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))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_in__rel__def,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 191.28/191.35 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__mod__code__numeral__def,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Nitpick_Orefl_H__def,axiom, % 191.28/191.35 ! [V_r_2,T_a] : % 191.28/191.35 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 191.28/191.35 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_adjust__def,axiom, % 191.28/191.35 ! [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))))))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__step,axiom, % 191.28/191.35 ! [V_m,V_n] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Loop__sound__lemma,axiom, % 191.28/191.35 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_peek__and__def,axiom, % 191.28/191.35 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 191.28/191.35 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 191.28/191.35 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__zero,axiom, % 191.28/191.35 ! [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) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__base,axiom, % 191.28/191.35 ! [V_n,V_m] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 191.28/191.35 => 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) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__div__mod,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Loop,axiom, % 191.28/191.35 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_hoare__derivs_OIf,axiom, % 191.28/191.35 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.28/191.35 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pair__imageI,axiom, % 191.28/191.35 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),V_A_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_of__int__num,axiom, % 191.28/191.35 ! [V_k_2,T_a] : % 191.28/191.35 ( class_Rings_Oring__1(T_a) % 191.28/191.35 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 191.28/191.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__rec__add__eq__if,axiom, % 191.28/191.35 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_splitI,axiom, % 191.28/191.35 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_prod__caseI,axiom, % 191.28/191.35 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mem__splitI,axiom, % 191.28/191.35 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_splitD,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_splitD_H,axiom, % 191.28/191.35 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_ca_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__rec__0,axiom, % 191.28/191.35 ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__rec__Suc,axiom, % 191.28/191.35 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),V_nat_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__paired__All,axiom, % 191.28/191.35 ! [T_b,T_a,V_P_2] : % 191.28/191.35 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 191.28/191.35 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Pair__eq,axiom, % 191.28/191.35 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.35 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2) % 191.28/191.35 <=> ( V_a_2 = V_a_H_2 % 191.28/191.35 & V_b_2 = V_b_H_2 ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Pair__inject,axiom, % 191.28/191.35 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 191.28/191.35 ( 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) % 191.28/191.35 => ~ ( V_a = V_a_H % 191.28/191.35 => V_b != V_b_H ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__weak__cong,axiom, % 191.28/191.35 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 191.28/191.35 ( V_p_2 = V_q_2 % 191.28/191.35 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_q_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__mod__div,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_prod_Osimps_I2_J,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__conv,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__if,axiom, % 191.28/191.35 ! [V_m_2,V_n_2] : % 191.28/191.35 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 191.28/191.35 => 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) ) % 191.28/191.35 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__eta,axiom, % 191.28/191.35 ! [V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2 ). % 191.28/191.35 % 191.28/191.35 fof(fact_swap__inj__on,axiom, % 191.28/191.35 ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(tc_prod(T_a,T_b),tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_b,T_a)),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))),V_A_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__twice,axiom, % 191.28/191.35 ! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__rec__number__of,axiom, % 191.28/191.35 ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Nitpick_OFrac__def,axiom, % 191.28/191.35 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)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__def,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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))) ) ) ) ) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => 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))) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__pdivmod,axiom, % 191.28/191.35 ! [V_l_2,V_k_2] : % 191.28/191.35 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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) ) % 191.28/191.35 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)))) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_apsnd__conv,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),hAPP(V_f_2,V_y_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_apsnd__compose,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_a,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_x_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negateSnd__def,axiom, % 191.28/191.35 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negateSnd__eq,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pdivmod__def,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pdivmod__posDivAlg,axiom, % 191.28/191.35 ! [V_k,V_l] : % 191.28/191.35 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__code,axiom, % 191.28/191.35 ! [V_l_2,V_k_2] : % 191.28/191.35 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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) ) % 191.28/191.35 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)))) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 191.28/191.35 ! [V_n_2,T_a] : % 191.28/191.35 ( class_Rings_Osemiring__1(T_a) % 191.28/191.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_Groups_Oone__class_Oone(T_a)),V_n_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 191.28/191.35 ! [V_a,V_r,V_q,V_c,V_b] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 191.28/191.35 => 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)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 191.28/191.35 ! [V_c,V_r,V_q,V_b,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 191.28/191.35 => 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)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__rel__unique,axiom, % 191.28/191.35 ! [V_qr_H,V_qr,V_n,V_m] : % 191.28/191.35 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 191.28/191.35 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 191.28/191.35 => V_qr = V_qr_H ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__eq,axiom, % 191.28/191.35 ! [V_qr,V_n,V_m] : % 191.28/191.35 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 191.28/191.35 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 191.28/191.35 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 191.28/191.35 ! [V_i_2,V_inc_2,T_a] : % 191.28/191.35 ( class_Rings_Osemiring__1(T_a) % 191.28/191.35 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 191.28/191.35 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 191.28/191.35 ( class_Rings_Osemiring__1(T_a) % 191.28/191.35 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__eq,axiom, % 191.28/191.35 ! [V_r,V_q,V_n,V_m] : % 191.28/191.35 ( 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))) % 191.28/191.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__eq,axiom, % 191.28/191.35 ! [V_r,V_q,V_n,V_m] : % 191.28/191.35 ( 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))) % 191.28/191.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__rel,axiom, % 191.28/191.35 ! [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)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__rel__add1__eq,axiom, % 191.28/191.35 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( 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))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 191.28/191.35 => 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)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_MGT__alternD,axiom, % 191.28/191.35 ! [V_ca_2,V_G_2] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ostate__not__singleton % 191.28/191.35 => ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg_Opsimps,axiom, % 191.28/191.35 ! [V_b_2,V_a_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( ( 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))) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ ( 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))) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => 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))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_zmult2__lemma,axiom, % 191.28/191.35 ! [V_c,V_r,V_q,V_b,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 191.28/191.35 => 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)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_triple__valid__def,axiom, % 191.28/191.35 ! [V_t_2,V_n_2,T_a] : % 191.28/191.35 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 191.28/191.35 <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_accp_Osimps,axiom, % 191.28/191.35 ! [V_a_2,V_r_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 191.28/191.35 <=> ! [B_x] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 191.28/191.35 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_accp_Oequations,axiom, % 191.28/191.35 ! [V_a_2,V_r_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 191.28/191.35 <=> ! [B_x] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 191.28/191.35 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_accp__downward,axiom, % 191.28/191.35 ! [V_a_2,V_b_2,V_r_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 191.28/191.35 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_unique__remainder,axiom, % 191.28/191.35 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( 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))) % 191.28/191.35 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => V_r = V_r_H ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_unique__quotient,axiom, % 191.28/191.35 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( 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))) % 191.28/191.35 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => V_q = V_q_H ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_self__remainder,axiom, % 191.28/191.35 ! [V_r,V_q,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__rel__0,axiom, % 191.28/191.35 ! [V_b] : % 191.28/191.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_accp__subset,axiom, % 191.28/191.35 ! [V_R2_2,V_R1_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R1_2),V_R2_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_a,V_R2_2)),c_Wellfounded_Oaccp(T_a,V_R1_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__rel__neg,axiom, % 191.28/191.35 ! [V_qr,V_b,V_a] : % 191.28/191.35 ( 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)) % 191.28/191.35 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__correct,axiom, % 191.28/191.35 ! [V_a,V_b] : % 191.28/191.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_self__quotient,axiom, % 191.28/191.35 ! [V_r,V_q,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__rel__mod,axiom, % 191.28/191.35 ! [V_r,V_q,V_b,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__rel__div,axiom, % 191.28/191.35 ! [V_r,V_q,V_b,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg__correct,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__rel__div__mod,axiom, % 191.28/191.35 ! [V_a,V_b] : % 191.28/191.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg__correct,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_zadd1__lemma,axiom, % 191.28/191.35 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( 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))) % 191.28/191.35 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_zminus1__lemma,axiom, % 191.28/191.35 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => 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))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__relI,axiom, % 191.28/191.35 ! [V_r,V_q,V_b,V_a] : % 191.28/191.35 ( 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) % 191.28/191.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 191.28/191.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 191.28/191.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 191.28/191.35 => 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))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_zmult1__lemma,axiom, % 191.28/191.35 ! [V_a,V_r,V_q,V_c,V_b] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 => 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)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_MGT__alternI,axiom, % 191.28/191.35 ! [V_ca_2,V_G_2] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__int__rel__def,axiom, % 191.28/191.35 ! [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))))))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg_Opsimps,axiom, % 191.28/191.35 ! [V_b_2,V_a_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => 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) ) % 191.28/191.35 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => 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))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_norm__frac_Opsimps,axiom, % 191.28/191.35 ! [V_b_2,V_a_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 191.28/191.35 => 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)) ) % 191.28/191.35 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 191.28/191.35 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 191.28/191.35 => 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))) ) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_negDivAlg_Opinduct,axiom, % 191.28/191.35 ! [V_P_2,V_a1_2,V_a0_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ! [B_a,B_b] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( ~ ( 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))) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_posDivAlg_Opinduct,axiom, % 191.28/191.35 ! [V_P_2,V_a1_2,V_a0_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ! [B_a,B_b] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 191.28/191.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__gcd_Opsimps,axiom, % 191.28/191.35 ! [V_y_2,V_x_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.35 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 191.28/191.35 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.35 => 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)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 191.28/191.35 ! [V_f_2,V_A_2,T_a] : % 191.28/191.35 ( ! [B_x] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.35 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__pos__neg__1__number__of,axiom, % 191.28/191.35 ! [V_w] : % 191.28/191.35 ( 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))) % 191.28/191.35 => 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))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_in__measure,axiom, % 191.28/191.35 ! [V_f_2,V_y_2,V_x_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))) % 191.28/191.35 <=> 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))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 191.28/191.35 ! [V_f_2,V_A_2,T_a] : % 191.28/191.35 ( ! [B_x] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.35 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_snd__eqD,axiom, % 191.28/191.35 ! [V_a,V_y,V_x,T_a,T_b] : % 191.28/191.35 ( 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 % 191.28/191.35 => V_y = V_a ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_snd__conv,axiom, % 191.28/191.35 ! [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 ). % 191.28/191.35 % 191.28/191.35 fof(fact_apsnd__eq__conv,axiom, % 191.28/191.35 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 191.28/191.35 ( hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2) % 191.28/191.35 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_snd__apsnd,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapsnd(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_snd__def,axiom, % 191.28/191.35 ! [V_p_2,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,T_a),hAPP(c_COMBK(tc_fun(T_a,T_a),T_b),c_COMBI(T_a))),V_p_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__int__def,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__neg__pos,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__pos__pos,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__pos__pos__1__number__of,axiom, % 191.28/191.35 ! [V_w] : % 191.28/191.35 ( 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))) % 191.28/191.35 => 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))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__pos__neg,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => 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)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__neg__neg,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => 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)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Oremove,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.35 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_norm__frac_Opinduct,axiom, % 191.28/191.35 ! [V_P_2,V_a1_2,V_a0_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ! [B_a,B_b] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_finite__pointwise,axiom, % 191.28/191.35 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_G_2,T_b,V_U_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 191.28/191.35 => ( ! [B_p] : % 191.28/191.35 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) % 191.28/191.35 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2)) % 191.28/191.35 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ocommute__left__comp,axiom, % 191.28/191.35 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),V_g_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ocommute__comp,axiom, % 191.28/191.35 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 191.28/191.35 ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e,V_F_2,V_fa_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mod__nat__def,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 191.28/191.35 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ocommute__comp_H_H,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ocommute__left__comp_H,axiom, % 191.28/191.35 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ocommute__comp_H,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Oeq__fold,axiom, % 191.28/191.35 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Oinsert,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ounion__inter,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Oinsert__remove,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding_Ounion,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.35 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.35 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__pos__neg__1__number__of,axiom, % 191.28/191.35 ! [V_w] : % 191.28/191.35 ( 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))) % 191.28/191.35 => 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))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_inj__vimage__singleton,axiom, % 191.28/191.35 ! [V_a_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_nat__gcd_Opinduct,axiom, % 191.28/191.35 ! [V_P_2,V_a1_2,V_a0_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ! [B_x,B_y] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_prod__eqI,axiom, % 191.28/191.35 ! [V_q,V_p,T_b,T_a] : % 191.28/191.35 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 191.28/191.35 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 191.28/191.35 => V_p = V_q ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_Pair__fst__snd__eq,axiom, % 191.28/191.35 ! [T_b,T_a,V_t_2,V_s_2] : % 191.28/191.35 ( V_s_2 = V_t_2 % 191.28/191.35 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 191.28/191.35 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_The__split,axiom, % 191.28/191.35 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fst__eqD,axiom, % 191.28/191.35 ! [V_a,V_y,V_x,T_b,T_a] : % 191.28/191.35 ( 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 % 191.28/191.35 => V_x = V_a ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fst__conv,axiom, % 191.28/191.35 ! [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 ). % 191.28/191.35 % 191.28/191.35 fof(fact_fst__apsnd,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_a,T_c),V_x_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fst__def,axiom, % 191.28/191.35 ! [V_p_2,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_a),c_COMBK(T_a,T_b)),V_p_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pair__collapse,axiom, % 191.28/191.35 ! [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 ). % 191.28/191.35 % 191.28/191.35 fof(fact_surjective__pairing,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__comp,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,V_f_2,T_d,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_a),T_b,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_x_2))),hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_prod__case__beta,axiom, % 191.28/191.35 ! [V_p_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__int__def,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__beta,axiom, % 191.28/191.35 ! [V_z_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_z_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_z_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__comp__eq,axiom, % 191.28/191.35 ! [V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),tc_prod(T_a,T_b)),V_f_2),hAPP(hAPP(c_COMBB(T_a,T_d,tc_prod(T_a,T_b)),V_g_2),c_Product__Type_Ofst(T_a,T_b)))),c_Product__Type_Osnd(T_a,T_b)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),T_a),V_f_2),V_g_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__def,axiom, % 191.28/191.35 ! [V_p_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_split__paired__The,axiom, % 191.28/191.35 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),V_P_2) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_The__split__eq,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_the__inv__into__def,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fold__def,axiom, % 191.28/191.35 ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__def,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fold1__def,axiom, % 191.28/191.35 ! [V_A_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__neg__pos,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__pos__pos,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_the__elem__def,axiom, % 191.28/191.35 ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__pos__pos__1__number__of,axiom, % 191.28/191.35 ! [V_w] : % 191.28/191.35 ( 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))) % 191.28/191.35 => 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))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__pos__neg,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => 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)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__neg__neg,axiom, % 191.28/191.35 ! [V_b,V_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 191.28/191.35 => 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)))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_prod__size__simp,axiom, % 191.28/191.35 ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_conjI__realizer,axiom, % 191.28/191.35 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 191.28/191.35 ( hBOOL(hAPP(V_P_2,V_p_2)) % 191.28/191.35 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 191.28/191.35 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) % 191.28/191.35 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_exI__realizer,axiom, % 191.28/191.35 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_div__nat__def,axiom, % 191.28/191.35 ! [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)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_divmod__nat__rel__def,axiom, % 191.28/191.35 ! [V_qr_2,V_n_2,V_m_2] : % 191.28/191.35 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 191.28/191.35 <=> ( 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)) % 191.28/191.35 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.35 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.28/191.35 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 191.28/191.35 => ( 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))) % 191.28/191.35 & 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)) ) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 191.28/191.35 => ( 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))) % 191.28/191.35 & 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))) ) ) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_range,axiom, % 191.28/191.35 ! [V_s,V_k] : % 191.28/191.35 ( 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)) % 191.28/191.35 => 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)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_flat__lub__def,axiom, % 191.28/191.35 ! [V_b_2,V_A_2,T_a] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 191.28/191.35 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 191.28/191.35 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mlex__leq,axiom, % 191.28/191.35 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_mlex__less,axiom, % 191.28/191.35 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 191.28/191.35 ( 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))) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__image_Oreindex,axiom, % 191.28/191.35 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.28/191.35 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 191.28/191.35 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_b,T_a,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_prod_Orecs,axiom, % 191.28/191.35 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__reindex__nonzero,axiom, % 191.28/191.35 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 191.28/191.35 ( class_Groups_Ocomm__monoid__add(T_c) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.35 => ( ! [B_x] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 191.28/191.35 => ! [B_y] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 191.28/191.35 => ( B_x != B_y % 191.28/191.35 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 191.28/191.35 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 191.28/191.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_S_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__image_Odistrib,axiom, % 191.28/191.35 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.28/191.35 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__image_Oeq__fold,axiom, % 191.28/191.35 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 191.28/191.35 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_map__add__map__of__foldr,axiom, % 191.28/191.35 ! [V_ps_2,V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)) = c_List_Ofoldr(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)))))),c_Option_Ooption_OSome(T_b))),V_ps_2,V_m_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_in__lex__prod,axiom, % 191.28/191.35 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) % 191.28/191.35 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2)) % 191.28/191.35 | ( V_a_2 = V_a_H_2 % 191.28/191.35 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_in__finite__psubset,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a))) % 191.28/191.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.35 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_same__fstI,axiom, % 191.28/191.35 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 191.28/191.35 ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__idem_Ounion__idem,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.35 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 191.28/191.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__idem_Oidem__comp,axiom, % 191.28/191.35 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__idem_Oidem__left__comp,axiom, % 191.28/191.35 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__idem_Oin__comp__idem,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.35 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_folding__idem_Oinsert__idem,axiom, % 191.28/191.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 191.28/191.35 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__nonneg__0,axiom, % 191.28/191.35 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Oordered__ab__group__add(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 191.28/191.35 => ( ! [B_i] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 191.28/191.35 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_b) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 191.28/191.35 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_setsum__nonneg__leq__bound,axiom, % 191.28/191.35 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 191.28/191.35 ( class_Groups_Oordered__ab__group__add(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 191.28/191.35 => ( ! [B_i] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 191.28/191.35 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_full__small__int__def,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_small_H_Osimps,axiom, % 191.28/191.35 ! [V_f_2,V_i_2,V_d_2] : % 191.28/191.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 191.28/191.35 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_sum__diff__distrib,axiom, % 191.28/191.35 ! [V_n_2,V_P_2,V_Q_2] : % 191.28/191.35 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) % 191.28/191.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_small_H_Opsimps,axiom, % 191.28/191.35 ! [V_i_2,V_d_2,V_f_2] : % 191.28/191.35 ( 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)))) % 191.28/191.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 191.28/191.35 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 191.28/191.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 191.28/191.35 => 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)) ) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_small__int__def,axiom, % 191.28/191.35 ! [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))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_apfst__apsnd,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_apfst__compose,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_d,V_f_2),V_g_2)),V_x_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_snd__apfst,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapfst(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_c,T_a),V_x_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_fst__apfst,axiom, % 191.28/191.35 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_apfst__eq__conv,axiom, % 191.28/191.35 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 191.28/191.35 ( hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2) % 191.28/191.35 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_apfst__conv,axiom, % 191.28/191.35 ! [V_y_2,V_x_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_x_2)),V_y_2) ). % 191.28/191.35 % 191.28/191.35 fof(fact_apsnd__apfst__commute,axiom, % 191.28/191.35 ! [V_p_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,V_g_2),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_d,V_f_2),V_p_2)) ). % 191.28/191.35 % 191.28/191.35 fof(fact_small__prod__def,axiom, % 191.28/191.35 ! [V_d_2,V_f_2,T_a,T_b] : % 191.28/191.35 ( ( class_Smallcheck_Osmall(T_b) % 191.28/191.35 & class_Smallcheck_Osmall(T_a) ) % 191.28/191.35 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_apsnd__apfst,axiom, % 191.28/191.35 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_x_2))) ). % 191.28/191.35 % 191.28/191.35 fof(fact_small_H_Opinduct,axiom, % 191.28/191.35 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 191.28/191.35 ( 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)))) % 191.28/191.35 => ( ! [B_f,B_d,B_i] : % 191.28/191.35 ( 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)))) % 191.28/191.35 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 191.28/191.35 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 191.28/191.35 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_pair__lessI2,axiom, % 191.28/191.35 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 191.28/191.35 => 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)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_INFI__fold__inf,axiom, % 191.28/191.35 ! [V_f_2,V_A_2,T_a,T_b] : % 191.28/191.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.35 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_INT__D,axiom, % 191.28/191.35 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_INT__E,axiom, % 191.28/191.35 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.28/191.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 191.28/191.35 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_INF1__E,axiom, % 191.28/191.35 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 191.28/191.35 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 191.28/191.35 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_INF1__D,axiom, % 191.28/191.35 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 191.28/191.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.35 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_INF2__E,axiom, % 191.28/191.35 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 191.28/191.35 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 191.28/191.35 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 191.28/191.35 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 191.28/191.35 % 191.28/191.35 fof(fact_INF2__D,axiom, % 191.28/191.36 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__INT,axiom, % 191.28/191.36 ! [V_A_2,T_b,V_I_2,T_a] : % 191.28/191.36 ( ? [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 191.28/191.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF__INT__eq2,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__iff,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__subset__iff,axiom, % 191.28/191.36 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__Int__distrib,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I7_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I6_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I7_J,axiom, % 191.28/191.36 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Un__INT__distrib,axiom, % 191.28/191.36 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I6_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Un__INT__distrib2,axiom, % 191.28/191.36 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I5_J,axiom, % 191.28/191.36 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I5_J,axiom, % 191.28/191.36 ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Pow__INT__eq,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a] : % 191.28/191.36 ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_vimage__INT,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF__commute,axiom, % 191.28/191.36 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INFI__apply,axiom, % 191.28/191.36 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.36 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I8_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I8_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Inter__def,axiom, % 191.28/191.36 ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I10_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I10_J,axiom, % 191.28/191.36 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_le__INF__iff,axiom, % 191.28/191.36 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2))) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF__less__iff,axiom, % 191.28/191.36 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 191.28/191.36 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.36 & class_Orderings_Olinorder(T_a) ) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2)) % 191.28/191.36 <=> ? [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__insert__distrib,axiom, % 191.28/191.36 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__lower,axiom, % 191.28/191.36 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF__INT__eq,axiom, % 191.28/191.36 ! [V_x_2,V_r_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__absorb,axiom, % 191.28/191.36 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF__const,axiom, % 191.28/191.36 ! [V_M_2,T_a,V_A_2,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__constant,axiom, % 191.28/191.36 ! [V_ca_2,T_b,T_a,V_A_2] : % 191.28/191.36 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__empty,axiom, % 191.28/191.36 ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I2_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I1_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__insert,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__Un,axiom, % 191.28/191.36 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Un__Inter,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Inter__image__eq,axiom, % 191.28/191.36 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INTER__eq__Inter__image,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF__subset,axiom, % 191.28/191.36 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I1_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I2_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I3_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I3_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF__leI,axiom, % 191.28/191.36 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Int__Inter__image,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__greaterThan__UNIV,axiom, % 191.28/191.36 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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_pair__lessI1,axiom, % 191.28/191.36 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 191.28/191.36 => 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)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inf__INFI__fold__inf,axiom, % 191.28/191.36 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_pair__leqI2,axiom, % 191.28/191.36 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 191.28/191.36 => 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)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_smin__insertI,axiom, % 191.28/191.36 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 191.28/191.36 => ( 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)) % 191.28/191.36 => ( 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)) % 191.28/191.36 => 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)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_smax__insertI,axiom, % 191.28/191.36 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 191.28/191.36 => ( 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)) % 191.28/191.36 => ( 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)) % 191.28/191.36 => 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)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_smin__emptyI,axiom, % 191.28/191.36 ! [V_X_2] : % 191.28/191.36 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 191.28/191.36 => 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)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_smax__emptyI,axiom, % 191.28/191.36 ! [V_Y_2] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 191.28/191.36 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 191.28/191.36 => 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)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF1__iff,axiom, % 191.28/191.36 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INF2__iff,axiom, % 191.28/191.36 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_pair__leqI1,axiom, % 191.28/191.36 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 191.28/191.36 => 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)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_wmax__insertI,axiom, % 191.28/191.36 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 191.28/191.36 => ( 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)) % 191.28/191.36 => ( 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)) % 191.28/191.36 => 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)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_wmin__insertI,axiom, % 191.28/191.36 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 191.28/191.36 => ( 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)) % 191.28/191.36 => ( 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)) % 191.28/191.36 => 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)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_wmin__emptyI,axiom, % 191.28/191.36 ! [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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_wmax__emptyI,axiom, % 191.28/191.36 ! [V_X_2] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 191.28/191.36 => 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)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_min__weak__def,axiom, % 191.28/191.36 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)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_max__weak__def,axiom, % 191.28/191.36 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)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_min__rpair__set,axiom, % 191.28/191.36 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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_max__strict__def,axiom, % 191.28/191.36 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 191.28/191.36 % 191.28/191.36 fof(fact_max__ext__additive,axiom, % 191.28/191.36 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_min__strict__def,axiom, % 191.28/191.36 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 191.28/191.36 % 191.28/191.36 fof(fact_max__rpair__set,axiom, % 191.28/191.36 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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_max__extp__max__ext__eq,axiom, % 191.28/191.36 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 191.28/191.36 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_less__than__iff,axiom, % 191.28/191.36 ! [V_y_2,V_x_2] : % 191.28/191.36 ( 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)) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_intrel__iff,axiom, % 191.28/191.36 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 191.28/191.36 ( 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)) % 191.28/191.36 <=> 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) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_pair__less__def,axiom, % 191.28/191.36 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 191.28/191.36 % 191.28/191.36 fof(fact_mlex__prod__def,axiom, % 191.28/191.36 ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_image__INT,axiom, % 191.28/191.36 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 191.28/191.36 => ( ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 191.28/191.36 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_rp__inv__image__rp,axiom, % 191.28/191.36 ! [V_f_2,T_b,V_P_2,T_a] : % 191.28/191.36 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 191.28/191.36 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_rp__inv__image__def,axiom, % 191.28/191.36 ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_in__inv__image,axiom, % 191.28/191.36 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2))) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUPR__fold__sup,axiom, % 191.28/191.36 ! [V_f_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_strong__setprod__reindex__cong,axiom, % 191.28/191.36 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 191.28/191.36 ( class_Groups_Ocomm__monoid__mult(T_c) % 191.28/191.36 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.36 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 191.28/191.36 => ( ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2),B_x) ) % 191.28/191.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__I,axiom, % 191.28/191.36 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP1__I,axiom, % 191.28/191.36 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP2__I,axiom, % 191.28/191.36 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP__UN__eq2,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UNION__empty__conv_I2_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__constant,axiom, % 191.28/191.36 ! [V_ca_2,T_b,T_a,V_A_2] : % 191.28/191.36 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__empty2,axiom, % 191.28/191.36 ! [V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UNION__empty__conv_I1_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a] : % 191.28/191.36 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__Un,axiom, % 191.28/191.36 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__Un__distrib,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__iff,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.28/191.36 <=> ? [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I9_J,axiom, % 191.28/191.36 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I9_J,axiom, % 191.28/191.36 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__Pow__subset,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__subset__iff,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I5_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I4_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I5_J,axiom, % 191.28/191.36 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Int__UN__distrib,axiom, % 191.28/191.36 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I4_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Int__UN__distrib2,axiom, % 191.28/191.36 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I6_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I6_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_vimage__UN,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP__commute,axiom, % 191.28/191.36 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUPR__apply,axiom, % 191.28/191.36 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.36 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I8_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I8_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Union__def,axiom, % 191.28/191.36 ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I10_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_image__UN,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Oimage(T_b,T_a,V_f_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I10_J,axiom, % 191.28/191.36 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__o,axiom, % 191.28/191.36 ! [V_f_2,V_g_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_c,tc_fun(T_a,tc_HOL_Obool),T_b,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_g_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__UN,axiom, % 191.28/191.36 ! [V_B_2,T_b,V_A_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP__le__iff,axiom, % 191.28/191.36 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_2)) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_less__SUP__iff,axiom, % 191.28/191.36 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 191.28/191.36 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.36 & class_Orderings_Olinorder(T_a) ) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2))) % 191.28/191.36 <=> ? [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP__const,axiom, % 191.28/191.36 ! [V_M_2,T_a,V_A_2,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__insert__distrib,axiom, % 191.28/191.36 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__upper,axiom, % 191.28/191.36 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP__UN__eq,axiom, % 191.28/191.36 ! [V_x_2,V_r_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__absorb,axiom, % 191.28/191.36 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I1_J,axiom, % 191.28/191.36 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__singleton,axiom, % 191.28/191.36 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I1_J,axiom, % 191.28/191.36 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I2_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I3_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I2_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I3_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__insert,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I7_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I7_J,axiom, % 191.28/191.36 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_image__Union,axiom, % 191.28/191.36 ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Int__Union,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Int__Union2,axiom, % 191.28/191.36 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Compl__UN,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Compl__INT,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_vimage__Union,axiom, % 191.28/191.36 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UNION__eq__Union__image,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Union__image__eq,axiom, % 191.28/191.36 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__lessThan__UNIV,axiom, % 191.28/191.36 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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__atMost__UNIV,axiom, % 191.28/191.36 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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__atLeast__UNIV,axiom, % 191.28/191.36 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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP__subset,axiom, % 191.28/191.36 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_B_2),V_f_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_image__eq__UN,axiom, % 191.28/191.36 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__extend__simps_I4_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_vimage__eq__UN,axiom, % 191.28/191.36 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__UN__finite__eq,axiom, % 191.28/191.36 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_le__SUPI,axiom, % 191.28/191.36 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_M_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Un__Union__image,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__le__add__shift,axiom, % 191.28/191.36 ! [V_k_2,V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_INT__simps_I4_J,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 191.28/191.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_sup__SUPR__fold__sup,axiom, % 191.28/191.36 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__le__eq__Un0,axiom, % 191.28/191.36 ! [V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_measure__def,axiom, % 191.28/191.36 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 191.28/191.36 % 191.28/191.36 fof(fact_irrefl__def,axiom, % 191.28/191.36 ! [V_r_2,T_a] : % 191.28/191.36 ( c_Relation_Oirrefl(T_a,V_r_2) % 191.28/191.36 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_nat__def,axiom, % 191.28/191.36 ! [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)))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Field__insert,axiom, % 191.28/191.36 ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP1__iff,axiom, % 191.28/191.36 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 191.28/191.36 <=> ? [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_SUP2__iff,axiom, % 191.28/191.36 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 191.28/191.36 <=> ? [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__extend__simps_I9_J,axiom, % 191.28/191.36 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__simps_I9_J,axiom, % 191.28/191.36 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__UN__flatten,axiom, % 191.28/191.36 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_ball__UN,axiom, % 191.28/191.36 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 191.28/191.36 ( ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 191.28/191.36 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 => ! [B_xa] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 191.28/191.36 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Field__Union,axiom, % 191.28/191.36 ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Rep__Integ__inject,axiom, % 191.28/191.36 ! [V_y_2,V_x_2] : % 191.28/191.36 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 191.28/191.36 <=> V_x_2 = V_y_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Field__empty,axiom, % 191.28/191.36 ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_mono__Field,axiom, % 191.28/191.36 ! [V_s_2,V_r_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Field__Un,axiom, % 191.28/191.36 ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__Field,axiom, % 191.28/191.36 ! [V_r_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__finite2__subset,axiom, % 191.28/191.36 ! [V_B_2,V_k_2,V_A_2,T_a] : % 191.28/191.36 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__finite2__eq,axiom, % 191.28/191.36 ! [V_B_2,V_k_2,V_A_2,T_a] : % 191.28/191.36 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__finite__subset,axiom, % 191.28/191.36 ! [V_C_2,V_A_2,T_a] : % 191.28/191.36 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Id__on__def,axiom, % 191.28/191.36 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__mapk__SomeI,axiom, % 191.28/191.36 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.36 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_c),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) % 191.28/191.36 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_a),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equiv__intrel__iff,axiom, % 191.28/191.36 ! [V_y_2,V_x_2] : % 191.28/191.36 ( 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)))) % 191.28/191.36 <=> 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)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inj__mapI,axiom, % 191.28/191.36 ! [V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.36 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__empty,axiom, % 191.28/191.36 ! [V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__Un,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__Id__on,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inj__map,axiom, % 191.28/191.36 ! [V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) % 191.28/191.36 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inj__map__eq__map,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.36 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 191.28/191.36 <=> V_xs_2 = V_ys_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inj__mapD,axiom, % 191.28/191.36 ! [V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) % 191.28/191.36 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__injective,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 191.28/191.36 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 191.28/191.36 => V_xs_2 = V_ys_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__ident,axiom, % 191.28/191.36 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 191.28/191.36 % 191.28/191.36 fof(fact_List_Omap_Ocomp,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__comp__map,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_List_Omap_Ocompositionality,axiom, % 191.28/191.36 ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__map,axiom, % 191.28/191.36 ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__UN,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_c,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__Int__subset,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_foldr__map,axiom, % 191.28/191.36 ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__mono,axiom, % 191.28/191.36 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Un__Image,axiom, % 191.28/191.36 ! [V_A_2,V_S_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_S_2),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Id__on__def_H,axiom, % 191.28/191.36 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__INT__subset,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_c,V_r_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__iff,axiom, % 191.28/191.36 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 191.28/191.36 <=> ? [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 191.28/191.36 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_rev__ImageI,axiom, % 191.28/191.36 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Id__on__empty,axiom, % 191.28/191.36 ! [T_a] : c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__eq__UN,axiom, % 191.28/191.36 ! [V_B_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Id__on__eqI,axiom, % 191.28/191.36 ! [V_A_2,T_a,V_b_2,V_a_2] : % 191.28/191.36 ( V_a_2 = V_b_2 % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Id__on__iff,axiom, % 191.28/191.36 ! [V_A_2,V_y_2,V_x_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2))) % 191.28/191.36 <=> ( V_x_2 = V_y_2 % 191.28/191.36 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__singleton__iff,axiom, % 191.28/191.36 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_of__int,axiom, % 191.28/191.36 ! [V_j_2,V_i_2,T_a] : % 191.28/191.36 ( class_Rings_Oring__1(T_a) % 191.28/191.36 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_j_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_One__int__def,axiom, % 191.28/191.36 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))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_mult,axiom, % 191.28/191.36 ! [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))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Rep__Integ__inverse,axiom, % 191.28/191.36 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 191.28/191.36 % 191.28/191.36 fof(fact_infinite__UNIV__listI,axiom, % 191.28/191.36 ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_minus,axiom, % 191.28/191.36 ! [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))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Zero__int__def,axiom, % 191.28/191.36 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))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_int__def,axiom, % 191.28/191.36 ! [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))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_add,axiom, % 191.28/191.36 ! [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))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_nat,axiom, % 191.28/191.36 ! [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) ). % 191.28/191.36 % 191.28/191.36 fof(fact_minus__int__def,axiom, % 191.28/191.36 ! [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))))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_less,axiom, % 191.28/191.36 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 191.28/191.36 ( 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))))))) % 191.28/191.36 <=> 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))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_le,axiom, % 191.28/191.36 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 191.28/191.36 ( 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))))))) % 191.28/191.36 <=> 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))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_eq__Abs__Integ,axiom, % 191.28/191.36 ! [V_z_2] : % 191.28/191.36 ~ ! [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))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotient__def,axiom, % 191.28/191.36 ! [V_r_2,V_A_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),c_Relation_OImage(T_a,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__map,axiom, % 191.28/191.36 ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_option__map__o__empty,axiom, % 191.28/191.36 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 191.28/191.36 % 191.28/191.36 fof(fact_option__map__comp,axiom, % 191.28/191.36 ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Option_Omap_Ocompositionality,axiom, % 191.28/191.36 ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Option_Omap_Ocomp,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_dom__option__map,axiom, % 191.28/191.36 ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_option__map__Some,axiom, % 191.28/191.36 ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_option__map__eq__Some,axiom, % 191.28/191.36 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 191.28/191.36 <=> ? [B_z] : % 191.28/191.36 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 191.28/191.36 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_option__map__is__None,axiom, % 191.28/191.36 ! [V_opt_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 191.28/191.36 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_option__map__None,axiom, % 191.28/191.36 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotient__empty,axiom, % 191.28/191.36 ! [V_r_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotient__is__empty2,axiom, % 191.28/191.36 ! [V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) % 191.28/191.36 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotient__is__empty,axiom, % 191.28/191.36 ! [V_r_2,V_A_2,T_a] : % 191.28/191.36 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 191.28/191.36 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_option__map__o__map__upd,axiom, % 191.28/191.36 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotient__diff1,axiom, % 191.28/191.36 ! [V_a_2,V_A_2,V_r_2,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotientI,axiom, % 191.28/191.36 ! [V_r_2,V_A_2,V_x_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_singleton__quotient,axiom, % 191.28/191.36 ! [V_r_2,V_x_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_card__quotient__disjoint,axiom, % 191.28/191.36 ! [V_r_2,V_A_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) % 191.28/191.36 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Option_Omap__def,axiom, % 191.28/191.36 ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equiv__class__nondisjoint,axiom, % 191.28/191.36 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_subset__equiv__class,axiom, % 191.28/191.36 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotientE,axiom, % 191.28/191.36 ! [V_r_2,V_A_2,V_X_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ~ ! [B_x] : % 191.28/191.36 ( V_X_2 = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.28/191.36 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equiv__intrel,axiom, % 191.28/191.36 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) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Union__quotient,axiom, % 191.28/191.36 ! [V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equiv__class__self,axiom, % 191.28/191.36 ! [V_a_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotient__disj,axiom, % 191.28/191.36 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( V_X_2 = V_Y_2 % 191.28/191.36 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equiv__class__eq,axiom, % 191.28/191.36 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.36 => hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotient__eqI,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.36 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_quotient__eq__iff,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 191.28/191.36 => ( V_X_2 = V_Y_2 % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_eq__equiv__class__iff,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 191.28/191.36 => ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_eq__equiv__class,axiom, % 191.28/191.36 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 191.28/191.36 ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.28/191.36 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equiv__class__eq__iff,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.36 <=> ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.28/191.36 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.36 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equiv__class__subset,axiom, % 191.28/191.36 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_eq__equiv__class__iff2,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 191.28/191.36 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__equiv__class,axiom, % 191.28/191.36 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__equiv__class2,axiom, % 191.28/191.36 ! [V_a2_2,V_a1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 191.28/191.36 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 191.28/191.36 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 191.28/191.36 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__map__restrict,axiom, % 191.28/191.36 ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__set,axiom, % 191.28/191.36 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__eq__conv,axiom, % 191.28/191.36 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2) % 191.28/191.36 <=> ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 191.28/191.36 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__map,axiom, % 191.28/191.36 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_congruent2__implies__congruent,axiom, % 191.28/191.36 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 191.28/191.36 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__inj__on,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 191.28/191.36 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) % 191.28/191.36 => V_xs_2 = V_ys_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inj__on__map__eq__map,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 191.28/191.36 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 191.28/191.36 <=> V_xs_2 = V_ys_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__fun__upd,axiom, % 191.28/191.36 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 191.28/191.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__eq__dom,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,T_b,T_a] : % 191.28/191.36 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 191.28/191.36 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__SomeD,axiom, % 191.28/191.36 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__is__SomeD,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_dom__map__of__conv__image__fst,axiom, % 191.28/191.36 ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inj__on__mapI,axiom, % 191.28/191.36 ! [V_A_2,V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2))) % 191.28/191.36 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_congruent2D,axiom, % 191.28/191.36 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_c,T_b,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y1_2),V_z1_2)),V_r1_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y2_2),V_z2_2)),V_r2_2)) % 191.28/191.36 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__eq__None__iff,axiom, % 191.28/191.36 ! [V_x_2,V_xys_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 191.28/191.36 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_congruentD,axiom, % 191.28/191.36 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2)) % 191.28/191.36 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__map__keys,axiom, % 191.28/191.36 ! [V_m_2,T_b,V_xs_2,T_a] : % 191.28/191.36 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 191.28/191.36 => hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_congruent2__implies__congruent__UN,axiom, % 191.28/191.36 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 191.28/191.36 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 191.28/191.36 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 191.28/191.36 => c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_c,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__equiv__class__inject,axiom, % 191.28/191.36 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 191.28/191.36 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Y_2),V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 => ! [B_y] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 191.28/191.36 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ) ) % 191.28/191.36 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__equiv__class__type2,axiom, % 191.28/191.36 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 191.28/191.36 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 191.28/191.36 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A1_2),V_r1_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A2_2),V_r2_2))) % 191.28/191.36 => ( ! [B_x1] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 191.28/191.36 => ! [B_x2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UN__equiv__class__type,axiom, % 191.28/191.36 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.36 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.36 => ( ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_ran__distinct,axiom, % 191.28/191.36 ! [V_al_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2))) % 191.28/191.36 => c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Integ__def,axiom, % 191.28/191.36 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) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__is__SomeI,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) % 191.28/191.36 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__map,axiom, % 191.28/191.36 ! [V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 191.28/191.36 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 191.28/191.36 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Rep__Integ,axiom, % 191.28/191.36 ! [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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__inject__set,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 191.28/191.36 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2))) % 191.28/191.36 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 191.28/191.36 <=> hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Some__eq__map__of__iff,axiom, % 191.28/191.36 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 191.28/191.36 => ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__eq__Some__iff,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 191.28/191.36 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__map__of__compr,axiom, % 191.28/191.36 ! [V_xs_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 191.28/191.36 => hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b)))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_greaterThanLessThan__upto,axiom, % 191.28/191.36 ! [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)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_weak__map__of__SomeI,axiom, % 191.28/191.36 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2))) % 191.28/191.36 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_CollectI,axiom, % 191.28/191.36 ! [T_a,V_a_2,V_P_2] : % 191.28/191.36 ( hBOOL(hAPP(V_P_2,V_a_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__Collect__conjI,axiom, % 191.28/191.36 ! [V_Q_2,V_P_2,T_a] : % 191.28/191.36 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 191.28/191.36 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__upto,axiom, % 191.28/191.36 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_UNIV__def,axiom, % 191.28/191.36 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fTrue)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__Collect__disjI,axiom, % 191.28/191.36 ! [V_Q_2,V_P_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)))) % 191.28/191.36 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 191.28/191.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insert__Collect,axiom, % 191.28/191.36 ! [V_P_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_empty__def,axiom, % 191.28/191.36 ! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__empty__eq,axiom, % 191.28/191.36 ! [V_P_2,T_a] : % 191.28/191.36 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_empty__Collect__eq,axiom, % 191.28/191.36 ! [V_P_2,T_a] : % 191.28/191.36 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 191.28/191.36 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__disj__eq,axiom, % 191.28/191.36 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__mem__eq,axiom, % 191.28/191.36 ! [V_A_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)) = V_A_2 ). % 191.28/191.36 % 191.28/191.36 fof(fact_mem__Collect__eq,axiom, % 191.28/191.36 ! [V_P_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 191.28/191.36 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_CollectD,axiom, % 191.28/191.36 ! [V_P_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 191.28/191.36 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_CollectE,axiom, % 191.28/191.36 ! [V_P_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 191.28/191.36 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__conj__eq,axiom, % 191.28/191.36 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_vimage__Collect__eq,axiom, % 191.28/191.36 ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__neg__eq,axiom, % 191.28/191.36 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__def,axiom, % 191.28/191.36 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__upto,axiom, % 191.28/191.36 ! [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) ). % 191.28/191.36 % 191.28/191.36 fof(fact_atLeastAtMost__upto,axiom, % 191.28/191.36 ! [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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insert__compr__raw,axiom, % 191.28/191.36 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insert__compr,axiom, % 191.28/191.36 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Un__def,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Int__Collect,axiom, % 191.28/191.36 ! [V_P_2,V_A_2,V_x_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))) % 191.28/191.36 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.36 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Int__def,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__conv__if,axiom, % 191.28/191.36 ! [T_a,V_a_2,V_P_2] : % 191.28/191.36 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 191.28/191.36 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) % 191.28/191.36 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 191.28/191.36 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__conv__if2,axiom, % 191.28/191.36 ! [T_a,V_a_2,V_P_2] : % 191.28/191.36 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 191.28/191.36 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) % 191.28/191.36 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 191.28/191.36 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_singleton__conv,axiom, % 191.28/191.36 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_singleton__conv2,axiom, % 191.28/191.36 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__diff__eq,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__Collect__not,axiom, % 191.28/191.36 ! [V_P_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) % 191.28/191.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insert__def,axiom, % 191.28/191.36 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Compl__eq,axiom, % 191.28/191.36 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_vimage__def,axiom, % 191.28/191.36 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__imp__eq,axiom, % 191.28/191.36 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_dom__def,axiom, % 191.28/191.36 ! [V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_b)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_setsum__setsum__restrict,axiom, % 191.28/191.36 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 191.28/191.36 ( class_Groups_Ocomm__monoid__add(T_c) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 191.28/191.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_c),tc_fun(tc_fun(T_a,tc_HOL_Obool),T_c),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c)),hAPP(c_COMBC(T_a,T_b,T_c),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inj__graph,axiom, % 191.28/191.36 ! [T_b,T_a] : c_Fun_Oinj__on(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Set_OCollect(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool)),hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_if__image__distrib,axiom, % 191.28/191.36 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Collect__all__eq,axiom, % 191.28/191.36 ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_dom__if,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,V_P_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_a),c_If(tc_Option_Ooption(T_b))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_g_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__psubset__def,axiom, % 191.28/191.36 ! [T_a] : c_Wellfounded_Ofinite__psubset(T_a) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_a)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_setsum__restrict__set_H,axiom, % 191.28/191.36 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_setsum__image__gen,axiom, % 191.28/191.36 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 191.28/191.36 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),T_b,T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_a),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_S_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inv__image__def,axiom, % 191.28/191.36 ! [V_f_2,V_r_2,T_a,T_b] : hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_b,T_b)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),T_a),c_COMBB(T_b,tc_prod(T_b,T_b),T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_prod(T_b,T_b)),T_a),c_Product__Type_OPair(T_b,T_b)),V_f_2))),V_f_2)))),V_r_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_atLeastLessThan__upto,axiom, % 191.28/191.36 ! [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)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Image__singleton,axiom, % 191.28/191.36 ! [V_a_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_a))),hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2))),V_r_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_setsum__cases,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 191.28/191.36 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_greaterThanAtMost__upto,axiom, % 191.28/191.36 ! [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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Nitpick_Oprod__def,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_b,T_a] : c_Nitpick_Oprod(T_a,T_b,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_int__ge__less__than__def,axiom, % 191.28/191.36 ! [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)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_int__ge__less__than2__def,axiom, % 191.28/191.36 ! [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)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__Collect__less__nat,axiom, % 191.28/191.36 ! [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)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__Collect__le__nat,axiom, % 191.28/191.36 ! [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)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__Collect__subsets,axiom, % 191.28/191.36 ! [V_A_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 191.28/191.36 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 191.28/191.36 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Pow__def,axiom, % 191.28/191.36 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__M__bounded__by__nat,axiom, % 191.28/191.36 ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 191.28/191.36 ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_nat__seg__image__imp__finite,axiom, % 191.28/191.36 ! [V_n_2,V_f_2,T_a,V_A_2] : % 191.28/191.36 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2))) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_card__less__Suc2,axiom, % 191.28/191.36 ! [V_i_2,V_M_2] : % 191.28/191.36 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 191.28/191.36 => 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))))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_card__less,axiom, % 191.28/191.36 ! [V_i_2,V_M_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 191.28/191.36 => 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) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_card__less__Suc,axiom, % 191.28/191.36 ! [V_i_2,V_M_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 191.28/191.36 => 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))))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_dom__override__on,axiom, % 191.28/191.36 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Fun_Ooverride__on(T_a,tc_Option_Ooption(T_b),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2)))))),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_nat__list__def,axiom, % 191.28/191.36 ! [V_l_2] : % 191.28/191.36 ( c_List_Onat__list(V_l_2) % 191.28/191.36 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_setsum__multicount,axiom, % 191.28/191.36 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 191.28/191.36 => ( ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 191.28/191.36 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 ) % 191.28/191.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_T_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_override__on__apply__notin,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_override__on__apply__in,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_override__on__emptyset,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,T_b,T_a] : c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_f_2 ). % 191.28/191.36 % 191.28/191.36 fof(fact_override__on__def,axiom, % 191.28/191.36 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 191.28/191.36 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) % 191.28/191.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.36 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omin(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omax(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 191.28/191.36 ! [V_x_2,V_A_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__image__set,axiom, % 191.28/191.36 ! [V_f_2,T_b,V_P_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_a)),c_fequal)),V_f_2)))),V_P_2))))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__Collect__bounded__ex,axiom, % 191.28/191.36 ! [V_Q_2,T_b,V_P_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))))) % 191.28/191.36 <=> ! [B_y] : % 191.28/191.36 ( hBOOL(hAPP(V_P_2,B_y)) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_ran__def,axiom, % 191.28/191.36 ! [V_m_2,T_a,T_b] : c_Map_Oran(T_b,T_a,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_a)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Pow__Compl,axiom, % 191.28/191.36 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_a))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_add__Max__commute,axiom, % 191.28/191.36 ! [V_k_2,V_N_2,T_a] : % 191.28/191.36 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.28/191.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_add__Min__commute,axiom, % 191.28/191.36 ! [V_k_2,V_N_2,T_a] : % 191.28/191.36 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 191.28/191.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_sup__Inf2__distrib,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : % 191.28/191.36 ( class_Lattices_Odistrib__lattice(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_sup__Inf1__distrib,axiom, % 191.28/191.36 ! [V_x_2,V_A_2,T_a] : % 191.28/191.36 ( class_Lattices_Odistrib__lattice(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inf__Sup2__distrib,axiom, % 191.28/191.36 ! [V_B_2,V_A_2,T_a] : % 191.28/191.36 ( class_Lattices_Odistrib__lattice(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 191.28/191.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_inf__Sup1__distrib,axiom, % 191.28/191.36 ! [V_x_2,V_A_2,T_a] : % 191.28/191.36 ( class_Lattices_Odistrib__lattice(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 191.28/191.36 ! [V_x_2,V_A_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_setsum__multicount__gen,axiom, % 191.28/191.36 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 191.28/191.36 => ( ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 191.28/191.36 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_s_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) ) % 191.28/191.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equivp__equiv,axiom, % 191.28/191.36 ! [V_A_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 191.28/191.36 <=> c_Equiv__Relations_Oequivp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_A_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_Id__onE,axiom, % 191.28/191.36 ! [V_A_2,V_ca_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) % 191.28/191.36 => ~ ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.36 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_identity__equivp,axiom, % 191.28/191.36 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equivp__def,axiom, % 191.28/191.36 ! [V_R_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 191.28/191.36 <=> ! [B_x,B_y] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 191.28/191.36 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equivp__reflp,axiom, % 191.28/191.36 ! [V_x_2,V_R_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 191.28/191.36 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equivp__symp,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_R_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_equivp__transp,axiom, % 191.28/191.36 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 191.28/191.36 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 191.28/191.36 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_type__definition__Integ,axiom, % 191.28/191.36 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) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__remove1__eq,axiom, % 191.28/191.36 ! [V_x_2,V_xs_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.36 => hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_remove1__commute,axiom, % 191.28/191.36 ! [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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__remove1,axiom, % 191.28/191.36 ! [V_x,V_xs,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.36 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_in__set__remove1,axiom, % 191.28/191.36 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 191.28/191.36 ( V_a_2 != V_b_2 % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2)))) % 191.28/191.36 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_notin__set__remove1,axiom, % 191.28/191.36 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2)))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_remove1__idem,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__remove1__subset,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_type__definition_OAbs__image,axiom, % 191.28/191.36 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 191.28/191.36 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 191.28/191.36 => hAPP(c_Set_Oimage(T_b,T_a,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_type__definition_ORep__range,axiom, % 191.28/191.36 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 191.28/191.36 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 191.28/191.36 => hAPP(c_Set_Oimage(T_a,T_b,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_type__definition_ORep__inject,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 191.28/191.36 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 191.28/191.36 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 191.28/191.36 <=> V_x_2 = V_y_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_type__definition_ORep__inverse,axiom, % 191.28/191.36 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 191.28/191.36 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 191.28/191.36 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_type__definition_OAbs__inject,axiom, % 191.28/191.36 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 191.28/191.36 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 191.28/191.36 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 191.28/191.36 <=> V_x_2 = V_y_2 ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_type__definition_OAbs__inverse,axiom, % 191.28/191.36 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 191.28/191.36 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 191.28/191.36 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_type__definition_ORep,axiom, % 191.28/191.36 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 191.28/191.36 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_sorted__list__of__set__remove,axiom, % 191.28/191.36 ! [V_x_2,V_A_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_ImageE,axiom, % 191.28/191.36 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 191.28/191.36 => ~ ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) % 191.28/191.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_sorted__list__of__set__insert,axiom, % 191.28/191.36 ! [V_x_2,V_A_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__zip__map,axiom, % 191.28/191.36 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ) % 191.28/191.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_remove1__insort,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__zipI1,axiom, % 191.28/191.36 ! [V_ys,T_b,V_xs,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.36 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__zipI2,axiom, % 191.28/191.36 ! [V_xs,T_b,V_ys,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 191.28/191.36 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_fun__left__comm__insort,axiom, % 191.28/191.36 ! [T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insort__left__comm,axiom, % 191.28/191.36 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insort__key__left__comm,axiom, % 191.28/191.36 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 191.28/191.36 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__insort,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( class_Orderings_Olinorder(T_b) % 191.28/191.36 => hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_zip__same__conv__map,axiom, % 191.28/191.36 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_zip__map__fst__snd,axiom, % 191.28/191.36 ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2 ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__insort,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( class_Orderings_Olinorder(T_b) % 191.28/191.36 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))) % 191.28/191.36 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__zip__map,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_g_2,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__zip__map2,axiom, % 191.28/191.36 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_zip__same,axiom, % 191.28/191.36 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2)))) % 191.28/191.36 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 & V_a_2 = V_b_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__zip__leftD,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__zip__rightD,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_in__set__zipE,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 191.28/191.36 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_zip__map__map,axiom, % 191.28/191.36 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_zip__map1,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_zip__map2,axiom, % 191.28/191.36 ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insort__insert__insort__key,axiom, % 191.28/191.36 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 191.28/191.36 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insort__insert__insort,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__insort__insert,axiom, % 191.28/191.36 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 191.28/191.36 ( class_Orderings_Olinorder(T_b) % 191.28/191.36 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.36 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insort__insert__triv,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__insort__insert,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_insort__insert__key__triv,axiom, % 191.28/191.36 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 191.28/191.36 ( class_Orderings_Olinorder(T_a) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 191.28/191.36 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__zip__upd,axiom, % 191.28/191.36 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 191.28/191.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 191.28/191.36 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 191.28/191.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 191.28/191.36 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_2)) % 191.28/191.36 => hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__removeAll__inj__on,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__removeAll,axiom, % 191.28/191.36 ! [V_x,V_xs,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.36 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__eq__imp__length__eq,axiom, % 191.28/191.36 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_2),V_ys_2) % 191.28/191.36 => 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) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_length__map,axiom, % 191.28/191.36 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ). % 191.28/191.36 % 191.28/191.36 fof(fact_neq__if__length__neq,axiom, % 191.28/191.36 ! [V_ys,V_xs,T_a] : % 191.28/191.36 ( 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) % 191.28/191.36 => V_xs != V_ys ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_length__insort,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 191.28/191.36 ( class_Orderings_Olinorder(T_b) % 191.28/191.36 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_length__zip,axiom, % 191.28/191.36 ! [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)) ). % 191.28/191.36 % 191.28/191.36 fof(fact_card__length,axiom, % 191.28/191.36 ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_removeAll__id,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__card,axiom, % 191.28/191.36 ! [V_xs_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.36 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_card__distinct,axiom, % 191.28/191.36 ! [V_xs_2,T_a] : % 191.28/191.36 ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 191.28/191.36 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__zip__inject,axiom, % 191.28/191.36 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 191.28/191.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 191.28/191.36 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 191.28/191.36 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 191.28/191.36 => ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) % 191.28/191.36 => V_ys_2 = V_zs_2 ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__fst__zip,axiom, % 191.28/191.36 ! [V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.36 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__snd__zip,axiom, % 191.28/191.36 ! [V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.36 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__remove1__removeAll,axiom, % 191.28/191.36 ! [V_x,V_xs,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.36 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_length__pos__if__in__set,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_zip__eq__conv,axiom, % 191.28/191.36 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.36 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 191.28/191.36 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2 % 191.28/191.36 & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2 ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__removeAll__inj,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 191.28/191.36 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.36 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__lists__length__eq,axiom, % 191.28/191.36 ! [V_n_2,V_A_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__zip__is__None,axiom, % 191.28/191.36 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.36 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b) % 191.28/191.36 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_map__of__zip__is__Some,axiom, % 191.28/191.36 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_length__remove1,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 191.28/191.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_dom__map__of__zip,axiom, % 191.28/191.36 ! [V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.36 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.36 => c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_finite__lists__length__le,axiom, % 191.28/191.36 ! [V_n_2,V_A_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__removeAll,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_length__sublist,axiom, % 191.28/191.36 ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__zip,axiom, % 191.28/191.36 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_a,T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_list__eq__iff__nth__eq,axiom, % 191.28/191.36 ! [T_a,V_ys_2,V_xs_2] : % 191.28/191.36 ( V_xs_2 = V_ys_2 % 191.28/191.36 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 191.28/191.36 & ! [B_i] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_nth__zip,axiom, % 191.28/191.36 ! [V_ys,T_b,V_xs,T_a,V_i] : % 191.28/191.36 ( 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))) % 191.28/191.36 => ( 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))) % 191.28/191.36 => 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)) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__sublistI,axiom, % 191.28/191.36 ! [V_I_2,V_xs_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.36 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_all__set__conv__all__nth,axiom, % 191.28/191.36 ! [V_P_2,V_xs_2,T_a] : % 191.28/191.36 ( ! [B_x] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.36 <=> ! [B_i] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_nth__map,axiom, % 191.28/191.36 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__conv__nth,axiom, % 191.28/191.36 ! [V_xs_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.36 <=> ! [B_i] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 => ! [B_j] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 => ( B_i != B_j % 191.28/191.36 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_nth__eq__iff__index__eq,axiom, % 191.28/191.36 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 => ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) % 191.28/191.36 <=> V_i_2 = V_j_2 ) ) ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__sublist,axiom, % 191.28/191.36 ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_notin__set__sublistI,axiom, % 191.28/191.36 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_in__set__sublistD,axiom, % 191.28/191.36 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__sublist__subset,axiom, % 191.28/191.36 ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_in__set__conv__nth,axiom, % 191.28/191.36 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.36 <=> ? [B_i] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_nth__mem,axiom, % 191.28/191.36 ! [V_xs_2,T_a,V_n_2] : % 191.28/191.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.36 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 191.28/191.36 % 191.28/191.36 fof(fact_set__conv__nth,axiom, % 191.28/191.36 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 191.28/191.36 % 191.28/191.36 fof(fact_distinct__list__update,axiom, % 191.28/191.36 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 191.28/191.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 191.28/191.37 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__setsum__nth,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__list__update,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__update__nat,axiom, % 191.28/191.37 ! [V_n,V_ns,V_k] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__list__update__neq,axiom, % 191.28/191.37 ! [V_x,V_xs,T_a,V_j,V_i] : % 191.28/191.37 ( V_i != V_j % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__id,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__update,axiom, % 191.28/191.37 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__overwrite,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__swap,axiom, % 191.28/191.37 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 191.28/191.37 ( V_i != V_i_H % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 191.28/191.37 ! [V_ns_2] : % 191.28/191.37 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 <=> ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 191.28/191.37 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip__update,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_update__zip,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__beyond,axiom, % 191.28/191.37 ! [V_x,V_i,V_xs,T_a] : % 191.28/191.37 ( 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)) % 191.28/191.37 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_elem__le__listsum__nat,axiom, % 191.28/191.37 ! [V_ns,V_k] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__0,axiom, % 191.28/191.37 ! [V_xs_2,T_b,T_a] : % 191.28/191.37 ( class_Groups_Omonoid__add(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__addf,axiom, % 191.28/191.37 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__mult__const,axiom, % 191.28/191.37 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] : % 191.28/191.37 ( class_Rings_Osemiring__0(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_ca_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__const__mult,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] : % 191.28/191.37 ( class_Rings_Osemiring__0(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__subtractf,axiom, % 191.28/191.37 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 191.28/191.37 ( class_Groups_Oab__group__add(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__update__subsetI,axiom, % 191.28/191.37 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2)) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__update__subset__insert,axiom, % 191.28/191.37 ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__list__update,axiom, % 191.28/191.37 ! [V_x,V_j,V_xs,T_a,V_i] : % 191.28/191.37 ( 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))) % 191.28/191.37 => ( ( V_i = V_j % 191.28/191.37 => 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 ) % 191.28/191.37 & ( V_i != V_j % 191.28/191.37 => 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) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__same__conv,axiom, % 191.28/191.37 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.37 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 191.28/191.37 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__list__update__eq,axiom, % 191.28/191.37 ! [V_x,V_xs,T_a,V_i] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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 ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__abs,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2)))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_uminus__listsum__map,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.37 ( class_Groups_Oab__group__add(T_a) % 191.28/191.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct__listsum__conv__Setsum,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.37 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__update__memI,axiom, % 191.28/191.37 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_n_2),V_x_2)))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 191.28/191.37 ! [V_f_2,V_xs_2,T_a,T_b] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.37 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 191.28/191.37 ! [V_l_2,V_k_2,V_f_2,T_a] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 191.28/191.37 ! [V_j_2,V_i_2,V_f_2,T_a] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__triv,axiom, % 191.28/191.37 ! [V_xs_2,V_r_2,T_b,T_a] : % 191.28/191.37 ( class_Rings_Osemiring__1(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__map__remove1,axiom, % 191.28/191.37 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_select__weight__member,axiom, % 191.28/191.37 ! [V_s_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_pick__member,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_i_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_select__weight__def,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_pick__same,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_l_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.37 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_l_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_scomp__apply,axiom, % 191.28/191.37 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_scomp__scomp,axiom, % 191.28/191.37 ! [V_h_2,V_g_2,V_f_2,T_f,T_e,T_b,T_d,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_d,T_b),hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,tc_prod(T_c,T_d)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,T_b),V_f_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),T_e),c_Product__Type_Oscomp(T_f,T_c,T_d,T_b)),V_g_2)),V_h_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 191.28/191.37 ! [V_m_2,V_n_2] : % 191.28/191.37 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 191.28/191.37 <=> V_n_2 = V_m_2 ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 191.28/191.37 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.37 % 191.28/191.37 fof(fact_times__code__numeral__code,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_scomp__Pair,axiom, % 191.28/191.37 ! [V_x_2,T_c,T_b,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_c,tc_prod(T_b,T_c)),V_x_2),c_Product__Type_OPair(T_b,T_c)) = V_x_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_Pair__scomp,axiom, % 191.28/191.37 ! [V_f_2,V_x_2,T_b,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_a,T_b),hAPP(c_Product__Type_OPair(T_c,T_a),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zero__code__numeral__def,axiom, % 191.28/191.37 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_scomp__def,axiom, % 191.28/191.37 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_one__code__numeral__def,axiom, % 191.28/191.37 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_less__code__numeral__code,axiom, % 191.28/191.37 ! [V_m_2,V_n_2] : % 191.28/191.37 ( 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))) % 191.28/191.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_code__numeral_Oof__nat__inject,axiom, % 191.28/191.37 ! [V_y_2,V_x_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 191.28/191.37 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 191.28/191.37 <=> V_x_2 = V_y_2 ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_number__of__code__numeral__def,axiom, % 191.28/191.37 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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_plus__code__numeral__code,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_less__eq__code__numeral__code,axiom, % 191.28/191.37 ! [V_m_2,V_n_2] : % 191.28/191.37 ( 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))) % 191.28/191.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_subtract__code__numeral__code,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_code__numeral__not__eq__zero,axiom, % 191.28/191.37 ! [V_i_2] : % 191.28/191.37 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 191.28/191.37 <=> 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)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_scomp__unfold,axiom, % 191.28/191.37 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(V_f_2,V_x_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_iterate_Osimps,axiom, % 191.28/191.37 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 191.28/191.37 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.37 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2) ) % 191.28/191.37 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.37 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_a,tc_prod(T_b,T_a)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_b,T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Nitpick_Osetsum_H__def,axiom, % 191.28/191.37 ! [V_f_2,V_A_2,T_a,T_b] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.37 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_someI,axiom, % 191.28/191.37 ! [T_a,V_x_2,V_P_2] : % 191.28/191.37 ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.37 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_tfl__some,axiom, % 191.28/191.37 ! [T_a,B_P] : % 191.28/191.37 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 191.28/191.37 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_someI__ex,axiom, % 191.28/191.37 ! [T_a,V_P_2] : % 191.28/191.37 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 191.28/191.37 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_some__eq__ex,axiom, % 191.28/191.37 ! [T_a,V_P_2] : % 191.28/191.37 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 191.28/191.37 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_some__eq__trivial,axiom, % 191.28/191.37 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_some__sym__eq__trivial,axiom, % 191.28/191.37 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_exE__some,axiom, % 191.28/191.37 ! [T_a,V_ca_2,V_P_2] : % 191.28/191.37 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 191.28/191.37 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 191.28/191.37 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Nitpick_Ocard_H__def,axiom, % 191.28/191.37 ! [V_A_2,T_a] : % 191.28/191.37 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_LeastM__def,axiom, % 191.28/191.37 ! [V_P_2,V_m_2,T_a,T_b] : % 191.28/191.37 ( class_Orderings_Oord(T_b) % 191.28/191.37 => c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_LeastM__nat__lemma,axiom, % 191.28/191.37 ! [V_m_2,T_a,V_k_2,V_P_2] : % 191.28/191.37 ( hBOOL(hAPP(V_P_2,V_k_2)) % 191.28/191.37 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 191.28/191.37 & ! [B_y] : % 191.28/191.37 ( hBOOL(hAPP(V_P_2,B_y)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y))) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_LeastM__nat__le,axiom, % 191.28/191.37 ! [T_a,V_m_2,V_x_2,V_P_2] : % 191.28/191.37 ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_split__paired__Eps,axiom, % 191.28/191.37 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Eps__split__eq,axiom, % 191.28/191.37 ! [V_y_2,V_x_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Eps__split,axiom, % 191.28/191.37 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_GreatestM__def,axiom, % 191.28/191.37 ! [V_P_2,V_m_2,T_a,T_b] : % 191.28/191.37 ( class_Orderings_Oord(T_b) % 191.28/191.37 => hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_select__def,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : c_Random_Oselect(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_LeastM__natI,axiom, % 191.28/191.37 ! [V_m_2,T_a,V_k_2,V_P_2] : % 191.28/191.37 ( hBOOL(hAPP(V_P_2,V_k_2)) % 191.28/191.37 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nat__of__of__nat,axiom, % 191.28/191.37 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 191.28/191.37 % 191.28/191.37 fof(fact_of__nat__nat__of,axiom, % 191.28/191.37 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 191.28/191.37 % 191.28/191.37 fof(fact_nat__of__inverse,axiom, % 191.28/191.37 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 191.28/191.37 % 191.28/191.37 fof(fact_code__numeral_Onat__of__inject,axiom, % 191.28/191.37 ! [V_y_2,V_x_2] : % 191.28/191.37 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 191.28/191.37 <=> V_x_2 = V_y_2 ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 191.28/191.37 ! [V_l_2,V_k_2] : % 191.28/191.37 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 191.28/191.37 <=> V_k_2 = V_l_2 ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_type__definition__code__numeral,axiom, % 191.28/191.37 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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_less__code__numeral__def,axiom, % 191.28/191.37 ! [V_m_2,V_n_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 191.28/191.37 <=> 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nat__of,axiom, % 191.28/191.37 ! [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)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nat__of__number,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_int__of__def,axiom, % 191.28/191.37 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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_less__eq__code__numeral__def,axiom, % 191.28/191.37 ! [V_m_2,V_n_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 191.28/191.37 <=> 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nat__of__code,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nat__of__aux__def,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Suc__code__numeral__def,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_minus__code__numeral__def,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_of__nat__inverse,axiom, % 191.28/191.37 ! [V_y_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 191.28/191.37 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_plus__code__numeral__def,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_div__code__numeral__def,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_times__code__numeral__def,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_mod__code__numeral__def,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_code__numeral__decr,axiom, % 191.28/191.37 ! [V_k] : % 191.28/191.37 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_select__weigth__select,axiom, % 191.28/191.37 ! [T_a,V_xs_2] : % 191.28/191.37 ( V_xs_2 != c_List_Olist_ONil(T_a) % 191.28/191.37 => c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_a,V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Greatest__def,axiom, % 191.28/191.37 ! [T_a] : % 191.28/191.37 ( class_Orderings_Oord(T_a) % 191.28/191.37 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__nonempty,axiom, % 191.28/191.37 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update_Osimps_I1_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__code_I1_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__simps_I1_J,axiom, % 191.28/191.37 ! [T_a] : % 191.28/191.37 ( class_Groups_Omonoid__add(T_a) % 191.28/191.37 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_List_Oset_Osimps_I1_J,axiom, % 191.28/191.37 ! [T_a] : hAPP(c_List_Oset(T_a),c_List_Olist_ONil(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__empty2,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__empty,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__0__conv,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Osize_I3_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sublist__nil,axiom, % 191.28/191.37 ! [V_A_2,T_a] : c_List_Osublist(T_a,c_List_Olist_ONil(T_a),V_A_2) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct_Osimps_I1_J,axiom, % 191.28/191.37 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_remove1_Osimps_I1_J,axiom, % 191.28/191.37 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldr_Osimps_I1_J,axiom, % 191.28/191.37 ! [V_a_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_a_2) = V_a_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip_Osimps_I1_J,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip__Nil,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_insort__not__Nil,axiom, % 191.28/191.37 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 191.28/191.37 ( class_Orderings_Olinorder(T_b) % 191.28/191.37 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_removeAll_Osimps_I1_J,axiom, % 191.28/191.37 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Nil__is__map__conv,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.37 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map_Osimps_I1_J,axiom, % 191.28/191.37 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__is__Nil__conv,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.37 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__of__Cons__code_I1_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_upto__empty,axiom, % 191.28/191.37 ! [V_i,V_j] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 191.28/191.37 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sorted__list__of__set__empty,axiom, % 191.28/191.37 ! [T_a] : % 191.28/191.37 ( class_Orderings_Olinorder(T_a) % 191.28/191.37 => c_List_Olinorder__class_Osorted__list__of__set(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sublist__empty,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__of_Osimps_I1_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__greater__0__conv,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.37 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_select,axiom, % 191.28/191.37 ! [V_s_2,T_a,V_xs_2] : % 191.28/191.37 ( V_xs_2 != c_List_Olist_ONil(T_a) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_pick_Osimps,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a,V_i] : % 191.28/191.37 ( ( 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))) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( ~ 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))) % 191.28/191.37 => 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))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__list__update,axiom, % 191.28/191.37 ! [V_x,V_k,T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => ( ( 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)) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 191.28/191.37 & ( 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)) % 191.28/191.37 => 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) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Osimps_I2_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Osimps_I3_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last_Osimps,axiom, % 191.28/191.37 ! [V_x,T_a,V_xs] : % 191.28/191.37 ( ( V_xs = c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 191.28/191.37 & ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__ConsR,axiom, % 191.28/191.37 ! [V_x,T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__ConsL,axiom, % 191.28/191.37 ! [V_x,T_a,V_xs] : % 191.28/191.37 ( V_xs = c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_insort__key_Osimps_I1_J,axiom, % 191.28/191.37 ! [V_x_2,V_f_2,T_a,T_b] : % 191.28/191.37 ( class_Orderings_Olinorder(T_b) % 191.28/191.37 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip__Cons__Cons,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_removeAll_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_xs,T_a,V_y,V_x] : % 191.28/191.37 ( ( V_x = V_y % 191.28/191.37 => 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) ) % 191.28/191.37 & ( V_x != V_y % 191.28/191.37 => 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)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_insort__key_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 191.28/191.37 ( class_Orderings_Olinorder(T_a) % 191.28/191.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 191.28/191.37 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 191.28/191.37 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldr_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Oinject,axiom, % 191.28/191.37 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2) % 191.28/191.37 <=> ( V_a_2 = V_a_H_2 % 191.28/191.37 & V_list_2 = V_list_H_2 ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_not__Cons__self2,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 191.28/191.37 % 191.28/191.37 fof(fact_not__Cons__self,axiom, % 191.28/191.37 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 191.28/191.37 % 191.28/191.37 fof(fact_remove1_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_xs,T_a,V_y,V_x] : % 191.28/191.37 ( ( V_x = V_y % 191.28/191.37 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 191.28/191.37 & ( V_x != V_y % 191.28/191.37 => 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)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_impossible__Cons,axiom, % 191.28/191.37 ! [V_x,V_ys,V_xs,T_a] : % 191.28/191.37 ( 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))) % 191.28/191.37 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__subset__Cons,axiom, % 191.28/191.37 ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__ConsD,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) % 191.28/191.37 => ( V_y_2 = V_x_2 % 191.28/191.37 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_List_Oset_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__simps_I2_J,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a] : % 191.28/191.37 ( class_Groups_Omonoid__add(T_a) % 191.28/191.37 => 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)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__code_I2_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__code_I3_J,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__Cons__Suc,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__Cons__0,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth_Osimps,axiom, % 191.28/191.37 ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__map,axiom, % 191.28/191.37 ! [V_f_2,T_b,T_a,V_xs_2] : % 191.28/191.37 ( V_xs_2 != c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_a,V_xs_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 191.28/191.37 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__of__Cons__code_I2_J,axiom, % 191.28/191.37 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 191.28/191.37 ( ( V_l = V_k % 191.28/191.37 => 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) ) % 191.28/191.37 & ( V_l != V_k % 191.28/191.37 => 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) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__in__set,axiom, % 191.28/191.37 ! [T_a,V_as_2] : % 191.28/191.37 ( V_as_2 != c_List_Olist_ONil(T_a) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Osize_I4_J,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__Cons_H,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a,V_n] : % 191.28/191.37 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 191.28/191.37 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_select__weight__cons__zero,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sublist__singleton,axiom, % 191.28/191.37 ! [V_x_2,T_a,V_A_2] : % 191.28/191.37 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 191.28/191.37 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 191.28/191.37 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = c_List_Olist_ONil(T_a) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__Cons__number__of,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a,V_v] : % 191.28/191.37 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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 ) % 191.28/191.37 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__of_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__conv__nth,axiom, % 191.28/191.37 ! [T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__Cons__def,axiom, % 191.28/191.37 ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip__Cons,axiom, % 191.28/191.37 ! [V_ys_2,V_y_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_a,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),T_a),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_a),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),c_List_Ozip(T_a,T_b)),V_ys_2))),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Osimps_I5_J,axiom, % 191.28/191.37 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Osimps_I4_J,axiom, % 191.28/191.37 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),c_List_Olist_ONil(T_b)) = V_f1_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_upto_Osimps,axiom, % 191.28/191.37 ! [V_j,V_i] : % 191.28/191.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 191.28/191.37 => 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)) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 191.28/191.37 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_upto__rec__number__of,axiom, % 191.28/191.37 ! [V_n,V_m] : % 191.28/191.37 ( ( 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))) % 191.28/191.37 => 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))) ) % 191.28/191.37 & ( ~ 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))) % 191.28/191.37 => 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) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__Cons__sing__Nil,axiom, % 191.28/191.37 ! [V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_a,tc_List_Olist(T_a),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_A_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip__Cons1,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_b,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_b),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)))),hAPP(c_List_Ozip(T_a,T_b),V_xs_2))),V_ys_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_upto_Opsimps,axiom, % 191.28/191.37 ! [V_j_2,V_i_2] : % 191.28/191.37 ( 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))) % 191.28/191.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 191.28/191.37 => 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)) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 191.28/191.37 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_anamorph_Osimps,axiom, % 191.28/191.37 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 191.28/191.37 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.37 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2) ) % 191.28/191.37 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.37 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listset_Osimps_I1_J,axiom, % 191.28/191.37 ! [T_a] : c_List_Olistset(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__Cons,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = c_List_Oset__Cons(T_a,hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__Nil1,axiom, % 191.28/191.37 ! [V_r_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.37 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__Nil2,axiom, % 191.28/191.37 ! [V_r_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.37 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel_ONil,axiom, % 191.28/191.37 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__eq__len,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.37 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__mono,axiom, % 191.28/191.37 ! [V_s_2,V_r_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_List_Olistrel(T_a,V_s_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel_OCons,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__Nil,axiom, % 191.28/191.37 ! [V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listset_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_As_2,V_A_2,T_a] : c_List_Olistset(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_a,V_A_2,c_List_Olistset(T_a,V_As_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__iff__nth,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.37 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 191.28/191.37 & ! [B_n] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_n))),V_r_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_upto_Opinduct,axiom, % 191.28/191.37 ! [V_P_2,V_a1_2,V_a0_2] : % 191.28/191.37 ( 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))) % 191.28/191.37 => ( ! [B_i,B_j] : % 191.28/191.37 ( 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))) % 191.28/191.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 191.28/191.37 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) ) % 191.28/191.37 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 191.28/191.37 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sublist__Cons,axiom, % 191.28/191.37 ! [V_A_2,V_l_2,V_x_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_a)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olist_ONil(T_a))),c_List_Osublist(T_a,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__eq__Cons__conv,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) % 191.28/191.37 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 191.28/191.37 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 191.28/191.37 | ? [B_ys_H] : % 191.28/191.37 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 191.28/191.37 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Cons__eq__append__conv,axiom, % 191.28/191.37 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) % 191.28/191.37 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 191.28/191.37 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 191.28/191.37 | ? [B_ys_H] : % 191.28/191.37 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 191.28/191.37 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append1__eq__conv,axiom, % 191.28/191.37 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) % 191.28/191.37 <=> ( V_xs_2 = V_ys_2 % 191.28/191.37 & V_x_2 = V_y_2 ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__append,axiom, % 191.28/191.37 ! [V_xs,T_a,V_ys] : % 191.28/191.37 ( ( V_ys = c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 191.28/191.37 & ( V_ys != c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__Nil,axiom, % 191.28/191.37 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 191.28/191.37 % 191.28/191.37 fof(fact_Nil__is__append__conv,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 191.28/191.37 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 191.28/191.37 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__Nil2,axiom, % 191.28/191.37 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 191.28/191.37 % 191.28/191.37 fof(fact_self__append__conv,axiom, % 191.28/191.37 ! [V_ys_2,T_a,V_xs_2] : % 191.28/191.37 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 191.28/191.37 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_self__append__conv2,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_ys_2] : % 191.28/191.37 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__is__Nil__conv,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 191.28/191.37 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 191.28/191.37 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__self__conv,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 191.28/191.37 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__self__conv2,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__appendR,axiom, % 191.28/191.37 ! [V_xs,T_a,V_ys] : % 191.28/191.37 ( V_ys != c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__appendL,axiom, % 191.28/191.37 ! [V_xs,T_a,V_ys] : % 191.28/191.37 ( V_ys = c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_eq__Nil__appendI,axiom, % 191.28/191.37 ! [T_a,V_ys,V_xs] : % 191.28/191.37 ( V_xs = V_ys % 191.28/191.37 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__append,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_removeAll__append,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldr__append,axiom, % 191.28/191.37 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_a_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__eq__appendI,axiom, % 191.28/191.37 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 191.28/191.37 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 191.28/191.37 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__same__eq,axiom, % 191.28/191.37 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2) % 191.28/191.37 <=> V_ys_2 = V_zs_2 ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_same__append__eq,axiom, % 191.28/191.37 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2) % 191.28/191.37 <=> V_ys_2 = V_zs_2 ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__eq__append__conv2,axiom, % 191.28/191.37 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2) % 191.28/191.37 <=> ? [B_us] : % 191.28/191.37 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 191.28/191.37 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 191.28/191.37 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 191.28/191.37 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__assoc,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__of__append,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__append,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip__append,axiom, % 191.28/191.37 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 191.28/191.37 ( 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) % 191.28/191.37 => ( 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) % 191.28/191.37 => 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)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__append,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__append,axiom, % 191.28/191.37 ! [V_ys,V_xs,T_a] : % 191.28/191.37 ( class_Groups_Omonoid__add(T_a) % 191.28/191.37 => 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)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__Cons,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Cons__eq__appendI,axiom, % 191.28/191.37 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 191.28/191.37 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 191.28/191.37 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__append__length,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__append__length__plus,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__append1,axiom, % 191.28/191.37 ! [V_x,V_ys,V_xs,T_a,V_i] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__length,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_remove1__append,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)),V_ys_2) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oremove1(T_a,V_x_2,V_ys_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__snoc,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct__append,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 191.28/191.37 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.37 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 191.28/191.37 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__append,axiom, % 191.28/191.37 ! [V_ys,V_xs,T_a,V_n] : % 191.28/191.37 ( ( 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))) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( ~ 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))) % 191.28/191.37 => 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))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__update__append,axiom, % 191.28/191.37 ! [V_x,V_ys,V_xs,T_a,V_n] : % 191.28/191.37 ( ( 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))) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( ~ 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))) % 191.28/191.37 => 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)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sublist__append,axiom, % 191.28/191.37 ! [V_A_2,V_l_H_2,V_l_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Osublist(T_a,V_l_2,V_A_2)),c_List_Osublist(T_a,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_l_2)))),V_A_2)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Cons__in__lex,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2))) % 191.28/191.37 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.37 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) % 191.28/191.37 | ( V_x_2 = V_y_2 % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2))) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrelp__listrel__eq,axiom, % 191.28/191.37 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 191.28/191.37 ( c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2) % 191.28/191.37 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrelp_Oequations_I2_J,axiom, % 191.28/191.37 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 191.28/191.37 ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2)) % 191.28/191.37 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 191.28/191.37 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrelp_OCons,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 191.28/191.37 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 191.28/191.37 => c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrelp_ONil,axiom, % 191.28/191.37 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrelp_Oequations_I1_J,axiom, % 191.28/191.37 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Nil2__notin__lex,axiom, % 191.28/191.37 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Nil__notin__lex,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lenlex__conv,axiom, % 191.28/191.37 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_List_Olex(T_a,V_r_2)))))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lenlex__def,axiom, % 191.28/191.37 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_a),c_Wellfounded_Oless__than,c_List_Olex(T_a,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_COMBI(tc_List_Olist(T_a)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upds__append1,axiom, % 191.28/191.37 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 191.28/191.37 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__Cons2,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.37 => ~ ! [B_x,B_xs] : % 191.28/191.37 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2)) % 191.28/191.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__add__upds,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__upds(T_a,T_b,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upds__Nil2,axiom, % 191.28/191.37 ! [V_as_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,c_List_Olist_ONil(T_b)) = V_m_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upds__Nil1,axiom, % 191.28/191.37 ! [V_bs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,c_List_Olist_ONil(T_a),V_bs_2) = V_m_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upds__apply__nontin,axiom, % 191.28/191.37 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => hAPP(c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_fun__upds__append2__drop,axiom, % 191.28/191.37 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.37 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_fun__upds__append__drop,axiom, % 191.28/191.37 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.37 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upds__Cons,axiom, % 191.28/191.37 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upds__list__update2__drop,axiom, % 191.28/191.37 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_i_2)) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 191.28/191.37 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upds__twist,axiom, % 191.28/191.37 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 191.28/191.37 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 191.28/191.37 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_restrict__map__upds,axiom, % 191.28/191.37 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_D_2)) % 191.28/191.37 => c_Map_Orestrict__map(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_a),V_xs_2))),V_xs_2,V_ys_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__Cons1,axiom, % 191.28/191.37 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.37 => ~ ! [B_y,B_ys] : % 191.28/191.37 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2)) % 191.28/191.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__iff__zip,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.37 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 191.28/191.37 & ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),B_x)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Powp__def,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 191.28/191.37 <=> ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 191.28/191.37 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_INFI__bool__eq,axiom, % 191.28/191.37 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_ball__UNIV,axiom, % 191.28/191.37 ! [V_P_2,T_a] : % 191.28/191.37 ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 191.28/191.37 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.37 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_ball__empty,axiom, % 191.28/191.37 ! [V_P_2,T_a,B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 191.28/191.37 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Collect__ball__eq,axiom, % 191.28/191.37 ! [V_P_2,V_A_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_congruent__def,axiom, % 191.28/191.37 ! [V_f_2,V_r_2,T_b,T_a] : % 191.28/191.37 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 191.28/191.37 <=> ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_INTER__def,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_member(T_a))),V_B_2)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Inf__Sup,axiom, % 191.28/191.37 ! [V_A_2,T_a] : % 191.28/191.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.37 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_a))))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sup__Inf,axiom, % 191.28/191.37 ! [V_A_2,T_a] : % 191.28/191.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.37 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a)))))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__eq__iff__zip__eq,axiom, % 191.28/191.37 ! [T_a,V_ys_2,V_xs_2] : % 191.28/191.37 ( V_xs_2 = V_ys_2 % 191.28/191.37 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 191.28/191.37 & ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_WT__bodies__def,axiom, % 191.28/191.37 ( c_Com_OWT__bodies % 191.28/191.37 <=> ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__append__left__rightI,axiom, % 191.28/191.37 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2)))),c_List_Olexord(T_a,V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_snoc__listrel1__snoc__iff,axiom, % 191.28/191.37 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.37 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.37 & V_x_2 = V_y_2 ) % 191.28/191.37 | ( V_xs_2 = V_ys_2 % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_triples__valid__Suc,axiom, % 191.28/191.37 ! [V_n_2,V_ts_2,T_a] : % 191.28/191.37 ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 191.28/191.37 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 191.28/191.37 => ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 191.28/191.37 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_hoare__valids__def,axiom, % 191.28/191.37 ! [V_ts_2,V_G_2,T_a] : % 191.28/191.37 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) % 191.28/191.37 <=> ! [B_n] : % 191.28/191.37 ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_G_2)) % 191.28/191.37 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 191.28/191.37 => ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 191.28/191.37 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel1__mono,axiom, % 191.28/191.37 ! [V_s_2,V_r_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel1(T_a,V_s_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Inter__eq,axiom, % 191.28/191.37 ! [V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))),c_member(T_a)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel1I2,axiom, % 191.28/191.37 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel1__eq__len,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.37 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_not__listrel1__Nil,axiom, % 191.28/191.37 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_not__Nil__listrel1,axiom, % 191.28/191.37 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__listrel1I,axiom, % 191.28/191.37 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.37 & V_us_2 = V_vs_2 ) % 191.28/191.37 | ( V_xs_2 = V_ys_2 % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__Nil__right,axiom, % 191.28/191.37 ! [V_r_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__append__leftI,axiom, % 191.28/191.37 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Cons__listrel1__Cons,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.37 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.37 & V_xs_2 = V_ys_2 ) % 191.28/191.37 | ( V_x_2 = V_y_2 % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel1I1,axiom, % 191.28/191.37 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__lex,axiom, % 191.28/191.37 ! [V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2))) % 191.28/191.37 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 191.28/191.37 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel1I,axiom, % 191.28/191.37 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.37 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2)) % 191.28/191.37 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__cons__cons,axiom, % 191.28/191.37 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) % 191.28/191.37 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.37 | ( V_a_2 = V_b_2 % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel1__iff__update,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.37 <=> ? [B_y,B_n] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2)) % 191.28/191.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.37 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__take__index__conv,axiom, % 191.28/191.37 ! [V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 191.28/191.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))) % 191.28/191.37 & hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),V_y_2) = V_x_2 ) % 191.28/191.37 | ? [B_i] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))) % 191.28/191.37 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_in__set__takeD,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__take__subset,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sublist__upt__eq__take,axiom, % 191.28/191.37 ! [V_n_2,V_l_2,T_a] : c_List_Osublist(T_a,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_l_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__Nil,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__0,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__eq__Nil,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 191.28/191.37 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__map,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__zip,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__take,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct__take,axiom, % 191.28/191.37 ! [V_i,V_xs,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.37 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__take,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__take,axiom, % 191.28/191.37 ! [V_xs,T_a,V_n,V_i] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__Suc__Cons,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__all,axiom, % 191.28/191.37 ! [V_n,V_xs,T_a] : % 191.28/191.37 ( 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)) % 191.28/191.37 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__take__subset__set__take,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__append,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__1__Cons,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__Cons,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otake(T_a)),V_xs_2)),V_n_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__Cons_H,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a,V_n] : % 191.28/191.37 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_dom__map__upds,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))),c_Map_Odom(T_a,T_b,V_m_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__Cons__number__of,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a,V_v] : % 191.28/191.37 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upd__upds__conv__if,axiom, % 191.28/191.37 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 191.28/191.37 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) % 191.28/191.37 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) % 191.28/191.37 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__Suc__conv__app__nth,axiom, % 191.28/191.37 ! [V_xs,T_a,V_i] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel1E,axiom, % 191.28/191.37 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.37 => ~ ! [B_x,B_y] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) % 191.28/191.37 => ! [B_us,B_vs] : % 191.28/191.37 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 191.28/191.37 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__append__leftD,axiom, % 191.28/191.37 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) % 191.28/191.37 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate1__def,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : hAPP(c_List_Orotate1(T_a),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)))),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel1__subset__listrel,axiom, % 191.28/191.37 ! [V_r_H_2,V_r_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) % 191.28/191.37 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel(T_a,V_r_H_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__rotate1,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate1__is__Nil__conv,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__on__Id__on,axiom, % 191.28/191.37 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct1__rotate,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 191.28/191.37 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__rotate1,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__on__empty,axiom, % 191.28/191.37 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__on__Un,axiom, % 191.28/191.37 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.37 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 191.28/191.37 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__on__Int,axiom, % 191.28/191.37 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.37 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 191.28/191.37 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__onD,axiom, % 191.28/191.37 ! [V_a_2,V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__onD1,axiom, % 191.28/191.37 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__onD2,axiom, % 191.28/191.37 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__simps,axiom, % 191.28/191.37 ! [V_xs,V_x,T_b,T_a] : % 191.28/191.37 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 191.28/191.37 & 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate1__length01,axiom, % 191.28/191.37 ! [V_xs,T_a] : % 191.28/191.37 ( 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))) % 191.28/191.37 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__on__def_H,axiom, % 191.28/191.37 ! [V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.37 <=> ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x)) ) % 191.28/191.37 & ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_reflp__def,axiom, % 191.28/191.37 ! [V_r_2,T_a] : % 191.28/191.37 ( c_Predicate_Oreflp(T_a,V_r_2) % 191.28/191.37 <=> c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexn__length,axiom, % 191.28/191.37 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2))) % 191.28/191.37 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 191.28/191.37 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_reflpE,axiom, % 191.28/191.37 ! [V_x_2,V_r_2,T_a] : % 191.28/191.37 ( c_Predicate_Oreflp(T_a,V_r_2) % 191.28/191.37 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexn_Osimps_I1_J,axiom, % 191.28/191.37 ! [V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lex__def,axiom, % 191.28/191.37 ! [V_r_2,T_a] : c_List_Olex(T_a,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_a,V_r_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexn_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_n_2,V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_a,tc_List_Olist(T_a)),tc_prod(T_a,tc_List_Olist(T_a))),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_Product__Type_Omap__pair(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),c_Wellfounded_Olex__prod(T_a,tc_List_Olist(T_a),V_r_2,hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2)))))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_upd__conv__take__nth__drop,axiom, % 191.28/191.37 ! [V_a,V_xs,T_a,V_i] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair__imageI,axiom, % 191.28/191.37 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_R_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)),V_R_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__take__drop__id,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__take,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__drop,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_in__set__dropD,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__drop__subset,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__Nil,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair_Ocompositionality,axiom, % 191.28/191.37 ! [V_prod_2,V_i_2,V_h_2,T_f,T_e,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_e,T_a,T_f,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_e,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_g_2),V_i_2)),V_prod_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair__compose,axiom, % 191.28/191.37 ! [V_g2_2,V_g1_2,T_f,V_f2_2,V_f1_2,T_e,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_f2_2,V_g2_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair_Ocomp,axiom, % 191.28/191.37 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_b,T_a,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g_2),V_i_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_snd__comp__map__pair,axiom, % 191.28/191.37 ! [V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_c),T_c,tc_prod(T_a,T_b),c_Product__Type_Osnd(T_d,T_c)),c_Product__Type_Omap__pair(T_a,T_d,T_b,T_c,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_c,tc_prod(T_a,T_b),V_g_2),c_Product__Type_Osnd(T_a,T_b)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_fst__comp__map__pair,axiom, % 191.28/191.37 ! [V_g_2,V_f_2,T_b,T_a,T_d,T_c] : hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,tc_prod(T_a,T_b),c_Product__Type_Ofst(T_c,T_d)),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,tc_prod(T_a,T_b),V_f_2),c_Product__Type_Ofst(T_a,T_b)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__map,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__zip,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__drop,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__0,axiom, % 191.28/191.37 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair__ident,axiom, % 191.28/191.37 ! [V_z_2,T_b,T_a] : hAPP(c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)),V_z_2) = V_z_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct__drop,axiom, % 191.28/191.37 ! [V_i,V_xs,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.37 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__drop,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_fst__map__pair,axiom, % 191.28/191.37 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_snd__prod__fun,axiom, % 191.28/191.37 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Omap__pair(T_c,T_b,T_d,T_a,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__Suc__Cons,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__1__Cons,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__via__drop,axiom, % 191.28/191.37 ! [V_ys,V_y,V_xs,V_n,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 191.28/191.37 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair__simp,axiom, % 191.28/191.37 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__drop__subset__set__drop,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__all,axiom, % 191.28/191.37 ! [V_n,V_xs,T_a] : % 191.28/191.37 ( 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)) % 191.28/191.37 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__eq__Nil,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 191.28/191.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_n_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__append,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__eq__conv__conj,axiom, % 191.28/191.37 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 191.28/191.37 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) % 191.28/191.37 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_last__drop,axiom, % 191.28/191.37 ! [V_xs,T_a,V_n] : % 191.28/191.37 ( 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))) % 191.28/191.37 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__Cons,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Odrop(T_a)),V_xs_2),V_n_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair__def,axiom, % 191.28/191.37 ! [V_g_2,V_f_2,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),T_a),c_COMBB(T_d,tc_prod(T_c,T_d),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_a),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_g_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__Cons_H,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a,V_n] : % 191.28/191.37 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__drop,axiom, % 191.28/191.37 ! [V_xs,T_a,V_i,V_n] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__eq__append__conv__if,axiom, % 191.28/191.37 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) % 191.28/191.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) % 191.28/191.37 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) % 191.28/191.37 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) % 191.28/191.37 => ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 % 191.28/191.37 & hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair__surj,axiom, % 191.28/191.37 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 191.28/191.37 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.37 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 191.28/191.37 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__drop_H,axiom, % 191.28/191.37 ! [V_xs,T_a,V_i] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__Cons__number__of,axiom, % 191.28/191.37 ! [V_xs,V_x,T_a,V_v] : % 191.28/191.37 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 => 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) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__add,axiom, % 191.28/191.37 ! [V_xs,T_a,V_j,V_i] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip__append2,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_zip__append1,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_id__take__nth__drop,axiom, % 191.28/191.37 ! [V_xs,T_a,V_i] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__hd__drop,axiom, % 191.28/191.37 ! [V_xs,T_a,V_n] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_prod__fun__imageE,axiom, % 191.28/191.37 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2))) % 191.28/191.37 => ~ ! [B_x,B_y] : % 191.28/191.37 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 191.28/191.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_R_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_hd_Osimps,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_hd__map,axiom, % 191.28/191.37 ! [V_f_2,T_b,T_a,V_xs_2] : % 191.28/191.37 ( V_xs_2 != c_List_Olist_ONil(T_a) % 191.28/191.37 => hAPP(c_List_Ohd(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_a),V_xs_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_hd__append2,axiom, % 191.28/191.37 ! [V_ys,T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_hd__append,axiom, % 191.28/191.37 ! [V_ys,T_a,V_xs] : % 191.28/191.37 ( ( V_xs = c_List_Olist_ONil(T_a) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_hd__in__set,axiom, % 191.28/191.37 ! [T_a,V_xs_2] : % 191.28/191.37 ( V_xs_2 != c_List_Olist_ONil(T_a) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_hd__conv__nth,axiom, % 191.28/191.37 ! [T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_hd__drop__conv__nth,axiom, % 191.28/191.37 ! [V_n,T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => ( 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))) % 191.28/191.37 => 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) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate1__hd__tl,axiom, % 191.28/191.37 ! [T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_hd__rotate__conv__nth,axiom, % 191.28/191.37 ! [V_n,T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__tl,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_tl__drop,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__rotate,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_tl_Osimps_I1_J,axiom, % 191.28/191.37 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__is__Nil__conv,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,T_a] : % 191.28/191.37 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 191.28/191.37 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__map,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(c_List_Orotate(T_a,V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__tl,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Otl(T_b),V_xs_2)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__rotate,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct__rotate,axiom, % 191.28/191.37 ! [V_xs_2,V_n_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 191.28/191.37 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct__tl,axiom, % 191.28/191.37 ! [V_xs,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.37 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__rotate,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_tl_Osimps_I2_J,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate1__rotate__swap,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_tl__append2,axiom, % 191.28/191.37 ! [V_ys,T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__tl,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__conv__mod,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__Suc,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__Suc,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_tl__append,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,hAPP(c_List_Otl(T_a),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a)),V_ys_2))),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__add,axiom, % 191.28/191.37 ! [V_n_2,V_m_2,T_a] : c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orotate(T_a,V_m_2)),c_List_Orotate(T_a,V_n_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__id,axiom, % 191.28/191.37 ! [V_xs,T_a,V_n] : % 191.28/191.37 ( 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) % 191.28/191.37 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__length01,axiom, % 191.28/191.37 ! [V_n,V_xs,T_a] : % 191.28/191.37 ( 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))) % 191.28/191.37 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__tl,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_tl__take,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__Suc,axiom, % 191.28/191.37 ! [V_n,T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate__drop__take,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_fold1__set,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 191.28/191.37 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 191.28/191.37 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Otl(T_a),V_xs_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Osize_I2_J,axiom, % 191.28/191.37 ! [V_list_2,V_a_2,V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldr__conv__foldl,axiom, % 191.28/191.37 ! [V_a_2,V_xs_2,T_a] : % 191.28/191.37 ( class_Groups_Oab__semigroup__add(T_a) % 191.28/191.37 => c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_start__le__sum,axiom, % 191.28/191.37 ! [V_ns_2,V_n_2,V_m_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldl__Cons,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldl__absorb0,axiom, % 191.28/191.37 ! [V_zs_2,V_x_2,T_a] : % 191.28/191.37 ( class_Groups_Omonoid__add(T_a) % 191.28/191.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldl__assoc,axiom, % 191.28/191.37 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 191.28/191.37 ( class_Groups_Osemigroup__add(T_a) % 191.28/191.37 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldl__map,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_c,V_a_2,V_g_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,T_a)),T_a),c_COMBB(T_b,T_a,T_c)),V_g_2)),V_f_2),V_a_2),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldl__Nil,axiom, % 191.28/191.37 ! [V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),c_List_Olist_ONil(T_b)) = V_a_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldl__append,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2)),V_ys_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__size__map,axiom, % 191.28/191.37 ! [V_xs_2,V_g_2,T_b,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_b,hAPP(c_Fun_Ocomp(T_a,tc_Nat_Onat,T_b,V_f_2),V_g_2),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__foldl,axiom, % 191.28/191.37 ! [T_a] : % 191.28/191.37 ( class_Groups_Omonoid__add(T_a) % 191.28/191.37 => c_List_Omonoid__add__class_Olistsum(T_a) = c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldl__foldr1__lemma,axiom, % 191.28/191.37 ! [V_xs_2,V_a_2,T_a] : % 191.28/191.37 ( class_Groups_Omonoid__add(T_a) % 191.28/191.37 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_foldl__foldr1,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( class_Groups_Omonoid__add(T_a) % 191.28/191.37 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2) = c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sum__eq__0__conv,axiom, % 191.28/191.37 ! [V_ns_2,V_m_2] : % 191.28/191.37 ( 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) % 191.28/191.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.37 & ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 191.28/191.37 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list_Osize_I1_J,axiom, % 191.28/191.37 ! [V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.37 % 191.28/191.37 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 191.28/191.37 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 191.28/191.37 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 191.28/191.37 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sup__set__fold,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.37 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Inf__set__fold,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.37 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sup__fin__set__fold,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( class_Lattices_Olattice(T_a) % 191.28/191.37 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Inf__fin__set__fold,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( class_Lattices_Olattice(T_a) % 191.28/191.37 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Min__fin__set__fold,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( class_Orderings_Olinorder(T_a) % 191.28/191.37 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Max__fin__set__fold,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( class_Orderings_Olinorder(T_a) % 191.28/191.37 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_min__max_OInf__fin__set__fold,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( class_Orderings_Olinorder(T_a) % 191.28/191.37 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_min__max_OSup__fin__set__fold,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( class_Orderings_Olinorder(T_a) % 191.28/191.37 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_SUPR__set__fold,axiom, % 191.28/191.37 ! [V_f_2,V_xs_2,T_b,T_a] : % 191.28/191.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_INFI__set__fold,axiom, % 191.28/191.37 ! [V_f_2,V_xs_2,T_b,T_a] : % 191.28/191.37 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 191.28/191.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_f_2)),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__size__estimation,axiom, % 191.28/191.37 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__size__estimation_H,axiom, % 191.28/191.37 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__upds__fold__map__upd,axiom, % 191.28/191.37 ! [V_vs_2,V_ks_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),T_b))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b))))),c_Option_Ooption_OSome(T_b))),V_m_2),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ks_2),V_vs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_elem__le__sum,axiom, % 191.28/191.37 ! [V_ns_2,V_n_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 191.28/191.37 => 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))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__size__conv__listsum,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_a,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_image__split__eq__Sigma,axiom, % 191.28/191.37 ! [V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Set_Oimage(T_c,tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_Oimage(T_c,T_b,V_g_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_a),c_Set_Ovimage(T_c,T_a,V_f_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_A_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__append__rightI,axiom, % 191.28/191.37 ! [V_r_2,V_x_2,T_a,V_y_2] : % 191.28/191.37 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_SigmaI,axiom, % 191.28/191.37 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_UNIV__Times__UNIV,axiom, % 191.28/191.37 ! [T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_SigmaE2,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 191.28/191.37 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.37 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_SigmaD2,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_SigmaD1,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_mem__Sigma__iff,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 191.28/191.37 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_finite__cartesian__product,axiom, % 191.28/191.37 ! [V_B_2,T_b,V_A_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__Un__distrib2,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Times__Un__distrib1,axiom, % 191.28/191.37 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__Un__distrib1,axiom, % 191.28/191.37 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__Diff__distrib2,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Times__Diff__distrib1,axiom, % 191.28/191.37 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__Diff__distrib1,axiom, % 191.28/191.37 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Compl__Times__UNIV1,axiom, % 191.28/191.37 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Compl__Times__UNIV2,axiom, % 191.28/191.37 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_card__cartesian__product,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Id__on__subset__Times,axiom, % 191.28/191.37 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId__on(T_a,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_equiv__type,axiom, % 191.28/191.37 ! [V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Times__eq__cancel2,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 191.28/191.37 => ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) % 191.28/191.37 <=> V_A_2 = V_B_2 ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__empty1,axiom, % 191.28/191.37 ! [V_B_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Times__empty,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_b,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) % 191.28/191.37 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.37 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__empty2,axiom, % 191.28/191.37 ! [V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__Union,axiom, % 191.28/191.37 ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__Int__distrib1,axiom, % 191.28/191.37 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Times__Int__distrib1,axiom, % 191.28/191.37 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__Int__distrib2,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_setsum__cartesian__product,axiom, % 191.28/191.37 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_setprod__cartesian__product,axiom, % 191.28/191.37 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__mult(T_a) % 191.28/191.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_card__cartesian__product__singleton,axiom, % 191.28/191.37 ! [V_A_2,V_x_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Times__subset__cancel2,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)))) % 191.28/191.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Image__subset,axiom, % 191.28/191.37 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_C_2)),V_B_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_finite__cartesian__productD1,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 191.28/191.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_finite__cartesian__productD2,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_b,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 191.28/191.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_SetCompr__Sigma__eq,axiom, % 191.28/191.37 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),V_Q_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Collect__split,axiom, % 191.28/191.37 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_OCollect(T_b),V_Q_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_fst__image__times,axiom, % 191.28/191.37 ! [V_A_2,T_b,T_a,V_B_2] : % 191.28/191.37 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.37 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.37 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.37 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = V_A_2 ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_snd__image__times,axiom, % 191.28/191.37 ! [V_B_2,T_b,T_a,V_A_2] : % 191.28/191.37 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.37 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.37 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.37 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = V_B_2 ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair__surj__on,axiom, % 191.28/191.37 ! [V_B_H_2,V_B_2,V_g_2,T_c,T_d,V_A_H_2,V_A_2,V_f_2,T_a,T_b] : % 191.28/191.37 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 191.28/191.37 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 191.28/191.37 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_H_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_H_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_swap__product,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_prod(T_a,T_b)),hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__on__def,axiom, % 191.28/191.37 ! [V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 191.28/191.37 & ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_insert__times__insert,axiom, % 191.28/191.37 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_finite__equiv__class,axiom, % 191.28/191.37 ! [V_X_2,V_r_2,V_A_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair__inj__on,axiom, % 191.28/191.37 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 191.28/191.37 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 191.28/191.37 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 191.28/191.37 => c_Fun_Oinj__on(tc_prod(T_a,T_c),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_a,T_b,T_c,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_UN__Times__distrib,axiom, % 191.28/191.37 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_b,T_a,T_d,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_c,T_d),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_c),c_Product__Type_OSigma(T_a,T_b)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),T_d),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_F_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Sigma__def,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_finite__quotient,axiom, % 191.28/191.37 ! [V_r_2,V_A_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_vimage__Times,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,tc_prod(T_b,T_c),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_b,T_a,c_Product__Type_Ofst(T_b,T_c)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_c,T_a,c_Product__Type_Osnd(T_b,T_c)),V_f_2)),V_B_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_setsum__mult__setsum__if__inj,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 191.28/191.37 ( class_Rings_Osemiring__0(T_c) % 191.28/191.37 => ( c_Fun_Oinj__on(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) % 191.28/191.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 191.28/191.37 ! [V_A_2,V_I_2,T_b,T_a] : % 191.28/191.37 ? [B_f] : % 191.28/191.37 ( c_Fun_Oinj__on(T_a,tc_prod(T_b,T_a),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) % 191.28/191.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_prod(T_b,T_a),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_I_2),V_A_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_surj__id,axiom, % 191.28/191.37 ! [T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_image__id,axiom, % 191.28/191.37 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_id__o,axiom, % 191.28/191.37 ! [V_g_2,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_g_2) = V_g_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_o__id,axiom, % 191.28/191.37 ! [V_f_2,T_b,T_a] : hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_f_2),c_Fun_Oid(T_a)) = V_f_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_o__eq__id__dest,axiom, % 191.28/191.37 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 191.28/191.37 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_ca_2) % 191.28/191.37 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_List_Omap_Oid,axiom, % 191.28/191.37 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_List_Omap_Oidentity,axiom, % 191.28/191.37 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_rotate0,axiom, % 191.28/191.37 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_folding_Oempty,axiom, % 191.28/191.37 ! [V_F_2,V_f_2,T_b,T_a] : % 191.28/191.37 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 191.28/191.37 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_inj__on__id,axiom, % 191.28/191.37 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Option_Omap_Oid,axiom, % 191.28/191.37 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Option_Omap_Oidentity,axiom, % 191.28/191.37 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_apfst__id,axiom, % 191.28/191.37 ! [T_b,T_a] : c_Product__Type_Oapfst(T_a,T_a,T_b,c_Fun_Oid(T_a)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_id__def,axiom, % 191.28/191.37 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 191.28/191.37 % 191.28/191.37 fof(fact_apsnd__id,axiom, % 191.28/191.37 ! [T_a,T_b] : c_Product__Type_Oapsnd(T_b,T_b,T_a,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_id__apply,axiom, % 191.28/191.37 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 191.28/191.37 % 191.28/191.37 fof(fact_vimage__id,axiom, % 191.28/191.37 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 191.28/191.37 % 191.28/191.37 fof(fact_of__int__eq__id,axiom, % 191.28/191.37 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair_Oidentity,axiom, % 191.28/191.37 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__pair_Oid,axiom, % 191.28/191.37 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_Fun_Oid(T_a),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_apfst__def,axiom, % 191.28/191.37 ! [V_f_2,T_b,T_c,T_a] : c_Product__Type_Oapfst(T_a,T_c,T_b,V_f_2) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_b,V_f_2,c_Fun_Oid(T_b)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_apsnd__def,axiom, % 191.28/191.37 ! [V_f_2,T_a,T_c,T_b] : c_Product__Type_Oapsnd(T_b,T_c,T_a,V_f_2) = c_Product__Type_Omap__pair(T_a,T_a,T_b,T_c,c_Fun_Oid(T_a),V_f_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_split__Pair,axiom, % 191.28/191.37 ! [T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_setsum__reindex__id,axiom, % 191.28/191.37 ! [V_B_2,V_f_2,T_a,T_b] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_b) % 191.28/191.37 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 191.28/191.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_setprod__reindex__id,axiom, % 191.28/191.37 ! [V_B_2,V_f_2,T_a,T_b] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__mult(T_b) % 191.28/191.37 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 191.28/191.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_setprod__Sigma,axiom, % 191.28/191.37 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__mult(T_c) % 191.28/191.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 191.28/191.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_refl__onI,axiom, % 191.28/191.37 ! [V_A_2,V_r_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 191.28/191.37 => ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) % 191.28/191.37 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_setsum__Sigma,axiom, % 191.28/191.37 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__add(T_c) % 191.28/191.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 191.28/191.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_fold__image__Sigma,axiom, % 191.28/191.37 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 191.28/191.37 ( class_Groups_Ocomm__monoid__mult(T_c) % 191.28/191.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 191.28/191.37 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(T_a,T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),T_a),c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c))),V_g_2)),c_Groups_Oone__class_Oone(T_c))),V_B_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,tc_prod(T_a,T_b),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_g_2)),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_card__SigmaI,axiom, % 191.28/191.37 ! [V_B_2,T_b,V_A_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 191.28/191.37 => hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),V_B_2)),V_A_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_finite__SigmaI,axiom, % 191.28/191.37 ! [V_B_2,T_b,V_A_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.37 => ( ! [B_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 191.28/191.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__subset,axiom, % 191.28/191.37 ! [V_A_2,V_r_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2))))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__Nil__left,axiom, % 191.28/191.37 ! [V_r_2,V_y_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 191.28/191.37 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lists_ONil,axiom, % 191.28/191.37 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lists__mono,axiom, % 191.28/191.37 ! [V_B_2,V_A_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olists(T_a,V_A_2)),c_List_Olists(T_a,V_B_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__in__lists__conv,axiom, % 191.28/191.37 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2))) % 191.28/191.37 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lists__UNIV,axiom, % 191.28/191.37 ! [T_a] : c_List_Olists(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_equiv__listrel,axiom, % 191.28/191.37 ! [V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.37 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listrel__refl__on,axiom, % 191.28/191.37 ! [V_r_2,V_A_2,T_a] : % 191.28/191.37 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.37 => c_Relation_Orefl__on(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_Cons__in__lists__iff,axiom, % 191.28/191.37 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2))) % 191.28/191.37 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_in__lists__conv__set,axiom, % 191.28/191.37 ! [V_A_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 191.28/191.37 <=> ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lists__eq__set,axiom, % 191.28/191.37 ! [V_A_2,T_a] : c_List_Olists(T_a,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lists__empty,axiom, % 191.28/191.37 ! [T_a] : c_List_Olists(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_listsum__mono,axiom, % 191.28/191.37 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 191.28/191.37 ( ( class_Groups_Omonoid__add(T_b) % 191.28/191.37 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 191.28/191.37 => ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_g_2),V_xs_2)))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 191.28/191.37 ! [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))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__irreflexive,axiom, % 191.28/191.37 ! [V_y_2,V_r_2,T_a] : % 191.28/191.37 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) % 191.28/191.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lexord__linear,axiom, % 191.28/191.37 ! [V_y_2,V_x_2,V_r_2,T_a] : % 191.28/191.37 ( ! [B_a,B_b] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2)) % 191.28/191.37 | B_a = B_b % 191.28/191.37 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2)) ) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 191.28/191.37 | V_x_2 = V_y_2 % 191.28/191.37 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_lists_Osimps,axiom, % 191.28/191.37 ! [V_A_2,V_a_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 191.28/191.37 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 191.28/191.37 | ? [B_a,B_l] : % 191.28/191.37 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 191.28/191.37 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_list__size__pointwise,axiom, % 191.28/191.37 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 191.28/191.37 ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_a,V_g_2,V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_butlast__take,axiom, % 191.28/191.37 ! [V_xs,T_a,V_n] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__take__lemma,axiom, % 191.28/191.37 ! [V_ys,V_xs,T_a,V_k] : % 191.28/191.37 ( 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))) % 191.28/191.37 => ( 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))) % 191.28/191.37 => ( ! [B_i] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 191.28/191.37 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 191.28/191.37 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__butlast,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Obutlast(T_b,V_xs_2)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_butlast_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_x,T_a,V_xs] : % 191.28/191.37 ( ( V_xs = c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 191.28/191.37 & ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_in__set__butlastD,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_butlast_Osimps_I1_J,axiom, % 191.28/191.37 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_butlast__drop,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_drop__butlast,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_butlast__append,axiom, % 191.28/191.37 ! [V_xs,T_a,V_ys] : % 191.28/191.37 ( ( V_ys = c_List_Olist_ONil(T_a) % 191.28/191.37 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 191.28/191.37 & ( V_ys != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct__butlast,axiom, % 191.28/191.37 ! [T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.37 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_in__set__butlast__appendI,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 191.28/191.37 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_butlast__snoc,axiom, % 191.28/191.37 ! [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 ). % 191.28/191.37 % 191.28/191.37 fof(fact_take__butlast,axiom, % 191.28/191.37 ! [V_xs,T_a,V_n] : % 191.28/191.37 ( 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))) % 191.28/191.37 => 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) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__butlast,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_butlast__conv__take,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_butlast__list__update,axiom, % 191.28/191.37 ! [V_x,V_xs,T_a,V_k] : % 191.28/191.37 ( ( 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)) % 191.28/191.37 => 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) ) % 191.28/191.37 & ( 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)) % 191.28/191.37 => 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) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_append__butlast__last__id,axiom, % 191.28/191.37 ! [T_a,V_xs] : % 191.28/191.37 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.37 => 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 ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_snoc__eq__iff__butlast,axiom, % 191.28/191.37 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 191.28/191.37 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2 % 191.28/191.37 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 191.28/191.37 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 191.28/191.37 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_transpose__aux__max,axiom, % 191.28/191.37 ! [V_xss_2,T_b,V_xs_2,T_a] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_partition__set,axiom, % 191.28/191.37 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 191.28/191.37 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 191.28/191.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_partition__filter__conv,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__map,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_partition__filter2,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__id__conv,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.37 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 191.28/191.37 <=> ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__empty__conv,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.37 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 191.28/191.37 <=> ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__append,axiom, % 191.28/191.37 ! [V_ys_2,V_xs_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter_Osimps_I1_J,axiom, % 191.28/191.37 ! [V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sum__length__filter__compl,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_removeAll__filter__not__eq,axiom, % 191.28/191.37 ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_removeAll__filter__not,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 191.28/191.37 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.37 => hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__insort__triv,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 191.28/191.37 ( class_Orderings_Olinorder(T_b) % 191.28/191.37 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.37 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__filter,axiom, % 191.28/191.37 ! [V_xs_2,V_Q_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_Q_2)),V_P_2)),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__remove1,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_Q_2,T_a] : hAPP(c_List_Ofilter(T_a,V_Q_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_remove1__filter__not,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 191.28/191.37 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.37 => c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_distinct__filter,axiom, % 191.28/191.37 ! [V_P_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.37 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_partition__filter1,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 191.28/191.37 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.37 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) % 191.28/191.37 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.37 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__filter__le,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__is__subset,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__filter,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)))),V_P_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__filter__map,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__filter__less,axiom, % 191.28/191.37 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.37 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_set__minus__filter__out,axiom, % 191.28/191.37 ! [V_y_2,V_xs_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_partition__P,axiom, % 191.28/191.37 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 191.28/191.37 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 191.28/191.37 => ( ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 191.28/191.37 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.37 & ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 191.28/191.37 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_partition_Osimps_I1_J,axiom, % 191.28/191.37 ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_filter__in__sublist,axiom, % 191.28/191.37 ! [V_s_2,V_xs_2,T_a] : % 191.28/191.37 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.37 => hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_a,V_xs_2,V_s_2) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_partition_Osimps_I2_J,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__filter__conv__card,axiom, % 191.28/191.37 ! [V_xs_2,V_p_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_a),V_xs_2))))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__filter__def,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),V_f_2)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_a)))),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_transpose__max__length,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_transpose__map__map,axiom, % 191.28/191.37 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),c_List_Otranspose(T_b,V_xs_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_transpose_Osimps_I2_J,axiom, % 191.28/191.37 ! [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) ). % 191.28/191.37 % 191.28/191.37 fof(fact_transpose_Osimps_I1_J,axiom, % 191.28/191.37 ! [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)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_transpose__empty,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : % 191.28/191.37 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 191.28/191.37 <=> ! [B_x] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.37 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__filter__simps_I2_J,axiom, % 191.28/191.37 ! [V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__of__filter__in,axiom, % 191.28/191.37 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 191.28/191.37 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) % 191.28/191.37 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 191.28/191.37 => hAPP(hAPP(c_Map_Omap__of(T_b,T_a),hAPP(c_List_Ofilter(tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) ) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__filter__simps_I1_J,axiom, % 191.28/191.37 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_sublist__shift__lemma__Suc,axiom, % 191.28/191.37 ! [V_is_2,V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_a,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_a,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ). % 191.28/191.37 % 191.28/191.37 fof(fact_select__weigth__drop__zero,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_pick__drop__zero,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : c_Random_Opick(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_a,V_xs_2) ). % 191.28/191.37 % 191.28/191.37 fof(fact_nth__transpose,axiom, % 191.28/191.37 ! [V_xs_2,T_a,V_i_2] : % 191.28/191.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 191.28/191.37 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)) ) ). % 191.28/191.37 % 191.28/191.37 fof(fact_length__transpose,axiom, % 191.28/191.37 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 191.28/191.37 % 191.28/191.37 fof(fact_map__filter__map__filter,axiom, % 191.28/191.37 ! [V_xs_2,V_P_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = c_List_Omap__filter(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),T_b),c_If(tc_Option_Ooption(T_a))),V_P_2)),hAPP(hAPP(c_COMBB(T_a,tc_Option_Ooption(T_a),T_b),c_Option_Ooption_OSome(T_a)),V_f_2))),c_Option_Ooption_ONone(T_a)),V_xs_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_insort__key__remove1,axiom, % 191.28/191.38 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 191.28/191.38 => ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 % 191.28/191.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sublist__def,axiom, % 191.28/191.38 ! [V_A_2,V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted_ONil,axiom, % 191.28/191.38 ! [T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__single,axiom, % 191.28/191.38 ! [V_x,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__same,axiom, % 191.28/191.38 ! [V_xs_2,V_g_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__map__same,axiom, % 191.28/191.38 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__filter,axiom, % 191.28/191.38 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__butlast,axiom, % 191.28/191.38 ! [V_xs,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__insort__insert__key,axiom, % 191.28/191.38 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_drop__upt,axiom, % 191.28/191.38 ! [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) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__drop,axiom, % 191.28/191.38 ! [V_n,V_xs,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_hd__upt,axiom, % 191.28/191.38 ! [V_j,V_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__take,axiom, % 191.28/191.38 ! [V_n,V_xs,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__distinct__set__unique,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 191.28/191.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 191.28/191.38 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 191.28/191.38 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted_Oequations_I1_J,axiom, % 191.28/191.38 ! [T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__0,axiom, % 191.28/191.38 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__insort,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) % 191.28/191.38 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__upto,axiom, % 191.28/191.38 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__upt,axiom, % 191.28/191.38 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__remove1,axiom, % 191.28/191.38 ! [V_a,V_xs,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__list__of__set__range,axiom, % 191.28/191.38 ! [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) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__upt,axiom, % 191.28/191.38 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__insort__insert,axiom, % 191.28/191.38 ! [V_x_2,V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__conv__Cons,axiom, % 191.28/191.38 ! [V_j,V_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => 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)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__rec,axiom, % 191.28/191.38 ! [V_j,V_i] : % 191.28/191.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => 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)) ) % 191.28/191.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__tl,axiom, % 191.28/191.38 ! [V_xs,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_map__Suc__upt,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__map__remove1,axiom, % 191.28/191.38 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__insort__key,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2))) % 191.28/191.38 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_atLeastLessThan__upt,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_set__upt,axiom, % 191.28/191.38 ! [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) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__conv__Nil,axiom, % 191.28/191.38 ! [V_i,V_j] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 191.28/191.38 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__eq__Nil__conv,axiom, % 191.28/191.38 ! [V_j_2,V_i_2] : % 191.28/191.38 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 191.28/191.38 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__many,axiom, % 191.28/191.38 ! [V_zs,V_y,V_x,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 191.28/191.38 => 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))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__many__eq,axiom, % 191.28/191.38 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))) % 191.28/191.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 191.28/191.38 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__add__eq__append,axiom, % 191.28/191.38 ! [V_k,V_j,V_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => 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))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__Suc__append,axiom, % 191.28/191.38 ! [V_j,V_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => 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))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__Suc,axiom, % 191.28/191.38 ! [V_j,V_i] : % 191.28/191.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => 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))) ) % 191.28/191.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_take__upt,axiom, % 191.28/191.38 ! [V_n,V_m,V_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) % 191.28/191.38 => 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)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__upt,axiom, % 191.28/191.38 ! [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) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__Cons,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 191.28/191.38 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 & ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__append,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 191.28/191.38 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 191.28/191.38 & ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => ! [B_xa] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__rec__number__of,axiom, % 191.28/191.38 ! [V_n,V_m] : % 191.28/191.38 ( ( 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))) % 191.28/191.38 => 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))) ) % 191.28/191.38 & ( ~ 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))) % 191.28/191.38 => 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) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_upt__eq__Cons__conv,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 191.28/191.38 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 191.28/191.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 191.28/191.38 & V_i_2 = V_x_2 % 191.28/191.38 & 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 ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_last__upt,axiom, % 191.28/191.38 ! [V_j,V_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => 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)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_filter__insort,axiom, % 191.28/191.38 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 191.28/191.38 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_map__nth,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_atLeastAtMost__upt,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_atLeast__upt,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 191.28/191.38 ! [V_n_2,V_m_2,V_f_2,T_a] : % 191.28/191.38 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 191.28/191.38 ! [V_n_2,V_m_2,V_f_2,T_a] : % 191.28/191.38 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_nth__upt,axiom, % 191.28/191.38 ! [V_j,V_k,V_i] : % 191.28/191.38 ( 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)) % 191.28/191.38 => 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) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_greaterThanAtMost__upt,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted_Oequations_I2_J,axiom, % 191.28/191.38 ! [V_a1_2,V_a2_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 191.28/191.38 <=> ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 191.28/191.38 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_greaterThanLessThan__upt,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_nth__map__upt,axiom, % 191.28/191.38 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 191.28/191.38 ( 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))) % 191.28/191.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__list__of__set,axiom, % 191.28/191.38 ! [V_A_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.38 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 191.28/191.38 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 191.28/191.38 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_atMost__upto,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_insort__remove1,axiom, % 191.28/191.38 ! [V_xs_2,V_a_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__equals__nth__mono,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 <=> ! [B_j] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => ! [B_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j))) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__nth__mono,axiom, % 191.28/191.38 ! [V_j,V_i,V_xs,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => ( 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))) % 191.28/191.38 => 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))) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_map__sorted__distinct__set__unique,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 191.28/191.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 191.28/191.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 191.28/191.38 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 191.28/191.38 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sublist__shift__lemma,axiom, % 191.28/191.38 ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose__rectangle,axiom, % 191.28/191.38 ! [V_n_2,T_a,V_xs_2] : % 191.28/191.38 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 191.28/191.38 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.28/191.38 => ( ! [B_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 191.28/191.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),B_i)) = V_n_2 ) % 191.28/191.38 => c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose_Opsimps_I2_J,axiom, % 191.28/191.38 ! [V_xss_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2))) % 191.28/191.38 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)) = c_List_Otranspose(T_a,V_xss_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose_Opsimps_I1_J,axiom, % 191.28/191.38 ! [T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) % 191.28/191.38 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose__column,axiom, % 191.28/191.38 ! [V_i_2,V_xs_2,T_a] : % 191.28/191.38 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 191.28/191.38 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose__aux__filter__head,axiom, % 191.28/191.38 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_inj__on__rev,axiom, % 191.28/191.38 ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev_Osimps_I1_J,axiom, % 191.28/191.38 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Nil__is__rev__conv,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 191.28/191.38 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__is__Nil__conv,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 191.28/191.38 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_singleton__rev__conv,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2) % 191.28/191.38 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__singleton__conv,axiom, % 191.28/191.38 ! [V_x_2,V_xs_2,T_a] : % 191.28/191.38 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) % 191.28/191.38 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat__conv__foldl,axiom, % 191.28/191.38 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__concat,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__map,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__foldl__cons,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_foldl__conv__concat,axiom, % 191.28/191.38 ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__rev,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 191.28/191.38 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__append,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat__append,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__rev,axiom, % 191.28/191.38 ! [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) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__is__rev__conv,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 191.28/191.38 <=> V_xs_2 = V_ys_2 ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__swap,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 191.28/191.38 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__rev__ident,axiom, % 191.28/191.38 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsum__rev,axiom, % 191.28/191.38 ! [V_xs,T_a] : % 191.28/191.38 ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.38 => 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) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_set__rev,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_zip__rev,axiom, % 191.28/191.38 ! [V_ys,T_b,V_xs,T_a] : % 191.28/191.38 ( 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) % 191.28/191.38 => 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)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__filter,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_foldl__foldr,axiom, % 191.28/191.38 ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_foldr__foldl,axiom, % 191.28/191.38 ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat_Osimps_I1_J,axiom, % 191.28/191.38 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat_Osimps_I2_J,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat__eq__Nil__conv,axiom, % 191.28/191.38 ! [V_xss_2,T_a] : % 191.28/191.38 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 191.28/191.38 <=> ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 191.28/191.38 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Nil__eq__concat__conv,axiom, % 191.28/191.38 ! [V_xss_2,T_a] : % 191.28/191.38 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 191.28/191.38 <=> ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 191.28/191.38 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_map__concat,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_filter__concat,axiom, % 191.28/191.38 ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev_Osimps_I2_J,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__eq__Cons__iff,axiom, % 191.28/191.38 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 191.28/191.38 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 191.28/191.38 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__concat,axiom, % 191.28/191.38 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_set__concat,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_hd__rev,axiom, % 191.28/191.38 ! [T_a,V_xs] : % 191.28/191.38 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.38 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_last__rev,axiom, % 191.28/191.38 ! [T_a,V_xs] : % 191.28/191.38 ( V_xs != c_List_Olist_ONil(T_a) % 191.28/191.38 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__transpose,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__drop,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__take,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rotate__rev,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose_Osimps_I3_J,axiom, % 191.28/191.38 ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__nth,axiom, % 191.28/191.38 ! [V_xs,T_a,V_n] : % 191.28/191.38 ( 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))) % 191.28/191.38 => 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))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat__eq__concat__iff,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 191.28/191.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 191.28/191.38 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 191.28/191.38 <=> V_xs_2 = V_ys_2 ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat__injective,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 191.28/191.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 191.28/191.38 => V_xs_2 = V_ys_2 ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rev__update,axiom, % 191.28/191.38 ! [V_y,V_xs,T_a,V_k] : % 191.28/191.38 ( 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))) % 191.28/191.38 => 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) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat__map__singleton,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__rev__nth__mono,axiom, % 191.28/191.38 ! [V_j,V_i,V_xs,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 191.28/191.38 => ( 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))) % 191.28/191.38 => 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))) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_foldr__max__sorted,axiom, % 191.28/191.38 ! [V_y_2,V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 191.28/191.38 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 191.28/191.38 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 191.28/191.38 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 191.28/191.38 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose_Opsimps_I3_J,axiom, % 191.28/191.38 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2))) % 191.28/191.38 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__transpose__sorted,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 191.28/191.38 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 191.28/191.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 191.28/191.38 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 191.28/191.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose__column__length,axiom, % 191.28/191.38 ! [V_i_2,V_xs_2,T_a] : % 191.28/191.38 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 191.28/191.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose__aux__filter__tail,axiom, % 191.28/191.38 ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_nth__nth__transpose__sorted,axiom, % 191.28/191.38 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 191.28/191.38 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)))) % 191.28/191.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transpose__transpose,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 191.28/191.38 => c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),V_xs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 191.28/191.38 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__map,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_zip__takeWhile__fst,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_zip__takeWhile__snd,axiom, % 191.28/191.38 ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_set__takeWhileD,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__eq__all__conv,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 191.28/191.38 <=> ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__takeWhile__le,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__eq__take,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__takeWhile,axiom, % 191.28/191.38 ! [V_P_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__tail,axiom, % 191.28/191.38 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 191.28/191.38 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile_Osimps_I2_J,axiom, % 191.28/191.38 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 191.28/191.38 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) % 191.28/191.38 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__takeWhile,axiom, % 191.28/191.38 ! [V_P_2,V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile_Osimps_I1_J,axiom, % 191.28/191.38 ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.38 % 191.28/191.38 fof(fact_return__list__def,axiom, % 191.28/191.38 ! [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) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__append1,axiom, % 191.28/191.38 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_nth__length__takeWhile,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__nth,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 191.28/191.38 => hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_map__upds__def,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__not__last,axiom, % 191.28/191.38 ! [T_a,V_xs_2] : % 191.28/191.38 ( V_xs_2 != c_List_Olist_ONil(T_a) % 191.28/191.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.38 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 191.28/191.38 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 191.28/191.38 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2),V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transfer__nat__int__list__return__embed,axiom, % 191.28/191.38 ! [V_l] : % 191.28/191.38 ( c_List_Onat__list(V_l) % 191.28/191.38 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__remdups__concat,axiom, % 191.28/191.38 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__remdups,axiom, % 191.28/191.38 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__remdups__leq,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remdups__map__remdups,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_set__remdups,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remdups_Osimps_I1_J,axiom, % 191.28/191.38 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remdups__eq__nil__right__iff,axiom, % 191.28/191.38 ! [V_x_2,T_a] : % 191.28/191.38 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 191.28/191.38 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remdups__eq__nil__iff,axiom, % 191.28/191.38 ! [V_x_2,T_a] : % 191.28/191.38 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 191.28/191.38 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__remdups,axiom, % 191.28/191.38 ! [V_l,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__remdups__id,axiom, % 191.28/191.38 ! [V_xs,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.38 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remdups__id__iff__distinct,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 191.28/191.38 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__remdups__eq,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 191.28/191.38 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remdups__remdups,axiom, % 191.28/191.38 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remdups__filter,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remove1__remdups,axiom, % 191.28/191.38 ! [V_x,V_xs,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.38 => 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)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_embed__list__def,axiom, % 191.28/191.38 ! [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) ). % 191.28/191.38 % 191.28/191.38 fof(fact_remdups_Osimps_I2_J,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2) ) % 191.28/191.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__remdups__card__conv,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 191.28/191.38 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 191.28/191.38 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),c_List_Oremdups(T_a,V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__neq__rev,axiom, % 191.28/191.38 ! [V_x_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile__neq__rev,axiom, % 191.28/191.38 ! [V_x_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__dropWhile__le,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__dropWhile,axiom, % 191.28/191.38 ! [V_P_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile_Osimps_I2_J,axiom, % 191.28/191.38 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 191.28/191.38 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2) ) % 191.28/191.38 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__dropWhile,axiom, % 191.28/191.38 ! [V_P_2,V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile_Osimps_I1_J,axiom, % 191.28/191.38 ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile__eq__Nil__conv,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 191.28/191.38 <=> ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__dropWhile__id,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_hd__dropWhile,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 191.28/191.38 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile__map,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile__append1,axiom, % 191.28/191.38 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_ys_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile__eq__Cons__conv,axiom, % 191.28/191.38 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 191.28/191.38 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) % 191.28/191.38 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile__eq__drop,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile__nth,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 191.28/191.38 => hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsum__map__filter,axiom, % 191.28/191.38 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 191.28/191.38 ( class_Groups_Omonoid__add(T_b) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 191.28/191.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__nth__monoI,axiom, % 191.28/191.38 ! [V_xs,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( ! [B_i,B_j] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 191.28/191.38 => ( 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))) % 191.28/191.38 => 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))) ) ) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_n__lists_Osimps_I2_J,axiom, % 191.28/191.38 ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sublists__powset,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__n__lists,axiom, % 191.28/191.38 ! [V_n,V_xs,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__set__sublists,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__n__lists,axiom, % 191.28/191.38 ! [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) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__n__lists__elem,axiom, % 191.28/191.38 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)))) % 191.28/191.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sublists_Osimps_I1_J,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_n__lists__Nil,axiom, % 191.28/191.38 ! [T_a,V_n] : % 191.28/191.38 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.38 => 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))) ) % 191.28/191.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.38 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_n__lists_Osimps_I1_J,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sublists_Osimps_I2_J,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_set__n__lists,axiom, % 191.28/191.38 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__sublists,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_product_Osimps_I2_J,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__the__def,axiom, % 191.28/191.38 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_product_Osimps_I1_J,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__product,axiom, % 191.28/191.38 ! [V_ys,T_b,V_xs,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_product__list__set,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_List_Oset(T_b),V_ys_2))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_map__of__zip__enum__inject,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_a,T_b] : % 191.28/191.38 ( ( class_Enum_Oenum(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) ) % 191.28/191.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 191.28/191.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 191.28/191.38 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2))) % 191.28/191.38 => V_xs_2 = V_ys_2 ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sort__foldl__insort,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__prod__def,axiom, % 191.28/191.38 ! [T_b,T_a] : % 191.28/191.38 ( ( class_Enum_Oenum(T_a) % 191.28/191.38 & class_Enum_Oenum(T_b) ) % 191.28/191.38 => 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)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__distinct,axiom, % 191.28/191.38 ! [T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__option__def,axiom, % 191.28/191.38 ! [T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(hAPP(c_List_Omap(T_a,tc_Option_Ooption(T_a)),c_Option_Ooption_OSome(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__sort,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 191.28/191.38 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_filter__sort,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__sort,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__sort,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sort__key__simps_I1_J,axiom, % 191.28/191.38 ! [V_f_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_set__sort,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_in__enum,axiom, % 191.28/191.38 ! [V_x_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_UNIV__enum,axiom, % 191.28/191.38 ! [T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__UNIV,axiom, % 191.28/191.38 ! [T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__sort__key,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_b,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Osort__key(T_b,T_a,V_f_2,V_xs_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sort__key__simps_I2_J,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__fun__code,axiom, % 191.28/191.38 ! [T_b,T_a] : % 191.28/191.38 ( ( class_Enum_Oenum(T_a) % 191.28/191.38 & class_HOL_Oequal(T_a) % 191.28/191.38 & class_Enum_Oenum(T_b) ) % 191.28/191.38 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__fun__def,axiom, % 191.28/191.38 ! [T_b,T_a] : % 191.28/191.38 ( ( class_Enum_Oenum(T_a) % 191.28/191.38 & class_Enum_Oenum(T_b) ) % 191.28/191.38 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),c_List_Oremdups(T_a,V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_all__n__lists__def,axiom, % 191.28/191.38 ! [V_n_2,V_P_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 191.28/191.38 <=> ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_ex__n__lists__def,axiom, % 191.28/191.38 ! [V_n_2,V_P_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 191.28/191.38 <=> ? [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) % 191.28/191.38 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__ex__fun__code,axiom, % 191.28/191.38 ! [V_P_2,T_a,T_b] : % 191.28/191.38 ( ( class_Enum_Oenum(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) % 191.28/191.38 & class_HOL_Oequal(T_a) ) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 191.28/191.38 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__all__fun__code,axiom, % 191.28/191.38 ! [V_P_2,T_a,T_b] : % 191.28/191.38 ( ( class_Enum_Oenum(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) % 191.28/191.38 & class_HOL_Oequal(T_a) ) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 191.28/191.38 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__ex__option__def,axiom, % 191.28/191.38 ! [V_P_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 191.28/191.38 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 191.28/191.38 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__all__option__def,axiom, % 191.28/191.38 ! [V_P_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 191.28/191.38 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 191.28/191.38 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__ex,axiom, % 191.28/191.38 ! [V_P_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 191.28/191.38 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__all,axiom, % 191.28/191.38 ! [V_P_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 191.28/191.38 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_exists__code,axiom, % 191.28/191.38 ! [V_P_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 191.28/191.38 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_all__code,axiom, % 191.28/191.38 ! [V_P_2,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 191.28/191.38 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__ex__prod__def,axiom, % 191.28/191.38 ! [V_P_2,T_a,T_b] : % 191.28/191.38 ( ( class_Enum_Oenum(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) ) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 191.28/191.38 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__all__prod__def,axiom, % 191.28/191.38 ! [V_P_2,T_a,T_b] : % 191.28/191.38 ( ( class_Enum_Oenum(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) ) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 191.28/191.38 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_order__fun_I1_J,axiom, % 191.28/191.38 ! [V_g_2,V_f_2,T_a,T_b] : % 191.28/191.38 ( ( class_Orderings_Oorder(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) ) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.28/191.38 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_order__fun_I2_J,axiom, % 191.28/191.38 ! [V_g_2,V_f_2,T_a,T_b] : % 191.28/191.38 ( ( class_Orderings_Oorder(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) ) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.28/191.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.28/191.38 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2)))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__all__fun__def,axiom, % 191.28/191.38 ! [V_P_2,T_a,T_b] : % 191.28/191.38 ( ( class_Enum_Oenum(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) ) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 191.28/191.38 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_enum__ex__fun__def,axiom, % 191.28/191.38 ! [V_P_2,T_a,T_b] : % 191.28/191.38 ( ( class_Enum_Oenum(T_b) % 191.28/191.38 & class_Enum_Oenum(T_a) ) % 191.28/191.38 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 191.28/191.38 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_map__of__zip__enum__is__Some,axiom, % 191.28/191.38 ! [V_x,V_ys,T_b,T_a] : % 191.28/191.38 ( class_Enum_Oenum(T_a) % 191.28/191.38 => ( 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)) % 191.28/191.38 => ? [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) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__eq__filter,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 191.28/191.38 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.38 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__eq__take__P__nth,axiom, % 191.28/191.38 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 191.28/191.38 ( ! [B_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 191.28/191.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 191.28/191.38 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_length__takeWhile__less__P__nth,axiom, % 191.28/191.38 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 191.28/191.38 ( ! [B_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 191.28/191.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_lists__Int__eq,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_lists__IntI,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,V_l_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 191.28/191.38 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsp_ONil,axiom, % 191.28/191.38 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_append__in__listsp__conv,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 191.28/191.38 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 191.28/191.38 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_in__listsp__conv__set,axiom, % 191.28/191.38 ! [V_xs_2,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 191.28/191.38 <=> ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsp_Oequations_I1_J,axiom, % 191.28/191.38 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsp__conj__eq,axiom, % 191.28/191.38 ! [V_x_2,V_B_2,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2)) % 191.28/191.38 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 191.28/191.38 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsp__infI,axiom, % 191.28/191.38 ! [V_B_2,V_l_2,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 191.28/191.38 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 191.28/191.38 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsp__inf__eq,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsp_Oequations_I2_J,axiom, % 191.28/191.38 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 191.28/191.38 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 191.28/191.38 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsp__mono,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listsp__lists__eq,axiom, % 191.28/191.38 ! [V_x_2,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) % 191.28/191.38 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__def,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.38 & ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted_Osimps,axiom, % 191.28/191.38 ! [V_a_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 191.28/191.38 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 191.28/191.38 | ? [B_xs,B_x] : % 191.28/191.38 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 191.28/191.38 & ! [B_xa] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 191.28/191.38 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__Cons,axiom, % 191.28/191.38 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) % 191.28/191.38 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 191.28/191.38 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__map1,axiom, % 191.28/191.38 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2) % 191.28/191.38 <=> c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__map2,axiom, % 191.28/191.38 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2)) % 191.28/191.38 <=> c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__eq,axiom, % 191.28/191.38 ! [T_a,V_ys_2,V_xs_2] : % 191.28/191.38 ( V_xs_2 = V_ys_2 % 191.28/191.38 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__lengthD,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__dropI,axiom, % 191.28/191.38 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 191.28/191.38 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_bs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__takeI,axiom, % 191.28/191.38 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_ys_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__Nil2,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 191.28/191.38 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__Nil,axiom, % 191.28/191.38 ! [V_ys_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 191.28/191.38 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__rev1,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 191.28/191.38 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__rev,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2)) % 191.28/191.38 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__append,axiom, % 191.28/191.38 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.38 => ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2)) % 191.28/191.38 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__appendI,axiom, % 191.28/191.38 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 191.28/191.38 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2) % 191.28/191.38 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__nthD2,axiom, % 191.28/191.38 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__nthD,axiom, % 191.28/191.38 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__conv__all__nth,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 191.28/191.38 & ! [B_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__update__cong,axiom, % 191.28/191.38 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 191.28/191.38 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__update__cong2,axiom, % 191.28/191.38 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 191.28/191.38 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 191.28/191.38 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2I,axiom, % 191.28/191.38 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_a_2),V_b_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 191.28/191.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) % 191.28/191.38 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_SigmaE,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 191.28/191.38 => ~ ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.38 => ! [B_y] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 191.28/191.38 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_all__nth__imp__all__set,axiom, % 191.28/191.38 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 191.28/191.38 ( ! [B_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_List_Oinsert__def,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 191.28/191.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__insert,axiom, % 191.28/191.38 ! [V_x,V_xs,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_insert__remdups,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_in__set__insert,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_List_Oset__insert,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oinsert(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_insert__Nil,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_not__in__set__insert,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_escape,axiom, % 191.28/191.38 ! [V_Q_2,V_ca_2,V_G_2,T_a,V_P_2] : % 191.28/191.38 ( ! [B_Z,B_s] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 191.28/191.38 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) % 191.28/191.38 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 191.28/191.38 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 191.28/191.38 ( ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.38 & class_Groups_Ocomm__monoid__mult(T_a) ) % 191.28/191.38 => ( V_A_2 = V_B_2 % 191.28/191.38 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 191.28/191.38 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 191.28/191.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_concat__map__maps,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_maps__def,axiom, % 191.28/191.38 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_maps__simps_I2_J,axiom, % 191.28/191.38 ! [V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 191.28/191.38 % 191.28/191.38 fof(fact_maps__simps_I1_J,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_finite__conv__nat__seg__image,axiom, % 191.28/191.38 ! [V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.38 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_distinct__concat,axiom, % 191.28/191.38 ! [V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 191.28/191.38 => ( ! [B_ys] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 191.28/191.38 => ( ! [B_ys] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => ! [B_zs] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => ( B_ys != B_zs % 191.28/191.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),B_ys)),hAPP(c_List_Oset(T_a),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 191.28/191.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 191.28/191.38 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 191.28/191.38 ( ( class_Groups_Ocomm__monoid__add(T_a) % 191.28/191.38 & class_Groups_Ocomm__monoid__mult(T_a) ) % 191.28/191.38 => ( V_A_2 = V_B_2 % 191.28/191.38 => ( c_Nat__Transfer_Onat__set(V_B_2) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 191.28/191.38 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 191.28/191.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_accp__acc__eq,axiom, % 191.28/191.38 ! [V_x_2,V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2)) % 191.28/191.38 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Cons__acc__listrel1I,axiom, % 191.28/191.38 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_lists__accD,axiom, % 191.28/191.38 ! [V_r_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_lists__accI,axiom, % 191.28/191.38 ! [V_r_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acc__subset,axiom, % 191.28/191.38 ! [V_R2_2,V_R1_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acc__downward,axiom, % 191.28/191.38 ! [V_a_2,V_r_2,V_b_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acc_Osimps,axiom, % 191.28/191.38 ! [V_r_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 191.28/191.38 <=> ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_measures__lesseq,axiom, % 191.28/191.38 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 191.28/191.38 ( 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))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__def,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_s_2))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__compI,axiom, % 191.28/191.38 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_ca_2)),V_s_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__UNION__distrib,axiom, % 191.28/191.38 ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2)),V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__UNION__distrib2,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,V_I_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__distrib,axiom, % 191.28/191.38 ! [V_T_2,V_S_2,V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__distrib2,axiom, % 191.28/191.38 ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_T_2),V_R_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_O__assoc,axiom, % 191.28/191.38 ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__empty1,axiom, % 191.28/191.38 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__empty2,axiom, % 191.28/191.38 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_union__comp__emptyR,axiom, % 191.28/191.38 ! [V_C_2,V_B_2,V_A_2,T_a] : % 191.28/191.38 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 191.28/191.38 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 191.28/191.38 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_union__comp__emptyL,axiom, % 191.28/191.38 ! [V_B_2,V_C_2,V_A_2,T_a] : % 191.28/191.38 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 191.28/191.38 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 191.28/191.38 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__mono,axiom, % 191.28/191.38 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_H_2),V_s_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rel__comp__subset__Sigma,axiom, % 191.28/191.38 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2)))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_in__measures_I1_J,axiom, % 191.28/191.38 ! [V_y_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_measures__def,axiom, % 191.28/191.38 ! [V_fs_2,T_a] : c_List_Omeasures(T_a,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_a),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_a),c_List_Omap(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_a,tc_Nat_Onat),T_a,tc_Nat_Onat),c_COMBI(tc_fun(T_a,tc_Nat_Onat))))),V_fs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_max__ext__compat,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_min__ext__compat,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_measures__less,axiom, % 191.28/191.38 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 191.28/191.38 ( 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))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_in__measures_I2_J,axiom, % 191.28/191.38 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) % 191.28/191.38 <=> ( 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))) % 191.28/191.38 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 191.28/191.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_pred__comp__rel__comp__eq,axiom, % 191.28/191.38 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 191.28/191.38 ( c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_s_2),V_x_2,V_y_2) % 191.28/191.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_reduction__pairI,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_R_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 191.28/191.38 => c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__less__than,axiom, % 191.28/191.38 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 191.28/191.38 % 191.28/191.38 fof(fact_pred__comp_Ointros,axiom, % 191.28/191.38 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 191.28/191.38 => c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__empty,axiom, % 191.28/191.38 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__inv__image,axiom, % 191.28/191.38 ! [V_f_2,T_b,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__lex,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__lex__prod,axiom, % 191.28/191.38 ! [V_rb_2,T_b,V_ra_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_ra_2) % 191.28/191.38 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 191.28/191.38 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__lenlex,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__measure,axiom, % 191.28/191.38 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__acc__iff,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acc__wfD,axiom, % 191.28/191.38 ! [V_x_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__measures,axiom, % 191.28/191.38 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__comp__self,axiom, % 191.28/191.38 ! [V_R_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_R_2) % 191.28/191.38 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__union__merge,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) % 191.28/191.38 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__no__loop,axiom, % 191.28/191.38 ! [V_R_2,T_a] : % 191.28/191.38 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 191.28/191.38 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfE__pf,axiom, % 191.28/191.38 ! [V_A_2,V_R_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_R_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),V_A_2))) % 191.28/191.38 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__Int1,axiom, % 191.28/191.38 ! [V_r_H_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__Int2,axiom, % 191.28/191.38 ! [V_r_H_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__less,axiom, % 191.28/191.38 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)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__subset,axiom, % 191.28/191.38 ! [V_p_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2)) % 191.28/191.38 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__irrefl,axiom, % 191.28/191.38 ! [V_a_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__asym,axiom, % 191.28/191.38 ! [V_x_2,V_a_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2)) % 191.28/191.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__not__sym,axiom, % 191.28/191.38 ! [V_x_2,V_a_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2)) % 191.28/191.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__not__refl,axiom, % 191.28/191.38 ! [V_a_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_min__ext__wf,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__finite__psubset,axiom, % 191.28/191.38 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__mlex,axiom, % 191.28/191.38 ! [V_f_2,V_R_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_R_2) % 191.28/191.38 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_pred__comp_Oequations,axiom, % 191.28/191.38 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 191.28/191.38 ( c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a1_2,V_a3_2) % 191.28/191.38 <=> ? [B_b] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 191.28/191.38 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__pair__less,axiom, % 191.28/191.38 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 191.28/191.38 % 191.28/191.38 fof(fact_max__ext__wf,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__int__ge__less__than2,axiom, % 191.28/191.38 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__int__ge__less__than,axiom, % 191.28/191.38 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__lexn,axiom, % 191.28/191.38 ! [V_n_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 <=> ~ ? [B_f] : % 191.28/191.38 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__union__compatible,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_R_2) % 191.28/191.38 => ( c_Wellfounded_Owf(T_a,V_S_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 191.28/191.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf,axiom, % 191.28/191.38 ! [T_a] : % 191.28/191.38 ( class_Orderings_Owellorder(T_a) % 191.28/191.38 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_a)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_reduction__pair__def,axiom, % 191.28/191.38 ! [V_P_2,T_a] : % 191.28/191.38 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 191.28/191.38 <=> ( c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)) % 191.28/191.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_reduction__pair__lemma,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,V_P_2,T_a] : % 191.28/191.38 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) % 191.28/191.38 => ( c_Wellfounded_Owf(T_a,V_S_2) % 191.28/191.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__map__pair__image,axiom, % 191.28/191.38 ! [V_f_2,T_b,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 191.28/191.38 => c_Wellfounded_Owf(T_b,hAPP(c_Set_Oimage(tc_prod(T_a,T_a),tc_prod(T_b,T_b),c_Product__Type_Omap__pair(T_a,T_b,T_a,T_b,V_f_2,V_f_2)),V_r_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__if__measure,axiom, % 191.28/191.38 ! [T_a,V_g_2,V_f_2,V_P_2] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.38 => 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))) ) % 191.28/191.38 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),V_g_2))))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_max__extp_Oequations,axiom, % 191.28/191.38 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 191.28/191.38 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 191.28/191.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 191.28/191.38 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.38 & ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 191.28/191.38 => ? [B_xa] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 191.28/191.38 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_pred__nat__def,axiom, % 191.28/191.38 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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__same__fst,axiom, % 191.28/191.38 ! [T_a,V_R_2,T_b,V_P_2] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.38 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 191.28/191.38 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__pred__nat,axiom, % 191.28/191.38 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 191.28/191.38 % 191.28/191.38 fof(fact_max__ext_Ointros,axiom, % 191.28/191.38 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 191.28/191.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 191.28/191.38 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 191.28/191.38 => ? [B_xa] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 191.28/191.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Nitpick_Ozero__frac__def,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Nitpick_Oone__frac__def,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 191.28/191.38 ! [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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Nitpick_Ofrac__def,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__Collect__split,axiom, % 191.28/191.38 ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_RangeI,axiom, % 191.28/191.38 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__empty__iff,axiom, % 191.28/191.38 ! [V_r_2,T_a,T_b] : % 191.28/191.38 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.38 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__empty,axiom, % 191.28/191.38 ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__Un__eq,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__Union,axiom, % 191.28/191.38 ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__Id__on,axiom, % 191.28/191.38 ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_finite__Range,axiom, % 191.28/191.38 ! [V_r_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_snd__eq__Range,axiom, % 191.28/191.38 ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__iff,axiom, % 191.28/191.38 ! [V_r_2,T_b,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 191.28/191.38 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__insert,axiom, % 191.28/191.38 ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__Int__subset,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__Diff__subset,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_RangeP__Range__eq,axiom, % 191.28/191.38 ! [V_x_2,V_r_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2)) % 191.28/191.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_RangeE,axiom, % 191.28/191.38 ! [V_r_2,T_b,V_b_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 191.28/191.38 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_RangeP_Ointros,axiom, % 191.28/191.38 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 191.28/191.38 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_RangeP_Oequations,axiom, % 191.28/191.38 ! [V_a2_2,V_r_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 191.28/191.38 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__Un,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => ( c_Wellfounded_Owf(T_a,V_s_2) % 191.28/191.38 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.38 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_foldl__apply,axiom, % 191.28/191.38 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hAPP(c_Fun_Ocomp(T_c,T_c,T_b,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_h_2),hAPP(V_g_2,B_x)) ) % 191.28/191.38 => hAPP(c_List_Ofoldl(T_c,T_a,hAPP(c_COMBC(T_a,T_c,T_c),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_g_2),V_s_2),V_xs_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_DomainI,axiom, % 191.28/191.38 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__mono,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_s_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__empty__iff,axiom, % 191.28/191.38 ! [V_r_2,T_b,T_a] : % 191.28/191.38 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.38 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__empty,axiom, % 191.28/191.38 ! [T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__Un__eq,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__Id__on,axiom, % 191.28/191.38 ! [V_A_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_finite__Domain,axiom, % 191.28/191.38 ! [V_r_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_fst__eq__Domain,axiom, % 191.28/191.38 ! [V_R_2,T_b,T_a] : hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),V_R_2) = hAPP(c_Relation_ODomain(T_a,T_b),V_R_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__iff,axiom, % 191.28/191.38 ! [V_r_2,T_b,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 191.28/191.38 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__insert,axiom, % 191.28/191.38 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__Int__subset,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__Diff__subset,axiom, % 191.28/191.38 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2))),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Field__def,axiom, % 191.28/191.38 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__Union,axiom, % 191.28/191.38 ! [V_S_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_a,T_b)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__Collect__split,axiom, % 191.28/191.38 ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_DomainP__Domain__eq,axiom, % 191.28/191.38 ! [V_x_2,V_r_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2)) % 191.28/191.38 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_DomainE,axiom, % 191.28/191.38 ! [V_r_2,T_b,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 191.28/191.38 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_DomainP_Ointros,axiom, % 191.28/191.38 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 191.28/191.38 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_DomainP_Oequations,axiom, % 191.28/191.38 ! [V_a1_2,V_r_2,T_b,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 191.28/191.38 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfP__def,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_OwfP(T_a,V_r_2) % 191.28/191.38 <=> c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Rep__Integ__induct,axiom, % 191.28/191.38 ! [V_P_2,V_y_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 191.28/191.38 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfP__empty,axiom, % 191.28/191.38 ! [T_a] : c_Wellfounded_OwfP(T_a,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfP__subset,axiom, % 191.28/191.38 ! [V_p_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_OwfP(T_a,V_r_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_p_2),V_r_2)) % 191.28/191.38 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfP__accp__iff,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_OwfP(T_a,V_r_2) % 191.28/191.38 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_accp__wfPD,axiom, % 191.28/191.38 ! [V_x_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_OwfP(T_a,V_r_2) % 191.28/191.38 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__in__rel,axiom, % 191.28/191.38 ! [V_R_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_R_2) % 191.28/191.38 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfP__wf__eq,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)) % 191.28/191.38 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfP__acyclicP,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_OwfP(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Rep__Integ__cases,axiom, % 191.28/191.38 ! [V_y_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 191.28/191.38 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__acyclic,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acyclic__subset,axiom, % 191.28/191.38 ! [V_r_2,V_s_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.38 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__iff__acyclic__if__finite,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 191.28/191.38 => ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_finite__acyclic__wf,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 191.28/191.38 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Nitpick_Owf_H__def,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Nitpick_Owf_H(T_a,V_r_2) % 191.28/191.38 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 191.28/191.38 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 191.28/191.38 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_inj__on__INTER,axiom, % 191.28/191.38 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 191.28/191.38 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.38 => ( ! [B_i] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 191.28/191.38 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 191.28/191.38 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_zip__obtain__same__length,axiom, % 191.28/191.38 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 191.28/191.38 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)) % 191.28/191.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)))) ) % 191.28/191.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_map__of__eqI,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,T_b,T_a] : % 191.28/191.38 ( hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)) = hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))) % 191.28/191.38 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),B_x) ) % 191.28/191.38 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_the__eq__trivial,axiom, % 191.28/191.38 ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_the__sym__eq__trivial,axiom, % 191.28/191.38 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_pigeonhole__infinite,axiom, % 191.28/191.38 ! [V_f_2,T_b,V_A_2,T_a] : % 191.28/191.38 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 191.28/191.38 => ? [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.38 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Abs__Integ__induct,axiom, % 191.28/191.38 ! [V_x_2,V_P_2] : % 191.28/191.38 ( ! [B_y] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 191.28/191.38 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 191.28/191.38 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Abs__Integ__cases,axiom, % 191.28/191.38 ! [V_x_2] : % 191.28/191.38 ~ ! [B_y] : % 191.28/191.38 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 191.28/191.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_finite__UN__I,axiom, % 191.28/191.38 ! [V_B_2,T_b,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.38 => ( ! [B_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 191.28/191.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 191.28/191.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_inj__on__diff__nat,axiom, % 191.28/191.38 ! [V_k_2,V_N_2] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 191.28/191.38 => 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) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfP__SUP,axiom, % 191.28/191.38 ! [T_a,V_r_2,T_b] : % 191.28/191.38 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 191.28/191.38 => ( ! [B_i,B_j] : % 191.28/191.38 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 191.28/191.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Predicate_ODomainP(T_b,T_b,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_b,T_b,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 191.28/191.38 => c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_pos__not__random__dseq__def,axiom, % 191.28/191.38 ! [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)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_dropWhile__append2,axiom, % 191.28/191.38 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.38 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_a,V_P_2,V_ys_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__all2__all__nthI,axiom, % 191.28/191.38 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 191.28/191.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) % 191.28/191.38 => ( ! [B_n] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_b_2),B_n))) ) % 191.28/191.38 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_mem__splitE,axiom, % 191.28/191.38 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),V_p_2))) % 191.28/191.38 => ~ ! [B_x,B_y] : % 191.28/191.38 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 191.28/191.38 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_mem__splitI2,axiom, % 191.28/191.38 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 191.28/191.38 ( ! [B_a,B_b] : % 191.28/191.38 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_finite__sorted__distinct__unique,axiom, % 191.28/191.38 ! [V_A_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 191.28/191.38 => ? [B_x] : % 191.28/191.38 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 191.28/191.38 & c_List_Olinorder__class_Osorted(T_a,B_x) % 191.28/191.38 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 191.28/191.38 & ! [B_y] : % 191.28/191.38 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 191.28/191.38 & c_List_Olinorder__class_Osorted(T_a,B_y) % 191.28/191.38 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 191.28/191.38 => B_y = B_x ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_takeWhile__append2,axiom, % 191.28/191.38 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 191.28/191.38 ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.38 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_OtakeWhile(T_a,V_P_2,V_ys_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_insort__is__Cons,axiom, % 191.28/191.38 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 191.28/191.38 ( class_Orderings_Olinorder(T_b) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 191.28/191.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wfI__pf,axiom, % 191.28/191.38 ! [V_R_2,T_a] : % 191.28/191.38 ( ! [B_A] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),B_A))) % 191.28/191.38 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 191.28/191.38 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_filter__eq__Cons__iff,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 191.28/191.38 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) % 191.28/191.38 <=> ? [B_us,B_vs] : % 191.28/191.38 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) % 191.28/191.38 & ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 191.28/191.38 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.38 & hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Cons__eq__filter__iff,axiom, % 191.28/191.38 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 191.28/191.38 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) % 191.28/191.38 <=> ? [B_us,B_vs] : % 191.28/191.38 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) % 191.28/191.38 & ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 191.28/191.38 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.38 & hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Sigma__mono,axiom, % 191.28/191.38 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) ) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_C_2),V_D_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acc_OaccI,axiom, % 191.28/191.38 ! [V_r_2,V_x_2,T_a] : % 191.28/191.38 ( ! [B_y] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_not__acc__down,axiom, % 191.28/191.38 ! [V_R_2,V_x_2,T_a] : % 191.28/191.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 191.28/191.38 => ~ ! [B_z] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__ball__nth,axiom, % 191.28/191.38 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_max__ext_Osimps,axiom, % 191.28/191.38 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 191.28/191.38 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 191.28/191.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 191.28/191.38 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 191.28/191.38 & ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 191.28/191.38 => ? [B_xa] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 191.28/191.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sorted_OCons,axiom, % 191.28/191.38 ! [V_x_2,V_xs_2,T_a] : % 191.28/191.38 ( class_Orderings_Olinorder(T_a) % 191.28/191.38 => ( ! [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 191.28/191.38 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 191.28/191.38 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__no__infinite__down__chainE,axiom, % 191.28/191.38 ! [V_f_2,V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__ex__length,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 191.28/191.38 <=> ? [B_n] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.38 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_less__eq,axiom, % 191.28/191.38 ! [V_n_2,V_m_2] : % 191.28/191.38 ( 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))) % 191.28/191.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__trancl,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__ex__simps_I1_J,axiom, % 191.28/191.38 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 191.28/191.38 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.38 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__ex__iff,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 191.28/191.38 <=> ? [B_x] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.38 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__ex__rev,axiom, % 191.28/191.38 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 191.28/191.38 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__ex__append,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 191.28/191.38 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 191.28/191.38 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 191.28/191.38 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_list__ex__simps_I2_J,axiom, % 191.28/191.38 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_less__than__def,axiom, % 191.28/191.38 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acyclic__def,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 191.28/191.38 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl_Or__into__trancl,axiom, % 191.28/191.38 ! [V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__subset__Field2,axiom, % 191.28/191.38 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_Relation_OField(T_a),V_r_2))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_r__into__trancl_H,axiom, % 191.28/191.38 ! [V_r_2,V_p_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__empty,axiom, % 191.28/191.38 ! [T_a] : c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__domain,axiom, % 191.28/191.38 ! [V_r_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__range,axiom, % 191.28/191.38 ! [V_r_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ORange(T_a,T_a),V_r_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_finite__trancl,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_r__r__into__trancl,axiom, % 191.28/191.38 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_R_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_R_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__into__trancl2,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__trans,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__mono,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,V_p_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__unfold,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__subset__Sigma,axiom, % 191.28/191.38 ! [V_A_2,V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__Int__subset,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__insert,axiom, % 191.28/191.38 ! [V_r_2,V_x_2,V_y_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBC(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),V_y_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_reflcl__set__eq,axiom, % 191.28/191.38 ! [V_y_2,V_x_2,V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),c_fequal),V_x_2),V_y_2)) % 191.28/191.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_r__into__rtrancl,axiom, % 191.28/191.38 ! [V_r_2,V_p_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl_Ortrancl__refl,axiom, % 191.28/191.38 ! [V_r_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_IdI,axiom, % 191.28/191.38 ! [V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Relation_OId(T_a))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__into__rtrancl,axiom, % 191.28/191.38 ! [V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listrel__rtrancl__refl,axiom, % 191.28/191.38 ! [V_r_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__trancl__trancl,axiom, % 191.28/191.38 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__rtrancl__trancl,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__into__trancl1,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtranclD,axiom, % 191.28/191.38 ! [V_R_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 191.28/191.38 => ( V_a_2 = V_b_2 % 191.28/191.38 | ( V_a_2 != V_b_2 % 191.28/191.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__into__trancl2,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__eq__or__trancl,axiom, % 191.28/191.38 ! [V_R_2,V_y_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 191.28/191.38 <=> ( V_x_2 = V_y_2 % 191.28/191.38 | ( V_x_2 != V_y_2 % 191.28/191.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__rtrancl__absorb,axiom, % 191.28/191.38 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__trancl__absorb,axiom, % 191.28/191.38 ! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_reflcl__trancl,axiom, % 191.28/191.38 ! [V_r_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__reflcl,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__unfold__right,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__unfold__left,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_r__comp__rtrancl__eq,axiom, % 191.28/191.38 ! [V_r_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__idemp__self__comp,axiom, % 191.28/191.38 ! [V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__unfold,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__Int__subset,axiom, % 191.28/191.38 ! [V_r_2,V_s_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),V_s_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__Un__subset,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__mono,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__subset,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 191.28/191.38 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__subset__rtrancl,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Image__closed__trancl,axiom, % 191.28/191.38 ! [V_X_2,V_r_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2)) % 191.28/191.38 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__empty,axiom, % 191.28/191.38 ! [T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a) ). % 191.28/191.38 % 191.28/191.38 fof(fact_in__rtrancl__UnI,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,V_x_2,T_a] : % 191.28/191.38 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 191.28/191.38 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__reflcl,axiom, % 191.28/191.38 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__Un__rtrancl,axiom, % 191.28/191.38 ! [V_S_2,V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__reflcl__absorb,axiom, % 191.28/191.38 ! [V_R_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__r__diff__Id,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__idemp,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__trans,axiom, % 191.28/191.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_refl__rtrancl,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__rtrancl,axiom, % 191.28/191.38 ! [V_R_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__rtrancl,axiom, % 191.28/191.38 ! [V_R_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Domain__Id,axiom, % 191.28/191.38 ! [T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Range__Id,axiom, % 191.28/191.38 ! [T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listrel__rtrancl__trans,axiom, % 191.28/191.38 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 191.28/191.38 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_refl__Id,axiom, % 191.28/191.38 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_pair__in__Id__conv,axiom, % 191.28/191.38 ! [V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a))) % 191.28/191.38 <=> V_a_2 = V_b_2 ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Image__Id,axiom, % 191.28/191.38 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 191.28/191.38 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Id__O__R,axiom, % 191.28/191.38 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_b),c_Relation_OId(T_a)),V_R_2) = V_R_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_R__O__Id,axiom, % 191.28/191.38 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_b),V_R_2),c_Relation_OId(T_b)) = V_R_2 ). % 191.28/191.38 % 191.28/191.38 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 191.28/191.38 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_pair__leq__def,axiom, % 191.28/191.38 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))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Not__Domain__rtrancl,axiom, % 191.28/191.38 ! [V_y_2,V_R_2,V_x_2,T_a] : % 191.28/191.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 191.28/191.38 <=> V_x_2 = V_y_2 ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acc__downwards,axiom, % 191.28/191.38 ! [V_b_2,V_r_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acc__downwards__aux,axiom, % 191.28/191.38 ! [V_r_2,V_a_2,V_b_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_wf__insert,axiom, % 191.28/191.38 ! [V_r_2,V_x_2,V_y_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) % 191.28/191.38 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.38 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 191.28/191.38 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__listrel1__eq__len,axiom, % 191.28/191.38 ! [V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 191.28/191.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acyclic__insert,axiom, % 191.28/191.38 ! [V_r_2,V_x_2,V_y_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) % 191.28/191.38 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 191.28/191.38 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_listrel__reflcl__if__listrel1,axiom, % 191.28/191.38 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 191.28/191.38 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_refl__reflcl,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_Id__def,axiom, % 191.28/191.38 ! [T_a] : c_Relation_OId(T_a) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_a),tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),tc_prod(T_a,T_a)),c_COMBB(tc_prod(T_a,T_a),tc_HOL_Obool,T_a)),c_fequal)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_irrefl__diff__Id,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Relation_Oirrefl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ). % 191.28/191.38 % 191.28/191.38 fof(fact_pred__nat__trancl__eq__le,axiom, % 191.28/191.38 ! [V_n_2,V_m_2] : % 191.28/191.38 ( 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))) % 191.28/191.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_trancl__subset__Sigma__aux,axiom, % 191.28/191.38 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 191.28/191.38 => ( V_a_2 = V_b_2 % 191.28/191.38 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_irrefl__tranclI,axiom, % 191.28/191.38 ! [V_x_2,V_r_2,T_a] : % 191.28/191.38 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 191.28/191.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_sequence__trans,axiom, % 191.28/191.38 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 191.28/191.38 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__converse,axiom, % 191.28/191.38 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__converseI,axiom, % 191.28/191.38 ! [V_r_2,V_x_2,V_y_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_rtrancl__converseD,axiom, % 191.28/191.38 ! [V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 191.28/191.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_converse__Id,axiom, % 191.28/191.38 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 191.28/191.38 % 191.28/191.38 fof(fact_acyclic__converse,axiom, % 191.28/191.38 ! [V_r_2,T_a] : % 191.28/191.38 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 191.28/191.38 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_converse__UNION,axiom, % 191.28/191.38 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_converse__rel__comp,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_a),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_a),V_s_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) ). % 191.28/191.38 % 191.28/191.38 fof(fact_equiv__comp__eq,axiom, % 191.28/191.38 ! [V_r_2,V_A_2,T_a] : % 191.28/191.38 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 191.28/191.38 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 ) ). % 191.28/191.38 % 191.28/191.38 fof(fact_converse__inv__image,axiom, % 191.28/191.38 ! [V_f_2,V_R_2,T_b,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),hAPP(c_Relation_Oconverse(T_b,T_b),V_R_2)),V_f_2) ). % 191.28/191.38 % 191.28/191.38 fof(fact_converse__Un,axiom, % 191.28/191.38 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_in__listrel1__converse,axiom, % 191.28/191.39 ! [V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_listrel1__converse,axiom, % 191.28/191.39 ! [V_r_2,T_a] : c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converse__INTER,axiom, % 191.28/191.39 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converse__converse,axiom, % 191.28/191.39 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = V_r_2 ). % 191.28/191.39 % 191.28/191.39 fof(fact_Field__converse,axiom, % 191.28/191.39 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_OField(T_a),V_r_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converse__Id__on,axiom, % 191.28/191.39 ! [V_A_2,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = c_Relation_OId__on(T_a,V_A_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_finite__converse,axiom, % 191.28/191.39 ! [V_r_2,T_b,T_a] : % 191.28/191.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 191.28/191.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converse__iff,axiom, % 191.28/191.39 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converseI,axiom, % 191.28/191.39 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converseD,axiom, % 191.28/191.39 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_refl__on__converse,axiom, % 191.28/191.39 ! [V_r_2,V_A_2,T_a] : % 191.28/191.39 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 191.28/191.39 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converse__Int,axiom, % 191.28/191.39 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Range__def,axiom, % 191.28/191.39 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Domain__converse,axiom, % 191.28/191.39 ! [V_r_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) = hAPP(c_Relation_ORange(T_b,T_a),V_r_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Range__converse,axiom, % 191.28/191.39 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_trancl__converse,axiom, % 191.28/191.39 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_trancl__converseI,axiom, % 191.28/191.39 ! [V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_trancl__converseD,axiom, % 191.28/191.39 ! [V_r_2,V_y_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_wf__converse__trancl,axiom, % 191.28/191.39 ! [V_r_2,T_a] : % 191.28/191.39 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 191.28/191.39 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Image__subset__eq,axiom, % 191.28/191.39 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)),V_B_2)) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_refl__on__comp__subset,axiom, % 191.28/191.39 ! [V_r_2,V_A_2,T_a] : % 191.28/191.39 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_comp__equivI,axiom, % 191.28/191.39 ! [V_A_2,V_r_2,T_a] : % 191.28/191.39 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 % 191.28/191.39 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 191.28/191.39 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_finite__acyclic__wf__converse,axiom, % 191.28/191.39 ! [V_r_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 191.28/191.39 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 191.28/191.39 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converse__def,axiom, % 191.28/191.39 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_a)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_a)))),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))))),V_r_2))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Image__INT__eq,axiom, % 191.28/191.39 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 191.28/191.39 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 191.28/191.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 191.28/191.39 => hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_total__on__diff__Id,axiom, % 191.28/191.39 ! [V_r_2,V_A_2,T_a] : % 191.28/191.39 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) % 191.28/191.39 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_single__valued__Id,axiom, % 191.28/191.39 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_total__on__converse,axiom, % 191.28/191.39 ! [V_r_2,V_A_2,T_a] : % 191.28/191.39 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 191.28/191.39 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_single__valued__Id__on,axiom, % 191.28/191.39 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_total__on__empty,axiom, % 191.28/191.39 ! [V_r_2,T_a] : c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_single__valued__subset,axiom, % 191.28/191.39 ! [V_s_2,V_r_2,T_b,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 191.28/191.39 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 191.28/191.39 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_single__valued__rel__comp,axiom, % 191.28/191.39 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 191.28/191.39 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 191.28/191.39 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 191.28/191.39 => c_Relation_Osingle__valued(T_a,T_c,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_single__valuedD,axiom, % 191.28/191.39 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 191.28/191.39 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2)) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2)) % 191.28/191.39 => V_y_2 = V_z_2 ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_single__valued__def,axiom, % 191.28/191.39 ! [V_r_2,T_b,T_a] : % 191.28/191.39 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 191.28/191.39 <=> ! [B_x,B_y] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) % 191.28/191.39 => ! [B_z] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) % 191.28/191.39 => B_y = B_z ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_total__on__def,axiom, % 191.28/191.39 ! [V_r_2,V_A_2,T_a] : % 191.28/191.39 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 191.28/191.39 <=> ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.39 => ! [B_xa] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 191.28/191.39 => ( B_x != B_xa % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2)) % 191.28/191.39 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2)) ) ) ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_single__valued__confluent,axiom, % 191.28/191.39 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 191.28/191.39 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 191.28/191.39 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Image__Int__eq,axiom, % 191.28/191.39 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 191.28/191.39 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 191.28/191.39 => hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 191.28/191.39 ! [V_R_2,V_p_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_acyclicI,axiom, % 191.28/191.39 ! [V_r_2,T_a] : % 191.28/191.39 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 191.28/191.39 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_single__valued__rel__pow,axiom, % 191.28/191.39 ! [V_n_2,V_R_2,T_a] : % 191.28/191.39 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 191.28/191.39 => c_Relation_Osingle__valued(T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__0__E,axiom, % 191.28/191.39 ! [V_R_2,V_y_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) % 191.28/191.39 => V_x_2 = V_y_2 ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__0__I,axiom, % 191.28/191.39 ! [V_R_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__Suc__I2,axiom, % 191.28/191.39 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__Suc__I,axiom, % 191.28/191.39 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2)) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_funpow__swap1,axiom, % 191.28/191.39 ! [V_x_2,V_n_2,T_a,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_funpow__mult,axiom, % 191.28/191.39 ! [V_f_2,V_m_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_comp__funpow,axiom, % 191.28/191.39 ! [V_f_2,V_n_2,T_b,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_f_2)) = c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_wf__exp,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,T_a] : % 191.28/191.39 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) % 191.28/191.39 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__1,axiom, % 191.28/191.39 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ). % 191.28/191.39 % 191.28/191.39 fof(fact_relpow_Osimps_I2_J,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__commute,axiom, % 191.28/191.39 ! [V_n_2,V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__add,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_funpow__add,axiom, % 191.28/191.39 ! [V_f_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_funpow_Osimps_I2_J,axiom, % 191.28/191.39 ! [V_f_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__imp__rtrancl,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,V_p_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rtrancl__power,axiom, % 191.28/191.39 ! [V_R_2,V_p_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 191.28/191.39 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_relpow_Osimps_I1_J,axiom, % 191.28/191.39 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_a) ). % 191.28/191.39 % 191.28/191.39 fof(fact_funpow_Osimps_I1_J,axiom, % 191.28/191.39 ! [V_f_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_a) ). % 191.28/191.39 % 191.28/191.39 fof(fact_trancl__power,axiom, % 191.28/191.39 ! [V_R_2,V_p_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 191.28/191.39 <=> ? [B_n] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 191.28/191.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 191.28/191.39 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_funpow__code__def,axiom, % 191.28/191.39 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__E2,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 191.28/191.39 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.39 => V_x_2 != V_z_2 ) % 191.28/191.39 => ~ ! [B_y,B_m] : % 191.28/191.39 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 191.28/191.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rotate__def,axiom, % 191.28/191.39 ! [V_n_2,T_a] : c_List_Orotate(T_a,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_n_2),c_List_Orotate1(T_a)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__E,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 191.28/191.39 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 191.28/191.39 => V_x_2 != V_z_2 ) % 191.28/191.39 => ~ ! [B_y,B_m] : % 191.28/191.39 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) % 191.28/191.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rtrancl__Un__separatorE,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) % 191.28/191.39 => ( ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) % 191.28/191.39 => ! [B_y] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2)) % 191.28/191.39 => B_x = B_y ) ) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rtrancl__Un__separator__converseE,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) % 191.28/191.39 => ( ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) % 191.28/191.39 => ! [B_y] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_Q_2)) % 191.28/191.39 => B_y = B_x ) ) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__Suc__D2,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 191.28/191.39 => ? [B_y] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 191.28/191.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__Suc__E,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 191.28/191.39 => ~ ! [B_y] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 191.28/191.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__pow__Suc__E2,axiom, % 191.28/191.39 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 191.28/191.39 => ~ ! [B_y] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 191.28/191.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_tranclD,axiom, % 191.28/191.39 ! [V_R_2,V_y_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 191.28/191.39 => ? [B_z] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2)) % 191.28/191.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_tranclD2,axiom, % 191.28/191.39 ! [V_R_2,V_y_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 191.28/191.39 => ? [B_z] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 191.28/191.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_IdE,axiom, % 191.28/191.39 ! [V_p_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 191.28/191.39 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_in__set__conv__decomp,axiom, % 191.28/191.39 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.39 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_in__set__conv__decomp__first,axiom, % 191.28/191.39 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.39 <=> ? [B_ys] : % 191.28/191.39 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) % 191.28/191.39 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_in__set__conv__decomp__last,axiom, % 191.28/191.39 ! [V_xs_2,V_x_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.39 <=> ? [B_ys,B_zs] : % 191.28/191.39 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) % 191.28/191.39 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_wf__eq__minimal,axiom, % 191.28/191.39 ! [V_r_2,T_a] : % 191.28/191.39 ( c_Wellfounded_Owf(T_a,V_r_2) % 191.28/191.39 <=> ! [B_Q] : % 191.28/191.39 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 191.28/191.39 => ? [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 191.28/191.39 & ! [B_y] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2)) % 191.28/191.39 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_transfer__nat__int__set__cong,axiom, % 191.28/191.39 ! [V_P_H_2,V_P_2] : % 191.28/191.39 ( ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 191.28/191.39 => ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.39 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 191.28/191.39 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Int__Collect__mono,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 191.28/191.39 => ( ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 191.28/191.39 => ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.39 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_a),V_Q_2)))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_converseE,axiom, % 191.28/191.39 ! [V_r_2,V_yx_2,T_b,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_yx_2),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 191.28/191.39 => ~ ! [B_x,B_y] : % 191.28/191.39 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 191.28/191.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),B_y)),V_r_2)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_rel__compE,axiom, % 191.28/191.39 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2))) % 191.28/191.39 => ~ ! [B_x,B_y,B_z] : % 191.28/191.39 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),B_x),B_y)),V_r_2)) % 191.28/191.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),B_z)),V_s_2)) ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Oplus__frac__def,axiom, % 191.28/191.39 ! [V_r_2,V_q_2,T_a] : c_Nitpick_Oplus__frac(T_a,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_a),V_q_2),hAPP(c_Nitpick_Odenom(T_a),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_a),tc_Int_Oint),c_Nitpick_Ofrac(T_a)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_a),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_a),V_r_2)))))),c_COMBI(tc_Int_Oint))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Otimes__frac__def,axiom, % 191.28/191.39 ! [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))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Oof__frac__def,axiom, % 191.28/191.39 ! [V_q,T_a,T_b] : % 191.28/191.39 ( ( class_Rings_Oinverse(T_b) % 191.28/191.39 & class_Rings_Oring__1(T_b) ) % 191.28/191.39 => 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))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 191.28/191.39 ! [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)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 191.28/191.39 ! [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))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Oless__frac__def,axiom, % 191.28/191.39 ! [V_r_2,V_q_2,T_a] : % 191.28/191.39 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 191.28/191.39 ! [V_r_2,V_q_2,T_a] : % 191.28/191.39 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Odenom__def,axiom, % 191.28/191.39 ! [T_a] : c_Nitpick_Odenom(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Nitpick_Onum__def,axiom, % 191.28/191.39 ! [T_a] : c_Nitpick_Onum(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__all__length,axiom, % 191.28/191.39 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.39 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 191.28/191.39 <=> ! [B_n] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 191.28/191.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_internal__split__def,axiom, % 191.28/191.39 ! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c) ). % 191.28/191.39 % 191.28/191.39 fof(fact_Ball__set__list__all,axiom, % 191.28/191.39 ! [V_P_2,V_xs_2,T_a] : % 191.28/191.39 ( ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.39 => hBOOL(hAPP(V_P_2,B_x)) ) % 191.28/191.39 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__all__simps_I1_J,axiom, % 191.28/191.39 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 191.28/191.39 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 191.28/191.39 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.39 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__all__iff,axiom, % 191.28/191.39 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.39 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 191.28/191.39 <=> ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__all__rev,axiom, % 191.28/191.39 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.39 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 191.28/191.39 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__all__append,axiom, % 191.28/191.39 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 191.28/191.39 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 191.28/191.39 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 191.28/191.39 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__all__simps_I2_J,axiom, % 191.28/191.39 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__all__iff__raw,axiom, % 191.28/191.39 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.39 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 191.28/191.39 <=> ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_internal__split__conv,axiom, % 191.28/191.39 ! [V_b_2,V_a_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__ex1__simps_I2_J,axiom, % 191.28/191.39 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 191.28/191.39 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 191.28/191.39 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.39 => c_List_Olist__all(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) % 191.28/191.39 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 191.28/191.39 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_finite__less__ub,axiom, % 191.28/191.39 ! [V_u_2,V_f_2] : % 191.28/191.39 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 191.28/191.39 => 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)))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__ex1__simps_I1_J,axiom, % 191.28/191.39 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_exists1__code,axiom, % 191.28/191.39 ! [V_P_2,T_a] : % 191.28/191.39 ( class_Enum_Oenum(T_a) % 191.28/191.39 => ( ? [B_x] : % 191.28/191.39 ( hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.39 & ! [B_y] : % 191.28/191.39 ( hBOOL(hAPP(V_P_2,B_y)) % 191.28/191.39 => B_y = B_x ) ) % 191.28/191.39 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_list__ex1__iff,axiom, % 191.28/191.39 ! [V_xs_2,V_P_2,T_a] : % 191.28/191.39 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 191.28/191.39 <=> ? [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.39 & hBOOL(hAPP(V_P_2,B_x)) % 191.28/191.39 & ! [B_y] : % 191.28/191.39 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 191.28/191.39 & hBOOL(hAPP(V_P_2,B_y)) ) % 191.28/191.39 => B_y = B_x ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_measure__function__int,axiom, % 191.28/191.39 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))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_equal__fun__def,axiom, % 191.28/191.39 ! [V_g_2,V_f_2,T_a,T_b] : % 191.28/191.39 ( ( class_HOL_Oequal(T_b) % 191.28/191.39 & class_Enum_Oenum(T_a) ) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 191.28/191.39 <=> ! [B_x] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 191.28/191.39 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_equal,axiom, % 191.28/191.39 ! [T_a] : % 191.28/191.39 ( class_HOL_Oequal(T_a) % 191.28/191.39 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_equal__refl,axiom, % 191.28/191.39 ! [V_x,T_a] : % 191.28/191.39 ( class_HOL_Oequal(T_a) % 191.28/191.39 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_equal__eq,axiom, % 191.28/191.39 ! [V_y_2,V_x_2,T_a] : % 191.28/191.39 ( class_HOL_Oequal(T_a) % 191.28/191.39 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 191.28/191.39 <=> V_x_2 = V_y_2 ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__equal,axiom, % 191.28/191.39 ! [T_a] : % 191.28/191.39 ( class_HOL_Oequal(T_a) % 191.28/191.39 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_measure__fst,axiom, % 191.28/191.39 ! [T_b,V_f_2,T_a] : % 191.28/191.39 ( c_FunDef_Ois__measure(T_a,V_f_2) % 191.28/191.39 => c_FunDef_Ois__measure(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_a,T_b)),V_f_2),c_Product__Type_Ofst(T_a,T_b))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_measure__snd,axiom, % 191.28/191.39 ! [T_b,V_f_2,T_a] : % 191.28/191.39 ( c_FunDef_Ois__measure(T_a,V_f_2) % 191.28/191.39 => c_FunDef_Ois__measure(tc_prod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_b,T_a)),V_f_2),c_Product__Type_Osnd(T_b,T_a))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_is__measure_Ointros,axiom, % 191.28/191.39 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_is__measure_Oequations,axiom, % 191.28/191.39 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_is__measure_Osimps,axiom, % 191.28/191.39 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_measure__size,axiom, % 191.28/191.39 ! [T_a] : % 191.28/191.39 ( class_Nat_Osize(T_a) % 191.28/191.39 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_transfer__morphism__int__nat,axiom, % 191.28/191.39 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)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 191.28/191.39 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 191.28/191.39 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.39 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_a) ) % 191.28/191.39 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.39 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I5_J,axiom, % 191.28/191.39 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I2_J,axiom, % 191.28/191.39 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I8_J,axiom, % 191.28/191.39 ! [V_k2_2] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I12_J,axiom, % 191.28/191.39 ! [V_k1_2] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I7_J,axiom, % 191.28/191.39 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I11_J,axiom, % 191.28/191.39 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I4_J,axiom, % 191.28/191.39 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I10_J,axiom, % 191.28/191.39 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I3_J,axiom, % 191.28/191.39 ! [V_k2_2] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I9_J,axiom, % 191.28/191.39 ! [V_k1_2] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I1_J,axiom, % 191.28/191.39 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I16_J,axiom, % 191.28/191.39 ! [V_k2_2,V_k1_2] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__number__of__int__code,axiom, % 191.28/191.39 ! [V_l_2,V_k_2] : % 191.28/191.39 ( 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))) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I13_J,axiom, % 191.28/191.39 ! [V_k2_2,V_k1_2] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 191.28/191.39 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I6_J,axiom, % 191.28/191.39 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_equal__int__def,axiom, % 191.28/191.39 ! [V_l_2,V_k_2] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 191.28/191.39 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I14_J,axiom, % 191.28/191.39 ! [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))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__code_I15_J,axiom, % 191.28/191.39 ! [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))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_bool_Osize_I3_J,axiom, % 191.28/191.39 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(fact_bool_Osize_I4_J,axiom, % 191.28/191.39 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 191.28/191.39 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Opos__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__DSequence_Opos__empty__def,axiom, % 191.28/191.39 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 191.28/191.39 % 191.28/191.39 fof(fact_eq__int__refl,axiom, % 191.28/191.39 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_pos__empty__def,axiom, % 191.28/191.39 ! [V_seed_2,V_size_2,V_nrandom_2,T_a] : c_New__Random__Sequence_Opos__empty(T_a,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_a) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__DSequence_Opos__bind__def,axiom, % 191.28/191.39 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Opos__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_pos__bind__def,axiom, % 191.28/191.39 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_size__code,axiom, % 191.28/191.39 ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),T_a),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_lazy__sequence__size__code,axiom, % 191.28/191.39 ! [V_xq_2,V_s_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_a,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_a),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_seq__case,axiom, % 191.28/191.39 ! [V_xq_2,V_g_2,V_f_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f_2,V_g_2,V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(T_a,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),T_a),V_g_2)),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_yieldn__def,axiom, % 191.28/191.39 ! [T_a] : c_Lazy__Sequence_Oyieldn(T_a) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_a),T_a,c_Lazy__Sequence_Oyield(T_a)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 191.28/191.39 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 191.28/191.39 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_lazy__sequence_Oinject,axiom, % 191.28/191.39 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 191.28/191.39 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2) % 191.28/191.39 <=> ( V_a_2 = V_a_H_2 % 191.28/191.39 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact__01,axiom, % 191.28/191.39 ! [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)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 191.28/191.39 ! [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))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_pos__map__def,axiom, % 191.28/191.39 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Opos__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),T_b,c_New__Random__Sequence_Opos__single(T_a)),V_f_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 191.28/191.39 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 191.28/191.39 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.39 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_a) ) % 191.28/191.39 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 191.28/191.39 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 191.28/191.39 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Oneg__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_pos__single__def,axiom, % 191.28/191.39 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_a,V_x_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__DSequence_Opos__single__def,axiom, % 191.28/191.39 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 191.28/191.39 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Oneg__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_neg__bind__def,axiom, % 191.28/191.39 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact__02,axiom, % 191.28/191.39 ! [V_s2_2,V_s1_2,T_b,T_a] : c_Lazy__Sequence_Oproduct(T_a,T_b,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_a,tc_prod(T_a,T_b),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_a),c_Lazy__Sequence_Obind(T_b,tc_prod(T_a,T_b),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_b),c_Lazy__Sequence_Osingle(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))) ). % 191.28/191.39 % 191.28/191.39 fof(fact_neg__map__def,axiom, % 191.28/191.39 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Oneg__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),T_b,c_New__Random__Sequence_Oneg__single(T_a)),V_f_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_small__lazy__list_Osimps,axiom, % 191.28/191.39 ! [V_d_2,T_a] : % 191.28/191.39 ( class_Lazy__Sequence_Osmall__lazy(T_a) % 191.28/191.39 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_a),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),c_Lazy__Sequence_Oproduct(T_a,tc_List_Olist(T_a),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)))),c_List_Olist_OCons(T_a))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_a)))) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact_small__lazy__prod__def,axiom, % 191.28/191.39 ! [V_d,T_b,T_a] : % 191.28/191.39 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 191.28/191.39 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 191.28/191.39 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ). % 191.28/191.39 % 191.28/191.39 fof(fact__03,axiom, % 191.28/191.39 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_neg__single__def,axiom, % 191.28/191.39 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_a,V_x_2) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__DSequence_Opos__union__def,axiom, % 191.28/191.39 ! [V_i_2,V_yq_2,V_xq_2,T_a] : hAPP(c_New__DSequence_Opos__union(T_a,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_a,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_New__DSequence_Oneg__single__def,axiom, % 191.28/191.39 ! [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) ). % 191.28/191.39 % 191.28/191.39 fof(fact_pos__union__def,axiom, % 191.28/191.39 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_a] : c_New__Random__Sequence_Opos__union(T_a,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_a,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 191.28/191.39 % 191.28/191.39 fof(fact_small__lazy_H_Osimps,axiom, % 191.28/191.39 ! [V_i,V_d] : % 191.28/191.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 191.28/191.39 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 191.28/191.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 191.28/191.39 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ). % 191.28/191.39 % 191.28/191.39 %----Arity declarations (239) % 191.28/191.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 191.28/191.39 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Lattices_Obounded__lattice(T_1) % 191.28/191.39 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 191.28/191.39 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Lattices_Obounded__lattice(T_1) % 191.28/191.39 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Lattices_Obounded__lattice(T_1) % 191.28/191.39 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Lattices_Olattice(T_1) % 191.28/191.39 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Lattices_Olattice(T_1) % 191.28/191.39 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Lattices_Odistrib__lattice(T_1) % 191.28/191.39 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Lattices_Oboolean__algebra(T_1) % 191.28/191.39 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Orderings_Opreorder,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Orderings_Opreorder(T_1) % 191.28/191.39 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Finite__Set_Ofinite,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Finite__Set_Ofinite(T_2) % 191.28/191.39 & class_Finite__Set_Ofinite(T_1) ) % 191.28/191.39 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Lattices_Olattice,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Lattices_Olattice(T_1) % 191.28/191.39 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Orderings_Oorder,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Orderings_Oorder(T_1) % 191.28/191.39 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Orderings_Otop,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Orderings_Otop(T_1) % 191.28/191.39 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Orderings_Oord,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Orderings_Oord(T_1) % 191.28/191.39 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Orderings_Obot,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Orderings_Obot(T_1) % 191.28/191.39 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Groups_Ouminus,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Groups_Ouminus(T_1) % 191.28/191.39 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Groups_Ominus,axiom, % 191.28/191.39 ! [T_2,T_1] : % 191.28/191.39 ( class_Groups_Ominus(T_1) % 191.28/191.39 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__HOL_Oequal,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Enum_Oenum(T_2) % 191.28/191.39 & class_HOL_Oequal(T_1) ) % 191.28/191.39 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_fun__Enum_Oenum,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Enum_Oenum(T_2) % 191.28/191.39 & class_Enum_Oenum(T_1) ) % 191.28/191.39 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_Com_Ocom) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Com__Ocom__Nat_Osize,axiom, % 191.28/191.39 class_Nat_Osize(tc_Com_Ocom) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 191.28/191.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 191.28/191.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 191.28/191.39 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 191.28/191.39 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 191.28/191.39 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 191.28/191.39 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 191.28/191.39 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 191.28/191.39 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 191.28/191.39 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 191.28/191.39 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 191.28/191.39 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 191.28/191.39 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 191.28/191.39 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 191.28/191.39 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 191.28/191.39 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 191.28/191.39 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 191.28/191.39 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 191.28/191.39 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 191.28/191.39 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 191.28/191.39 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 191.28/191.39 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 191.28/191.39 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 191.28/191.39 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 191.28/191.39 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 191.28/191.39 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 191.28/191.39 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 191.28/191.39 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 191.28/191.39 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 191.28/191.39 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 191.28/191.39 class_Divides_Osemiring__div(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 191.28/191.39 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 191.28/191.39 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 191.28/191.39 class_Groups_Oab__group__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 191.28/191.39 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 191.28/191.39 class_Rings_Oordered__ring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 191.28/191.39 class_Orderings_Opreorder(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 191.28/191.39 class_Orderings_Olinorder(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 191.28/191.39 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 191.28/191.39 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 191.28/191.39 class_Groups_Omonoid__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 191.28/191.39 class_Smallcheck_Osmall(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 191.28/191.39 class_Rings_Osemiring__1(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 191.28/191.39 class_Rings_Osemiring__0(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 191.28/191.39 class_Lattices_Olattice(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 191.28/191.39 class_Groups_Ogroup__add(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 191.28/191.39 class_Divides_Oring__div(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 191.28/191.39 class_Rings_Omult__zero(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 191.28/191.39 class_Orderings_Oorder(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 191.28/191.39 class_Int_Oring__char__0(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 191.28/191.39 class_Int_Onumber__ring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 191.28/191.39 class_Rings_Osemiring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Orderings_Oord,axiom, % 191.28/191.39 class_Orderings_Oord(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 191.28/191.39 class_Groups_Ouminus(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 191.28/191.39 class_Groups_Osgn__if(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 191.28/191.39 class_Groups_Oabs__if(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 191.28/191.39 class_Rings_Oring__1(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Ominus,axiom, % 191.28/191.39 class_Groups_Ominus(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Power_Opower,axiom, % 191.28/191.39 class_Power_Opower(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Ozero,axiom, % 191.28/191.39 class_Groups_Ozero(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oring,axiom, % 191.28/191.39 class_Rings_Oring(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Rings_Oidom,axiom, % 191.28/191.39 class_Rings_Oidom(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Int_Onumber,axiom, % 191.28/191.39 class_Int_Onumber(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__Groups_Oone,axiom, % 191.28/191.39 class_Groups_Oone(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Int__Oint__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_Int_Oint) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 191.28/191.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 191.28/191.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 191.28/191.39 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 191.28/191.39 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 191.28/191.39 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 191.28/191.39 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 191.28/191.39 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 191.28/191.39 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 191.28/191.39 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 191.28/191.39 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 191.28/191.39 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 191.28/191.39 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 191.28/191.39 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 191.28/191.39 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 191.28/191.39 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 191.28/191.39 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 191.28/191.39 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 191.28/191.39 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 191.28/191.39 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 191.28/191.39 class_Orderings_Owellorder(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 191.28/191.39 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 191.28/191.39 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 191.28/191.39 class_Orderings_Opreorder(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 191.28/191.39 class_Orderings_Olinorder(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 191.28/191.39 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 191.28/191.39 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 191.28/191.39 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 191.28/191.39 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 191.28/191.39 class_Lattices_Olattice(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 191.28/191.39 class_Rings_Omult__zero(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 191.28/191.39 class_Orderings_Oorder(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 191.28/191.39 class_Rings_Osemiring(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 191.28/191.39 class_Orderings_Oord(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 191.28/191.39 class_Orderings_Obot(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 191.28/191.39 class_Groups_Ominus(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Power_Opower,axiom, % 191.28/191.39 class_Power_Opower(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 191.28/191.39 class_Groups_Ozero(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Int_Onumber,axiom, % 191.28/191.39 class_Int_Onumber(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Groups_Oone,axiom, % 191.28/191.39 class_Groups_Oone(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nat__Onat__Nat_Osize,axiom, % 191.28/191.39 class_Nat_Osize(tc_Nat_Onat) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 191.28/191.39 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 191.28/191.39 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 191.28/191.39 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 191.28/191.39 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 191.28/191.39 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 191.28/191.39 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 191.28/191.39 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 191.28/191.39 class_Orderings_Opreorder(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 191.28/191.39 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 191.28/191.39 class_Lattices_Olattice(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 191.28/191.39 class_Orderings_Oorder(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 191.28/191.39 class_Orderings_Otop(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 191.28/191.39 class_Orderings_Oord(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 191.28/191.39 class_Orderings_Obot(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 191.28/191.39 class_Groups_Ouminus(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 191.28/191.39 class_Groups_Ominus(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 191.28/191.39 class_Enum_Oenum(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_HOL__Obool__Nat_Osize,axiom, % 191.28/191.39 class_Nat_Osize(tc_HOL_Obool) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_Com_Ostate) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Com__Ostate__Nat_Osize,axiom, % 191.28/191.39 class_Nat_Osize(tc_Com_Ostate) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Com__Ovname__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_Com_Ovname) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Com__Ovname__Nat_Osize,axiom, % 191.28/191.39 class_Nat_Osize(tc_Com_Ovname) ). % 191.28/191.39 % 191.28/191.39 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 191.28/191.39 ! [T_1] : % 191.28/191.39 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 191.28/191.39 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_List__Olist__HOL_Oequal,axiom, % 191.28/191.39 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_List__Olist__Nat_Osize,axiom, % 191.28/191.39 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_sum__Finite__Set_Ofinite,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Finite__Set_Ofinite(T_2) % 191.28/191.39 & class_Finite__Set_Ofinite(T_1) ) % 191.28/191.39 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_sum__HOL_Oequal,axiom, % 191.28/191.39 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_sum__Enum_Oenum,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Enum_Oenum(T_2) % 191.28/191.39 & class_Enum_Oenum(T_1) ) % 191.28/191.39 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_sum__Nat_Osize,axiom, % 191.28/191.39 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 191.28/191.39 ! [T_1] : % 191.28/191.39 ( class_Finite__Set_Ofinite(T_1) % 191.28/191.39 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 191.28/191.39 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 191.28/191.39 ! [T_1] : % 191.28/191.39 ( class_Enum_Oenum(T_1) % 191.28/191.39 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Option__Ooption__Nat_Osize,axiom, % 191.28/191.39 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom, % 191.28/191.39 ! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom, % 191.28/191.39 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 191.28/191.39 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 191.28/191.39 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_prod__Finite__Set_Ofinite,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Finite__Set_Ofinite(T_2) % 191.28/191.39 & class_Finite__Set_Ofinite(T_1) ) % 191.28/191.39 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_prod__Smallcheck_Osmall,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Smallcheck_Osmall(T_2) % 191.28/191.39 & class_Smallcheck_Osmall(T_1) ) % 191.28/191.39 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_prod__HOL_Oequal,axiom, % 191.28/191.39 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_prod__Enum_Oenum,axiom, % 191.28/191.39 ! [T_1,T_2] : % 191.28/191.39 ( ( class_Enum_Oenum(T_2) % 191.28/191.39 & class_Enum_Oenum(T_1) ) % 191.28/191.39 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 191.28/191.39 % 191.28/191.39 fof(arity_prod__Nat_Osize,axiom, % 191.28/191.39 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 191.28/191.39 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 191.28/191.39 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 191.28/191.39 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 191.28/191.39 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 191.28/191.39 class_Nat_Osize(tc_Product__Type_Ounit) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 191.28/191.39 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 191.28/191.39 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 191.28/191.39 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 191.28/191.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 191.28/191.39 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 191.28/191.39 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 191.28/191.39 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 191.28/191.39 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 191.28/191.39 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 191.28/191.39 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 191.28/191.39 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 191.28/191.39 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 191.28/191.39 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 191.28/191.39 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 191.28/191.39 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 191.28/191.39 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 191.28/191.39 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 191.28/191.39 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 191.28/191.39 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 191.28/191.39 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 191.28/191.39 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 191.28/191.39 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 191.28/191.39 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 191.28/191.39 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 191.28/191.39 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 191.28/191.39 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 191.28/191.39 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 191.28/191.39 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 191.28/191.39 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 191.28/191.39 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 191.28/191.39 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 191.28/191.39 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 191.28/191.39 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 191.28/191.39 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 191.28/191.39 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 191.28/191.39 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 191.28/191.39 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 191.28/191.39 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 191.28/191.39 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 191.28/191.39 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 191.28/191.39 % 191.28/191.39 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 191.28/191.39 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 191.28/191.39 % 191.28/191.39 %----Helper facts (20) % 191.28/191.39 fof(help_c__COMBI__1,axiom, % 191.28/191.39 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 191.28/191.39 % 191.28/191.39 fof(help_c__COMBK__1,axiom, % 191.28/191.39 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 191.28/191.39 % 191.28/191.39 fof(help_c__COMBB__1,axiom, % 191.28/191.39 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__COMBC__1,axiom, % 191.28/191.39 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__COMBS__1,axiom, % 191.28/191.39 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fequal__1,axiom, % 191.28/191.39 ! [V_y_2,V_x_2] : % 191.28/191.39 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 191.28/191.39 | V_x_2 = V_y_2 ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fequal__2,axiom, % 191.28/191.39 ! [V_y_2,V_x_2] : % 191.28/191.39 ( V_x_2 != V_y_2 % 191.28/191.39 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fFalse__1,axiom, % 191.28/191.39 ~ hBOOL(c_fFalse) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fTrue__1,axiom, % 191.28/191.39 hBOOL(c_fTrue) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fNot__1,axiom, % 191.28/191.39 ! [V_P_2] : % 191.28/191.39 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 191.28/191.39 | ~ hBOOL(V_P_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fNot__2,axiom, % 191.28/191.39 ! [V_P_2] : % 191.28/191.39 ( ~ ~ hBOOL(V_P_2) % 191.28/191.39 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fconj__1,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2] : % 191.28/191.39 ( ~ hBOOL(V_P_2) % 191.28/191.39 | ~ hBOOL(V_Q_2) % 191.28/191.39 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fconj__2,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2] : % 191.28/191.39 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 191.28/191.39 | hBOOL(V_P_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fconj__3,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2] : % 191.28/191.39 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 191.28/191.39 | hBOOL(V_Q_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fdisj__1,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2] : % 191.28/191.39 ( ~ hBOOL(V_P_2) % 191.28/191.39 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fdisj__2,axiom, % 191.28/191.39 ! [V_P_2,V_Q_2] : % 191.28/191.39 ( ~ hBOOL(V_Q_2) % 191.28/191.39 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fdisj__3,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2] : % 191.28/191.39 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 191.28/191.39 | hBOOL(V_P_2) % 191.28/191.39 | hBOOL(V_Q_2) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fimplies__1,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2] : % 191.28/191.39 ( hBOOL(V_P_2) % 191.28/191.39 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fimplies__2,axiom, % 191.28/191.39 ! [V_P_2,V_Q_2] : % 191.28/191.39 ( ~ hBOOL(V_Q_2) % 191.28/191.39 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 191.28/191.39 % 191.28/191.39 fof(help_c__fimplies__3,axiom, % 191.28/191.39 ! [V_Q_2,V_P_2] : % 191.28/191.39 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 191.28/191.39 | ~ hBOOL(V_P_2) % 191.28/191.39 | hBOOL(V_Q_2) ) ). % 191.28/191.39 % 191.28/191.39 %----Conjectures (5) % 191.28/191.39 fof(conj_0,hypothesis, % 191.28/191.39 c_Com_OWT__bodies ). % 191.28/191.39 % 191.28/191.39 fof(conj_1,hypothesis, % 191.28/191.39 hBOOL(hAPP(c_Com_OWT,v_c)) ). % 191.28/191.39 % 191.28/191.39 fof(conj_2,hypothesis, % 191.28/191.39 v_Sledgehammer_058wt__2(v_ca) ). % 191.28/191.39 % 191.28/191.39 fof(conj_3,hypothesis, % 191.28/191.39 ! [B_pn] : % 191.28/191.39 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 191.28/191.39 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 191.28/191.39 % 191.28/191.39 fof(conj_4,conjecture, % 191.28/191.39 hBOOL(hAPP(c_Com_OWT,v_ca)) ). % 191.28/191.39 % 191.28/191.39 %------------------------------------------------------------------------------ % 191.28/191.39 %------------------------------------------- % 191.28/191.39 % Proof found % 191.28/191.39 % SZS status Theorem for theBenchmark % 191.28/191.39 % SZS output start Proof % 191.49/191.39 %ClaNum:10234(EqnAxiom:2897) % 191.49/191.39 %VarNum:70008(SingletonVarNum:20453) % 191.49/191.39 %MaxLitNum:8 % 191.49/191.39 %MaxfuncDepth:15 % 191.49/191.39 %SharedTerms:1107 % 191.49/191.39 %goalClause: 4500 % 191.49/191.39 %singleGoalClaCount:1 % 191.49/191.39 [2898]P1(a5000) % 191.49/191.39 [2902]P4(a193) % 191.49/191.39 [2903]P5(a874) % 191.49/191.39 [2904]P5(a880) % 191.49/191.39 [2905]P6(a874) % 191.49/191.39 [2906]P6(a880) % 191.49/191.39 [2907]P6(a1) % 191.49/191.39 [2908]P7(a874) % 191.49/191.39 [2909]P8(a874) % 191.49/191.39 [2910]P8(a883) % 191.49/191.39 [2911]P101(a874) % 191.49/191.39 [2912]P101(a880) % 191.49/191.39 [2913]P101(a1) % 191.49/191.39 [2914]P67(a874) % 191.49/191.39 [2915]P67(a880) % 191.49/191.39 [2916]P67(a1) % 191.49/191.39 [2917]P67(a104) % 191.49/191.39 [2918]P102(a874) % 191.49/191.39 [2919]P102(a880) % 191.49/191.39 [2920]P102(a1) % 191.49/191.39 [2921]P99(a874) % 191.49/191.39 [2922]P99(a880) % 191.49/191.39 [2923]P99(a1) % 191.49/191.39 [2924]P9(a874) % 191.49/191.39 [2925]P68(a1) % 191.49/191.39 [2926]P106(a1) % 191.49/191.39 [2927]P79(a874) % 191.49/191.39 [2928]P80(a874) % 191.49/191.39 [2929]P80(a1) % 191.49/191.39 [2930]P69(a880) % 191.49/191.39 [2931]P69(a1) % 191.49/191.39 [2932]P69(a104) % 191.49/191.39 [2933]P70(a880) % 191.49/191.39 [2934]P70(a1) % 191.49/191.39 [2935]P70(a104) % 191.49/191.39 [2936]P71(a880) % 191.49/191.39 [2937]P71(a1) % 191.49/191.39 [2938]P71(a104) % 191.49/191.39 [2939]P72(a880) % 191.49/191.39 [2940]P72(a1) % 191.49/191.39 [2941]P72(a104) % 191.49/191.39 [2942]P107(a874) % 191.49/191.39 [2943]P75(a1) % 191.49/191.39 [2944]P100(a874) % 191.49/191.39 [2945]P112(a1) % 191.49/191.39 [2946]P115(a880) % 191.49/191.39 [2947]P115(a1) % 191.49/191.39 [2948]P115(a104) % 191.49/191.39 [2949]P73(a880) % 191.49/191.39 [2950]P73(a1) % 191.49/191.39 [2951]P73(a104) % 191.49/191.39 [2952]P137(a880) % 191.49/191.39 [2953]P137(a1) % 191.49/191.39 [2954]P117(a1) % 191.49/191.39 [2955]P116(a880) % 191.49/191.39 [2956]P116(a1) % 191.49/191.39 [2957]P116(a104) % 191.49/191.39 [2958]P138(a880) % 191.49/191.39 [2959]P138(a1) % 191.49/191.39 [2960]P138(a104) % 191.49/191.39 [2961]P76(a880) % 191.49/191.39 [2962]P76(a1) % 191.49/191.39 [2963]P76(a104) % 191.49/191.39 [2964]P81(a1) % 191.49/191.39 [2965]P108(a874) % 191.49/191.39 [2966]P108(a880) % 191.49/191.39 [2967]P108(a1) % 191.49/191.39 [2968]P108(a104) % 191.49/191.39 [2969]P109(a880) % 191.49/191.39 [2970]P109(a1) % 191.49/191.39 [2971]P109(a104) % 191.49/191.39 [2972]P110(a874) % 191.49/191.39 [2973]P110(a880) % 191.49/191.39 [2974]P110(a1) % 191.49/191.39 [2975]P110(a104) % 191.49/191.39 [2976]P111(a874) % 191.49/191.39 [2977]P111(a880) % 191.49/191.39 [2978]P111(a1) % 191.49/191.39 [2979]P111(a104) % 191.49/191.39 [2980]P82(a880) % 191.49/191.39 [2981]P82(a1) % 191.49/191.39 [2982]P82(a104) % 191.49/191.39 [2983]P120(a1) % 191.49/191.39 [2984]P123(a880) % 191.49/191.39 [2985]P123(a1) % 191.49/191.39 [2986]P123(a104) % 191.49/191.39 [2987]P83(a880) % 191.49/191.39 [2988]P83(a1) % 191.49/191.39 [2989]P83(a104) % 191.49/191.39 [2990]P85(a880) % 191.49/191.39 [2991]P85(a1) % 191.49/191.39 [2992]P85(a104) % 191.49/191.39 [2993]P88(a880) % 191.49/191.39 [2994]P88(a1) % 191.49/191.39 [2995]P88(a104) % 191.49/191.39 [2996]P139(a1) % 191.49/191.39 [2997]P126(a1) % 191.49/191.39 [2998]P92(a880) % 191.49/191.39 [2999]P92(a1) % 191.49/191.39 [3000]P92(a104) % 191.49/191.39 [3001]P84(a880) % 191.49/191.39 [3002]P84(a1) % 191.49/191.39 [3003]P84(a104) % 191.49/191.39 [3004]P77(a1) % 191.49/191.39 [3005]P127(a880) % 191.49/191.39 [3006]P127(a1) % 191.49/191.39 [3007]P127(a104) % 191.49/191.39 [3008]P141(a1) % 191.49/191.39 [3009]P128(a880) % 191.49/191.39 [3010]P128(a1) % 191.49/191.39 [3011]P128(a104) % 191.49/191.39 [3012]P142(a880) % 191.49/191.39 [3013]P142(a1) % 191.49/191.39 [3014]P142(a104) % 191.49/191.39 [3015]P124(a1) % 191.49/191.39 [3016]P125(a1) % 191.49/191.39 [3017]P89(a880) % 191.49/191.39 [3018]P89(a1) % 191.49/191.39 [3019]P89(a104) % 191.49/191.39 [3020]P121(a880) % 191.49/191.39 [3021]P121(a1) % 191.49/191.39 [3022]P121(a104) % 191.49/191.39 [3023]P129(a880) % 191.49/191.39 [3024]P129(a1) % 191.49/191.39 [3025]P129(a104) % 191.49/191.39 [3026]P90(a1) % 191.49/191.39 [3027]P140(a1) % 191.49/191.39 [3028]P93(a1) % 191.49/191.39 [3029]P86(a880) % 191.49/191.39 [3030]P86(a1) % 191.49/191.39 [3031]P86(a104) % 191.49/191.39 [3032]P133(a880) % 191.49/191.39 [3033]P133(a1) % 191.49/191.39 [3034]P133(a104) % 191.49/191.39 [3035]P135(a880) % 191.49/191.39 [3036]P135(a1) % 191.49/191.39 [3037]P135(a104) % 191.49/191.39 [3038]P134(a880) % 191.49/191.39 [3039]P134(a1) % 191.49/191.39 [3040]P134(a104) % 191.49/191.39 [3041]P130(a880) % 191.49/191.39 [3042]P130(a1) % 191.49/191.39 [3043]P130(a104) % 191.49/191.39 [3044]P131(a1) % 191.49/191.39 [3045]P132(a1) % 191.49/191.39 [3046]P94(a1) % 191.49/191.39 [3047]P95(a880) % 191.49/191.39 [3048]P95(a1) % 191.49/191.39 [3049]P95(a104) % 191.49/191.39 [3050]P103(a880) % 191.49/191.39 [3051]P103(a1) % 191.49/191.39 [3052]P103(a104) % 191.49/191.39 [3053]P143(a880) % 191.49/191.39 [3054]P143(a1) % 191.49/191.39 [3055]P143(a104) % 191.49/191.39 [3056]P87(a1) % 191.49/191.39 [3057]P136(a1) % 191.49/191.39 [3058]P74(a1) % 191.49/191.39 [3059]P60(a880) % 191.49/191.39 [3060]P60(a1) % 191.49/191.39 [3061]P60(a104) % 191.49/191.39 [3062]P61(a1) % 191.49/191.39 [3063]P113(a880) % 191.49/191.39 [3064]P113(a1) % 191.49/191.39 [3065]P113(a104) % 191.49/191.39 [3066]P144(a880) % 191.49/191.39 [3067]P144(a1) % 191.49/191.39 [3068]P144(a104) % 191.49/191.39 [3069]P145(a883) % 191.49/191.39 [3070]P145(a1) % 191.49/191.39 [3071]P78(a880) % 191.49/191.39 [3072]P78(a1) % 191.49/191.39 [3073]P78(a104) % 191.49/191.39 [3074]P91(a880) % 191.49/191.39 [3075]P91(a1) % 191.49/191.39 [3076]P91(a104) % 191.49/191.39 [3077]P62(a874) % 191.49/191.39 [3078]P62(a883) % 191.49/191.39 [3079]P96(a874) % 191.49/191.39 [3080]P96(a875) % 191.49/191.39 [3081]P96(a876) % 191.49/191.39 [3082]P96(a880) % 191.49/191.39 [3083]P96(a883) % 191.49/191.39 [3084]P96(a1) % 191.49/191.39 [3085]P96(a104) % 191.49/191.39 [3086]P96(a329) % 191.49/191.39 [3087]P96(a878) % 191.49/191.39 [3088]P114(a880) % 191.49/191.39 [3089]P105(a874) % 191.49/191.39 [3090]P105(a875) % 191.49/191.39 [3091]P105(a876) % 191.49/191.39 [3092]P105(a880) % 191.49/191.39 [3093]P105(a883) % 191.49/191.39 [3094]P105(a104) % 191.49/191.39 [3095]P105(a329) % 191.49/191.39 [3096]P105(a878) % 191.49/191.39 [3097]P104(a883) % 191.49/191.39 [3098]P104(a1) % 191.49/191.39 [3099]P98(a874) % 191.49/191.39 [3100]P148(a886) % 191.49/191.39 [3120]P40(a880,a254) % 191.49/191.39 [3121]P40(a880,a323) % 191.49/191.39 [4481]~E(a102,a84) % 191.49/191.39 [4482]~P4(a247) % 191.49/191.39 [2899]E(f2(a1),a84) % 191.49/191.39 [2900]E(f3(a104),a4) % 191.49/191.39 [2901]E(f105(a104),a5) % 191.49/191.39 [3101]E(f194(a880),f2(a880)) % 191.49/191.39 [3102]E(f32(a24),f2(a880)) % 191.49/191.39 [3103]E(f85(a193),f2(a880)) % 191.49/191.39 [3104]E(f85(a247),f2(a880)) % 191.49/191.39 [3105]E(f106(a880),f248(a880)) % 191.49/191.39 [3106]E(f115(a880),f249(a880)) % 191.49/191.39 [3107]E(f107(a1),f35(a1)) % 191.49/191.39 [3108]P10(f79(a1)) % 191.49/191.39 [3109]P10(f2(a1)) % 191.49/191.39 [3159]P4(f333(a25,a24)) % 191.49/191.39 [3160]P4(f333(a25,a887)) % 191.49/191.39 [3175]P40(f889(a880,a880),a36) % 191.49/191.39 [3520]E(f326(a880,a880,a254,a254),a36) % 191.49/191.39 [4483]~E(f79(a1),f2(a1)) % 191.49/191.39 [4500]~P4(f333(a25,a886)) % 191.49/191.39 [3110]E(f116(f2(a880)),f2(a880)) % 191.49/191.39 [3111]E(f6(f2(a104)),f2(a880)) % 191.49/191.39 [3123]E(f333(f80(a1),a84),a84) % 191.49/191.39 [3126]E(f333(a117,f2(a880)),f79(a880)) % 191.49/191.39 [3127]E(f333(a109,f79(a1)),f79(a880)) % 191.49/191.39 [3128]E(f333(a5,f79(a880)),f79(a104)) % 191.49/191.39 [3130]E(f333(a5,f2(a880)),f2(a104)) % 191.49/191.39 [3132]E(f333(f108(a1),a84),f2(a1)) % 191.49/191.39 [3133]E(f333(f108(a104),a84),f2(a104)) % 191.49/191.39 [3134]E(f333(a109,f2(a1)),f2(a880)) % 191.49/191.39 [3135]E(f333(f195(a874),a193),f2(a880)) % 191.49/191.39 [3136]E(f333(f195(a874),a247),f2(a880)) % 191.49/191.39 [3137]E(f333(f195(a876),a24),f2(a880)) % 191.49/191.39 [3138]E(f333(f108(a880),a84),f2(a880)) % 191.49/191.39 [3143]E(f333(f80(a1),f79(a1)),a102) % 191.49/191.39 [3150]E(f333(f80(a1),f2(a1)),f2(a1)) % 191.49/191.39 [3152]E(f333(f195(a104),f2(a104)),f2(a880)) % 191.49/191.39 [3153]E(f333(f105(a1),f79(a880)),f79(a1)) % 191.49/191.39 [3154]E(f333(f105(a1),f2(a880)),f2(a1)) % 191.49/191.39 [3171]E(f333(a109,f79(a1)),f333(a117,f2(a880))) % 191.49/191.39 [3172]E(f333(f178(a877,a876),a27),a28) % 191.49/191.39 [3173]E(f324(f889(a880,a880),a36),a37) % 191.49/191.39 [3174]E(f325(f889(a880,a880),a36),a38) % 191.49/191.39 [3195]E(f333(f256(a880),f2(a880)),f194(f890(a880,a874))) % 191.49/191.39 [3196]E(f333(f257(a880),f2(a880)),f258(f890(a880,a874))) % 191.49/191.39 [3204]P42(f194(f890(a1,a874))) % 191.49/191.39 [3239]E(f333(f333(f3(a104),f2(a104)),f79(a104)),f2(a104)) % 191.49/191.39 [3316]P4(f333(f333(f251(a1),a102),f2(a1))) % 191.49/191.39 [3341]P4(f333(f333(f251(a1),f2(a1)),f79(a1))) % 191.49/191.39 [3342]P4(f333(f333(f250(a1),f2(a1)),f79(a1))) % 191.49/191.39 [3513]P4(f333(f63(a877),f184(a877,a876,a28))) % 191.49/191.39 [3549]E(f333(f333(f290(a880,a880,a880),a323),f309(a880,a323)),a254) % 191.49/191.39 [3588]P43(a1,a880,a109,f333(f250(a1),f2(a1))) % 191.49/191.39 [3592]E(f333(f333(f43(a880,f890(a880,a874)),f258(f890(a880,a874))),f305(a880)),f194(f890(a880,a874))) % 191.49/191.39 [3593]E(f333(f333(f44(a880,f890(a880,a874)),f258(f890(a880,a874))),f256(a880)),f258(f890(a880,a874))) % 191.49/191.39 [3594]E(f333(f333(f44(a880,f890(a880,a874)),f258(f890(a880,a874))),f302(a880)),f258(f890(a880,a874))) % 191.49/191.39 [3595]E(f333(f333(f44(a880,f890(a880,a874)),f258(f890(a880,a874))),f257(a880)),f258(f890(a880,a874))) % 191.49/191.39 [3612]P28(a880,a1,f105(a1),f258(f890(a880,a874))) % 191.49/191.39 [3623]P43(a880,a1,f105(a1),f333(f18(a874,a880),a193)) % 191.49/191.39 [3751]E(f333(f74(a880,a104,a1,a5),a109),f108(a104)) % 191.49/191.39 [3973]P56(a104,a880,a21,a5,f258(f890(a880,a874))) % 191.49/191.39 [3981]P56(a1,f890(f889(a880,a880),a874),a111,a90,a103) % 191.49/191.39 [4242]E(f273(a1,a1,a1,a1,f35(a1),f80(a1)),a52) % 191.49/191.39 [4507]~E(f333(f108(a1),a102),f333(f108(a1),a84)) % 191.49/191.39 [4508]~P4(f333(a200,f79(a1))) % 191.49/191.39 [4509]~P4(f333(a200,f2(a1))) % 191.49/191.39 [4557]~P4(f333(f333(f251(a1),a84),f2(a1))) % 191.49/191.39 [3188]E(f333(f333(f3(a1),a102),a102),a84) % 191.49/191.39 [3202]E(f333(f105(a1),f333(a117,f2(a880))),f79(a1)) % 191.49/191.39 [3265]E(f333(f39(a883),f258(f890(a883,a874))),f79(a880)) % 191.49/191.39 [3286]P4(f333(a200,f333(f108(a1),a102))) % 191.49/191.39 [3287]P4(f333(f333(f251(a1),a102),a84)) % 191.49/191.39 [3289]P4(f333(f333(f250(a1),a102),a84)) % 191.49/191.39 [3353]E(f333(f333(f311(a880),f2(a880)),f194(f890(a880,a874))),f333(f302(a880),f2(a880))) % 191.49/191.39 [3408]P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),a84))) % 191.49/191.39 [3420]E(f333(f312(a880,a880,a117),f258(f890(a880,a874))),f333(f305(a880),f2(a880))) % 191.49/191.39 [3459]P12(f889(a880,a880),f258(f890(f889(a880,a880),a874)),a113) % 191.49/191.39 [3759]E(f333(f74(a880,a1,a104,f105(a1)),a21),a22) % 191.49/191.39 [3823]P40(a880,f333(f255(f889(a880,a880)),f333(f272(a880,a880,a874),f251(a880)))) % 191.49/191.39 [4546]~P4(f333(a200,f333(f108(a1),a84))) % 191.49/191.39 [4547]~P4(f333(f333(f251(a1),a84),a84)) % 191.49/191.39 [4548]~P4(f333(f333(f251(a1),a84),a102)) % 191.49/191.39 [4549]~P4(f333(f333(f251(a1),a102),a102)) % 191.49/191.39 [4550]~P4(f333(f333(f250(a1),a84),a102)) % 191.49/191.39 [4551]~P4(f333(f333(f92(a1),a84),a102)) % 191.49/191.39 [4552]~P4(f333(f333(f92(a1),a102),a84)) % 191.49/191.39 [4567]~P4(f333(f63(a880),f258(f890(a880,a874)))) % 191.49/191.39 [4568]~P4(f333(f63(a1),f258(f890(a1,a874)))) % 191.49/191.39 [4422]E(f333(f272(a1,a1,a874),f333(f333(f10(f890(a1,a874),f890(a1,a874),a1),f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f251(a1),f2(a1))))),f333(f333(f9(a1,a1,f890(a1,a874)),f333(f333(f10(f890(a1,f890(a1,a874)),f890(a1,f890(a1,a874)),a1),f9(a1,a1,a874)),f333(f333(f10(f890(a1,a1),f890(a1,f890(a1,a874)),a1),f333(f10(a1,f890(a1,a874),a1),a330)),a227))),f79(a1)))),a223) % 191.49/191.39 [3522]E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a102)),a102),a102) % 191.49/191.39 [3559]E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84),f333(f80(a1),a102)) % 191.49/191.39 [3597]E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84),f333(f333(f3(a1),a84),a102)) % 191.49/191.39 [3692]E(f333(f333(f62(f889(a880,a880)),f258(f890(f889(a880,a880),a874))),a113),a103) % 191.49/191.39 [3761]E(f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),f79(a1)) % 191.49/191.39 [3762]E(f333(f108(a104),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),f79(a104)) % 191.49/191.39 [3763]E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),f79(a880)) % 191.49/191.39 [3771]E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),f333(a117,f2(a880))) % 191.49/191.39 [4102]E(f333(f333(f115(f890(f889(f889(a880,a880),f889(a880,a880)),a874)),a36),f309(f889(a880,a880),f194(f890(f889(f889(a880,a880),f889(a880,a880)),a874)))),a71) % 191.49/191.39 [4168]E(f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),f79(a880)),f2(a880))),f194(f890(f889(a880,a880),a874))))),f79(a1)) % 191.49/191.39 [4169]E(f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),f2(a880)),f2(a880))),f194(f890(f889(a880,a880),a874))))),f2(a1)) % 191.49/191.39 [4184]E(f333(f255(f889(a880,a880)),f333(f272(a880,a880,a874),f333(f333(f10(a880,f890(a880,a874),a880),f333(f9(a880,a880,a874),a330)),a117))),a323) % 191.49/191.39 [3923]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),a102),a84) % 191.49/191.39 [4234]E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(a117,f333(a117,f333(a117,f2(a880))))) % 191.49/191.39 [4302]P29(f890(f889(a880,a880),a874),f333(f333(f263(f890(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a874),f890(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a874)),a37),a72)) % 191.49/191.39 [4303]P29(f890(f889(a880,a880),a874),f333(f333(f263(f890(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a874),f890(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a874)),a38),a70)) % 191.49/191.39 [4314]P10(f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))) % 191.49/191.39 [4340]E(f333(f333(f115(f890(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a874)),f325(f889(a880,a880),a71)),f333(f333(f311(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),f194(f890(f889(a880,a880),a874))),f194(f890(f889(a880,a880),a874)))),f194(f890(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a874)))),a70) % 191.49/191.39 [4341]E(f333(f333(f115(f890(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a874)),f324(f889(a880,a880),a71)),f333(f333(f311(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),f194(f890(f889(a880,a880),a874))),f194(f890(f889(a880,a880),a874)))),f194(f890(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a874)))),a72) % 191.49/191.39 [4346]E(f333(f105(a1),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))) % 191.49/191.39 [4360]P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))))) % 191.49/191.39 [4357]E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)),f333(a117,f333(a117,f2(a880)))) % 191.49/191.39 [4358]E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)),f333(f333(f81(a880),f79(a880)),f79(a880))) % 191.49/191.39 [4359]E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)),f333(f39(a874),f258(f890(a874,a874)))) % 191.49/191.39 [4402]P10(f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))) % 191.49/191.39 [4403]E(f333(a109,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(a117,f333(a117,f2(a880)))) % 191.49/191.39 [4424]E(f333(f105(a1),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))) % 191.49/191.40 [4436]P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.40 [3122]P11(x31221,a330) % 191.49/191.40 [3521]P28(a880,a880,a117,x35211) % 191.49/191.40 [3112]P96(f879(x31121)) % 191.49/191.40 [3113]P96(f884(x31131)) % 191.49/191.40 [3114]P96(f881(x31141)) % 191.49/191.40 [3115]P96(f882(x31151)) % 191.49/191.40 [3116]P105(f879(x31161)) % 191.49/191.40 [3117]P105(f884(x31171)) % 191.49/191.40 [3118]P105(f881(x31181)) % 191.49/191.40 [3119]P105(f882(x31191)) % 191.49/191.40 [3139]P40(a1,f110(x31391)) % 191.49/191.40 [3140]P40(a1,f112(x31401)) % 191.49/191.40 [3142]P41(x31421,f197(x31421)) % 191.49/191.40 [3192]P40(f890(x31921,a874),f308(x31921)) % 191.49/191.40 [3230]E(f46(a1,x32301,x32301),f2(a1)) % 191.49/191.40 [3283]P18(x32831,f890(x32831,a874),f311(x32831)) % 191.49/191.40 [4485]~E(f333(a26,x44851),a24) % 191.49/191.40 [4487]~E(f333(a117,x44871),x44871) % 191.49/191.40 [4497]~E(f333(a117,x44971),f2(a880)) % 191.49/191.40 [3124]E(f333(f195(a880),x31241),x31241) % 191.49/191.40 [3125]E(f333(f108(a1),x31251),x31251) % 191.49/191.40 [3141]E(f333(a90,f334(x31411)),x31411) % 191.49/191.40 [3155]E(f119(x31551,f118(x31551)),f118(x31551)) % 191.49/191.40 [3156]E(f153(x31561,f118(x31561)),f118(x31561)) % 191.49/191.40 [3161]E(f32(f333(a26,x31611)),f2(a880)) % 191.49/191.40 [3168]E(f333(f169(x31681),f118(x31681)),f118(x31681)) % 191.49/191.40 [3169]E(f333(f172(x31691),f118(x31691)),f118(x31691)) % 191.49/191.40 [3170]E(f333(f170(x31701),f118(x31701)),f118(x31701)) % 191.49/191.40 [3176]E(f333(f108(a1),x31761),f333(f107(a1),x31761)) % 191.49/191.40 [3177]E(f333(a90,f333(a111,x31771)),x31771) % 191.49/191.40 [3179]E(f333(a5,f333(a21,x31791)),x31791) % 191.49/191.40 [3180]E(f333(a21,f333(a5,x31801)),x31801) % 191.49/191.40 [3181]P10(f333(f105(a1),x31811)) % 191.49/191.40 [3186]E(f333(f195(f884(x31861)),f197(x31861)),f2(a880)) % 191.49/191.40 [3187]E(f333(f195(f881(x31871)),f118(x31871)),f2(a880)) % 191.49/191.40 [3191]E(f333(f195(a876),f333(a26,x31911)),f2(a880)) % 191.49/191.40 [3200]E(f241(x32001,f197(x32001)),f194(f890(x32001,a874))) % 191.49/191.40 [3207]E(f333(f333(f3(a880),x32071),f2(a880)),x32071) % 191.49/191.40 [3208]E(f333(f333(f81(a880),x32081),f2(a880)),x32081) % 191.49/191.40 [3209]E(f333(f333(f81(a1),x32091),f2(a1)),x32091) % 191.49/191.40 [3210]E(f333(f333(f82(a880),x32101),f79(a880)),x32101) % 191.49/191.40 [3211]E(f333(f333(f82(a1),x32111),f79(a1)),x32111) % 191.49/191.40 [3212]E(f333(f333(f249(a880),x32121),f2(a880)),x32121) % 191.49/191.40 [3213]E(f333(f333(f82(a880),x32131),f2(a880)),f2(a880)) % 191.49/191.40 [3214]E(f333(f333(f40(a1),x32141),f2(a1)),f2(a1)) % 191.49/191.40 [3215]E(f333(f333(f248(a880),x32151),f2(a880)),f2(a880)) % 191.49/191.40 [3221]E(f333(f173(x32211),f118(x32211)),f194(f890(x32211,a874))) % 191.49/191.40 [3225]P4(f333(f138(x32251),f118(x32251))) % 191.49/191.40 [3231]E(f333(f155(x32311,x32311),f7(x32311)),f35(f881(x32311))) % 191.49/191.40 [3232]E(f333(f155(x32321,x32321),f35(x32321)),f35(f881(x32321))) % 191.49/191.40 [3233]E(f333(f208(x32331,x32331),f7(x32331)),f35(f884(x32331))) % 191.49/191.40 [3234]E(f333(f208(x32341,x32341),f35(x32341)),f35(f884(x32341))) % 191.49/191.40 [3235]E(f46(a1,x32351,f2(a1)),x32351) % 191.49/191.40 [3236]E(f333(f250(a880),f333(a117,x32361)),f333(f251(a880),x32361)) % 191.49/191.40 [3237]E(f333(f256(a880),f333(a117,x32371)),f333(f302(a880),x32371)) % 191.49/191.40 [3238]E(f333(f257(a880),f333(a117,x32381)),f333(f305(a880),x32381)) % 191.49/191.40 [3240]E(f46(a1,f2(a1),x32401),f2(a1)) % 191.49/191.40 [3249]E(f333(f333(f81(a880),x32491),f79(a880)),f333(a117,x32491)) % 191.49/191.40 [3259]E(f333(f303(a880,x32591),f2(a880)),f194(f890(a880,a874))) % 191.49/191.40 [3271]E(f304(a880,f2(a880),x32711),f333(f302(a880),x32711)) % 191.49/191.40 [3319]E(f333(f333(f3(a880),f333(a117,x33191)),f79(a880)),x33191) % 191.49/191.40 [3332]E(f48(f2(a1),x33321),f333(f333(f263(a1,a1),f2(a1)),f2(a1))) % 191.49/191.40 [3383]P4(f333(f333(f251(a880),x33831),f333(a117,x33831))) % 191.49/191.40 [3395]P4(f333(f333(f251(a880),f2(a880)),f333(a117,x33951))) % 191.49/191.40 [3679]E(f333(f333(f3(a104),f333(a5,f333(a117,f333(a21,x36791)))),f79(a104)),x36791) % 191.49/191.40 [3743]P4(f333(f333(f250(a1),f333(f80(a1),f333(f105(a1),x37431))),f2(a1))) % 191.49/191.40 [3888]P4(f333(f333(f251(a1),f333(f80(a1),f333(f105(a1),f333(a117,x38881)))),f2(a1))) % 191.49/191.40 [4513]~E(f258(f890(x45131,a874)),f194(f890(x45131,a874))) % 191.49/191.40 [4560]~P4(f333(f333(f251(a880),x45601),f2(a880))) % 191.49/191.40 [4574]~P4(f333(f333(f251(a1),f333(f105(a1),x45741)),f2(a1))) % 191.49/191.40 [3190]E(f180(x31901,f118(f881(x31901))),f118(f881(x31901))) % 191.49/191.40 [3193]E(f333(f333(f82(a1),a84),x31931),a84) % 191.49/191.40 [3194]E(f333(f333(f81(a1),a84),x31941),x31941) % 191.49/191.40 [3197]E(f333(a109,f333(f105(a1),x31971)),x31971) % 191.49/191.40 [3198]E(f333(f333(f3(a1),x31981),a84),x31981) % 191.49/191.40 [3199]E(f333(f333(f81(a1),x31991),a84),x31991) % 191.49/191.40 [3201]E(f333(f333(f3(a880),x32011),x32011),f2(a880)) % 191.49/191.40 [3205]E(f333(f80(a1),f333(f80(a1),x32051)),x32051) % 191.49/191.40 [3206]E(f333(f39(a880),f333(f256(a880),x32061)),x32061) % 191.49/191.40 [3216]E(f333(f333(f81(a880),f2(a880)),x32161),x32161) % 191.49/191.40 [3217]E(f333(f333(f81(a1),f2(a1)),x32171),x32171) % 191.49/191.40 [3218]E(f333(f333(f82(a880),f79(a880)),x32181),x32181) % 191.49/191.40 [3219]E(f333(f333(f82(a1),f79(a1)),x32191),x32191) % 191.49/191.40 [3220]E(f333(f333(f249(a880),f2(a880)),x32201),x32201) % 191.49/191.40 [3226]E(f333(f333(f3(a880),f2(a880)),x32261),f2(a880)) % 191.49/191.40 [3227]E(f333(f333(f82(a880),f2(a880)),x32271),f2(a880)) % 191.49/191.40 [3228]E(f333(f333(f40(a1),f2(a1)),x32281),f2(a1)) % 191.49/191.40 [3229]E(f333(f333(f248(a880),f2(a880)),x32291),f2(a880)) % 191.49/191.40 [3246]E(f333(f303(a880,f2(a880)),x32461),f333(f256(a880),x32461)) % 191.49/191.40 [3247]E(f333(f333(f82(a1),a102),x32471),f333(f80(a1),x32471)) % 191.49/191.40 [3251]E(f333(a109,f333(f108(a1),x32511)),f333(f108(a880),x32511)) % 191.49/191.40 [3252]E(f333(a21,f333(f108(a104),x32521)),f333(f108(a880),x32521)) % 191.49/191.40 [3253]E(f333(f39(a880),f333(f302(a880),x32531)),f333(a117,x32531)) % 191.49/191.40 [3263]E(f333(f333(f81(a880),f79(a880)),x32631),f333(a117,x32631)) % 191.49/191.40 [3267]E(f333(f76(a1),f333(f105(a1),x32671)),f333(f105(a1),x32671)) % 191.49/191.40 [3268]E(f333(f107(a1),f333(f105(a1),x32681)),f333(f105(a1),x32681)) % 191.49/191.40 [3273]E(f333(f39(x32731),f194(f890(x32731,a874))),f2(a880)) % 191.49/191.40 [3275]E(f333(f333(f40(a880),x32751),f333(a117,f2(a880))),x32751) % 191.49/191.40 [3284]E(f46(a880,x32841,f333(a117,f2(a880))),f2(a880)) % 191.49/191.40 [3285]E(f46(a1,x32851,f333(f108(a1),a102)),f2(a1)) % 191.49/191.40 [3301]E(f333(f333(f40(a1),x33011),f333(f108(a1),a102)),f333(f80(a1),x33011)) % 191.49/191.40 [3305]E(f140(a880,f333(f303(a880,x33051),f2(a880))),f118(a880)) % 191.49/191.40 [3306]E(f333(f333(f81(a1),x33061),f79(a1)),f333(f333(f3(a1),x33061),a102)) % 191.49/191.40 [3307]E(f333(f333(f3(a1),x33071),f79(a1)),f333(f333(f81(a1),x33071),a102)) % 191.49/191.40 [3312]P4(f333(f333(f201(a24),x33121),x33121)) % 191.49/191.40 [3313]P4(f333(f333(f250(a880),x33131),x33131)) % 191.49/191.40 [3314]P4(f333(f333(f250(a1),x33141),x33141)) % 191.49/191.40 [3315]P4(f333(f333(f92(a1),x33151),x33151)) % 191.49/191.40 [3320]E(f333(f80(a1),f333(f108(a1),x33201)),f333(f108(a1),f333(f80(a1),x33201))) % 191.49/191.40 [3321]P4(f333(f63(a880),f333(f256(a880),x33211))) % 191.49/191.40 [3322]P4(f333(f63(a880),f333(f302(a880),x33221))) % 191.49/191.40 [3330]E(f162(x33301,f258(f890(x33301,a874))),f258(f890(f881(x33301),a874))) % 191.49/191.40 [3335]P4(f333(f333(f250(a880),f2(a880)),x33351)) % 191.49/191.40 [3346]E(f333(f333(f81(a880),f116(x33461)),f333(a117,f2(a880))),f116(f333(a117,x33461))) % 191.49/191.40 [3347]E(f333(f255(x33471),f333(f18(a874,x33471),a247)),f194(f890(x33471,a874))) % 191.49/191.40 [3348]E(f333(f255(x33481),f333(f18(a874,x33481),a193)),f258(f890(x33481,a874))) % 191.49/191.40 [3352]E(f333(f333(f311(a880),x33521),f333(f256(a880),x33521)),f333(f256(a880),f333(a117,x33521))) % 191.49/191.40 [3364]E(f333(f333(f81(a1),f79(a1)),f333(f105(a1),x33641)),f333(f105(a1),f333(a117,x33641))) % 191.49/191.40 [3367]E(f333(f333(f152(f881(x33671)),f118(x33671)),f118(f881(x33671))),f55(x33671,f118(x33671))) % 191.49/191.40 [3386]E(f194(f890(f889(x33861,x33861),a874)),f260(x33861,f194(f890(x33861,a874)))) % 191.49/191.40 [3387]E(f333(f310(x33871),f258(f890(x33871,a874))),f258(f890(f890(x33871,a874),a874))) % 191.49/191.40 [3388]E(f333(f80(f890(x33881,a874)),f194(f890(x33881,a874))),f258(f890(x33881,a874))) % 191.49/191.40 [3389]E(f333(f80(f890(x33891,a874)),f258(f890(x33891,a874))),f194(f890(x33891,a874))) % 191.49/191.40 [3391]P4(f333(f63(x33911),f194(f890(x33911,a874)))) % 191.49/191.40 [3393]E(f333(f303(a880,x33931),f333(a117,x33931)),f333(f333(f311(a880),x33931),f194(f890(a880,a874)))) % 191.49/191.40 [3394]E(f86(f889(a880,a880),f49(x33941,f2(a880))),f333(f333(f263(a880,a880),f2(a880)),x33941)) % 191.49/191.40 [3407]E(f333(f333(f311(a880),f333(a117,x34071)),f333(f302(a880),x34071)),f333(f302(a880),f333(a117,x34071))) % 191.49/191.40 [3411]P40(x34111,f194(f890(f889(x34111,x34111),a874))) % 191.49/191.40 [3414]P4(f333(f333(f250(a1),f2(a1)),f333(f105(a1),x34141))) % 191.49/191.40 [3422]E(f333(f333(f81(a880),f333(f195(a880),x34221)),f333(a117,f2(a880))),f333(f195(a880),f333(a117,x34221))) % 191.49/191.40 [3529]P42(f333(f312(a880,a1,f105(a1)),x35291)) % 191.49/191.40 [3566]P50(x35661,f194(f890(x35661,a874)),f194(f890(f889(x35661,x35661),a874))) % 191.49/191.40 [3585]E(f333(f333(f263(a1,a1),f333(f108(a1),a102)),f333(f333(f3(a1),x35851),f79(a1))),f51(f333(f108(a1),a102),x35851)) % 191.49/191.40 [3635]P59(x36351,f333(f18(f890(x36351,a874),x36351),f333(f18(a874,x36351),a247))) % 191.49/191.40 [3834]P4(f333(f333(f335(f890(f889(a880,a880),a874)),f334(x38341)),a103)) % 191.49/191.40 [3857]P4(f333(f333(f335(f890(f889(a880,a880),a874)),f333(a111,x38571)),a103)) % 191.49/191.40 [3990]P28(x39901,f890(x39901,a874),f333(f333(f9(x39901,f890(x39901,a874),f890(x39901,a874)),f311(x39901)),f194(f890(x39901,a874))),f258(f890(x39901,a874))) % 191.49/191.40 [4545]~E(f333(a5,f333(a117,f333(a21,x45451))),f2(a104)) % 191.49/191.40 [4553]~P4(f333(a200,f333(f105(a1),x45531))) % 191.49/191.40 [4556]~P4(f333(f333(f251(a880),x45561),x45561)) % 191.49/191.40 [4569]~P4(f333(f333(f250(a880),f333(a117,x45691)),x45691)) % 191.49/191.40 [3337]E(f333(a109,f333(f80(a1),f333(f105(a1),x33371))),f2(a880)) % 191.49/191.40 [3340]E(f333(f333(f81(a1),f333(f80(a1),x33401)),x33401),f2(a1)) % 191.49/191.40 [3345]E(f333(f39(a1),f333(f303(a1,f2(a1)),x33451)),f333(a109,x33451)) % 191.49/191.40 [3357]E(f333(f333(f264(a880),f333(a117,f2(a880))),x33571),f333(a117,f2(a880))) % 191.49/191.40 [3456]E(f333(f286(x34561),f194(f890(f889(x34561,x34561),a874))),f194(f890(x34561,a874))) % 191.49/191.40 [3463]E(f41(f890(x34631,a874),f194(f890(f890(x34631,a874),a874))),f194(f890(x34631,a874))) % 191.49/191.40 [3464]E(f41(f890(x34641,a874),f258(f890(f890(x34641,a874),a874))),f258(f890(x34641,a874))) % 191.49/191.40 [3465]E(f42(f890(x34651,a874),f194(f890(f890(x34651,a874),a874))),f258(f890(x34651,a874))) % 191.49/191.40 [3466]E(f42(f890(x34661,a874),f258(f890(f890(x34661,a874),a874))),f194(f890(x34661,a874))) % 191.49/191.40 [3511]E(f333(f333(f311(f881(x35111)),f118(x35111)),f194(f890(f881(x35111),a874))),f163(x35111,f118(f890(x35111,a874)))) % 191.49/191.40 [3512]E(f333(f333(f311(f881(x35121)),f118(x35121)),f194(f890(f881(x35121),a874))),f162(x35121,f194(f890(x35121,a874)))) % 191.49/191.40 [3548]E(f333(f333(f81(a880),f6(x35481)),f333(a117,f2(a880))),f6(f333(a5,f333(a117,f333(a21,x35481))))) % 191.49/191.40 [3577]E(f333(f39(a1),f333(f312(a880,a1,f105(a1)),x35771)),f333(f39(a880),x35771)) % 191.49/191.40 [3580]P4(f333(f333(f250(a880),x35801),f333(f333(f82(a880),x35801),x35801))) % 191.49/191.40 [3616]E(f333(f312(a1,a880,a109),f304(a1,f2(a1),f333(f105(a1),x36161))),f333(f302(a880),x36161)) % 191.49/191.40 [3630]E(f333(f333(f40(a880),f333(a117,f2(a880))),f333(f108(a880),x36301)),f333(a109,f333(f333(f40(a1),f79(a1)),f333(f108(a1),x36301)))) % 191.49/191.40 [3632]E(f333(f173(a880),f140(a880,f333(f303(a880,f2(a880)),f333(a117,x36321)))),f333(f302(a880),x36321)) % 191.49/191.40 [3633]E(f333(f333(f81(a880),f333(f195(a104),x36331)),f333(a117,f2(a880))),f333(f195(a104),f333(a5,f333(a117,f333(a21,x36331))))) % 191.49/191.40 [3653]E(f333(f312(a1,a880,a109),f333(f312(a880,a1,f105(a1)),x36531)),x36531) % 191.49/191.40 [3684]E(f333(f333(f311(a880),f2(a880)),f333(f312(a880,a880,a117),f333(f256(a880),x36841))),f333(f256(a880),f333(a117,x36841))) % 191.49/191.40 [3691]P54(x36911,x36911,f309(x36911,f194(f890(f889(x36911,x36911),a874)))) % 191.49/191.40 [3697]P4(f333(a200,f333(f80(a1),f333(f105(a1),f333(a117,x36971))))) % 191.49/191.40 [3708]E(f333(f333(f3(f890(a880,a874)),f333(f257(a880),x37081)),f333(f333(f311(a880),x37081),f194(f890(a880,a874)))),f333(f257(a880),f333(a117,x37081))) % 191.49/191.40 [3734]E(f333(f333(f311(f890(x37341,a874)),f194(f890(x37341,a874))),f194(f890(f890(x37341,a874),a874))),f333(f310(x37341),f194(f890(x37341,a874)))) % 191.49/191.40 [3764]E(f333(f333(f3(f890(a880,a874)),f333(f305(a880),x37641)),f333(f333(f311(a880),f333(a117,x37641)),f194(f890(a880,a874)))),f333(f305(a880),f333(a117,x37641))) % 191.49/191.40 [3773]E(f333(f333(f311(f884(x37731)),f197(x37731)),f333(f312(x37731,f884(x37731),f242(x37731)),f258(f890(x37731,a874)))),f258(f890(f884(x37731),a874))) % 191.49/191.40 [4250]P18(x42501,f890(x42501,a874),f333(f333(f10(f890(x42501,a874),f890(f890(x42501,a874),f890(x42501,a874)),x42501),f333(f9(f890(x42501,a874),f890(x42501,a874),f890(x42501,a874)),f3(f890(x42501,a874)))),f333(f333(f9(x42501,f890(x42501,a874),f890(x42501,a874)),f311(x42501)),f194(f890(x42501,a874))))) % 191.49/191.40 [4339]E(f333(f255(f889(a1,a1)),f333(f272(a1,a1,a874),f333(f333(f10(f890(a1,a874),f890(a1,a874),a1),f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),x43391)))),f251(a1)))),f112(x43391)) % 191.49/191.40 [4378]E(f333(f255(f889(a1,a1)),f333(f272(a1,a1,a874),f333(f333(f20(a1,f890(a1,a874),f890(a1,a874)),f333(f333(f10(f890(a874,a874),f890(f890(a1,a874),f890(a1,a874)),a1),f10(a874,a874,a1)),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),x43781)))),f251(a1)))),f110(x43781)) % 191.49/191.40 [4443]E(f333(f255(f889(f890(x44431,a874),f890(x44431,a874))),f333(f272(f890(x44431,a874),f890(x44431,a874),a874),f333(f333(f9(f890(x44431,a874),f890(f890(x44431,a874),a874),f890(f890(x44431,a874),a874)),f333(f333(f10(f890(f890(x44431,a874),f890(a874,a874)),f890(f890(f890(x44431,a874),a874),f890(f890(x44431,a874),a874)),f890(x44431,a874)),f20(f890(x44431,a874),a874,a874)),f333(f333(f10(f890(f890(x44431,a874),a874),f890(f890(x44431,a874),f890(a874,a874)),f890(x44431,a874)),f333(f10(a874,f890(a874,a874),f890(x44431,a874)),a331)),f251(f890(x44431,a874))))),f63(x44431)))),f308(x44431)) % 191.49/191.40 [4573]~P4(f333(f63(f881(x45731)),f258(f890(f881(x45731),a874)))) % 191.49/191.40 [4584]~P4(f333(f333(f250(a1),f2(a1)),f333(f80(a1),f333(f105(a1),f333(a117,x45841))))) % 191.49/191.40 [3489]E(f333(f333(f3(a1),f333(f333(f81(a1),x34891),a102)),a102),x34891) % 191.49/191.40 [3504]E(f333(f173(a880),f140(a880,f333(f303(a880,f2(a880)),x35041))),f333(f256(a880),x35041)) % 191.49/191.40 [3789]E(f333(f288(x37891,x37891),f309(x37891,f194(f890(f889(x37891,x37891),a874)))),f309(x37891,f194(f890(f889(x37891,x37891),a874)))) % 191.49/191.40 [3835]P4(f333(f333(f250(a880),x38351),f333(f333(f82(a880),x38351),f333(f333(f82(a880),x38351),x38351)))) % 191.49/191.40 [4106]P4(f333(f63(a880),f333(f255(a880),f333(f333(f9(a880,a880,a874),f251(a880)),x41061)))) % 191.49/191.40 [4107]P4(f333(f63(a880),f333(f255(a880),f333(f333(f9(a880,a880,a874),f250(a880)),x41071)))) % 191.49/191.40 [4396]E(f333(f255(f889(x43961,x43961)),f333(f333(f10(f890(x43961,a874),a874,f889(x43961,x43961)),f87(x43961)),f333(f333(f9(f889(x43961,x43961),f890(x43961,f889(x43961,x43961)),f890(x43961,a874)),f333(f333(f10(f890(f889(x43961,x43961),a874),f890(f890(x43961,f889(x43961,x43961)),f890(x43961,a874)),f889(x43961,x43961)),f10(f889(x43961,x43961),a874,x43961)),a330)),f333(f333(f20(x43961,x43961,f889(x43961,x43961)),f263(x43961,x43961)),f7(x43961))))),f309(x43961,f194(f890(f889(x43961,x43961),a874)))) % 191.49/191.40 [4576]~E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45761)),x45761),a84) % 191.49/191.40 [4577]~E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45771)),x45771),f2(a1)) % 191.49/191.40 [3968]E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),a102),x39681))),f333(f333(f3(a1),a102),x39681)),f333(f333(f3(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x39681)),x39681))) % 191.49/191.40 [4086]E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f80(a1),x40861)),a102))),f333(f333(f81(a1),f333(f80(a1),x40861)),a102)),f333(f80(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x40861)),x40861))) % 191.49/191.40 [4163]E(f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x41631),f2(a880))),f194(f890(f889(a880,a880),a874))))),f333(f105(a1),x41631)) % 191.49/191.40 [4174]E(f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),f338(x41741)),f552(x41741))),f194(f890(f889(a880,a880),a874))))),x41741) % 191.49/191.40 [4182]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),a102),x41821))),f333(f333(f3(a1),a102),x41821))),a102),f333(f333(f3(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41821)),x41821))) % 191.49/191.40 [4212]E(f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),x42121)),f333(f312(a880,a1,f105(a1)),f333(f255(a880),f333(f333(f10(a1,a874,a880),x42121),f105(a1))))) % 191.49/191.40 [4258]P42(f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),x42581))) % 191.49/191.40 [4280]P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),x42801),f194(f890(f889(a880,a880),a874)))),a72)) % 191.49/191.40 [4286]E(f333(f312(a1,a880,a109),f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),f333(f333(f10(a880,a874,a1),x42861),a109)))),f333(f255(a880),x42861)) % 191.49/191.40 [4456]E(f314(a880,f333(f333(f44(f889(a880,a880),f890(a880,a874)),f333(a111,x44561)),f333(f272(a880,a880,f890(a880,a874)),f333(f333(f9(a880,f890(a880,a874),f890(a880,f890(a880,a874))),f333(f333(f10(f890(a880,f890(f890(a880,a874),f890(a880,a874))),f890(f890(a880,a874),f890(a880,f890(a880,a874))),a880),f9(a880,f890(a880,a874),f890(a880,a874))),f333(f333(f10(f890(a880,a880),f890(a880,f890(f890(a880,a874),f890(a880,a874))),a880),f333(f10(a880,f890(f890(a880,a874),f890(a880,a874)),a880),f311(a880))),f3(a880)))),f194(f890(a880,a874)))))),f333(a109,x44561)) % 191.49/191.40 [4588]~P4(f333(f333(f92(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45881)),x45881))) % 191.49/191.40 [3939]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x39391)),x39391)),a102),f333(f333(f81(a1),x39391),x39391)) % 191.49/191.40 [4197]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),x41971),a102))),f333(f333(f3(a1),x41971),a102))),a102),f333(f333(f3(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41971)),x41971)),a102)) % 191.49/191.40 [4587]~E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45871)),x45871)),a102),a102) % 191.49/191.40 [4597]~P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45971)),x45971)),a84)) % 191.49/191.40 [4159]E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41591)),x41591)),a102)),f333(f333(f89(a880,a880),f333(f108(a880),x41591)),f333(f333(f20(a880,a880,a880),f81(a880)),f7(a880)))) % 191.49/191.40 [4165]E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),a102),x41651))),f333(f333(f3(a1),a102),x41651)),f333(f333(f3(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41651)),x41651)),a102))) % 191.49/191.40 [4196]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f80(a1),x41961))),f333(f80(a1),x41961))),a102),f333(f80(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41961)),x41961)),a102))) % 191.49/191.40 [4220]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),a84),x42201))),f333(f333(f3(a1),a84),x42201))),a102),f333(f333(f3(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42201)),x42201)),a102))) % 191.49/191.40 [4471]E(f333(a90,f333(f333(f44(f889(a880,a880),f890(f889(a880,a880),a874)),f333(a111,x44711)),f333(f272(a880,a880,f890(f889(a880,a880),a874)),f333(f333(f10(f890(a880,f890(f889(a880,a880),a874)),f890(a880,f890(f889(a880,a880),a874)),a880),f333(f10(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874),a880),f287(f889(a880,a880),f889(a880,a880),a113))),f333(f333(f9(a880,f890(f889(a880,a880),a874),f890(a880,f890(f889(a880,a880),a874))),f333(f333(f10(f890(a880,f890(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f890(f890(f889(a880,a880),a874),f890(a880,f890(f889(a880,a880),a874))),a880),f9(a880,f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f10(f890(a880,f889(a880,a880)),f890(a880,f890(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),a880),f333(f10(f889(a880,a880),f890(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),a880),f311(f889(a880,a880)))),f333(f9(a880,a880,f889(a880,a880)),f263(a880,a880))))),f194(f890(f889(a880,a880),a874))))))),f333(f80(a1),x44711)) % 191.49/191.40 [4598]~P4(f333(f333(f92(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45981)),x45981)),a102))) % 191.49/191.40 [4223]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42231)),x42231)),a102)),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),x42231),a102))),f333(f333(f81(a1),x42231),a102))) % 191.49/191.40 [4361]E(f333(f333(f81(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),x43611),f333(a117,f333(a117,f333(a117,x43611)))) % 191.49/191.40 [4600]~P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x46001)),x46001)),a102)),a102)) % 191.49/191.40 [4404]E(f333(f333(f81(a880),x44041),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(a117,f333(a117,x44041))) % 191.49/191.40 [4405]E(f333(f333(f82(a880),x44051),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f333(f81(a880),x44051),x44051)) % 191.49/191.40 [4406]E(f333(f333(f40(a880),f333(f333(f81(a880),x44061),x44061)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x44061) % 191.49/191.40 [4437]E(f46(a880,f333(a117,f333(a117,x44371)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f46(a880,x44371,f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.40 [4434]E(f333(f333(f81(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x44341),f333(a117,f333(a117,x44341))) % 191.49/191.40 [4435]E(f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x44351),f333(f333(f81(a880),x44351),x44351)) % 191.49/191.40 [4447]E(f333(f333(f40(a880),f333(a117,f333(a117,x44471))),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(a117,f333(f333(f40(a880),x44471),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.40 [4479]E(f333(f272(a1,a1,f889(a1,a1)),f333(f333(f20(a1,f890(a1,f889(a1,a1)),f890(a1,f889(a1,a1))),f333(f333(f10(f890(a1,f890(f889(a1,a1),f889(a1,a1))),f890(f890(a1,f889(a1,a1)),f890(a1,f889(a1,a1))),a1),f20(a1,f889(a1,a1),f889(a1,a1))),f333(f333(f10(f890(a1,f889(a1,a1)),f890(a1,f890(f889(a1,a1),f889(a1,a1))),a1),f333(f20(a1,f889(a1,a1),f890(f889(a1,a1),f889(a1,a1))),f333(f333(f10(a874,f890(f889(a1,a1),f890(f889(a1,a1),f889(a1,a1))),a1),f101(f889(a1,a1))),f333(f333(f10(a1,a874,a1),f333(f250(a1),f2(a1))),f333(f333(f9(a1,a1,a1),f3(a1)),x44791))))),f333(f333(f9(a1,f890(a1,a1),f890(a1,f889(a1,a1))),f333(f333(f10(f890(a1,f889(a1,a1)),f890(f890(a1,a1),f890(a1,f889(a1,a1))),a1),f10(a1,f889(a1,a1),a1)),f333(f333(f10(a1,f890(a1,f889(a1,a1)),a1),f263(a1,a1)),f333(f333(f9(a1,a1,a1),f333(f333(f10(a1,f890(a1,a1),a1),f81(a1)),f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))),f79(a1))))),f333(f333(f9(a1,a1,a1),f3(a1)),x44791))))),f333(f333(f10(a1,f890(a1,f889(a1,a1)),a1),f263(a1,a1)),f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))))),f45(x44791)) % 191.49/191.40 [3162]P96(f888(x31621,x31622)) % 191.49/191.40 [3163]P96(f889(x31631,x31632)) % 191.49/191.40 [3164]P96(f885(x31641,x31642)) % 191.49/191.40 [3165]P105(f888(x31651,x31652)) % 191.49/191.40 [3166]P105(f889(x31661,x31662)) % 191.49/191.40 [3167]P105(f885(x31671,x31672)) % 191.49/191.40 [3184]P17(a1,f179(x31841,x31842)) % 191.49/191.40 [3185]P40(x31851,f154(x31851,x31852)) % 191.49/191.40 [3248]P34(x32481,x32482,f118(x32481)) % 191.49/191.40 [3279]P50(x32791,x32792,f260(x32791,x32792)) % 191.49/191.40 [3280]P54(x32801,x32801,f260(x32801,x32802)) % 191.49/191.40 [3551]P28(x35511,x35511,f7(x35511),x35512) % 191.49/191.40 [3552]P28(x35521,x35521,f35(x35521),x35522) % 191.49/191.40 [3561]P35(x35611,x35612,f118(x35611),f118(x35611)) % 191.49/191.40 [3562]P28(x35621,f884(x35621),f242(x35621),x35622) % 191.49/191.40 [3571]P28(f881(x35711),f881(x35711),f170(x35711),x35712) % 191.49/191.40 [4490]~E(f34(x44901,x44902),a24) % 191.49/191.40 [4491]~E(f33(x44911,x44912),a24) % 191.49/191.40 [4522]~P36(x45221,x45222,f118(x45221)) % 191.49/191.40 [4523]~P38(x45231,x45232,f118(x45231)) % 191.49/191.40 [3144]E(f333(f7(x31441),x31442),x31442) % 191.49/191.40 [3145]E(f333(f255(x31451),x31452),x31452) % 191.49/191.40 [3147]E(f333(f35(x31471),x31472),x31472) % 191.49/191.40 [3157]E(f333(f198(x31571),x31572),f120(x31571)) % 191.49/191.40 [3182]E(f86(x31821,f333(a330,x31822)),x31822) % 191.49/191.40 [3183]E(f91(x31831,f333(a330,x31832)),x31832) % 191.49/191.40 [3203]E(f333(f137(x32031,x32032),f118(x32031)),f118(x32031)) % 191.49/191.40 [3222]E(f153(x32221,f153(x32221,x32222)),f153(x32221,x32222)) % 191.49/191.40 [3223]E(f309(x32231,f309(x32231,x32232)),f309(x32231,x32232)) % 191.49/191.40 [3243]E(f333(f333(f127(x32431),x32432),f118(x32431)),x32432) % 191.49/191.40 [3254]E(f333(f333(f174(x32541),x32542),f118(x32541)),f118(x32541)) % 191.49/191.40 [3255]E(f333(f333(f139(x32551),x32552),f118(x32551)),f118(x32551)) % 191.49/191.40 [3257]E(f243(x32571,x32572,f197(x32571)),f2(a880)) % 191.49/191.40 [3258]E(f156(x32581,x32582,f118(x32581)),f2(a880)) % 191.49/191.40 [3260]E(f171(x32601,x32602,f118(x32601)),f118(x32601)) % 191.49/191.40 [3261]E(f177(x32611,x32612,f118(x32611)),f118(x32611)) % 191.49/191.40 [3262]E(f175(x32621,f118(x32621),x32622),f118(x32621)) % 191.49/191.40 [3266]E(f333(f173(x32661),f153(x32661,x32662)),f333(f173(x32661),x32662)) % 191.49/191.40 [3269]E(f333(f259(x32691,x32691),f260(x32691,x32692)),x32692) % 191.49/191.40 [3270]E(f333(f261(x32701,x32701),f260(x32701,x32702)),x32702) % 191.49/191.40 [3278]E(f333(f288(x32781,x32781),f260(x32781,x32782)),f260(x32781,x32782)) % 191.49/191.40 [3293]E(f309(f881(x32931),f158(x32931,x32932)),f159(x32931,f309(x32931,x32932))) % 191.49/191.40 [3295]P4(f333(f138(a1),f179(x32951,x32952))) % 191.49/191.40 [3303]E(f333(f259(x33031,x33031),f309(x33031,x33032)),f258(f890(x33031,a874))) % 191.49/191.40 [3304]E(f333(f261(x33041,x33041),f309(x33041,x33042)),f258(f890(x33041,a874))) % 191.49/191.40 [3308]P4(f333(f138(x33081),f153(x33081,x33082))) % 191.49/191.40 [3310]P4(f333(f161(x33101,x33102),f118(x33101))) % 191.49/191.40 [3318]E(f333(f173(a1),f179(x33181,x33182)),f304(a1,x33181,x33182)) % 191.49/191.40 [3333]P55(x33331,f194(f890(x33331,a874)),x33332) % 191.49/191.40 [3338]E(f333(f271(a1,a1),f47(x33381,x33382)),f46(a1,x33381,x33382)) % 191.49/191.40 [3339]E(f333(f303(a880,x33391),f333(a117,x33392)),f304(a880,x33391,x33392)) % 191.49/191.40 [3356]E(f333(f333(f152(x33561),x33562),f118(x33561)),f141(x33561,x33562,f118(x33561))) % 191.49/191.40 [3369]E(f304(a880,f333(a117,x33691),x33692),f306(a880,x33691,x33692)) % 191.49/191.40 [3372]P50(x33721,f258(f890(x33721,a874)),f309(x33721,x33722)) % 191.49/191.40 [3433]E(f333(f333(f3(a880),x34331),f333(a117,x34332)),f333(f39(a880),f307(a880,x34332,x34331))) % 191.49/191.40 [3490]E(f168(x34901,x34902,f118(x34901)),f333(f333(f263(f881(x34901),f881(x34901)),f118(x34901)),f118(x34901))) % 191.49/191.40 [3509]E(f333(f272(x35091,x35092,f889(x35091,x35092)),f263(x35091,x35092)),f35(f889(x35091,x35092))) % 191.49/191.40 [3514]P4(f333(f333(f335(f881(x35141)),f118(x35141)),f162(x35141,x35142))) % 191.49/191.40 [3515]E(f333(f195(f881(x35151)),f119(x35151,x35152)),f333(f333(f3(a880),f333(f195(f881(x35151)),x35152)),f79(a880))) % 191.49/191.40 [3523]P4(f333(f63(a880),f307(a880,x35231,x35232))) % 191.49/191.40 [3524]P4(f333(f63(a880),f306(a880,x35241,x35242))) % 191.49/191.40 [3525]P4(f333(f63(a880),f304(a880,x35251,x35252))) % 191.49/191.40 [3526]P4(f333(f63(a1),f307(a1,x35261,x35262))) % 191.49/191.40 [3527]P4(f333(f63(a1),f306(a1,x35271,x35272))) % 191.49/191.40 [3528]P4(f333(f63(a1),f304(a1,x35281,x35282))) % 191.49/191.40 [3629]E(f333(f312(a880,a880,a117),f304(a880,x36291,x36292)),f304(a880,f333(a117,x36291),f333(a117,x36292))) % 191.49/191.40 [3650]E(f333(f333(f290(x36501,x36501,x36501),f309(x36501,x36502)),f309(x36501,x36502)),f309(x36501,x36502)) % 191.49/191.40 [3682]E(f333(f333(f263(a104,a104),f333(f333(f40(a104),x36821),x36822)),f46(a104,x36821,x36822)),f23(x36821,x36822)) % 191.49/191.40 [3683]E(f333(f333(f263(a1,a1),f333(f333(f40(a1),x36831),x36832)),f46(a1,x36831,x36832)),f47(x36831,x36832)) % 191.49/191.40 [3712]E(f333(f333(f263(a880,a880),f333(f333(f40(a880),x37121),x37122)),f46(a880,x37121,x37122)),f86(f889(a880,a880),f49(x37121,x37122))) % 191.49/191.40 [3756]P4(f333(f333(f251(a880),f333(f333(f3(a880),x37561),x37562)),f333(a117,x37561))) % 191.49/191.40 [3856]E(f333(f333(f81(a1),f333(f333(f82(a1),x38561),f333(f333(f40(a1),x38562),x38561))),f46(a1,x38562,x38561)),x38562) % 191.49/191.40 [3860]E(f333(f333(f44(a880,f890(f889(f881(x38601),f881(x38601)),a874)),f258(f890(a880,a874))),f144(x38601,x38602)),f146(x38601,x38602)) % 191.49/191.40 [4081]P4(f333(f333(f335(f889(f881(x40811),f881(x40811))),f333(f333(f263(f881(x40811),f881(x40811)),f118(x40811)),f118(x40811))),f159(x40811,x40812))) % 191.49/191.40 [4244]E(f273(x42441,x42441,x42442,x42442,f7(x42441),f7(x42442)),f35(f889(x42441,x42442))) % 191.49/191.40 [4246]E(f273(x42461,x42461,x42462,x42462,f35(x42461),f35(x42462)),f35(f889(x42461,x42462))) % 191.49/191.40 [4499]~E(f333(f242(x44991),x44992),f197(x44991)) % 191.49/191.40 [4510]~P41(x45101,f333(f242(x45101),x45102)) % 191.49/191.40 [3241]E(f333(f246(x32411),f333(f242(x32411),x32412)),x32412) % 191.49/191.40 [3242]E(f333(f170(x32421),f333(f170(x32421),x32422)),x32422) % 191.49/191.40 [3244]E(f333(f333(f139(x32441),f2(a880)),x32442),x32442) % 191.49/191.40 [3256]E(f333(f333(f174(x32561),f2(a880)),x32562),f118(x32561)) % 191.49/191.40 [3264]E(f333(f333(f127(x32641),f118(x32641)),x32642),x32642) % 191.49/191.40 [3272]E(f333(f195(f884(x32721)),f333(f242(x32721),x32722)),f2(a880)) % 191.49/191.40 [3274]E(f41(f890(x32741,a874),f333(f310(x32741),x32742)),x32742) % 191.49/191.40 [3276]E(f333(f173(x32761),f333(f169(x32761),x32762)),f333(f173(x32761),x32762)) % 191.49/191.40 [3277]E(f333(f173(x32771),f333(f170(x32771),x32772)),f333(f173(x32771),x32772)) % 191.49/191.40 [3282]E(f333(f333(f3(a104),x32821),x32822),f333(f333(a4,x32821),x32822)) % 191.49/191.40 [3297]E(f333(f333(f81(a880),x32971),x32972),f333(f333(f81(a880),x32972),x32971)) % 191.49/191.40 [3298]E(f333(f333(f81(a1),x32981),x32982),f333(f333(f81(a1),x32982),x32981)) % 191.49/191.40 [3299]E(f333(f333(f82(a880),x32991),x32992),f333(f333(f82(a880),x32992),x32991)) % 191.49/191.40 [3300]E(f333(f333(f82(a1),x33001),x33002),f333(f333(f82(a1),x33002),x33001)) % 191.49/191.40 [3325]E(f333(f333(f189(x33251,x33251),f2(a880)),x33252),f35(x33251)) % 191.49/191.40 [3326]E(f333(f195(f881(x33261)),f333(f169(x33261),x33262)),f333(f195(f881(x33261)),x33262)) % 191.49/191.40 [3327]E(f333(f195(f881(x33271)),f333(f170(x33271),x33272)),f333(f195(f881(x33271)),x33272)) % 191.49/191.40 [3328]E(f175(x33281,x33282,f194(f890(a880,a874))),f118(x33281)) % 191.49/191.40 [3329]E(f333(f333(f155(x33291,x33291),f7(x33291)),x33292),x33292) % 191.49/191.40 [3331]E(f333(f262(a1,a1),f47(x33311,x33312)),f333(f333(f40(a1),x33311),x33312)) % 191.49/191.40 [3349]E(f333(f195(f881(x33491)),f153(x33491,x33492)),f333(f39(x33491),f333(f173(x33491),x33492))) % 191.49/191.40 [3350]E(f32(f33(x33501,x33502)),f333(f333(f81(a880),f32(x33502)),f333(a117,f2(a880)))) % 191.49/191.40 [3351]E(f333(f286(x33511),f333(f288(x33511,x33511),x33512)),f333(f286(x33511),x33512)) % 191.49/191.40 [3355]P4(f333(f63(x33551),f333(f173(x33551),x33552))) % 191.49/191.40 [3363]E(f333(f333(f81(a1),x33631),f333(f80(a1),x33632)),f333(f333(f3(a1),x33631),x33632)) % 191.49/191.40 [3371]P27(x33711,x33712,f194(f890(f879(x33711),a874))) % 191.49/191.40 [3373]E(f333(f313(x33731,x33731,f7(x33731)),x33732),x33732) % 191.49/191.40 [3374]E(f333(f313(x33741,x33741,f35(x33741)),x33742),x33742) % 191.49/191.40 [3375]E(f333(f312(x33751,x33751,f7(x33751)),x33752),x33752) % 191.49/191.40 [3376]E(f333(f312(x33761,x33761,f35(x33761)),x33762),x33762) % 191.49/191.40 [3377]P4(f333(f258(f890(x33771,a874)),x33772)) % 191.49/191.40 [3379]E(f333(f39(a880),f333(f303(a880,x33791),x33792)),f333(f333(f3(a880),x33792),x33791)) % 191.49/191.40 [3380]E(f333(f303(a880,f333(a117,x33801)),x33802),f307(a880,x33801,x33802)) % 191.49/191.40 [3392]E(f333(f333(f311(x33921),x33922),f194(f890(x33921,a874))),f333(f255(x33921),f333(a330,x33922))) % 191.49/191.40 [3396]E(f333(f333(f311(x33961),x33962),f194(f890(x33961,a874))),f241(x33961,f333(f242(x33961),x33962))) % 191.49/191.40 [3399]E(f309(x33991,f333(f288(x33991,x33991),x33992)),f333(f288(x33991,x33991),f309(x33991,x33992))) % 191.49/191.40 [3403]E(f333(f333(f81(a880),f333(a117,x34031)),x34032),f333(f333(f81(a880),x34031),f333(a117,x34032))) % 191.49/191.40 [3404]E(f333(f333(f3(a880),f333(a117,x34041)),f333(a117,x34042)),f333(f333(f3(a880),x34041),x34042)) % 191.49/191.40 [3409]E(f56(x34091,f2(a880),x34092),f333(f333(f152(f881(x34091)),f118(x34091)),f118(f881(x34091)))) % 191.49/191.40 [3410]E(f333(f39(a880),f306(a880,x34101,x34102)),f333(f333(f3(a880),x34102),x34101)) % 191.49/191.40 [3419]P40(x34191,f333(f333(f289(a880,x34191),a254),x34192)) % 191.49/191.40 [3421]P17(a880,f140(a880,f333(f303(a880,x34211),x34212))) % 191.49/191.40 [3423]P4(f333(f63(a880),f333(f303(a880,x34231),x34232))) % 191.49/191.40 [3424]P4(f333(f63(a1),f333(f303(a1,x34241),x34242))) % 191.49/191.40 [3426]E(f333(f288(f881(x34261),f881(x34261)),f158(x34261,x34262)),f158(x34261,f333(f288(x34261,x34261),x34262))) % 191.49/191.40 [3427]E(f333(f195(a876),f33(x34271,x34272)),f333(f333(f81(a880),f333(f195(a876),x34272)),f333(a117,f2(a880)))) % 191.49/191.40 [3429]E(f333(f303(a1,x34291),f333(f333(f81(a1),x34292),f79(a1))),f304(a1,x34291,x34292)) % 191.49/191.40 [3432]E(f333(f333(f40(a1),f333(f80(a1),x34321)),f333(f80(a1),x34322)),f333(f333(f40(a1),x34321),x34322)) % 191.49/191.40 [3440]E(f184(x34401,x34402,f333(f18(f884(x34402),x34401),f197(x34402))),f194(f890(x34401,a874))) % 191.49/191.40 [3441]E(f186(x34411,x34412,f333(f18(f884(x34412),x34411),f197(x34412))),f194(f890(x34412,a874))) % 191.49/191.40 [3442]E(f333(f333(f189(f889(x34421,x34421),a874),f79(a880)),x34422),x34422) % 191.49/191.40 [3444]E(f333(f333(f115(f890(x34441,a874)),x34442),f194(f890(x34441,a874))),x34442) % 191.49/191.40 [3445]E(f333(f333(f3(f890(x34451,a874)),x34452),f194(f890(x34451,a874))),x34452) % 191.49/191.40 [3446]E(f333(f333(f106(f890(x34461,a874)),x34462),f258(f890(x34461,a874))),x34462) % 191.49/191.40 [3447]E(f333(f262(a880,a880),f86(f889(a880,a880),f49(x34471,x34472))),f333(f333(f40(a880),x34471),x34472)) % 191.49/191.40 [3454]E(f315(x34541,f333(a22,x34542),f333(f80(a1),f333(a22,x34542))),f333(f333(f318(a1),x34541),x34542)) % 191.49/191.40 [3455]E(f304(a1,f333(f333(f81(a1),x34551),f79(a1)),x34552),f306(a1,x34551,x34552)) % 191.49/191.40 [3460]E(f333(f271(a880,a880),f86(f889(a880,a880),f49(x34601,x34602))),f46(a880,x34601,x34602)) % 191.49/191.40 [3467]E(f316(x34671,f333(a22,x34672),f333(f80(a1),f333(a22,x34672))),f317(a1,x34671,x34672)) % 191.49/191.40 [3470]P4(f333(f333(f335(x34701),x34702),f258(f890(x34701,a874)))) % 191.49/191.40 [3475]E(f333(f333(f3(a880),f333(a117,x34751)),x34752),f333(f39(a880),f304(a880,x34752,x34751))) % 191.49/191.40 [3500]E(f333(f333(f115(f890(x35001,a874)),x35002),f258(f890(x35001,a874))),f258(f890(x35001,a874))) % 191.49/191.40 [3501]E(f333(f333(f3(f890(x35011,a874)),x35012),f258(f890(x35011,a874))),f194(f890(x35011,a874))) % 191.49/191.40 [3502]E(f333(f333(f106(f890(x35021,a874)),x35022),f194(f890(x35021,a874))),f194(f890(x35021,a874))) % 191.49/191.40 [3517]E(f46(a1,f333(f80(a1),x35171),f333(f80(a1),x35172)),f333(f80(a1),f46(a1,x35171,x35172))) % 191.49/191.40 [3518]E(f46(a1,f333(f105(a1),x35181),f333(f105(a1),x35182)),f333(f105(a1),f46(a880,x35181,x35182))) % 191.49/191.40 [3530]E(f333(f195(f881(x35301)),f333(f172(x35301),x35302)),f333(f333(f3(a880),f333(f195(f881(x35301)),x35302)),f79(a880))) % 191.49/191.40 [3553]E(f333(f333(f40(a1),f46(a1,x35531,x35532)),x35532),f2(a1)) % 191.49/191.40 [3564]E(f333(a5,f46(a880,f333(a21,x35641),f333(a21,x35642))),f46(a104,x35641,x35642)) % 191.49/191.40 [3598]E(f333(a5,f333(f333(f3(a880),f333(a21,x35981)),f333(a21,x35982))),f333(f333(f3(a104),x35981),x35982)) % 191.49/191.40 [3599]E(f333(a5,f333(f333(f81(a880),f333(a21,x35991)),f333(a21,x35992))),f333(f333(f81(a104),x35991),x35992)) % 191.49/191.40 [3600]E(f333(a5,f333(f333(f82(a880),f333(a21,x36001)),f333(a21,x36002))),f333(f333(f82(a104),x36001),x36002)) % 191.49/191.40 [3601]E(f333(a5,f333(f333(f40(a880),f333(a21,x36011)),f333(a21,x36012))),f333(f333(f40(a104),x36011),x36012)) % 191.49/191.40 [3610]E(f333(f312(a880,a880,a117),f333(f303(a880,x36101),x36102)),f333(f303(a880,f333(a117,x36101)),f333(a117,x36102))) % 191.49/191.40 [3634]P4(f333(f49(x36341,x36342),f86(f889(a880,a880),f49(x36341,x36342)))) % 191.49/191.40 [3656]E(f333(f333(f81(a880),f333(f333(f81(a880),f32(x36561)),f32(x36562))),f333(a117,f2(a880))),f32(f34(x36561,x36562))) % 191.49/191.40 [3657]E(f46(a880,f333(a117,f46(a880,x36571,x36572)),x36572),f46(a880,f333(a117,x36571),x36572)) % 191.49/191.40 [3671]E(f333(f333(f44(f890(x36711,a874),f890(x36711,a874)),x36712),f7(f890(x36711,a874))),f41(f890(x36711,a874),x36712)) % 191.49/191.40 [3672]E(f333(f333(f43(f890(x36721,a874),f890(x36721,a874)),x36722),f7(f890(x36721,a874))),f42(f890(x36721,a874),x36722)) % 191.49/191.40 [3673]E(f333(f312(f881(x36731),f890(x36731,a874),f173(x36731)),f333(f173(f881(x36731)),f55(x36731,x36732))),f333(f310(x36731),f333(f173(x36731),x36732))) % 191.49/191.40 [3676]P4(f333(f333(f335(f890(x36761,a874)),x36762),f333(f310(x36761),x36762))) % 191.49/191.40 [3681]E(f46(a1,f333(f80(a1),f46(a1,x36811,x36812)),x36812),f46(a1,f333(f80(a1),x36811),x36812)) % 191.49/191.40 [3693]P4(f333(f333(f250(f890(x36931,a874)),x36932),f258(f890(x36931,a874)))) % 191.49/191.40 [3695]E(f333(f333(f290(x36951,x36951,x36951),f309(x36951,x36952)),f309(x36951,f309(x36951,x36952))),f309(x36951,x36952)) % 191.49/191.40 [3696]E(f333(f333(f115(f890(x36961,a874)),f333(f261(x36961,x36961),x36962)),f333(f259(x36961,x36961),x36962)),f333(f286(x36961),x36962)) % 191.49/191.40 [3717]E(f320(x37171,x37172,f258(f890(x37171,a874)),f258(f890(x37172,a874))),f258(f890(f888(x37171,x37172),a874))) % 191.49/191.40 [3765]P4(f333(f333(f250(a880),f46(a880,x37651,x37652)),x37651)) % 191.49/191.40 [3787]P4(f333(f333(f250(a1),f333(f80(a1),f333(f105(a1),x37871))),f333(f105(a1),x37872))) % 191.49/191.40 [3814]P4(f333(f333(f335(f890(x38141,a874)),f194(f890(x38141,a874))),f333(f310(x38141),x38142))) % 191.49/191.40 [3819]E(f309(x38191,f333(f333(f290(x38191,x38191,x38191),x38192),f309(x38191,x38192))),f309(x38191,x38192)) % 191.49/191.40 [3822]E(f333(f333(f290(x38221,x38221,x38221),f309(x38221,x38222)),x38222),f333(f333(f290(x38221,x38221,x38221),x38222),f309(x38221,x38222))) % 191.49/191.40 [3824]E(f333(a109,f333(f333(f81(a1),f333(f333(f3(a1),x38241),x38242)),f79(a1))),f333(f39(a1),f304(a1,x38242,x38241))) % 191.49/191.40 [3836]E(f333(f259(x38361,x38361),f333(f333(f290(x38361,x38361,x38361),x38362),f309(x38361,x38362))),f333(f259(x38361,x38361),x38362)) % 191.49/191.40 [3837]E(f333(f261(x38371,x38371),f333(f333(f290(x38371,x38371,x38371),x38372),f309(x38371,x38372))),f333(f261(x38371,x38371),x38372)) % 191.49/191.40 [3853]E(f333(f333(f81(a880),f333(f333(f81(a880),f333(f195(a876),x38531)),f333(f195(a876),x38532))),f333(a117,f2(a880))),f333(f195(a876),f34(x38531,x38532))) % 191.49/191.40 [3864]P28(a880,a880,f333(f333(f9(a880,a880,a880),f81(a880)),x38641),x38642) % 191.49/191.40 [3866]P17(a880,f333(f170(a880),f333(f333(f155(f881(x38661),a880),f195(f881(x38661))),f180(x38661,x38662)))) % 191.49/191.40 [3908]P4(f333(f333(f251(a1),f333(f80(a1),f333(f105(a1),f333(a117,x39081)))),f333(f105(a1),x39082))) % 191.49/191.40 [3954]E(f333(f143(f881(x39541),x39541,f333(f9(x39541,f881(x39541),f881(x39541)),f152(x39541)),f118(x39541)),x39542),f333(f170(x39541),x39542)) % 191.49/191.40 [4005]P4(f333(f333(f250(f890(f889(f881(x40051),f881(x40051)),a874)),f159(x40051,x40052)),f309(f881(x40051),f158(x40051,x40052)))) % 191.49/191.40 [4034]P4(f333(f49(x40341,x40342),f333(f333(f263(a880,a880),f333(f333(f40(a880),x40341),x40342)),f46(a880,x40341,x40342)))) % 191.49/191.40 [4045]P4(f333(f333(f250(f890(f889(f881(x40451),f881(x40451)),a874)),f158(x40451,f309(x40451,x40452))),f309(f881(x40451),f158(x40451,x40452)))) % 191.49/191.40 [4271]E(f333(f333(f274(f889(a104,a104),a104,f889(a104,a104),f889(x42711,f889(a104,a104))),f278(f333(f167(a104),f333(f333(f155(f889(a104,x42711),a104),f262(a104,x42711)),x42712)))),f333(f333(f10(x42711,f890(f889(a104,a104),f889(x42711,f889(a104,a104))),a104),f263(x42711,f889(a104,a104))),f279(x42711,x42712))),f277(x42711,x42712)) % 191.49/191.40 [4386]E(f333(f244(a880,f889(x43861,f882(x43861)),f2(a880),f333(f272(x43861,f882(x43861),a880),f333(f18(f890(f882(x43861),a880),x43861),f333(f333(f9(f882(x43861),a880,a880),f333(f333(f10(a880,f890(a880,a880),f882(x43861)),f81(a880)),f195(f882(x43861)))),f79(a880))))),f333(f134(x43861),x43862)),f333(f195(f882(x43861)),x43862)) % 191.49/191.40 [4470]E(f333(f272(f890(f889(x44701,x44701),a874),f890(f889(x44701,x44701),a874),f890(f890(x44702,x44701),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874)))),f333(f333(f9(f890(f889(x44701,x44701),a874),f890(f890(f889(x44701,x44701),a874),f890(f890(x44702,x44701),f890(f889(x44702,x44702),a874))),f890(f890(f889(x44701,x44701),a874),f890(f890(x44702,x44701),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874))))),f333(f333(f10(f890(f890(f890(x44702,x44701),f890(f889(x44702,x44702),a874)),f890(f890(x44702,x44701),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874)))),f890(f890(f890(f889(x44701,x44701),a874),f890(f890(x44702,x44701),f890(f889(x44702,x44702),a874))),f890(f890(f889(x44701,x44701),a874),f890(f890(x44702,x44701),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874))))),f890(f889(x44701,x44701),a874)),f10(f890(f890(x44702,x44701),f890(f889(x44702,x44702),a874)),f890(f890(x44702,x44701),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874))),f890(f889(x44701,x44701),a874))),f333(f333(f10(f890(f890(x44702,x44701),f890(f890(f889(x44702,x44702),a874),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874)))),f890(f890(f890(x44702,x44701),f890(f889(x44702,x44702),a874)),f890(f890(x44702,x44701),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874)))),f890(f889(x44701,x44701),a874)),f20(f890(x44702,x44701),f890(f889(x44702,x44702),a874),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874)))),f333(f333(f10(f890(f890(x44702,x44701),f890(f889(x44702,x44702),a874)),f890(f890(x44702,x44701),f890(f890(f889(x44702,x44702),a874),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874)))),f890(f889(x44701,x44701),a874)),f333(f10(f890(f889(x44702,x44702),a874),f890(f890(f889(x44702,x44702),a874),f889(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874))),f890(x44702,x44701)),f263(f890(f889(x44702,x44702),a874),f890(f889(x44702,x44702),a874)))),f289(x44701,x44702))))),f289(x44701,x44702))),f75(x44701,x44702)) % 191.49/191.40 [4554]~E(f333(f310(x45541),x45542),f194(f890(f890(x45541,a874),a874))) % 191.49/191.40 [4572]~P4(f333(f333(f335(x45721),x45722),f194(f890(x45721,a874)))) % 191.49/191.40 [4579]~P4(f333(f333(f251(f890(x45791,a874)),x45792),f194(f890(x45791,a874)))) % 191.49/191.40 [3382]E(f333(f333(f3(a880),x33821),f333(f333(f81(a880),x33821),x33822)),f2(a880)) % 191.49/191.40 [3384]E(f333(f333(f115(f890(x33841,a874)),x33842),x33842),x33842) % 191.49/191.40 [3385]E(f333(f333(f106(f890(x33851,a874)),x33852),x33852),x33852) % 191.49/191.40 [3412]E(f333(f333(f3(f890(x34121,a874)),x34122),x34122),f194(f890(x34121,a874))) % 191.49/191.40 [3415]E(f333(f144(x34151,x34152),f2(a880)),f194(f890(f889(f881(x34151),f881(x34151)),a874))) % 191.49/191.40 [3416]E(f333(f333(f81(a880),x34161),f333(a117,x34162)),f333(a117,f333(f333(f81(a880),x34161),x34162))) % 191.49/191.40 [3428]E(f202(f333(f105(a1),x34281),f333(f105(a1),x34282)),f333(f105(a1),f333(f333(f3(a880),x34281),x34282))) % 191.49/191.40 [3431]E(f333(f333(f40(a1),f333(f80(a1),x34311)),x34312),f333(f333(f40(a1),x34311),f333(f80(a1),x34312))) % 191.49/191.40 [3435]E(f333(f39(a1),f333(f303(a1,x34351),x34352)),f333(a109,f333(f333(f3(a1),x34352),x34351))) % 191.49/191.40 [3438]E(f333(f333(f81(a880),f333(a117,x34381)),x34382),f333(a117,f333(f333(f81(a880),x34381),x34382))) % 191.49/191.40 [3443]E(f333(f80(f890(x34431,a874)),f333(f80(f890(x34431,a874)),x34432)),x34432) % 191.49/191.40 [3457]E(f180(x34571,f333(f333(f152(f881(x34571)),f118(x34571)),x34572)),f180(x34571,x34572)) % 191.49/191.40 [3461]E(f333(f333(f81(a880),x34611),f333(f333(f82(a880),x34611),x34612)),f333(f333(f82(a880),x34611),f333(a117,x34612))) % 191.49/191.40 [3468]E(f333(f333(a4,f333(a5,x34681)),f333(a5,x34682)),f333(a5,f333(f333(f3(a880),x34681),x34682))) % 191.49/191.40 [3481]E(f333(f333(f82(a1),f333(f80(a1),x34811)),x34812),f333(f80(a1),f333(f333(f82(a1),x34811),x34812))) % 191.49/191.40 [3483]E(f333(f333(f264(a1),f333(f105(a1),x34831)),x34832),f333(f105(a1),f333(f333(f264(a880),x34831),x34832))) % 191.49/191.40 [3484]E(f333(f333(f81(a104),f333(a5,x34841)),f333(a5,x34842)),f333(a5,f333(f333(f81(a880),x34841),x34842))) % 191.49/191.40 [3485]E(f333(f333(f82(a104),f333(a5,x34851)),f333(a5,x34852)),f333(a5,f333(f333(f82(a880),x34851),x34852))) % 191.49/191.40 [3486]E(f333(f333(f248(a880),f333(a117,x34861)),f333(a117,x34862)),f333(a117,f333(f333(f248(a880),x34861),x34862))) % 191.49/191.40 [3487]E(f333(f333(f249(a880),f333(a117,x34871)),f333(a117,x34872)),f333(a117,f333(f333(f249(a880),x34871),x34872))) % 191.49/191.40 [3493]E(f333(f173(a880),f140(a880,f333(f303(a880,x34931),x34932))),f333(f303(a880,x34931),x34932)) % 191.49/191.40 [3494]E(f314(x34941,f333(f333(f311(x34941),x34942),f194(f890(x34941,a874)))),x34942) % 191.49/191.40 [3498]E(f333(f259(x34981,x34982),f194(f890(f889(x34981,x34982),a874))),f194(f890(x34982,a874))) % 191.49/191.40 [3499]E(f333(f261(x34991,x34992),f194(f890(f889(x34991,x34992),a874))),f194(f890(x34991,a874))) % 191.49/191.40 [3503]E(f333(a109,f333(f333(f3(a1),x35031),x35032)),f333(f39(a1),f306(a1,x35032,x35031))) % 191.49/191.40 [3508]E(f333(f333(f81(a880),x35081),f333(f333(f82(a880),x35082),x35081)),f333(f333(f82(a880),f333(a117,x35082)),x35081)) % 191.49/191.40 [3510]E(f333(f333(f62(x35101),f194(f890(x35101,a874))),x35102),f194(f890(f890(x35101,a874),a874))) % 191.49/191.40 [3519]E(f333(f195(f881(a880)),f140(a880,f333(f303(a880,x35191),x35192))),f333(f333(f3(a880),x35192),x35191)) % 191.49/191.40 [3534]E(f333(f333(f115(f890(x35341,a874)),f194(f890(x35341,a874))),x35342),x35342) % 191.49/191.40 [3535]E(f333(f333(f106(f890(x35351,a874)),f258(f890(x35351,a874))),x35352),x35352) % 191.49/191.40 [3536]E(f333(f333(f81(a1),f333(f80(a1),x35361)),f333(f80(a1),x35362)),f333(f80(a1),f333(f333(f81(a1),x35361),x35362))) % 191.49/191.40 [3539]E(f333(f333(f81(a1),f333(f108(a1),x35391)),f333(f108(a1),x35392)),f333(f108(a1),f333(f333(f81(a1),x35391),x35392))) % 191.49/191.40 [3541]E(f333(f333(f81(a1),f333(f105(a1),x35411)),f333(f105(a1),x35412)),f333(f105(a1),f333(f333(f81(a880),x35411),x35412))) % 191.49/191.40 [3542]E(f333(f333(f82(a1),f333(f108(a1),x35421)),f333(f108(a1),x35422)),f333(f108(a1),f333(f333(f82(a1),x35421),x35422))) % 191.49/191.40 [3544]E(f333(f333(f82(a1),f333(f105(a1),x35441)),f333(f105(a1),x35442)),f333(f105(a1),f333(f333(f82(a880),x35441),x35442))) % 191.49/191.40 [3545]E(f333(f333(f40(a1),f333(f105(a1),x35451)),f333(f105(a1),x35452)),f333(f105(a1),f333(f333(f40(a880),x35451),x35452))) % 191.49/191.40 [3565]E(f333(f333(f8(x35651,a880),f333(f18(a880,x35651),f79(a880))),x35652),f333(f39(x35651),x35652)) % 191.49/191.40 [3572]E(f333(f80(a1),f46(a1,f333(f80(a1),x35721),x35722)),f46(a1,x35721,f333(f80(a1),x35722))) % 191.49/191.40 [3574]E(f333(f173(a1),f179(x35741,f333(f333(f3(a1),x35742),f79(a1)))),f333(f303(a1,x35741),x35742)) % 191.49/191.40 [3578]P4(f333(f333(f250(a880),x35781),f333(f333(f81(a880),x35782),x35781))) % 191.49/191.40 [3579]P4(f333(f333(f250(a880),x35791),f333(f333(f81(a880),x35791),x35792))) % 191.49/191.40 [3582]E(f333(f333(f115(f890(x35821,a874)),f258(f890(x35821,a874))),x35822),f258(f890(x35821,a874))) % 191.49/191.40 [3583]E(f333(f333(f3(f890(x35831,a874)),f194(f890(x35831,a874))),x35832),f194(f890(x35831,a874))) % 191.49/191.40 [3584]E(f333(f333(f106(f890(x35841,a874)),f194(f890(x35841,a874))),x35842),f194(f890(x35841,a874))) % 191.49/191.40 [3589]E(f333(f333(f263(a1,a1),x35891),f333(f80(a1),x35892)),f333(a52,f333(f333(f263(a1,a1),x35891),x35892))) % 191.49/191.40 [3590]E(f333(f303(a1,f333(f333(f81(a1),x35901),f79(a1))),x35902),f307(a1,x35901,x35902)) % 191.49/191.40 [3602]E(f333(f333(f82(a880),x36021),f333(f333(f40(a880),x36022),x36021)),f333(f333(f3(a880),x36022),f46(a880,x36022,x36021))) % 191.49/191.40 [3603]E(f333(f333(f82(a1),x36031),f333(f333(f40(a1),x36032),x36031)),f333(f333(f3(a1),x36032),f46(a1,x36032,x36031))) % 191.49/191.40 [3607]E(f333(f173(a1),f179(f333(f333(f81(a1),x36071),f79(a1)),x36072)),f306(a1,x36071,x36072)) % 191.49/191.40 [3611]P4(f333(f333(f250(f890(x36111,a874)),x36112),x36112)) % 191.49/191.40 [3614]E(f333(f333(f115(f890(x36141,a874)),x36142),f333(f80(f890(x36141,a874)),x36142)),f258(f890(x36141,a874))) % 191.49/191.40 [3615]E(f333(f333(f106(f890(x36151,a874)),x36152),f333(f80(f890(x36151,a874)),x36152)),f194(f890(x36151,a874))) % 191.49/191.40 [3621]E(f333(f333(f3(a880),f333(f333(f3(a880),x36211),f79(a880))),x36212),f333(f333(f3(a880),x36211),f333(a117,x36212))) % 191.49/191.40 [3626]E(f333(f333(f3(f890(x36261,a874)),f258(f890(x36261,a874))),x36262),f333(f80(f890(x36261,a874)),x36262)) % 191.49/191.40 [3627]E(f333(f333(f3(a1),f333(f108(a1),x36271)),f333(f108(a1),x36272)),f333(f108(a1),f333(f333(f81(a1),x36271),f333(f80(a1),x36272)))) % 191.49/191.40 [3640]E(f333(f173(a880),f140(a880,f333(f303(a880,x36401),f333(a117,x36402)))),f304(a880,x36401,x36402)) % 191.49/191.40 [3648]P4(f333(f333(f333(f333(a203,a24),x36481),x36482),x36481)) % 191.49/191.40 [3654]E(f333(f195(f881(f881(x36541))),f55(x36541,x36542)),f333(f333(f264(a880),f333(a117,f333(a117,f2(a880)))),f333(f195(f881(x36541)),x36542))) % 191.49/191.40 [3674]E(f333(f333(f189(f889(x36741,x36741),a874),f2(a880)),x36742),f309(x36741,f194(f890(f889(x36741,x36741),a874)))) % 191.49/191.40 [3678]P4(f333(f138(a880),f140(a880,f333(f303(a880,x36781),x36782)))) % 191.49/191.40 [3694]E(f333(f312(a1,a880,a109),f304(a1,f333(f105(a1),x36941),f333(f105(a1),x36942))),f304(a880,x36941,x36942)) % 191.49/191.40 [3704]E(f191(a880,f2(a880),f7(a880),f333(f333(f3(a880),x37041),x37042)),f333(f333(f3(a880),x37041),f333(a117,x37042))) % 191.49/191.40 [3705]E(f333(a109,f333(f333(f3(a1),x37051),f333(f333(f81(a1),x37052),f79(a1)))),f333(f39(a1),f307(a1,x37052,x37051))) % 191.49/191.40 [3735]E(f333(f333(f155(a880,a880),a117),f140(a880,f333(f303(a880,x37351),x37352))),f140(a880,f333(f303(a880,f333(a117,x37351)),f333(a117,x37352)))) % 191.49/191.40 [3741]E(f333(f173(a1),f179(f333(f333(f81(a1),x37411),f79(a1)),f333(f333(f3(a1),x37412),f79(a1)))),f307(a1,x37411,x37412)) % 191.49/191.40 [3752]P4(f333(f333(f250(f890(x37521,a874)),f194(f890(x37521,a874))),x37522)) % 191.49/191.40 [3757]E(f86(x37571,f333(f333(f9(x37571,x37571,a874),a330),x37572)),x37572) % 191.49/191.40 [3758]E(f91(x37581,f333(f333(f9(x37581,x37581,a874),a330),x37582)),x37582) % 191.49/191.40 [3766]E(f333(f173(a880),f140(a880,f333(f303(a880,f333(a117,x37661)),f333(a117,x37662)))),f306(a880,x37661,x37662)) % 191.49/191.40 [3790]E(f333(f333(f270(x37901,x37902),f258(f890(x37901,a874))),f333(f18(f890(x37902,a874),x37901),f258(f890(x37902,a874)))),f258(f890(f889(x37901,x37902),a874))) % 191.49/191.40 [3826]E(f333(f255(x38261),f333(f333(f10(a874,a874,x38261),a328),x38262)),f333(f80(f890(x38261,a874)),f333(f255(x38261),x38262))) % 191.49/191.40 [3829]E(f333(f255(x38291),f333(f333(f9(x38291,x38291,a874),a330),x38292)),f333(f333(f311(x38291),x38292),f194(f890(x38291,a874)))) % 191.49/191.40 [3850]P4(f333(f333(f250(a880),f333(f39(x38501),f333(f173(x38501),x38502))),f333(f195(f881(x38501)),x38502))) % 191.49/191.40 [3851]P4(f333(f333(f250(a880),f333(f195(f881(x38511)),f153(x38511,x38512))),f333(f195(f881(x38511)),x38512))) % 191.49/191.40 [3861]E(f333(f255(x38611),f333(f333(f9(x38611,f890(x38611,a874),a874),f335(x38611)),x38612)),x38612) % 191.49/191.40 [3875]E(f333(f333(f174(x38751),f333(f333(f3(a880),f333(f195(f881(x38751)),x38752)),f79(a880))),x38752),f119(x38751,x38752)) % 191.49/191.40 [3895]E(f191(a880,f2(a880),f333(f333(f10(a880,a880,a880),a117),f333(f248(a880),x38951)),x38952),f333(f333(f248(a880),f333(a117,x38951)),x38952)) % 191.49/191.40 [3899]E(f41(f890(x38991,a874),f333(f312(f890(f889(x38991,x38991),a874),f890(x38991,a874),f286(x38991)),x38992)),f333(f286(x38991),f41(f890(f889(x38991,x38991),a874),x38992))) % 191.49/191.40 [3900]E(f191(a880,f333(a117,x39001),f333(f333(f10(a880,a880,a880),a117),f333(f249(a880),x39001)),x39002),f333(f333(f249(a880),f333(a117,x39001)),x39002)) % 191.49/191.40 [3902]E(f333(f333(f263(a1,a1),f333(f333(f40(a1),f333(f76(a1),x39021)),f333(f76(a1),x39022))),f46(a1,f333(f76(a1),x39021),f333(f76(a1),x39022))),f54(x39021,x39022)) % 191.49/191.40 [3924]P4(f333(f333(f250(f890(f890(x39241,a874),a874)),x39242),f333(f310(x39241),f41(f890(x39241,a874),x39242)))) % 191.49/191.40 [3959]E(f333(f333(f44(x39591,f890(x39591,a874)),x39592),f333(f333(f9(x39591,f890(x39591,a874),f890(x39591,a874)),f311(x39591)),f194(f890(x39591,a874)))),x39592) % 191.49/191.40 [3960]E(f333(f333(f290(x39601,x39601,x39601),f333(f288(x39601,x39601),x39602)),f309(x39601,f333(f288(x39601,x39601),x39602))),f333(f288(x39601,x39601),f333(f333(f290(x39601,x39601,x39601),x39602),f309(x39601,x39602)))) % 191.49/191.40 [4026]E(f333(f173(x40261),f333(f143(f881(x40261),f881(x40261),f127(x40261),f118(x40261)),x40262)),f333(f333(f44(f881(x40261),f890(x40261,a874)),f333(f173(f881(x40261)),x40262)),f173(x40261))) % 191.49/191.40 [4057]E(f333(f333(f115(f890(f889(x40571,x40571),a874)),f309(x40571,f194(f890(f889(x40571,x40571),a874)))),f333(f333(f290(x40571,x40571,x40571),f309(x40571,x40572)),x40572)),f309(x40571,x40572)) % 191.49/191.40 [4092]E(f333(f333(f182(x40921,x40921),x40922),x40922),f333(f333(f155(x40921,f889(x40921,x40921)),f333(f333(f20(x40921,x40921,f889(x40921,x40921)),f263(x40921,x40921)),f7(x40921))),x40922)) % 191.49/191.40 [4205]E(f333(f143(a880,f881(x42051),f333(f9(f881(x42051),a880,a880),f333(f333(f10(a880,f890(a880,a880),f881(x42051)),f249(a880)),f195(f881(x42051)))),f2(a880)),f333(f170(f881(x42051)),x42052)),f333(f195(f881(f881(x42051))),f180(x42051,x42052))) % 191.49/191.40 [4285]E(f333(f333(f289(f889(a880,f881(x42851)),f881(x42851)),f326(a880,f881(x42851),a254,f146(x42851,x42852))),f333(f333(f20(f881(x42851),f881(x42851),f889(a880,f881(x42851))),f333(f333(f10(a880,f890(f881(x42851),f889(a880,f881(x42851))),f881(x42851)),f263(a880,f881(x42851))),f195(f881(x42851)))),f7(f881(x42851)))),f147(x42851,x42852)) % 191.49/191.40 [4426]E(f333(f255(x44261),f333(f333(f10(f890(f890(x44261,a874),a874),a874,x44261),f88(f890(x44261,a874))),f333(f333(f10(f890(f890(x44261,a874),a874),f890(f890(x44261,a874),a874),x44261),f333(f20(f890(x44261,a874),a874,a874),f333(f333(f10(a874,f890(a874,a874),f890(x44261,a874)),a336),f333(f333(f9(f890(x44261,a874),f890(f890(x44261,a874),a874),a874),f335(f890(x44261,a874))),x44262)))),f335(x44261)))),f42(f890(x44261,a874),x44262)) % 191.49/191.40 [4580]~P4(f333(f333(f251(a1),f333(f105(a1),x45801)),f333(f80(a1),f333(f105(a1),x45802)))) % 191.49/191.40 [3506]E(f333(f333(f3(a880),f333(f333(f81(a880),x35061),x35062)),x35062),x35061) % 191.49/191.40 [3507]E(f333(f333(f3(a880),f333(f333(f81(a880),x35071),x35072)),x35071),x35072) % 191.49/191.40 [3573]E(f333(f333(f81(a880),f333(f333(f3(a880),x35731),x35732)),x35732),f333(f333(f249(a880),x35731),x35732)) % 191.49/191.40 [3680]E(f333(f333(f82(a880),f333(f333(f40(a880),x36801),x36802)),x36802),f333(f333(f3(a880),x36801),f46(a880,x36801,x36802))) % 191.49/191.40 [3709]E(f333(f173(a880),f140(a880,f333(f303(a880,f333(a117,x37091)),x37092))),f307(a880,x37091,x37092)) % 191.49/191.40 [3716]E(f333(f105(a1),f226(f333(a109,f333(f76(a1),x37161)),f333(a109,f333(f76(a1),x37162)))),f333(f333(a227,x37161),x37162)) % 191.49/191.40 [3718]E(f333(f333(f115(f890(x37181,a874)),f333(f80(f890(x37181,a874)),x37182)),x37182),f258(f890(x37181,a874))) % 191.49/191.40 [3719]E(f333(f333(f106(f890(x37191,a874)),f333(f80(f890(x37191,a874)),x37192)),x37192),f194(f890(x37191,a874))) % 191.49/191.40 [3731]P4(f333(f333(f250(a880),f333(f333(f3(a880),x37311),x37312)),x37311)) % 191.49/191.40 [3732]P4(f333(f333(f250(a880),f333(f333(f40(a880),x37321),x37322)),x37321)) % 191.49/191.40 [3754]P4(f333(f333(f251(a880),x37541),f333(a117,f333(f333(f81(a880),x37542),x37541)))) % 191.49/191.40 [3755]P4(f333(f333(f251(a880),x37551),f333(a117,f333(f333(f81(a880),x37551),x37552)))) % 191.49/191.40 [3777]E(f333(f333(f82(a880),f333(a109,f333(f76(a1),x37771))),f333(a109,f333(f76(a1),x37772))),f333(a109,f333(f76(a1),f333(f333(f82(a1),x37771),x37772)))) % 191.49/191.40 [3786]P4(f333(f333(f250(a1),f2(a1)),f333(f333(f264(a1),f333(f76(a1),x37861)),x37862))) % 191.49/191.40 [3855]E(f333(f287(f881(x38551),f881(x38551),f159(x38551,x38552)),f333(f333(f311(f881(x38551)),f118(x38551)),f194(f890(f881(x38551),a874)))),f333(f333(f311(f881(x38551)),f118(x38551)),f194(f890(f881(x38551),a874)))) % 191.49/191.40 [3873]E(f333(f333(f115(f890(f889(x38731,x38731),a874)),f309(x38731,x38732)),f309(x38731,f194(f890(f889(x38731,x38731),a874)))),f309(x38731,x38732)) % 191.49/191.40 [3955]E(f333(f255(f890(x39551,a874)),f333(f333(f9(f890(x39551,a874),f890(x39551,a874),a874),f250(f890(x39551,a874))),x39552)),f333(f310(x39551),x39552)) % 191.49/191.40 [3971]E(f333(f333(f155(a1,a880),a109),f333(f333(f127(a1),f333(f333(f155(a880,a1),f105(a1)),x39711)),f333(f333(f155(a880,a1),f105(a1)),x39712))),f333(f333(f127(a880),x39711),x39712)) % 191.49/191.40 [4004]E(f333(f312(a1,a1,f333(f333(f9(a1,a1,a1),f81(a1)),x40041)),f333(f303(a1,f2(a1)),f333(f333(f3(a1),x40042),x40041))),f333(f303(a1,x40041),x40042)) % 191.49/191.40 [4006]P51(x40061,f333(f333(f3(f890(f889(x40061,x40061),a874)),x40062),f309(x40061,f194(f890(f889(x40061,x40061),a874))))) % 191.49/191.40 [4024]E(f333(f195(f881(x40241)),f333(f143(f881(x40241),f881(x40241),f127(x40241),f118(x40241)),x40242)),f333(f167(a880),f333(f333(f155(f881(x40241),a880),f195(f881(x40241))),x40242))) % 191.49/191.40 [4029]P50(x40291,f258(f890(x40291,a874)),f333(f333(f115(f890(f889(x40291,x40291),a874)),x40292),f309(x40291,f194(f890(f889(x40291,x40291),a874))))) % 191.49/191.40 [4071]E(f191(a880,f2(a880),f333(f333(f10(a880,a880,a880),a117),f333(f333(f9(a880,a880,a880),f248(a880)),x40711)),x40712),f333(f333(f248(a880),x40712),f333(a117,x40711))) % 191.49/191.40 [4074]E(f191(a880,f333(a117,x40741),f333(f333(f10(a880,a880,a880),a117),f333(f333(f9(a880,a880,a880),f249(a880)),x40741)),x40742),f333(f333(f249(a880),x40742),f333(a117,x40741))) % 191.49/191.40 [4077]E(f333(f312(x40771,f881(x40771),f333(f333(f9(x40771,f881(x40771),f881(x40771)),f152(x40771)),f118(x40771))),x40772),f176(x40771,x40772,f333(f333(f311(f881(x40771)),f118(x40771)),f194(f890(f881(x40771),a874))))) % 191.49/191.40 [4078]E(f333(f333(f115(f890(f889(x40781,x40781),a874)),f333(f333(f290(x40781,x40781,x40781),x40782),f309(x40781,x40782))),f309(x40781,f194(f890(f889(x40781,x40781),a874)))),f309(x40781,x40782)) % 191.49/191.40 [4087]P4(f333(f333(f250(f890(f889(x40871,x40871),a874)),f260(x40871,x40872)),f333(f333(f270(x40871,x40871),x40872),f333(f18(f890(x40871,a874),x40871),x40872)))) % 191.49/191.40 [4090]E(f333(f312(a1,a880,a109),f333(f333(f115(f890(a1,a874)),f333(f312(a880,a1,f105(a1)),x40901)),f333(f312(a880,a1,f105(a1)),x40902))),f333(f333(f115(f890(a880,a874)),x40901),x40902)) % 191.49/191.40 [4091]E(f333(f312(a1,a880,a109),f333(f333(f106(f890(a1,a874)),f333(f312(a880,a1,f105(a1)),x40911)),f333(f312(a880,a1,f105(a1)),x40912))),f333(f333(f106(f890(a880,a874)),x40911),x40912)) % 191.49/191.40 [4095]E(f333(f255(x40951),f333(f333(f10(a874,a874,x40951),a328),f333(f333(f9(x40951,f890(x40951,a874),a874),f335(x40951)),x40952))),f333(f80(f890(x40951,a874)),x40952)) % 191.49/191.40 [4121]E(f333(f143(f881(x41211),f881(x41211),f127(x41211),f118(x41211)),f333(f333(f155(f881(x41211),f881(x41211)),f170(x41211)),f333(f170(f881(x41211)),x41212))),f333(f170(x41211),f333(f143(f881(x41211),f881(x41211),f127(x41211),f118(x41211)),x41212))) % 191.49/191.40 [4147]E(f333(f333(f44(a880,f890(f889(x41471,x41471),a874)),f258(f890(a880,a874))),f333(f333(f9(a880,f890(f889(x41471,x41471),a874),f890(f889(x41471,x41471),a874)),f189(f889(x41471,x41471),a874)),x41472)),f309(x41471,x41472)) % 191.49/191.40 [4164]E(f86(x41641,f333(f333(f10(f890(x41641,a874),a874,x41641),f333(a330,x41642)),f333(f333(f9(x41641,f890(x41641,a874),f890(x41641,a874)),f311(x41641)),f194(f890(x41641,a874))))),f314(x41641,x41642)) % 191.49/191.40 [4173]E(f333(f195(f881(x41731)),f153(x41731,f333(f143(f881(x41731),f881(x41731),f127(x41731),f118(x41731)),x41732))),f333(f39(x41731),f333(f333(f44(f881(x41731),f890(x41731,a874)),f333(f173(f881(x41731)),x41732)),f173(x41731)))) % 191.49/191.40 [4189]E(f333(f333(f115(f890(f889(x41891,x41891),a874)),x41892),f333(f333(f290(x41891,x41891,x41891),f333(f333(f290(x41891,x41891,x41891),x41892),f309(x41891,x41892))),x41892)),f333(f333(f290(x41891,x41891,x41891),x41892),f309(x41891,x41892))) % 191.49/191.40 [4217]P4(f333(f333(f250(f890(f889(x42171,x42171),a874)),f333(f333(f290(x42171,x42171,x42171),x42172),f309(x42171,x42172))),f333(f333(f270(x42171,x42171),f333(f286(x42171),x42172)),f333(f18(f890(x42171,a874),x42171),f333(f286(x42171),x42172))))) % 191.49/191.40 [4259]E(f333(f255(f881(x42591)),f333(f333(f9(f881(x42591),f890(x42591,a874),a874),f333(f333(f10(f890(x42591,a874),f890(f890(x42591,a874),a874),f881(x42591)),f250(f890(x42591,a874))),f173(x42591))),x42592)),f162(x42591,x42592)) % 191.49/191.40 [4273]E(f333(f157(f881(x42731),x42731,f118(x42731),f333(f333(f10(f881(x42731),f890(f881(x42731),f881(x42731)),x42731),f333(f9(f881(x42731),f881(x42731),f881(x42731)),f127(x42731))),f333(f333(f9(x42731,f881(x42731),f881(x42731)),f152(x42731)),f118(x42731)))),x42732),f333(f169(x42731),x42732)) % 191.49/191.40 [4312]P28(f890(x43121,x43122),f890(f889(x43121,x43122),a874),f333(f333(f10(f890(f889(x43121,x43122),a874),f890(f889(x43121,x43122),a874),f890(x43121,x43122)),f255(f889(x43121,x43122))),f333(f333(f10(f890(x43121,f890(x43122,a874)),f890(f889(x43121,x43122),a874),f890(x43121,x43122)),f272(x43121,x43122,a874)),f333(f10(x43122,f890(x43122,a874),x43121),f333(f9(x43122,x43122,a874),a330)))),f258(f890(f890(x43121,x43122),a874))) % 191.49/191.40 [4367]E(f333(f333(f44(x43671,f890(f889(x43671,x43671),a874)),x43672),f333(f333(f9(x43671,f890(f889(x43671,x43671),a874),f890(f889(x43671,x43671),a874)),f333(f333(f10(f889(x43671,x43671),f890(f890(f889(x43671,x43671),a874),f890(f889(x43671,x43671),a874)),x43671),f311(f889(x43671,x43671))),f333(f333(f20(x43671,x43671,f889(x43671,x43671)),f263(x43671,x43671)),f7(x43671)))),f194(f890(f889(x43671,x43671),a874)))),f260(x43671,x43672)) % 191.49/191.40 [4375]E(f212(x43751,f333(f333(f263(a1,a1),f333(f80(a1),f333(f333(f74(f889(a1,a1),a1,x43751,f262(a1,a1)),f222(x43751)),x43752))),f333(f333(f74(f889(a1,a1),a1,x43751,f271(a1,a1)),f222(x43751)),x43752))),f236(x43751,x43752)) % 191.49/191.40 [4465]E(f333(f255(f890(x44651,a874)),f333(f333(f10(f890(f890(x44651,a874),a874),a874,f890(x44651,a874)),f87(f890(x44651,a874))),f333(f333(f9(f890(x44651,a874),f890(f890(x44651,a874),a874),f890(f890(x44651,a874),a874)),f333(f333(f10(f890(f890(x44651,a874),f890(a874,a874)),f890(f890(f890(x44651,a874),a874),f890(f890(x44651,a874),a874)),f890(x44651,a874)),f20(f890(x44651,a874),a874,a874)),f333(f333(f10(f890(f890(x44651,a874),a874),f890(f890(x44651,a874),f890(a874,a874)),f890(x44651,a874)),f333(f10(a874,f890(a874,a874),f890(x44651,a874)),a331)),f333(f333(f9(f890(x44651,a874),f890(f890(x44651,a874),f890(x44651,a874)),f890(f890(x44651,a874),a874)),f333(f333(f10(f890(f890(x44651,a874),a874),f890(f890(f890(x44651,a874),f890(x44651,a874)),f890(f890(x44651,a874),a874)),f890(x44651,a874)),f10(f890(x44651,a874),a874,f890(x44651,a874))),a330)),f80(f890(x44651,a874)))))),f333(f333(f10(f890(f890(x44651,a874),a874),a874,f890(x44651,a874)),f333(f335(f890(x44651,a874)),x44652)),f310(x44651))))),f333(f310(x44651),f333(f80(f890(x44651,a874)),x44652))) % 191.49/191.40 [4582]~P4(f333(f333(f251(a880),f333(f333(f81(a880),x45821),x45822)),x45822)) % 191.49/191.40 [4583]~P4(f333(f333(f251(a880),f333(f333(f81(a880),x45831),x45832)),x45831)) % 191.49/191.40 [3791]E(f333(f333(f3(a880),x37911),f333(f333(f82(a880),f333(f333(f40(a880),x37911),x37912)),x37912)),f46(a880,x37911,x37912)) % 191.49/191.40 [3792]E(f333(f333(f3(a1),x37921),f333(f333(f82(a1),f333(f333(f40(a1),x37921),x37922)),x37922)),f46(a1,x37921,x37922)) % 191.49/191.40 [3827]E(f333(f333(f155(a880,x38271),f333(f166(x38271),x38272)),f140(a880,f333(f303(a880,f2(a880)),f333(f195(f881(x38271)),x38272)))),x38272) % 191.49/191.40 [3882]E(f333(f287(x38821,x38821,f309(x38821,f194(f890(f889(x38821,x38821),a874)))),x38822),x38822) % 191.49/191.40 [4007]E(f309(x40071,f333(f333(f115(f890(f889(x40071,x40071),a874)),x40072),f309(x40071,f194(f890(f889(x40071,x40071),a874))))),f309(x40071,x40072)) % 191.49/191.40 [4008]E(f309(x40081,f333(f333(f3(f890(f889(x40081,x40081),a874)),x40082),f309(x40081,f194(f890(f889(x40081,x40081),a874))))),f309(x40081,x40082)) % 191.49/191.40 [4186]E(f333(f105(a1),f333(f333(f40(a880),f333(f333(f82(a880),f333(a109,f333(f76(a1),x41861))),f333(a109,f333(f76(a1),x41862)))),f226(f333(a109,f333(f76(a1),x41861)),f333(a109,f333(f76(a1),x41862))))),f228(x41861,x41862)) % 191.49/191.40 [4209]E(f333(f333(f3(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42091)),x42091)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42092)),x42092)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),x42091),x42092))),f333(f333(f3(a1),x42091),x42092))),a102)) % 191.49/191.40 [4233]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42331)),x42331)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42332)),x42332)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),x42331),x42332))),f333(f333(f81(a1),x42331),x42332))) % 191.49/191.40 [4237]E(f333(f333(f274(f889(a104,a104),a104,f889(a104,a104),f889(x42371,f889(a104,a104))),f278(f333(a5,f333(f195(f881(x42371)),x42372)))),f333(f333(f10(x42371,f890(f889(a104,a104),f889(x42371,f889(a104,a104))),a104),f263(x42371,f889(a104,a104))),f333(f333(f10(a880,x42371,a104),f333(f166(x42371),x42372)),a21))),f284(x42371,x42372)) % 191.49/191.40 [4266]E(f333(f333(f3(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42661)),x42661)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42662)),x42662)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),f333(f333(f81(a1),x42661),a102)),x42662))),f333(f333(f3(a1),f333(f333(f81(a1),x42661),a102)),x42662))) % 191.49/191.40 [4317]E(f333(f143(a880,f881(x43171),f333(f9(f881(x43171),a880,a880),f333(f333(f10(a880,f890(a880,a880),f881(x43171)),f249(a880)),f195(f881(x43171)))),f2(a880)),f333(f170(f881(x43171)),f180(x43171,x43172))),f333(f195(f881(f881(x43171))),f333(f137(f881(x43171),f333(f333(f10(a874,a874,f881(x43171)),a328),f333(f333(f9(f881(x43171),f881(x43171),a874),a330),f118(x43171)))),x43172))) % 191.49/191.40 [4323]E(f333(f333(f44(a880,f890(x43231,a874)),f258(f890(a880,a874))),f333(f333(f9(a880,f890(a880,f890(x43231,a874)),f890(x43231,a874)),f333(f333(f10(f890(a880,a874),f890(f890(a880,f890(x43231,a874)),f890(x43231,a874)),a880),f44(a880,f890(x43231,a874))),f303(a880,f2(a880)))),x43232)),f333(f333(f44(a880,f890(x43231,a874)),f258(f890(a880,a874))),x43232)) % 191.49/191.40 [4344]P4(f333(f63(a880),f333(f255(a880),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),x43441)),f333(f333(f9(a880,a880,a874),f251(a880)),x43442))))) % 191.49/191.40 [4475]E(f333(f255(f889(f881(x44751),f881(x44751))),f333(f272(f881(x44751),f881(x44751),a874),f333(f333(f20(f881(x44751),f890(f881(x44751),a874),f890(f881(x44751),a874)),f333(f333(f10(f890(f881(x44751),f890(a874,a874)),f890(f890(f881(x44751),a874),f890(f881(x44751),a874)),f881(x44751)),f20(f881(x44751),a874,a874)),f333(f333(f10(f890(f881(x44751),a874),f890(f881(x44751),f890(a874,a874)),f881(x44751)),f333(f10(a874,f890(a874,a874),f881(x44751)),a332)),f333(f333(f9(f881(x44751),f890(f881(x44751),a880),f890(f881(x44751),a874)),f333(f333(f10(f890(a880,a874),f890(f890(f881(x44751),a880),f890(f881(x44751),a874)),f881(x44751)),f10(a880,a874,f881(x44751))),f333(f333(f10(a880,f890(a880,a874),f881(x44751)),f251(a880)),f195(f881(x44751))))),f195(f881(x44751)))))),f333(f333(f20(f881(x44751),f890(f881(x44751),a874),f890(f881(x44751),a874)),f333(f333(f10(f890(f881(x44751),f890(a874,a874)),f890(f890(f881(x44751),a874),f890(f881(x44751),a874)),f881(x44751)),f20(f881(x44751),a874,a874)),f333(f333(f10(f890(f881(x44751),a874),f890(f881(x44751),f890(a874,a874)),f881(x44751)),f333(f10(a874,f890(a874,a874),f881(x44751)),a331)),f333(f333(f9(f881(x44751),f890(f881(x44751),a880),f890(f881(x44751),a874)),f333(f333(f10(f890(a880,a874),f890(f890(f881(x44751),a880),f890(f881(x44751),a874)),f881(x44751)),f10(a880,a874,f881(x44751))),f333(f333(f10(a880,f890(a880,a874),f881(x44751)),a330),f195(f881(x44751))))),f195(f881(x44751)))))),f333(f333(f9(f881(x44751),f890(f889(f881(x44751),f881(x44751)),a874),f890(f881(x44751),a874)),f333(f333(f10(f890(f881(x44751),f890(f890(f889(f881(x44751),f881(x44751)),a874),a874)),f890(f890(f889(f881(x44751),f881(x44751)),a874),f890(f881(x44751),a874)),f881(x44751)),f9(f881(x44751),f890(f889(f881(x44751),f881(x44751)),a874),a874)),f333(f333(f10(f890(f881(x44751),f889(f881(x44751),f881(x44751))),f890(f881(x44751),f890(f890(f889(f881(x44751),f881(x44751)),a874),a874)),f881(x44751)),f333(f10(f889(f881(x44751),f881(x44751)),f890(f890(f889(f881(x44751),f881(x44751)),a874),a874),f881(x44751)),f335(f889(f881(x44751),f881(x44751))))),f263(f881(x44751),f881(x44751))))),f146(x44751,x44752)))))),f147(x44751,x44752)) % 191.49/191.40 [4601]~P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x46011)),x46011)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x46012)),x46012))) % 191.49/191.40 [4235]E(f333(a109,f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x42351),x42352)),f194(f890(f889(a880,a880),a874)))))),f333(f333(f3(a880),x42351),x42352)) % 191.49/191.40 [4240]E(f333(f333(f290(x42401,x42401,x42401),f333(f333(f115(f890(f889(x42401,x42401),a874)),x42402),f309(x42401,f194(f890(f889(x42401,x42401),a874))))),f309(x42401,f333(f333(f115(f890(f889(x42401,x42401),a874)),x42402),f309(x42401,f194(f890(f889(x42401,x42401),a874)))))),f309(x42401,x42402)) % 191.49/191.40 [4277]E(f277(x42771,f333(f137(f889(a104,x42771),f333(f272(a104,x42771,a874),f333(f333(f10(a874,f890(x42771,a874),a104),f18(a874,x42771)),f333(f251(a104),f2(a104))))),x42772)),f277(x42771,x42772)) % 191.49/191.40 [4278]E(f279(x42781,f333(f137(f889(a104,x42781),f333(f272(a104,x42781,a874),f333(f333(f10(a874,f890(x42781,a874),a104),f18(a874,x42781)),f333(f251(a104),f2(a104))))),x42782)),f279(x42781,x42782)) % 191.49/191.40 [4279]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),x42791),f333(f333(f3(a1),x42792),a102)))),f333(f333(f81(a1),x42791),f333(f333(f3(a1),x42792),a102)))),a102),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42791)),x42791)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42792)),x42792))) % 191.49/191.40 [4281]E(f333(f80(a1),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x42811),x42812)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x42812),x42811)),f194(f890(f889(a880,a880),a874)))))) % 191.49/191.40 [4337]E(f333(f333(f289(f881(a880),x43371),f146(a880,a254)),f333(f333(f9(x43371,f881(f890(x43371,a880)),f881(a880)),f333(f333(f10(f890(f890(x43371,a880),a880),f890(f881(f890(x43371,a880)),f881(a880)),x43371),f155(f890(x43371,a880),a880)),f333(f9(f890(x43371,a880),x43371,a880),f7(f890(x43371,a880))))),x43372)),f154(x43371,x43372)) % 191.49/191.40 [4364]E(f333(f333(f89(a1,a880),f333(f108(a1),f333(f333(f81(a1),x43641),a102))),f333(f333(f20(a1,a880,a880),f333(f333(f9(a1,a880,f890(a880,a880)),f333(f333(f10(a874,f890(a880,f890(a880,a880)),a1),f101(a880)),a200)),f2(a880))),f333(f333(f10(a880,a880,a1),a117),f333(f333(f10(a880,a880,a1),f333(f248(a880),x43642)),a109)))),f333(f333(f248(a880),f333(a117,x43642)),f333(f108(a880),x43641))) % 191.49/191.40 [4365]E(f333(f333(f89(a1,a880),f333(f108(a1),f333(f333(f81(a1),x43651),a102))),f333(f333(f20(a1,a880,a880),f333(f333(f9(a1,a880,f890(a880,a880)),f333(f333(f10(a874,f890(a880,f890(a880,a880)),a1),f101(a880)),a200)),f333(a117,x43652))),f333(f333(f10(a880,a880,a1),a117),f333(f333(f10(a880,a880,a1),f333(f249(a880),x43652)),a109)))),f333(f333(f249(a880),f333(a117,x43652)),f333(f108(a880),x43651))) % 191.49/191.40 [4385]E(f333(f143(f881(x43851),f881(x43851),f127(x43851),f118(x43851)),f333(f333(f155(f881(x43851),f881(x43851)),f157(f881(x43851),x43851,f118(x43851),f333(f333(f10(f881(x43851),f890(f881(x43851),f881(x43851)),x43851),f18(f881(x43851),f881(x43851))),f333(f333(f9(x43851,f881(x43851),f881(x43851)),f152(x43851)),f118(x43851))))),x43852)),f333(f333(f155(f881(x43851),x43851),f142(x43851)),f333(f137(f881(x43851),f333(f333(f10(a874,a874,f881(x43851)),a328),f333(f333(f9(f881(x43851),f881(x43851),a874),a330),f118(x43851)))),x43852))) % 191.49/191.40 [4457]E(f333(f272(a1,a1,a874),f333(f333(f9(a1,f890(a1,a874),f890(a1,a874)),f333(f333(f10(f890(a1,f890(a874,a874)),f890(f890(a1,a874),f890(a1,a874)),a1),f20(a1,a874,a874)),f333(f333(f10(f890(a1,a874),f890(a1,f890(a874,a874)),a1),f333(f10(a874,f890(a874,a874),a1),a331)),f333(f333(f10(f890(a1,a1),f890(a1,a874),a1),f333(f10(a1,a874,a1),f333(a330,x44571))),f333(f333(f10(a1,f890(a1,a1),a1),f81(a1)),f333(f82(a1),x44572)))))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),f333(a336,f333(f333(f251(a1),f2(a1)),x44572))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),f333(f333(f9(a1,a1,a874),f251(a1)),x44572))))),f333(f333(f10(a874,a874,a1),f333(a336,f333(a328,f333(f333(f251(a1),f2(a1)),x44572)))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f251(a1),x44572))),f333(f333(f9(a1,a1,a874),f250(a1)),f2(a1))))))),f50(x44571,x44572)) % 191.49/191.40 [4459]E(f333(f255(x44591),f333(f333(f10(f890(a880,a874),a874,x44591),f87(a880)),f333(f333(f9(x44591,f890(a880,a874),f890(a880,a874)),f333(f333(f10(f890(a880,f890(a874,a874)),f890(f890(a880,a874),f890(a880,a874)),x44591),f20(a880,a874,a874)),f333(f333(f10(f890(a880,a874),f890(a880,f890(a874,a874)),x44591),f333(f10(a874,f890(a874,a874),a880),a331)),f333(f333(f9(x44591,f890(a880,x44591),f890(a880,a874)),f333(f333(f10(f890(x44591,a874),f890(f890(a880,x44591),f890(a880,a874)),x44591),f10(x44591,a874,a880)),a330)),f333(f166(x44591),x44592))))),f333(f333(f9(a880,a880,a874),f251(a880)),f333(f195(f881(x44591)),x44592))))),f333(f173(x44591),x44592)) % 191.49/191.40 [4590]~E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45901)),x45901)),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45902)),x45902)) % 191.49/191.40 [4198]E(f333(f333(f3(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41981)),x41981)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41982)),x41982)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),x41981),x41982))),f333(f333(f3(a1),x41981),x41982))) % 191.49/191.40 [4199]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41991)),x41991)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x41992)),x41992)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),x41991),x41992))),f333(f333(f81(a1),x41991),x41992))) % 191.49/191.40 [4290]E(f333(f333(f3(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42901)),x42901)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42902)),x42902)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f3(a1),x42901),x42902))),f333(f333(f3(a1),x42901),x42902))),a102)) % 191.49/191.40 [4291]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42911)),x42911)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42912)),x42912)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),x42911),x42912))),f333(f333(f81(a1),x42911),x42912))),a102)) % 191.49/191.40 [4324]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f82(a1),x43241),x43242))),f333(f333(f82(a1),x43241),x43242))),a102)),x43242),f333(f333(f82(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x43241)),x43241)),x43242)) % 191.49/191.40 [4380]E(f333(f143(f881(f881(x43801)),f881(f881(x43801)),f127(f881(x43801)),f118(f881(x43801))),f333(f333(f155(f881(x43801),f881(f881(x43801))),f157(f881(f881(x43801)),x43801,f118(f881(x43801)),f333(f18(f890(f881(x43801),f881(f881(x43801))),x43801),f333(f333(f9(f881(x43801),f881(f881(x43801)),f881(f881(x43801))),f152(f881(x43801))),f118(f881(x43801)))))),x43802)),f333(f333(f155(f881(x43801),f881(x43801)),f172(x43801)),f333(f137(f881(x43801),f333(f333(f10(a874,a874,f881(x43801)),a328),f333(f333(f9(f881(x43801),f881(x43801),a874),a330),f118(x43801)))),x43802))) % 191.49/191.40 [4389]E(f333(f333(f89(a1,a880),f333(f108(a1),f333(f333(f81(a1),x43891),a102))),f333(f333(f20(a1,a880,a880),f333(f333(f9(a1,a880,f890(a880,a880)),f333(f333(f10(a874,f890(a880,f890(a880,a880)),a1),f101(a880)),a200)),f2(a880))),f333(f333(f10(a880,a880,a1),a117),f333(f333(f9(a1,a880,a880),f333(f333(f10(a880,f890(a880,a880),a1),f248(a880)),a109)),x43892)))),f333(f333(f248(a880),f333(f108(a880),x43891)),f333(a117,x43892))) % 191.49/191.40 [4390]E(f333(f333(f89(a1,a880),f333(f108(a1),f333(f333(f81(a1),x43901),a102))),f333(f333(f20(a1,a880,a880),f333(f333(f9(a1,a880,f890(a880,a880)),f333(f333(f10(a874,f890(a880,f890(a880,a880)),a1),f101(a880)),a200)),f333(a117,x43902))),f333(f333(f10(a880,a880,a1),a117),f333(f333(f9(a1,a880,a880),f333(f333(f10(a880,f890(a880,a880),a1),f249(a880)),a109)),x43902)))),f333(f333(f249(a880),f333(f108(a880),x43901)),f333(a117,x43902))) % 191.49/191.40 [4599]~P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45991)),x45991)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x45992)),x45992)),a102))) % 191.49/191.40 [4228]E(f333(f333(f264(a1),x42281),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42282)),x42282)),a102))),f333(f333(f89(a1,a1),f333(f333(f264(a1),x42281),f333(f108(a880),x42282))),f333(f333(f20(a1,a1,a1),f82(a1)),f7(a1)))) % 191.49/191.40 [4264]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f82(a1),x42641),x42642))),f333(f333(f82(a1),x42641),x42642))),a102),f333(f333(f82(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x42641)),x42641)),a102)),x42642)) % 191.49/191.40 [4326]E(f333(f333(f40(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x43261)),x43261)),a102))),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x43262)),x43262)),a102))),f333(f333(f40(a1),f333(f108(a1),x43261)),f333(f108(a1),x43262))) % 191.49/191.40 [4379]E(f333(f272(x43791,x43791,a874),f333(f333(f20(x43791,a874,f890(x43791,a874)),f333(f333(f10(f890(x43791,f890(a874,a874)),f890(a874,f890(x43791,a874)),x43791),f9(x43791,a874,a874)),f333(f333(f10(f890(x43791,a874),f890(x43791,f890(a874,a874)),x43791),f333(f10(a874,f890(a874,a874),x43791),a331)),a330))),x43792)),f260(x43791,x43792)) % 191.49/191.40 [4440]E(f46(a1,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x44401)),x44401)),a102)),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x44402)),x44402)),a102))),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f46(a1,f333(f108(a1),x44401),f333(f108(a1),x44402)))) % 191.49/191.40 [4407]E(f333(f333(f40(a880),x44071),f333(f333(f81(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),x44072)),f333(f333(f40(a880),x44071),f333(a117,f333(a117,f333(a117,x44072))))) % 191.49/191.40 [4408]E(f46(a880,x44081,f333(f333(f81(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),x44082)),f46(a880,x44081,f333(a117,f333(a117,f333(a117,x44082))))) % 191.49/191.40 [4409]E(f46(a880,f333(f333(f81(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),x44091),x44092),f46(a880,f333(a117,f333(a117,f333(a117,x44091))),x44092)) % 191.49/191.40 [4433]E(f126(f333(x44331,f333(f333(f82(a104),f333(f108(a104),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),x44332))),f333(f210(x44331),x44332)) % 191.49/191.40 [4438]E(f333(f333(f40(a880),f333(f333(f81(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),x44381)),x44382),f333(f333(f40(a880),f333(a117,f333(a117,f333(a117,x44381)))),x44382)) % 191.49/191.40 [4501]~E(f34(x45011,x45012),f333(a26,x45013)) % 191.49/191.40 [4502]~E(f33(x45021,x45022),f333(a26,x45023)) % 191.49/191.40 [4503]~E(f333(a26,x45031),f34(x45032,x45033)) % 191.49/191.40 [4504]~E(f333(a26,x45041),f33(x45042,x45043)) % 191.49/191.40 [4517]~E(f29(x45171,x45172,x45173),a24) % 191.49/191.40 [4518]~E(f31(x45181,x45182,x45183),a24) % 191.49/191.40 [4519]~E(f30(x45191,x45192,x45193),a24) % 191.49/191.40 [3224]E(f333(f199(x32241,x32242),x32243),f124(x32241,x32242)) % 191.49/191.40 [3245]E(f333(f209(x32451,x32452),x32453),f333(f128(x32451),x32452)) % 191.49/191.40 [3323]E(f333(f333(f155(x33231,x33232),x33233),f118(x33231)),f118(x33232)) % 191.49/191.40 [3324]E(f333(f333(f208(x33241,x33242),x33243),f197(x33241)),f197(x33242)) % 191.49/191.40 [3344]E(f32(f29(x33441,x33442,x33443)),f2(a880)) % 191.49/191.40 [3365]E(f333(f190(x33651,x33652,x33653),f2(a880)),x33652) % 191.49/191.40 [3366]E(f333(f195(a876),f29(x33661,x33662,x33663)),f2(a880)) % 191.49/191.40 [3368]E(f333(f333(f182(x33681,x33682),x33683),f118(x33682)),f118(f889(x33681,x33682))) % 191.49/191.40 [3402]E(f86(x34021,f64(x34021,x34022,x34023)),f333(f65(x34021,x34022),x34023)) % 191.49/191.40 [3453]E(f141(x34531,x34532,f153(x34531,x34533)),f153(x34531,f141(x34531,x34532,x34533))) % 191.49/191.40 [3471]E(f333(f262(f881(x34711),f881(x34711)),f168(x34711,x34712,x34713)),f333(f137(x34711,x34712),x34713)) % 191.49/191.40 [3546]E(f19(x35461,x35462,x35463,f2(a104)),x35462) % 191.49/191.40 [3547]E(f191(x35471,x35472,x35473,f2(a880)),x35472) % 191.49/191.40 [3554]E(f164(x35541,x35542,x35543,f118(x35541)),f118(x35542)) % 191.49/191.40 [3555]E(f165(x35551,x35552,x35553,f118(x35551)),f118(x35552)) % 191.49/191.40 [3563]E(f333(f333(f166(x35631),f333(f333(f152(x35631),x35632),x35633)),f2(a880)),x35632) % 191.49/191.40 [3591]E(f61(x35911,x35912,f118(x35911),x35913),f118(f889(x35911,x35912))) % 191.49/191.40 [3613]P28(x36131,x36132,x36133,f194(f890(x36131,a874))) % 191.49/191.40 [3768]E(f333(f74(x37681,x37682,x37681,x37683),f35(x37681)),x37683) % 191.49/191.40 [3941]P4(f333(f333(f335(f889(x39411,x39411)),f333(f333(f263(x39411,x39411),x39412),x39412)),f309(x39411,x39413))) % 191.49/191.40 [4592]~P4(f333(f333(f335(f889(f881(x45921),f881(x45921))),f333(f333(f263(f881(x45921),f881(x45921)),x45922),f118(x45921))),f146(x45921,x45923))) % 191.49/191.40 [4593]~P4(f333(f333(f335(f889(f881(x45931),f881(x45931))),f333(f333(f263(f881(x45931),f881(x45931)),x45932),f118(x45931))),f148(x45931,x45933))) % 191.49/191.40 [4594]~P4(f333(f333(f335(f889(f881(x45941),f881(x45941))),f333(f333(f263(f881(x45941),f881(x45941)),x45942),f118(x45941))),f158(x45941,x45943))) % 191.49/191.40 [4595]~P4(f333(f333(f335(f889(f881(x45951),f881(x45951))),f333(f333(f263(f881(x45951),f881(x45951)),f118(x45951)),x45952)),f146(x45951,x45953))) % 191.49/191.40 [4596]~P4(f333(f333(f335(f889(f881(x45961),f881(x45961))),f333(f333(f263(f881(x45961),f881(x45961)),f118(x45961)),x45962)),f158(x45961,x45963))) % 191.49/191.40 [3296]E(f333(f333(f211(x32961),x32962),x32963),f212(x32961,f225(x32962,x32963))) % 191.49/191.40 [3354]E(f333(f288(x33541,x33542),f333(f288(x33542,x33541),x33543)),x33543) % 191.49/191.40 [3378]E(f333(f333(f182(x33781,x33782),f118(x33781)),x33783),f118(f889(x33781,x33782))) % 191.49/191.40 [3381]E(f175(x33811,x33812,f333(f256(a880),x33813)),f333(f333(f174(x33811),x33813),x33812)) % 191.49/191.40 [3398]E(f153(x33981,f333(f137(x33981,x33982),x33983)),f333(f137(x33981,x33982),f153(x33981,x33983))) % 191.49/191.40 [3400]E(f333(f259(x34001,x34002),f333(f288(x34002,x34001),x34003)),f333(f261(x34002,x34001),x34003)) % 191.49/191.40 [3401]E(f333(f261(x34011,x34012),f333(f288(x34012,x34011),x34013)),f333(f259(x34012,x34011),x34013)) % 191.49/191.40 [3417]E(f333(f137(x34171,x34172),f333(f170(x34171),x34173)),f333(f170(x34171),f333(f137(x34171,x34172),x34173))) % 191.49/191.40 [3430]E(f333(f333(f139(x34301),x34302),f333(f172(x34301),x34303)),f333(f333(f139(x34301),f333(a117,x34302)),x34303)) % 191.49/191.40 [3448]E(f32(f30(x34481,x34482,x34483)),f333(f333(f81(a880),f32(x34483)),f333(a117,f2(a880)))) % 191.49/191.40 [3449]E(f333(f313(x34491,x34492,x34493),f194(f890(x34492,a874))),f194(f890(x34491,a874))) % 191.49/191.40 [3450]E(f333(f313(x34501,x34502,x34503),f258(f890(x34502,a874))),f258(f890(x34501,a874))) % 191.49/191.40 [3451]E(f333(f312(x34511,x34512,x34513),f194(f890(x34511,a874))),f194(f890(x34512,a874))) % 191.49/191.40 [3452]E(f333(f287(x34521,x34522,x34523),f194(f890(x34521,a874))),f194(f890(x34522,a874))) % 191.49/191.40 [3479]E(f333(f333(f311(x34791),x34792),f333(f173(x34791),x34793)),f333(f173(x34791),f141(x34791,x34792,x34793))) % 191.49/191.40 [3491]E(f243(x34911,x34912,f333(f242(x34911),x34913)),f333(f333(f81(a880),f333(x34912,x34913)),f333(a117,f2(a880)))) % 191.49/191.40 [3567]E(f333(f195(a876),f30(x35671,x35672,x35673)),f333(f333(f81(a880),f333(f195(a876),x35673)),f333(a117,f2(a880)))) % 191.49/191.40 [3568]E(f333(f312(f889(x35681,x35682),x35682,f271(x35681,x35682)),x35683),f333(f259(x35681,x35682),x35683)) % 191.49/191.40 [3569]E(f333(f312(f889(x35691,x35692),x35691,f262(x35691,x35692)),x35693),f333(f261(x35691,x35692),x35693)) % 191.49/191.40 [3639]E(f333(f333(f263(x36391,x36392),f333(f262(x36391,x36392),x36393)),f333(f271(x36391,x36392),x36393)),x36393) % 191.49/191.40 [3646]E(f333(f195(f882(x36461)),f129(x36461,x36462,x36463)),f333(f333(f81(a880),f333(f195(f882(x36461)),x36463)),f333(a117,f2(a880)))) % 191.49/191.40 [3649]E(f333(f333(f272(x36491,x36492,x36491),f18(x36491,x36492)),x36493),f333(f262(x36491,x36492),x36493)) % 191.49/191.40 [3669]E(f185(x36691,x36692,x36693,f333(f18(f884(x36692),x36691),f197(x36692))),x36693) % 191.49/191.40 [3670]E(f185(x36701,x36702,f333(f18(f884(x36702),x36701),f197(x36702)),x36703),x36703) % 191.49/191.40 [3720]E(f32(f31(x37201,x37202,x37203)),f333(f333(f81(a880),f333(f333(f81(a880),f32(x37202)),f32(x37203))),f333(a117,f2(a880)))) % 191.49/191.40 [3772]E(f333(f74(x37721,x37721,x37722,f35(x37721)),x37723),x37723) % 191.49/191.40 [3876]E(f333(f195(a876),f31(x38761,x38762,x38763)),f333(f333(f81(a880),f333(f333(f81(a880),f333(f195(a876),x38762)),f333(f195(a876),x38763))),f333(a117,f2(a880)))) % 191.49/191.40 [3950]P4(f333(f333(f250(f890(x39501,a874)),f333(f173(x39501),f333(f137(x39501,x39502),x39503))),f333(f173(x39501),x39503))) % 191.49/191.40 [3995]P4(f333(f333(f250(f890(x39951,a874)),f333(f173(x39951),f333(f333(f174(x39951),x39952),x39953))),f333(f173(x39951),x39953))) % 191.49/191.40 [3996]P4(f333(f333(f250(f890(x39961,a874)),f333(f173(x39961),f333(f333(f139(x39961),x39962),x39963))),f333(f173(x39961),x39963))) % 191.49/191.40 [4000]P4(f333(f333(f250(f890(x40001,a874)),f333(f173(x40001),f171(x40001,x40002,x40003))),f333(f173(x40001),x40003))) % 191.49/191.40 [4001]P4(f333(f333(f250(f890(x40011,a874)),f333(f173(x40011),f175(x40011,x40012,x40013))),f333(f173(x40011),x40012))) % 191.49/191.40 [4022]P28(f889(x40221,x40222),f889(x40222,x40221),f333(f272(x40221,x40222,f889(x40222,x40221)),f333(f9(x40222,x40221,f889(x40222,x40221)),f263(x40222,x40221))),x40223) % 191.49/191.40 [4033]E(f333(f333(f333(f189(f881(x40331),f881(x40331)),f46(a880,x40332,f333(f195(f881(x40331)),x40333))),f169(x40331)),x40333),f333(f333(f333(f189(f881(x40331),f881(x40331)),x40332),f169(x40331)),x40333)) % 191.49/191.40 [4075]P4(f333(f333(f335(f889(f881(x40751),f881(x40751))),f333(f333(f263(f881(x40751),f881(x40751)),x40752),x40752)),f159(x40751,f309(x40751,x40753)))) % 191.49/191.40 [4221]E(f86(f889(x42211,x42212),f333(f333(f20(f889(x42211,x42212),x42212,a874),f333(f333(f10(x42211,f890(x42212,a874),f889(x42211,x42212)),x42213),f262(x42211,x42212))),f271(x42211,x42212))),f86(f889(x42211,x42212),f333(f272(x42211,x42212,a874),x42213))) % 191.49/191.40 [4222]E(f91(f889(x42221,x42222),f333(f333(f20(f889(x42221,x42222),x42222,a874),f333(f333(f10(x42221,f890(x42222,a874),f889(x42221,x42222)),x42223),f262(x42221,x42222))),f271(x42221,x42222))),f91(f889(x42221,x42222),f333(f272(x42221,x42222,a874),x42223))) % 191.49/191.40 [4256]E(f333(f333(f289(f889(a880,x42561),x42561),f326(a880,x42561,a254,x42562)),f333(f333(f20(x42561,x42561,f889(a880,x42561)),f333(f333(f10(a880,f890(x42561,f889(a880,x42561)),x42561),f263(a880,x42561)),x42563)),f7(x42561))),f327(x42561,x42563,x42562)) % 191.49/191.40 [4319]E(f333(f273(x43191,x43191,x43192,x43192,f7(x43191),f7(x43192)),x43193),x43193) % 191.49/191.40 [4400]E(f333(f143(f881(f881(x44001)),f881(f881(x44001)),f127(f881(x44001)),f118(f881(x44001))),f333(f333(f155(f881(x44001),f881(f881(x44001))),f333(f333(f9(f881(x44001),f881(x44001),f881(f881(x44001))),f333(f333(f10(f890(x44001,f881(x44001)),f890(f881(x44001),f881(f881(x44001))),f881(x44001)),f155(x44001,f881(x44001))),f333(f9(x44001,f881(x44001),f881(x44001)),f152(x44001)))),x44002)),f56(x44001,x44003,x44002))),f56(x44001,f333(a117,x44003),x44002)) % 191.49/191.40 [4472]E(f333(f244(a880,f889(x44721,f882(x44721)),f2(a880),f333(f272(x44721,f882(x44721),a880),f333(f333(f9(x44721,a880,f890(f882(x44721),a880)),f333(f333(f10(f890(f882(x44721),f890(a880,a880)),f890(a880,f890(f882(x44721),a880)),x44721),f9(f882(x44721),a880,a880)),f333(f333(f10(f890(f882(x44721),a880),f890(f882(x44721),f890(a880,a880)),x44721),f333(f10(a880,f890(a880,a880),f882(x44721)),f81(a880))),f333(f333(f9(x44721,f890(f882(x44721),a880),f890(f882(x44721),a880)),f333(f333(f10(f890(a880,a880),f890(f890(f882(x44721),a880),f890(f882(x44721),a880)),x44721),f10(a880,a880,f882(x44721))),f333(f333(f10(a880,f890(a880,a880),x44721),f81(a880)),x44722))),f131(x44721,x44722))))),f79(a880)))),f333(f134(x44721),x44723)),f333(f131(x44721,x44722),x44723)) % 191.49/191.40 [4474]E(f333(f333(f89(a1,x44741),f228(f333(f333(f74(f889(a1,a1),a1,x44741,f271(a1,a1)),f222(x44741)),x44742),f333(f333(f74(f889(a1,a1),a1,x44741,f271(a1,a1)),f222(x44741)),x44743))),f333(f333(f20(a1,a1,x44741),f333(f333(f10(a1,f890(a1,x44741),a1),f211(x44741)),f333(f333(f20(a1,a1,a1),f333(f333(f10(a1,f890(a1,a1),a1),f81(a1)),f333(f333(f10(a1,a1,a1),f333(f82(a1),f333(f333(f74(f889(a1,a1),a1,x44741,f262(a1,a1)),f222(x44741)),x44742))),f333(f333(f9(a1,a1,a1),f40(a1)),f333(f333(f74(f889(a1,a1),a1,x44741,f271(a1,a1)),f222(x44741)),x44742))))),f333(f333(f10(a1,a1,a1),f333(f82(a1),f333(f333(f74(f889(a1,a1),a1,x44741,f262(a1,a1)),f222(x44741)),x44743))),f333(f333(f9(a1,a1,a1),f40(a1)),f333(f333(f74(f889(a1,a1),a1,x44741,f271(a1,a1)),f222(x44741)),x44743)))))),f7(a1))),f239(x44741,x44742,x44743)) % 191.49/191.40 [4512]~E(f333(f333(f152(x45121),x45122),x45123),x45123) % 191.49/191.40 [4521]~E(f333(f333(f152(x45211),x45212),x45213),f118(x45211)) % 191.49/191.40 [4543]~E(f333(f333(f311(x45431),x45432),x45433),f194(f890(x45431,a874))) % 191.49/191.40 [4570]~E(f333(f312(x45701,f890(x45701,a874),x45702),x45703),f333(f310(x45701),x45703)) % 191.49/191.40 [3359]E(f333(f333(f160(x33591,f118(x33591)),x33592),x33593),f118(x33591)) % 191.49/191.40 [3360]E(f333(f142(x33601),f333(f333(f152(x33601),x33602),x33603)),x33602) % 191.49/191.40 [3361]E(f333(f172(x33611),f333(f333(f152(x33611),x33612),x33613)),x33613) % 191.49/191.40 [3405]E(f333(f333(f139(x34051),f79(a880)),f333(f333(f152(x34051),x34052),x34053)),x34053) % 191.49/191.40 [3437]E(f119(x34371,f333(f333(f139(x34371),x34372),x34373)),f333(f333(f139(x34371),x34372),f119(x34371,x34373))) % 191.49/191.40 [3439]E(f333(f333(f160(x34391,x34392),x34393),f333(f333(f166(x34391),x34392),x34393)),x34392) % 191.49/191.40 [3462]E(f333(f333(f311(x34621),x34622),f333(f333(f311(x34621),x34622),x34623)),f333(f333(f311(x34621),x34622),x34623)) % 191.49/191.40 [3473]E(f333(f333(f178(x34731,x34732),f118(f889(x34731,x34732))),x34733),f197(x34732)) % 191.49/191.40 [3476]E(f333(f333(f311(x34761),x34762),f333(f173(x34761),x34763)),f333(f173(x34761),f333(f333(f152(x34761),x34762),x34763))) % 191.49/191.40 [3478]E(f333(f333(f139(x34781),x34782),f333(f172(x34781),x34783)),f333(f172(x34781),f333(f333(f139(x34781),x34782),x34783))) % 191.49/191.40 [3488]E(f333(f333(f174(x34881),f79(a880)),f333(f333(f152(x34881),x34882),x34883)),f333(f333(f152(x34881),x34882),f118(x34881))) % 191.49/191.40 [3533]E(f333(f65(x35331,x35332),f333(f333(f311(x35331),x35333),f194(f890(x35331,a874)))),x35333) % 191.49/191.40 [3575]E(f333(f333(f81(a880),x35751),f333(f333(f81(a880),x35752),x35753)),f333(f333(f81(a880),x35752),f333(f333(f81(a880),x35751),x35753))) % 191.49/191.40 [3576]E(f333(f333(f81(a1),x35761),f333(f333(f81(a1),x35762),x35763)),f333(f333(f81(a1),x35762),f333(f333(f81(a1),x35761),x35763))) % 191.49/191.40 [3581]E(f333(f333(f270(x35811,x35812),f194(f890(x35811,a874))),x35813),f194(f890(f889(x35811,x35812),a874))) % 191.49/191.40 [3605]E(f333(f333(f115(f890(x36051,a874)),x36052),x36053),f333(f333(f115(f890(x36051,a874)),x36053),x36052)) % 191.49/191.40 [3606]E(f333(f333(f106(f890(x36061,a874)),x36062),x36063),f333(f333(f106(f890(x36061,a874)),x36063),x36062)) % 191.49/191.40 [3608]E(f333(f333(f127(x36081),x36082),f333(f333(f152(x36081),x36083),f118(x36081))),f333(f169(x36081),f333(f333(f152(x36081),x36083),x36082))) % 191.49/191.40 [3609]E(f333(f333(f127(x36091),f333(f170(x36091),x36092)),f333(f170(x36091),x36093)),f333(f170(x36091),f333(f333(f127(x36091),x36093),x36092))) % 191.49/191.40 [3617]E(f333(f172(x36171),f333(f333(f174(x36171),f333(a117,x36172)),x36173)),f333(f333(f174(x36171),x36172),f333(f172(x36171),x36173))) % 191.49/191.40 [3624]P4(f333(f333(f335(x36241),x36242),f333(f333(f311(x36241),x36242),x36243))) % 191.49/191.40 [3628]E(f333(f333(f43(x36281,f890(x36282,a874)),f194(f890(x36281,a874))),x36283),f258(f890(x36282,a874))) % 191.49/191.40 [3631]E(f333(f287(x36311,x36311,f260(x36311,x36312)),x36313),f333(f333(f106(f890(x36311,a874)),x36312),x36313)) % 191.49/191.40 [3645]E(f333(f195(f881(x36451)),f333(f333(f152(x36451),x36452),x36453)),f333(f333(f81(a880),f333(f195(f881(x36451)),x36453)),f333(a117,f2(a880)))) % 191.49/191.40 [3651]E(f145(x36511,f333(f333(f127(x36511),x36512),f333(f333(f152(x36511),x36513),f118(x36511)))),x36513) % 191.49/191.40 [3652]E(f119(x36521,f333(f333(f127(x36521),x36522),f333(f333(f152(x36521),x36523),f118(x36521)))),x36522) % 191.49/191.40 [3658]E(f333(f333(f127(x36581),f333(f333(f174(x36581),x36582),x36583)),f333(f333(f139(x36581),x36582),x36583)),x36583) % 191.49/191.40 [3667]E(f333(f333(f3(a880),f333(f333(f81(a880),x36671),x36672)),f333(f333(f81(a880),x36673),x36672)),f333(f333(f3(a880),x36671),x36673)) % 191.49/191.40 [3668]E(f333(f333(f3(a880),f333(f333(f81(a880),x36681),x36682)),f333(f333(f81(a880),x36681),x36683)),f333(f333(f3(a880),x36682),x36683)) % 191.49/191.40 [3675]E(f333(f333(f127(x36751),f333(f170(x36751),x36752)),f333(f333(f152(x36751),x36753),f118(x36751))),f333(f170(x36751),f333(f333(f152(x36751),x36753),x36752))) % 191.49/191.40 [3677]E(f333(f333(f81(a880),f333(f195(f881(x36771)),x36772)),f333(f195(f881(x36771)),x36773)),f333(f195(f881(x36771)),f333(f333(f127(x36771),x36772),x36773))) % 191.49/191.40 [3687]E(f333(f333(f115(f890(x36871,a874)),f333(f173(x36871),x36872)),f333(f173(x36871),x36873)),f333(f173(x36871),f333(f333(f127(x36871),x36872),x36873))) % 191.49/191.40 [3688]E(f46(a880,f333(f333(f82(a880),x36881),x36882),f333(f333(f82(a880),x36881),x36883)),f333(f333(f82(a880),x36881),f46(a880,x36882,x36883))) % 191.49/191.40 [3701]E(f333(f333(f174(x37011),f333(f333(f3(a880),x37012),f79(a880))),f333(f172(x37011),x37013)),f333(f172(x37011),f333(f333(f174(x37011),x37012),x37013))) % 191.49/191.40 [3706]E(f333(f333(f106(f890(x37061,a874)),x37062),f333(f80(f890(x37061,a874)),x37063)),f333(f333(f3(f890(x37061,a874)),x37062),x37063)) % 191.49/191.40 [3707]E(f333(f333(f3(f890(x37071,a874)),x37072),f333(f80(f890(x37071,a874)),x37073)),f333(f333(f106(f890(x37071,a874)),x37072),x37073)) % 191.49/191.40 [3723]E(f333(f333(f270(x37231,x37232),x37233),f333(f18(f890(x37232,a874),x37231),f194(f890(x37232,a874)))),f194(f890(f889(x37231,x37232),a874))) % 191.49/191.40 [3725]E(f333(f333(f3(a880),f333(f333(f82(a880),x37251),x37252)),f333(f333(f82(a880),x37251),x37253)),f333(f333(f82(a880),x37251),f333(f333(f3(a880),x37252),x37253))) % 191.49/191.40 [3726]E(f333(f333(f81(a880),f333(f333(f82(a880),x37261),x37262)),f333(f333(f82(a880),x37261),x37263)),f333(f333(f82(a880),x37261),f333(f333(f81(a880),x37262),x37263))) % 191.49/191.40 [3727]E(f333(f333(f3(a1),f333(f333(f82(a1),x37271),x37272)),f333(f333(f82(a1),x37271),x37273)),f333(f333(f82(a1),x37271),f333(f333(f3(a1),x37272),x37273))) % 191.49/191.40 [3728]E(f333(f333(f81(a1),f333(f333(f82(a1),x37281),x37282)),f333(f333(f82(a1),x37281),x37283)),f333(f333(f82(a1),x37281),f333(f333(f81(a1),x37282),x37283))) % 191.49/191.40 [3729]E(f333(f333(f82(a1),f333(f333(f264(a1),x37291),x37292)),f333(f333(f264(a1),x37291),x37293)),f333(f333(f264(a1),x37291),f333(f333(f81(a880),x37292),x37293))) % 191.49/191.40 [3742]E(f333(f333(f44(x37421,f890(x37422,a874)),x37423),f333(f18(f890(x37422,a874),x37421),f194(f890(x37422,a874)))),f194(f890(x37422,a874))) % 191.49/191.40 [3744]E(f46(a880,f333(f333(f82(a880),x37441),x37442),f333(f333(f82(a880),x37443),x37442)),f333(f333(f82(a880),f46(a880,x37441,x37443)),x37442)) % 191.49/191.40 [3748]E(f46(a1,f333(f333(f3(a1),x37481),f46(a1,x37482,x37483)),x37483),f46(a1,f333(f333(f3(a1),x37481),x37482),x37483)) % 191.49/191.40 [3749]E(f46(a1,f333(f333(f82(a1),x37491),f46(a1,x37492,x37493)),x37493),f46(a1,f333(f333(f82(a1),x37491),x37492),x37493)) % 191.49/191.40 [3750]P4(f333(f333(f250(f890(x37501,a874)),x37502),f333(f333(f311(x37501),x37503),x37502))) % 191.49/191.40 [3753]E(f333(f312(f889(x37531,x37532),x37531,f262(x37531,x37532)),f333(f173(f889(x37531,x37532)),x37533)),f184(x37531,x37532,f333(f178(x37531,x37532),x37533))) % 191.49/191.40 [3806]P4(f333(f63(x38061),f184(x38061,x38062,f333(f178(x38061,x38062),x38063)))) % 191.49/191.40 [3831]E(f333(f333(f43(f890(x38311,a874),f890(x38311,a874)),x38312),f333(f115(f890(x38311,a874)),x38313)),f333(f333(f115(f890(x38311,a874)),x38313),f42(f890(x38311,a874),x38312))) % 191.49/191.40 [3832]E(f333(f333(f44(f890(x38321,a874),f890(x38321,a874)),x38322),f333(f106(f890(x38321,a874)),x38323)),f333(f333(f106(f890(x38321,a874)),x38323),f41(f890(x38321,a874),x38322))) % 191.49/191.40 [3840]E(f333(f173(x38401),f333(f333(f333(f189(f881(x38401),f881(x38401)),x38402),f169(x38401)),x38403)),f333(f173(x38401),x38403)) % 191.49/191.40 [3844]E(f333(f333(f174(x38441),f333(f195(f881(x38441)),f177(x38441,x38442,x38443))),x38443),f177(x38441,x38442,x38443)) % 191.49/191.40 [3845]E(f184(x38451,x38452,f333(f333(f10(x38452,f884(x38452),x38451),f242(x38452)),x38453)),f258(f890(x38451,a874))) % 191.49/191.40 [3849]E(f333(f195(f881(x38491)),f333(f333(f333(f189(f881(x38491),f881(x38491)),x38492),f169(x38491)),x38493)),f333(f195(f881(x38491)),x38493)) % 191.49/191.40 [3852]E(f333(f333(f272(x38521,x38522,x38522),f333(f18(f890(x38522,x38522),x38521),f7(x38522))),x38523),f333(f271(x38521,x38522),x38523)) % 191.49/191.40 [3858]E(f46(a1,f333(f333(f3(a1),f46(a1,x38581,x38582)),x38583),x38582),f46(a1,f333(f333(f3(a1),x38581),x38583),x38582)) % 191.49/191.40 [3859]E(f46(a1,f333(f333(f264(a1),f46(a1,x38591,x38592)),x38593),x38592),f46(a1,f333(f333(f264(a1),x38591),x38593),x38592)) % 191.49/191.40 [3862]E(f333(f333(f44(f890(f889(x38621,x38622),a874),f890(x38622,a874)),x38623),f259(x38621,x38622)),f333(f259(x38621,x38622),f41(f890(f889(x38621,x38622),a874),x38623))) % 191.49/191.40 [3863]E(f333(f333(f44(f890(f889(x38631,x38632),a874),f890(x38631,a874)),x38633),f261(x38631,x38632)),f333(f261(x38631,x38632),f41(f890(f889(x38631,x38632),a874),x38633))) % 191.49/191.40 [3886]E(f333(f74(x38861,x38861,x38861,x38862),f333(f333(f189(x38861,x38861),x38863),x38862)),f333(f333(f189(x38861,x38861),f333(a117,x38863)),x38862)) % 191.49/191.40 [3896]E(f244(f884(x38961),x38962,f197(x38961),f333(f333(f10(x38961,f884(x38961),x38962),f242(x38961)),x38963)),f333(f208(x38962,x38961),x38963)) % 191.49/191.40 [3903]E(f333(f333(f139(x39031),f333(f333(f3(a880),f333(f195(f881(x39031)),x39032)),x39033)),f333(f170(x39031),x39032)),f333(f170(x39031),f333(f333(f174(x39031),x39033),x39032))) % 191.49/191.40 [3904]E(f333(f333(f174(x39041),f333(f333(f3(a880),f333(f195(f881(x39041)),x39042)),x39043)),f333(f170(x39041),x39042)),f333(f170(x39041),f333(f333(f139(x39041),x39043),x39042))) % 191.49/191.40 [3907]E(f333(f333(f81(a880),f333(f167(a880),f333(f333(f155(x39071,a880),x39072),x39073))),f333(f195(f881(x39071)),x39073)),f156(x39071,x39072,x39073)) % 191.49/191.40 [3925]E(f333(f169(x39251),f333(f333(f333(f189(f881(x39251),f881(x39251)),x39252),f169(x39251)),x39253)),f333(f333(f333(f189(f881(x39251),f881(x39251)),f333(a117,x39252)),f169(x39251)),x39253)) % 191.49/191.40 [3942]P4(f333(f333(f250(a880),f333(f195(f881(x39421)),f333(f137(x39421,x39422),x39423))),f333(f195(f881(x39421)),x39423))) % 191.49/191.40 [3958]E(f333(f333(f115(f890(f890(x39581,a874),a874)),f333(f310(x39581),x39582)),f333(f312(f890(x39581,a874),f890(x39581,a874),f333(f311(x39581),x39583)),f333(f310(x39581),x39582))),f333(f310(x39581),f333(f333(f311(x39581),x39583),x39582))) % 191.49/191.40 [3977]P27(x39771,x39772,f333(f333(f311(f879(x39771)),f333(f333(f333(f93(x39771),x39773),a24),x39773)),f194(f890(f879(x39771),a874)))) % 191.49/191.40 [3992]P4(f333(f333(f250(a880),f333(f195(f881(x39921)),f177(x39921,x39922,x39923))),f333(f195(f881(x39921)),x39923))) % 191.49/191.40 [3999]E(f333(f261(x39991,x39992),f333(f255(f889(x39991,x39992)),f333(f272(x39991,x39992,a874),x39993))),f333(f255(x39991),f333(f333(f10(f890(x39992,a874),a874,x39991),f87(x39992)),x39993))) % 191.49/191.40 [4009]E(f333(f312(a880,a880,f333(f333(f9(a880,a880,a880),f81(a880)),x40091)),f304(a880,x40092,x40093)),f304(a880,f333(f333(f81(a880),x40092),x40091),f333(f333(f81(a880),x40093),x40091))) % 191.49/191.40 [4012]P4(f333(f63(f884(x40121)),f333(f312(x40122,f884(x40121),f333(f178(x40122,x40121),x40123)),f258(f890(x40122,a874))))) % 191.49/191.40 [4025]E(f333(f312(a880,a880,f333(f333(f9(a880,a880,a880),f81(a880)),x40251)),f333(f303(a880,x40252),x40253)),f333(f303(a880,f333(f333(f81(a880),x40252),x40251)),f333(f333(f81(a880),x40253),x40251))) % 191.49/191.40 [4042]E(f333(f333(f182(x40421,x40422),f333(f333(f155(f889(x40421,x40422),x40421),f262(x40421,x40422)),x40423)),f333(f333(f155(f889(x40421,x40422),x40422),f271(x40421,x40422)),x40423)),x40423) % 191.49/191.40 [4047]E(f333(f333(f81(a880),f333(f333(f82(a880),x40471),f46(a880,f333(f333(f40(a880),x40472),x40471),x40473))),f46(a880,x40472,x40471)),f46(a880,x40472,f333(f333(f82(a880),x40471),x40473))) % 191.49/191.40 [4060]E(f333(f333(f127(x40601),x40602),f333(f143(f881(x40601),f881(x40601),f127(x40601),f118(x40601)),x40603)),f333(f143(f881(x40601),f881(x40601),f127(x40601),x40602),x40603)) % 191.49/191.40 [4079]P4(f333(f333(f335(f889(x40791,x40791)),f333(f333(f263(x40791,x40791),x40792),x40792)),f333(f333(f189(f889(x40791,x40791),a874),f2(a880)),x40793))) % 191.49/191.40 [4085]E(f333(f255(x40851),f333(f333(f10(f890(x40852,a874),a874,x40851),f87(x40852)),f333(f9(x40852,x40851,a874),x40853))),f333(f259(x40852,x40851),f333(f255(f889(x40852,x40851)),f333(f272(x40852,x40851,a874),x40853)))) % 191.49/191.40 [4103]E(f333(f333(f115(f890(x41031,a874)),f333(f333(f44(a880,f890(x41031,a874)),f304(a880,f79(a880),x41032)),x41033)),f333(x41033,f2(a880))),f333(f333(f44(a880,f890(x41031,a874)),f333(f302(a880),x41032)),x41033)) % 191.49/191.40 [4118]E(f333(f143(f881(x41181),f881(x41181),f127(x41181),f118(x41181)),f333(f333(f155(f881(x41181),f881(x41181)),f137(x41181,x41182)),x41183)),f333(f137(x41181,x41182),f333(f143(f881(x41181),f881(x41181),f127(x41181),f118(x41181)),x41183))) % 191.49/191.40 [4123]E(f333(f271(f881(x41231),f881(x41231)),f168(x41231,x41232,x41233)),f333(f137(x41231,f333(f74(a874,a874,x41231,a328),x41232)),x41233)) % 191.49/191.40 [4138]E(f333(f333(f43(x41381,f890(x41382,a874)),f258(f890(x41381,a874))),f333(f333(f10(f890(x41382,a874),f890(x41382,a874),x41381),f255(x41382)),f333(f9(x41382,x41381,a874),x41383))),f333(f255(x41382),f333(f333(f10(f890(x41381,a874),a874,x41382),f88(x41381)),x41383))) % 191.49/191.40 [4167]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f82(a1),x41671),f333(f333(f40(a1),x41672),x41671))),f46(a1,x41672,x41671))),x41673),f333(f333(f81(a1),x41672),x41673)) % 191.49/191.40 [4207]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f82(a1),f333(f333(f40(a1),x42071),x42072)),x42072)),f46(a1,x42071,x42072))),x42073),f333(f333(f81(a1),x42071),x42073)) % 191.49/191.40 [4238]E(f86(f889(x42381,x42382),f333(f272(x42381,x42382,a874),f333(f333(f10(f890(x42382,f889(x42381,x42382)),f890(x42382,a874),x42381),f333(f10(f889(x42381,x42382),a874,x42382),x42383)),f263(x42381,x42382)))),f86(f889(x42381,x42382),x42383)) % 191.49/191.40 [4239]E(f91(f889(x42391,x42392),f333(f272(x42391,x42392,a874),f333(f333(f10(f890(x42392,f889(x42391,x42392)),f890(x42392,a874),x42391),f333(f10(f889(x42391,x42392),a874,x42392),x42393)),f263(x42391,x42392)))),f91(f889(x42391,x42392),x42393)) % 191.49/191.40 [4268]P4(f333(f333(f250(f890(x42681,a874)),f41(f890(x42681,a874),f333(f333(f106(f890(f890(x42681,a874),a874)),x42682),x42683))),f333(f333(f106(f890(x42681,a874)),f41(f890(x42681,a874),x42682)),f41(f890(x42681,a874),x42683)))) % 191.49/191.40 [4269]E(f333(f170(x42691),f333(f333(f333(f189(f881(x42691),f881(x42691)),f333(f333(f3(a880),f333(f195(f881(x42691)),x42692)),f46(a880,x42693,f333(f195(f881(x42691)),x42692)))),f169(x42691)),x42692)),f333(f333(f333(f189(f881(x42691),f881(x42691)),x42693),f169(x42691)),f333(f170(x42691),x42692))) % 191.49/191.40 [4282]E(f333(f255(x42821),f333(f333(f10(a874,a874,x42821),a328),f333(f333(f9(x42821,f884(x42822),a874),f333(f333(f10(f884(x42822),f890(f884(x42822),a874),x42821),a330),x42823)),f197(x42822)))),f184(x42821,x42822,x42823)) % 191.49/191.40 [4309]P4(f333(f333(f250(a880),f333(f195(f881(x43091)),f333(f333(f139(x43091),f333(f195(f881(x43091)),f177(x43091,x43092,x43093))),x43093))),f333(f195(f881(x43091)),x43093))) % 191.49/191.40 [4348]E(f333(f255(x43481),f333(f333(f10(f890(x43482,a874),a874,x43481),f87(x43482)),f333(f333(f10(f884(x43481),f890(x43482,a874),x43481),f333(f9(x43482,f884(x43481),a874),f333(f333(f10(f884(x43481),f890(f884(x43481),a874),x43482),a330),x43483))),f242(x43481)))),f186(x43482,x43481,x43483)) % 191.49/191.40 [4581]~P4(f333(f64(x45811,x45812,f194(f890(x45811,a874))),x45813)) % 191.49/191.40 [4591]~P4(f333(f333(f335(f889(x45911,x45911)),f333(f333(f263(x45911,x45911),x45912),x45913)),f154(x45911,f118(f890(x45911,a880))))) % 191.49/191.40 [3618]E(f333(f195(f881(x36181)),f333(f333(f174(x36181),x36182),x36183)),f333(f333(f248(a880),f333(f195(f881(x36181)),x36183)),x36182)) % 191.49/191.40 [3619]E(f333(f195(f881(x36191)),f333(f333(f139(x36191),x36192),x36193)),f333(f333(f3(a880),f333(f195(f881(x36191)),x36193)),x36192)) % 191.49/191.40 [3644]E(f333(f195(f881(f881(x36441))),f56(x36441,x36442,x36443)),f333(f333(f264(a880),f333(f195(f881(x36441)),x36443)),x36442)) % 191.49/191.40 [3660]E(f333(f333(f40(a880),f333(f333(f40(a880),x36601),x36602)),x36603),f333(f333(f40(a880),x36601),f333(f333(f82(a880),x36602),x36603))) % 191.49/191.40 [3661]E(f333(f333(f3(a880),f333(f333(f3(a880),x36611),x36612)),x36613),f333(f333(f3(a880),x36611),f333(f333(f81(a880),x36612),x36613))) % 191.49/191.40 [3662]E(f333(f333(f81(a880),f333(f333(f81(a880),x36621),x36622)),x36623),f333(f333(f81(a880),x36621),f333(f333(f81(a880),x36622),x36623))) % 191.49/191.40 [3663]E(f333(f333(f81(a1),f333(f333(f81(a1),x36631),x36632)),x36633),f333(f333(f81(a1),x36631),f333(f333(f81(a1),x36632),x36633))) % 191.49/191.40 [3664]E(f333(f333(f82(a880),f333(f333(f82(a880),x36641),x36642)),x36643),f333(f333(f82(a880),x36641),f333(f333(f82(a880),x36642),x36643))) % 191.49/191.40 [3665]E(f333(f333(f82(a1),f333(f333(f82(a1),x36651),x36652)),x36653),f333(f333(f82(a1),x36651),f333(f333(f82(a1),x36652),x36653))) % 191.49/191.40 [3666]E(f333(f333(f264(a1),f333(f333(f264(a1),x36661),x36662)),x36663),f333(f333(f264(a1),x36661),f333(f333(f82(a880),x36662),x36663))) % 191.49/191.40 [3685]E(f163(x36851,f333(f333(f152(f890(x36851,a874)),x36852),x36853)),f176(x36851,x36852,f163(x36851,x36853))) % 191.49/191.40 [3724]E(f333(f333(f3(a880),f333(f333(f3(a880),x37241),x37242)),x37243),f333(f333(f3(a880),f333(f333(f3(a880),x37241),x37243)),x37242)) % 191.49/191.40 [3730]E(f333(f242(f889(x37301,f882(x37301))),f333(f333(f263(x37301,f882(x37301)),x37302),x37303)),f333(f134(x37301),f129(x37301,x37302,x37303))) % 191.49/191.40 [3733]E(f333(f333(f106(f890(x37331,a874)),x37332),f333(f333(f3(f890(x37331,a874)),x37333),x37332)),f194(f890(x37331,a874))) % 191.49/191.40 [3778]E(f41(f890(x37781,a874),f333(f333(f311(f890(x37781,a874)),x37782),x37783)),f333(f333(f115(f890(x37781,a874)),x37782),f41(f890(x37781,a874),x37783))) % 191.49/191.40 [3779]E(f42(f890(x37791,a874),f333(f333(f311(f890(x37791,a874)),x37792),x37793)),f333(f333(f106(f890(x37791,a874)),x37792),f42(f890(x37791,a874),x37793))) % 191.49/191.40 [3781]E(f333(f333(f3(a880),f333(f333(f82(a880),x37811),x37812)),f333(f333(f82(a880),x37813),x37812)),f333(f333(f82(a880),f333(f333(f3(a880),x37811),x37813)),x37812)) % 191.49/191.40 [3782]E(f333(f333(f81(a880),f333(f333(f82(a880),x37821),x37822)),f333(f333(f82(a880),x37823),x37822)),f333(f333(f82(a880),f333(f333(f81(a880),x37821),x37823)),x37822)) % 191.49/191.40 [3783]E(f333(f333(f3(a1),f333(f333(f82(a1),x37831),x37832)),f333(f333(f82(a1),x37833),x37832)),f333(f333(f82(a1),f333(f333(f3(a1),x37831),x37833)),x37832)) % 191.49/191.40 [3784]E(f333(f333(f81(a1),f333(f333(f82(a1),x37841),x37842)),f333(f333(f82(a1),x37843),x37842)),f333(f333(f82(a1),f333(f333(f81(a1),x37841),x37843)),x37842)) % 191.49/191.40 [3785]E(f333(f333(f248(a880),f333(f333(f3(a880),x37851),x37852)),f333(f333(f3(a880),x37853),x37852)),f333(f333(f3(a880),f333(f333(f248(a880),x37851),x37853)),x37852)) % 191.49/191.40 [3809]E(f333(f333(f106(f890(f881(x38091),a874)),f161(x38091,x38092)),f161(x38091,x38093)),f161(x38091,f333(f333(f106(f890(x38091,a874)),x38092),x38093))) % 191.49/191.40 [3811]E(f333(f333(f115(f890(x38111,a874)),x38112),f333(f333(f115(f890(x38111,a874)),x38112),x38113)),f333(f333(f115(f890(x38111,a874)),x38112),x38113)) % 191.49/191.40 [3812]E(f333(f333(f115(f890(x38121,a874)),x38122),f333(f333(f3(f890(x38121,a874)),x38123),x38122)),f333(f333(f115(f890(x38121,a874)),x38122),x38123)) % 191.49/191.40 [3813]E(f333(f333(f106(f890(x38131,a874)),x38132),f333(f333(f106(f890(x38131,a874)),x38132),x38133)),f333(f333(f106(f890(x38131,a874)),x38132),x38133)) % 191.49/191.40 [3825]E(f333(f333(f290(x38251,x38252,x38252),x38253),f309(x38252,f194(f890(f889(x38252,x38252),a874)))),x38253) % 191.49/191.40 [3828]E(f333(f333(f115(f890(x38281,a874)),f333(f333(f311(x38281),x38282),f194(f890(x38281,a874)))),x38283),f333(f333(f311(x38281),x38282),x38283)) % 191.49/191.40 [3843]E(f333(f333(f3(a880),f333(f333(f3(a880),f333(a117,x38431)),x38432)),f333(a117,x38433)),f333(f333(f3(a880),f333(f333(f3(a880),x38431),x38432)),x38433)) % 191.49/191.40 [3870]E(f333(f333(f106(f890(f890(x38701,a874),a874)),f333(f310(x38701),x38702)),f333(f310(x38701),x38703)),f333(f310(x38701),f333(f333(f106(f890(x38701,a874)),x38702),x38703))) % 191.49/191.40 [3874]E(f333(f333(f115(f890(x38741,a874)),f333(f80(f890(x38741,a874)),x38742)),x38743),f333(f80(f890(x38741,a874)),f333(f333(f3(f890(x38741,a874)),x38742),x38743))) % 191.49/191.40 [3884]E(f333(f333(f311(x38841),x38842),f333(f333(f3(f890(x38841,a874)),x38843),f333(f333(f311(x38841),x38842),f194(f890(x38841,a874))))),f333(f333(f311(x38841),x38842),x38843)) % 191.49/191.40 [3893]P4(f333(f333(f250(f890(x38931,a874)),x38932),f333(f333(f115(f890(x38931,a874)),x38933),x38932))) % 191.49/191.40 [3894]P4(f333(f333(f250(f890(x38941,a874)),x38942),f333(f333(f115(f890(x38941,a874)),x38942),x38943))) % 191.49/191.40 [3897]E(f333(f333(f106(f890(x38971,a874)),f333(f80(f890(x38971,a874)),x38972)),f333(f80(f890(x38971,a874)),x38973)),f333(f80(f890(x38971,a874)),f333(f333(f115(f890(x38971,a874)),x38972),x38973))) % 191.49/191.40 [3898]E(f333(f333(f115(f890(x38981,a874)),f333(f80(f890(x38981,a874)),x38982)),f333(f80(f890(x38981,a874)),x38983)),f333(f80(f890(x38981,a874)),f333(f333(f106(f890(x38981,a874)),x38982),x38983))) % 191.49/191.40 [3912]P4(f333(f333(f250(f890(x39121,a874)),f333(f173(x39121),x39122)),f333(f173(x39121),f333(f333(f152(x39121),x39123),x39122)))) % 191.49/191.40 [3921]E(f333(f333(f115(f890(x39211,a874)),f333(f333(f3(f890(x39211,a874)),x39212),x39213)),f333(f333(f106(f890(x39211,a874)),x39212),x39213)),x39212) % 191.49/191.40 [3979]E(f333(f333(f8(x39791,a1),f333(f333(f10(a880,a1,x39791),f105(a1)),x39792)),x39793),f333(f105(a1),f333(f333(f8(x39791,a880),x39792),x39793))) % 191.49/191.40 [3980]E(f333(f333(f11(x39801,a1),f333(f333(f10(a880,a1,x39801),f105(a1)),x39802)),x39803),f333(f105(a1),f333(f333(f11(x39801,a880),x39802),x39803))) % 191.49/191.40 [4027]E(f333(f333(f127(x40271),f177(x40271,x40272,x40273)),f333(f333(f139(x40271),f333(f195(f881(x40271)),f177(x40271,x40272,x40273))),x40273)),x40273) % 191.49/191.40 [4031]E(f333(f80(f890(f889(x40311,x40312),a874)),f333(f333(f270(x40311,x40312),x40313),f333(f18(f890(x40312,a874),x40311),f258(f890(x40312,a874))))),f333(f333(f270(x40311,x40312),f333(f80(f890(x40311,a874)),x40313)),f333(f18(f890(x40312,a874),x40311),f258(f890(x40312,a874))))) % 191.49/191.40 [4032]E(f333(f80(f890(f889(x40321,x40322),a874)),f333(f333(f270(x40321,x40322),f258(f890(x40321,a874))),f333(f18(f890(x40322,a874),x40321),x40323))),f333(f333(f270(x40321,x40322),f258(f890(x40321,a874))),f333(f18(f890(x40322,a874),x40321),f333(f80(f890(x40322,a874)),x40323)))) % 191.49/191.40 [4080]E(f333(f333(f44(f890(x40801,a874),f890(x40801,a874)),x40802),f333(f333(f9(f890(x40801,a874),f890(x40801,a874),f890(x40801,a874)),f106(f890(x40801,a874))),x40803)),f333(f333(f106(f890(x40801,a874)),f41(f890(x40801,a874),x40802)),x40803)) % 191.49/191.40 [4088]E(f333(f143(f881(x40881),f881(x40881),f127(x40881),f118(x40881)),f333(f333(f152(f881(x40881)),x40882),x40883)),f333(f333(f127(x40881),x40882),f333(f143(f881(x40881),f881(x40881),f127(x40881),f118(x40881)),x40883))) % 191.49/191.40 [4109]E(f333(f333(f311(f890(x41091,a874)),f333(f287(x41091,x41091,x41092),f333(f333(f311(x41091),x41093),f194(f890(x41091,a874))))),f194(f890(f890(x41091,a874),a874))),f333(f333(f62(x41091),f333(f333(f311(x41091),x41093),f194(f890(x41091,a874)))),x41092)) % 191.49/191.40 [4119]E(f333(f333(f81(a880),f333(f333(f82(a880),x41191),f333(f333(f40(a880),x41192),x41193))),f333(f333(f40(a880),f333(f333(f82(a880),x41191),f46(a880,x41192,x41193))),x41193)),f333(f333(f40(a880),f333(f333(f82(a880),x41191),x41192)),x41193)) % 191.49/191.40 [4120]E(f333(f333(f81(a1),f333(f333(f82(a1),x41201),f333(f333(f40(a1),x41202),x41203))),f333(f333(f40(a1),f333(f333(f82(a1),x41201),f46(a1,x41202,x41203))),x41203)),f333(f333(f40(a1),f333(f333(f82(a1),x41201),x41202)),x41203)) % 191.49/191.40 [4154]E(f333(f333(f3(f890(x41541,a874)),f333(f173(x41541),x41542)),f333(f333(f311(x41541),x41543),f194(f890(x41541,a874)))),f333(f173(x41541),f333(f137(x41541,f333(f333(f10(a874,a874,x41541),a328),f333(a330,x41543))),x41542))) % 191.49/191.40 [4204]E(f333(f333(f127(x42041),f333(f143(f881(x42041),f881(x42041),f127(x42041),f118(x42041)),x42042)),f333(f143(f881(x42041),f881(x42041),f127(x42041),f118(x42041)),x42043)),f333(f143(f881(x42041),f881(x42041),f127(x42041),f118(x42041)),f333(f333(f127(f881(x42041)),x42042),x42043))) % 191.49/191.40 [4210]E(f333(f333(f263(f881(x42101),f881(x42101)),f333(f137(x42101,x42102),x42103)),f333(f137(x42101,f333(f74(a874,a874,x42101,a328),x42102)),x42103)),f168(x42101,x42102,x42103)) % 191.49/191.40 [4214]E(f333(f333(f81(a880),f333(f333(f81(a880),f333(f333(f40(a880),x42141),x42142)),f333(f333(f40(a880),x42143),x42142))),f333(f333(f40(a880),f333(f333(f81(a880),f46(a880,x42141,x42142)),f46(a880,x42143,x42142))),x42142)),f333(f333(f40(a880),f333(f333(f81(a880),x42141),x42143)),x42142)) % 191.49/191.40 [4215]E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f40(a1),x42151),x42152)),f333(f333(f40(a1),x42153),x42152))),f333(f333(f40(a1),f333(f333(f81(a1),f46(a1,x42151,x42152)),f46(a1,x42153,x42152))),x42152)),f333(f333(f40(a1),f333(f333(f81(a1),x42151),x42153)),x42152)) % 191.49/191.40 [4272]E(f333(f333(f106(f890(f881(x42721),a874)),f333(f333(f9(f881(x42721),f890(f881(x42721),a874),a874),f335(f881(x42721))),f162(x42721,x42722))),f333(f333(f9(f881(x42721),f890(f881(x42721),a874),a874),f335(f881(x42721))),f162(x42721,x42723))),f161(x42721,f333(f333(f106(f890(x42721,a874)),f333(f333(f9(x42721,f890(x42721,a874),a874),f335(x42721)),x42722)),f333(f333(f9(x42721,f890(x42721,a874),a874),f335(x42721)),x42723)))) % 191.49/191.40 [4284]E(f333(f255(x42841),f333(f333(f20(x42841,a874,a874),f333(f333(f10(a874,f890(a874,a874),x42841),a332),f333(f333(f9(x42841,x42841,a874),a330),x42842))),f333(f333(f9(x42841,f890(x42841,a874),a874),f335(x42841)),x42843))),f333(f333(f311(x42841),x42842),x42843)) % 191.49/191.40 [4306]E(f333(f333(f89(f881(f881(x43061)),f881(f881(x43061))),f55(x43061,x43062)),f333(f333(f20(f881(f881(x43061)),f881(f881(x43061)),f881(f881(x43061))),f333(f333(f10(f881(f881(x43061)),f890(f881(f881(x43061)),f881(f881(x43061))),f881(f881(x43061))),f127(f881(x43061))),f333(f155(f881(x43061),f881(x43061)),f333(f152(x43061),x43063)))),f7(f881(f881(x43061))))),f55(x43061,f333(f333(f152(x43061),x43063),x43062))) % 191.49/191.40 [4310]E(f333(f255(x43101),f333(f333(f20(x43101,a874,a874),f333(f333(f10(a874,f890(a874,a874),x43101),a332),f333(f333(f9(x43101,f890(x43101,a874),a874),f335(x43101)),x43102))),f333(f333(f9(x43101,f890(x43101,a874),a874),f335(x43101)),x43103))),f333(f333(f115(f890(x43101,a874)),x43102),x43103)) % 191.49/191.40 [4311]E(f333(f255(x43111),f333(f333(f20(x43111,a874,a874),f333(f333(f10(a874,f890(a874,a874),x43111),a331),f333(f333(f9(x43111,f890(x43111,a874),a874),f335(x43111)),x43112))),f333(f333(f9(x43111,f890(x43111,a874),a874),f335(x43111)),x43113))),f333(f333(f106(f890(x43111,a874)),x43112),x43113)) % 191.49/191.40 [4401]E(f333(f333(f44(x44011,f890(f890(x44011,a874),a874)),x44012),f333(f333(f9(x44011,f890(f890(x44011,a874),a874),f890(f890(x44011,a874),a874)),f333(f333(f10(f890(x44011,a874),f890(f890(f890(x44011,a874),a874),f890(f890(x44011,a874),a874)),x44011),f311(f890(x44011,a874))),f333(f333(f10(f890(x44011,a874),f890(x44011,a874),x44011),f287(x44011,x44011,x44013)),f333(f333(f9(x44011,f890(x44011,a874),f890(x44011,a874)),f311(x44011)),f194(f890(x44011,a874)))))),f194(f890(f890(x44011,a874),a874)))),f333(f333(f62(x44011),x44012),x44013)) % 191.49/191.40 [4410]E(f333(f333(f211(x44101),f333(f333(f82(a1),f333(f333(f74(f889(a1,a1),a1,x44101,f262(a1,a1)),f222(x44101)),x44102)),f333(f333(f74(f889(a1,a1),a1,x44101,f262(a1,a1)),f222(x44101)),x44103))),f333(f333(f82(a1),f333(f333(f74(f889(a1,a1),a1,x44101,f271(a1,a1)),f222(x44101)),x44102)),f333(f333(f74(f889(a1,a1),a1,x44101,f271(a1,a1)),f222(x44101)),x44103))),f237(x44101,x44102,x44103)) % 191.49/191.40 [4414]E(f333(f255(f881(x44141)),f333(f333(f20(f881(x44141),a874,a874),f333(f333(f10(a874,f890(a874,a874),f881(x44141)),a331),f333(f333(f9(f881(x44141),a880,a874),f333(f333(f10(a880,f890(a880,a874),f881(x44141)),a330),f195(f881(x44141)))),x44142))),f333(f333(f9(f881(x44141),f890(x44141,a874),a874),f333(f333(f10(f890(x44141,a874),f890(f890(x44141,a874),a874),f881(x44141)),f250(f890(x44141,a874))),f173(x44141))),f333(f173(x44141),x44143)))),f333(f173(f881(x44141)),f56(x44141,x44142,x44143))) % 191.49/191.40 [3798]E(f46(a880,f333(f333(f81(a880),f333(f333(f82(a880),x37981),x37982)),x37983),x37982),f46(a880,x37983,x37982)) % 191.49/191.40 [3842]E(f140(a880,f333(f303(a880,f333(f333(f81(a880),x38421),x38422)),x38423)),f333(f333(f139(a880),x38422),f140(a880,f333(f303(a880,x38421),x38423)))) % 191.49/191.40 [3883]E(f333(f333(f81(a1),f333(f105(a1),x38831)),f333(f333(f81(a1),f333(f105(a1),x38832)),x38833)),f333(f333(f81(a1),f333(f105(a1),f333(f333(f81(a880),x38831),x38832))),x38833)) % 191.49/191.40 [3889]E(f333(f333(f115(f890(x38891,a874)),f333(f333(f3(f890(x38891,a874)),x38892),x38893)),x38893),f333(f333(f115(f890(x38891,a874)),x38892),x38893)) % 191.49/191.40 [3890]E(f333(f333(f3(f890(x38901,a874)),f333(f333(f3(f890(x38901,a874)),x38902),x38903)),x38903),f333(f333(f3(f890(x38901,a874)),x38902),x38903)) % 191.49/191.40 [3913]E(f333(f333(f290(x39131,x39131,x39132),f309(x39131,f194(f890(f889(x39131,x39131),a874)))),x39133),x39133) % 191.49/191.40 [3919]E(f333(f333(f115(f890(x39191,a874)),f333(f286(x39191),x39192)),f333(f286(x39191),x39193)),f333(f286(x39191),f333(f333(f115(f890(f889(x39191,x39191),a874)),x39192),x39193))) % 191.49/191.40 [3930]E(f277(x39301,f333(f333(f152(f889(a104,x39301)),f333(f333(f263(a104,x39301),f2(a104)),x39302)),x39303)),f277(x39301,x39303)) % 191.49/191.40 [3933]E(f333(f333(f115(f890(x39331,a874)),f41(f890(x39331,a874),x39332)),f41(f890(x39331,a874),x39333)),f41(f890(x39331,a874),f333(f333(f115(f890(f890(x39331,a874),a874)),x39332),x39333))) % 191.49/191.40 [3934]E(f333(f333(f106(f890(x39341,a874)),f42(f890(x39341,a874),x39342)),f42(f890(x39341,a874),x39343)),f42(f890(x39341,a874),f333(f333(f115(f890(f890(x39341,a874),a874)),x39342),x39343))) % 191.49/191.40 [3972]E(f333(f333(f290(x39721,x39721,x39721),f333(f333(f189(f889(x39721,x39721),a874),x39722),x39723)),x39723),f333(f333(f189(f889(x39721,x39721),a874),f333(a117,x39722)),x39723)) % 191.49/191.40 [4018]P4(f333(f333(f250(f890(x40181,a874)),f333(f333(f3(f890(x40181,a874)),x40182),x40183)),x40182)) % 191.49/191.40 [4019]P4(f333(f333(f250(f890(x40191,a874)),f333(f333(f106(f890(x40191,a874)),x40192),x40193)),x40193)) % 191.49/191.40 [4020]P4(f333(f333(f250(f890(x40201,a874)),f333(f333(f106(f890(x40201,a874)),x40202),x40203)),x40202)) % 191.49/191.40 [4044]E(f309(x40441,f333(f333(f115(f890(f889(x40441,x40441),a874)),f309(x40441,x40442)),f309(x40441,x40443))),f309(x40441,f333(f333(f115(f890(f889(x40441,x40441),a874)),x40442),x40443))) % 191.49/191.40 [4048]E(f41(f890(x40481,a874),f333(f333(f311(f890(x40481,a874)),x40482),f333(f333(f311(f890(x40481,a874)),x40483),f194(f890(f890(x40481,a874),a874))))),f333(f333(f115(f890(x40481,a874)),x40482),x40483)) % 191.49/191.40 [4049]E(f42(f890(x40491,a874),f333(f333(f311(f890(x40491,a874)),x40492),f333(f333(f311(f890(x40491,a874)),x40493),f194(f890(f890(x40491,a874),a874))))),f333(f333(f106(f890(x40491,a874)),x40492),x40493)) % 191.49/191.40 [4055]E(f333(f333(f290(x40551,x40551,x40551),f333(f333(f189(f889(x40551,x40551),a874),x40552),x40553)),x40553),f333(f333(f290(x40551,x40551,x40551),x40553),f333(f333(f189(f889(x40551,x40551),a874),x40552),x40553))) % 191.49/191.40 [4124]E(f333(f333(f115(f890(x41241,a874)),f333(f255(x41241),f333(f333(f9(x41241,x41241,a874),a330),x41242))),x41243),f333(f333(f311(x41241),x41242),x41243)) % 191.49/191.40 [4125]E(f333(a109,f333(f333(f8(x41251,a1),f333(f333(f10(a880,a1,x41251),f105(a1)),x41252)),x41253)),f333(f333(f8(x41251,a880),x41252),x41253)) % 191.49/191.40 [4126]E(f333(a109,f333(f333(f11(x41261,a1),f333(f333(f10(a880,a1,x41261),f105(a1)),x41262)),x41263)),f333(f333(f11(x41261,a880),x41262),x41263)) % 191.49/191.40 [4201]E(f333(f157(f881(x42011),x42011,f333(f172(x42011),x42012),f333(f18(f890(f881(x42011),f881(x42011)),x42011),f333(f333(f9(f881(x42011),f881(x42011),f881(x42011)),f127(x42011)),x42012))),x42013),f333(f172(x42011),f333(f333(f127(x42011),x42013),x42012))) % 191.49/191.40 [4232]P4(f333(f333(f250(f890(f890(x42321,a874),a874)),f333(f333(f115(f890(f890(x42321,a874),a874)),f333(f310(x42321),x42322)),f333(f310(x42321),x42323))),f333(f310(x42321),f333(f333(f115(f890(x42321,a874)),x42322),x42323)))) % 191.49/191.40 [4325]E(f333(f255(x43251),f333(f333(f20(x43251,a874,a874),f333(f333(f10(a874,f890(a874,a874),x43251),a331),f333(f333(f9(x43251,f890(x43251,a874),a874),f335(x43251)),x43252))),f333(f333(f10(a874,a874,x43251),a328),f333(f333(f9(x43251,f890(x43251,a874),a874),f335(x43251)),x43253)))),f333(f333(f3(f890(x43251,a874)),x43252),x43253)) % 191.49/191.40 [4349]E(f333(f39(a880),f333(f255(a880),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),f333(f333(f9(a880,a880,a874),f251(a880)),f333(f195(f881(x43491)),x43492)))),f333(f333(f10(x43491,a874,a880),x43493),f333(f166(x43491),x43492))))),f333(f195(f881(x43491)),f333(f137(x43491,x43493),x43492))) % 191.49/191.40 [4351]E(f333(f195(f881(x43511)),f175(x43511,x43512,x43513)),f333(f39(a880),f333(f255(a880),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),f333(f333(f9(a880,a880,a874),f251(a880)),f333(f195(f881(x43511)),x43512)))),f333(f333(f9(a880,f890(a880,a874),a874),f335(a880)),x43513))))) % 191.49/191.40 [4462]E(f333(f333(f106(f890(f889(f881(x44621),f881(x44621)),a874)),f333(f312(f889(f889(x44621,f881(x44621)),f889(x44621,f881(x44621))),f889(f881(x44621),f881(x44621)),f273(f889(x44621,f881(x44621)),f881(x44621),f889(x44621,f881(x44621)),f881(x44621),f333(f272(x44621,f881(x44621),f881(x44621)),f152(x44621)),f333(f272(x44621,f881(x44621),f881(x44621)),f152(x44621)))),f326(x44621,f881(x44621),x44622,f333(f144(x44621,x44622),x44623)))),f333(f255(f889(f881(x44621),f881(x44621))),f333(f272(f881(x44621),f881(x44621),a874),f333(f333(f9(f881(x44621),f890(f881(x44621),a874),f890(f881(x44621),a874)),f333(f333(f10(f890(a874,a874),f890(f890(f881(x44621),a874),f890(f881(x44621),a874)),f881(x44621)),f10(a874,a874,f881(x44621))),f333(f333(f10(a874,f890(a874,a874),f881(x44621)),a331),f333(f333(f9(f881(x44621),a880,a874),f333(f333(f10(a880,f890(a880,a874),f881(x44621)),a330),f195(f881(x44621)))),f333(a117,x44623))))),f333(f333(f9(f881(x44621),a880,a874),f333(f333(f10(a880,f890(a880,a874),f881(x44621)),a330),f195(f881(x44621)))),f333(a117,x44623)))))),f333(f144(x44621,x44622),f333(a117,x44623))) % 191.49/191.40 [3935]E(f46(a880,f333(a117,f333(f333(f81(a880),f333(f333(f82(a880),x39351),x39352)),x39353)),x39352),f46(a880,f333(a117,x39353),x39352)) % 191.49/191.40 [4187]E(f333(f255(x41871),f333(f333(f20(x41871,a874,a874),f333(f333(f10(a874,f890(a874,a874),x41871),a331),x41872)),x41873)),f333(f333(f106(f890(x41871,a874)),f333(f255(x41871),x41872)),f333(f255(x41871),x41873))) % 191.49/191.40 [4188]E(f333(f255(x41881),f333(f333(f20(x41881,a874,a874),f333(f333(f10(a874,f890(a874,a874),x41881),a332),x41882)),x41883)),f333(f333(f115(f890(x41881,a874)),f333(f255(x41881),x41882)),f333(f255(x41881),x41883))) % 191.49/191.40 [4190]E(f333(f333(f127(x41901),f333(f333(f139(x41901),f46(a880,x41902,f333(f195(f881(x41901)),x41903))),x41903)),f333(f333(f174(x41901),f46(a880,x41902,f333(f195(f881(x41901)),x41903))),x41903)),f333(f333(f333(f189(f881(x41901),f881(x41901)),x41902),f169(x41901)),x41903)) % 191.49/191.40 [4195]E(f333(f255(x41951),f333(f333(f20(x41951,a874,a874),f333(f333(f10(a874,f890(a874,a874),x41951),a336),x41952)),x41953)),f333(f333(f115(f890(x41951,a874)),f333(f80(f890(x41951,a874)),f333(f255(x41951),x41952))),f333(f255(x41951),x41953))) % 191.49/191.40 [4216]E(f333(f333(f81(a880),f333(f195(f881(x42161)),f333(f137(x42161,x42162),x42163))),f333(f195(f881(x42161)),f333(f137(x42161,f333(f333(f10(a874,a874,x42161),a328),x42162)),x42163))),f333(f195(f881(x42161)),x42163)) % 191.49/191.40 [4241]P4(f333(f333(f250(f890(x42411,a874)),f333(f333(f115(f890(x42411,a874)),f42(f890(x42411,a874),x42412)),f42(f890(x42411,a874),x42413))),f42(f890(x42411,a874),f333(f333(f106(f890(f890(x42411,a874),a874)),x42412),x42413)))) % 191.49/191.40 [4254]E(f333(f173(x42541),f333(f137(x42541,f333(f333(f10(a874,a874,x42541),a328),f333(f333(f9(x42541,x42541,a874),a330),x42542))),x42543)),f333(f333(f3(f890(x42541,a874)),f333(f173(x42541),x42543)),f333(f333(f311(x42541),x42542),f194(f890(x42541,a874))))) % 191.49/191.40 [4263]P4(f333(f333(f250(f890(f889(x42631,x42631),a874)),f333(f333(f115(f890(f889(x42631,x42631),a874)),f309(x42631,x42632)),f309(x42631,x42633))),f309(x42631,f333(f333(f115(f890(f889(x42631,x42631),a874)),x42632),x42633)))) % 191.49/191.40 [4289]E(f333(f333(f82(a880),f333(a117,f333(a117,f2(a880)))),f333(f333(f8(a880,a880),f333(f333(f10(a880,a880,a880),f333(f81(a880),x42891)),f333(f333(f9(a880,a880,a880),f82(a880)),x42892))),f333(f256(a880),x42893))),f333(f333(f82(a880),x42893),f333(f333(f81(a880),x42891),f333(f333(f81(a880),x42891),f333(f333(f82(a880),f333(f333(f3(a880),x42893),f79(a880))),x42892))))) % 191.49/191.40 [4301]E(f333(f255(x43011),f333(f333(f20(x43011,a874,a874),f333(f333(f10(a874,f890(a874,a874),x43011),a331),f333(f333(f9(x43011,f890(x43011,a874),a874),f335(x43011)),f333(f173(x43011),x43012)))),x43013)),f333(f173(x43011),f333(f137(x43011,x43013),x43012))) % 191.49/191.40 [4461]E(f333(f255(x44611),f333(f333(f10(f890(a880,a874),a874,x44611),f87(a880)),f333(f333(f9(x44611,f890(a880,a874),f890(a880,a874)),f333(f333(f10(f890(a880,f890(a874,a874)),f890(f890(a880,a874),f890(a880,a874)),x44611),f20(a880,a874,a874)),f333(f333(f10(f890(a880,a874),f890(a880,f890(a874,a874)),x44611),f333(f10(a874,f890(a874,a874),a880),a331)),f333(f333(f9(x44611,f890(a880,x44611),f890(a880,a874)),f333(f333(f10(f890(x44611,a874),f890(f890(a880,x44611),f890(a880,a874)),x44611),f10(x44611,a874,a880)),a330)),f333(f166(x44611),x44612))))),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),f333(f333(f9(a880,a880,a874),f251(a880)),f333(f195(f881(x44611)),x44612)))),f333(f333(f9(a880,f890(a880,a874),a874),f335(a880)),x44613))))),f333(f173(x44611),f175(x44611,x44612,x44613))) % 191.49/191.40 [4338]E(f333(f255(x43381),f333(f333(f20(x43381,a874,a874),f333(f333(f10(a874,f890(a874,a874),x43381),a336),f333(f333(f10(a874,a874,x43381),a328),f333(f333(f9(x43381,x43381,a874),a330),x43382)))),x43383)),f333(f333(f311(x43381),x43382),f333(f255(x43381),x43383))) % 191.49/191.40 [4376]E(f333(f333(f155(f889(x43761,a880),x43761),f262(x43761,a880)),f333(f137(f889(x43761,a880),f333(f333(f9(f889(x43761,a880),f890(a880,a874),a874),f333(f333(f10(a880,f890(f890(a880,a874),a874),f889(x43761,a880)),f335(a880)),f271(x43761,a880))),x43762)),f333(f333(f182(x43761,a880),x43763),f140(a880,f333(f303(a880,f2(a880)),f333(f195(f881(x43761)),x43763)))))),f175(x43761,x43763,x43762)) % 191.49/191.40 [4446]E(f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f333(f8(a880,a1),f333(f333(f10(a1,a1,a880),f333(f81(a1),x44461)),f333(f333(f9(a880,a1,a1),f333(f333(f10(a1,f890(a1,a1),a880),f82(a1)),f105(a1))),x44462))),f333(f256(a880),x44463))),f333(f333(f82(a1),f333(f105(a1),x44463)),f333(f333(f81(a1),x44461),f333(f333(f81(a1),x44461),f333(f333(f82(a1),f333(f105(a1),f333(f333(f3(a880),x44463),f79(a880)))),x44462))))) % 191.49/191.40 [4455]E(f333(f255(f889(x44551,x44552)),f333(f272(x44551,x44552,a874),f333(f333(f9(x44551,f890(f889(x44552,x44551),a874),f890(x44552,a874)),f333(f333(f10(f890(x44552,f890(f890(f889(x44552,x44551),a874),a874)),f890(f890(f889(x44552,x44551),a874),f890(x44552,a874)),x44551),f9(x44552,f890(f889(x44552,x44551),a874),a874)),f333(f333(f10(f890(x44552,f889(x44552,x44551)),f890(x44552,f890(f890(f889(x44552,x44551),a874),a874)),x44551),f333(f10(f889(x44552,x44551),f890(f890(f889(x44552,x44551),a874),a874),x44552),f335(f889(x44552,x44551)))),f333(f9(x44552,x44551,f889(x44552,x44551)),f263(x44552,x44551))))),x44553))),f333(f288(x44552,x44551),x44553)) % 191.49/191.40 [4476]E(f333(f255(f881(x44761)),f333(f333(f10(f890(x44761,a874),a874,f881(x44761)),f87(x44761)),f333(f333(f10(f890(x44761,f890(f881(x44761),a874)),f890(x44761,a874),f881(x44761)),f333(f10(f890(f881(x44761),a874),a874,x44761),f87(f881(x44761)))),f333(f333(f9(f881(x44761),f890(x44761,f890(f881(x44761),a874)),f890(x44761,f890(f881(x44761),a874))),f333(f333(f10(f890(x44761,f890(f890(f881(x44761),a874),f890(f881(x44761),a874))),f890(f890(x44761,f890(f881(x44761),a874)),f890(x44761,f890(f881(x44761),a874))),f881(x44761)),f20(x44761,f890(f881(x44761),a874),f890(f881(x44761),a874))),f333(f333(f10(f890(x44761,f890(f881(x44761),f890(a874,a874))),f890(x44761,f890(f890(f881(x44761),a874),f890(f881(x44761),a874))),f881(x44761)),f333(f10(f890(f881(x44761),f890(a874,a874)),f890(f890(f881(x44761),a874),f890(f881(x44761),a874)),x44761),f20(f881(x44761),a874,a874))),f333(f333(f10(f890(x44761,f890(f881(x44761),a874)),f890(x44761,f890(f881(x44761),f890(a874,a874))),f881(x44761)),f333(f10(f890(f881(x44761),a874),f890(f881(x44761),f890(a874,a874)),x44761),f333(f10(a874,f890(a874,a874),f881(x44761)),a331))),f333(f333(f9(f881(x44761),f890(x44761,f890(f881(x44761),f881(x44761))),f890(x44761,f890(f881(x44761),a874))),f333(f333(f10(f890(f890(f881(x44761),f881(x44761)),f890(f881(x44761),a874)),f890(f890(x44761,f890(f881(x44761),f881(x44761))),f890(x44761,f890(f881(x44761),a874))),f881(x44761)),f10(f890(f881(x44761),f881(x44761)),f890(f881(x44761),a874),x44761)),f333(f333(f10(f890(f881(x44761),a874),f890(f890(f881(x44761),f881(x44761)),f890(f881(x44761),a874)),f881(x44761)),f10(f881(x44761),a874,f881(x44761))),a330))),f152(x44761)))))),f333(f333(f9(x44761,f890(f881(x44761),a874),f890(f881(x44761),a874)),f333(f333(f10(f890(a874,a874),f890(f890(f881(x44761),a874),f890(f881(x44761),a874)),x44761),f10(a874,a874,f881(x44761))),f333(f333(f10(a874,f890(a874,a874),x44761),a331),f333(f333(f9(x44761,f890(x44761,a874),a874),f335(x44761)),x44762)))),f333(f333(f9(f881(x44761),f890(f881(x44761),a874),a874),f335(f881(x44761))),x44763)))))),f176(x44761,x44762,x44763)) % 191.49/191.40 [4477]E(f333(f333(f89(a1,f889(a1,a1)),f333(f333(f3(a1),x44771),x44772)),f333(f333(f9(a1,f889(a1,a1),f889(a1,a1)),f333(f333(f20(a1,f889(a1,a1),f890(f889(a1,a1),f889(a1,a1))),f333(f333(f10(a874,f890(f889(a1,a1),f890(f889(a1,a1),f889(a1,a1))),a1),f101(f889(a1,a1))),f333(f250(a1),f2(a1)))),f333(f263(a1,a1),f333(f333(f81(a1),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x44773)),f79(a1))))),f333(f333(f263(a1,a1),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x44773)),x44771))),f333(f45(x44772),f333(f333(f263(a1,a1),x44773),x44771))) % 191.49/191.40 [4506]~E(f33(x45061,x45062),f34(x45063,x45064)) % 191.49/191.40 [4524]~E(f333(a26,x45241),f29(x45242,x45243,x45244)) % 191.49/191.40 [4525]~E(f333(a26,x45251),f31(x45252,x45253,x45254)) % 191.49/191.40 [4526]~E(f333(a26,x45261),f30(x45262,x45263,x45264)) % 191.49/191.40 [4527]~E(f29(x45271,x45272,x45273),f333(a26,x45274)) % 191.49/191.40 [4528]~E(f31(x45281,x45282,x45283),f333(a26,x45284)) % 191.49/191.40 [4529]~E(f30(x45291,x45292,x45293),f333(a26,x45294)) % 191.49/191.40 [3497]E(f333(f333(f333(f73(x34971,x34972),x34973),x34974),f333(x34973,x34974)),x34973) % 191.49/191.40 [3505]E(f121(x35051,f333(x35052,x35053),f333(x35054,x35053)),f333(f213(x35051,x35052,x35054),x35053)) % 191.49/191.40 [3556]E(f333(f333(f265(x35561,x35562,x35563),x35564),f2(a880)),x35562) % 191.49/191.40 [3596]E(f191(x35961,x35962,x35963,f333(a117,x35964)),f333(x35963,x35964)) % 191.49/191.40 [3636]E(f171(x36361,x36362,f171(x36361,x36363,x36364)),f171(x36361,x36363,f171(x36361,x36362,x36364))) % 191.49/191.40 [3637]E(f121(x36371,f129(x36371,x36372,x36373),x36374),f129(x36371,x36372,f121(x36371,x36373,x36374))) % 191.49/191.40 [3767]E(f333(f244(x37671,x37672,x37673,x37674),f197(x37672)),x37673) % 191.49/191.40 [3769]E(f333(f157(x37691,x37692,x37693,x37694),f118(x37692)),x37693) % 191.49/191.40 [3770]E(f333(f143(x37701,x37702,x37703,x37704),f118(x37702)),x37704) % 191.49/191.40 [3805]E(f333(f195(f885(x38051,x38052)),f230(x38051,x38052,x38053,x38054)),f2(a880)) % 191.49/191.40 [3880]E(f333(f244(f884(x38801),x38802,f197(x38801),f333(f18(f884(x38801),x38802),f197(x38801))),f333(x38803,x38804)),f197(x38801)) % 191.49/191.40 [3922]E(f333(f333(f115(f890(x39221,a874)),f184(x39221,x39222,x39223)),f184(x39221,x39222,x39224)),f184(x39221,x39222,f185(x39221,x39222,x39224,x39223))) % 191.49/191.40 [3956]E(f333(f333(f274(x39561,x39562,x39563,f889(x39562,x39563)),x39564),f263(x39562,x39563)),x39564) % 191.49/191.40 [3965]E(f245(x39651,x39652,x39653,x39654,f197(x39652)),x39653) % 191.49/191.40 [3966]E(f187(x39661,x39662,x39663,x39664,f118(x39662)),x39663) % 191.49/191.40 [3967]E(f187(x39671,x39672,x39673,f118(x39671),x39674),x39673) % 191.49/191.40 [4248]P44(x42481,x42482,x42483,x42484,f194(f890(x42481,a874)),x42484) % 191.49/191.40 [3302]E(f333(f333(f18(x33021,x33022),x33023),x33024),x33023) % 191.49/191.40 [3418]E(f333(f333(f208(x34181,x34182),x34183),f333(f242(x34181),x34184)),f333(f242(x34182),f333(x34183,x34184))) % 191.49/191.40 [3587]E(f171(x35871,x35872,f333(f137(x35871,x35873),x35874)),f333(f137(x35871,x35873),f171(x35871,x35872,x35874))) % 191.49/191.40 [3620]E(f333(f333(f66(x36201,x36202,x36203),x36204),f194(f890(x36201,a874))),x36204) % 191.49/191.40 [3643]E(f333(f333(f166(x36431),f333(f333(f152(x36431),x36432),x36433)),f333(a117,x36434)),f333(f333(f166(x36431),x36433),x36434)) % 191.49/191.40 [3686]P30(x36861,f2(a880),f333(f333(f333(f93(x36861),x36862),f333(a26,x36863)),x36864)) % 191.49/191.40 [3711]E(f333(f333(x37111,x37112),f333(f190(x37113,x37114,x37111),x37112)),f333(f190(x37113,x37114,x37111),f333(a117,x37112))) % 191.49/191.40 [3803]E(f333(f333(f160(x38031,f333(f333(f152(x38031),x38032),x38033)),f2(a880)),x38034),f333(f333(f152(x38031),x38034),x38033)) % 191.49/191.40 [3815]E(f333(f333(f44(f890(x38151,a874),f890(x38152,a874)),x38153),f313(x38152,x38151,x38154)),f333(f313(x38152,x38151,x38154),f41(f890(x38151,a874),x38153))) % 191.49/191.40 [3816]E(f333(f333(f44(f890(x38161,a874),f890(x38162,a874)),x38163),f312(x38161,x38162,x38164)),f333(f312(x38161,x38162,x38164),f41(f890(x38161,a874),x38163))) % 191.49/191.40 [3906]E(f184(x39061,x39062,f188(x39061,x39062,x39063,x39064)),f333(f333(f106(f890(x39061,a874)),f184(x39061,x39062,x39063)),x39064)) % 191.49/191.40 [3910]E(f333(f131(x39101,x39102),f129(x39101,x39103,x39104)),f333(f333(f81(a880),f333(f333(f81(a880),f333(x39102,x39103)),f333(f131(x39101,x39102),x39104))),f333(a117,f2(a880)))) % 191.49/191.40 [3929]E(f333(f143(x39291,x39292,f333(f9(x39292,x39291,x39291),x39293),x39294),f333(f170(x39292),f118(x39292))),x39294) % 191.49/191.40 [3978]E(f77(x39781,x39782,x39783,x39784,f194(f890(x39781,a874))),x39783) % 191.49/191.40 [4021]E(f333(f333(f333(f333(f73(x40211,f884(x40212)),f333(f18(f884(x40212),x40211),f197(x40212))),x40213),f197(x40212)),x40214),f197(x40212)) % 191.49/191.40 [4170]E(f333(f272(x41701,x41702,x41703),f333(f333(f10(f890(x41702,f889(x41701,x41702)),f890(x41702,x41703),x41701),f333(f10(f889(x41701,x41702),x41703,x41702),x41704)),f263(x41701,x41702))),x41704) % 191.49/191.40 [3495]E(f333(f271(x34951,x34952),f333(f333(f263(x34951,x34952),x34953),x34954)),x34954) % 191.49/191.40 [3496]E(f333(f262(x34961,x34962),f333(f333(f263(x34961,x34962),x34963),x34964)),x34963) % 191.49/191.40 [3531]E(f333(f195(f881(x35311)),f333(f333(f155(x35312,x35311),x35313),x35314)),f333(f195(f881(x35312)),x35314)) % 191.49/191.40 [3532]E(f333(f195(f881(x35321)),f333(f333(f160(x35321,x35322),x35323),x35324)),f333(f195(f881(x35321)),x35322)) % 191.49/191.40 [3550]E(f333(f333(f139(x35501),f333(a117,x35502)),f333(f333(f152(x35501),x35503),x35504)),f333(f333(f139(x35501),x35502),x35504)) % 191.49/191.40 [3622]E(f333(f333(f311(x36221),x36222),f333(f333(f311(x36221),x36223),x36224)),f333(f333(f311(x36221),x36223),f333(f333(f311(x36221),x36222),x36224))) % 191.49/191.40 [3625]E(f333(f333(f155(x36251,x36252),x36253),f119(x36251,x36254)),f119(x36252,f333(f333(f155(x36251,x36252),x36253),x36254))) % 191.49/191.40 [3641]E(f333(f170(x36411),f333(f333(f155(x36412,x36411),x36413),x36414)),f333(f333(f155(x36412,x36411),x36413),f333(f170(x36412),x36414))) % 191.49/191.40 [3642]E(f333(f333(f155(x36421,x36422),x36423),f333(f172(x36421),x36424)),f333(f172(x36422),f333(f333(f155(x36421,x36422),x36423),x36424))) % 191.49/191.40 [3655]E(f333(f333(f174(x36551),f333(a117,x36552)),f333(f333(f152(x36551),x36553),x36554)),f333(f333(f152(x36551),x36553),f333(f333(f174(x36551),x36552),x36554))) % 191.49/191.40 [3659]E(f333(f173(x36591),f333(f333(f155(x36592,x36591),x36593),x36594)),f333(f312(x36592,x36591,x36593),f333(f173(x36592),x36594))) % 191.49/191.40 [3710]E(f19(x37101,x37102,x37103,f333(a5,f333(a117,f333(a21,x37104)))),f333(x37103,x37104)) % 191.49/191.40 [3713]E(f333(f333(f127(x37131),f333(f137(x37131,x37132),x37133)),f333(f137(x37131,x37132),x37134)),f333(f137(x37131,x37132),f333(f333(f127(x37131),x37133),x37134))) % 191.49/191.40 [3721]E(f153(x37211,f333(f333(f155(x37212,x37211),x37213),f153(x37212,x37214))),f153(x37211,f333(f333(f155(x37212,x37211),x37213),x37214))) % 191.49/191.40 [3736]E(f333(f288(x37361,x37361),f333(f333(f289(x37362,x37361),x37363),x37364)),f333(f333(f289(x37362,x37361),f333(f288(x37362,x37362),x37363)),x37364)) % 191.49/191.40 [3745]E(f333(f333(f290(x37451,x37452,x37453),x37454),f194(f890(f889(x37452,x37453),a874))),f194(f890(f889(x37451,x37453),a874))) % 191.49/191.40 [3746]E(f333(f333(f174(x37461),f333(f333(f3(a880),x37462),x37463)),f333(f333(f139(x37461),x37463),x37464)),f333(f333(f139(x37461),x37463),f333(f333(f174(x37461),x37462),x37464))) % 191.49/191.40 [3795]E(f41(f890(x37951,a874),f333(f312(x37952,f890(x37951,a874),x37953),x37954)),f333(f333(f44(x37952,f890(x37951,a874)),x37954),x37953)) % 191.49/191.40 [3796]E(f42(f890(x37961,a874),f333(f312(x37962,f890(x37961,a874),x37963),x37964)),f333(f333(f43(x37962,f890(x37961,a874)),x37964),x37963)) % 191.49/191.40 [3797]E(f333(f195(f881(f889(x37971,x37972))),f333(f333(f182(x37971,x37972),x37973),x37974)),f333(f333(f248(a880),f333(f195(f881(x37971)),x37973)),f333(f195(f881(x37972)),x37974))) % 191.49/191.40 [3799]E(f333(f313(x37991,x37992,x37993),f333(f80(f890(x37992,a874)),x37994)),f333(f80(f890(x37991,a874)),f333(f313(x37991,x37992,x37993),x37994))) % 191.49/191.40 [3830]E(f333(f188(x38301,x38302,x38303,f194(f890(x38301,a874))),x38304),f197(x38302)) % 191.49/191.40 [3848]E(f333(f313(x38481,x38482,x38483),f333(f255(x38482),x38484)),f333(f255(x38481),f333(f333(f10(x38482,a874,x38481),x38484),x38483))) % 191.49/191.40 [3865]E(f333(f333(f166(x38651),f333(f333(f127(x38651),x38652),f333(f333(f152(x38651),x38653),x38654))),f333(f195(f881(x38651)),x38652)),x38653) % 191.49/191.40 [3869]E(f333(f188(x38691,x38692,f333(f18(f884(x38692),x38691),f197(x38692)),x38693),x38694),f197(x38692)) % 191.49/191.40 [3887]E(f333(f312(x38871,x38872,x38873),f333(f313(x38871,x38872,x38873),x38874)),f333(f333(f106(f890(x38872,a874)),x38874),f333(f312(x38871,x38872,x38873),f258(f890(x38871,a874))))) % 191.49/191.40 [3905]P4(f333(f333(f335(x39051),f333(x39052,x39053)),f333(f312(x39054,x39051,x39052),f258(f890(x39054,a874))))) % 191.49/191.40 [3918]E(f333(f333(f270(x39181,x39182),f333(f173(x39181),x39183)),f333(f18(f890(x39182,a874),x39181),f333(f173(x39182),x39184))),f333(f173(f889(x39181,x39182)),f61(x39181,x39182,x39183,x39184))) % 191.49/191.40 [3932]E(f156(x39321,x39322,f333(f333(f152(x39321),x39323),x39324)),f333(f333(f81(a880),f333(f333(f81(a880),f333(x39322,x39323)),f156(x39321,x39322,x39324))),f333(a117,f2(a880)))) % 191.49/191.40 [3948]E(f191(f881(x39481),f333(f333(f152(x39481),x39482),x39483),f333(f333(f9(a880,f881(x39481),f881(x39481)),f139(x39481)),x39483),x39484),f333(f333(f139(x39481),x39484),f333(f333(f152(x39481),x39482),x39483))) % 191.49/191.40 [3949]P28(x39491,f889(x39492,x39491),f337(x39493,x39494,x39492,x39491),f333(f333(f44(x39492,f890(x39491,a874)),x39494),x39493)) % 191.49/191.40 [3957]E(f333(f333(f3(f890(x39571,a874)),f333(f333(f3(f890(x39571,a874)),x39572),x39573)),f333(f333(f311(x39571),x39574),f194(f890(x39571,a874)))),f333(f333(f3(f890(x39571,a874)),x39572),f333(f333(f311(x39571),x39574),x39573))) % 191.49/191.40 [3970]E(f333(f333(f189(f890(x39701,x39702),f890(x39701,x39702)),x39703),f74(x39702,x39702,x39701,x39704)),f74(x39702,x39702,x39701,f333(f333(f189(x39702,x39702),x39703),x39704))) % 191.49/191.40 [4043]E(f333(f333(f333(f189(f881(x40431),f881(x40431)),x40432),f169(x40431)),f333(f333(f333(f189(f881(x40431),f881(x40431)),x40433),f169(x40431)),x40434)),f333(f333(f333(f189(f881(x40431),f881(x40431)),f333(f333(f81(a880),x40432),x40433)),f169(x40431)),x40434)) % 191.49/191.40 [4127]P4(f333(f333(f250(f890(x41271,a874)),f333(f173(x41271),f333(f333(f160(x41271,x41272),x41273),x41274))),f333(f333(f311(x41271),x41274),f333(f173(x41271),x41272)))) % 191.49/191.40 [4158]E(f333(f333(f44(f890(x41581,a874),f890(f889(x41581,x41582),a874)),x41583),f333(f333(f9(f890(x41581,a874),f890(x41581,f890(x41582,a874)),f890(f889(x41581,x41582),a874)),f270(x41581,x41582)),x41584)),f333(f333(f270(x41581,x41582),f41(f890(x41581,a874),x41583)),x41584)) % 191.49/191.40 [4200]E(f219(x42001,x42002,x42003,f333(f74(x42002,f890(a104,f890(a104,f890(f889(a104,a104),f890(a104,f882(x42002))))),x42001,f214(x42002)),x42004)),f220(x42001,x42002,x42004,x42003)) % 191.49/191.40 [4219]E(f216(x42191,x42192,x42193,f333(f74(x42192,f890(a104,f890(a104,f890(f889(a104,a104),f890(a104,f882(f884(x42192)))))),x42191,f215(x42192)),x42194)),f217(x42191,x42192,x42194,x42193)) % 191.49/191.40 [4226]P4(f333(f68(x42261,x42262,x42263,x42264,f194(f890(x42261,a874))),x42264)) % 191.49/191.40 [4267]E(f333(f333(f44(x42671,f890(x42672,a874)),x42673),f333(f333(f9(x42671,f890(x42672,a874),f890(x42672,a874)),f333(f333(f10(x42672,f890(f890(x42672,a874),f890(x42672,a874)),x42671),f311(x42672)),x42674)),f194(f890(x42672,a874)))),f333(f312(x42671,x42672,x42674),x42673)) % 191.49/191.40 [4274]P4(f333(f333(f250(f890(x42741,a874)),f333(f259(x42742,x42741),f333(f333(f106(f890(f889(x42742,x42741),a874)),x42743),x42744))),f333(f333(f106(f890(x42741,a874)),f333(f259(x42742,x42741),x42743)),f333(f259(x42742,x42741),x42744)))) % 191.49/191.40 [4275]P4(f333(f333(f250(f890(x42751,a874)),f333(f261(x42751,x42752),f333(f333(f106(f890(f889(x42751,x42752),a874)),x42753),x42754))),f333(f333(f106(f890(x42751,a874)),f333(f261(x42751,x42752),x42753)),f333(f261(x42751,x42752),x42754)))) % 191.49/191.40 [4335]P4(f333(f333(f250(f890(f889(x43351,x43352),a874)),f333(f312(x43352,f889(x43351,x43352),f337(x43353,x43354,x43351,x43352)),f333(f333(f44(x43351,f890(x43352,a874)),x43354),x43353))),f333(f333(f270(x43351,x43352),x43354),x43353))) % 191.49/191.40 [4336]E(f333(f123(x43361,f889(x43361,x43362),x43363),f333(f333(f10(f890(x43362,f882(f889(x43361,x43362))),f882(f889(x43361,x43362)),x43361),f123(x43362,f889(x43361,x43362),x43364)),f333(f333(f10(f890(x43362,f889(x43361,x43362)),f890(x43362,f882(f889(x43361,x43362))),x43361),f333(f10(f889(x43361,x43362),f882(f889(x43361,x43362)),x43362),f128(f889(x43361,x43362)))),f263(x43361,x43362)))),f133(x43361,x43362,x43363,x43364)) % 191.49/191.40 [4382]E(f86(f889(x43821,x43822),f333(f272(x43821,x43822,a874),f333(f333(f9(x43821,f890(x43822,a874),f890(x43822,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x43822,a874),f890(x43822,a874)),x43821),f10(a874,a874,x43822)),f333(f333(f10(a874,f890(a874,a874),x43821),a331),f333(a330,x43823)))),f333(a330,x43824)))),f333(f333(f263(x43821,x43822),x43823),x43824)) % 191.49/191.40 [4383]E(f91(f889(x43831,x43832),f333(f272(x43831,x43832,a874),f333(f333(f9(x43831,f890(x43832,a874),f890(x43832,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x43832,a874),f890(x43832,a874)),x43831),f10(a874,a874,x43832)),f333(f333(f10(a874,f890(a874,a874),x43831),a331),f333(a330,x43833)))),f333(a330,x43834)))),f333(f333(f263(x43831,x43832),x43833),x43834)) % 191.49/191.40 [4463]E(f333(f333(f272(f881(x44631),f881(x44631),f889(f881(x44631),f881(x44631))),f333(f333(f20(f881(x44631),f890(f881(x44631),f889(f881(x44631),f881(x44631))),f890(f881(x44631),f889(f881(x44631),f881(x44631)))),f333(f333(f10(f890(f881(x44631),f890(f889(f881(x44631),f881(x44631)),f889(f881(x44631),f881(x44631)))),f890(f890(f881(x44631),f889(f881(x44631),f881(x44631))),f890(f881(x44631),f889(f881(x44631),f881(x44631)))),f881(x44631)),f20(f881(x44631),f889(f881(x44631),f881(x44631)),f889(f881(x44631),f881(x44631)))),f333(f333(f10(f890(f881(x44631),f889(f881(x44631),f881(x44631))),f890(f881(x44631),f890(f889(f881(x44631),f881(x44631)),f889(f881(x44631),f881(x44631)))),f881(x44631)),f333(f10(f889(f881(x44631),f881(x44631)),f890(f889(f881(x44631),f881(x44631)),f889(f881(x44631),f881(x44631))),f881(x44631)),f333(f101(f889(f881(x44631),f881(x44631))),f333(x44632,x44633)))),f333(f333(f10(f881(x44631),f890(f881(x44631),f889(f881(x44631),f881(x44631))),f881(x44631)),f263(f881(x44631),f881(x44631))),f333(f152(x44631),x44633))))),f333(f333(f9(f881(x44631),f890(f881(x44631),f881(x44631)),f890(f881(x44631),f889(f881(x44631),f881(x44631)))),f333(f333(f10(f890(f881(x44631),f889(f881(x44631),f881(x44631))),f890(f890(f881(x44631),f881(x44631)),f890(f881(x44631),f889(f881(x44631),f881(x44631)))),f881(x44631)),f10(f881(x44631),f889(f881(x44631),f881(x44631)),f881(x44631))),f263(f881(x44631),f881(x44631)))),f333(f152(x44631),x44633)))),f168(x44631,x44632,x44634)),f168(x44631,x44632,f333(f333(f152(x44631),x44633),x44634))) % 191.49/191.40 [4469]E(f333(f143(f890(x44691,f884(x44692)),f889(x44691,x44692),f333(f9(f889(x44691,x44692),f890(x44691,f884(x44692)),f890(x44691,f884(x44692))),f333(f272(x44691,x44692,f890(f890(x44691,f884(x44692)),f890(x44691,f884(x44692)))),f333(f333(f9(x44691,f890(x44692,f884(x44692)),f890(x44692,f890(f890(x44691,f884(x44692)),f890(x44691,f884(x44692))))),f333(f333(f10(f890(f884(x44692),f890(f890(x44691,f884(x44692)),f890(x44691,f884(x44692)))),f890(f890(x44692,f884(x44692)),f890(x44692,f890(f890(x44691,f884(x44692)),f890(x44691,f884(x44692))))),x44691),f10(f884(x44692),f890(f890(x44691,f884(x44692)),f890(x44691,f884(x44692))),x44692)),f333(f333(f10(f890(f890(x44691,f884(x44692)),f890(f884(x44692),f890(x44691,f884(x44692)))),f890(f884(x44692),f890(f890(x44691,f884(x44692)),f890(x44691,f884(x44692)))),x44691),f9(f890(x44691,f884(x44692)),f884(x44692),f890(x44691,f884(x44692)))),f333(f9(f890(x44691,f884(x44692)),x44691,f890(f884(x44692),f890(x44691,f884(x44692)))),f73(x44691,f884(x44692)))))),f242(x44692)))),x44693),f333(f170(f889(x44691,x44692)),x44694)),f185(x44691,x44692,x44693,f333(f178(x44691,x44692),x44694))) % 191.49/191.40 [3570]E(f333(f195(f879(x35701)),f333(f333(f333(f93(x35701),x35702),x35703),x35704)),f2(a880)) % 191.49/191.40 [3689]E(f333(f333(f174(x36891),x36892),f333(f333(f174(x36891),x36893),x36894)),f333(f333(f174(x36891),f333(f333(f248(a880),x36892),x36893)),x36894)) % 191.49/191.40 [3690]E(f333(f333(f139(x36901),x36902),f333(f333(f139(x36901),x36903),x36904)),f333(f333(f139(x36901),f333(f333(f81(a880),x36902),x36903)),x36904)) % 191.49/191.40 [3702]E(f333(f333(f127(x37021),f333(f333(f152(x37021),x37022),x37023)),x37024),f333(f333(f152(x37021),x37022),f333(f333(f127(x37021),x37023),x37024))) % 191.49/191.40 [3703]E(f333(f333(f127(x37031),f333(f333(f127(x37031),x37032),x37033)),x37034),f333(f333(f127(x37031),x37032),f333(f333(f127(x37031),x37033),x37034))) % 191.49/191.40 [3780]E(f333(f333(f166(x37801),f333(f333(f152(x37801),x37802),x37803)),x37804),f191(x37801,x37802,f333(f166(x37801),x37803),x37804)) % 191.49/191.40 [3788]E(f333(f333(f189(x37881,x37881),x37882),f333(f333(f189(x37881,x37881),x37883),x37884)),f333(f333(f189(x37881,x37881),f333(f333(f82(a880),x37883),x37882)),x37884)) % 191.49/191.40 [3818]E(f333(f333(f115(f890(x38181,a874)),x38182),f333(f333(f311(x38181),x38183),x38184)),f333(f333(f311(x38181),x38183),f333(f333(f115(f890(x38181,a874)),x38182),x38184))) % 191.49/191.40 [3833]E(f333(f333(f333(f189(x38331,x38331),x38332),x38333),f333(x38333,x38334)),f333(x38333,f333(f333(f333(f189(x38331,x38331),x38332),x38333),x38334))) % 191.49/191.40 [3838]E(f333(f333(f290(x38381,x38382,x38383),f194(f890(f889(x38381,x38382),a874))),x38384),f194(f890(f889(x38381,x38383),a874))) % 191.49/191.40 [3854]E(f333(f333(f115(f890(x38541,a874)),f333(f333(f311(x38541),x38542),x38543)),x38544),f333(f333(f311(x38541),x38542),f333(f333(f115(f890(x38541,a874)),x38543),x38544))) % 191.49/191.40 [3871]E(f185(x38711,x38712,f333(f178(x38711,x38712),x38713),f333(f178(x38711,x38712),x38714)),f333(f178(x38711,x38712),f333(f333(f127(f889(x38711,x38712)),x38714),x38713))) % 191.49/191.40 [3872]E(f333(f39(f889(x38721,x38722)),f333(f333(f270(x38721,x38722),x38723),f333(f18(f890(x38722,a874),x38721),x38724))),f333(f333(f82(a880),f333(f39(x38721),x38723)),f333(f39(x38722),x38724))) % 191.49/191.40 [3878]E(f333(f333(f106(f890(x38781,a874)),f333(f333(f311(x38781),x38782),x38783)),f333(f333(f311(x38781),x38782),x38784)),f333(f333(f311(x38781),x38782),f333(f333(f106(f890(x38781,a874)),x38783),x38784))) % 191.49/191.40 [3891]E(f333(f333(f115(f890(x38911,a874)),x38912),f333(f333(f115(f890(x38911,a874)),x38913),x38914)),f333(f333(f115(f890(x38911,a874)),x38913),f333(f333(f115(f890(x38911,a874)),x38912),x38914))) % 191.49/191.40 [3892]E(f333(f333(f106(f890(x38921,a874)),x38922),f333(f333(f106(f890(x38921,a874)),x38923),x38924)),f333(f333(f106(f890(x38921,a874)),x38923),f333(f333(f106(f890(x38921,a874)),x38922),x38924))) % 191.49/191.40 [3901]E(f66(x39011,x39012,f333(f333(f10(x39012,f890(x39012,x39012),x39011),x39013),x39014)),f333(f67(x39012,x39011,x39013),x39014)) % 191.49/191.40 [3911]E(f180(x39111,f333(f333(f155(f881(x39112),f881(x39111)),f333(f155(x39112,x39111),x39113)),x39114)),f333(f333(f155(f881(x39112),f881(x39111)),f333(f155(x39112,x39111),x39113)),f180(x39112,x39114))) % 191.49/191.40 [3928]E(f333(f143(f881(x39281),f881(x39281),f127(x39281),f118(x39281)),f333(f333(f155(x39282,f881(x39281)),x39283),x39284)),f165(x39282,x39281,x39283,x39284)) % 191.49/191.40 [3931]E(f188(x39311,x39312,x39313,f333(f80(f890(x39311,a874)),f333(f333(f311(x39311),x39314),f194(f890(x39311,a874))))),f333(f333(f333(f73(x39311,f884(x39312)),x39313),x39314),f197(x39312))) % 191.49/191.40 [3974]E(f333(f333(f333(f73(x39741,f884(x39742)),f333(f178(x39741,x39742),x39743)),f333(f262(x39741,x39742),x39744)),f333(f242(x39742),f333(f271(x39741,x39742),x39744))),f333(f178(x39741,x39742),f333(f333(f152(f889(x39741,x39742)),x39744),x39743))) % 191.49/191.40 [3991]E(f333(f74(x39911,x39911,x39911,f333(f333(f189(x39911,x39911),x39912),x39913)),f333(f333(f189(x39911,x39911),x39914),x39913)),f333(f333(f189(x39911,x39911),f333(f333(f81(a880),x39912),x39914)),x39913)) % 191.49/191.40 [4013]E(f333(f333(f106(f890(x40131,a874)),f333(f333(f115(f890(x40131,a874)),x40132),x40133)),f333(f333(f115(f890(x40131,a874)),x40132),x40134)),f333(f333(f115(f890(x40131,a874)),x40132),f333(f333(f106(f890(x40131,a874)),x40133),x40134))) % 191.49/191.40 [4014]E(f333(f333(f106(f890(x40141,a874)),f333(f333(f3(f890(x40141,a874)),x40142),x40143)),f333(f333(f3(f890(x40141,a874)),x40142),x40144)),f333(f333(f3(f890(x40141,a874)),x40142),f333(f333(f115(f890(x40141,a874)),x40143),x40144))) % 191.49/191.40 [4015]E(f333(f333(f115(f890(x40151,a874)),f333(f333(f3(f890(x40151,a874)),x40152),x40153)),f333(f333(f3(f890(x40151,a874)),x40152),x40154)),f333(f333(f3(f890(x40151,a874)),x40152),f333(f333(f106(f890(x40151,a874)),x40153),x40154))) % 191.49/191.40 [4016]E(f333(f333(f115(f890(x40161,a874)),f333(f333(f106(f890(x40161,a874)),x40162),x40163)),f333(f333(f106(f890(x40161,a874)),x40162),x40164)),f333(f333(f106(f890(x40161,a874)),x40162),f333(f333(f115(f890(x40161,a874)),x40163),x40164))) % 191.49/191.40 [4017]E(f333(f333(f3(f890(x40171,a874)),f333(f333(f106(f890(x40171,a874)),x40172),x40173)),f333(f333(f106(f890(x40171,a874)),x40172),x40174)),f333(f333(f106(f890(x40171,a874)),x40172),f333(f333(f3(f890(x40171,a874)),x40173),x40174))) % 191.49/191.40 [4023]E(f333(f39(f889(x40231,x40232)),f333(f333(f270(x40231,x40232),f333(f333(f311(x40231),x40233),f194(f890(x40231,a874)))),f333(f18(f890(x40232,a874),x40231),x40234))),f333(f39(x40232),x40234)) % 191.49/191.40 [4058]E(f333(f333(f44(x40581,f890(x40582,a874)),x40583),f333(f333(f10(f890(x40582,a874),f890(x40582,a874),x40581),f80(f890(x40582,a874))),x40584)),f333(f80(f890(x40582,a874)),f333(f333(f43(x40581,f890(x40582,a874)),x40583),x40584))) % 191.49/191.40 [4059]E(f333(f333(f43(x40591,f890(x40592,a874)),x40593),f333(f333(f10(f890(x40592,a874),f890(x40592,a874),x40591),f80(f890(x40592,a874))),x40594)),f333(f80(f890(x40592,a874)),f333(f333(f44(x40591,f890(x40592,a874)),x40593),x40594))) % 191.49/191.40 [4073]E(f333(f333(f290(x40731,x40731,x40731),f333(f333(f189(f889(x40731,x40731),a874),x40732),x40733)),f333(f333(f189(f889(x40731,x40731),a874),x40734),x40733)),f333(f333(f189(f889(x40731,x40731),a874),f333(f333(f81(a880),x40732),x40734)),x40733)) % 191.49/191.40 [4104]E(f333(f333(f43(x41041,f890(f890(x41042,a874),a874)),x41043),f333(f333(f10(f890(x41042,a874),f890(f890(x41042,a874),a874),x41041),f310(x41042)),x41044)),f333(f310(x41042),f333(f333(f43(x41041,f890(x41042,a874)),x41043),x41044))) % 191.49/191.40 [4132]E(f333(f333(f43(f890(x41321,a874),f890(x41322,a874)),x41323),f333(f333(f9(f890(x41321,a874),f890(x41321,f890(x41322,a874)),f890(x41322,a874)),f43(x41321,f890(x41322,a874))),x41324)),f333(f333(f43(x41321,f890(x41322,a874)),f41(f890(x41321,a874),x41323)),x41324)) % 191.49/191.40 [4133]E(f333(f333(f44(f890(x41331,a874),f890(x41332,a874)),x41333),f333(f333(f9(f890(x41331,a874),f890(x41331,f890(x41332,a874)),f890(x41332,a874)),f44(x41331,f890(x41332,a874))),x41334)),f333(f333(f44(x41331,f890(x41332,a874)),f41(f890(x41331,a874),x41333)),x41334)) % 191.49/191.40 [4136]E(f333(f333(f155(x41361,x41362),x41363),f333(f143(f881(x41361),f881(x41361),f127(x41361),f118(x41361)),x41364)),f333(f143(f881(x41362),f881(x41362),f127(x41362),f118(x41362)),f333(f333(f155(f881(x41361),f881(x41362)),f333(f155(x41361,x41362),x41363)),x41364))) % 191.49/191.40 [4140]E(f191(f881(x41401),f118(x41401),f333(f333(f10(f881(x41401),f881(x41401),a880),f333(f152(x41401),x41402)),f333(f333(f9(a880,f881(x41401),f881(x41401)),f174(x41401)),x41403)),x41404),f333(f333(f174(x41401),x41404),f333(f333(f152(x41401),x41402),x41403))) % 191.49/191.40 [4180]P4(f333(f333(f250(f890(x41801,a874)),f333(f312(x41802,x41801,x41803),f333(f313(x41802,x41801,x41803),x41804))),x41804)) % 191.49/191.40 [4183]E(f333(f312(f889(x41831,x41832),f889(x41832,x41831),f333(f272(x41831,x41832,f889(x41832,x41831)),f333(f9(x41832,x41831,f889(x41832,x41831)),f263(x41832,x41831)))),f333(f333(f270(x41831,x41832),x41833),f333(f18(f890(x41832,a874),x41831),x41834))),f333(f333(f270(x41832,x41831),x41834),f333(f18(f890(x41831,a874),x41832),x41833))) % 191.49/191.40 [4192]E(f333(f333(f44(x41921,f890(x41922,a874)),x41923),f333(f333(f10(f890(x41921,a874),f890(x41922,a874),x41921),f313(x41922,x41921,x41924)),f333(f333(f9(x41921,f890(x41921,a874),f890(x41921,a874)),f311(x41921)),f194(f890(x41921,a874))))),f333(f313(x41922,x41921,x41924),x41923)) % 191.49/191.40 [4193]E(f333(f333(f44(x41931,f890(x41932,a874)),x41933),f333(f333(f10(f890(x41931,a874),f890(x41932,a874),x41931),f287(x41931,x41932,x41934)),f333(f333(f9(x41931,f890(x41931,a874),f890(x41931,a874)),f311(x41931)),f194(f890(x41931,a874))))),f333(f287(x41931,x41932,x41934),x41933)) % 191.49/191.40 [4288]E(f333(f333(f115(f890(x42881,a874)),f333(f333(f115(f890(x42881,a874)),f333(f333(f106(f890(x42881,a874)),x42882),x42883)),f333(f333(f106(f890(x42881,a874)),x42883),x42884))),f333(f333(f106(f890(x42881,a874)),x42884),x42882)),f333(f333(f106(f890(x42881,a874)),f333(f333(f106(f890(x42881,a874)),f333(f333(f115(f890(x42881,a874)),x42882),x42883)),f333(f333(f115(f890(x42881,a874)),x42883),x42884))),f333(f333(f115(f890(x42881,a874)),x42884),x42882))) % 191.49/191.40 [4350]E(f333(f143(f881(x43501),f881(x43501),f127(x43501),f118(x43501)),f333(f333(f155(x43502,f881(x43501)),f333(f333(f9(x43502,f881(x43501),f881(x43501)),f333(f333(f10(x43501,f890(f881(x43501),f881(x43501)),x43502),f152(x43501)),x43503)),f118(x43501))),x43504)),f333(f333(f155(x43502,x43501),x43503),x43504)) % 191.49/191.40 [4366]E(f333(f333(f89(a1,x43661),f333(f108(a1),f333(f333(f81(a1),x43662),a102))),f333(f333(f20(a1,x43661,x43661),f333(f333(f9(a1,x43661,f890(x43661,x43661)),f333(f333(f10(a874,f890(x43661,f890(x43661,x43661)),a1),f101(x43661)),a200)),x43663)),f333(f333(f10(a880,x43661,a1),x43664),a109))),f191(x43661,x43663,x43664,f333(f108(a880),x43662))) % 191.49/191.40 [4585]~P4(f333(f333(f194(f890(x45851,f890(x45852,a874))),x45853),x45854)) % 191.49/191.40 [3841]E(f333(f333(f166(x38411),f333(f333(f127(x38411),x38412),x38413)),f333(f333(f81(a880),f333(f195(f881(x38411)),x38412)),x38414)),f333(f333(f166(x38411),x38413),x38414)) % 191.49/191.40 [3847]E(f333(f333(f139(x38471),x38472),f333(f333(f174(x38471),f333(f333(f81(a880),x38473),x38472)),x38474)),f333(f333(f174(x38471),x38473),f333(f333(f139(x38471),x38472),x38474))) % 191.49/191.40 [3946]E(f333(f333(f115(f890(x39461,a874)),f333(f259(x39462,x39461),x39463)),f333(f259(x39462,x39461),x39464)),f333(f259(x39462,x39461),f333(f333(f115(f890(f889(x39462,x39461),a874)),x39463),x39464))) % 191.49/191.40 [3947]E(f333(f333(f115(f890(x39471,a874)),f333(f261(x39471,x39472),x39473)),f333(f261(x39471,x39472),x39474)),f333(f261(x39471,x39472),f333(f333(f115(f890(f889(x39471,x39472),a874)),x39473),x39474))) % 191.49/191.40 [3951]E(f333(f333(f115(f890(x39511,a874)),f333(f333(f115(f890(x39511,a874)),x39512),x39513)),x39514),f333(f333(f115(f890(x39511,a874)),x39512),f333(f333(f115(f890(x39511,a874)),x39513),x39514))) % 191.49/191.40 [3952]E(f333(f333(f3(f890(x39521,a874)),f333(f333(f106(f890(x39521,a874)),x39522),x39523)),x39524),f333(f333(f106(f890(x39521,a874)),x39522),f333(f333(f3(f890(x39521,a874)),x39523),x39524))) % 191.49/191.40 [3953]E(f333(f333(f106(f890(x39531,a874)),f333(f333(f106(f890(x39531,a874)),x39532),x39533)),x39534),f333(f333(f106(f890(x39531,a874)),x39532),f333(f333(f106(f890(x39531,a874)),x39533),x39534))) % 191.49/191.40 [3993]E(f333(f333(f115(f890(f889(x39931,x39932),a874)),f333(f288(x39932,x39931),x39933)),f333(f288(x39932,x39931),x39934)),f333(f288(x39932,x39931),f333(f333(f115(f890(f889(x39932,x39931),a874)),x39933),x39934))) % 191.49/191.40 [3994]E(f333(f333(f106(f890(f889(x39941,x39942),a874)),f333(f288(x39942,x39941),x39943)),f333(f288(x39942,x39941),x39944)),f333(f288(x39942,x39941),f333(f333(f106(f890(f889(x39942,x39941),a874)),x39943),x39944))) % 191.49/191.40 [4061]E(f333(f333(f106(f890(x40611,a874)),f333(f333(f115(f890(x40611,a874)),x40612),x40613)),f333(f333(f115(f890(x40611,a874)),x40614),x40613)),f333(f333(f115(f890(x40611,a874)),f333(f333(f106(f890(x40611,a874)),x40612),x40614)),x40613)) % 191.49/191.40 [4062]E(f333(f333(f115(f890(x40621,a874)),f333(f333(f3(f890(x40621,a874)),x40622),x40623)),f333(f333(f3(f890(x40621,a874)),x40624),x40623)),f333(f333(f3(f890(x40621,a874)),f333(f333(f115(f890(x40621,a874)),x40622),x40624)),x40623)) % 191.49/191.40 [4063]E(f333(f333(f115(f890(x40631,a874)),f333(f333(f106(f890(x40631,a874)),x40632),x40633)),f333(f333(f106(f890(x40631,a874)),x40634),x40633)),f333(f333(f106(f890(x40631,a874)),f333(f333(f115(f890(x40631,a874)),x40632),x40634)),x40633)) % 191.49/191.40 [4064]E(f333(f333(f3(f890(x40641,a874)),f333(f333(f106(f890(x40641,a874)),x40642),x40643)),f333(f333(f106(f890(x40641,a874)),x40644),x40643)),f333(f333(f106(f890(x40641,a874)),f333(f333(f3(f890(x40641,a874)),x40642),x40644)),x40643)) % 191.49/191.40 [4065]E(f333(f333(f3(f890(x40651,a874)),f333(f333(f106(f890(x40651,a874)),x40652),x40653)),f333(f333(f106(f890(x40651,a874)),x40654),x40653)),f333(f333(f3(f890(x40651,a874)),f333(f333(f106(f890(x40651,a874)),x40652),x40653)),x40654)) % 191.49/191.40 [4076]E(f333(f333(f3(f890(x40761,a874)),f333(f333(f3(f890(x40761,a874)),x40762),f333(f333(f311(x40761),x40763),f194(f890(x40761,a874))))),x40764),f333(f333(f3(f890(x40761,a874)),x40762),f333(f333(f311(x40761),x40763),x40764))) % 191.49/191.40 [4129]E(f333(f333(f115(f890(x41291,a874)),f333(f333(f311(x41291),x41292),f333(f333(f311(x41291),x41293),f194(f890(x41291,a874))))),f333(f286(x41291),x41294)),f333(f286(x41291),f333(f333(f311(f889(x41291,x41291)),f333(f333(f263(x41291,x41291),x41292),x41293)),x41294))) % 191.49/191.40 [4155]E(f333(f333(f44(a880,f890(x41551,a874)),f333(f302(a880),x41552)),f333(f333(f10(a880,f890(x41551,a874),a880),x41553),f333(f333(f9(a880,a880,a880),f81(a880)),x41554))),f333(f333(f44(a880,f890(x41551,a874)),f304(a880,x41554,f333(f333(f81(a880),x41552),x41554))),x41553)) % 191.49/191.40 [4156]E(f176(x41561,f333(f287(x41561,x41561,x41562),f333(f333(f311(x41561),x41563),f194(f890(x41561,a874)))),f333(f287(f881(x41561),f881(x41561),f159(x41561,x41562)),f333(f333(f311(f881(x41561)),x41564),f194(f890(f881(x41561),a874))))),f333(f287(f881(x41561),f881(x41561),f159(x41561,x41562)),f333(f333(f311(f881(x41561)),f333(f333(f152(x41561),x41563),x41564)),f194(f890(f881(x41561),a874))))) % 191.49/191.40 [4224]E(f333(f178(x42241,x42242),f333(f333(f155(x42241,f889(x42241,x42242)),f333(f333(f20(x42241,x42242,f889(x42241,x42242)),f263(x42241,x42242)),x42243)),x42244)),f188(x42241,x42242,f333(f74(x42242,f884(x42242),x42241,f242(x42242)),x42243),f333(f173(x42241),x42244))) % 191.49/191.40 [4230]E(f333(f255(x42301),f333(f333(f9(x42301,f890(x42302,a874),a874),f333(f333(f10(x42302,f890(f890(x42302,a874),a874),x42301),f335(x42302)),x42303)),x42304)),f333(f313(x42301,x42302,x42303),x42304)) % 191.49/191.40 [4318]E(f333(f255(x43181),f333(f333(f9(x43181,f890(f889(x43182,x43181),a874),a874),f333(f333(f10(f889(x43182,x43181),f890(f890(f889(x43182,x43181),a874),a874),x43181),f335(f889(x43182,x43181))),f333(f263(x43182,x43181),x43183))),x43184)),f333(f287(x43182,x43181,x43184),f333(f333(f311(x43182),x43183),f194(f890(x43182,a874))))) % 191.49/191.40 [4334]E(f333(f333(f155(f889(x43341,a880),x43341),f262(x43341,a880)),f333(f137(f889(x43341,a880),f333(f333(f10(a880,a874,f889(x43341,a880)),x43342),f333(f333(f10(a880,a880,f889(x43341,a880)),a117),f271(x43341,a880)))),f333(f333(f182(x43341,a880),x43343),x43344))),f333(f333(f155(f889(x43341,a880),x43341),f262(x43341,a880)),f333(f137(f889(x43341,a880),f333(f333(f10(a880,a874,f889(x43341,a880)),x43342),f271(x43341,a880))),f333(f333(f182(x43341,a880),x43343),f333(f333(f155(a880,a880),a117),x43344))))) % 191.49/191.40 [4342]P4(f333(f333(f250(f890(f890(x43421,a874),a874)),f333(f333(f44(x43422,f890(f890(x43421,a874),a874)),x43423),f333(f333(f10(f890(x43421,a874),f890(f890(x43421,a874),a874),x43422),f310(x43421)),x43424))),f333(f310(x43421),f333(f333(f44(x43422,f890(x43421,a874)),x43423),x43424)))) % 191.49/191.40 [4388]E(f333(f333(f89(a1,x43881),f333(f108(a1),f333(f333(f81(a1),x43882),a102))),f333(f333(f20(a1,x43881,x43881),f333(f333(f9(a1,x43881,f890(x43881,x43881)),f333(f333(f10(a874,f890(x43881,f890(x43881,x43881)),a1),f101(x43881)),a200)),x43883)),f333(f333(f20(a1,x43881,x43881),f333(f333(f10(a880,f890(x43881,x43881),a1),x43884),a109)),f333(f333(f10(a880,x43881,a1),f190(x43881,x43883,x43884)),a109)))),f333(f190(x43881,x43883,x43884),f333(f108(a880),x43882))) % 191.49/191.40 [4391]E(f333(f333(f155(x43911,x43912),f333(f74(f884(x43912),x43912,x43911,f246(x43912)),x43913)),f333(f137(x43911,f333(f333(f10(a874,a874,x43911),a328),f333(f333(f9(x43911,f884(x43912),a874),f333(f333(f10(f884(x43912),f890(f884(x43912),a874),x43911),a330),x43913)),f197(x43912)))),x43914)),f164(x43911,x43912,x43913,x43914)) % 191.49/191.40 [4420]E(f333(f255(f889(x44201,x44202)),f333(f272(x44201,x44202,a874),f333(f333(f9(x44201,f890(x44202,a874),f890(x44202,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x44202,a874),f890(x44202,a874)),x44201),f10(a874,a874,x44202)),f333(f333(f10(a874,f890(a874,a874),x44201),a331),f333(f333(f9(x44201,f890(x44201,a874),a874),f335(x44201)),x44203)))),f333(f333(f9(x44202,f890(x44202,a874),a874),f335(x44202)),x44204)))),f238(x44201,x44202,x44203,x44204)) % 191.49/191.40 [4458]E(f333(f333(f44(x44581,f890(f889(x44581,x44582),a874)),x44583),f333(f333(f20(x44581,f890(x44582,f890(f889(x44581,x44582),a874)),f890(f889(x44581,x44582),a874)),f333(f333(f10(f890(x44582,a874),f890(f890(x44582,f890(f889(x44581,x44582),a874)),f890(f889(x44581,x44582),a874)),x44581),f44(x44582,f890(f889(x44581,x44582),a874))),x44584)),f333(f333(f9(x44581,f890(f889(x44581,x44582),a874),f890(x44582,f890(f889(x44581,x44582),a874))),f333(f333(f10(f890(x44582,f890(f890(f889(x44581,x44582),a874),f890(f889(x44581,x44582),a874))),f890(f890(f889(x44581,x44582),a874),f890(x44582,f890(f889(x44581,x44582),a874))),x44581),f9(x44582,f890(f889(x44581,x44582),a874),f890(f889(x44581,x44582),a874))),f333(f333(f10(f890(x44582,f889(x44581,x44582)),f890(x44582,f890(f890(f889(x44581,x44582),a874),f890(f889(x44581,x44582),a874))),x44581),f333(f10(f889(x44581,x44582),f890(f890(f889(x44581,x44582),a874),f890(f889(x44581,x44582),a874)),x44582),f311(f889(x44581,x44582)))),f263(x44581,x44582)))),f194(f890(f889(x44581,x44582),a874))))),f333(f333(f270(x44581,x44582),x44583),x44584)) % 191.49/191.40 [4002]E(f333(f333(f127(x40021),f333(f333(f174(x40021),x40022),x40023)),f333(f333(f174(x40021),f333(f333(f3(a880),x40022),f333(f195(f881(x40021)),x40023))),x40024)),f333(f333(f174(x40021),x40022),f333(f333(f127(x40021),x40023),x40024))) % 191.49/191.40 [4003]E(f333(f333(f127(x40031),f333(f333(f139(x40031),x40032),x40033)),f333(f333(f139(x40031),f333(f333(f3(a880),x40032),f333(f195(f881(x40031)),x40033))),x40034)),f333(f333(f139(x40031),x40032),f333(f333(f127(x40031),x40033),x40034))) % 191.49/191.40 [4052]E(f333(f333(f81(a880),f333(f333(f82(a880),x40521),x40522)),f333(f333(f81(a880),f333(f333(f82(a880),x40523),x40522)),x40524)),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f81(a880),x40521),x40523)),x40522)),x40524)) % 191.49/191.40 [4251]P4(f333(f333(f250(f890(x42511,a874)),f333(f333(f3(f890(x42511,a874)),f333(f259(x42512,x42511),x42513)),f333(f259(x42512,x42511),x42514))),f333(f259(x42512,x42511),f333(f333(f3(f890(f889(x42512,x42511),a874)),x42513),x42514)))) % 191.49/191.40 [4252]P4(f333(f333(f250(f890(x42521,a874)),f333(f333(f3(f890(x42521,a874)),f333(f261(x42521,x42522),x42523)),f333(f261(x42521,x42522),x42524))),f333(f261(x42521,x42522),f333(f333(f3(f890(f889(x42521,x42522),a874)),x42523),x42524)))) % 191.49/191.40 [4368]E(f333(f333(f81(a1),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x43681),x43682)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x43683),x43684)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),f333(f333(f81(a880),x43681),x43683)),f333(f333(f81(a880),x43682),x43684))),f194(f890(f889(a880,a880),a874)))))) % 191.49/191.40 [4415]E(f333(f333(f82(a1),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x44151),x44152)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x44153),x44154)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),f333(f333(f81(a880),f333(f333(f82(a880),x44151),x44153)),f333(f333(f82(a880),x44152),x44154))),f333(f333(f81(a880),f333(f333(f82(a880),x44151),x44154)),f333(f333(f82(a880),x44152),x44153)))),f194(f890(f889(a880,a880),a874)))))) % 191.49/191.40 [4441]E(f333(f255(x44411),f333(f333(f10(f890(x44412,a874),a874,x44411),f88(x44412)),f333(f333(f10(f890(x44412,a874),f890(x44412,a874),x44411),f333(f20(x44412,a874,a874),f333(f333(f10(a874,f890(a874,a874),x44412),a336),f333(f333(f9(x44412,f890(x44412,a874),a874),f335(x44412)),x44413)))),f333(f333(f9(x44411,f890(x44412,f890(x44411,a874)),f890(x44412,a874)),f333(f333(f10(f890(f890(x44411,a874),a874),f890(f890(x44412,f890(x44411,a874)),f890(x44412,a874)),x44411),f10(f890(x44411,a874),a874,x44412)),f335(x44411))),x44414)))),f333(f333(f43(x44412,f890(x44411,a874)),x44413),x44414)) % 191.49/191.40 [4473]E(f333(f333(f290(x44731,x44731,x44731),f333(f333(f311(f889(x44731,x44731)),f333(f333(f263(x44731,x44731),x44732),x44733)),x44734)),f309(x44731,f333(f333(f311(f889(x44731,x44731)),f333(f333(f263(x44731,x44731),x44732),x44733)),x44734))),f333(f333(f115(f890(f889(x44731,x44731),a874)),f333(f333(f290(x44731,x44731,x44731),x44734),f309(x44731,x44734))),f333(f255(f889(x44731,x44731)),f333(f272(x44731,x44731,a874),f333(f333(f9(x44731,f890(x44731,a874),f890(x44731,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x44731,a874),f890(x44731,a874)),x44731),f10(a874,a874,x44731)),f333(f333(f10(a874,f890(a874,a874),x44731),a331),f333(f333(f9(x44731,f890(f889(x44731,x44731),a874),a874),f333(f333(f10(f889(x44731,x44731),f890(f890(f889(x44731,x44731),a874),a874),x44731),f335(f889(x44731,x44731))),f333(f333(f9(x44731,x44731,f889(x44731,x44731)),f263(x44731,x44731)),x44732))),f309(x44731,x44734))))),f333(f333(f9(x44731,f890(f889(x44731,x44731),a874),a874),f333(f333(f10(f889(x44731,x44731),f890(f890(f889(x44731,x44731),a874),a874),x44731),f335(f889(x44731,x44731))),f333(f263(x44731,x44731),x44733))),f309(x44731,x44734))))))) % 191.49/191.40 [4253]E(f333(f137(x42531,f333(f333(f20(x42531,a874,a874),f333(f333(f10(a874,f890(a874,a874),x42531),a331),x42532)),x42533)),x42534),f333(f137(x42531,x42533),f333(f137(x42531,x42532),x42534))) % 191.49/191.40 [4362]E(f333(f333(f127(x43621),f333(f333(f333(f101(f881(x43621)),f333(f333(f335(a880),f2(a880)),x43622)),f333(f333(f152(x43621),x43623),f118(x43621))),f118(x43621))),f175(x43621,x43624,f333(f255(a880),f333(f333(f9(a880,f890(a880,a874),a874),f333(f333(f10(a880,f890(f890(a880,a874),a874),a880),f335(a880)),a117)),x43622)))),f175(x43621,f333(f333(f152(x43621),x43623),x43624),x43622)) % 191.49/191.40 [4467]E(f333(f255(f889(x44671,x44672)),f333(f333(f10(f890(a880,a874),a874,f889(x44671,x44672)),f87(a880)),f333(f333(f9(f889(x44671,x44672),f890(a880,a874),f890(a880,a874)),f333(f333(f10(f890(a880,f890(a874,a874)),f890(f890(a880,a874),f890(a880,a874)),f889(x44671,x44672)),f20(a880,a874,a874)),f333(f333(f10(f890(a880,a874),f890(a880,f890(a874,a874)),f889(x44671,x44672)),f333(f10(a874,f890(a874,a874),a880),a331)),f333(f333(f9(f889(x44671,x44672),f890(a880,f889(x44671,x44672)),f890(a880,a874)),f333(f333(f10(f890(f889(x44671,x44672),a874),f890(f890(a880,f889(x44671,x44672)),f890(a880,a874)),f889(x44671,x44672)),f10(f889(x44671,x44672),a874,a880)),a330)),f333(f333(f20(a880,x44672,f889(x44671,x44672)),f333(f333(f10(x44671,f890(x44672,f889(x44671,x44672)),a880),f263(x44671,x44672)),f333(f166(x44671),x44673))),f333(f166(x44672),x44674)))))),f333(f333(f9(a880,a880,a874),f251(a880)),f333(f333(f248(a880),f333(f195(f881(x44671)),x44673)),f333(f195(f881(x44672)),x44674)))))),f333(f173(f889(x44671,x44672)),f333(f333(f182(x44671,x44672),x44673),x44674))) % 191.49/191.40 [4381]E(f333(f255(f889(x43811,x43812)),f333(f272(x43811,x43812,a874),f333(f333(f9(x43811,f890(x43812,a874),f890(x43812,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x43812,a874),f890(x43812,a874)),x43811),f10(a874,a874,x43812)),f333(f333(f10(a874,f890(a874,a874),x43811),a331),x43813))),x43814))),f333(f333(f270(x43811,x43812),f333(f255(x43811),x43813)),f333(f18(f890(x43812,a874),x43811),f333(f255(x43812),x43814)))) % 191.49/191.40 [4384]E(f333(f255(f889(x43841,x43842)),f333(f272(x43841,x43842,a874),f333(f333(f20(x43841,f890(x43842,a874),f890(x43842,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x43842,a874),f890(x43842,a874)),x43841),f10(a874,a874,x43842)),f333(f333(f10(a874,f890(a874,a874),x43841),a331),x43843))),x43844))),f333(f333(f270(x43841,x43842),f333(f255(x43841),x43843)),f333(f333(f10(f890(x43842,a874),f890(x43842,a874),x43841),f255(x43842)),x43844))) % 191.49/191.40 [4398]E(f333(f255(x43981),f333(f333(f10(f890(x43982,a874),a874,x43981),f88(x43982)),f333(f333(f10(f890(x43982,a874),f890(x43982,a874),x43981),f333(f20(x43982,a874,a874),f333(f333(f10(a874,f890(a874,a874),x43982),a336),f333(f333(f9(x43982,f890(x43982,a874),a874),f335(x43982)),x43983)))),x43984))),f333(f333(f43(x43982,f890(x43981,a874)),x43983),f333(f333(f10(f890(x43981,a874),f890(x43981,a874),x43982),f255(x43981)),f333(f9(x43981,x43982,a874),x43984)))) % 191.49/191.40 [4453]E(f333(f333(f155(f889(x44531,a880),x44531),f262(x44531,a880)),f333(f137(f889(x44531,a880),f333(f333(f9(f889(x44531,a880),f890(a880,a874),a874),f333(f333(f10(a880,f890(f890(a880,a874),a874),f889(x44531,a880)),f335(a880)),f271(x44531,a880))),x44532)),f333(f333(f182(x44531,a880),x44533),f140(a880,f333(f303(a880,x44534),f333(f333(f81(a880),x44534),f333(f195(f881(x44531)),x44533))))))),f333(f333(f155(f889(x44531,a880),x44531),f262(x44531,a880)),f333(f137(f889(x44531,a880),f333(f333(f9(f889(x44531,a880),f890(a880,a874),a874),f333(f333(f10(a880,f890(f890(a880,a874),a874),f889(x44531,a880)),f335(a880)),f333(f333(f9(f889(x44531,a880),a880,a880),f333(f333(f10(a880,f890(a880,a880),f889(x44531,a880)),f81(a880)),f271(x44531,a880))),x44534))),x44532)),f333(f333(f182(x44531,a880),x44533),f140(a880,f333(f303(a880,f2(a880)),f333(f195(f881(x44531)),x44533))))))) % 191.49/191.40 [4454]E(f333(a117,f333(f333(f249(a880),f333(f195(f881(x44541)),x44542)),f333(f143(a880,f881(x44543),f333(f9(f881(x44543),a880,a880),f333(f333(f10(a880,f890(a880,a880),f881(x44543)),f249(a880)),f333(f333(f9(f881(x44543),a880,a880),f333(f333(f10(a880,f890(a880,a880),f881(x44543)),f3(a880)),f195(f881(x44543)))),f333(a117,f2(a880))))),f2(a880)),f333(f170(f881(x44543)),f333(f137(f881(x44543),f333(f333(f10(a874,a874,f881(x44543)),a328),f333(f333(f9(f881(x44543),f881(x44543),a874),a330),f118(x44543)))),x44544))))),f333(f333(f249(a880),f333(a117,f333(f195(f881(x44541)),x44542))),f333(f143(a880,f881(x44543),f333(f9(f881(x44543),a880,a880),f333(f333(f10(a880,f890(a880,a880),f881(x44543)),f249(a880)),f195(f881(x44543)))),f2(a880)),f333(f170(f881(x44543)),x44544)))) % 191.49/191.40 [4397]E(f333(f333(f127(x43971),f175(x43971,x43972,x43973)),f175(x43971,x43974,f333(f255(a880),f333(f333(f9(a880,f890(a880,a874),a874),f333(f333(f10(a880,f890(f890(a880,a874),a874),a880),f335(a880)),f333(f333(f9(a880,a880,a880),f81(a880)),f333(f195(f881(x43971)),x43972)))),x43973)))),f175(x43971,f333(f333(f127(x43971),x43972),x43974),x43973)) % 191.49/191.40 [4460]E(f333(f333(f152(f881(x44601)),f333(f333(f152(x44601),x44602),f333(f143(f881(x44601),f881(x44601),f127(x44601),f118(x44601)),f333(f333(f155(f881(x44601),f881(x44601)),f157(f881(x44601),x44601,f118(x44601),f333(f333(f10(f881(x44601),f890(f881(x44601),f881(x44601)),x44601),f18(f881(x44601),f881(x44601))),f333(f333(f9(x44601,f881(x44601),f881(x44601)),f152(x44601)),f118(x44601))))),x44603)))),f180(x44601,f333(f333(f152(f881(x44601)),x44604),f333(f143(f881(f881(x44601)),f881(f881(x44601)),f127(f881(x44601)),f118(f881(x44601))),f333(f333(f155(f881(x44601),f881(f881(x44601))),f157(f881(f881(x44601)),x44601,f118(f881(x44601)),f333(f18(f890(f881(x44601),f881(f881(x44601))),x44601),f333(f333(f9(f881(x44601),f881(f881(x44601)),f881(f881(x44601))),f152(f881(x44601))),f118(f881(x44601)))))),x44603))))),f180(x44601,f333(f333(f152(f881(x44601)),f333(f333(f152(x44601),x44602),x44604)),x44603))) % 191.49/191.40 [4468]E(f333(f255(f889(x44681,x44681)),f333(f272(x44681,x44681,a874),f333(f333(f9(x44681,f890(f889(x44682,x44682),a874),f890(x44681,a874)),f333(f333(f10(f890(x44681,f890(f890(f889(x44682,x44682),a874),a874)),f890(f890(f889(x44682,x44682),a874),f890(x44681,a874)),x44681),f9(x44681,f890(f889(x44682,x44682),a874),a874)),f333(f333(f10(f890(x44681,f889(x44682,x44682)),f890(x44681,f890(f890(f889(x44682,x44682),a874),a874)),x44681),f333(f10(f889(x44682,x44682),f890(f890(f889(x44682,x44682),a874),a874),x44681),f335(f889(x44682,x44682)))),f333(f333(f9(x44681,f890(x44681,x44682),f890(x44681,f889(x44682,x44682))),f333(f333(f10(f890(x44682,f889(x44682,x44682)),f890(f890(x44681,x44682),f890(x44681,f889(x44682,x44682))),x44681),f10(x44682,f889(x44682,x44682),x44681)),f333(f333(f10(x44682,f890(x44682,f889(x44682,x44682)),x44681),f263(x44682,x44682)),x44683))),x44683)))),x44684))),f333(f333(f289(x44682,x44681),x44684),x44683)) % 191.49/191.40 [4530]~E(f34(x45301,x45302),f29(x45303,x45304,x45305)) % 191.49/191.40 [4531]~E(f34(x45311,x45312),f31(x45313,x45314,x45315)) % 191.49/191.40 [4532]~E(f34(x45321,x45322),f30(x45323,x45324,x45325)) % 191.49/191.40 [4533]~E(f33(x45331,x45332),f29(x45333,x45334,x45335)) % 191.49/191.40 [4534]~E(f33(x45341,x45342),f31(x45343,x45344,x45345)) % 191.49/191.40 [4535]~E(f33(x45351,x45352),f30(x45353,x45354,x45355)) % 191.49/191.40 [4536]~E(f29(x45361,x45362,x45363),f34(x45364,x45365)) % 191.49/191.40 [4537]~E(f29(x45371,x45372,x45373),f33(x45374,x45375)) % 191.49/191.40 [4538]~E(f31(x45381,x45382,x45383),f34(x45384,x45385)) % 191.49/191.40 [4539]~E(f31(x45391,x45392,x45393),f33(x45394,x45395)) % 191.49/191.40 [4540]~E(f30(x45401,x45402,x45403),f34(x45404,x45405)) % 191.49/191.40 [4541]~E(f30(x45411,x45412,x45413),f33(x45414,x45415)) % 191.49/191.40 [3944]E(f333(f185(x39441,x39442,x39443,x39444),x39445),f333(f244(f884(x39442),x39442,f333(x39443,x39445),f242(x39442)),f333(x39444,x39445))) % 191.49/191.40 [4028]E(f185(x40281,x40282,f185(x40281,x40282,x40283,x40284),x40285),f185(x40281,x40282,x40283,f185(x40281,x40282,x40284,x40285))) % 191.49/191.40 [4206]E(f333(f333(f115(f890(x42061,a874)),f333(f173(x42061),f333(f333(f174(x42061),f333(f195(f881(x42062)),x42063)),x42064))),f184(x42061,x42062,x42065)),f184(x42061,x42062,f187(x42061,x42062,x42065,x42064,x42063))) % 191.49/191.40 [3776]E(f333(f333(f272(x37761,x37762,x37763),x37764),x37765),f333(f333(x37764,f333(f262(x37761,x37762),x37765)),f333(f271(x37761,x37762),x37765))) % 191.49/191.40 [3800]E(f333(f244(x38001,x38002,x38003,x38004),f333(f242(x38002),x38005)),f333(x38004,x38005)) % 191.49/191.40 [3810]E(f333(f333(f333(f67(x38101,x38102,x38103),x38104),x38105),f194(f890(x38102,a874))),x38105) % 191.49/191.40 [3975]E(f245(x39751,x39752,x39753,x39754,f333(f242(x39752),x39755)),f333(x39754,x39755)) % 191.49/191.40 [4082]E(f333(f74(f884(x40821),f884(x40822),f884(x40823),f333(f208(x40821,x40822),x40824)),f333(f208(x40823,x40821),x40825)),f333(f208(x40823,x40822),f333(f74(x40821,x40822,x40823,x40824),x40825))) % 191.49/191.40 [4084]E(f333(f74(f881(x40841),f881(x40842),f881(x40843),f333(f155(x40841,x40842),x40844)),f333(f155(x40843,x40841),x40845)),f333(f155(x40843,x40842),f333(f74(x40841,x40842,x40843,x40844),x40845))) % 191.49/191.40 [4137]E(f333(f244(x41371,f889(x41372,f882(x41372)),x41373,f333(f272(x41372,f882(x41372),x41371),x41374)),f333(f134(x41372),x41375)),f132(x41371,x41372,x41373,x41374,x41375)) % 191.49/191.40 [4157]E(f86(x41571,f68(x41572,x41571,x41573,x41574,x41575)),f333(f333(f66(x41572,x41571,x41573),x41574),x41575)) % 191.49/191.40 [4194]E(f333(f333(f81(a880),f333(f333(f81(a880),f333(x41941,f333(f262(x41942,x41943),x41944))),f333(x41945,f333(f271(x41942,x41943),x41944)))),f333(a117,f2(a880))),f276(x41942,x41943,x41941,x41945,x41944)) % 191.49/191.40 [4393]E(f164(x43931,x43932,f333(f333(f9(x43931,f884(x43932),f884(x43932)),f333(f333(f20(x43931,f884(x43932),f890(f884(x43932),f884(x43932))),f333(f333(f10(a874,f890(f884(x43932),f890(f884(x43932),f884(x43932))),x43931),f101(f884(x43932))),x43933)),f333(f333(f10(x43932,f884(x43932),x43931),f242(x43932)),x43934))),f197(x43932)),x43935),f333(f333(f155(x43931,x43932),x43934),f333(f137(x43931,x43933),x43935))) % 191.49/191.40 [4578]~E(f333(f333(f333(f73(x45781,f884(x45782)),x45783),x45784),f333(f242(x45782),x45785)),f333(f18(f884(x45782),x45781),f197(x45782))) % 191.49/191.40 [3714]E(f333(f333(f174(x37141),x37142),f333(f333(f155(x37143,x37141),x37144),x37145)),f333(f333(f155(x37143,x37141),x37144),f333(f333(f174(x37143),x37142),x37145))) % 191.49/191.40 [3715]E(f333(f333(f139(x37151),x37152),f333(f333(f155(x37153,x37151),x37154),x37155)),f333(f333(f155(x37153,x37151),x37154),f333(f333(f139(x37153),x37152),x37155))) % 191.49/191.40 [3740]E(f333(f333(f155(x37401,x37402),x37403),f333(f333(f152(x37401),x37404),x37405)),f333(f333(f152(x37402),f333(x37403,x37404)),f333(f333(f155(x37401,x37402),x37403),x37405))) % 191.49/191.40 [3804]E(f333(f312(x38041,x38042,x38043),f333(f333(f311(x38041),x38044),x38045)),f333(f333(f311(x38042),f333(x38043,x38044)),f333(f312(x38041,x38042,x38043),x38045))) % 191.49/191.40 [3867]E(f333(f333(f182(x38671,x38672),f333(f333(f174(x38671),x38673),x38674)),f333(f333(f174(x38672),x38673),x38675)),f333(f333(f174(f889(x38671,x38672)),x38673),f333(f333(f182(x38671,x38672),x38674),x38675))) % 191.49/191.40 [3868]E(f333(f333(f182(x38681,x38682),f333(f333(f139(x38681),x38683),x38684)),f333(f333(f139(x38682),x38683),x38685)),f333(f333(f139(f889(x38681,x38682)),x38683),f333(f333(f182(x38681,x38682),x38684),x38685))) % 191.49/191.40 [3877]E(f333(f333(f160(x38771,f333(f333(f152(x38771),x38772),x38773)),f333(a117,x38774)),x38775),f333(f333(f152(x38771),x38772),f333(f333(f160(x38771,x38773),x38774),x38775))) % 191.49/191.40 [3879]E(f333(f244(f884(x38791),x38792,f197(x38791),x38793),f333(f333(f18(f884(x38792),x38794),f197(x38792)),x38795)),f197(x38791)) % 191.49/191.40 [3881]E(f333(f333(f127(x38811),f333(f333(f155(x38812,x38811),x38813),x38814)),f333(f333(f155(x38812,x38811),x38813),x38815)),f333(f333(f155(x38812,x38811),x38813),f333(f333(f127(x38812),x38814),x38815))) % 191.49/191.40 [3885]E(f333(f333(x38851,x38852),f333(f333(f265(x38853,x38854,x38851),x38852),x38855)),f333(f333(f265(x38853,x38854,x38851),x38852),f333(a117,x38855))) % 191.49/191.40 [3914]E(f165(x39141,x39142,x39143,f333(f333(f152(x39141),x39144),x39145)),f333(f333(f127(x39142),f333(x39143,x39144)),f165(x39141,x39142,x39143,x39145))) % 191.49/191.40 [3926]E(f333(f333(f290(x39261,x39262,x39263),f333(f288(x39262,x39261),x39264)),f333(f288(x39263,x39262),x39265)),f333(f288(x39263,x39261),f333(f333(f290(x39263,x39262,x39261),x39265),x39264))) % 191.49/191.40 [3961]E(f333(f333(f333(f189(f881(x39611),f881(x39611)),x39612),f169(x39611)),f333(f333(f155(x39613,x39611),x39614),x39615)),f333(f333(f155(x39613,x39611),x39614),f333(f333(f333(f189(f881(x39613),f881(x39613)),x39612),f169(x39613)),x39615))) % 191.49/191.40 [3962]E(f333(f333(f274(x39621,x39622,x39621,x39623),f333(f263(x39622,x39621),x39624)),x39625),f333(x39625,x39624)) % 191.49/191.40 [3989]E(f156(x39891,x39892,f333(f333(f155(x39893,x39891),x39894),x39895)),f156(x39893,f333(f74(x39891,a880,x39893,x39892),x39894),x39895)) % 191.49/191.40 [4050]E(f333(f333(f74(f884(x40501),f884(x40502),x40503,f333(f208(x40501,x40502),x40504)),f333(f18(f884(x40501),x40503),f197(x40501))),x40505),f197(x40502)) % 191.49/191.40 [4051]E(f177(f889(x40511,x40512),f333(f74(x40512,a874,f889(x40511,x40512),x40513),f271(x40511,x40512)),f333(f333(f182(x40511,x40512),x40514),x40515)),f333(f333(f182(x40511,x40512),x40514),f177(x40512,x40513,x40515))) % 191.49/191.40 [4056]E(f333(f312(x40561,x40562,f333(f333(f10(x40563,x40562,x40561),x40564),x40565)),f258(f890(x40561,a874))),f333(f312(x40563,x40562,x40564),f333(f312(x40561,x40563,x40565),f258(f890(x40561,a874))))) % 191.49/191.40 [4067]E(f177(f889(x40671,x40672),f333(f74(x40671,a874,f889(x40671,x40672),x40673),f262(x40671,x40672)),f333(f333(f182(x40671,x40672),x40674),x40675)),f333(f333(f182(x40671,x40672),f177(x40671,x40673,x40674)),x40675)) % 191.49/191.40 [4089]E(f333(f333(f115(f890(x40891,a874)),f333(f313(x40891,x40892,x40893),f333(f333(f311(x40892),x40894),f194(f890(x40892,a874))))),f333(f313(x40891,x40892,x40893),x40895)),f333(f313(x40891,x40892,x40893),f333(f333(f311(x40892),x40894),x40895))) % 191.49/191.40 [4145]E(f333(f333(f127(f889(x41451,x41452)),f333(f333(f155(x41452,f889(x41451,x41452)),f333(f263(x41451,x41452),x41453)),x41454)),f61(x41451,x41452,x41455,x41454)),f61(x41451,x41452,f333(f333(f152(x41451),x41453),x41455),x41454)) % 191.49/191.40 [4146]E(f333(f333(f155(x41461,x41462),x41463),f177(x41461,f333(f74(x41462,a874,x41461,x41464),x41463),x41465)),f177(x41462,x41464,f333(f333(f155(x41461,x41462),x41463),x41465))) % 191.49/191.40 [4152]E(f333(f143(x41521,x41522,f333(f9(x41522,x41521,x41521),f333(f9(x41521,x41522,x41521),x41523)),x41524),f333(f170(x41522),f333(f170(x41522),x41525))),f333(f143(x41521,x41522,x41523,x41524),x41525)) % 191.49/191.40 [4153]E(f333(f333(f333(f73(x41531,f884(x41532)),f188(x41531,x41532,x41533,x41534)),x41535),f333(x41533,x41535)),f188(x41531,x41532,x41533,f333(f333(f311(x41531),x41535),x41534))) % 191.49/191.40 [4227]E(f333(f244(f881(x42271),x42271,f164(x42272,x42271,x42273,x42274),f333(f333(f9(x42271,f881(x42271),f881(x42271)),f152(x42271)),f164(x42272,x42271,x42273,x42274))),f333(x42273,x42275)),f164(x42272,x42271,x42273,f333(f333(f152(x42272),x42275),x42274))) % 191.49/191.40 [4261]P4(f333(f333(f250(f890(x42611,a874)),f333(f312(x42612,x42611,x42613),f333(f333(f106(f890(x42612,a874)),x42614),x42615))),f333(f333(f106(f890(x42611,a874)),f333(f312(x42612,x42611,x42613),x42614)),f333(f312(x42612,x42611,x42613),x42615)))) % 191.49/191.40 [4262]P4(f333(f333(f250(f890(x42621,a874)),f333(f287(x42622,x42621,x42623),f333(f333(f106(f890(x42622,a874)),x42624),x42625))),f333(f333(f106(f890(x42621,a874)),f333(f287(x42622,x42621,x42623),x42624)),f333(f287(x42622,x42621,x42623),x42625)))) % 191.49/191.40 [4369]E(f333(f271(x43691,x43692),f333(f273(x43693,x43691,x43692,x43692,x43694,f35(x43692)),x43695)),f333(f271(x43693,x43692),x43695)) % 191.49/191.40 [4370]E(f333(f262(x43701,x43702),f333(f273(x43701,x43701,x43703,x43702,f35(x43701),x43704),x43705)),f333(f262(x43701,x43703),x43705)) % 191.49/191.40 [4464]E(f333(f143(f890(x44641,f884(x44642)),f889(x44641,x44642),f333(f333(f10(f890(x44641,f890(x44642,f890(x44641,f884(x44642)))),f890(f889(x44641,x44642),f890(x44641,f884(x44642))),f890(x44641,f884(x44642))),f272(x44641,x44642,f890(x44641,f884(x44642)))),f333(f333(f9(f890(x44641,f884(x44642)),f890(x44642,f884(x44642)),f890(x44641,f890(x44642,f890(x44641,f884(x44642))))),f333(f333(f10(f890(x44641,f890(f890(x44642,f884(x44642)),f890(x44642,f890(x44641,f884(x44642))))),f890(f890(x44642,f884(x44642)),f890(x44641,f890(x44642,f890(x44641,f884(x44642))))),f890(x44641,f884(x44642))),f9(x44641,f890(x44642,f884(x44642)),f890(x44642,f890(x44641,f884(x44642))))),f333(f333(f10(f890(x44641,f890(f884(x44642),f890(x44641,f884(x44642)))),f890(x44641,f890(f890(x44642,f884(x44642)),f890(x44642,f890(x44641,f884(x44642))))),f890(x44641,f884(x44642))),f333(f10(f890(f884(x44642),f890(x44641,f884(x44642))),f890(f890(x44642,f884(x44642)),f890(x44642,f890(x44641,f884(x44642)))),x44641),f10(f884(x44642),f890(x44641,f884(x44642)),x44642))),f73(x44641,f884(x44642))))),f242(x44642))),x44643),f333(f333(f182(x44641,x44642),x44644),x44645)),f187(x44641,x44642,x44643,x44644,x44645)) % 191.49/191.40 [4466]P27(x44661,x44662,f333(f333(f311(f879(x44661)),f333(f333(f333(f93(x44661),f333(f333(f9(x44661,f890(a875,a874),f890(a875,a874)),f333(f333(f10(f890(a875,f890(a874,a874)),f890(f890(a875,a874),f890(a875,a874)),x44661),f20(a875,a874,a874)),f333(f333(f10(f890(a875,a874),f890(a875,f890(a874,a874)),x44661),f333(f10(a874,f890(a874,a874),a875),a331)),x44663))),f333(f333(f10(a874,a874,a875),a328),x44664))),f33(x44664,x44665)),x44663)),f194(f890(f879(x44661),a874)))) % 191.49/191.40 [3557]E(f333(f333(f333(f333(f214(x35571),x35572),x35573),x35574),x35575),f209(x35571,x35572)) % 191.49/191.40 [3558]E(f333(f333(f333(f333(f215(x35581),x35582),x35583),x35584),x35585),f199(x35581,x35582)) % 191.49/191.40 [3604]E(f98(x36041,x36042,f333(f333(f333(f93(x36041),x36043),x36044),x36045)),f2(a880)) % 191.49/191.40 [3698]E(f333(f333(f333(f333(f73(x36981,x36982),x36983),x36984),x36985),x36984),x36985) % 191.49/191.40 [3915]E(f333(f333(f43(x39151,f890(x39152,a874)),f333(f333(f311(x39151),x39153),x39154)),x39155),f333(f333(f106(f890(x39152,a874)),f333(x39155,x39153)),f333(f333(f43(x39151,f890(x39152,a874)),x39154),x39155))) % 191.49/191.40 [3916]E(f333(f333(f44(x39161,f890(x39162,a874)),f333(f333(f311(x39161),x39163),x39164)),x39165),f333(f333(f115(f890(x39162,a874)),f333(x39165,x39163)),f333(f333(f44(x39161,f890(x39162,a874)),x39164),x39165))) % 191.49/191.40 [3969]E(f333(f123(x39691,x39692,f333(x39693,x39694)),f333(f333(f9(x39691,a104,f882(x39692)),x39695),x39694)),f333(f206(x39691,x39692,x39693,x39695),x39694)) % 191.49/191.40 [3982]E(f333(f333(f115(f890(x39821,a874)),f333(f313(x39821,x39822,x39823),x39824)),f333(f313(x39821,x39822,x39823),x39825)),f333(f313(x39821,x39822,x39823),f333(f333(f115(f890(x39822,a874)),x39824),x39825))) % 191.49/191.40 [3983]E(f333(f333(f3(f890(x39831,a874)),f333(f313(x39831,x39832,x39833),x39834)),f333(f313(x39831,x39832,x39833),x39835)),f333(f313(x39831,x39832,x39833),f333(f333(f3(f890(x39832,a874)),x39834),x39835))) % 191.49/191.40 [3984]E(f333(f333(f106(f890(x39841,a874)),f333(f313(x39841,x39842,x39843),x39844)),f333(f313(x39841,x39842,x39843),x39845)),f333(f313(x39841,x39842,x39843),f333(f333(f106(f890(x39842,a874)),x39844),x39845))) % 191.49/191.40 [3985]E(f333(f333(f115(f890(x39851,a874)),f333(f312(x39852,x39851,x39853),x39854)),f333(f312(x39852,x39851,x39853),x39855)),f333(f312(x39852,x39851,x39853),f333(f333(f115(f890(x39852,a874)),x39854),x39855))) % 191.49/191.40 [3986]E(f333(f333(f115(f890(x39861,a874)),f333(f287(x39862,x39861,x39863),x39864)),f333(f287(x39862,x39861,x39863),x39865)),f333(f287(x39862,x39861,x39863),f333(f333(f115(f890(x39862,a874)),x39864),x39865))) % 191.49/191.40 [3988]E(f188(x39881,x39882,f188(x39881,x39882,x39883,x39884),x39885),f188(x39881,x39882,x39883,f333(f333(f106(f890(x39881,a874)),x39884),x39885))) % 191.49/191.40 [4046]E(f333(f333(f160(x40461,f333(f333(f127(x40461),x40462),f333(f333(f152(x40461),x40463),x40464))),f333(f195(f881(x40461)),x40462)),x40465),f333(f333(f127(x40461),x40462),f333(f333(f152(x40461),x40465),x40464))) % 191.49/191.40 [4054]E(f333(f333(f43(x40541,f890(x40542,a874)),x40543),f333(f333(f10(f890(x40542,a874),f890(x40542,a874),x40541),f333(f311(x40542),x40544)),x40545)),f333(f333(f311(x40542),x40544),f333(f333(f43(x40541,f890(x40542,a874)),x40543),x40545))) % 191.49/191.40 [4122]E(f188(x41221,x41222,f333(f333(f333(f73(x41221,f884(x41222)),x41223),x41224),f333(f242(x41222),x41225)),f333(f80(f890(x41221,a874)),f333(f333(f311(x41221),x41224),f194(f890(x41221,a874))))),f188(x41221,x41222,x41223,f333(f80(f890(x41221,a874)),f333(f333(f311(x41221),x41224),f194(f890(x41221,a874)))))) % 191.49/191.40 [4211]E(f333(f333(f155(x42111,x42112),x42113),f333(f137(x42111,f333(f74(x42112,a874,x42111,x42114),x42113)),x42115)),f333(f137(x42112,x42114),f333(f333(f155(x42111,x42112),x42113),x42115))) % 191.49/191.40 [4218]E(f333(f195(f881(x42181)),f333(f137(x42181,x42182),f333(f333(f155(x42183,x42181),x42184),x42185))),f333(f195(f881(x42183)),f333(f137(x42183,f333(f74(x42181,a874,x42183,x42182),x42184)),x42185))) % 191.49/191.40 [4355]E(f333(f333(f115(f890(x43551,a874)),f333(f333(f3(f890(x43551,a874)),f184(x43551,x43552,x43553)),f333(f255(x43551),f333(f333(f9(x43551,f890(x43551,a874),a874),f335(x43551)),f333(f333(f3(f890(x43551,a874)),x43554),f184(x43551,x43552,x43555)))))),f333(f255(x43551),f333(f333(f9(x43551,f890(x43551,a874),a874),f335(x43551)),f333(f333(f106(f890(x43551,a874)),x43554),f184(x43551,x43552,x43555))))),f184(x43551,x43552,f77(x43551,f884(x43552),x43553,x43555,x43554))) % 191.49/191.40 [4448]E(f333(f157(f881(f889(x44481,x44482)),x44482,f118(f889(x44481,x44482)),f333(f333(f9(x44482,f890(f881(x44482),f881(f889(x44481,x44482))),f890(f881(x44482),f881(f889(x44481,x44482)))),f333(f333(f10(f890(f881(f889(x44481,x44482)),f881(f889(x44481,x44482))),f890(f890(f881(x44482),f881(f889(x44481,x44482))),f890(f881(x44482),f881(f889(x44481,x44482)))),x44482),f10(f881(f889(x44481,x44482)),f881(f889(x44481,x44482)),f881(x44482))),f333(f333(f10(f889(x44481,x44482),f890(f881(f889(x44481,x44482)),f881(f889(x44481,x44482))),x44482),f152(f889(x44481,x44482))),f333(f263(x44481,x44482),x44483)))),f333(f182(x44481,x44482),x44484))),x44485),f333(f333(f182(x44481,x44482),f333(f333(f152(x44481),x44483),x44484)),x44485)) % 191.49/191.40 [3909]E(f333(f333(f160(x39091,f333(f333(f160(x39091,x39092),x39093),x39094)),x39093),x39095),f333(f333(f160(x39091,x39092),x39093),x39095)) % 191.49/191.40 [3963]E(f333(f259(x39631,x39632),f333(f333(f311(f889(x39631,x39632)),f333(f333(f263(x39631,x39632),x39633),x39634)),x39635)),f333(f333(f311(x39632),x39634),f333(f259(x39631,x39632),x39635))) % 191.49/191.40 [3964]E(f333(f261(x39641,x39642),f333(f333(f311(f889(x39641,x39642)),f333(f333(f263(x39641,x39642),x39643),x39644)),x39645)),f333(f333(f311(x39641),x39643),f333(f261(x39641,x39642),x39645))) % 191.49/191.40 [4010]E(f125(x40101,x40102,f333(x40103,x40104),f333(f333(f9(x40101,a104,f882(f884(x40102))),x40105),x40104)),f333(f204(x40101,x40102,x40103,x40105),x40104)) % 191.49/191.40 [4039]E(f333(f333(f115(f890(f889(x40391,x40392),a874)),f333(f333(f270(x40391,x40392),x40393),x40394)),f333(f333(f270(x40391,x40392),x40395),x40394)),f333(f333(f270(x40391,x40392),f333(f333(f115(f890(x40391,a874)),x40393),x40395)),x40394)) % 191.49/191.40 [4040]E(f333(f333(f3(f890(f889(x40401,x40402),a874)),f333(f333(f270(x40401,x40402),x40403),x40404)),f333(f333(f270(x40401,x40402),x40405),x40404)),f333(f333(f270(x40401,x40402),f333(f333(f3(f890(x40401,a874)),x40403),x40405)),x40404)) % 191.49/191.40 [4041]E(f333(f333(f106(f890(f889(x40411,x40412),a874)),f333(f333(f270(x40411,x40412),x40413),x40414)),f333(f333(f270(x40411,x40412),x40415),x40414)),f333(f333(f270(x40411,x40412),f333(f333(f106(f890(x40411,a874)),x40413),x40415)),x40414)) % 191.49/191.40 [4100]E(f333(f333(f106(f890(x41001,a874)),f333(f333(f43(x41002,f890(x41001,a874)),x41003),x41004)),f333(f333(f43(x41002,f890(x41001,a874)),x41005),x41004)),f333(f333(f43(x41002,f890(x41001,a874)),f333(f333(f115(f890(x41002,a874)),x41003),x41005)),x41004)) % 191.49/191.40 [4101]E(f333(f333(f115(f890(x41011,a874)),f333(f333(f44(x41012,f890(x41011,a874)),x41013),x41014)),f333(f333(f44(x41012,f890(x41011,a874)),x41015),x41014)),f333(f333(f44(x41012,f890(x41011,a874)),f333(f333(f115(f890(x41012,a874)),x41013),x41015)),x41014)) % 191.49/191.40 [4115]E(f333(f333(f43(x41151,f890(x41152,a874)),x41153),f333(f333(f10(f890(x41152,a874),f890(x41152,a874),x41151),f333(f115(f890(x41152,a874)),x41154)),x41155)),f333(f333(f115(f890(x41152,a874)),x41154),f333(f333(f43(x41151,f890(x41152,a874)),x41153),x41155))) % 191.49/191.40 [4116]E(f333(f333(f44(x41161,f890(x41162,a874)),x41163),f333(f333(f10(f890(x41162,a874),f890(x41162,a874),x41161),f333(f3(f890(x41162,a874)),x41164)),x41165)),f333(f333(f3(f890(x41162,a874)),x41164),f333(f333(f43(x41161,f890(x41162,a874)),x41163),x41165))) % 191.49/191.40 [4117]E(f333(f333(f44(x41171,f890(x41172,a874)),x41173),f333(f333(f10(f890(x41172,a874),f890(x41172,a874),x41171),f333(f106(f890(x41172,a874)),x41174)),x41175)),f333(f333(f106(f890(x41172,a874)),x41174),f333(f333(f44(x41171,f890(x41172,a874)),x41173),x41175))) % 191.49/191.40 [4151]E(f185(x41511,x41512,x41513,f333(f178(x41511,x41512),f333(f170(f889(x41511,x41512)),f333(f333(f182(x41511,x41512),x41514),x41515)))),f187(x41511,x41512,x41513,x41514,x41515)) % 191.49/191.40 [4171]E(f191(f881(x41711),f333(f333(f152(x41711),x41712),x41713),f333(f333(f10(f881(x41711),f881(x41711),a880),f333(f152(x41711),x41714)),f333(f333(f9(a880,x41711,f881(x41711)),f160(x41711,x41713)),x41712)),x41715),f333(f333(f160(x41711,f333(f333(f152(x41711),x41714),x41713)),x41715),x41712)) % 191.49/191.40 [4175]E(f333(f333(f43(x41751,f890(f889(x41752,x41753),a874)),x41754),f333(f333(f10(f890(f889(x41753,x41752),a874),f890(f889(x41752,x41753),a874),x41751),f288(x41753,x41752)),x41755)),f333(f288(x41753,x41752),f333(f333(f43(x41751,f890(f889(x41753,x41752),a874)),x41754),x41755))) % 191.49/191.40 [4176]E(f333(f333(f44(x41761,f890(f889(x41762,x41763),a874)),x41764),f333(f333(f10(f890(f889(x41763,x41762),a874),f890(f889(x41762,x41763),a874),x41761),f288(x41763,x41762)),x41765)),f333(f288(x41763,x41762),f333(f333(f44(x41761,f890(f889(x41763,x41762),a874)),x41764),x41765))) % 191.49/191.40 [4236]E(f184(x42361,x42362,f333(f333(f20(x42361,f884(x42363),f884(x42362)),f333(f333(f10(f890(x42363,x42362),f890(f884(x42363),f884(x42362)),x42361),f208(x42363,x42362)),x42364)),x42365)),f184(x42361,x42363,x42365)) % 191.49/191.40 [4287]P4(f333(f333(f250(f890(x42871,a874)),f333(f333(f3(f890(x42871,a874)),f333(f312(x42872,x42871,x42873),x42874)),f333(f312(x42872,x42871,x42873),x42875))),f333(f312(x42872,x42871,x42873),f333(f333(f3(f890(x42872,a874)),x42874),x42875)))) % 191.49/191.40 [4452]E(f333(f157(f881(f889(x44521,x44522)),x44521,f118(f889(x44521,x44522)),f333(f333(f9(x44521,f890(f881(x44521),f881(f889(x44521,x44522))),f890(f881(x44521),f881(f889(x44521,x44522)))),f333(f333(f10(f890(f881(f889(x44521,x44522)),f881(f889(x44521,x44522))),f890(f890(f881(x44521),f881(f889(x44521,x44522))),f890(f881(x44521),f881(f889(x44521,x44522)))),x44521),f10(f881(f889(x44521,x44522)),f881(f889(x44521,x44522)),f881(x44521))),f333(f333(f10(f889(x44521,x44522),f890(f881(f889(x44521,x44522)),f881(f889(x44521,x44522))),x44521),f152(f889(x44521,x44522))),f333(f333(f9(x44521,x44522,f889(x44521,x44522)),f263(x44521,x44522)),x44523)))),f333(f333(f9(f881(x44521),f881(x44522),f881(f889(x44521,x44522))),f182(x44521,x44522)),x44524))),x44525),f333(f333(f182(x44521,x44522),x44525),f333(f333(f152(x44522),x44523),x44524))) % 191.49/191.40 [4139]E(f333(f333(f115(f890(x41391,a874)),f333(f287(x41392,x41391,x41393),x41394)),f333(f287(x41392,x41391,x41395),x41394)),f333(f287(x41392,x41391,f333(f333(f115(f890(f889(x41392,x41391),a874)),x41393),x41395)),x41394)) % 191.49/191.40 [4178]E(f333(f333(f127(f889(x41781,x41782)),f333(f333(f182(x41781,x41782),x41783),f333(f333(f174(x41782),f333(f195(f881(x41781)),x41783)),x41784))),f333(f333(f182(x41781,x41782),x41785),f333(f333(f139(x41782),f333(f195(f881(x41781)),x41783)),x41784))),f333(f333(f182(x41781,x41782),f333(f333(f127(x41781),x41783),x41785)),x41784)) % 191.49/191.40 [4292]E(f333(f333(f270(x42921,x42922),x42923),f333(f333(f20(x42921,f890(x42922,a874),f890(x42922,a874)),f333(f333(f10(f890(x42922,a874),f890(f890(x42922,a874),f890(x42922,a874)),x42921),f115(f890(x42922,a874))),x42924)),x42925)),f333(f333(f115(f890(f889(x42921,x42922),a874)),f333(f333(f270(x42921,x42922),x42923),x42924)),f333(f333(f270(x42921,x42922),x42923),x42925))) % 191.49/191.40 [4293]E(f333(f333(f270(x42931,x42932),x42933),f333(f333(f20(x42931,f890(x42932,a874),f890(x42932,a874)),f333(f333(f10(f890(x42932,a874),f890(f890(x42932,a874),f890(x42932,a874)),x42931),f3(f890(x42932,a874))),x42934)),x42935)),f333(f333(f3(f890(f889(x42931,x42932),a874)),f333(f333(f270(x42931,x42932),x42933),x42934)),f333(f333(f270(x42931,x42932),x42933),x42935))) % 191.49/191.40 [4294]E(f333(f333(f270(x42941,x42942),x42943),f333(f333(f20(x42941,f890(x42942,a874),f890(x42942,a874)),f333(f333(f10(f890(x42942,a874),f890(f890(x42942,a874),f890(x42942,a874)),x42941),f106(f890(x42942,a874))),x42944)),x42945)),f333(f333(f106(f890(f889(x42941,x42942),a874)),f333(f333(f270(x42941,x42942),x42943),x42944)),f333(f333(f270(x42941,x42942),x42943),x42945))) % 191.49/191.40 [4298]E(f333(f333(f43(x42981,f890(x42982,a874)),x42983),f333(f333(f9(x42981,f890(x42982,a874),f890(x42982,a874)),f333(f333(f10(f890(x42982,a874),f890(f890(x42982,a874),f890(x42982,a874)),x42981),f115(f890(x42982,a874))),x42984)),x42985)),f333(f333(f115(f890(x42982,a874)),f333(f333(f43(x42981,f890(x42982,a874)),x42983),x42984)),x42985)) % 191.49/191.40 [4299]E(f333(f333(f44(x42991,f890(x42992,a874)),x42993),f333(f333(f9(x42991,f890(x42992,a874),f890(x42992,a874)),f333(f333(f10(f890(x42992,a874),f890(f890(x42992,a874),f890(x42992,a874)),x42991),f3(f890(x42992,a874))),x42994)),x42995)),f333(f333(f3(f890(x42992,a874)),f333(f333(f44(x42991,f890(x42992,a874)),x42993),x42994)),x42995)) % 191.49/191.40 [4300]E(f333(f333(f44(x43001,f890(x43002,a874)),x43003),f333(f333(f9(x43001,f890(x43002,a874),f890(x43002,a874)),f333(f333(f10(f890(x43002,a874),f890(f890(x43002,a874),f890(x43002,a874)),x43001),f106(f890(x43002,a874))),x43004)),x43005)),f333(f333(f106(f890(x43002,a874)),f333(f333(f44(x43001,f890(x43002,a874)),x43003),x43004)),x43005)) % 191.49/191.40 [4304]E(f333(f333(f43(x43041,f890(x43042,a874)),x43043),f333(f333(f20(x43041,f890(x43042,a874),f890(x43042,a874)),f333(f333(f10(f890(x43042,a874),f890(f890(x43042,a874),f890(x43042,a874)),x43041),f106(f890(x43042,a874))),x43044)),x43045)),f333(f333(f106(f890(x43042,a874)),f333(f333(f43(x43041,f890(x43042,a874)),x43043),x43044)),f333(f333(f43(x43041,f890(x43042,a874)),x43043),x43045))) % 191.49/191.40 [4305]E(f333(f333(f44(x43051,f890(x43052,a874)),x43053),f333(f333(f20(x43051,f890(x43052,a874),f890(x43052,a874)),f333(f333(f10(f890(x43052,a874),f890(f890(x43052,a874),f890(x43052,a874)),x43051),f115(f890(x43052,a874))),x43054)),x43055)),f333(f333(f115(f890(x43052,a874)),f333(f333(f44(x43051,f890(x43052,a874)),x43053),x43054)),f333(f333(f44(x43051,f890(x43052,a874)),x43053),x43055))) % 191.49/191.40 [4315]E(f333(f333(f43(x43151,f890(x43152,a874)),x43153),f333(f333(f20(x43151,f890(x43152,a874),f890(x43152,a874)),f333(f333(f10(f890(x43152,a874),f890(f890(x43152,a874),f890(x43152,a874)),x43151),f106(f890(x43152,a874))),x43154)),x43155)),f333(f333(f106(f890(x43152,a874)),f42(f890(x43152,a874),f333(f312(x43151,f890(x43152,a874),x43154),x43153))),f42(f890(x43152,a874),f333(f312(x43151,f890(x43152,a874),x43155),x43153)))) % 191.49/191.40 [4316]E(f333(f333(f44(x43161,f890(x43162,a874)),x43163),f333(f333(f20(x43161,f890(x43162,a874),f890(x43162,a874)),f333(f333(f10(f890(x43162,a874),f890(f890(x43162,a874),f890(x43162,a874)),x43161),f115(f890(x43162,a874))),x43164)),x43165)),f333(f333(f115(f890(x43162,a874)),f41(f890(x43162,a874),f333(f312(x43161,f890(x43162,a874),x43164),x43163))),f41(f890(x43162,a874),f333(f312(x43161,f890(x43162,a874),x43165),x43163)))) % 191.49/191.40 [4352]E(f333(f333(f139(x43521),f333(f195(f881(x43521)),f177(x43521,x43522,f333(f333(f155(x43523,x43521),x43524),x43525)))),f333(f333(f155(x43523,x43521),x43524),x43525)),f333(f333(f155(x43523,x43521),x43524),f333(f333(f139(x43523),f333(f195(f881(x43523)),f177(x43523,f333(f74(x43521,a874,x43523,x43522),x43524),x43525))),x43525))) % 191.49/191.40 [4229]E(f333(f333(f127(f889(x42291,x42292)),f333(f333(f182(x42291,x42292),f333(f333(f174(x42291),f333(f195(f881(x42292)),x42293)),x42294)),x42293)),f333(f333(f182(x42291,x42292),f333(f333(f139(x42291),f333(f195(f881(x42292)),x42293)),x42294)),x42295)),f333(f333(f182(x42291,x42292),x42294),f333(f333(f127(x42292),x42293),x42295))) % 191.49/191.40 [4343]E(f86(x43431,f333(f333(f20(x43431,a874,a874),f333(f333(f10(a874,f890(a874,a874),x43431),a331),f333(f333(f9(x43431,f890(x43431,a874),a874),f335(x43431)),x43432))),f333(f333(f9(x43431,x43433,a874),f333(f333(f10(x43433,f890(x43433,a874),x43431),a330),x43434)),x43435))),f333(f78(x43431,x43433,x43432,x43434),x43435)) % 191.49/191.40 [4399]E(f333(f333(f89(a1,x43991),f333(f108(a1),f333(f333(f81(a1),x43992),a102))),f333(f333(f20(a1,x43991,x43991),f333(f333(f9(a1,x43991,f890(x43991,x43991)),f333(f333(f10(a874,f890(x43991,f890(x43991,x43991)),a1),f101(x43991)),a200)),f191(x43991,x43993,x43994,x43995))),f333(f333(f10(a880,x43991,a1),x43994),f333(f333(f9(a1,a880,a880),f333(f333(f10(a880,f890(a880,a880),a1),f81(a880)),a109)),x43995)))),f191(x43991,x43993,x43994,f333(f333(f81(a880),f333(f108(a880),x43992)),x43995))) % 191.49/191.40 [4449]E(f333(f178(x44491,x44492),f333(f333(f155(f889(x44491,x44493),f889(x44491,x44492)),f333(f272(x44491,x44493,f889(x44491,x44492)),f333(f333(f9(x44491,f890(x44493,x44492),f890(x44493,f889(x44491,x44492))),f333(f333(f10(f890(x44492,f889(x44491,x44492)),f890(f890(x44493,x44492),f890(x44493,f889(x44491,x44492))),x44491),f10(x44492,f889(x44491,x44492),x44493)),f263(x44491,x44492))),x44494))),x44495)),f333(f74(f884(x44493),f884(x44492),x44491,f333(f208(x44493,x44492),x44494)),f333(f178(x44491,x44493),x44495))) % 191.49/191.40 [4392]E(f184(x43921,x43922,f333(f333(f20(x43921,f884(x43922),f884(x43922)),f333(f333(f20(x43921,f884(x43922),f890(f884(x43922),f884(x43922))),f333(f333(f10(a874,f890(f884(x43922),f890(f884(x43922),f884(x43922))),x43921),f101(f884(x43922))),x43923)),x43924)),x43925)),f333(f333(f115(f890(x43921,a874)),f333(f333(f106(f890(x43921,a874)),f184(x43921,x43922,x43924)),f333(f255(x43921),x43923))),f333(f333(f106(f890(x43921,a874)),f184(x43921,x43922,x43925)),f333(f255(x43921),f333(f333(f10(a874,a874,x43921),a328),x43923))))) % 191.49/191.40 [4445]E(f333(f333(f89(a1,x44451),f333(f108(a1),f333(f333(f81(a1),x44452),a102))),f333(f333(f20(a1,x44451,x44451),f333(f333(f9(a1,x44451,f890(x44451,x44451)),f333(f333(f10(a874,f890(x44451,f890(x44451,x44451)),a1),f101(x44451)),a200)),f333(f190(x44451,x44453,x44454),x44455))),f333(f333(f20(a1,x44451,x44451),f333(f333(f10(a880,f890(x44451,x44451),a1),x44454),f333(f333(f9(a1,a880,a880),f333(f333(f10(a880,f890(a880,a880),a1),f81(a880)),a109)),x44455))),f333(f333(f10(a880,x44451,a1),f190(x44451,x44453,x44454)),f333(f333(f9(a1,a880,a880),f333(f333(f10(a880,f890(a880,a880),a1),f81(a880)),a109)),x44455))))),f333(f190(x44451,x44453,x44454),f333(f333(f81(a880),f333(f108(a880),x44452)),x44455))) % 191.49/191.40 [4478]E(f333(f255(f889(x44781,x44782)),f333(f272(x44781,x44782,a874),f333(f333(f10(f890(x44782,f890(x44783,a874)),f890(x44782,a874),x44781),f333(f10(f890(x44783,a874),a874,x44782),f87(x44783))),f333(f333(f9(x44781,f890(x44782,f890(x44783,a874)),f890(x44782,f890(x44783,a874))),f333(f333(f10(f890(f890(x44783,a874),f890(x44783,a874)),f890(f890(x44782,f890(x44783,a874)),f890(x44782,f890(x44783,a874))),x44781),f10(f890(x44783,a874),f890(x44783,a874),x44782)),f333(f333(f10(f890(x44783,f890(a874,a874)),f890(f890(x44783,a874),f890(x44783,a874)),x44781),f20(x44783,a874,a874)),f333(f333(f10(f890(x44783,a874),f890(x44783,f890(a874,a874)),x44781),f333(f10(a874,f890(a874,a874),x44783),a331)),f333(f333(f9(x44781,f890(f889(x44781,x44783),a874),f890(x44783,a874)),f333(f333(f10(f890(x44783,f890(f890(f889(x44781,x44783),a874),a874)),f890(f890(f889(x44781,x44783),a874),f890(x44783,a874)),x44781),f9(x44783,f890(f889(x44781,x44783),a874),a874)),f333(f333(f10(f890(x44783,f889(x44781,x44783)),f890(x44783,f890(f890(f889(x44781,x44783),a874),a874)),x44781),f333(f10(f889(x44781,x44783),f890(f890(f889(x44781,x44783),a874),a874),x44783),f335(f889(x44781,x44783)))),f263(x44781,x44783)))),x44784))))),f333(f333(f9(x44782,f890(f889(x44783,x44782),a874),f890(x44783,a874)),f333(f333(f10(f890(x44783,f890(f890(f889(x44783,x44782),a874),a874)),f890(f890(f889(x44783,x44782),a874),f890(x44783,a874)),x44782),f9(x44783,f890(f889(x44783,x44782),a874),a874)),f333(f333(f10(f890(x44783,f889(x44783,x44782)),f890(x44783,f890(f890(f889(x44783,x44782),a874),a874)),x44782),f333(f10(f889(x44783,x44782),f890(f890(f889(x44783,x44782),a874),a874),x44783),f335(f889(x44783,x44782)))),f333(f9(x44783,x44782,f889(x44783,x44782)),f263(x44783,x44782))))),x44785))))),f333(f333(f290(x44781,x44783,x44782),x44784),x44785)) % 191.49/191.40 [4562]~E(f31(x45621,x45622,x45623),f29(x45624,x45625,x45626)) % 191.49/191.40 [4565]~E(f30(x45651,x45652,x45653),f29(x45654,x45655,x45656)) % 191.49/191.40 [4566]~E(f30(x45661,x45662,x45663),f31(x45664,x45665,x45666)) % 191.49/191.40 [3998]E(f132(x39981,x39982,x39983,x39984,f129(x39982,x39985,x39986)),f333(f333(x39984,x39985),x39986)) % 191.49/191.40 [4068]E(f233(x40681,x40682,x40683,x40684,f230(x40681,x40682,x40685,x40686)),f333(f333(x40684,x40685),x40686)) % 191.49/191.40 [4069]E(f234(x40691,x40692,x40693,x40694,f230(x40691,x40692,x40695,x40696)),f333(f333(x40694,x40695),x40696)) % 191.49/191.40 [4208]E(f187(x42081,x42082,f185(x42081,x42082,x42083,x42084),x42085,x42086),f185(x42081,x42082,x42083,f187(x42081,x42082,x42084,x42085,x42086))) % 191.49/191.40 [4332]E(f333(f74(f889(x43321,x43322),x43322,f889(x43323,x43324),f271(x43321,x43322)),f273(x43323,x43321,x43324,x43322,x43325,x43326)),f333(f74(x43324,x43322,f889(x43323,x43324),x43326),f271(x43323,x43324))) % 191.49/191.40 [4333]E(f333(f74(f889(x43331,x43332),x43331,f889(x43333,x43334),f262(x43331,x43332)),f273(x43333,x43331,x43334,x43332,x43335,x43336)),f333(f74(x43333,x43331,f889(x43333,x43334),x43335),f262(x43333,x43334))) % 191.49/191.40 [3938]E(f333(f333(f74(x39381,x39382,x39383,x39384),x39385),x39386),f333(x39384,f333(x39385,x39386))) % 191.49/191.40 [4128]E(f235(x41281,x41282,x41283,x41284,f230(x41281,x41282,x41285,x41286)),f333(f333(f81(a880),f333(f333(f81(a880),f333(x41283,x41285)),f333(x41284,x41286))),f333(a117,f2(a880)))) % 191.49/191.40 [3739]E(f333(f333(f272(x37391,x37392,x37393),x37394),f333(f333(f263(x37391,x37392),x37395),x37396)),f333(f333(x37394,x37395),x37396)) % 191.49/191.40 [3801]E(f333(f333(f333(f10(x38011,x38012,x38013),x38014),x38015),x38016),f333(x38014,f333(x38015,x38016))) % 191.49/191.40 [3802]E(f333(f333(f333(f9(x38021,x38022,x38023),x38024),x38025),x38026),f333(f333(x38024,x38026),x38025)) % 191.49/191.40 [3820]E(f333(f333(f333(f20(x38201,x38202,x38203),x38204),x38205),x38206),f333(f333(x38204,x38206),f333(x38205,x38206))) % 191.49/191.40 [3839]E(f333(f157(x38391,x38392,x38393,x38394),f333(f333(f152(x38392),x38395),x38396)),f333(f333(x38394,x38395),x38396)) % 191.49/191.40 [3943]E(f333(f333(f152(f889(x39431,x39432)),f333(f333(f263(x39431,x39432),x39433),x39434)),f333(f333(f182(x39431,x39432),x39435),x39436)),f333(f333(f182(x39431,x39432),f333(f333(f152(x39431),x39433),x39435)),f333(f333(f152(x39432),x39434),x39436))) % 191.49/191.40 [3945]E(f333(f333(f155(x39451,x39452),x39453),f333(f333(f160(x39451,x39454),x39455),x39456)),f333(f333(f160(x39452,f333(f333(f155(x39451,x39452),x39453),x39454)),x39455),f333(x39453,x39456))) % 191.49/191.40 [3987]E(f333(f143(x39871,x39872,x39873,x39874),f333(f333(f152(x39872),x39875),x39876)),f333(f143(x39871,x39872,x39873,f333(f333(x39873,x39874),x39875)),x39876)) % 191.49/191.40 [4011]E(f275(x40111,x40112,x40113,x40114,f333(f333(f263(x40111,x40112),x40115),x40116)),f333(f333(x40114,x40115),x40116)) % 191.49/191.40 [4094]E(f333(f333(f44(x40941,f890(x40942,a874)),x40943),f333(f74(x40944,f890(x40942,a874),x40941,x40945),x40946)),f333(f333(f44(x40944,f890(x40942,a874)),f333(f312(x40941,x40944,x40946),x40943)),x40945)) % 191.49/191.40 [4142]E(f333(f333(f155(x41421,x41422),x41423),f333(f333(f155(x41424,x41421),x41425),x41426)),f333(f333(f155(x41424,x41422),f333(f74(x41421,x41422,x41424,x41423),x41425)),x41426)) % 191.49/191.40 [4144]E(f333(f333(f208(x41441,x41442),x41443),f333(f333(f208(x41444,x41441),x41445),x41446)),f333(f333(f208(x41444,x41442),f333(f74(x41441,x41442,x41444,x41443),x41445)),x41446)) % 191.49/191.40 [4149]E(f333(f313(x41491,x41492,f333(f74(x41493,x41492,x41491,x41494),x41495)),x41496),f333(f313(x41491,x41493,x41495),f333(f313(x41493,x41492,x41494),x41496))) % 191.49/191.40 [4150]E(f333(f312(x41501,x41502,f333(f74(x41503,x41502,x41501,x41504),x41505)),x41506),f333(f312(x41503,x41502,x41504),f333(f312(x41501,x41503,x41505),x41506))) % 191.49/191.40 [4177]E(f185(x41771,x41772,x41773,f333(f333(f333(f73(x41771,f884(x41772)),x41774),x41775),f333(f242(x41772),x41776))),f333(f333(f333(f73(x41771,f884(x41772)),f185(x41771,x41772,x41773,x41774)),x41775),f333(f242(x41772),x41776))) % 191.49/191.40 [4179]E(f333(f143(x41791,x41792,x41793,f333(f143(x41791,x41792,x41793,x41794),x41795)),x41796),f333(f143(x41791,x41792,x41793,x41794),f333(f333(f127(x41792),x41795),x41796))) % 191.49/191.40 [4320]E(f333(f273(x43201,x43201,x43202,x43203,f35(x43201),x43204),f333(f333(f263(x43201,x43202),x43205),x43206)),f333(f333(f263(x43201,x43203),x43205),f333(x43204,x43206))) % 191.49/191.40 [4321]E(f333(f273(x43211,x43212,x43213,x43213,x43214,f35(x43213)),f333(f333(f263(x43211,x43213),x43215),x43216)),f333(f333(f263(x43212,x43213),f333(x43214,x43215)),x43216)) % 191.49/191.40 [4425]E(f333(f333(f155(f889(x44251,x44252),f889(x44251,x44253)),f333(f272(x44251,x44252,f889(x44251,x44253)),f333(f333(f9(x44251,f890(x44252,x44253),f890(x44252,f889(x44251,x44253))),f333(f333(f10(f890(x44253,f889(x44251,x44253)),f890(f890(x44252,x44253),f890(x44252,f889(x44251,x44253))),x44251),f10(x44253,f889(x44251,x44253),x44252)),f263(x44251,x44253))),x44254))),f333(f333(f182(x44251,x44252),x44255),x44256)),f333(f333(f182(x44251,x44253),x44255),f333(f333(f155(x44252,x44253),x44254),x44256))) % 191.49/191.40 [3807]E(f99(x38071,x38072,x38073,f333(f333(f333(f93(x38071),x38074),x38075),x38076)),f333(f333(f333(x38073,x38074),x38075),x38076)) % 191.49/191.40 [3808]E(f100(x38081,x38082,x38083,f333(f333(f333(f93(x38081),x38084),x38085),x38086)),f333(f333(f333(x38083,x38084),x38085),x38086)) % 191.49/191.40 [3997]E(f333(f333(f74(x39971,x39972,x39973,f333(f18(x39972,x39971),x39974)),x39975),x39976),x39974) % 191.49/191.40 [4030]E(f333(f312(x40301,x40302,x40303),f333(f312(x40304,x40301,x40305),x40306)),f333(f312(x40304,x40302,f333(f333(f10(x40301,x40302,x40304),x40303),x40305)),x40306)) % 191.49/191.40 [4035]E(f333(f333(f43(x40351,f890(x40352,a874)),f333(f312(x40353,x40351,x40354),x40355)),x40356),f333(f333(f43(x40353,f890(x40352,a874)),x40355),f333(f333(f10(x40351,f890(x40352,a874),x40353),x40356),x40354))) % 191.49/191.40 [4036]E(f333(f333(f44(x40361,f890(x40362,a874)),f333(f312(x40363,x40361,x40364),x40365)),x40366),f333(f333(f44(x40363,f890(x40362,a874)),x40365),f333(f333(f10(x40361,f890(x40362,a874),x40363),x40366),x40364))) % 191.49/191.40 [4037]E(f333(f333(f43(x40371,f890(x40372,a874)),x40373),f333(f333(f10(x40374,f890(x40372,a874),x40371),x40375),x40376)),f333(f333(f43(x40374,f890(x40372,a874)),f333(f312(x40371,x40374,x40376),x40373)),x40375)) % 191.49/191.40 [4038]E(f333(f333(f44(x40381,f890(x40382,a874)),x40383),f333(f333(f10(x40384,f890(x40382,a874),x40381),x40385),x40386)),f333(f333(f44(x40384,f890(x40382,a874)),f333(f312(x40381,x40384,x40386),x40383)),x40385)) % 191.49/191.40 [4096]E(f333(f333(f43(x40961,f890(x40962,a874)),x40963),f333(f333(f10(f890(x40964,a874),f890(x40962,a874),x40961),f313(x40962,x40964,x40965)),x40966)),f333(f313(x40962,x40964,x40965),f333(f333(f43(x40961,f890(x40964,a874)),x40963),x40966))) % 191.49/191.40 [4097]E(f333(f333(f44(x40971,f890(x40972,a874)),x40973),f333(f333(f10(f890(x40974,a874),f890(x40972,a874),x40971),f313(x40972,x40974,x40975)),x40976)),f333(f313(x40972,x40974,x40975),f333(f333(f44(x40971,f890(x40974,a874)),x40973),x40976))) % 191.49/191.40 [4098]E(f333(f333(f44(x40981,f890(x40982,a874)),x40983),f333(f333(f10(f890(x40984,a874),f890(x40982,a874),x40981),f312(x40984,x40982,x40985)),x40986)),f333(f312(x40984,x40982,x40985),f333(f333(f44(x40981,f890(x40984,a874)),x40983),x40986))) % 191.49/191.40 [4099]E(f333(f333(f44(x40991,f890(x40992,a874)),x40993),f333(f333(f10(f890(x40994,a874),f890(x40992,a874),x40991),f287(x40994,x40992,x40995)),x40996)),f333(f287(x40994,x40992,x40995),f333(f333(f44(x40991,f890(x40994,a874)),x40993),x40996))) % 191.49/191.40 [4185]E(f333(f143(x41851,x41852,f333(f9(x41852,x41851,x41851),x41853),x41854),f333(f170(x41852),f333(f333(f152(x41852),x41855),x41856))),f333(f333(x41853,x41855),f333(f143(x41851,x41852,f333(f9(x41852,x41851,x41851),x41853),x41854),f333(f170(x41852),x41856)))) % 191.49/191.40 [4249]E(f333(f333(f20(f889(x42491,x42492),x42492,x42493),f333(f333(f10(x42494,f890(x42492,x42493),f889(x42491,x42492)),x42495),f333(f333(f10(x42491,x42494,f889(x42491,x42492)),x42496),f262(x42491,x42492)))),f271(x42491,x42492)),f333(f272(x42491,x42492,x42493),f333(f333(f10(x42494,f890(x42492,x42493),x42491),x42495),x42496))) % 191.49/191.40 [4255]E(f333(f143(x42551,x42552,f333(f9(x42552,x42551,x42551),x42553),f333(f143(x42551,x42552,f333(f9(x42552,x42551,x42551),x42553),x42554),f333(f170(x42552),x42555))),f333(f170(x42552),x42556)),f333(f143(x42551,x42552,f333(f9(x42552,x42551,x42551),x42553),x42554),f333(f170(x42552),f333(f333(f127(x42552),x42556),x42555)))) % 191.49/191.40 [4257]E(f333(f333(f155(f889(x42571,x42572),f889(x42573,x42572)),f333(f272(x42571,x42572,f889(x42573,x42572)),f333(f333(f10(x42573,f890(x42572,f889(x42573,x42572)),x42571),f263(x42573,x42572)),x42574))),f333(f333(f182(x42571,x42572),x42575),x42576)),f333(f333(f182(x42573,x42572),f333(f333(f155(x42571,x42573),x42574),x42575)),x42576)) % 191.49/191.40 [4308]P4(f333(f333(f250(f890(x43081,a874)),f333(f287(x43082,x43081,x43083),f333(f333(f43(x43084,f890(x43082,a874)),x43085),x43086))),f333(f333(f43(x43084,f890(x43081,a874)),x43085),f333(f333(f10(f890(x43082,a874),f890(x43081,a874),x43084),f287(x43082,x43081,x43083)),x43086)))) % 191.49/191.40 [4108]E(f333(f333(f182(x41081,x41082),f333(f333(f160(x41081,x41083),x41084),f333(f262(x41081,x41082),x41085))),f333(f333(f160(x41082,x41086),x41084),f333(f271(x41081,x41082),x41085))),f333(f333(f160(f889(x41081,x41082),f333(f333(f182(x41081,x41082),x41083),x41086)),x41084),x41085)) % 191.49/191.40 [4166]E(f333(f333(f115(f890(f889(x41661,x41662),a874)),f333(f333(f290(x41661,x41663,x41662),x41664),x41665)),f333(f333(f290(x41661,x41663,x41662),x41664),x41666)),f333(f333(f290(x41661,x41663,x41662),x41664),f333(f333(f115(f890(f889(x41663,x41662),a874)),x41665),x41666))) % 191.49/191.40 [4270]E(f333(f333(f311(f889(x42701,x42702)),f333(f333(f263(x42701,x42702),x42703),x42704)),f333(f333(f115(f890(f889(x42701,x42702),a874)),f333(f333(f270(x42701,x42702),x42705),f333(f18(f890(x42702,a874),x42701),f333(f333(f311(x42702),x42704),x42706)))),f333(f333(f270(x42701,x42702),f333(f333(f311(x42701),x42703),x42705)),f333(f18(f890(x42702,a874),x42701),x42706)))),f333(f333(f270(x42701,x42702),f333(f333(f311(x42701),x42703),x42705)),f333(f18(f890(x42702,a874),x42701),f333(f333(f311(x42702),x42704),x42706)))) % 191.49/191.40 [4347]E(f333(f333(f106(f890(x43471,a874)),f333(f313(x43471,x43472,f333(f74(f889(x43472,x43473),x43472,x43471,f262(x43472,x43473)),x43474)),x43475)),f333(f313(x43471,x43473,f333(f74(f889(x43472,x43473),x43473,x43471,f271(x43472,x43473)),x43474)),x43476)),f333(f313(x43471,f889(x43472,x43473),x43474),f333(f333(f270(x43472,x43473),x43475),f333(f18(f890(x43473,a874),x43472),x43476)))) % 191.49/191.40 [4093]E(f333(f333(f333(f73(x40931,x40932),f333(f333(f333(f73(x40931,x40932),x40933),x40934),x40935)),x40934),x40936),f333(f333(f333(f73(x40931,x40932),x40933),x40934),x40936)) % 191.49/191.40 [4191]E(f333(f333(f115(f890(f889(x41911,x41912),a874)),f333(f333(f290(x41911,x41913,x41912),x41914),x41915)),f333(f333(f290(x41911,x41913,x41912),x41916),x41915)),f333(f333(f290(x41911,x41913,x41912),f333(f333(f115(f890(f889(x41911,x41913),a874)),x41914),x41916)),x41915)) % 191.49/191.40 [4330]E(f333(f333(f43(x43301,f890(x43302,a874)),x43303),f333(f333(f9(x43301,f890(x43304,f890(x43302,a874)),f890(x43302,a874)),f333(f333(f10(f890(x43304,a874),f890(f890(x43304,f890(x43302,a874)),f890(x43302,a874)),x43301),f43(x43304,f890(x43302,a874))),x43305)),x43306)),f333(f333(f43(x43304,f890(x43302,a874)),f333(f333(f44(x43301,f890(x43304,a874)),x43303),x43305)),x43306)) % 191.49/191.40 [4331]E(f333(f333(f44(x43311,f890(x43312,a874)),x43313),f333(f333(f9(x43311,f890(x43314,f890(x43312,a874)),f890(x43312,a874)),f333(f333(f10(f890(x43314,a874),f890(f890(x43314,f890(x43312,a874)),f890(x43312,a874)),x43311),f44(x43314,f890(x43312,a874))),x43315)),x43316)),f333(f333(f44(x43314,f890(x43312,a874)),f333(f333(f44(x43311,f890(x43314,a874)),x43313),x43315)),x43316)) % 191.49/191.40 [4387]E(f333(f272(x43871,x43872,f889(x43873,x43874)),f333(f333(f9(x43871,f890(x43872,x43874),f890(x43872,f889(x43873,x43874))),f333(f333(f10(f890(x43874,f889(x43873,x43874)),f890(f890(x43872,x43874),f890(x43872,f889(x43873,x43874))),x43871),f10(x43874,f889(x43873,x43874),x43872)),f333(f333(f10(x43873,f890(x43874,f889(x43873,x43874)),x43871),f263(x43873,x43874)),x43875))),x43876)),f273(x43871,x43873,x43872,x43874,x43875,x43876)) % 191.49/191.40 [4307]E(f333(f333(f333(f73(x43071,f884(x43072)),f188(x43071,x43072,x43073,f333(f333(f3(f890(x43071,a874)),x43074),f333(f333(f311(x43071),x43075),f194(f890(x43071,a874)))))),x43075),x43076),f333(f333(f333(f73(x43071,f884(x43072)),f188(x43071,x43072,x43073,x43074)),x43075),x43076)) % 191.49/191.40 [4418]E(f333(f312(x44181,x44182,f333(f333(f20(x44181,x44182,x44182),f333(f333(f20(x44181,x44182,f890(x44182,x44182)),f333(f333(f10(a874,f890(x44182,f890(x44182,x44182)),x44181),f101(x44182)),x44183)),x44184)),x44185)),x44186),f333(f333(f115(f890(x44182,a874)),f333(f312(x44181,x44182,x44184),f333(f333(f106(f890(x44181,a874)),x44186),f333(f255(x44181),x44183)))),f333(f312(x44181,x44182,x44185),f333(f333(f106(f890(x44181,a874)),x44186),f333(f255(x44181),f333(f333(f10(a874,a874,x44181),a328),x44183)))))) % 191.49/191.40 [4431]E(f333(f312(x44311,f889(x44312,x44313),f333(f333(f20(x44311,x44313,f889(x44312,x44313)),f333(f333(f10(x44312,f890(x44313,f889(x44312,x44313)),x44311),f263(x44312,x44313)),x44314)),x44315)),x44316),f333(f333(f270(x44312,x44313),f333(f312(x44311,x44312,x44314),x44316)),f333(f333(f10(f890(x44311,a874),f890(x44313,a874),x44312),f312(x44311,x44313,x44315)),f333(f333(f9(x44312,f890(x44311,a874),f890(x44311,a874)),f333(f333(f10(f890(x44311,a874),f890(f890(x44311,a874),f890(x44311,a874)),x44312),f106(f890(x44311,a874))),f333(f333(f10(f890(x44312,a874),f890(x44311,a874),x44312),f313(x44311,x44312,x44314)),f333(f333(f9(x44312,f890(x44312,a874),f890(x44312,a874)),f311(x44312)),f194(f890(x44312,a874)))))),x44316)))) % 191.49/191.40 [4371]E(f333(f271(x43711,x43712),f333(f273(x43713,x43711,x43714,x43712,x43715,x43716),x43717)),f333(x43716,f333(f271(x43713,x43714),x43717))) % 191.49/191.40 [4372]E(f333(f262(x43721,x43722),f333(f273(x43723,x43721,x43724,x43722,x43725,x43726),x43727)),f333(x43725,f333(f262(x43723,x43724),x43727))) % 191.49/191.40 [4070]E(f333(f333(f182(x40701,x40702),f333(f333(f160(x40701,x40703),x40704),x40705)),f333(f333(f160(x40702,x40706),x40704),x40707)),f333(f333(f160(f889(x40701,x40702),f333(f333(f182(x40701,x40702),x40703),x40706)),x40704),f333(f333(f263(x40701,x40702),x40705),x40707))) % 191.49/191.40 [4135]E(f333(f333(f333(f274(x41351,x41352,x41353,x41354),x41355),x41356),x41357),f333(f333(f272(x41352,x41353,x41354),x41356),f333(x41355,x41357))) % 191.49/191.40 [4148]E(f333(f333(f333(f274(x41481,x41482,x41483,x41484),x41485),x41486),x41487),f333(f333(x41486,f333(f262(x41482,x41483),f333(x41485,x41487))),f333(f271(x41482,x41483),f333(x41485,x41487)))) % 191.49/191.40 [4181]E(f187(x41811,x41812,f333(f333(f333(f73(x41811,f884(x41812)),x41813),x41814),f333(f242(x41812),x41815)),x41816,x41817),f187(x41811,x41812,x41813,f333(f333(f152(x41811),x41814),x41816),f333(f333(f152(x41812),x41815),x41817))) % 191.49/191.40 [4202]E(f333(f74(x42021,x42022,x42023,x42024),f333(f74(x42025,x42021,x42023,x42026),x42027)),f333(f74(x42025,x42022,x42023,f333(f74(x42021,x42022,x42025,x42024),x42026)),x42027)) % 191.49/191.40 [4265]E(f333(f74(f884(x42651),f884(x42652),x42653,f333(f208(x42651,x42652),x42654)),f333(f333(f333(f73(x42653,f884(x42651)),x42655),x42656),f333(f242(x42651),x42657))),f333(f333(f333(f73(x42653,f884(x42652)),f333(f74(f884(x42651),f884(x42652),x42653,f333(f208(x42651,x42652),x42654)),x42655)),x42656),f333(f242(x42652),f333(x42654,x42657)))) % 191.49/191.40 [4394]E(f333(f273(x43941,x43942,x43943,x43943,x43944,f35(x43943)),f333(f273(x43941,x43941,x43945,x43943,f35(x43941),x43946),x43947)),f333(f333(f263(x43942,x43943),f333(x43944,f333(f262(x43941,x43945),x43947))),f333(x43946,f333(f271(x43941,x43945),x43947)))) % 191.49/191.40 [4395]E(f333(f273(x43951,x43951,x43952,x43953,f35(x43951),x43954),f333(f273(x43955,x43951,x43952,x43952,x43956,f35(x43952)),x43957)),f333(f333(f263(x43951,x43953),f333(x43956,f333(f262(x43955,x43952),x43957))),f333(x43954,f333(f271(x43955,x43952),x43957)))) % 191.49/191.40 [4416]E(f333(f273(x44161,x44162,x44163,x44163,x44164,f35(x44163)),f333(f273(x44165,x44161,x44163,x44163,x44166,f35(x44163)),x44167)),f333(f273(x44165,x44162,x44163,x44163,f333(f74(x44161,x44162,x44165,x44164),x44166),f35(x44163)),x44167)) % 191.49/191.40 [4417]E(f333(f273(x44171,x44171,x44172,x44173,f35(x44171),x44174),f333(f273(x44171,x44171,x44175,x44172,f35(x44171),x44176),x44177)),f333(f273(x44171,x44171,x44175,x44173,f35(x44171),f333(f74(x44172,x44173,x44175,x44174),x44176)),x44177)) % 191.49/191.40 [4428]E(f333(f273(x44281,x44282,x44283,x44283,x44284,f35(x44283)),f333(f273(x44281,x44281,x44285,x44283,f35(x44281),x44286),x44287)),f333(f273(x44282,x44282,x44285,x44283,f35(x44282),x44286),f333(f273(x44281,x44282,x44285,x44285,x44284,f35(x44285)),x44287))) % 191.49/191.40 [4105]E(f333(f333(f290(x41051,x41052,x41053),f333(f333(f290(x41051,x41054,x41052),x41055),x41056)),x41057),f333(f333(f290(x41051,x41054,x41053),x41055),f333(f333(f290(x41054,x41052,x41053),x41056),x41057))) % 191.49/191.40 [4172]E(f333(f333(f272(x41721,x41722,x41723),f333(f74(x41724,f890(x41722,x41723),x41721,x41725),x41726)),x41727),f333(f333(x41725,f333(x41726,f333(f262(x41721,x41722),x41727))),f333(f271(x41721,x41722),x41727))) % 191.49/191.40 [4231]E(f333(f74(x42311,x42312,x42313,x42314),f333(f333(f333(f73(x42313,x42311),x42315),x42316),x42317)),f333(f333(f333(f73(x42313,x42312),f333(f74(x42311,x42312,x42313,x42314),x42315)),x42316),f333(x42314,x42317))) % 191.49/191.40 [4260]E(f333(f143(x42601,x42602,f333(f9(x42602,x42601,x42601),x42603),x42604),f333(f170(x42602),f333(f333(f155(x42605,x42602),x42606),x42607))),f333(f143(x42601,x42605,f333(f9(x42605,x42601,x42601),f333(f74(x42602,f890(x42601,x42601),x42605,x42603),x42606)),x42604),f333(f170(x42605),x42607))) % 191.49/191.40 [4203]E(f333(f333(f44(x42031,f890(f889(x42032,x42033),a874)),x42034),f333(f333(f10(f890(f889(x42035,x42033),a874),f890(f889(x42032,x42033),a874),x42031),f333(f290(x42032,x42035,x42033),x42036)),x42037)),f333(f333(f290(x42032,x42035,x42033),x42036),f333(f333(f44(x42031,f890(f889(x42035,x42033),a874)),x42034),x42037))) % 191.49/191.40 [4353]E(f333(f333(f44(x43531,f890(f889(x43532,x43533),a874)),x43534),f333(f333(f9(x43531,f890(f889(x43535,x43533),a874),f890(f889(x43532,x43533),a874)),f333(f333(f10(f890(f889(x43532,x43535),a874),f890(f890(f889(x43535,x43533),a874),f890(f889(x43532,x43533),a874)),x43531),f290(x43532,x43535,x43533)),x43536)),x43537)),f333(f333(f290(x43532,x43535,x43533),f333(f333(f44(x43531,f890(f889(x43532,x43535),a874)),x43534),x43536)),x43537)) % 191.49/191.40 [4354]E(f333(f143(x43541,x43542,f333(f333(f9(x43541,f890(x43542,x43543),f890(x43542,x43541)),f333(f333(f10(f890(x43543,x43541),f890(f890(x43542,x43543),f890(x43542,x43541)),x43541),f10(x43543,x43541,x43542)),x43544)),x43545),x43546),x43547),f333(f143(x43541,x43543,x43544,x43546),f333(f333(f155(x43542,x43543),x43545),x43547))) % 191.49/191.40 [4429]E(f333(f333(f43(x44291,f890(x44292,a874)),x44293),f333(f333(f10(f890(x44294,f890(x44292,a874)),f890(x44292,a874),x44291),f333(f43(x44294,f890(x44292,a874)),x44295)),f333(f333(f9(x44291,f890(x44294,f890(x44292,a874)),f890(x44294,f890(x44292,a874))),f333(f333(f10(f890(f890(x44292,a874),f890(x44292,a874)),f890(f890(x44294,f890(x44292,a874)),f890(x44294,f890(x44292,a874))),x44291),f10(f890(x44292,a874),f890(x44292,a874),x44294)),f333(f333(f10(f890(x44292,a874),f890(f890(x44292,a874),f890(x44292,a874)),x44291),f115(f890(x44292,a874))),x44296))),x44297))),f333(f333(f115(f890(x44292,a874)),f333(f333(f43(x44291,f890(x44292,a874)),x44293),x44296)),f333(f333(f43(x44294,f890(x44292,a874)),x44295),x44297))) % 191.49/191.40 [4430]E(f333(f333(f44(x44301,f890(x44302,a874)),x44303),f333(f333(f10(f890(x44304,f890(x44302,a874)),f890(x44302,a874),x44301),f333(f44(x44304,f890(x44302,a874)),x44305)),f333(f333(f9(x44301,f890(x44304,f890(x44302,a874)),f890(x44304,f890(x44302,a874))),f333(f333(f10(f890(f890(x44302,a874),f890(x44302,a874)),f890(f890(x44304,f890(x44302,a874)),f890(x44304,f890(x44302,a874))),x44301),f10(f890(x44302,a874),f890(x44302,a874),x44304)),f333(f333(f10(f890(x44302,a874),f890(f890(x44302,a874),f890(x44302,a874)),x44301),f106(f890(x44302,a874))),x44306))),x44307))),f333(f333(f106(f890(x44302,a874)),f333(f333(f44(x44301,f890(x44302,a874)),x44303),x44306)),f333(f333(f44(x44304,f890(x44302,a874)),x44305),x44307))) % 191.49/191.40 [4421]E(f206(x44211,x44212,f333(f333(f333(x44213,x44214),x44215),x44216),f333(f333(f9(x44211,f889(a104,a104),f890(a104,f882(x44212))),f333(f333(f9(x44211,a104,f890(f889(a104,a104),f890(a104,f882(x44212)))),f333(f333(f9(x44211,a104,f890(a104,f890(f889(a104,a104),f890(a104,f882(x44212))))),x44217),x44214)),x44215)),x44216)),f333(f333(f333(f219(x44211,x44212,x44213,x44217),x44214),x44215),x44216)) % 191.49/191.40 [4432]E(f207(x44321,x44322,f333(f333(f333(x44323,x44324),x44325),x44326),f333(f333(f9(x44321,f889(a104,a104),f890(a104,f882(x44322))),f333(f333(f9(x44321,a104,f890(f889(a104,a104),f890(a104,f882(x44322)))),f333(f333(f9(x44321,a104,f890(a104,f890(f889(a104,a104),f890(a104,f882(x44322))))),x44327),x44324)),x44325)),x44326)),f221(x44321,x44322,x44323,x44327,x44324,x44325,x44326)) % 191.49/191.40 [4427]E(f204(x44271,x44272,f333(f333(f333(x44273,x44274),x44275),x44276),f333(f333(f9(x44271,f889(a104,a104),f890(a104,f882(f884(x44272)))),f333(f333(f9(x44271,a104,f890(f889(a104,a104),f890(a104,f882(f884(x44272))))),f333(f333(f9(x44271,a104,f890(a104,f890(f889(a104,a104),f890(a104,f882(f884(x44272)))))),x44277),x44274)),x44275)),x44276)),f333(f333(f333(f216(x44271,x44272,x44273,x44277),x44274),x44275),x44276)) % 191.49/191.40 [4442]E(f205(x44421,x44422,f333(f333(f333(x44423,x44424),x44425),x44426),f333(f333(f9(x44421,f889(a104,a104),f890(a104,f882(f884(x44422)))),f333(f333(f9(x44421,a104,f890(f889(a104,a104),f890(a104,f882(f884(x44422))))),f333(f333(f9(x44421,a104,f890(a104,f890(f889(a104,a104),f890(a104,f882(f884(x44422)))))),x44427),x44424)),x44425)),x44426)),f218(x44421,x44422,x44423,x44427,x44424,x44425,x44426)) % 191.49/191.40 [4322]E(f333(f273(x43221,x43222,x43223,x43224,x43225,x43226),f333(f333(f263(x43221,x43223),x43227),x43228)),f333(f333(f263(x43222,x43224),f333(x43225,x43227)),f333(x43226,x43228))) % 191.49/191.40 [4444]E(f333(f333(f155(f889(x44441,x44442),f889(x44443,x44444)),f333(f272(x44441,x44442,f889(x44443,x44444)),f333(f333(f9(x44441,f890(x44442,x44444),f890(x44442,f889(x44443,x44444))),f333(f333(f10(f890(x44444,f889(x44443,x44444)),f890(f890(x44442,x44444),f890(x44442,f889(x44443,x44444))),x44441),f10(x44444,f889(x44443,x44444),x44442)),f333(f333(f10(x44443,f890(x44444,f889(x44443,x44444)),x44441),f263(x44443,x44444)),x44445))),x44446))),f333(f333(f182(x44441,x44442),x44447),x44448)),f333(f333(f182(x44443,x44444),f333(f333(f155(x44441,x44443),x44445),x44447)),f333(f333(f155(x44442,x44444),x44446),x44448))) % 191.49/191.40 [4450]E(f333(f333(f155(f889(x44501,x44502),x44503),f333(f272(x44501,x44502,x44503),f333(f333(f10(f890(x44502,f889(x44501,x44504)),f890(x44502,x44503),x44501),f333(f10(f889(x44501,x44504),x44503,x44502),x44505)),f333(f333(f9(x44501,f890(x44502,x44504),f890(x44502,f889(x44501,x44504))),f333(f333(f10(f890(x44504,f889(x44501,x44504)),f890(f890(x44502,x44504),f890(x44502,f889(x44501,x44504))),x44501),f10(x44504,f889(x44501,x44504),x44502)),f263(x44501,x44504))),x44506)))),f333(f333(f182(x44501,x44502),x44507),x44508)),f333(f333(f155(f889(x44501,x44504),x44503),x44505),f333(f333(f182(x44501,x44504),x44507),f333(f333(f155(x44502,x44504),x44506),x44508)))) % 191.49/191.40 [4363]E(f333(f333(f155(f889(x43631,x43632),x43633),f333(f272(x43631,x43632,x43633),f333(f333(f10(f890(x43632,f889(x43634,x43632)),f890(x43632,x43633),x43631),f333(f10(f889(x43634,x43632),x43633,x43632),x43635)),f333(f333(f10(x43634,f890(x43632,f889(x43634,x43632)),x43631),f263(x43634,x43632)),x43636)))),f333(f333(f182(x43631,x43632),x43637),x43638)),f333(f333(f155(f889(x43634,x43632),x43633),x43635),f333(f333(f182(x43634,x43632),f333(f333(f155(x43631,x43634),x43636),x43637)),x43638))) % 191.49/191.40 [4313]E(f333(f333(f272(x43131,x43132,x43133),f333(f333(f10(f890(x43132,f889(x43134,x43135)),f890(x43132,x43133),x43131),f333(f10(f889(x43134,x43135),x43133,x43132),f333(f272(x43134,x43135,x43133),x43136))),x43137)),x43138),f333(f333(f272(x43134,x43135,x43133),x43136),f333(f333(f272(x43131,x43132,f889(x43134,x43135)),x43137),x43138))) % 191.49/191.40 [4451]E(f333(f333(f44(f889(x44511,x44512),f890(f889(x44513,x44514),a874)),f333(f333(f270(x44511,x44512),x44515),f333(f18(f890(x44512,a874),x44511),x44516))),f333(f272(x44511,x44512,f890(f889(x44513,x44514),a874)),f333(f333(f9(x44511,f890(x44512,f890(x44513,f890(x44514,a874))),f890(x44512,f890(f889(x44513,x44514),a874))),f333(f333(f10(f890(f890(x44513,f890(x44514,a874)),f890(f889(x44513,x44514),a874)),f890(f890(x44512,f890(x44513,f890(x44514,a874))),f890(x44512,f890(f889(x44513,x44514),a874))),x44511),f10(f890(x44513,f890(x44514,a874)),f890(f889(x44513,x44514),a874),x44512)),f333(f333(f10(f890(x44513,a874),f890(f890(x44513,f890(x44514,a874)),f890(f889(x44513,x44514),a874)),x44511),f270(x44513,x44514)),x44517))),f333(f333(f10(f890(x44514,a874),f890(x44513,f890(x44514,a874)),x44512),f18(f890(x44514,a874),x44513)),x44518)))),f333(f333(f270(x44513,x44514),f333(f333(f44(x44511,f890(x44513,a874)),x44515),x44517)),f333(f18(f890(x44514,a874),x44513),f333(f333(f44(x44512,f890(x44514,a874)),x44516),x44518)))) % 191.49/191.40 [4377]E(f333(f333(f274(x43771,x43772,x43773,x43774),f333(f333(f274(x43771,x43775,x43776,f889(x43772,x43773)),x43777),x43778)),x43779),f333(f333(f274(x43771,x43775,x43776,x43774),x43777),f333(f333(f9(x43775,f890(x43772,f890(x43773,x43774)),f890(x43776,x43774)),f333(f333(f10(f890(x43776,f889(x43772,x43773)),f890(f890(x43772,f890(x43773,x43774)),f890(x43776,x43774)),x43775),f274(x43776,x43772,x43773,x43774)),x43778)),x43779))) % 191.49/191.40 [4413]E(f333(f74(f889(x44131,x44132),f889(x44133,x44134),f889(x44135,x44136),f273(x44131,x44133,x44132,x44134,x44137,x44138)),f273(x44135,x44131,x44136,x44132,x44139,x441310)),f273(x44135,x44133,x44136,x44134,f333(f74(x44131,x44133,x44135,x44137),x44139),f333(f74(x44132,x44134,x44136,x44138),x441310))) % 191.49/191.40 [4419]E(f333(f273(x44191,x44192,x44193,x44194,x44195,x44196),f333(f273(x44197,x44191,x44198,x44193,x44199,x441910),x441911)),f333(f273(x44197,x44192,x44198,x44194,f333(f74(x44191,x44192,x44197,x44195),x44199),f333(f74(x44193,x44194,x44198,x44196),x441910)),x441911)) % 191.49/191.40 [4603]~P96(x46031)+E(f92(x46031),a330) % 191.49/191.40 [4604]~P8(x46041)+P8(f884(x46041)) % 191.49/191.40 [4605]~P62(x46051)+P62(f884(x46051)) % 191.49/191.40 [4606]~P104(x46061)+P104(f881(x46061)) % 191.49/191.40 [4609]~P142(x46091)+~E(f79(x46091),f2(x46091)) % 191.49/191.40 [4611]~E(x46111,f2(a104))+E(f333(a22,x46111),f2(a1)) % 191.49/191.40 [4612]~E(x46121,f2(a1))+E(f83(a1,x46121),f2(a1)) % 191.49/191.40 [4619]~P143(x46191)+P33(x46191,f2(x46191)) % 191.49/191.40 [4621]~P109(x46211)+P17(x46211,f118(x46211)) % 191.49/191.40 [4631]P4(x46311)+P4(f333(a328,x46311)) % 191.49/191.40 [4674]~P143(x46741)+~P33(x46741,f79(x46741)) % 191.49/191.40 [4719]~P4(x47191)+~P4(f333(a328,x47191)) % 191.49/191.40 [4742]E(f333(a109,x47421),f2(a880))+~P4(f333(a200,x47421)) % 191.49/191.40 [4806]~P73(x48061)+P19(x48061,x48061,f82(x48061)) % 191.49/191.40 [4807]~P101(x48071)+P18(x48071,x48071,f115(x48071)) % 191.49/191.40 [4808]~P102(x48081)+P18(x48081,x48081,f106(x48081)) % 191.49/191.40 [4809]~P97(x48091)+P18(x48091,x48091,f82(x48091)) % 191.49/191.40 [4810]~P109(x48101)+P18(x48101,x48101,f248(x48101)) % 191.49/191.40 [4811]~P109(x48111)+P18(x48111,x48111,f249(x48111)) % 191.49/191.40 [4616]~E(x46161,f2(a880))+E(f333(f105(a1),x46161),f2(a1)) % 191.49/191.40 [4624]~P94(x46241)+E(f333(f108(x46241),a84),f2(x46241)) % 191.49/191.40 [4627]~E(f553(x46271),f2(a880))+E(f333(f167(a880),x46271),f2(a880)) % 191.49/191.40 [4628]~P111(x46281)+E(f252(x46281,f250(x46281)),f248(x46281)) % 191.49/191.40 [4629]~P111(x46291)+E(f253(x46291,f250(x46291)),f249(x46291)) % 191.49/191.40 [4630]~P90(x46301)+E(f83(x46301,f2(x46301)),f2(x46301)) % 191.49/191.40 [4639]~P143(x46391)+E(f333(f105(x46391),f79(a880)),f79(x46391)) % 191.49/191.40 [4640]~P143(x46401)+E(f333(f105(x46401),f2(a880)),f2(x46401)) % 191.49/191.40 [4641]~P140(x46411)+E(f333(f107(x46411),f79(a1)),f79(x46411)) % 191.49/191.40 [4642]~P140(x46421)+E(f333(f107(x46421),f2(a1)),f2(x46421)) % 191.49/191.40 [4643]E(x46431,f2(a880))+~E(f333(f105(a1),x46431),f2(a1)) % 191.49/191.40 [4668]~P79(x46681)+E(f333(f80(x46681),f194(x46681)),f258(x46681)) % 191.49/191.40 [4669]~P79(x46691)+E(f333(f80(x46691),f258(x46691)),f194(x46691)) % 191.49/191.40 [4670]~P75(x46701)+E(f333(f80(x46701),f2(x46701)),f2(x46701)) % 191.49/191.40 [4671]~P120(x46711)+E(f333(f76(x46711),f79(x46711)),f79(x46711)) % 191.49/191.40 [4672]~P87(x46721)+E(f333(f76(x46721),f2(x46721)),f2(x46721)) % 191.49/191.40 [4673]~P84(x46731)+E(f333(f167(x46731),f118(x46731)),f2(x46731)) % 191.49/191.40 [4694]~P39(x46941)+P42(f333(f173(a1),x46941)) % 191.49/191.40 [4724]~P94(x47241)+E(f333(f80(x47241),f79(x47241)),f333(f108(x47241),a102)) % 191.49/191.40 [4741]~P94(x47411)+P33(x47411,f333(f108(x47411),a84)) % 191.49/191.40 [4758]~P62(x47581)+E(f333(f173(x47581),f57(x47581)),f258(f890(x47581,a874))) % 191.49/191.40 [4768]P39(x47681)+~P42(f333(f173(a1),x47681)) % 191.49/191.40 [4769]~P62(x47691)+P4(f333(f138(x47691),f57(x47691))) % 191.49/191.40 [4812]E(f333(f105(a1),f333(a109,x48121)),x48121)+P4(f333(a200,x48121)) % 191.49/191.40 [4829]~P111(x48291)+E(f94(x48291,x48291,f7(x48291)),f95(x48291)) % 191.49/191.40 [4880]~P113(x48801)+E(f265(x48801,f79(x48801),f82(x48801)),f264(x48801)) % 191.49/191.40 [4910]~P94(x49101)+~P33(x49101,f333(f108(x49101),a102)) % 191.49/191.40 [4920]E(f333(a28,x49201),f197(a876))+P4(f333(a25,f333(a26,x49201))) % 191.49/191.40 [5050]E(f333(f76(a1),x50501),x50501)+P4(f333(f333(f251(a1),x50501),f2(a1))) % 191.49/191.40 [5071]~E(f333(a109,x50711),f2(a880))+P4(f333(f333(f250(a1),x50711),f2(a1))) % 191.49/191.40 [5131]~P4(f333(a200,x51311))+P4(f333(f333(f251(a1),x51311),f2(a1))) % 191.49/191.40 [5170]~P140(x51701)+P4(f333(f333(f335(x51701),f79(x51701)),f114(x51701))) % 191.49/191.40 [5171]~P143(x51711)+P4(f333(f333(f335(x51711),f79(x51711)),f192(x51711))) % 191.49/191.40 [5172]~P140(x51721)+P4(f333(f333(f335(x51721),f2(x51721)),f114(x51721))) % 191.49/191.40 [5173]~P143(x51731)+P4(f333(f333(f335(x51731),f2(x51731)),f192(x51731))) % 191.49/191.40 [5174]~P123(x51741)+P4(f333(f333(f251(x51741),f2(x51741)),f79(x51741))) % 191.49/191.40 [5175]~P123(x51751)+P4(f333(f333(f250(x51751),f2(x51751)),f79(x51751))) % 191.49/191.40 [5178]E(f333(f242(a876),f740(x51781)),f333(a28,x51781))+~P4(f333(a25,f333(a26,x51781))) % 191.49/191.40 [5179]E(f333(f242(a876),f831(x51791)),f333(a28,x51791))+~P4(f333(a25,f333(a26,x51791))) % 191.49/191.40 [5234]E(x52341,f2(a880))+~P4(f333(f333(f250(a880),x52341),f2(a880))) % 191.49/191.40 [5279]E(f333(a109,x52791),f2(a880))+~P4(f333(f333(f250(a1),x52791),f2(a1))) % 191.49/191.40 [5342]P4(f333(a200,x53421))+~P4(f333(f333(f251(a1),x53421),f2(a1))) % 191.49/191.40 [5347]~P109(x53471)+P19(x53471,f881(x53471),f149(x53471,x53471,f7(x53471))) % 191.49/191.40 [5364]P42(x53641)+~P4(f333(f333(f250(a1),f2(a1)),f340(x53641))) % 191.49/191.40 [5370]E(f333(f76(a1),x53701),f333(f80(a1),x53701))+~P4(f333(f333(f251(a1),x53701),f2(a1))) % 191.49/191.40 [5540]~P123(x55401)+~P4(f333(f333(f251(x55401),f79(x55401)),f2(x55401))) % 191.49/191.40 [5541]~P123(x55411)+~P4(f333(f333(f250(x55411),f79(x55411)),f2(x55411))) % 191.49/191.40 [5551]~E(x55511,f2(a1))+P4(f333(f333(f251(a1),f333(f76(a1),x55511)),f79(a1))) % 191.49/191.40 [5552]~E(x55521,f2(a880))+P4(f333(f333(f250(a1),f333(f105(a1),x55521)),f2(a1))) % 191.49/191.40 [5672]~P84(x56721)+E(f143(x56721,x56721,f81(x56721),f2(x56721)),f167(x56721)) % 191.49/191.40 [5843]~P103(x58431)+P28(a880,x58431,f105(x58431),f258(f890(a880,a874))) % 191.49/191.40 [6039]E(x60391,f2(a880))+~P4(f333(f333(f250(a1),f333(f105(a1),x60391)),f2(a1))) % 191.49/191.40 [6040]E(x60401,f2(a1))+~P4(f333(f333(f251(a1),f333(f76(a1),x60401)),f79(a1))) % 191.49/191.40 [7903]E(x79031,f333(a5,f2(a880)))+P4(f333(f333(f251(a880),f333(f333(f3(a880),f333(a21,x79031)),f333(a117,f2(a880)))),f333(a21,x79031))) % 191.49/191.40 [8748]~P4(f333(f333(f251(a1),x87481),f2(a1)))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x87481)),x87481)),f2(a1))) % 191.49/191.40 [9131]P4(f333(f333(f251(a1),x91311),f2(a1)))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x91311)),x91311)),f2(a1))) % 191.49/191.40 [9588]~P4(f333(f333(f251(a1),x95881),f2(a1)))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95881)),x95881)),a102)),f2(a1))) % 191.49/191.40 [9759]P4(f333(f333(f251(a1),x97591),f2(a1)))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97591)),x97591)),a102)),f2(a1))) % 191.49/191.40 [4727]E(x47271,f2(a1))+E(f333(f333(f40(a1),x47271),x47271),f79(a1)) % 191.49/191.40 [4870]~P9(x48701)+E(f41(x48701,f194(f890(x48701,a874))),f194(x48701)) % 191.49/191.40 [4871]~P9(x48711)+E(f41(x48711,f258(f890(x48711,a874))),f258(x48711)) % 191.49/191.40 [4872]~P9(x48721)+E(f42(x48721,f194(f890(x48721,a874))),f258(x48721)) % 191.49/191.40 [4873]~P9(x48731)+E(f42(x48731,f258(f890(x48731,a874))),f194(x48731)) % 191.49/191.40 [4874]~P109(x48741)+E(f140(x48741,f194(f890(x48741,a874))),f118(x48741)) % 191.49/191.40 [5009]E(x50091,f2(a880))+P4(f333(f333(f251(a880),f2(a880)),x50091)) % 191.49/191.40 [5028]~P10(x50281)+P4(f333(f333(f250(a1),f2(a1)),x50281)) % 191.49/191.40 [5062]~E(f333(f108(a880),x50621),f2(a880))+P4(f333(f333(f250(a1),x50621),a84)) % 191.49/191.40 [5067]P42(x50671)+P4(f333(f333(f335(a1),f340(x50671)),x50671)) % 191.49/191.40 [5068]E(x50681,f333(a5,f2(a880)))+P4(f333(f333(f250(a104),f79(a104)),x50681)) % 191.49/191.40 [5105]P4(f333(a200,x51051))+P4(f333(f333(f250(a1),f2(a1)),x51051)) % 191.49/191.40 [5152]E(f333(f105(a1),f333(a109,x51521)),f2(a1))+P4(f333(f333(f250(a1),f2(a1)),x51521)) % 191.49/191.40 [5220]E(f333(f105(a1),f333(f108(a880),x52201)),f333(f108(a1),x52201))+P4(f333(a200,f333(f108(a1),x52201))) % 191.49/191.40 [5240]E(f333(f108(a880),x52401),f2(a880))+~P4(f333(a200,f333(f108(a1),x52401))) % 191.49/191.40 [5241]E(f333(f108(a880),x52411),f2(a880))+~P4(f333(f333(f250(a1),x52411),a84)) % 191.49/191.40 [5276]P10(x52761)+~P4(f333(f333(f250(a1),f2(a1)),x52761)) % 191.49/191.40 [5350]E(f333(a117,f842(x53501)),x53501)+~P4(f333(f333(f251(a880),f2(a880)),x53501)) % 191.49/191.40 [5358]E(f333(a117,f333(f108(a880),x53581)),f79(a880))+~P4(f333(a200,f333(f108(a1),x53581))) % 191.49/191.40 [5366]E(f333(f105(a1),f390(x53661)),x53661)+~P4(f333(f333(f251(a1),f2(a1)),x53661)) % 191.49/191.40 [5373]~E(x53731,f333(a5,f2(a880)))+~P4(f333(f333(f250(a104),f79(a104)),x53731)) % 191.49/191.40 [5380]E(f333(f105(a1),f333(f108(a880),x53801)),f2(a1))+~P4(f333(a200,f333(f108(a1),x53801))) % 191.49/191.40 [5406]E(f333(f167(a880),x54061),f2(a880))+P4(f333(f333(f335(a880),f553(x54061)),f333(f173(a880),x54061))) % 191.49/191.40 [5427]E(f333(f105(a1),f333(a109,x54271)),x54271)+~P4(f333(f333(f250(a1),f2(a1)),x54271)) % 191.49/191.40 [5436]~P4(f333(a200,x54361))+~P4(f333(f333(f250(a1),f2(a1)),x54361)) % 191.49/191.40 [5533]E(f333(f333(f81(a880),f79(a880)),f333(f108(a880),x55331)),f79(a880))+~P4(f333(f333(f251(a1),x55331),a84)) % 191.49/191.40 [5591]E(x55911,f2(a880))+~P4(f333(f333(f251(a880),x55911),f333(a117,f2(a880)))) % 191.49/191.40 [5631]E(f333(f333(f3(a880),f333(f108(a880),x56311)),f79(a880)),f2(a880))+~P4(f333(f333(f250(a1),x56311),a84)) % 191.49/191.40 [5632]E(f333(f333(f81(a880),f333(f108(a880),x56321)),f79(a880)),f79(a880))+~P4(f333(f333(f251(a1),x56321),a84)) % 191.49/191.40 [5642]~P42(x56421)+E(f333(f39(a880),f333(f312(a1,a880,a109),x56421)),f333(f39(a1),x56421)) % 191.49/191.40 [5673]~P109(x56731)+E(f252(x56731,f333(f9(x56731,x56731,a874),f250(x56731))),f249(x56731)) % 191.49/191.40 [5674]~P109(x56741)+E(f253(x56741,f333(f9(x56741,x56741,a874),f250(x56741))),f248(x56741)) % 191.49/191.40 [5684]E(f46(a880,f333(a117,f2(a880)),f333(f108(a880),x56841)),f333(a117,f2(a880)))+~P4(f333(a200,f333(f108(a1),x56841))) % 191.49/191.40 [5693]P4(f333(f333(f251(a1),f2(a1)),x56931))+~P4(f333(f333(f250(a1),f79(a1)),x56931)) % 191.49/191.40 [5694]~P4(f333(f333(f251(a1),f2(a1)),x56941))+P4(f333(f333(f250(a1),f79(a1)),x56941)) % 191.49/191.40 [5705]E(f333(a117,f333(f333(f3(a880),x57051),f79(a880))),x57051)+~P4(f333(f333(f251(a880),f2(a880)),x57051)) % 191.49/191.40 [5762]P4(f333(f333(f251(a880),f2(a880)),f390(x57621)))+~P4(f333(f333(f251(a1),f2(a1)),x57621)) % 191.49/191.40 [5821]E(f46(a1,f333(f108(a1),a102),x58211),f333(f333(f3(a1),x58211),f79(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x58211)) % 191.49/191.40 [5855]~P4(f333(f333(f251(a1),a84),x58551))+P4(f333(f333(f251(a880),f2(a880)),f333(f108(a880),x58551))) % 191.49/191.40 [5905]P4(f333(f333(f251(a880),f2(a880)),f333(a109,x59051)))+~P4(f333(f333(f251(a1),f2(a1)),x59051)) % 191.49/191.40 [5956]~P4(f333(f333(f251(a880),f2(a880)),x59561))+P4(f333(f333(f251(a1),f2(a1)),f333(f105(a1),x59561))) % 191.49/191.40 [5994]~P4(f333(f333(f251(a880),f2(a880)),f333(a109,x59941)))+P4(f333(f333(f251(a1),f2(a1)),x59941)) % 191.49/191.40 [6009]~P42(x60091)+E(f333(f312(a880,a1,f105(a1)),f333(f312(a1,a880,a109),x60091)),x60091) % 191.49/191.40 [6020]P4(f333(f333(f251(a1),a84),x60201))+~P4(f333(f333(f251(a880),f2(a880)),f333(f108(a880),x60201))) % 191.49/191.40 [6068]~P62(x60681)+E(f333(f333(f152(f884(x60681)),f197(x60681)),f333(f333(f155(x60681,f884(x60681)),f242(x60681)),f57(x60681))),f57(f884(x60681))) % 191.49/191.40 [6079]P4(f333(f333(f251(a880),f2(a880)),x60791))+~P4(f333(f333(f251(a1),f2(a1)),f333(f105(a1),x60791))) % 191.49/191.40 [6191]E(f333(f312(a880,a1,f105(a1)),f333(f256(a880),f333(a109,x61911))),f333(f303(a1,f2(a1)),x61911))+~P4(f333(f333(f250(a1),f2(a1)),x61911)) % 191.49/191.40 [6206]~P123(x62061)+P4(f333(f333(f251(x62061),f2(x62061)),f333(f333(f81(x62061),f79(x62061)),f79(x62061)))) % 191.49/191.40 [6257]P4(f333(f333(f251(a880),f333(a117,f2(a880))),f333(a109,x62571)))+~P4(f333(f333(f251(a1),f79(a1)),x62571)) % 191.49/191.40 [6349]E(x63491,f2(a1))+P4(f333(f50(f2(a1),x63491),f333(f333(f263(a1,a1),f2(a1)),f2(a1)))) % 191.49/191.40 [6515]~P4(f333(f333(f251(a880),f333(a117,f2(a880))),f333(a109,x65151)))+P4(f333(f333(f251(a1),f79(a1)),x65151)) % 191.49/191.40 [6929]~P114(x69291)+P40(x69291,f333(f255(f889(x69291,x69291)),f333(f272(x69291,x69291,a874),f251(x69291)))) % 191.49/191.40 [5578]E(f333(f108(a880),f333(f333(f3(a1),x55781),a102)),f333(a117,f333(f108(a880),x55781)))+P4(f333(a200,f333(f108(a1),x55781))) % 191.49/191.40 [5594]~P39(x55941)+E(f333(f333(f155(a880,a1),f105(a1)),f333(f333(f155(a1,a880),a109),x55941)),x55941) % 191.49/191.40 [5711]E(f333(f80(a1),f333(f105(a1),f333(a117,f391(x57111)))),x57111)+~P4(f333(f333(f251(a1),x57111),f2(a1))) % 191.49/191.40 [5721]E(f333(f333(f81(a880),f79(a880)),f333(f108(a880),x57211)),f333(f108(a880),f333(f333(f3(a1),x57211),a102)))+P4(f333(f333(f251(a1),x57211),a84)) % 191.49/191.40 [5764]E(f333(f333(f40(a1),f333(f108(a1),a102)),x57641),f333(f108(a1),a102))+~P4(f333(f333(f251(a1),f2(a1)),x57641)) % 191.49/191.40 [5851]E(f333(f333(f3(a880),f333(f108(a880),x58511)),f79(a880)),f333(f108(a880),f333(f333(f81(a1),x58511),a102)))+P4(f333(f333(f250(a1),x58511),a84)) % 191.49/191.40 [5852]E(f333(f333(f81(a880),f333(f108(a880),x58521)),f79(a880)),f333(f108(a880),f333(f333(f3(a1),x58521),a102)))+P4(f333(f333(f251(a1),x58521),a84)) % 191.49/191.40 [5893]E(f333(a109,f333(f333(f81(a1),f79(a1)),x58931)),f333(a117,f333(a109,x58931)))+~P4(f333(f333(f250(a1),f2(a1)),x58931)) % 191.49/191.40 [5929]E(f333(a117,f333(f333(f3(a880),x59291),f333(a117,f2(a880)))),x59291)+~P4(f333(f333(f251(a880),f2(a880)),x59291)) % 191.49/191.40 [6139]E(f46(a880,f333(a117,f2(a880)),f333(f108(a880),x61391)),f333(a109,f46(a1,f79(a1),f333(f108(a1),x61391))))+P4(f333(a200,f333(f108(a1),x61391))) % 191.49/191.40 [6362]~P4(f333(f63(x63621),f258(f890(x63621,a874))))+P4(f333(f63(f884(x63621)),f258(f890(f884(x63621),a874)))) % 191.49/191.40 [6449]~P4(f333(f333(f250(a1),f2(a1)),x64491))+P4(f333(f333(f251(a1),f2(a1)),f333(f333(f81(a1),f79(a1)),x64491))) % 191.49/191.40 [6456]E(f333(f262(a1,a1),f48(f79(a1),f333(f108(a1),x64561))),f333(f333(f40(a1),f79(a1)),f333(f108(a1),x64561)))+~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x64561))) % 191.49/191.40 [6475]E(f333(f271(a1,a1),f48(f79(a1),f333(f108(a1),x64751))),f46(a1,f79(a1),f333(f108(a1),x64751)))+~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x64751))) % 191.49/191.40 [6487]P4(f333(f63(x64871),f258(f890(x64871,a874))))+~P4(f333(f63(f884(x64871)),f258(f890(f884(x64871),a874)))) % 191.49/191.40 [6823]~P4(f333(f63(x68231),f258(f890(x68231,a874))))+P4(f333(f333(f251(a880),f2(a880)),f333(f39(x68231),f258(f890(x68231,a874))))) % 191.49/191.40 [7398]P4(f333(f63(a880),x73981))+~P4(f333(f63(a1),f333(f312(a880,a1,f105(a1)),x73981))) % 191.49/191.40 [8779]P27(a875,a891,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),f333(a26,x87791)),f201(f333(a26,x87791)))),f194(f890(f879(a875),a874))))+~P4(f333(f333(f335(a877),x87791),f184(a877,a876,a28))) % 191.49/191.40 [5607]~E(a102,x56071)+E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x56071)),x56071),a102) % 191.49/191.40 [5608]~E(x56081,a102)+E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x56081)),x56081),a102) % 191.49/191.40 [6148]E(x61481,a102)+~E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x61481)),x61481),a102) % 191.49/191.40 [6149]E(a102,x61491)+~E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x61491)),x61491),a102) % 191.49/191.40 [6418]~E(f333(f108(a880),x64181),f2(a880))+P4(f333(a200,f333(f108(a1),f333(f333(f81(a1),x64181),a102)))) % 191.49/191.40 [7076]E(f333(f108(a880),x70761),f2(a880))+~P4(f333(a200,f333(f108(a1),f333(f333(f81(a1),x70761),a102)))) % 191.49/191.40 [7673]E(f333(a111,f718(x76731)),x76731)+~P4(f333(f333(f335(f890(f889(a880,a880),a874)),x76731),a103)) % 191.49/191.40 [6529]~P94(x65291)+E(f333(f108(x65291),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),f79(x65291)) % 191.49/191.40 [6946]~P4(f333(a200,f333(f108(a1),x69461)))+E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x69461)),x69461)),f2(a880)) % 191.49/191.40 [7853]~P4(f333(f333(f251(a1),f333(f108(a1),x78531)),f2(a1)))+E(f333(f262(a1,a1),f333(a52,f51(f333(f80(a1),f79(a1)),f333(f80(a1),f333(f108(a1),x78531))))),f333(f333(f40(a1),f79(a1)),f333(f108(a1),x78531))) % 191.49/191.40 [7861]~P4(f333(f333(f251(a1),f333(f108(a1),x78611)),f2(a1)))+E(f333(f271(a1,a1),f333(a52,f51(f333(f80(a1),f79(a1)),f333(f80(a1),f333(f108(a1),x78611))))),f46(a1,f79(a1),f333(f108(a1),x78611))) % 191.49/191.40 [8045]~P4(f333(f333(f250(a1),a84),x80451))+P4(f333(f333(f251(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x80451)),x80451))) % 191.49/191.40 [8046]~P4(f333(f333(f251(a1),a102),x80461))+P4(f333(f333(f251(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x80461)),x80461))) % 191.49/191.40 [8047]~P4(f333(f333(f250(a1),a84),x80471))+P4(f333(f333(f250(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x80471)),x80471))) % 191.49/191.40 [8048]~P4(f333(f333(f250(a1),a102),x80481))+P4(f333(f333(f250(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x80481)),x80481))) % 191.49/191.40 [8049]~P4(f333(f333(f92(a1),a102),x80491))+P4(f333(f333(f92(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x80491)),x80491))) % 191.49/191.40 [8387]~P94(x83871)+~P33(x83871,f333(f108(x83871),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))) % 191.49/191.40 [8511]P4(f333(f333(f251(a1),a102),x85111))+~P4(f333(f333(f251(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x85111)),x85111))) % 191.49/191.40 [8512]P4(f333(f333(f250(a1),a84),x85121))+~P4(f333(f333(f251(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x85121)),x85121))) % 191.49/191.40 [8513]P4(f333(f333(f250(a1),a84),x85131))+~P4(f333(f333(f250(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x85131)),x85131))) % 191.49/191.40 [8514]P4(f333(f333(f250(a1),a102),x85141))+~P4(f333(f333(f250(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x85141)),x85141))) % 191.49/191.40 [8515]P4(f333(f333(f92(a1),a102),x85151))+~P4(f333(f333(f92(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x85151)),x85151))) % 191.49/191.40 [8720]E(f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x87201)),x87201)),f333(f333(f89(a880,a880),f333(f108(a880),x87201)),f333(f333(f10(a880,a880,a880),a117),f333(f333(f20(a880,a880,a880),f81(a880)),f7(a880)))))+P4(f333(a200,f333(f108(a1),x87201))) % 191.49/191.40 [9560]E(x95601,f194(f890(f889(a880,a880),a874)))+P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),x95601),f194(f890(f889(a880,a880),a874)))),a37)) % 191.49/191.40 [7763]~E(a84,x77631)+E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x77631)),x77631)),a102),a84) % 191.49/191.40 [7764]~E(x77641,a84)+E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x77641)),x77641)),a102),a84) % 191.49/191.40 [8403]E(x84031,a84)+~E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x84031)),x84031)),a102),a84) % 191.49/191.40 [8404]E(a84,x84041)+~E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x84041)),x84041)),a102),a84) % 191.49/191.40 [8735]~P4(f333(a200,f333(f108(a1),x87351)))+P4(f333(a200,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x87351)),x87351)))) % 191.49/191.40 [8736]~P4(f333(f333(f251(a1),x87361),a84))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x87361)),x87361)),a84)) % 191.49/191.40 [8737]~P4(f333(f333(f251(a1),x87371),a102))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x87371)),x87371)),a102)) % 191.49/191.40 [8738]~P4(f333(f333(f251(a1),x87381),a84))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x87381)),x87381)),a84)) % 191.49/191.40 [8739]~P4(f333(f333(f250(a1),x87391),a102))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x87391)),x87391)),a102)) % 191.49/191.40 [8740]~P4(f333(f333(f92(a1),x87401),a102))+P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x87401)),x87401)),a102)) % 191.49/191.40 [8813]~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x88131)))+P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x88131)),x88131)))) % 191.49/191.40 [9121]P4(f333(a200,f333(f108(a1),x91211)))+~P4(f333(a200,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x91211)),x91211)))) % 191.49/191.40 [9122]P4(f333(f333(f251(a1),x91221),a84))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x91221)),x91221)),a84)) % 191.49/191.40 [9123]P4(f333(f333(f251(a1),x91231),a84))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x91231)),x91231)),a84)) % 191.49/191.40 [9124]P4(f333(f333(f251(a1),x91241),a102))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x91241)),x91241)),a102)) % 191.49/191.40 [9125]P4(f333(f333(f250(a1),x91251),a102))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x91251)),x91251)),a102)) % 191.49/191.40 [9126]P4(f333(f333(f92(a1),x91261),a102))+~P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x91261)),x91261)),a102)) % 191.49/191.40 [9612]~P4(f333(f63(f889(a880,a880)),x96121))+P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),f194(f890(f889(a880,a880),a874))),x96121)),a70)) % 191.49/191.40 [9283]~P4(f333(f333(f251(a1),a84),x92831))+P4(f333(f333(f251(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x92831)),x92831)),a102))) % 191.49/191.40 [9284]~P4(f333(f333(f251(a1),a102),x92841))+P4(f333(f333(f251(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x92841)),x92841)),a102))) % 191.49/191.40 [9285]~P4(f333(f333(f250(a1),a84),x92851))+P4(f333(f333(f250(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x92851)),x92851)),a102))) % 191.49/191.40 [9286]~P4(f333(f333(f251(a1),a102),x92861))+P4(f333(f333(f250(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x92861)),x92861)),a102))) % 191.49/191.40 [9287]~P4(f333(f333(f92(a1),a84),x92871))+P4(f333(f333(f92(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x92871)),x92871)),a102))) % 191.49/191.40 [9502]P4(f333(f333(f251(a1),a84),x95021))+~P4(f333(f333(f251(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95021)),x95021)),a102))) % 191.49/191.40 [9503]P4(f333(f333(f251(a1),a102),x95031))+~P4(f333(f333(f251(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95031)),x95031)),a102))) % 191.49/191.40 [9504]P4(f333(f333(f251(a1),a102),x95041))+~P4(f333(f333(f250(a1),a102),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95041)),x95041)),a102))) % 191.49/191.40 [9505]P4(f333(f333(f250(a1),a84),x95051))+~P4(f333(f333(f250(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95051)),x95051)),a102))) % 191.49/191.40 [9506]P4(f333(f333(f92(a1),a84),x95061))+~P4(f333(f333(f92(a1),a84),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95061)),x95061)),a102))) % 191.49/191.40 [9582]~P4(f333(a200,f333(f108(a1),x95821)))+P4(f333(a200,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95821)),x95821)),a102)))) % 191.49/191.40 [9583]~P4(f333(f333(f251(a1),x95831),a84))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95831)),x95831)),a102)),a84)) % 191.49/191.40 [9584]~P4(f333(f333(f250(a1),x95841),a102))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95841)),x95841)),a102)),a102)) % 191.49/191.40 [9585]~P4(f333(f333(f250(a1),x95851),a84))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95851)),x95851)),a102)),a84)) % 191.49/191.40 [9586]~P4(f333(f333(f250(a1),x95861),a102))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95861)),x95861)),a102)),a102)) % 191.49/191.40 [9587]~P4(f333(f333(f92(a1),x95871),a84))+P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95871)),x95871)),a102)),a84)) % 191.49/191.40 [9591]~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x95911)))+P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95911)),x95911)),a102)))) % 191.49/191.40 [9753]P4(f333(a200,f333(f108(a1),x97531)))+~P4(f333(a200,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97531)),x97531)),a102)))) % 191.49/191.40 [9754]P4(f333(f333(f251(a1),x97541),a84))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97541)),x97541)),a102)),a84)) % 191.49/191.40 [9755]P4(f333(f333(f250(a1),x97551),a84))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97551)),x97551)),a102)),a84)) % 191.49/191.40 [9756]P4(f333(f333(f250(a1),x97561),a102))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97561)),x97561)),a102)),a102)) % 191.49/191.40 [9757]P4(f333(f333(f250(a1),x97571),a102))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97571)),x97571)),a102)),a102)) % 191.49/191.40 [9758]P4(f333(f333(f92(a1),x97581),a84))+~P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97581)),x97581)),a102)),a84)) % 191.49/191.40 [9862]~P94(x98621)+E(f333(f333(f81(x98621),f79(x98621)),f79(x98621)),f333(f108(x98621),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))) % 191.49/191.40 [9937]~P143(x99371)+E(f333(f333(f264(x99371),f79(x99371)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f79(x99371)) % 191.49/191.40 [9938]~P143(x99381)+E(f333(f333(f264(x99381),f2(x99381)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f2(x99381)) % 191.49/191.40 [10075]~P4(f333(f333(f251(a880),f79(a880)),x100751))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f40(a880),x100751),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.40 [10079]~P4(f333(f333(f251(a880),f2(a880)),x100791))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f40(a880),f333(f333(f81(a880),x100791),f79(a880))),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.40 [10098]~E(f46(a880,x100981,f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f79(a880))+P4(f333(f333(f251(a880),f2(a880)),f46(a880,x100981,f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.40 [10117]E(f46(a880,x101171,f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f79(a880))+~P4(f333(f333(f251(a880),f2(a880)),f46(a880,x101171,f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.40 [4647]~P40(x46471,x46472)+P57(x46471,x46472) % 191.49/191.40 [4648]~P45(x46481,x46482)+P57(x46481,x46482) % 191.49/191.40 [4607]~E(x46071,x46072)+E(f280(x46071,x46072),f79(a104)) % 191.49/191.40 [4610]E(f226(x46101,x46102),x46101)+~E(x46102,f2(a880)) % 191.49/191.40 [4615]P41(x46151,x46152)+~E(x46152,f197(x46151)) % 191.49/191.40 [4618]~E(x46182,f118(x46181))+E(f153(x46181,x46182),f118(x46181)) % 191.49/191.40 [4622]~P41(x46222,x46221)+E(x46221,f197(x46222)) % 191.49/191.40 [4638]~E(f153(x46382,x46381),f118(x46382))+E(x46381,f118(x46382)) % 191.49/191.40 [4652]~P5(x46522)+P5(f890(x46521,x46522)) % 191.49/191.40 [4653]~P6(x46532)+P6(f890(x46531,x46532)) % 191.49/191.40 [4654]~P98(x46542)+P7(f890(x46541,x46542)) % 191.49/191.40 [4655]~P6(x46552)+P101(f890(x46551,x46552)) % 191.49/191.40 [4656]~P67(x46562)+P67(f890(x46561,x46562)) % 191.49/191.40 [4657]~P6(x46572)+P102(f890(x46571,x46572)) % 191.49/191.40 [4658]~P99(x46582)+P99(f890(x46581,x46582)) % 191.49/191.40 [4659]~P9(x46592)+P9(f890(x46591,x46592)) % 191.49/191.40 [4660]~P79(x46602)+P79(f890(x46601,x46602)) % 191.49/191.40 [4661]~P80(x46612)+P80(f890(x46611,x46612)) % 191.49/191.40 [4662]~P107(x46622)+P107(f890(x46621,x46622)) % 191.49/191.40 [4663]~P98(x46632)+P100(f890(x46631,x46632)) % 191.49/191.40 [4664]~P108(x46642)+P108(f890(x46641,x46642)) % 191.49/191.40 [4665]~P110(x46652)+P110(f890(x46651,x46652)) % 191.49/191.40 [4666]~P111(x46662)+P111(f890(x46661,x46662)) % 191.49/191.40 [4667]~P98(x46672)+P98(f890(x46671,x46672)) % 191.49/191.40 [4679]E(x46791,x46792)+~E(f333(a26,x46791),f333(a26,x46792)) % 191.49/191.40 [4681]E(x46811,x46812)+~E(f333(a117,x46811),f333(a117,x46812)) % 191.49/191.40 [4682]E(x46821,x46822)+~E(f333(a111,x46821),f333(a111,x46822)) % 191.49/191.40 [4683]E(x46831,x46832)+~E(f333(a5,x46831),f333(a5,x46832)) % 191.49/191.40 [4685]E(x46851,x46852)+~E(f333(a21,x46851),f333(a21,x46852)) % 191.49/191.40 [4785]~P60(x47851)+E(f46(x47851,x47852,x47852),f2(x47851)) % 191.49/191.40 [4819]~P40(x48191,x48192)+P40(f881(x48191),f146(x48191,x48192)) % 191.49/191.40 [4820]~P40(x48201,x48202)+P40(f881(x48201),f147(x48201,x48202)) % 191.49/191.40 [4915]~P40(x49151,x49152)+P40(f890(x49151,a874),f324(x49151,x49152)) % 191.49/191.40 [4916]~P40(x49161,x49162)+P40(f890(x49161,a874),f325(x49161,x49162)) % 191.49/191.40 [5034]~P10(x50341)+P42(f304(a1,x50341,x50342)) % 191.49/191.40 [5134]~P40(x51341,x51342)+P59(x51341,f69(x51341,x51341,x51342)) % 191.49/191.40 [5636]~P81(x56361)+P28(x56361,x56361,f80(x56361),x56362) % 191.49/191.40 [4633]~E(x46332,f118(x46331))+E(f333(f169(x46331),x46332),f118(x46331)) % 191.49/191.40 [4634]~E(x46342,f118(x46341))+E(f333(f170(x46341),x46342),f118(x46341)) % 191.49/191.40 [4689]E(x46891,f333(a109,x46892))+~E(f333(f105(a1),x46891),x46892) % 191.49/191.40 [4692]E(x46921,f118(x46922))+~E(f333(f169(x46922),x46921),f118(x46922)) % 191.49/191.40 [4693]E(x46931,f118(x46932))+~E(f333(f170(x46932),x46931),f118(x46932)) % 191.49/191.40 [4711]~P94(x47111)+E(f333(f108(x47111),x47112),f333(f107(x47111),x47112)) % 191.49/191.40 [4716]~E(x47162,f197(x47161))+E(f241(x47161,x47162),f194(f890(x47161,a874))) % 191.49/191.40 [4718]~P8(x47181)+P4(f333(f63(x47181),x47182)) % 191.49/191.40 [4725]E(x47251,f197(x47252))+E(f333(f242(x47252),f339(x47252,x47251)),x47251) % 191.49/191.40 [4726]E(x47261,f197(x47262))+E(f333(f242(x47262),f472(x47262,x47261)),x47261) % 191.49/191.40 [4728]~E(f623(x47282,x47281),f118(x47281))+E(f180(x47281,x47282),f118(f881(x47281))) % 191.49/191.40 [4737]~E(x47372,f118(x47371))+E(f333(f173(x47371),x47372),f194(f890(x47371,a874))) % 191.49/191.40 [4738]~E(x47382,f118(x47381))+E(f194(f890(x47381,a874)),f333(f173(x47381),x47382)) % 191.49/191.40 [4740]E(x47401,x47402)+~E(f333(f105(a1),x47401),f333(f105(a1),x47402)) % 191.49/191.40 [4743]E(f224(x47431,x47432),f2(a880))+P4(f333(f63(x47431),x47432)) % 191.49/191.40 [4763]~P120(x47631)+E(f83(x47631,f83(x47631,x47632)),f83(x47631,x47632)) % 191.49/191.40 [4776]~P115(x47761)+E(f333(f333(f264(x47761),x47762),f79(a880)),x47762) % 191.49/191.40 [4777]~P83(x47771)+E(f333(f333(f264(x47771),x47772),f79(a880)),x47772) % 191.49/191.40 [4779]E(x47791,x47792)+E(f280(x47791,x47792),f333(f333(f81(a104),x47792),f79(a104))) % 191.49/191.40 [4782]E(f333(f39(x47821),x47822),f2(a880))+P4(f333(f63(x47821),x47822)) % 191.49/191.40 [4786]~E(f153(x47861,x47862),x47862)+P4(f333(f138(x47861),x47862)) % 191.49/191.40 [4789]~P7(x47891)+E(f333(f333(f115(x47891),x47892),f194(x47891)),x47892) % 191.49/191.40 [4790]~P75(x47901)+E(f333(f333(f3(x47901),x47902),f2(x47901)),x47902) % 191.49/191.40 [4791]~P100(x47911)+E(f333(f333(f106(x47911),x47912),f258(x47911)),x47912) % 191.49/191.40 [4792]~P69(x47921)+E(f333(f333(f81(x47921),x47922),f2(x47921)),x47922) % 191.49/191.40 [4793]~P115(x47931)+E(f333(f333(f81(x47931),x47932),f2(x47931)),x47932) % 191.49/191.40 [4794]~P84(x47941)+E(f333(f333(f81(x47941),x47942),f2(x47941)),x47942) % 191.49/191.40 [4795]~P115(x47951)+E(f333(f333(f82(x47951),x47952),f79(x47951)),x47952) % 191.49/191.40 [4796]~P76(x47961)+E(f333(f333(f82(x47961),x47962),f79(x47961)),x47962) % 191.49/191.40 [4797]~P83(x47971)+E(f333(f333(f82(x47971),x47972),f79(x47971)),x47972) % 191.49/191.40 [4798]~P118(x47981)+E(f333(f333(f291(x47981),x47982),f79(x47981)),x47982) % 191.49/191.40 [4799]~P60(x47991)+E(f333(f333(f40(x47991),x47992),f79(x47991)),x47992) % 191.49/191.40 [4800]~P115(x48001)+E(f333(f333(f264(x48001),x48002),f2(a880)),f79(x48001)) % 191.49/191.40 [4801]~P113(x48011)+E(f333(f333(f264(x48011),x48012),f2(a880)),f79(x48011)) % 191.49/191.40 [4802]~E(x48022,f194(f890(x48021,a874)))+E(f333(f39(x48021),x48022),f2(a880)) % 191.49/191.40 [4813]~P60(x48131)+E(f46(x48131,x48132,f2(x48131)),x48132) % 191.49/191.40 [4821]~P100(x48211)+E(f333(f333(f115(x48211),x48212),f258(x48211)),f258(x48211)) % 191.49/191.40 [4822]~P7(x48221)+E(f333(f333(f106(x48221),x48222),f194(x48221)),f194(x48221)) % 191.49/191.40 [4823]~P115(x48231)+E(f333(f333(f82(x48231),x48232),f2(x48231)),f2(x48231)) % 191.49/191.40 [4824]~P128(x48241)+E(f333(f333(f82(x48241),x48242),f2(x48241)),f2(x48241)) % 191.49/191.40 [4825]~P119(x48251)+E(f333(f333(f291(x48251),x48252),f2(x48251)),f2(x48251)) % 191.49/191.40 [4826]~P60(x48261)+E(f333(f333(f40(x48261),x48262),f2(x48261)),f2(x48261)) % 191.49/191.40 [4827]E(x48271,f197(x48272))+~E(f241(x48272,x48271),f194(f890(x48272,a874))) % 191.49/191.40 [4830]~P60(x48301)+E(f46(x48301,x48302,f79(x48301)),f2(x48301)) % 191.49/191.40 [4831]~P60(x48311)+E(f46(x48311,f2(x48311),x48312),f2(x48311)) % 191.49/191.40 [4858]E(x48581,f2(a880))+E(f56(x48582,x48581,f118(x48582)),f118(f881(x48582))) % 191.49/191.40 [4882]P40(x48821,x48822)+~E(f722(x48822,x48821),f194(f890(x48821,a874))) % 191.49/191.40 [4883]E(x48831,f118(x48832))+~E(f333(f173(x48832),x48831),f194(f890(x48832,a874))) % 191.49/191.40 [4884]E(x48841,f118(x48842))+~E(f194(f890(x48842,a874)),f333(f173(x48842),x48841)) % 191.49/191.40 [4887]~E(x48871,x48872)+P4(f333(f333(a330,x48871),x48872)) % 191.49/191.40 [4897]P4(x48971)+P4(f333(f333(a336,x48971),x48972)) % 191.49/191.40 [4898]E(x48981,f118(x48982))+E(f333(f333(f166(x48982),x48981),f2(a880)),f333(f142(x48982),x48981)) % 191.49/191.40 [4901]E(f153(x49011,x49012),x49012)+~P4(f333(f138(x49011),x49012)) % 191.49/191.40 [4906]~P4(x49062)+P4(f333(f333(a336,x49061),x49062)) % 191.49/191.40 [4907]~P4(x49072)+P4(f333(f333(a332,x49071),x49072)) % 191.49/191.40 [4908]~P4(x49081)+P4(f333(f333(a332,x49081),x49082)) % 191.49/191.40 [4918]~E(f554(x49182,x49181),f580(x49182,x49181))+P4(f333(f138(x49181),x49182)) % 191.49/191.40 [4926]E(f333(f255(x49261),x49262),f194(f890(x49261,a874)))+P4(f333(x49262,f555(x49262))) % 191.49/191.40 [4927]E(f194(f890(x49271,a874)),f333(f255(x49271),x49272))+P4(f333(x49272,f567(x49272))) % 191.49/191.40 [4991]~P120(x49911)+E(f333(f333(f82(x49911),x49912),f83(x49911,x49912)),f333(f76(x49911),x49912)) % 191.49/191.40 [5002]~E(x50021,f2(a1))+E(f47(x50021,x50022),f333(f333(f263(a1,a1),f2(a1)),f2(a1))) % 191.49/191.40 [5033]~P57(x50331,x50332)+P57(x50331,f333(f288(x50331,x50331),x50332)) % 191.49/191.40 [5051]~E(f333(a28,x50511),f333(f242(a876),x50512))+P4(f333(a25,f333(a26,x50511))) % 191.49/191.40 [5056]E(x50561,x50562)+~P4(f333(f333(a330,x50561),x50562)) % 191.49/191.40 [5060]~P4(f333(a25,x50602))+P4(f333(a25,f33(x50601,x50602))) % 191.49/191.40 [5069]P4(x50691)+~P4(f333(f333(a331,x50692),x50691)) % 191.49/191.40 [5070]P4(x50701)+~P4(f333(f333(a331,x50701),x50702)) % 191.49/191.40 [5074]~P107(x50741)+P4(f333(f333(f250(x50741),x50742),f258(x50741))) % 191.49/191.40 [5078]E(x50781,x50782)+~E(f333(x50781,f412(x50782,x50781)),f333(x50782,f412(x50782,x50781))) % 191.49/191.40 [5107]E(x51071,f2(a880))+E(f226(x51071,f46(a880,x51072,x51071)),f226(x51072,x51071)) % 191.49/191.40 [5112]~P109(x51121)+P17(x51121,f333(f333(f152(x51121),x51122),f118(x51121))) % 191.49/191.40 [5114]E(x51141,f2(a1))+P4(f333(f50(x51142,x51141),f47(x51142,x51141))) % 191.49/191.40 [5132]~E(x51321,x51322)+P4(f333(f333(f251(a880),x51321),f333(a117,x51322))) % 191.49/191.40 [5142]~E(x51421,f2(a880))+P4(f333(f333(f251(a880),x51421),f333(a117,x51422))) % 191.49/191.40 [5151]P4(f333(x51511,x51512))+P4(f333(f333(f250(a1),f2(a1)),f342(x51511))) % 191.49/191.40 [5188]P4(f333(a25,x51881))+~P4(f333(a25,f33(x51882,x51881))) % 191.49/191.40 [5190]P4(f333(a25,x51901))+~P4(f333(a25,f34(x51902,x51901))) % 191.49/191.40 [5192]P4(f333(a25,x51921))+~P4(f333(a25,f34(x51921,x51922))) % 191.49/191.40 [5224]P57(x52241,x52242)+~P57(x52241,f333(f288(x52241,x52241),x52242)) % 191.49/191.40 [5227]~E(f46(a880,x52272,x52271),f2(a880))+E(f333(f333(f82(a880),x52271),f403(x52271,x52272)),x52272) % 191.49/191.40 [5228]~E(f46(a1,x52282,x52281),f2(a1))+E(f333(f333(f82(a1),x52281),f343(x52281,x52282)),x52282) % 191.49/191.40 [5255]~P4(f333(x52551,x52552))+P4(f333(f333(f250(a1),f2(a1)),f341(x52551))) % 191.49/191.40 [5267]E(f333(f333(f3(a880),f333(a109,x52671)),f333(a109,x52672)),f333(a109,x52671))+~P4(f333(a200,x52672)) % 191.49/191.40 [5299]E(f281(x52991,x52992),f79(a104))+~P4(f333(f333(f250(a104),x52991),f79(a104))) % 191.49/191.40 [5392]E(f333(f333(f166(x53921),x53922),f554(x53922,x53921)),f333(f333(f166(x53921),x53922),f580(x53922,x53921)))+P4(f333(f138(x53921),x53922)) % 191.49/191.40 [5437]~P4(f333(x54371,f91(x54372,x54371)))+P4(f333(x54371,f584(x54372,x54371))) % 191.49/191.40 [5500]P59(x55001,x55002)+~P4(f333(f321(x55001,x55002),f679(x55002,x55001))) % 191.49/191.40 [5643]~E(f333(a117,f46(a880,x56431,x56432)),x56432)+E(f46(a880,f333(a117,x56431),x56432),f2(a880)) % 191.49/191.40 [5700]P40(x57001,x57002)+P4(f333(f333(f335(x57001),f784(x57002,x57001)),f785(x57002,x57001))) % 191.49/191.40 [5707]~P94(x57071)+P4(f333(f333(f335(x57071),f333(f108(x57071),x57072)),f114(x57071))) % 191.49/191.40 [5708]~P140(x57081)+P4(f333(f333(f335(x57081),f333(f105(x57081),x57082)),f114(x57081))) % 191.49/191.40 [5709]~P143(x57091)+P4(f333(f333(f335(x57091),f333(f105(x57091),x57092)),f192(x57091))) % 191.49/191.40 [5710]~P140(x57101)+P4(f333(f333(f335(x57101),f333(f107(x57101),x57102)),f114(x57101))) % 191.49/191.40 [5854]E(f333(a117,f46(a880,x58541,x58542)),x58542)+E(f46(a880,f333(a117,x58541),x58542),f333(a117,f46(a880,x58541,x58542))) % 191.49/191.40 [6269]P40(x62691,x62692)+~P4(f333(f333(f335(x62691),f680(x62692,x62691)),f322(x62691,x62692))) % 191.49/191.40 [6303]~P123(x63031)+~P4(f333(f333(f251(x63031),f333(f105(x63031),x63032)),f2(x63031))) % 191.49/191.40 [6304]~P87(x63041)+~P4(f333(f333(f251(x63041),f333(f76(x63041),x63042)),f2(x63041))) % 191.49/191.40 [6391]P4(f333(f333(f251(a1),x63911),f46(a1,x63912,x63911)))+~P4(f333(f333(f251(a1),x63911),f2(a1))) % 191.49/191.40 [6489]E(f333(f333(f311(a880),f333(a117,x64891)),f304(a880,x64892,x64891)),f304(a880,x64892,f333(a117,x64891)))+~P4(f333(f333(f250(a880),x64892),f333(a117,x64891))) % 191.49/191.40 [6573]~P109(x65731)+P17(x65731,f151(x65731,x65731,f7(x65731),x65732)) % 191.49/191.40 [6703]E(f333(f169(x67031),x67032),x67032)+~P4(f333(f333(f250(a880),f333(f195(f881(x67031)),x67032)),f79(a880))) % 191.49/191.40 [6723]~P87(x67231)+P4(f333(f333(f250(x67231),f333(f80(x67231),f333(f76(x67231),x67232))),f2(x67231))) % 191.49/191.40 [6756]~P40(x67561,x67562)+P40(x67561,f333(f333(f290(x67561,x67561,x67561),x67562),f309(x67561,x67562))) % 191.49/191.40 [6968]~P4(f333(f333(f251(a1),x69682),f2(a1)))+P4(f333(f333(f250(a1),f46(a1,x69681,x69682)),f2(a1))) % 191.49/191.40 [7354]~P143(x73541)+E(f196(x73541,f333(f333(f9(x73541,x73541,x73541),f81(x73541)),f79(x73541)),x73542,f2(x73541)),f333(f105(x73541),x73542)) % 191.49/191.40 [7381]~P125(x73811)+~P4(f333(f333(f251(x73811),f333(f333(f82(x73811),x73812),x73812)),f2(x73811))) % 191.49/191.40 [10151]~P120(x101511)+~P4(f333(f333(f251(x101511),f333(f333(f264(x101511),x101512),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f2(x101511))) % 191.49/191.40 [4690]~E(x46902,f118(x46901))+E(f333(f195(f881(x46901)),x46902),f2(a880)) % 191.49/191.40 [4729]~E(x47291,f2(a880))+E(f333(f333(f81(a880),x47291),x47292),x47292) % 191.49/191.40 [4730]~E(x47302,f2(a880))+E(f333(f333(f82(a880),x47301),x47302),f2(a880)) % 191.49/191.40 [4732]~E(x47321,f2(a880))+E(f333(f333(f82(a880),x47321),x47322),f2(a880)) % 191.49/191.40 [4733]~E(x47332,f2(a1))+E(f333(f333(f40(a1),x47331),x47332),f2(a1)) % 191.49/191.40 [4734]~E(x47342,f2(a880))+E(f333(f333(f264(a880),x47341),x47342),f79(a880)) % 191.49/191.40 [4744]E(x47441,f118(x47442))+~E(f333(f195(f881(x47442)),x47441),f2(a880)) % 191.49/191.40 [4745]~P6(x47451)+E(f333(f333(f115(x47451),x47452),x47452),x47452) % 191.49/191.40 [4747]~P101(x47471)+E(f333(f333(f115(x47471),x47472),x47472),x47472) % 191.49/191.40 [4748]~P6(x47481)+E(f333(f333(f106(x47481),x47482),x47482),x47482) % 191.49/191.40 [4750]~P102(x47501)+E(f333(f333(f106(x47501),x47502),x47502),x47502) % 191.49/191.40 [4752]~P97(x47521)+E(f333(f333(f82(x47521),x47522),x47522),x47522) % 191.49/191.40 [4754]~P109(x47541)+E(f333(f333(f248(x47541),x47542),x47542),x47542) % 191.49/191.40 [4756]~P109(x47561)+E(f333(f333(f249(x47561),x47562),x47562),x47562) % 191.49/191.40 [4775]~P75(x47751)+E(f333(f333(f3(x47751),x47752),x47752),f2(x47751)) % 191.49/191.40 [4787]~P79(x47871)+E(f333(f80(x47871),f333(f80(x47871),x47872)),x47872) % 191.49/191.40 [4788]~P75(x47881)+E(f333(f80(x47881),f333(f80(x47881),x47882)),x47882) % 191.49/191.40 [4805]~E(x48052,f2(a880))+E(f333(f333(f264(a880),x48051),x48052),f333(a117,f2(a880))) % 191.49/191.40 [4839]~P7(x48391)+E(f333(f333(f115(x48391),f194(x48391)),x48392),x48392) % 191.49/191.40 [4840]~P100(x48401)+E(f333(f333(f106(x48401),f258(x48401)),x48402),x48402) % 191.49/191.40 [4841]~P69(x48411)+E(f333(f333(f81(x48411),f2(x48411)),x48412),x48412) % 191.49/191.40 [4842]~P115(x48421)+E(f333(f333(f81(x48421),f2(x48421)),x48422),x48422) % 191.49/191.40 [4843]~P84(x48431)+E(f333(f333(f81(x48431),f2(x48431)),x48432),x48432) % 191.49/191.40 [4844]~P115(x48441)+E(f333(f333(f82(x48441),f79(x48441)),x48442),x48442) % 191.49/191.40 [4845]~P76(x48451)+E(f333(f333(f82(x48451),f79(x48451)),x48452),x48452) % 191.49/191.40 [4846]~P83(x48461)+E(f333(f333(f82(x48461),f79(x48461)),x48462),x48462) % 191.49/191.40 [4863]~P100(x48631)+E(f333(f333(f115(x48631),f258(x48631)),x48632),f258(x48631)) % 191.49/191.40 [4864]~P7(x48641)+E(f333(f333(f106(x48641),f194(x48641)),x48642),f194(x48641)) % 191.49/191.40 [4865]~P115(x48651)+E(f333(f333(f82(x48651),f2(x48651)),x48652),f2(x48651)) % 191.49/191.40 [4866]~P128(x48661)+E(f333(f333(f82(x48661),f2(x48661)),x48662),f2(x48661)) % 191.49/191.40 [4867]~P118(x48671)+E(f333(f333(f291(x48671),f2(x48671)),x48672),f2(x48671)) % 191.49/191.40 [4868]~P60(x48681)+E(f333(f333(f40(x48681),f2(x48681)),x48682),f2(x48681)) % 191.49/191.40 [4869]~P83(x48691)+E(f333(f333(f264(x48691),f79(x48691)),x48692),f79(x48691)) % 191.49/191.40 [4877]E(x48771,f118(x48772))+E(f145(x48772,f333(f170(x48772),x48771)),f333(f142(x48772),x48771)) % 191.49/191.40 [4878]E(x48781,f118(x48782))+E(f333(f142(x48782),f333(f170(x48782),x48781)),f145(x48782,x48781)) % 191.49/191.40 [4879]E(x48791,f2(a880))+~E(f333(f333(f81(a880),x48792),x48791),x48792) % 191.49/191.40 [4885]~P94(x48851)+E(f333(f107(x48851),f333(f108(a1),x48852)),f333(f108(x48851),x48852)) % 191.49/191.40 [4886]~P140(x48861)+E(f333(f107(x48861),f333(f105(a1),x48862)),f333(f105(x48861),x48862)) % 191.49/191.40 [4893]E(x48931,f79(a880))+~E(f333(f333(f82(a880),x48932),x48931),f79(a880)) % 191.49/191.40 [4894]E(x48941,f79(a880))+~E(f333(f333(f82(a880),x48941),x48942),f79(a880)) % 191.49/191.40 [4895]E(x48951,f2(a880))+~E(f333(f333(f81(a880),x48952),x48951),f2(a880)) % 191.49/191.40 [4896]E(x48961,f2(a880))+~E(f333(f333(f81(a880),x48961),x48962),f2(a880)) % 191.49/191.40 [4911]~P87(x49111)+E(f333(f76(x49111),f333(f80(x49111),x49112)),f333(f76(x49111),x49112)) % 191.49/191.40 [4912]~P120(x49121)+E(f333(f76(x49121),f333(f105(x49121),x49122)),f333(f105(x49121),x49122)) % 191.49/191.40 [4913]~P87(x49131)+E(f333(f76(x49131),f333(f76(x49131),x49132)),f333(f76(x49131),x49132)) % 191.49/191.40 [4914]~P69(x49141)+E(f333(f167(x49141),f333(f170(x49141),x49142)),f333(f167(x49141),x49142)) % 191.49/191.40 [4919]~E(x49191,f333(a117,f2(a880)))+E(f333(f333(f264(a880),x49191),x49192),f333(a117,f2(a880))) % 191.49/191.40 [4929]~P75(x49291)+E(f333(f333(f3(x49291),f2(x49291)),x49292),f333(f80(x49291),x49292)) % 191.49/191.40 [4930]~E(x49302,f2(a880))+E(f140(a880,f333(f303(a880,x49301),x49302)),f118(a880)) % 191.49/191.40 [4939]~P94(x49391)+E(f333(f333(f81(x49391),x49392),f333(f108(x49391),a84)),x49392) % 191.49/191.40 [4940]E(x49401,f2(a1))+E(f48(f333(f76(a1),x49402),f333(f76(a1),x49401)),f54(x49402,x49401)) % 191.49/191.40 [4954]~E(x49541,x49542)+P4(f333(f333(f250(a880),x49541),x49542)) % 191.49/191.40 [4961]~E(x49611,f2(a104))+E(f333(f333(f81(a880),f333(a21,x49611)),x49612),x49612) % 191.49/191.40 [4971]~P10(x49711)+P10(f333(f333(f264(a1),x49711),x49712)) % 191.49/191.40 [4972]~P79(x49721)+E(f333(f333(f115(x49721),x49722),f333(f80(x49721),x49722)),f258(x49721)) % 191.49/191.40 [4973]~P79(x49731)+E(f333(f333(f106(x49731),x49732),f333(f80(x49731),x49732)),f194(x49731)) % 191.49/191.40 [4974]~P75(x49741)+E(f333(f333(f81(x49741),x49742),f333(f80(x49741),x49742)),f2(x49741)) % 191.49/191.40 [4999]E(x49991,f2(a880))+~E(f333(f80(a1),f333(f105(a1),x49992)),f333(f105(a1),x49991)) % 191.49/191.40 [5000]E(x50001,f2(a880))+~E(f333(f80(a1),f333(f105(a1),x50001)),f333(f105(a1),x50002)) % 191.49/191.40 [5010]E(f202(x50101,x50102),f2(a1))+P4(f333(f333(f250(a1),x50102),x50101)) % 191.49/191.40 [5011]E(f179(x50111,x50112),f118(a1))+P4(f333(f333(f250(a1),x50111),x50112)) % 191.49/191.40 [5024]E(x50241,f333(a117,f2(a880)))+~E(f333(f333(f82(a880),x50242),x50241),f333(a117,f2(a880))) % 191.49/191.40 [5025]E(x50251,f333(a117,f2(a880)))+~E(f333(f333(f82(a880),x50251),x50252),f333(a117,f2(a880))) % 191.49/191.40 [5026]~P108(x50261)+P4(f333(f333(f250(x50261),x50262),x50262)) % 191.49/191.40 [5027]~P96(x50271)+P4(f333(f333(f92(x50271),x50272),x50272)) % 191.49/191.40 [5030]~P94(x50301)+E(f333(f333(f82(x50301),x50302),f333(f108(x50301),a102)),f333(f80(x50301),x50302)) % 191.49/191.40 [5048]~P94(x50481)+E(f333(f80(x50481),f333(f108(x50481),x50482)),f333(f108(x50481),f333(f80(a1),x50482))) % 191.49/191.40 [5049]~P140(x50491)+E(f333(f80(x50491),f333(f107(x50491),x50492)),f333(f107(x50491),f333(f80(a1),x50492))) % 191.49/191.40 [5079]~E(x50791,f333(a117,x50792))+P4(f333(f333(f251(a880),f2(a880)),x50791)) % 191.49/191.40 [5096]~P109(x50961)+E(f333(f80(f890(x50961,a874)),f333(f256(x50961),x50962)),f333(f257(x50961),x50962)) % 191.49/191.40 [5097]~P109(x50971)+E(f333(f80(f890(x50971,a874)),f333(f302(x50971),x50972)),f333(f305(x50971),x50972)) % 191.49/191.40 [5098]~P109(x50981)+E(f333(f80(f890(x50981,a874)),f333(f305(x50981),x50982)),f333(f302(x50981),x50982)) % 191.49/191.40 [5099]~P109(x50991)+E(f333(f80(f890(x50991,a874)),f333(f257(x50991),x50992)),f333(f256(x50991),x50992)) % 191.49/191.40 [5106]~E(f333(f105(a1),x51062),x51061)+P4(f333(f333(f250(a1),f2(a1)),x51061)) % 191.49/191.40 [5113]~E(x51132,f2(a1))+E(f54(x51131,x51132),f333(f333(f263(a1,a1),f2(a1)),f333(f76(a1),x51131))) % 191.49/191.40 [5115]~P5(x51151)+P4(f333(f333(f250(x51151),f194(x51151)),x51152)) % 191.49/191.40 [5150]~P4(f333(x51501,x51502))+P4(f333(x51501,f333(a109,f341(x51501)))) % 191.49/191.40 [5176]~P120(x51761)+E(f333(f333(f82(x51761),f83(x51761,x51762)),f333(f76(x51761),x51762)),x51762) % 191.49/191.40 [5177]E(x51771,x51772)+~P4(f333(f333(f201(a24),x51771),x51772)) % 191.49/191.40 [5186]~E(x51862,f2(a880))+E(f86(f889(a880,a880),f49(x51861,x51862)),f333(f333(f263(a880,a880),f2(a880)),x51861)) % 191.49/191.40 [5197]~E(x51971,x51972)+~P4(f333(f333(f251(a880),x51971),x51972)) % 191.49/191.40 [5198]~E(x51981,x51982)+~P4(f333(f333(f251(a1),x51981),x51982)) % 191.49/191.40 [5201]~P143(x52011)+E(f333(f333(f81(x52011),f79(x52011)),f333(f105(x52011),x52012)),f333(f105(x52011),f333(a117,x52012))) % 191.49/191.40 [5205]~E(x52051,f2(a880))+~P4(f333(f333(f251(a880),x52052),x52051)) % 191.49/191.40 [5221]E(f153(x52211,x52212),x52212)+~E(f333(f195(f881(x52211)),f153(x52211,x52212)),f333(f195(f881(x52211)),x52212)) % 191.49/191.40 [5222]E(f333(f39(x52221),f333(f173(x52221),x52222)),f333(f195(f881(x52221)),x52222))+~P4(f333(f138(x52221),x52222)) % 191.49/191.40 [5232]~P4(f333(x52321,f344(x52321)))+P4(f333(x52321,f333(f105(a1),x52322))) % 191.49/191.40 [5243]E(f281(x52431,x52432),f79(a104))+~P4(f333(f333(f251(a104),x52432),x52431)) % 191.49/191.40 [5244]E(f179(x52441,x52442),f118(a1))+~P4(f333(f333(f251(a1),x52442),x52441)) % 191.49/191.40 [5245]E(f135(x52451,x52452),f120(a1))+~P4(f333(f333(f251(a1),x52451),x52452)) % 191.49/191.40 [5248]~P110(x52481)+E(f304(x52481,x52482,x52482),f333(f333(f311(x52481),x52482),f194(f890(x52481,a874)))) % 191.49/191.40 [5270]~E(f333(f333(f3(a880),x52701),x52702),f2(a880))+P4(f333(f333(f250(a880),x52701),x52702)) % 191.49/191.40 [5271]~E(f333(f333(f3(a1),x52711),x52712),f2(a1))+P4(f333(f333(f92(a1),x52711),x52712)) % 191.49/191.40 [5296]~E(x52962,f2(a880))+E(f56(x52961,x52962,f118(x52961)),f333(f333(f152(f881(x52961)),f118(x52961)),f118(f881(x52961)))) % 191.49/191.40 [5300]~P108(x53001)+~P4(f333(f333(f251(x53001),x53002),x53002)) % 191.49/191.40 [5303]~E(f46(a1,x53031,x53032),f2(a1))+E(f46(a1,x53031,f333(f80(a1),x53032)),f2(a1)) % 191.49/191.40 [5305]~E(f46(a1,x53051,x53052),f2(a1))+E(f46(a1,f333(f80(a1),x53051),x53052),f2(a1)) % 191.49/191.40 [5313]E(f333(f303(a880,x53131),f333(a117,x53132)),f194(f890(a880,a874)))+P4(f333(f333(f250(a880),x53131),x53132)) % 191.49/191.40 [5333]E(f140(a880,f333(f303(a880,x53331),x53332)),f118(a880))+P4(f333(f333(f251(a880),x53331),x53332)) % 191.49/191.40 [5338]~E(f333(f39(x53381),f333(f173(x53381),x53382)),f333(f195(f881(x53381)),x53382))+P4(f333(f138(x53381),x53382)) % 191.49/191.40 [5343]~P4(f333(f138(x53431),x53432))+P4(f333(f138(x53431),f333(f169(x53431),x53432))) % 191.49/191.40 [5344]~P4(f333(f138(x53441),x53442))+P4(f333(f138(x53441),f333(f172(x53441),x53442))) % 191.49/191.40 [5345]~P4(f333(f138(x53451),x53452))+P4(f333(f138(x53451),f333(f170(x53451),x53452))) % 191.49/191.40 [5352]P4(f333(x53521,x53522))+~P4(f333(x53521,f333(a109,f342(x53521)))) % 191.49/191.40 [5353]P4(f333(f333(f250(a880),x53532),x53531))+P4(f333(f333(f250(a880),x53531),x53532)) % 191.49/191.40 [5354]P4(f333(f333(f250(a1),x53542),x53541))+P4(f333(f333(f250(a1),x53541),x53542)) % 191.49/191.40 [5356]~P87(x53561)+P4(f333(f333(f250(x53561),x53562),f333(f76(x53561),x53562))) % 191.49/191.40 [5359]P4(f333(x53591,f386(x53591)))+~P4(f333(x53591,f333(f105(a1),x53592))) % 191.49/191.40 [5384]E(f333(f333(f3(a880),x53841),x53842),f2(a880))+~P4(f333(f333(f250(a880),x53841),x53842)) % 191.49/191.40 [5385]E(f333(f333(f3(a1),x53851),x53852),f2(a1))+~P4(f333(f333(f92(a1),x53851),x53852)) % 191.49/191.40 [5386]E(f333(f333(f40(a880),x53861),x53862),f2(a880))+~P4(f333(f333(f251(a880),x53861),x53862)) % 191.49/191.40 [5404]E(f46(a880,x54041,x54042),x54041)+~P4(f333(f333(f251(a880),x54041),x54042)) % 191.49/191.40 [5413]E(f46(a1,x54131,f333(f80(a1),x54132)),f292(x54131,x54132))+P4(f333(f333(f250(a1),f2(a1)),x54132)) % 191.49/191.40 [5425]E(f333(f333(f3(a1),x54251),x54252),f202(x54251,x54252))+~P4(f333(f333(f250(a1),x54252),x54251)) % 191.49/191.40 [5444]P4(f333(f333(f250(a1),f2(a1)),f344(x54441)))+P4(f333(x54441,f333(f105(a1),x54442))) % 191.49/191.40 [5456]~P62(x54561)+P4(f333(f333(f335(x54561),x54562),f333(f173(x54561),f57(x54561)))) % 191.49/191.40 [5458]~P123(x54581)+P4(f333(f333(f250(x54581),f2(x54581)),f333(f105(x54581),x54582))) % 191.49/191.40 [5459]~P87(x54591)+P4(f333(f333(f250(x54591),f2(x54591)),f333(f76(x54591),x54592))) % 191.49/191.40 [5486]E(f333(f333(f81(a880),x54861),f345(x54862,x54861)),x54862)+~P4(f333(f333(f250(a880),x54861),x54862)) % 191.49/191.40 [5501]E(f304(a1,x55011,x55012),f194(f890(a1,a874)))+~P4(f333(f333(f251(a1),x55012),x55011)) % 191.49/191.40 [5504]~P120(x55041)+E(f333(f333(f82(x55041),f333(f76(x55041),x55042)),f333(f76(x55041),x55042)),f333(f333(f82(x55041),x55042),x55042)) % 191.49/191.40 [5509]E(f140(a880,f333(f303(a880,x55091),f333(a117,x55092))),f118(a880))+P4(f333(f333(f250(a880),x55091),x55092)) % 191.49/191.40 [5511]E(f333(f333(f40(a1),x55111),x55112),f293(x55111,x55112))+~P4(f333(f333(f250(a1),f2(a1)),x55112)) % 191.49/191.40 [5531]P4(f333(f138(x55311),x55312))+~P4(f333(f138(x55311),f333(f169(x55311),x55312))) % 191.49/191.40 [5532]P4(f333(f138(x55321),x55322))+~P4(f333(f138(x55321),f333(f170(x55321),x55322))) % 191.49/191.40 [5553]P4(f333(f63(a880),x55531))+P4(f333(f333(f335(a880),f362(x55531,x55532)),x55531)) % 191.49/191.40 [5554]P4(f333(f63(a880),x55541))+P4(f333(f333(f335(a880),f371(x55541,x55542)),x55541)) % 191.49/191.40 [5555]P4(f333(f333(f251(a880),x55552),f333(a117,x55551)))+P4(f333(f333(f251(a880),x55551),x55552)) % 191.49/191.40 [5556]E(f46(a1,x55561,x55562),f292(x55561,x55562))+~P4(f333(f333(f250(a1),f2(a1)),x55562)) % 191.49/191.40 [5559]E(f140(a880,f333(f303(a880,x55591),x55592)),f118(a880))+~P4(f333(f333(f250(a880),x55592),x55591)) % 191.49/191.40 [5560]~P81(x55601)+E(f333(f312(x55601,x55601,f80(x55601)),f333(f256(x55601),x55602)),f333(f305(x55601),f333(f80(x55601),x55602))) % 191.49/191.40 [5561]~P81(x55611)+E(f333(f312(x55611,x55611,f80(x55611)),f333(f302(x55611),x55612)),f333(f257(x55611),f333(f80(x55611),x55612))) % 191.49/191.40 [5562]~P81(x55621)+E(f333(f312(x55621,x55621,f80(x55621)),f333(f305(x55621),x55622)),f333(f256(x55621),f333(f80(x55621),x55622))) % 191.49/191.40 [5563]~P81(x55631)+E(f333(f312(x55631,x55631,f80(x55631)),f333(f257(x55631),x55632)),f333(f302(x55631),f333(f80(x55631),x55632))) % 191.49/191.40 [5574]E(x55741,f194(f890(x55742,a874)))+P4(f333(f333(f335(x55742),f768(x55741,x55742)),x55741)) % 191.49/191.40 [5575]E(x55751,f194(f890(x55752,a874)))+P4(f333(f333(f335(x55752),f670(x55751,x55752)),x55751)) % 191.49/191.40 [5586]~P4(f333(f333(f251(a880),x55861),x55862))+P4(f333(f333(f250(a880),x55861),x55862)) % 191.49/191.40 [5587]~P4(f333(f333(f251(a1),x55871),x55872))+P4(f333(f333(f250(a1),x55871),x55872)) % 191.49/191.40 [5603]E(f48(x56031,x56032),f333(f333(f263(a1,a1),f2(a1)),x56031))+~P4(f333(f333(f251(a1),x56031),x56032)) % 191.49/191.40 [5604]E(f225(f333(f80(a1),x56041),f333(f80(a1),x56042)),f225(x56041,x56042))+~P4(f333(f333(f251(a1),x56042),f2(a1))) % 191.49/191.40 [5617]E(x56171,x56172)+~E(f333(a5,f333(a117,f333(a21,x56171))),f333(a5,f333(a117,f333(a21,x56172)))) % 191.49/191.40 [5622]E(f48(x56221,x56222),f333(f333(f263(a1,a1),f2(a1)),x56221))+~P4(f333(f333(f250(a1),x56222),f2(a1))) % 191.49/191.40 [5649]E(f46(a880,f333(f108(a880),x56491),f333(f108(a880),x56492)),f2(a880))+~P4(f333(a200,f333(f108(a1),x56491))) % 191.49/191.40 [5664]P4(f333(f333(f250(a1),f2(a1)),f386(x56641)))+~P4(f333(x56641,f333(f105(a1),x56642))) % 191.49/191.40 [5698]P42(f304(a1,x56981,x56982))+~P4(f333(f333(f250(a1),f2(a1)),x56981)) % 191.49/191.40 [5703]~P4(f333(f63(x57031),x57032))+P4(f333(f63(f890(x57031,a874)),f333(f310(x57031),x57032))) % 191.49/191.40 [5716]E(f333(f333(f81(a1),x57161),f333(f105(a1),f392(x57162,x57161))),x57162)+~P4(f333(f333(f250(a1),x57161),x57162)) % 191.49/191.40 [5724]P4(f333(f333(f250(a880),x57241),x57242))+P4(f333(f333(f250(a880),f333(a117,x57242)),x57241)) % 191.49/191.40 [5768]E(f333(f333(f40(a880),f333(f108(a880),x57681)),f333(f108(a880),x57682)),f2(a880))+~P4(f333(a200,f333(f108(a1),x57681))) % 191.49/191.40 [5769]E(f333(f333(f82(a880),f333(f108(a880),x57691)),f333(f108(a880),x57692)),f2(a880))+~P4(f333(f333(f251(a1),x57691),a84)) % 191.49/191.40 [5771]P4(f333(f333(f251(a880),x57711),f333(a117,x57712)))+~P4(f333(f333(f251(a880),x57711),x57712)) % 191.49/191.40 [5773]P4(f333(f333(f251(a880),x57731),f333(a117,x57732)))+~P4(f333(f333(f250(a880),x57731),x57732)) % 191.49/191.40 [5775]P4(f333(f333(f250(a880),x57751),f333(a117,x57752)))+~P4(f333(f333(f250(a880),x57751),x57752)) % 191.49/191.40 [5778]~E(x57781,x57782)+P4(f333(f333(f251(a1),x57781),f333(f333(f81(a1),x57782),f79(a1)))) % 191.49/191.40 [5781]E(f46(a1,x57811,x57812),f2(a1))+E(f333(f333(f3(a1),x57812),f46(a1,x57811,x57812)),f46(a1,f333(f80(a1),x57811),x57812)) % 191.49/191.40 [5790]E(x57901,f118(x57902))+P4(f333(f333(f335(x57902),f145(x57902,x57901)),f333(f173(x57902),x57901))) % 191.49/191.40 [5802]E(f86(f889(a880,a880),f49(x58021,x58022)),f333(f333(f263(a880,a880),f2(a880)),x58021))+~P4(f333(f333(f251(a880),x58021),x58022)) % 191.49/191.40 [5835]E(f333(f333(f3(a880),f333(f108(a880),x58351)),f333(f108(a880),x58352)),f333(f108(a880),x58351))+~P4(f333(f333(f251(a1),x58352),a84)) % 191.49/191.40 [5836]E(f333(f333(f81(a880),f333(f108(a880),x58361)),f333(f108(a880),x58362)),f333(f108(a880),x58362))+~P4(f333(f333(f251(a1),x58361),a84)) % 191.49/191.40 [5841]E(f333(a117,f333(f333(f81(a880),x58411),f844(x58412,x58411))),x58412)+~P4(f333(f333(f251(a880),x58411),x58412)) % 191.49/191.40 [5864]P4(f333(x58641,x58642))+~P4(f333(x58641,f333(a90,f717(x58642,x58641)))) % 191.49/191.40 [5872]~P4(f333(f333(f251(a880),x58721),f333(a117,x58722)))+P4(f333(f333(f250(a880),x58721),x58722)) % 191.49/191.40 [5918]E(f333(f333(f311(a880),x59181),f333(f303(a880,x59182),x59181)),f333(f303(a880,x59182),f333(a117,x59181)))+~P4(f333(f333(f250(a880),x59182),x59181)) % 191.49/191.40 [5922]E(x59221,f118(x59222))+E(f333(f333(f127(x59222),f119(x59222,x59221)),f333(f333(f152(x59222),f145(x59222,x59221)),f118(x59222))),x59221) % 191.49/191.40 [5935]P4(f333(f63(x59351),x59352))+~P4(f333(f333(f251(a880),f2(a880)),f333(f39(x59351),x59352))) % 191.49/191.40 [5937]~E(x59371,f194(f890(x59372,a874)))+~P4(f333(f333(f251(a880),f2(a880)),f333(f39(x59372),x59371))) % 191.49/191.40 [5949]~P4(f333(f333(f251(a880),x59491),x59492))+P4(f333(f333(f250(a880),f333(a117,x59491)),x59492)) % 191.49/191.40 [5957]~P109(x59571)+E(f151(x59571,x59571,f7(x59571),f153(x59571,x59572)),f140(x59571,f333(f173(x59571),x59572))) % 191.49/191.40 [5960]E(x59601,f118(x59602))+P4(f333(f333(f335(x59602),f333(f142(x59602),x59601)),f333(f173(x59602),x59601))) % 191.49/191.40 [5966]~P123(x59661)+P4(f333(f333(f251(x59661),x59662),f333(f333(f81(x59661),x59662),f79(x59661)))) % 191.49/191.40 [5968]~P87(x59681)+P4(f333(f333(f250(x59681),f333(f80(x59681),x59682)),f333(f76(x59681),x59682))) % 191.49/191.40 [6001]P4(f333(f63(a880),x60011))+~P4(f333(f333(f251(a880),f371(x60011,x60012)),x60012)) % 191.49/191.40 [6002]P4(f333(f63(a880),x60021))+~P4(f333(f333(f250(a880),f362(x60021,x60022)),x60022)) % 191.49/191.40 [6006]~P4(f333(f63(f889(x60061,x60061)),x60062))+P4(f333(f63(x60061),f333(f286(x60061),x60062))) % 191.49/191.40 [6060]~P4(f333(f333(f251(a880),x60602),f333(a117,x60601)))+~P4(f333(f333(f251(a880),x60601),x60602)) % 191.49/191.40 [6061]~P110(x60611)+E(f333(f333(f106(f890(x60611,a874)),f333(f302(x60611),x60612)),f333(f257(x60611),x60612)),f333(f333(f311(x60611),x60612),f194(f890(x60611,a874)))) % 191.49/191.40 [6074]P4(f333(f63(x60741),x60742))+~P4(f333(f63(f890(x60741,a874)),f333(f310(x60741),x60742))) % 191.49/191.40 [6099]P4(f333(f333(f251(a880),f333(a117,x60991)),f333(a117,x60992)))+~P4(f333(f333(f251(a880),x60991),x60992)) % 191.49/191.40 [6100]P4(f333(f333(f251(a880),f333(a21,x61001)),f333(a21,x61002)))+~P4(f333(f333(f251(a104),x61001),x61002)) % 191.49/191.40 [6101]P4(f333(f333(f251(a104),f333(a5,x61011)),f333(a5,x61012)))+~P4(f333(f333(f251(a880),x61011),x61012)) % 191.49/191.40 [6102]P4(f333(f333(f250(a880),f333(a117,x61021)),f333(a117,x61022)))+~P4(f333(f333(f250(a880),x61021),x61022)) % 191.49/191.40 [6103]P4(f333(f333(f250(a880),f333(a21,x61031)),f333(a21,x61032)))+~P4(f333(f333(f250(a104),x61031),x61032)) % 191.49/191.40 [6104]P4(f333(f333(f250(a104),f333(a5,x61041)),f333(a5,x61042)))+~P4(f333(f333(f250(a880),x61041),x61042)) % 191.49/191.40 [6107]E(x61071,x61072)+~E(f333(f312(a880,a1,f105(a1)),x61071),f333(f312(a880,a1,f105(a1)),x61072)) % 191.49/191.40 [6123]P4(f333(f333(f251(a880),x61231),x61232))+~P4(f333(f333(f251(a880),f333(a117,x61231)),x61232)) % 191.49/191.40 [6126]P4(f333(f333(f251(a880),x61261),x61262))+~P4(f333(f333(f250(a880),f333(a117,x61261)),x61262)) % 191.49/191.40 [6127]P4(f333(f333(f250(a880),x61271),x61272))+~P4(f333(f333(f250(a880),f333(a117,x61271)),x61272)) % 191.49/191.40 [6142]E(f46(a1,x61421,x61422),f2(a1))+E(f333(f333(f3(a1),f46(a1,x61421,x61422)),x61422),f46(a1,x61421,f333(f80(a1),x61422))) % 191.49/191.40 [6209]E(f333(f39(f890(x62091,a874)),f333(f310(x62091),x62092)),f333(f333(f264(a880),f333(a117,f333(a117,f2(a880)))),f333(f39(x62091),x62092)))+~P4(f333(f63(x62091),x62092)) % 191.49/191.40 [6212]E(x62121,f118(x62122))+E(f333(f333(f166(x62122),x62121),f333(f333(f3(a880),f333(f195(f881(x62122)),x62121)),f79(a880))),f145(x62122,x62121)) % 191.49/191.40 [6237]E(x62371,f118(x62372))+E(f333(f333(f127(x62372),f333(f172(x62372),x62371)),f333(f333(f152(x62372),f333(f142(x62372),x62371)),f118(x62372))),f333(f169(x62372),x62371)) % 191.49/191.40 [6266]~P4(f333(f63(x62661),f41(f890(x62661,a874),x62662)))+P4(f333(f63(f890(x62661,a874)),x62662)) % 191.49/191.40 [6289]P4(f333(f333(f250(a880),f333(f108(a880),x62891)),f333(f108(a880),x62892)))+~P4(f333(f333(f250(a1),x62891),a84)) % 191.49/191.40 [6305]~P4(f333(f333(f251(a1),x63051),x63052))+P4(f333(f333(f251(a1),x63051),f333(f333(f81(a1),x63052),f79(a1)))) % 191.49/191.40 [6306]~P4(f333(f333(f250(a1),x63061),x63062))+P4(f333(f333(f251(a1),x63061),f333(f333(f81(a1),x63062),f79(a1)))) % 191.49/191.40 [6307]~P4(f333(f333(f251(a1),x63071),x63072))+P4(f333(f333(f250(a1),x63071),f333(f333(f3(a1),x63072),f79(a1)))) % 191.49/191.40 [6309]~P4(f333(f333(f251(a1),x63091),x63092))+P4(f333(f333(f251(a1),f333(f108(a1),x63091)),f333(f108(a1),x63092))) % 191.49/191.40 [6311]~P4(f333(f333(f251(a880),x63111),x63112))+P4(f333(f333(f251(a1),f333(f105(a1),x63111)),f333(f105(a1),x63112))) % 191.49/191.40 [6312]~P4(f333(f333(f250(a1),x63121),x63122))+P4(f333(f333(f250(a880),f333(f108(a880),x63121)),f333(f108(a880),x63122))) % 191.49/191.40 [6313]~P4(f333(f333(f250(a1),x63131),x63132))+P4(f333(f333(f250(a1),f333(f108(a1),x63131)),f333(f108(a1),x63132))) % 191.49/191.40 [6315]~P4(f333(f333(f250(a880),x63151),x63152))+P4(f333(f333(f250(a1),f333(f105(a1),x63151)),f333(f105(a1),x63152))) % 191.49/191.40 [6316]~P4(f333(f333(f92(a1),x63161),x63162))+P4(f333(f333(f92(a1),f333(f108(a1),x63161)),f333(f108(a1),x63162))) % 191.49/191.40 [6334]~P4(f333(f333(f250(a880),x63341),x63342))+~P4(f333(f333(f250(a880),f333(a117,x63342)),x63341)) % 191.49/191.40 [6378]~P4(f333(f333(f251(a880),f333(a117,x63781)),f333(a117,x63782)))+P4(f333(f333(f251(a880),x63781),x63782)) % 191.49/191.40 [6379]~P4(f333(f333(f251(a104),f333(a5,x63791)),f333(a5,x63792)))+P4(f333(f333(f251(a880),x63791),x63792)) % 191.49/191.40 [6380]~P4(f333(f333(f251(a880),f333(a109,x63801)),f333(a109,x63802)))+P4(f333(f333(f251(a1),x63801),x63802)) % 191.49/191.40 [6381]~P4(f333(f333(f251(a880),f333(a21,x63811)),f333(a21,x63812)))+P4(f333(f333(f251(a104),x63811),x63812)) % 191.49/191.40 [6382]~P4(f333(f333(f250(a880),f333(a117,x63821)),f333(a117,x63822)))+P4(f333(f333(f250(a880),x63821),x63822)) % 191.49/191.40 [6383]~P4(f333(f333(f250(a104),f333(a5,x63831)),f333(a5,x63832)))+P4(f333(f333(f250(a880),x63831),x63832)) % 191.49/191.40 [6384]~P4(f333(f333(f250(a880),f333(a21,x63841)),f333(a21,x63842)))+P4(f333(f333(f250(a104),x63841),x63842)) % 191.49/191.40 [6424]~P4(f333(f333(f251(a880),f333(a109,x64242)),f333(a109,x64241)))+P4(f333(f333(f251(a1),f2(a1)),x64241)) % 191.49/191.40 [6455]P4(f333(f333(f250(a1),f2(a1)),f46(a1,x64551,x64552)))+~P4(f333(f333(f251(a1),f2(a1)),x64552)) % 191.49/191.40 [6609]P40(x66091,x66092)+~E(f333(f333(f290(x66091,x66091,x66091),x66092),x66092),f194(f890(f889(x66091,x66091),a874))) % 191.49/191.40 [6621]~P40(x66211,x66212)+P40(x66211,f333(f333(f290(x66211,x66211,x66211),x66212),x66212)) % 191.49/191.40 [6633]P4(f333(f333(f251(a1),x66331),x66332))+~P4(f333(f333(f250(a1),x66331),f333(f333(f3(a1),x66332),f79(a1)))) % 191.49/191.40 [6634]P4(f333(f333(f250(a1),x66341),x66342))+~P4(f333(f333(f251(a1),x66341),f333(f333(f81(a1),x66342),f79(a1)))) % 191.49/191.40 [6637]P4(f333(f333(f251(a880),x66371),x66372))+~P4(f333(f333(f251(a1),f333(f105(a1),x66371)),f333(f105(a1),x66372))) % 191.49/191.40 [6638]P4(f333(f333(f251(a1),x66381),x66382))+~P4(f333(f333(f251(a880),f333(f108(a880),x66381)),f333(f108(a880),x66382))) % 191.49/191.40 [6639]P4(f333(f333(f251(a1),x66391),x66392))+~P4(f333(f333(f251(a1),f333(f108(a1),x66391)),f333(f108(a1),x66392))) % 191.49/191.40 [6641]P4(f333(f333(f250(a880),x66411),x66412))+~P4(f333(f333(f250(a1),f333(f105(a1),x66411)),f333(f105(a1),x66412))) % 191.49/191.40 [6642]P4(f333(f333(f250(a1),x66421),x66422))+~P4(f333(f333(f250(a1),f333(f108(a1),x66421)),f333(f108(a1),x66422))) % 191.49/191.40 [6643]P4(f333(f333(f92(a1),x66431),x66432))+~P4(f333(f333(f92(a1),f333(f108(a1),x66431)),f333(f108(a1),x66432))) % 191.49/191.40 [6736]~E(f656(x67362,x67361),f118(x67361))+E(f333(f143(f881(x67361),f881(x67361),f127(x67361),f118(x67361)),x67362),f118(x67361)) % 191.49/191.40 [6737]~E(f657(x67372,x67371),f118(x67371))+E(f333(f143(f881(x67371),f881(x67371),f127(x67371),f118(x67371)),x67372),f118(x67371)) % 191.49/191.40 [6744]~P9(x67441)+E(f333(f143(x67441,x67441,f115(x67441),f194(x67441)),x67442),f41(x67441,f333(f173(x67441),x67442))) % 191.49/191.40 [6745]~P9(x67451)+E(f333(f143(x67451,x67451,f106(x67451),f258(x67451)),x67452),f42(x67451,f333(f173(x67451),x67452))) % 191.49/191.40 [6757]E(x67571,f2(a104))+E(f333(f333(f81(a880),f333(a21,f333(f333(f3(a104),x67571),f79(a104)))),f333(a117,x67572)),f333(f333(f81(a880),f333(a21,x67571)),x67572)) % 191.49/191.40 [6801]P4(f333(f333(f251(a1),f333(f333(f3(a1),x68011),x68012)),f2(a1)))+~P4(f333(f333(f251(a1),x68011),x68012)) % 191.49/191.40 [6825]~P109(x68251)+E(f333(f333(f115(f890(x68251,a874)),f333(f333(f311(x68251),x68252),f194(f890(x68251,a874)))),f333(f305(x68251),x68252)),f333(f257(x68251),x68252)) % 191.49/191.40 [6898]~P59(x68981,x68982)+P40(x68981,f333(f255(f889(x68981,x68981)),f333(f272(x68981,x68981,a874),x68982))) % 191.49/191.40 [6899]~P59(x68991,x68992)+P57(x68991,f333(f255(f889(x68991,x68991)),f333(f272(x68991,x68991,a874),x68992))) % 191.49/191.40 [6900]E(x69001,f194(f890(x69002,a874)))+~P4(f333(f333(f250(f890(x69002,a874)),x69001),f194(f890(x69002,a874)))) % 191.49/191.40 [6984]~P4(f333(f333(f251(a880),f2(a880)),x69842))+P4(f333(f333(f251(a880),f46(a880,x69841,x69842)),x69842)) % 191.49/191.40 [6986]~P4(f333(f333(f251(a1),f2(a1)),x69862))+P4(f333(f333(f251(a1),f46(a1,x69861,x69862)),x69862)) % 191.49/191.40 [6987]~P4(f333(f333(f251(a880),f2(a880)),x69872))+P4(f333(f333(f250(a880),f46(a880,x69871,x69872)),x69872)) % 191.49/191.40 [6988]~P4(f333(f333(f250(a1),f2(a1)),x69881))+P4(f333(f333(f250(a1),f46(a1,x69881,x69882)),x69881)) % 191.49/191.40 [7066]~P110(x70661)+E(f333(f333(f3(f890(x70661,a874)),f333(f333(f311(x70661),x70662),f194(f890(x70661,a874)))),f333(f256(x70661),x70662)),f333(f333(f311(x70661),x70662),f194(f890(x70661,a874)))) % 191.49/191.40 [7138]~P52(x71381,x71382)+P50(x71381,f258(f890(x71381,a874)),f333(f255(f889(x71381,x71381)),f333(f272(x71381,x71381,a874),x71382))) % 191.49/191.40 [7139]P4(f333(x71391,x71392))+P4(f333(f333(f335(f890(f889(a880,a880),a874)),f717(x71392,x71391)),a103)) % 191.49/191.40 [7184]E(f333(f333(f127(a880),f140(a880,f333(f303(a880,x71841),x71842))),f333(f333(f152(a880),x71842),f118(a880))),f140(a880,f333(f303(a880,x71841),f333(a117,x71842))))+~P4(f333(f333(f250(a880),x71841),x71842)) % 191.49/191.40 [7316]E(x73161,f2(a880))+~E(f333(f143(a880,a880,f81(a880),x73161),x73162),f2(a880)) % 191.49/191.40 [7344]~P4(f333(f333(f251(a1),f333(f333(f3(a1),x73441),x73442)),f2(a1)))+P4(f333(f333(f251(a1),x73441),x73442)) % 191.49/191.40 [7372]P40(x73721,x73722)+~P40(x73721,f333(f333(f290(x73721,x73721,x73721),x73722),x73722)) % 191.49/191.40 [7401]~P4(f333(f333(f250(a880),f333(a117,x74011)),x74012))+P4(f191(a874,a247,f333(f250(a880),x74011),x74012)) % 191.49/191.40 [7555]P28(a880,a880,f333(f333(f9(a880,a880,a880),f3(a880)),x75551),x75552)+P4(f333(f333(f335(a880),f724(x75551,x75552)),x75552)) % 191.49/191.40 [7609]E(f333(f333(f333(f67(a880,x76091,f81(a880)),f333(f18(a880,x76091),f79(a880))),f2(a880)),x76092),f333(f39(x76091),x76092))+~P4(f333(f63(x76091),x76092)) % 191.49/191.40 [7651]P28(a880,a880,f333(f333(f9(a880,a880,a880),f3(a880)),x76511),x76512)+~P4(f333(f333(f250(a880),x76511),f724(x76511,x76512))) % 191.49/191.40 [7708]P40(x77081,x77082)+P4(f333(f333(f250(f890(x77081,a874)),f722(x77082,x77081)),f333(f287(x77081,x77081,x77082),f722(x77082,x77081)))) % 191.49/191.40 [7713]P59(x77131,x77132)+~P40(x77131,f333(f255(f889(x77131,x77131)),f333(f272(x77131,x77131,a874),x77132))) % 191.49/191.40 [7785]P4(f333(f333(f250(a880),f333(a117,x77851)),x77852))+~P4(f191(a874,a247,f333(f250(a880),x77851),x77852)) % 191.49/191.40 [7841]P4(f333(f333(f335(f889(a880,a880)),f333(f333(f263(a880,a880),x78411),x78412)),f309(a880,a323)))+~P4(f333(f333(f250(a880),x78411),x78412)) % 191.49/191.40 [7929]P52(x79291,x79292)+~P50(x79291,f258(f890(x79291,a874)),f333(f255(f889(x79291,x79291)),f333(f272(x79291,x79291,a874),x79292))) % 191.49/191.40 [7987]~P4(f333(f138(x79871),x79872))+P4(f333(f138(f890(x79871,a874)),f333(f333(f155(f881(x79871),f890(x79871,a874)),f173(x79871)),f55(x79871,x79872)))) % 191.49/191.40 [8200]~P40(x82001,f333(f288(x82001,x82001),x82002))+P40(x82001,f333(f288(x82001,x82001),f333(f333(f290(x82001,x82001,x82001),x82002),f309(x82001,x82002)))) % 191.49/191.40 [8318]P4(f333(f63(f889(x83181,x83181)),f333(f333(f290(x83181,x83181,x83181),x83182),f309(x83181,x83182))))+~P4(f333(f63(f889(x83181,x83181)),x83182)) % 191.49/191.40 [8346]E(x83461,f2(a1))+P4(f333(f50(x83462,x83461),f333(f333(f263(a1,a1),f333(f333(f40(a1),x83462),x83461)),f46(a1,x83462,x83461)))) % 191.49/191.40 [8357]~P4(f333(f333(f335(f889(a880,a880)),f333(f333(f263(a880,a880),x83571),x83572)),f309(a880,a323)))+P4(f333(f333(f250(a880),x83571),x83572)) % 191.49/191.40 [8376]~P84(x83761)+E(f333(f143(x83761,x83761,f333(f9(x83761,x83761,x83761),f81(x83761)),f2(x83761)),f333(f170(x83761),x83762)),f333(f143(x83761,x83761,f81(x83761),f2(x83761)),x83762)) % 191.49/191.40 [8554]~P109(x85541)+E(f333(f143(f881(x85541),x85541,f333(f9(x85541,f881(x85541),f881(x85541)),f149(x85541,x85541,f7(x85541))),f118(x85541)),x85542),f151(x85541,x85541,f7(x85541),x85542)) % 191.49/191.40 [8661]P4(f333(f333(f335(f889(a880,a880)),f333(f333(f263(a880,a880),x86611),x86612)),f333(f333(f290(a880,a880,a880),a323),f309(a880,a323))))+~P4(f333(f333(f251(a880),x86611),x86612)) % 191.49/191.40 [8702]~P4(f333(f63(f889(x87021,x87021)),f333(f333(f290(x87021,x87021,x87021),x87022),f309(x87021,x87022))))+P4(f333(f63(f889(x87021,x87021)),x87022)) % 191.49/191.40 [8960]P57(x89601,x89602)+P4(f333(f333(f335(f889(x89601,x89601)),f333(f333(f263(x89601,x89601),f762(x89602,x89601)),f762(x89602,x89601))),f333(f333(f290(x89601,x89601,x89601),x89602),f309(x89601,x89602)))) % 191.49/191.40 [8961]P57(x89611,x89612)+P4(f333(f333(f335(f889(x89611,x89611)),f333(f333(f263(x89611,x89611),f770(x89612,x89611)),f770(x89612,x89611))),f333(f333(f290(x89611,x89611,x89611),x89612),f309(x89611,x89612)))) % 191.49/191.40 [9062]~P4(f333(f333(f335(f889(a880,a880)),f333(f333(f263(a880,a880),x90621),x90622)),f333(f333(f290(a880,a880,a880),a323),f309(a880,a323))))+P4(f333(f333(f251(a880),x90621),x90622)) % 191.49/191.40 [5092]~P94(x50921)+E(f333(f333(f81(x50921),f333(f108(x50921),a84)),x50922),x50922) % 191.49/191.40 [5120]~P79(x51201)+E(f333(f333(f115(x51201),f333(f80(x51201),x51202)),x51202),f258(x51201)) % 191.49/191.40 [5121]~P79(x51211)+E(f333(f333(f106(x51211),f333(f80(x51211),x51212)),x51212),f194(x51211)) % 191.49/191.40 [5122]~P68(x51221)+E(f333(f333(f81(x51221),f333(f80(x51221),x51222)),x51222),f2(x51221)) % 191.49/191.40 [5123]~P75(x51231)+E(f333(f333(f81(x51231),f333(f80(x51231),x51232)),x51232),f2(x51231)) % 191.49/191.40 [5154]~P94(x51541)+E(f333(f333(f82(x51541),f333(f108(x51541),a102)),x51542),f333(f80(x51541),x51542)) % 191.49/191.40 [5327]~P112(x53271)+E(f333(f333(f82(x53271),f333(f80(x53271),f79(x53271))),x53272),f333(f80(x53271),x53272)) % 191.49/191.40 [5369]E(f333(f76(a1),x53691),f79(a1))+~E(f333(f76(a1),f333(f333(f82(a1),x53691),x53692)),f79(a1)) % 191.49/191.40 [5461]~P94(x54611)+E(f333(f333(f81(x54611),f79(x54611)),f333(f108(x54611),x54612)),f333(f108(x54611),f333(f333(f3(a1),x54612),a102))) % 191.49/191.40 [5512]~P6(x55121)+E(f12(x55121,f333(f333(f311(x55121),x55122),f194(f890(x55121,a874)))),x55122) % 191.49/191.40 [5513]~P6(x55131)+E(f13(x55131,f333(f333(f311(x55131),x55132),f194(f890(x55131,a874)))),x55132) % 191.49/191.40 [5514]~P9(x55141)+E(f41(x55141,f333(f333(f311(x55141),x55142),f194(f890(x55141,a874)))),x55142) % 191.49/191.40 [5515]~P9(x55151)+E(f42(x55151,f333(f333(f311(x55151),x55152),f194(f890(x55151,a874)))),x55152) % 191.49/191.40 [5516]~P109(x55161)+E(f16(x55161,f333(f333(f311(x55161),x55162),f194(f890(x55161,a874)))),x55162) % 191.49/191.40 [5517]~P109(x55171)+E(f17(x55171,f333(f333(f311(x55171),x55172),f194(f890(x55171,a874)))),x55172) % 191.49/191.40 [5539]E(f333(f333(f81(a880),x55391),f333(f333(f3(a880),x55392),x55391)),x55392)+P4(f333(f333(f251(a880),x55392),x55391)) % 191.49/191.40 [5569]E(x55691,f118(x55692))+P4(f333(f333(f251(a880),f2(a880)),f333(f195(f881(x55692)),x55691))) % 191.49/191.40 [5695]~P109(x56951)+E(f14(x56951,f248(x56951),f333(f333(f311(x56951),x56952),f194(f890(x56951,a874)))),x56952) % 191.49/191.40 [5696]~P109(x56961)+E(f15(x56961,f249(x56961),f333(f333(f311(x56961),x56962),f194(f890(x56961,a874)))),x56962) % 191.49/191.40 [5758]E(f333(f333(f3(a880),x57581),f333(f333(f3(a880),x57581),x57582)),x57582)+~P4(f333(f333(f250(a880),x57582),x57581)) % 191.49/191.40 [5759]E(f333(f333(f81(a880),x57591),f333(f333(f3(a880),x57592),x57591)),x57592)+~P4(f333(f333(f250(a880),x57591),x57592)) % 191.49/191.40 [5780]E(f46(a880,f333(f333(f3(a880),x57801),x57802),x57802),f46(a880,x57801,x57802))+P4(f333(f333(f251(a880),x57801),x57802)) % 191.49/191.40 [5791]E(f333(f80(a1),f333(f333(f40(a1),x57911),f333(f80(a1),x57912))),f293(x57911,x57912))+P4(f333(f333(f250(a1),f2(a1)),x57912)) % 191.49/191.40 [5793]~E(x57932,f2(a880))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f264(a880),x57931),x57932))) % 191.49/191.40 [5844]~P94(x58441)+E(f333(f333(f81(x58441),f333(f80(x58441),f79(x58441))),f333(f108(x58441),x58442)),f333(f108(x58441),f333(f333(f81(a1),x58442),a102))) % 191.49/191.40 [5845]E(f333(f333(f264(a880),f333(f108(a880),x58451)),x58452),f333(f333(f264(a880),f2(a880)),x58452))+~P4(f333(a200,f333(f108(a1),x58451))) % 191.49/191.40 [5941]E(f333(f142(a880),f140(a880,f333(f303(a880,x59411),x59412))),x59411)+~P4(f333(f333(f251(a880),x59411),x59412)) % 191.49/191.40 [5961]E(f333(f333(f82(a880),f333(f108(a880),x59611)),f333(f108(a880),x59612)),f333(f108(a880),f333(f333(f82(a1),x59611),x59612)))+P4(f333(f333(f251(a1),x59611),a84)) % 191.49/191.40 [5967]~P125(x59671)+P4(f333(f333(f250(x59671),f2(x59671)),f333(f333(f82(x59671),x59672),x59672))) % 191.49/191.40 [5979]E(f333(f333(f3(a880),f333(a117,x59791)),x59792),f333(a117,f333(f333(f3(a880),x59791),x59792)))+~P4(f333(f333(f250(a880),x59792),x59791)) % 191.49/191.40 [5982]E(f46(a880,f333(f333(f3(a880),x59821),x59822),x59822),f46(a880,x59821,x59822))+~P4(f333(f333(f250(a880),x59822),x59821)) % 191.49/191.40 [6035]E(f333(f333(f264(a880),f333(a109,x60351)),x60352),f333(a109,f333(f333(f264(a1),x60351),x60352)))+~P4(f333(f333(f250(a1),f2(a1)),x60351)) % 191.49/191.40 [6051]P4(f333(f138(x60511),x60512))+P4(f333(f333(f251(a880),f554(x60512,x60511)),f333(f195(f881(x60511)),x60512))) % 191.49/191.40 [6052]P4(f333(f138(x60521),x60522))+P4(f333(f333(f251(a880),f580(x60522,x60521)),f333(f195(f881(x60521)),x60522))) % 191.49/191.40 [6067]~E(x60671,f118(x60672))+~P4(f333(f333(f251(a880),f2(a880)),f333(f195(f881(x60672)),x60671))) % 191.49/191.40 [6081]E(f145(a880,f140(a880,f333(f303(a880,x60811),x60812))),f333(f333(f3(a880),x60812),f79(a880)))+~P4(f333(f333(f251(a880),x60811),x60812)) % 191.49/191.40 [6084]E(f333(f333(f81(a1),x60841),f333(f105(a1),f333(a117,f393(x60842,x60841)))),x60842)+~P4(f333(f333(f251(a1),x60841),x60842)) % 191.49/191.40 [6091]E(x60911,f2(a880))+E(f333(f333(f82(a880),x60912),f333(f333(f264(a880),x60912),f333(f333(f3(a880),x60911),f79(a880)))),f333(f333(f264(a880),x60912),x60911)) % 191.49/191.40 [6117]E(f333(f333(f82(a880),f333(a109,x61171)),f333(a109,x61172)),f333(a109,f333(f333(f82(a1),x61171),x61172)))+~P4(f333(f333(f250(a1),f2(a1)),x61171)) % 191.49/191.40 [6118]E(f333(f333(f40(a880),f333(a109,x61181)),f333(a109,x61182)),f333(a109,f333(f333(f40(a1),x61181),x61182)))+~P4(f333(f333(f250(a1),f2(a1)),x61181)) % 191.49/191.40 [6132]~P115(x61321)+E(f333(f333(f81(x61321),x61322),x61322),f333(f333(f82(x61321),f333(f333(f81(x61321),f79(x61321)),f79(x61321))),x61322)) % 191.49/191.40 [6151]E(f333(f333(f3(a1),f333(f105(a1),x61511)),f333(f105(a1),x61512)),f333(f105(a1),f333(f333(f3(a880),x61511),x61512)))+~P4(f333(f333(f250(a880),x61512),x61511)) % 191.49/191.40 [6153]E(f333(f333(f263(a1,a1),f333(f108(a1),a102)),f333(f333(f81(a1),x61531),x61532)),f51(x61531,x61532))+~P4(f333(f333(f250(a1),x61532),f2(a1))) % 191.49/191.40 [6188]E(f180(x61881,x61882),f118(f881(x61881)))+P4(f333(f333(f335(f881(x61881)),f623(x61882,x61881)),f333(f173(f881(x61881)),x61882))) % 191.49/191.40 [6197]E(f121(a1,f333(f128(a1),x61971),f135(x61972,f333(f333(f81(a1),x61971),f79(a1)))),f135(x61972,x61971))+P4(f333(f333(f251(a1),x61972),x61971)) % 191.49/191.40 [6272]E(f333(f333(f152(a1),x62721),f179(f333(f333(f81(a1),x62721),f79(a1)),x62722)),f179(x62721,x62722))+~P4(f333(f333(f250(a1),x62721),x62722)) % 191.49/191.40 [6308]~P4(f333(f333(f251(a880),x63082),x63081))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f3(a880),x63081),x63082))) % 191.49/191.40 [6337]~P4(f333(f333(f251(a880),x63371),f333(a109,x63372)))+P4(f333(f333(f251(a1),f333(f105(a1),x63371)),x63372)) % 191.49/191.40 [6368]~P109(x63681)+E(f333(f333(f115(f890(x63681,a874)),f333(f256(x63681),x63682)),f333(f333(f311(x63681),x63682),f194(f890(x63681,a874)))),f333(f302(x63681),x63682)) % 191.49/191.40 [6371]~P4(f333(f333(f251(a880),f2(a880)),x63711))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f264(a880),x63711),x63712))) % 191.49/191.40 [6372]~P4(f333(f333(f250(a1),f2(a1)),x63721))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f264(a1),x63721),x63722))) % 191.49/191.40 [6400]~E(f333(x64001,f2(a880)),f2(a880))+E(f333(f333(f8(a880,a880),x64001),f304(a880,f333(a117,f2(a880)),x64002)),f333(f333(f8(a880,a880),x64001),f304(a880,f2(a880),x64002))) % 191.49/191.40 [6478]E(f333(f333(f311(a1),x64781),f304(a1,f333(f333(f81(a1),x64781),f79(a1)),x64782)),f304(a1,x64781,x64782))+P4(f333(f333(f251(a1),x64782),x64781)) % 191.49/191.40 [6479]P4(f333(f333(f251(a880),x64791),f333(a109,x64792)))+~P4(f333(f333(f251(a1),f333(f105(a1),x64791)),x64792)) % 191.49/191.40 [6576]E(f333(a109,f333(f333(f40(a1),f333(f108(a1),x65761)),f333(f108(a1),x65762))),f333(f333(f40(a880),f333(f108(a880),x65761)),f333(f108(a880),x65762)))+P4(f333(a200,f333(f108(a1),x65761))) % 191.49/191.40 [6635]P4(f333(f333(f251(a880),x66351),x66352))+~P4(f333(f333(f251(a880),f2(a880)),f333(f333(f3(a880),x66352),x66351))) % 191.49/191.40 [6679]P4(f333(f333(f251(a880),f2(a880)),x66791))+~P4(f333(f333(f251(a880),f2(a880)),f333(f333(f82(a880),x66792),x66791))) % 191.49/191.40 [6680]P4(f333(f333(f251(a880),f2(a880)),x66801))+~P4(f333(f333(f251(a880),f2(a880)),f333(f333(f82(a880),x66801),x66802))) % 191.49/191.40 [6697]~P4(f333(f333(f250(a1),x66971),f2(a1)))+E(f333(f333(f82(a880),f333(a109,f333(f80(a1),x66971))),f333(a109,f333(f80(a1),x66972))),f333(a109,f333(f333(f82(a1),x66971),x66972))) % 191.49/191.40 [6755]~E(x67552,f194(f890(x67551,a874)))+P4(f333(f333(f250(f890(x67551,a874)),x67552),f333(f80(f890(x67551,a874)),x67552))) % 191.49/191.40 [6865]~P4(f333(f333(f251(a1),x68651),x68652))+P4(f333(f333(f250(a1),f333(f333(f81(a1),x68651),f79(a1))),x68652)) % 191.49/191.40 [6930]E(x69301,f2(a880))+~P4(f333(f333(f250(a1),f333(f105(a1),x69302)),f333(f80(a1),f333(f105(a1),x69301)))) % 191.49/191.40 [6931]E(x69311,f2(a880))+~P4(f333(f333(f250(a1),f333(f105(a1),x69311)),f333(f80(a1),f333(f105(a1),x69312)))) % 191.49/191.40 [7037]E(f333(f333(f263(a1,a1),f333(f108(a1),a102)),f333(f333(f81(a1),x70371),x70372)),f51(x70371,x70372))+~P4(f333(f333(f250(a1),f2(a1)),f333(f333(f81(a1),x70371),x70372))) % 191.49/191.40 [7078]~P29(x70781,x70782)+P40(x70781,f333(f262(f890(f889(x70781,x70781),a874),f890(f889(x70781,x70781),a874)),x70782)) % 191.49/191.40 [7096]~P4(f333(f333(f250(a880),f333(a117,f2(a880))),x70961))+P4(f333(f333(f250(a880),f333(a117,f2(a880))),f333(f333(f264(a880),x70961),x70962))) % 191.49/191.40 [7318]~P4(f333(f333(f251(a880),f2(a880)),x73181))+P4(f333(f333(f251(a880),f333(f333(f3(a880),x73181),f333(a117,x73182))),x73181)) % 191.49/191.40 [7355]P4(f333(f333(f250(a880),f333(a117,f2(a880))),x73551))+~P4(f333(f333(f250(a880),f333(a117,f2(a880))),f333(f333(f82(a880),x73552),x73551))) % 191.49/191.40 [7356]P4(f333(f333(f250(a880),f333(a117,f2(a880))),x73561))+~P4(f333(f333(f250(a880),f333(a117,f2(a880))),f333(f333(f82(a880),x73561),x73562))) % 191.49/191.40 [7359]P4(f333(f333(f250(a880),f333(f333(f166(a880),x73591),x73592)),f333(f167(a880),x73591)))+~P4(f333(f333(f251(a880),x73592),f333(f195(f881(a880)),x73591))) % 191.49/191.40 [7400]P4(f333(f333(f251(a1),x74001),x74002))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),x74001),f79(a1))),x74002)) % 191.49/191.40 [7445]P4(f333(f63(x74451),f258(f890(x74451,a874))))+~P4(f333(f63(f890(x74452,x74451)),f258(f890(f890(x74452,x74451),a874)))) % 191.49/191.40 [7446]P4(f333(f63(x74461),f258(f890(x74461,a874))))+~P4(f333(f63(f888(x74462,x74461)),f258(f890(f888(x74462,x74461),a874)))) % 191.49/191.40 [7447]P4(f333(f63(x74471),f258(f890(x74471,a874))))+~P4(f333(f63(f888(x74471,x74472)),f258(f890(f888(x74471,x74472),a874)))) % 191.49/191.40 [7486]E(x74861,f194(f890(x74862,a874)))+~P4(f333(f333(f250(f890(x74862,a874)),x74861),f333(f80(f890(x74862,a874)),x74861))) % 191.49/191.40 [7619]E(f333(f143(f881(x76191),f881(x76191),f127(x76191),f118(x76191)),x76192),f118(x76191))+P4(f333(f333(f335(f881(x76191)),f656(x76192,x76191)),f333(f173(f881(x76191)),x76192))) % 191.49/191.40 [7620]E(f333(f143(f881(x76201),f881(x76201),f127(x76201),f118(x76201)),x76202),f118(x76201))+P4(f333(f333(f335(f881(x76201)),f657(x76202,x76201)),f333(f173(f881(x76201)),x76202))) % 191.49/191.40 [7948]~P115(x79481)+E(f333(f333(f82(x79481),f333(f333(f81(x79481),f79(x79481)),f79(x79481))),f333(f333(f8(a880,x79481),f105(x79481)),f304(a880,f79(a880),x79482))),f333(f333(f82(x79481),f333(f105(x79481),x79482)),f333(f333(f81(x79481),f333(f105(x79481),x79482)),f79(x79481)))) % 191.49/191.40 [8003]P4(f333(f333(f335(a880),x80031),x80032))+~P4(f333(f333(f335(a1),f333(f105(a1),x80031)),f333(f312(a880,a1,f105(a1)),x80032))) % 191.49/191.40 [8170]~P4(f333(f63(x81701),x81702))+E(f333(f312(a880,x81701,f684(x81702,x81701)),f333(f255(a880),f333(f333(f9(a880,a880,a874),f251(a880)),f685(x81702,x81701)))),x81702) % 191.49/191.40 [8454]P51(x84541,x84542)+P4(f333(f333(f335(f889(x84541,x84541)),f333(f333(f263(x84541,x84541),f535(x84542,x84541)),f535(x84542,x84541))),x84542)) % 191.49/191.40 [8698]~P4(f333(f333(f251(f890(a880,a874)),x86981),x86982))+P4(f333(f333(f251(f890(a1,a874)),f333(f312(a880,a1,f105(a1)),x86981)),f333(f312(a880,a1,f105(a1)),x86982))) % 191.49/191.40 [8728]~P94(x87281)+E(f333(f333(f3(x87281),f79(x87281)),f333(f108(x87281),x87282)),f333(f108(x87281),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),f333(f80(a1),x87282)))) % 191.49/191.40 [8802]~P4(f333(f333(f335(a880),x88021),f333(f173(a880),x88022)))+P4(f333(f333(f250(a880),x88021),f333(f143(a880,a880,f81(a880),f2(a880)),x88022))) % 191.49/191.40 [8898]P47(x88981,x88982)+~P4(f333(f333(f335(f889(x88981,x88981)),f333(f333(f263(x88981,x88981),f497(x88982,x88981)),f497(x88982,x88981))),x88982)) % 191.49/191.40 [9037]~P4(f333(f333(f251(f890(a1,a874)),f333(f312(a880,a1,f105(a1)),x90371)),f333(f312(a880,a1,f105(a1)),x90372)))+P4(f333(f333(f251(f890(a880,a874)),x90371),x90372)) % 191.49/191.40 [9038]~P4(f333(f333(f250(f890(a1,a874)),f333(f312(a880,a1,f105(a1)),x90381)),f333(f312(a880,a1,f105(a1)),x90382)))+P4(f333(f333(f250(f890(a880,a874)),x90381),x90382)) % 191.49/191.40 [10017]~P104(x100171)+E(f121(f881(x100171),f333(f128(f881(x100171)),f118(x100171)),f333(f333(f333(f101(f882(f881(x100171))),f333(f333(f251(a1),f2(a1)),x100172)),f333(f123(f889(x100171,f881(x100171)),f881(x100171),f133(x100171,f881(x100171),f136(x100171,f333(f333(f3(a1),x100172),f79(a1))),f136(f881(x100171),f333(f333(f3(a1),x100172),f79(a1))))),f333(f272(x100171,f881(x100171),f882(f881(x100171))),f333(f333(f10(f890(f881(x100171),f881(x100171)),f890(f881(x100171),f882(f881(x100171))),x100171),f333(f10(f881(x100171),f882(f881(x100171)),f881(x100171)),f128(f881(x100171)))),f152(x100171))))),f120(f881(x100171)))),f136(f881(x100171),x100172)) % 191.49/191.40 [10038]~P4(f333(f63(x100381),x100382))+E(f333(f195(f881(x100381)),f91(f881(x100381),f333(f333(f20(f881(x100381),a874,a874),f333(f333(f10(a874,f890(a874,a874),f881(x100381)),a331),f333(f333(f9(f881(x100381),f890(x100381,a874),a874),f333(f333(f10(f890(x100381,a874),f890(f890(x100381,a874),a874),f881(x100381)),a330),f173(x100381))),x100382))),f138(x100381)))),f224(x100381,x100382)) % 191.49/191.40 [10218]~P27(a875,x102181,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),x102182),f201(x102182))),f194(f890(f879(a875),a874))))+P27(a875,x102181,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),f333(f333(f10(f890(a875,f890(a875,a874)),f890(a875,a874),a875),f333(f10(f890(a875,a874),a874,a875),f88(a875))),f333(f333(f10(f890(a875,a874),f890(a875,f890(a875,a874)),a875),f333(f9(a875,f890(a875,a874),f890(a875,a874)),f333(f333(f10(f890(a875,f890(a874,a874)),f890(f890(a875,a874),f890(a875,a874)),a875),f20(a875,a874,a874)),f333(f333(f10(f890(a875,a874),f890(a875,f890(a874,a874)),a875),f333(f10(a874,f890(a874,a874),a875),a336)),f201(x102182))))),a330))),x102182),a330)),f194(f890(f879(a875),a874)))) % 191.49/191.40 [6080]E(f333(f333(f81(a880),f333(f333(f3(a880),x60801),x60802)),x60802),x60801)+~P4(f333(f333(f250(a880),x60802),x60801)) % 191.49/191.40 [6145]E(f333(f333(f40(a880),f333(f333(f82(a880),x61451),x61452)),x61452),x61451)+~P4(f333(f333(f251(a880),f2(a880)),x61452)) % 191.49/191.40 [6146]E(f333(f333(f40(a880),f333(f333(f82(a880),x61461),x61462)),x61461),x61462)+~P4(f333(f333(f251(a880),f2(a880)),x61461)) % 191.49/191.40 [6152]~P69(x61521)+E(f333(f333(f8(a880,x61521),f333(f166(x61521),x61522)),f333(f303(a880,f2(a880)),f333(f195(f881(x61521)),x61522))),f333(f167(x61521),x61522)) % 191.49/191.40 [6264]E(f46(a880,f333(a117,f333(f333(f82(a880),x62641),x62642)),x62641),f79(a880))+~P4(f333(f333(f251(a880),f79(a880)),x62641)) % 191.49/191.40 [6270]E(f333(a117,f333(f333(f81(a880),f333(f108(a880),x62701)),x62702)),f333(f333(f81(a880),f79(a880)),x62702))+~P4(f333(a200,f333(f108(a1),x62701))) % 191.49/191.40 [6298]E(f333(a109,f333(f333(f264(a1),f333(f108(a1),x62981)),x62982)),f333(f333(f264(a880),f333(f108(a880),x62981)),x62982))+P4(f333(a200,f333(f108(a1),x62981))) % 191.49/191.40 [6527]E(f333(f333(f3(a880),x65271),f333(f108(a880),f333(f333(f81(a1),x65272),a102))),f333(f333(f3(a880),f333(a117,x65271)),f333(f108(a880),x65272)))+~P4(f333(f333(f251(a1),a84),x65272)) % 191.49/191.40 [6608]E(x66081,f2(a880))+E(f333(a117,f333(f333(f81(a880),f333(f333(f3(a880),x66081),f79(a880))),x66082)),f333(f333(f81(a880),x66081),x66082)) % 191.49/191.40 [6649]E(x66491,f2(a1))+P4(f333(f333(f251(a1),f2(a1)),f333(f333(f264(a1),f333(f76(a1),x66491)),x66492))) % 191.49/191.40 [6664]~E(x66642,f2(a880))+P4(f333(f333(f251(a1),f2(a1)),f333(f333(f264(a1),f333(f76(a1),x66641)),x66642))) % 191.49/191.40 [6701]E(x67011,f2(a880))+E(f333(f333(f81(a880),x67012),f333(f333(f82(a880),f333(f333(f3(a880),x67011),f79(a880))),x67012)),f333(f333(f82(a880),x67011),x67012)) % 191.49/191.40 [6749]~P4(f333(f333(f250(a1),x67491),x67492))+P4(f333(f333(f251(a1),f333(f333(f81(a1),x67491),a102)),x67492)) % 191.49/191.40 [6868]E(f333(f333(f152(a880),x68681),f140(a880,f333(f303(a880,f333(a117,x68681)),x68682))),f140(a880,f333(f303(a880,x68681),x68682)))+~P4(f333(f333(f251(a880),x68681),x68682)) % 191.49/191.40 [7072]E(x70721,f118(x70722))+E(f277(x70722,f333(f333(f155(x70722,f889(a104,x70722)),f333(f263(a104,x70722),f79(a104))),x70721)),f284(x70722,x70721)) % 191.49/191.40 [7293]P4(f333(f333(f250(a1),x72931),x72932))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),x72931),a102)),x72932)) % 191.49/191.40 [7294]E(x72941,x72942)+~E(f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x72941)),x72941),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x72942)),x72942)) % 191.49/191.40 [7760]~P4(f333(f333(f251(a880),x77601),x77602))+P4(f333(f333(f335(f889(a880,a880)),f333(f333(f263(a880,a880),x77601),x77602)),a254)) % 191.49/191.40 [7975]~P4(f333(f333(f251(a104),f2(a104)),x79751))+P4(f333(f333(f251(a104),f333(f262(a104,f889(a104,a104)),f333(f278(x79751),x79752))),x79751)) % 191.49/191.40 [8296]~P87(x82961)+P4(f333(f333(f250(x82961),f333(f76(x82961),f333(f167(x82961),x82962))),f333(f167(x82961),f333(f333(f155(x82961,x82961),f76(x82961)),x82962)))) % 191.49/191.40 [8320]P4(f333(f333(f251(a880),x83201),x83202))+~P4(f333(f333(f335(f889(a880,a880)),f333(f333(f263(a880,a880),x83201),x83202)),a254)) % 191.49/191.40 [8477]E(f333(f333(f263(x84771,x84771),f788(x84772,x84771)),f788(x84772,x84771)),x84772)+~P4(f333(f333(f335(f889(x84771,x84771)),x84772),f309(x84771,f194(f890(f889(x84771,x84771),a874))))) % 191.49/191.40 [8520]E(f333(f303(a880,x85201),f333(f333(f81(a880),x85201),f333(f39(a880),x85202))),x85202)+~P4(f333(f333(f250(f890(a880,a874)),x85202),f333(f303(a880,x85201),f333(f333(f81(a880),x85201),f333(f39(a880),x85202))))) % 191.49/191.40 [8971]E(f177(f881(x89711),f333(f333(f10(a874,a874,f881(x89711)),a328),f333(f333(f9(f881(x89711),f881(x89711),a874),a330),f118(x89711))),x89712),f180(x89711,f180(x89711,x89712)))+~P17(a880,f333(f170(a880),f333(f333(f155(f881(x89711),a880),f195(f881(x89711))),x89712))) % 191.49/191.40 [9652]P27(a875,x96521,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),f333(a26,x96522)),f201(f333(a26,x96522)))),f194(f890(f879(a875),a874))))+~P27(a875,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),f333(a26,x96522)),f201(f333(a26,x96522)))),x96521),f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),f333(f246(a876),f333(a28,x96522))),f201(f333(f246(a876),f333(a28,x96522))))),f194(f890(f879(a875),a874)))) % 191.49/191.40 [9834]P4(f333(a200,x98342))+E(f333(f333(f89(a1,a880),f333(f333(f3(a1),x98341),x98342)),f333(f333(f20(a1,a880,a880),f333(f333(f9(a1,a880,f890(a880,a880)),f333(f333(f10(a874,f890(a880,f890(a880,a880)),a1),f101(a880)),a200)),f2(a880))),a109)),f333(f333(f3(a880),f333(a109,x98341)),f333(a109,x98342))) % 191.49/191.40 [9847]E(f333(f333(f89(a1,a880),f333(f108(a1),f333(f333(f81(a1),x98471),f333(f80(a1),x98472)))),f333(f333(f20(a1,a880,a880),f333(f333(f9(a1,a880,f890(a880,a880)),f333(f333(f10(a874,f890(a880,f890(a880,a880)),a1),f101(a880)),a200)),f2(a880))),a109)),f333(f333(f3(a880),f333(f108(a880),x98471)),f333(f108(a880),x98472)))+P4(f333(f333(f251(a1),x98472),a84)) % 191.49/191.40 [9848]~P29(x98481,x98482)+P4(f333(f333(f250(f890(f889(x98481,x98481),a874)),f333(f333(f290(x98481,x98481,x98481),f333(f262(f890(f889(x98481,x98481),a874),f890(f889(x98481,x98481),a874)),x98482)),f333(f271(f890(f889(x98481,x98481),a874),f890(f889(x98481,x98481),a874)),x98482))),f333(f262(f890(f889(x98481,x98481),a874),f890(f889(x98481,x98481),a874)),x98482))) % 191.49/191.40 [9902]~E(f333(f39(a880),f333(f255(a880),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),f333(f333(f9(a880,f890(a880,a874),a874),f335(a880)),x99021))),f333(f333(f9(a880,a880,a874),f251(a880)),f333(a117,x99022))))),f2(a880))+~P4(f333(f333(f335(a880),f2(a880)),x99021)) % 191.49/191.40 [10006]~P9(x100061)+E(f41(x100061,f333(f255(x100061),f333(f333(f10(f890(x100061,a874),a874,x100061),f88(x100061)),f333(f333(f10(f890(x100061,a874),f890(x100061,a874),x100061),f333(f20(x100061,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100061),a336),f333(f333(f9(x100061,f890(x100061,a874),a874),f335(x100061)),x100062)))),f250(x100061))))),f42(x100061,x100062)) % 191.49/191.40 [10033]~P40(x100331,x100332)+P59(x100331,f333(f333(f9(x100331,f890(f889(x100331,x100331),a874),f890(x100331,a874)),f333(f333(f10(f890(x100331,f890(f890(f889(x100331,x100331),a874),a874)),f890(f890(f889(x100331,x100331),a874),f890(x100331,a874)),x100331),f9(x100331,f890(f889(x100331,x100331),a874),a874)),f333(f333(f10(f890(x100331,f889(x100331,x100331)),f890(x100331,f890(f890(f889(x100331,x100331),a874),a874)),x100331),f333(f10(f889(x100331,x100331),f890(f890(f889(x100331,x100331),a874),a874),x100331),f335(f889(x100331,x100331)))),f263(x100331,x100331)))),x100332)) % 191.49/191.40 [10034]~P12(x100341,f258(f890(x100341,a874)),x100342)+P11(x100341,f333(f333(f9(x100341,f890(f889(x100341,x100341),a874),f890(x100341,a874)),f333(f333(f10(f890(x100341,f890(f890(f889(x100341,x100341),a874),a874)),f890(f890(f889(x100341,x100341),a874),f890(x100341,a874)),x100341),f9(x100341,f890(f889(x100341,x100341),a874),a874)),f333(f333(f10(f890(x100341,f889(x100341,x100341)),f890(x100341,f890(f890(f889(x100341,x100341),a874),a874)),x100341),f333(f10(f889(x100341,x100341),f890(f890(f889(x100341,x100341),a874),a874),x100341),f335(f889(x100341,x100341)))),f263(x100341,x100341)))),x100342)) % 191.49/191.40 [10065]P40(x100651,x100652)+~P59(x100651,f333(f333(f9(x100651,f890(f889(x100651,x100651),a874),f890(x100651,a874)),f333(f333(f10(f890(x100651,f890(f890(f889(x100651,x100651),a874),a874)),f890(f890(f889(x100651,x100651),a874),f890(x100651,a874)),x100651),f9(x100651,f890(f889(x100651,x100651),a874),a874)),f333(f333(f10(f890(x100651,f889(x100651,x100651)),f890(x100651,f890(f890(f889(x100651,x100651),a874),a874)),x100651),f333(f10(f889(x100651,x100651),f890(f890(f889(x100651,x100651),a874),a874),x100651),f335(f889(x100651,x100651)))),f263(x100651,x100651)))),x100652)) % 191.49/191.40 [10066]P12(x100661,f258(f890(x100661,a874)),x100662)+~P11(x100661,f333(f333(f9(x100661,f890(f889(x100661,x100661),a874),f890(x100661,a874)),f333(f333(f10(f890(x100661,f890(f890(f889(x100661,x100661),a874),a874)),f890(f890(f889(x100661,x100661),a874),f890(x100661,a874)),x100661),f9(x100661,f890(f889(x100661,x100661),a874),a874)),f333(f333(f10(f890(x100661,f889(x100661,x100661)),f890(x100661,f890(f890(f889(x100661,x100661),a874),a874)),x100661),f333(f10(f889(x100661,x100661),f890(f890(f889(x100661,x100661),a874),a874),x100661),f335(f889(x100661,x100661)))),f263(x100661,x100661)))),x100662)) % 191.49/191.40 [7249]E(f333(f333(f81(a880),f333(f108(a880),f333(f333(f3(a1),x72491),a102))),x72492),f333(a117,f333(f333(f81(a880),f333(f108(a880),x72491)),x72492)))+P4(f333(a200,f333(f108(a1),x72491))) % 191.49/191.40 [7739]~P94(x77391)+E(f333(f333(f81(x77391),f333(f333(f81(x77391),f79(x77391)),f333(f108(x77391),x77392))),f333(f108(x77391),x77392)),f333(f108(x77391),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x77392)),x77392))) % 191.49/191.40 [9087]~P4(f333(f333(f251(a1),x90871),x90872))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x90871)),x90871)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x90872)),x90872))) % 191.49/191.40 [9089]~P4(f333(f333(f250(a1),x90891),x90892))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x90891)),x90891)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x90892)),x90892))) % 191.49/191.40 [9090]~P4(f333(f333(f92(a1),x90901),x90902))+P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x90901)),x90901)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x90902)),x90902))) % 191.49/191.40 [9329]~P4(f333(f63(x93291),x93292))+P4(f333(f63(f890(x93291,a874)),f333(f255(f890(x93291,a874)),f333(f333(f9(f890(x93291,a874),f890(x93291,a874),a874),f250(f890(x93291,a874))),x93292)))) % 191.49/191.40 [9354]P4(f333(f333(f251(a1),x93541),x93542))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x93541)),x93541)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x93542)),x93542))) % 191.49/191.40 [9356]P4(f333(f333(f250(a1),x93561),x93562))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x93561)),x93561)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x93562)),x93562))) % 191.49/191.40 [9357]P4(f333(f333(f92(a1),x93571),x93572))+~P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x93571)),x93571)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x93572)),x93572))) % 191.49/191.40 [9382]~E(f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),x93821),f194(f890(f889(a880,a880),a874)))),f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),x93822),f194(f890(f889(a880,a880),a874)))))+P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),x93821),x93822)),a113)) % 191.49/191.40 [9457]E(f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),x94571),f194(f890(f889(a880,a880),a874)))),f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),x94572),f194(f890(f889(a880,a880),a874)))))+~P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),x94571),x94572)),a113)) % 191.49/191.40 [9507]P4(f333(f333(f250(a1),f2(a1)),f803(x95071,x95072)))+E(f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),x95071)),f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),x95072))) % 191.49/191.40 [9623]~P4(f333(f333(f250(a1),x96231),x96232))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x96231)),x96231)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x96232)),x96232))) % 191.49/191.40 [9625]~P4(f333(f333(f250(a1),x96251),x96252))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x96251)),x96251)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x96252)),x96252))) % 191.49/191.40 [9782]P4(f333(f333(f250(a1),x97821),x97822))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97821)),x97821)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97822)),x97822))) % 191.49/191.40 [9784]P4(f333(f333(f250(a1),x97841),x97842))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97841)),x97841)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97842)),x97842))) % 191.49/191.40 [10016]~P9(x100161)+E(f42(x100161,f333(f255(x100161),f333(f333(f10(f890(x100161,a874),a874,x100161),f88(x100161)),f333(f333(f10(f890(x100161,a874),f890(x100161,a874),x100161),f333(f20(x100161,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100161),a336),f333(f333(f9(x100161,f890(x100161,a874),a874),f335(x100161)),x100162)))),f333(f9(x100161,x100161,a874),f250(x100161)))))),f41(x100161,x100162)) % 191.49/191.40 [10037]P4(f333(f333(f335(a880),f2(a880)),x100371))+E(f333(f39(a880),f333(f255(a880),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),f333(f333(f9(a880,f890(a880,a874),a874),f333(f333(f10(a880,f890(f890(a880,a874),a874),a880),f335(a880)),a117)),x100371))),f333(f333(f9(a880,a880,a874),f251(a880)),x100372)))),f333(f39(a880),f333(f255(a880),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),f333(f333(f9(a880,f890(a880,a874),a874),f335(a880)),x100371))),f333(f333(f9(a880,a880,a874),f251(a880)),f333(a117,x100372)))))) % 191.49/191.40 [7806]~P94(x78061)+E(f333(f333(f82(x78061),x78062),f333(f108(x78061),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),x78062) % 191.49/191.40 [8036]~P94(x80361)+E(f333(f333(f81(x80361),f333(f108(x80361),x80362)),f79(x80361)),f333(f108(x80361),f333(f333(f81(a1),x80362),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))) % 191.49/191.40 [8081]P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x80812)))+E(f333(f333(f264(a1),x80811),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x80812)),x80812))),f79(a1)) % 191.49/191.40 [9096]E(x90961,x90962)+~E(f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x90961)),x90961)),a102),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x90962)),x90962)),a102)) % 191.49/191.40 [9368]~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x93682)))+E(f333(f333(f264(a1),x93681),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x93682)),x93682))),f333(f333(f89(a1,a1),f333(f333(f264(a1),x93681),f333(f108(a880),x93682))),f333(f333(f20(a1,a1,a1),f333(f333(f10(a1,f890(a1,a1),a1),f82(a1)),f333(f82(a1),x93681))),f7(a1)))) % 191.49/191.40 [9744]~P4(f333(f333(f250(a880),f811(x97442,x97441)),f333(x97441,f811(x97442,x97441))))+P4(f333(f63(a880),f333(f255(a880),f333(f333(f9(a880,a880,a874),f333(f333(f10(a880,f890(a880,a874),a880),f250(a880)),x97441)),x97442)))) % 191.49/191.40 [9893]~P4(f333(f333(f251(a880),f333(f108(a880),x98931)),f333(a117,x98932)))+P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x98931),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f9(a1,a880,a874),f333(f333(f10(a880,f890(a880,a874),a1),f251(a880)),a109)),x98932)))) % 191.49/191.40 [9894]~P4(f333(f333(f250(a880),f333(f108(a880),x98941)),f333(a117,x98942)))+P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x98941),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f9(a1,a880,a874),f333(f333(f10(a880,f890(a880,a874),a1),f250(a880)),a109)),x98942)))) % 191.49/191.40 [9930]P4(f333(f333(f251(a880),f333(f108(a880),x99301)),f333(a117,x99302)))+~P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x99301),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f9(a1,a880,a874),f333(f333(f10(a880,f890(a880,a874),a1),f251(a880)),a109)),x99302)))) % 191.49/191.40 [9931]P4(f333(f333(f250(a880),f333(f108(a880),x99311)),f333(a117,x99312)))+~P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x99311),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f9(a1,a880,a874),f333(f333(f10(a880,f890(a880,a874),a1),f250(a880)),a109)),x99312)))) % 191.49/191.40 [9960]~P4(f333(f333(f251(a880),f333(a117,x99602)),f333(f108(a880),x99601)))+P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x99601),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f10(a880,a874,a1),f333(f251(a880),x99602)),a109))))) % 191.49/191.40 [9961]~P4(f333(f333(f250(a880),f333(a117,x99612)),f333(f108(a880),x99611)))+P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x99611),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f10(a880,a874,a1),f333(f250(a880),x99612)),a109))))) % 191.49/191.40 [10004]P4(f333(f333(f251(a880),f333(a117,x100041)),f333(f108(a880),x100042)))+~P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x100042),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f10(a880,a874,a1),f333(f251(a880),x100041)),a109))))) % 191.49/191.40 [10005]P4(f333(f333(f250(a880),f333(a117,x100051)),f333(f108(a880),x100052)))+~P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x100052),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f10(a880,a874,a1),f333(f250(a880),x100051)),a109))))) % 191.49/191.40 [10082]~P4(f333(f333(f335(a880),f2(a880)),x100821))+E(f333(a117,f333(f39(a880),f333(f255(a880),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),f333(f333(f9(a880,f890(a880,a874),a874),f333(f333(f10(a880,f890(f890(a880,a874),a874),a880),f335(a880)),a117)),x100821))),f333(f333(f9(a880,a880,a874),f251(a880)),x100822))))),f333(f39(a880),f333(f255(a880),f333(f333(f20(a880,a874,a874),f333(f333(f10(a874,f890(a874,a874),a880),a331),f333(f333(f9(a880,f890(a880,a874),a874),f335(a880)),x100821))),f333(f333(f9(a880,a880,a874),f251(a880)),f333(a117,x100822)))))) % 191.49/191.40 [8666]~P94(x86661)+E(f333(f333(f82(x86661),f333(f108(x86661),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),x86662),x86662) % 191.49/191.40 [8706]~P94(x87061)+E(f333(f333(f81(x87061),f79(x87061)),f333(f108(x87061),x87062)),f333(f108(x87061),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),x87062))) % 191.49/191.40 [8744]~P94(x87441)+E(f333(f333(f3(x87441),f333(f108(x87441),x87442)),f79(x87441)),f333(f108(x87441),f333(f333(f81(a1),x87442),f333(f80(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))))) % 191.49/191.40 [8828]~P94(x88281)+E(f333(f333(f82(x88281),f333(f333(f81(x88281),f79(x88281)),f79(x88281))),f333(f108(x88281),x88282)),f333(f108(x88281),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x88282)),x88282)),a102))) % 191.49/191.40 [8858]~P4(f333(f333(f251(a880),f333(f108(a880),a84)),x88582))+E(f333(f333(f3(a880),x88581),f333(f333(f3(a880),x88582),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),f333(f333(f3(a880),f333(a117,x88581)),x88582)) % 191.49/191.40 [8885]~P94(x88851)+E(f333(f108(x88851),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x88852)),x88852)),a102)),f333(f333(f81(x88851),f333(f333(f81(x88851),f2(x88851)),f333(f108(x88851),x88852))),f333(f108(x88851),x88852))) % 191.49/191.40 [9471]~P4(f333(f333(f251(a1),x94711),x94712))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x94711)),x94711)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x94712)),x94712)),a102))) % 191.49/191.40 [9473]~P4(f333(f333(f251(a1),x94731),x94732))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x94731)),x94731)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x94732)),x94732)),a102))) % 191.49/191.40 [9637]P4(f333(f333(f251(a1),x96371),x96372))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x96371)),x96371)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x96372)),x96372)),a102))) % 191.49/191.40 [9639]P4(f333(f333(f251(a1),x96391),x96392))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x96391)),x96391)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x96392)),x96392)),a102))) % 191.49/191.40 [9687]~P83(x96871)+E(f333(f333(f264(x96871),x96872),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)))),f333(f333(f82(x96871),f333(f333(f82(x96871),x96872),x96872)),x96872)) % 191.49/191.40 [9736]~P4(f333(f333(f251(a1),x97361),x97362))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97361)),x97361)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97362)),x97362)),a102))) % 191.49/191.40 [9738]~P4(f333(f333(f250(a1),x97381),x97382))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97381)),x97381)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97382)),x97382)),a102))) % 191.49/191.40 [9739]~P4(f333(f333(f92(a1),x97391),x97392))+P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97391)),x97391)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x97392)),x97392)),a102))) % 191.49/191.40 [9843]P4(f333(f333(f251(a1),x98431),x98432))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x98431)),x98431)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x98432)),x98432)),a102))) % 191.49/191.40 [9845]P4(f333(f333(f250(a1),x98451),x98452))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x98451)),x98451)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x98452)),x98452)),a102))) % 191.49/191.40 [9846]P4(f333(f333(f92(a1),x98461),x98462))+~P4(f333(f333(f92(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x98461)),x98461)),a102)),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x98462)),x98462)),a102))) % 191.49/191.40 [9490]~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x94902)))+E(f333(f333(f40(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x94901)),x94901))),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x94902)),x94902)),a102))),f333(f333(f40(a1),f333(f108(a1),x94901)),f333(f108(a1),x94902))) % 191.49/191.40 [9513]P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x95132)))+E(f333(f333(f40(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95131)),x95131))),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x95132)),x95132)),a102))),f333(f333(f40(a1),f333(f333(f81(a1),f333(f108(a1),x95131)),f79(a1))),f333(f108(a1),x95132))) % 191.49/191.40 [9994]~E(f333(a117,x99942),f333(f108(a880),x99941))+P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x99941),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f9(a1,a880,a874),f333(f333(f10(a880,f890(a880,a874),a1),a330),a109)),x99942))))) % 191.49/191.40 [9995]~E(f333(f108(a880),x99951),f333(a117,x99952))+P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x99951),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f9(a1,a880,a874),f333(f333(f10(a880,f890(a880,a874),a1),a330),a109)),x99952))))) % 191.49/191.40 [10040]E(f333(a117,x100401),f333(f108(a880),x100402))+~P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x100402),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f9(a1,a880,a874),f333(f333(f10(a880,f890(a880,a874),a1),a330),a109)),x100401))))) % 191.49/191.40 [10041]E(f333(f108(a880),x100411),f333(a117,x100412))+~P4(f333(f333(f89(a1,a874),f333(f108(a1),f333(f333(f81(a1),x100411),a102))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a336),f333(f333(f10(a874,a874,a1),a328),a200))),f333(f333(f9(a1,a880,a874),f333(f333(f10(a880,f890(a880,a874),a1),a330),a109)),x100412))))) % 191.49/191.40 [10138]~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x101382)))+E(f46(a1,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x101381)),x101381)),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x101382)),x101382)),a102))),f333(f333(f81(a1),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f46(a1,f333(f108(a1),x101381),f333(f108(a1),x101382)))),f79(a1))) % 191.49/191.40 [10140]P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x101402)))+E(f46(a1,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x101401)),x101401)),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x101402)),x101402)),a102))),f333(f333(f3(a1),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f46(a1,f333(f333(f81(a1),f333(f108(a1),x101401)),f79(a1)),f333(f108(a1),x101402)))),f79(a1))) % 191.49/191.40 [9940]~P115(x99401)+E(f333(f333(f82(x99401),x99402),x99402),f333(f333(f264(x99401),x99402),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.40 [9941]~P83(x99411)+E(f333(f333(f264(x99411),x99412),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f333(f82(x99411),x99412),x99412)) % 191.49/191.40 [9942]~P94(x99421)+E(f333(f333(f82(x99421),x99422),f333(f108(x99421),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f333(f81(x99421),x99422),x99422)) % 191.49/191.40 [10020]~P140(x100201)+E(f333(f333(f264(x100201),f333(f80(x100201),x100202)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f333(f264(x100201),x100202),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.40 [10021]~P120(x100211)+E(f333(f333(f264(x100211),f333(f76(x100211),x100212)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f333(f264(x100211),x100212),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.40 [10019]~P94(x100191)+E(f333(f333(f82(x100191),f333(f108(x100191),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x100192),f333(f333(f81(x100191),x100192),x100192)) % 191.49/191.40 [10058]~P120(x100581)+E(f333(f76(x100581),f333(f333(f264(x100581),x100582),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x100581),x100582),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.40 [10073]~P120(x100731)+P4(f333(f333(f250(x100731),f2(x100731)),f333(f333(f264(x100731),x100732),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.40 [10071]~P94(x100711)+E(f333(f333(f264(x100711),f333(f108(x100711),a102)),f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x100712)),f79(x100711)) % 191.49/191.40 [10072]~P140(x100721)+E(f333(f333(f264(x100721),f333(f80(x100721),f79(x100721))),f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x100722)),f79(x100721)) % 191.49/191.40 [10163]~P4(f333(f333(f250(a1),f2(a1)),x101632))+E(f46(a1,f333(f333(f81(a1),f79(a1)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101631)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101632)),f333(f333(f81(a1),f79(a1)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f46(a1,x101631,x101632)))) % 191.49/191.40 [10174]~P4(f333(f333(f250(a1),f2(a1)),x101742))+E(f333(f333(f40(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101741))),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101742)),f333(f333(f40(a1),x101741),x101742)) % 191.49/191.40 [10175]~P4(f333(f333(f250(a1),x101752),f2(a1)))+E(f333(f333(f40(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101751))),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101752)),f333(f333(f40(a1),f333(f333(f81(a1),x101751),f79(a1))),x101752)) % 191.49/191.40 [10176]~P4(f333(f333(f250(a1),x101762),f2(a1)))+E(f46(a1,f333(f333(f81(a1),f79(a1)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101761)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101762)),f333(f333(f3(a1),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f46(a1,f333(f333(f81(a1),x101761),f79(a1)),x101762))),f79(a1))) % 191.49/191.40 [10121]~P94(x101211)+E(f333(f333(f264(x101211),f333(f108(x101211),a102)),f333(a117,f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101212))),f333(f108(x101211),a102)) % 191.49/191.40 [10123]~P140(x101231)+E(f333(f333(f264(x101231),f333(f80(x101231),f79(x101231))),f333(a117,f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101232))),f333(f80(x101231),f79(x101231))) % 191.49/191.40 [5128]~P27(x51281,x51282,x51283)+P31(x51281,x51282,x51283) % 191.49/191.40 [8018]~E(x80182,x80183)+P37(x80181,x80181,a330,x80182,x80183) % 191.49/191.40 [8575]E(x85751,x85752)+~P37(x85753,x85753,a330,x85751,x85752) % 191.49/191.40 [5133]~P40(x51331,x51333)+P40(x51331,f327(x51331,x51332,x51333)) % 191.49/191.40 [5308]P30(x53081,x53082,x53083)+~P30(x53081,f333(a117,x53082),x53083) % 191.49/191.40 [5393]~P12(x53931,x53932,x53933)+P12(f881(x53931),f162(x53931,x53932),f159(x53931,x53933)) % 191.49/191.40 [5394]~P50(x53941,x53942,x53943)+P50(f881(x53941),f162(x53941,x53942),f159(x53941,x53943)) % 191.49/191.40 [5506]P54(x55061,x55062,x55063)+~E(f743(x55063,x55062,x55061),f744(x55063,x55062,x55061)) % 191.49/191.40 [5507]P55(x55071,x55072,x55073)+~E(f766(x55073,x55072,x55071),f767(x55073,x55072,x55071)) % 191.49/191.40 [6438]P31(x64381,x64382,x64383)+~P30(x64381,f600(x64383,x64382,x64381),f607(x64383,x64382,x64381)) % 191.49/191.40 [4687]~E(x46871,f197(x46872))+~E(x46871,f333(f242(x46872),x46873)) % 191.49/191.40 [4735]~E(f333(f170(x47352),x47351),x47353)+E(x47351,f333(f170(x47352),x47353)) % 191.49/191.40 [4736]~E(x47362,f333(f170(x47361),x47363))+E(f333(f170(x47361),x47362),x47363) % 191.49/191.40 [4783]E(x47831,x47832)+~E(f333(f242(x47833),x47831),f333(f242(x47833),x47832)) % 191.49/191.40 [4784]E(x47841,x47842)+~E(f333(f170(x47843),x47841),f333(f170(x47843),x47842)) % 191.49/191.40 [4987]~P11(x49873,x49871)+P4(f333(f333(x49871,x49872),x49872)) % 191.49/191.40 [4988]~P52(x49883,x49881)+P4(f333(f333(x49881,x49882),x49882)) % 191.49/191.40 [4990]~P59(x49901,x49902)+P4(f333(f321(x49901,x49902),x49903)) % 191.49/191.40 [5052]~P40(x50521,x50522)+P40(f881(x50521),f333(f144(x50521,x50522),x50523)) % 191.49/191.40 [5057]~P4(f333(x50572,x50573))+~E(f333(f255(x50571),x50572),f194(f890(x50571,a874))) % 191.49/191.40 [5058]~P4(f333(x50582,x50583))+~E(f194(f890(x50581,a874)),f333(f255(x50581),x50582)) % 191.49/191.40 [5089]~P4(f333(x50891,x50893))+P4(f333(x50891,f91(x50892,x50891))) % 191.49/191.40 [5213]~E(x52132,x52133)+P4(f333(f333(f335(x52131),x52132),f333(a330,x52133))) % 191.49/191.40 [5225]P4(f333(x52251,x52252))+~P4(f333(x52251,f583(x52251,x52253))) % 191.49/191.40 [5272]E(f333(f170(x52721),x52722),f333(f333(f152(x52721),x52723),f118(x52721)))+~E(x52722,f333(f333(f152(x52721),x52723),f118(x52721))) % 191.49/191.40 [5273]~E(x52733,f333(f333(f152(x52731),x52732),f118(x52731)))+E(f333(f333(f152(x52731),x52732),f118(x52731)),f333(f170(x52731),x52733)) % 191.49/191.40 [5301]~E(x53013,f333(f18(f884(x53012),x53011),f197(x53012)))+E(f184(x53011,x53012,x53013),f194(f890(x53011,a874))) % 191.49/191.40 [5322]~P36(x53221,x53222,x53223)+P36(x53221,x53222,f333(f170(x53221),x53223)) % 191.49/191.40 [5323]~P34(x53231,x53232,x53233)+P34(x53231,x53232,f333(f170(x53231),x53233)) % 191.49/191.40 [5326]E(f333(f39(x53261),f739(x53262,x53263,x53261)),x53262)+~E(f333(f39(x53261),x53263),f333(a117,x53262)) % 191.49/191.40 [5332]~P40(x53321,x53323)+P4(f333(f333(f335(x53321),x53322),f322(x53321,x53323))) % 191.49/191.40 [5335]~E(f333(f170(x53352),x53351),f333(f333(f152(x53352),x53353),f118(x53352)))+E(x53351,f333(f333(f152(x53352),x53353),f118(x53352))) % 191.49/191.40 [5336]~E(f333(f333(f152(x53362),x53363),f118(x53362)),f333(f170(x53362),x53361))+E(x53361,f333(f333(f152(x53362),x53363),f118(x53362))) % 191.49/191.40 [5351]E(x53511,f333(f18(f884(x53512),x53513),f197(x53512)))+~E(f184(x53513,x53512,x53511),f194(f890(x53513,a874))) % 191.49/191.40 [5357]E(f86(f889(a880,a880),f49(x53571,x53572)),x53573)+~P4(f333(f49(x53571,x53572),x53573)) % 191.49/191.40 [5365]~E(x53653,f333(f242(x53651),x53652))+P4(f333(f333(f335(x53651),x53652),f241(x53651,x53653))) % 191.49/191.40 [5397]P36(x53971,x53972,x53973)+~P36(x53971,x53972,f333(f170(x53971),x53973)) % 191.49/191.40 [5398]P34(x53981,x53982,x53983)+~P34(x53981,x53982,f333(f170(x53981),x53983)) % 191.49/191.40 [5460]~E(x54602,f118(x54601))+P4(f333(f333(f335(f881(x54601)),x54602),f162(x54601,x54603))) % 191.49/191.40 [5467]~P50(x54671,x54672,x54673)+P50(x54671,x54672,f333(f288(x54671,x54671),x54673)) % 191.49/191.40 [5468]~P55(x54681,x54682,x54683)+P55(x54681,x54682,f333(f288(x54681,x54681),x54683)) % 191.49/191.40 [5487]~P60(x54871)+E(f46(x54871,f46(x54871,x54872,x54873),x54873),f46(x54871,x54872,x54873)) % 191.49/191.40 [5580]E(x55801,x55802)+~P4(f333(f333(f335(x55803),x55801),f333(a330,x55802))) % 191.49/191.40 [5627]~P143(x56271)+E(f196(x56271,x56272,f2(a880),x56273),x56273) % 191.49/191.40 [5647]P50(x56471,x56472,x56473)+~P50(x56471,x56472,f333(f288(x56471,x56471),x56473)) % 191.49/191.40 [5648]P55(x56481,x56482,x56483)+~P55(x56481,x56482,f333(f288(x56481,x56481),x56483)) % 191.49/191.40 [5652]~P109(x56522)+E(f151(x56521,x56522,x56523,f118(x56521)),f118(x56521)) % 191.49/191.40 [5665]E(f171(x56651,x56652,f153(x56651,x56653)),f153(x56651,f171(x56651,x56652,x56653)))+~P4(f333(f138(x56651),x56653)) % 191.49/191.40 [5671]E(x56711,f333(f242(x56712),x56713))+~P4(f333(f333(f335(x56712),x56713),f241(x56712,x56711))) % 191.49/191.40 [5756]~P4(f333(a25,x57563))+P4(f333(a25,f30(x57561,x57562,x57563))) % 191.49/191.40 [5767]E(f333(f137(x57671,x57672),x57673),f118(x57671))+P4(f333(x57672,f624(x57673,x57672,x57671))) % 191.49/191.40 [5910]~P4(f333(f138(x59101),x59103))+P4(f333(f138(x59101),f171(x59101,x59102,x59103))) % 191.49/191.40 [5911]~P4(f333(f138(x59111),x59112))+P4(f333(f138(x59111),f175(x59111,x59112,x59113))) % 191.49/191.40 [5912]~P4(f333(f138(x59121),x59123))+P4(f333(f138(x59121),f177(x59121,x59122,x59123))) % 191.49/191.40 [5913]~P4(f333(f138(x59131),x59133))+P4(f333(f138(x59131),f141(x59131,x59132,x59133))) % 191.49/191.40 [5914]~P146(x59141,x59143,x59142)+P4(f333(x59141,f46(a1,x59142,x59143))) % 191.49/191.40 [5932]~P36(x59323,x59321,x59322)+P4(f333(x59321,f745(x59322,x59321,x59323))) % 191.49/191.40 [5933]~P38(x59333,x59331,x59332)+P4(f333(x59331,f812(x59332,x59331,x59333))) % 191.49/191.40 [5955]E(f333(f137(x59551,x59552),x59553),f177(x59551,x59552,x59553))+P4(f333(x59552,f672(x59553,x59552,x59551))) % 191.49/191.40 [5997]~P4(f333(f138(x59971),x59973))+P4(f333(f138(f881(x59971)),f56(x59971,x59972,x59973))) % 191.49/191.40 [6018]P4(f333(a25,f29(x60181,x60182,x60183)))+~P4(f333(a25,f333(a26,x60182))) % 191.49/191.40 [6030]~P110(x60301)+E(f333(f333(f106(f890(x60301,a874)),f333(f256(x60301),x60302)),f304(x60301,x60302,x60303)),f194(f890(x60301,a874))) % 191.49/191.40 [6031]~P110(x60311)+E(f333(f333(f106(f890(x60311,a874)),f333(f302(x60311),x60312)),f307(x60311,x60312,x60313)),f194(f890(x60311,a874))) % 191.49/191.40 [6032]~P110(x60321)+E(f333(f333(f106(f890(x60321,a874)),f333(f302(x60321),x60322)),f306(x60321,x60322,x60323)),f194(f890(x60321,a874))) % 191.49/191.40 [6181]P4(f333(a25,x61811))+~P4(f333(a25,f30(x61812,x61813,x61811))) % 191.49/191.40 [6183]P4(f333(a25,x61831))+~P4(f333(a25,f31(x61832,x61833,x61831))) % 191.49/191.40 [6185]P4(f333(a25,x61851))+~P4(f333(a25,f31(x61852,x61851,x61853))) % 191.49/191.40 [6260]E(f333(f137(x62601,x62602),x62603),x62603)+~P4(f333(x62602,f625(x62603,x62602,x62601))) % 191.49/191.40 [6262]E(f333(f333(f311(x62621),f866(x62622,x62623,x62621)),f739(x62622,x62623,x62621)),x62623)+~E(f333(f39(x62621),x62623),f333(a117,x62622)) % 191.49/191.40 [6278]P146(x62781,x62782,x62783)+~P4(f333(x62781,f46(a1,x62783,x62782))) % 191.49/191.40 [6324]P34(x63241,x63242,x63243)+~P4(f333(x63242,f798(x63242,x63243,x63241))) % 191.49/191.40 [6325]P34(x63251,x63252,x63253)+~P4(f333(x63252,f809(x63253,x63252,x63251))) % 191.49/191.40 [6326]P34(x63261,x63262,x63263)+~P4(f333(x63262,f810(x63263,x63262,x63261))) % 191.49/191.40 [6328]E(f177(x63281,x63282,x63283),x63283)+~P4(f333(x63282,f655(x63283,x63282,x63281))) % 191.49/191.40 [6364]~P4(f333(a25,f29(x63642,x63641,x63643)))+P4(f333(a25,f333(a26,x63641))) % 191.49/191.40 [6407]~P4(f333(x64072,f594(x64073,x64072,x64071)))+P4(f333(f267(x64071,x64072),x64073)) % 191.49/191.40 [6408]~P4(f333(x64082,f674(x64083,x64082,x64081)))+P4(f333(f161(x64081,x64082),x64083)) % 191.49/191.40 [6650]~P4(f333(f321(x66501,x66502),f483(x66503,x66502,x66501)))+P4(f333(f321(x66501,x66502),x66503)) % 191.49/191.40 [6651]~P4(f333(f321(x66511,x66512),f500(x66513,x66512,x66511)))+P4(f333(f321(x66511,x66512),x66513)) % 191.49/191.40 [7250]~P60(x72501)+E(f333(f333(f81(x72501),f333(f333(f82(x72501),x72502),f333(f333(f40(x72501),x72503),x72502))),f46(x72501,x72503,x72502)),x72503) % 191.49/191.40 [7700]E(f333(f333(f263(x77001,x77001),f569(x77002,x77003,x77001)),f569(x77002,x77003,x77001)),x77003)+~P4(f333(f333(f335(f889(x77001,x77001)),x77003),f260(x77001,x77002))) % 191.49/191.40 [7819]~P4(f333(f333(f335(x78191),f694(x78193,x78192,x78191)),f322(x78191,x78193)))+P4(f333(f333(f335(x78191),x78192),f322(x78191,x78193))) % 191.49/191.40 [7820]~P4(f333(f333(f335(x78201),f747(x78203,x78202,x78201)),f322(x78201,x78203)))+P4(f333(f333(f335(x78201),x78202),f322(x78201,x78203))) % 191.49/191.40 [7821]~P4(f333(f333(f335(x78211),f756(x78213,x78212,x78211)),f322(x78211,x78213)))+P4(f333(f333(f335(x78211),x78212),f322(x78211,x78213))) % 191.49/191.40 [7999]~P60(x79991)+E(f333(f333(f81(x79991),f333(f333(f82(x79991),f333(f333(f40(x79991),x79992),x79993)),x79993)),f46(x79991,x79992,x79993)),x79992) % 191.49/191.40 [8050]~E(f333(f39(x80501),x80502),f333(a117,x80503))+~P4(f333(f333(f335(x80501),f866(x80503,x80502,x80501)),f739(x80503,x80502,x80501))) % 191.49/191.40 [8662]P4(f333(f333(f250(f890(f889(x86621,x86621),a874)),f309(x86621,x86622)),f309(x86621,x86623)))+~P4(f333(f333(f250(f890(f889(x86621,x86621),a874)),x86622),f309(x86621,x86623))) % 191.49/191.40 [8940]E(x89401,f118(x89402))+~P4(f333(f333(f335(f889(f881(x89402),f881(x89402))),f333(f333(f263(f881(x89402),f881(x89402)),x89401),f118(x89402))),f159(x89402,x89403))) % 191.49/191.40 [8965]E(x89651,f118(x89652))+~P4(f333(f333(f335(f889(f881(x89652),f881(x89652))),f333(f333(f263(f881(x89652),f881(x89652)),f118(x89652)),x89651)),f159(x89652,x89653))) % 191.49/191.40 [9073]E(f333(f333(f152(x90731),f635(x90732,x90733,x90731)),f636(x90732,x90733,x90731)),x90733)+~P4(f333(f333(f335(f889(f881(x90731),f881(x90731))),f333(f333(f263(f881(x90731),f881(x90731)),f118(x90731)),x90733)),f148(x90731,x90732))) % 191.49/191.40 [9322]~P125(x93221)+~P4(f333(f333(f251(x93221),f333(f333(f81(x93221),f333(f333(f82(x93221),x93222),x93222)),f333(f333(f82(x93221),x93223),x93223))),f2(x93221))) % 191.49/191.40 [9377]P4(f333(f63(x93771),x93772))+~P4(f333(f333(f335(f889(f890(x93771,a874),f890(x93771,a874))),f333(f333(f263(f890(x93771,a874),f890(x93771,a874)),x93773),x93772)),f308(x93771))) % 191.49/191.40 [9679]~P48(x96791,x96792,x96793)+P4(f333(f333(f251(a1),f333(f333(f74(f889(a1,a1),a1,x96791,f262(a1,a1)),f222(x96791)),f239(x96791,x96792,f236(x96791,x96793)))),f2(a1))) % 191.49/191.40 [9680]~P49(x96801,x96802,x96803)+P4(f333(f333(f250(a1),f333(f333(f74(f889(a1,a1),a1,x96801,f262(a1,a1)),f222(x96801)),f239(x96801,x96802,f236(x96801,x96803)))),f2(a1))) % 191.49/191.40 [9819]P48(x98191,x98192,x98193)+~P4(f333(f333(f251(a1),f333(f333(f74(f889(a1,a1),a1,x98191,f262(a1,a1)),f222(x98191)),f239(x98191,x98192,f236(x98191,x98193)))),f2(a1))) % 191.49/191.40 [9820]P49(x98201,x98202,x98203)+~P4(f333(f333(f250(a1),f333(f333(f74(f889(a1,a1),a1,x98201,f262(a1,a1)),f222(x98201)),f239(x98201,x98202,f236(x98201,x98203)))),f2(a1))) % 191.49/191.40 [10212]~P120(x102121)+~P4(f333(f333(f251(x102121),f333(f333(f81(x102121),f333(f333(f264(x102121),x102122),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x102121),x102123),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))),f2(x102121))) % 191.49/191.40 [4766]~E(x47663,f118(x47661))+E(f333(f333(f127(x47661),x47662),x47663),x47662) % 191.49/191.40 [4767]~E(x47672,f118(x47671))+E(f333(f333(f127(x47671),x47672),x47673),x47673) % 191.49/191.40 [4774]~E(x47742,f2(a880))+E(f333(f333(f174(x47741),x47742),x47743),f118(x47741)) % 191.49/191.40 [4778]~E(x47783,f118(x47781))+E(f333(f333(f174(x47781),x47782),x47783),f118(x47781)) % 191.49/191.40 [4818]~E(x48181,x48183)+E(x48181,f333(f333(f127(x48182),f118(x48182)),x48183)) % 191.49/191.40 [4904]~P5(x49042)+E(f333(f194(f890(x49041,x49042)),x49043),f194(x49042)) % 191.49/191.40 [4905]~P107(x49052)+E(f333(f258(f890(x49051,x49052)),x49053),f258(x49052)) % 191.49/191.40 [4924]E(x49241,f118(x49242))+~E(f333(f333(f127(x49242),x49243),x49241),x49243) % 191.49/191.40 [4925]E(x49251,f118(x49252))+~E(f333(f333(f127(x49252),x49251),x49253),x49253) % 191.49/191.40 [4933]E(x49331,f118(x49332))+~E(f333(f333(f127(x49332),x49333),x49331),f118(x49332)) % 191.49/191.40 [4934]E(x49341,f118(x49342))+~E(f333(f333(f127(x49342),x49341),x49343),f118(x49342)) % 191.49/191.40 [4957]~E(x49572,f2(a880))+E(f333(f333(f82(a880),x49571),x49572),f333(f333(f82(a880),x49573),x49572)) % 191.49/191.40 [4959]~E(x49591,f2(a880))+E(f333(f333(f82(a880),x49591),x49592),f333(f333(f82(a880),x49591),x49593)) % 191.49/191.40 [5012]~P6(x50121)+E(f333(f333(f115(x50121),x50122),x50123),f333(f333(f115(x50121),x50123),x50122)) % 191.49/191.40 [5014]~P101(x50141)+E(f333(f333(f115(x50141),x50142),x50143),f333(f333(f115(x50141),x50143),x50142)) % 191.49/191.40 [5015]~P6(x50151)+E(f333(f333(f106(x50151),x50152),x50153),f333(f333(f106(x50151),x50153),x50152)) % 191.49/191.40 [5017]~P102(x50171)+E(f333(f333(f106(x50171),x50172),x50173),f333(f333(f106(x50171),x50173),x50172)) % 191.49/191.40 [5018]~P115(x50181)+E(f333(f333(f81(x50181),x50182),x50183),f333(f333(f81(x50181),x50183),x50182)) % 191.49/191.40 [5019]~P115(x50191)+E(f333(f333(f82(x50191),x50192),x50193),f333(f333(f82(x50191),x50193),x50192)) % 191.49/191.40 [5021]~P109(x50211)+E(f333(f333(f248(x50211),x50212),x50213),f333(f333(f248(x50211),x50213),x50212)) % 191.49/191.40 [5023]~P109(x50231)+E(f333(f333(f249(x50231),x50232),x50233),f333(f333(f249(x50231),x50233),x50232)) % 191.49/191.40 [5084]E(f46(a880,x50841,x50842),f2(a880))+~E(x50841,f333(f333(f82(a880),x50842),x50843)) % 191.49/191.40 [5085]E(f46(a1,x50851,x50852),f2(a1))+~E(x50851,f333(f333(f82(a1),x50852),x50853)) % 191.49/191.40 [5145]E(x51451,x51452)+~E(f333(f333(f81(a880),x51453),x51451),f333(f333(f81(a880),x51453),x51452)) % 191.49/191.40 [5146]E(x51461,x51462)+~E(f333(f333(f81(a880),x51461),x51463),f333(f333(f81(a880),x51462),x51463)) % 191.49/191.40 [5155]~P79(x51551)+E(f333(f333(f106(x51551),x51552),f333(f80(x51551),x51553)),f333(f333(f3(x51551),x51552),x51553)) % 191.49/191.40 [5156]~P68(x51561)+E(f333(f333(f81(x51561),x51562),f333(f80(x51561),x51563)),f333(f333(f3(x51561),x51562),x51563)) % 191.49/191.40 [5157]~P75(x51571)+E(f333(f333(f81(x51571),x51572),f333(f80(x51571),x51573)),f333(f333(f3(x51571),x51572),x51573)) % 191.49/191.40 [5158]~P112(x51581)+E(f333(f333(f81(x51581),x51582),f333(f80(x51581),x51583)),f333(f333(f3(x51581),x51582),x51583)) % 191.49/191.40 [5159]~P75(x51591)+E(f333(f333(f3(x51591),x51592),f333(f80(x51591),x51593)),f333(f333(f81(x51591),x51592),x51593)) % 191.49/191.40 [5206]~P4(f333(x52063,x52062))+P4(f333(f333(f335(x52061),x52062),x52063)) % 191.49/191.40 [5208]~P69(x52082)+E(f333(f333(f8(x52081,x52082),x52083),f194(f890(x52081,a874))),f2(x52082)) % 191.49/191.40 [5210]~P76(x52102)+E(f333(f333(f11(x52101,x52102),x52103),f194(f890(x52101,a874))),f79(x52102)) % 191.49/191.40 [5260]~E(x52602,f333(f333(f81(a880),x52601),x52603))+P4(f333(f333(f250(a880),x52601),x52602)) % 191.49/191.40 [5263]~E(x52632,f194(f890(x52631,a874)))+E(f333(f333(f62(x52631),x52632),x52633),f194(f890(f890(x52631,a874),a874))) % 191.49/191.40 [5264]~E(x52642,f194(f890(x52641,a874)))+E(f194(f890(f890(x52641,a874),a874)),f333(f333(f62(x52641),x52642),x52643)) % 191.49/191.40 [5340]~E(f333(f259(x53402,x53403),x53401),f194(f890(x53403,a874)))+E(x53401,f194(f890(f889(x53402,x53403),a874))) % 191.49/191.40 [5341]~E(f333(f261(x53412,x53413),x53411),f194(f890(x53412,a874)))+E(x53411,f194(f890(f889(x53412,x53413),a874))) % 191.49/191.40 [5371]E(f333(f259(x53711,x53712),x53713),f194(f890(x53712,a874)))+~E(x53713,f194(f890(f889(x53711,x53712),a874))) % 191.49/191.40 [5372]E(f333(f261(x53721,x53722),x53723),f194(f890(x53721,a874)))+~E(x53723,f194(f890(f889(x53721,x53722),a874))) % 191.49/191.40 [5375]E(f283(x53751,x53752,x53753),f333(f333(f3(a104),x53752),x53753))+P4(f333(f333(f251(a104),x53752),x53753)) % 191.49/191.40 [5391]P4(f333(x53911,x53912))+~P4(f333(f333(f335(x53913),x53912),x53911)) % 191.49/191.40 [5430]E(x54301,x54302)+~E(f333(f80(f890(x54303,a874)),x54301),f333(f80(f890(x54303,a874)),x54302)) % 191.49/191.40 [5435]E(f315(x54351,x54352,x54353),f197(f881(a329)))+~P4(f333(f333(f251(a1),x54352),x54353)) % 191.49/191.40 [5440]~E(x54401,f194(f890(x54402,a874)))+~P4(f333(f333(f335(x54402),x54403),x54401)) % 191.49/191.40 [5469]~E(x54692,f333(f333(f81(a1),x54691),f333(f105(a1),x54693)))+P4(f333(f333(f250(a1),x54691),x54692)) % 191.49/191.40 [5485]E(f333(f333(f311(x54851),x54852),x54853),x54853)+~P4(f333(f333(f335(x54851),x54852),x54853)) % 191.49/191.40 [5496]E(x54961,f194(f890(x54962,a874)))+~E(f333(f333(f62(x54962),x54961),x54963),f194(f890(f890(x54962,a874),a874))) % 191.49/191.40 [5497]E(x54971,f194(f890(x54972,a874)))+~E(f194(f890(f890(x54972,a874),a874)),f333(f333(f62(x54972),x54971),x54973)) % 191.49/191.40 [5503]~P106(x55031)+E(f333(f333(f82(x55031),f333(f80(x55031),x55032)),f333(f80(x55031),x55033)),f333(f333(f82(x55031),x55032),x55033)) % 191.49/191.40 [5505]~P63(x55051)+E(f333(f333(f291(x55051),f333(f80(x55051),x55052)),f333(f80(x55051),x55053)),f333(f333(f291(x55051),x55052),x55053)) % 191.49/191.40 [5535]~P4(f333(x55353,x55352))+P4(f333(f333(f335(x55351),x55352),f333(f255(x55351),x55353))) % 191.49/191.40 [5573]E(f171(x55731,x55732,x55733),x55733)+P4(f333(f333(f335(x55731),x55732),f333(f173(x55731),x55733))) % 191.49/191.40 [5656]~P4(f333(f138(x56561),x56563))+P4(f333(f138(x56561),f333(f137(x56561,x56562),x56563))) % 191.49/191.40 [5701]~P60(x57011)+E(f333(f333(f40(x57011),f46(x57011,x57012,x57013)),x57013),f2(x57011)) % 191.49/191.40 [5720]E(f175(x57201,f333(f333(f152(x57201),x57202),f118(x57201)),x57203),f118(x57201))+P4(f333(f333(f335(a880),f2(a880)),x57203)) % 191.49/191.40 [5777]E(f333(f333(f152(x57771),x57772),x57773),f141(x57771,x57772,x57773))+P4(f333(f333(f335(x57771),x57772),f333(f173(x57771),x57773))) % 191.49/191.40 [5786]E(x57861,x57862)+~E(f333(f333(f82(a880),f333(a117,x57863)),x57861),f333(f333(f82(a880),f333(a117,x57863)),x57862)) % 191.49/191.40 [5787]~E(x57872,f333(f333(f81(a1),x57871),f333(f105(a1),f333(a117,x57873))))+P4(f333(f333(f251(a1),x57871),x57872)) % 191.49/191.40 [5892]~E(x58923,f118(x58921))+E(f333(f333(f333(f189(f881(x58921),f881(x58921)),x58922),f169(x58921)),x58923),f118(x58921)) % 191.49/191.40 [5896]P4(f333(x58961,x58962))+~P4(f333(f333(f335(x58963),x58962),f333(f255(x58963),x58961))) % 191.49/191.40 [5928]E(x59281,x59282)+~E(f333(f333(f311(x59283),x59281),f194(f890(x59283,a874))),f333(f333(f311(x59283),x59282),f194(f890(x59283,a874)))) % 191.49/191.40 [5938]~P110(x59381)+E(f333(f333(f106(f890(x59381,a874)),f333(f256(x59381),x59382)),f333(f303(x59381,x59382),x59383)),f194(f890(x59381,a874))) % 191.49/191.40 [5981]E(f141(x59811,x59812,x59813),x59813)+~P4(f333(f333(f335(x59811),x59812),f333(f173(x59811),x59813))) % 191.49/191.40 [6005]~P81(x60051)+E(f333(f312(x60051,x60051,f80(x60051)),f333(f303(x60051,x60052),x60053)),f306(x60051,f333(f80(x60051),x60053),f333(f80(x60051),x60052))) % 191.49/191.40 [6014]E(f333(f195(f881(x60141)),f171(x60141,x60142,x60143)),f333(f195(f881(x60141)),x60143))+P4(f333(f333(f335(x60141),x60142),f333(f173(x60141),x60143))) % 191.49/191.40 [6066]~P110(x60661)+E(f333(f333(f106(f890(x60661,a874)),f333(f303(x60661,x60662),x60663)),f333(f257(x60661),x60663)),f194(f890(x60661,a874))) % 191.49/191.40 [6089]~P81(x60891)+E(f333(f312(x60891,x60891,f80(x60891)),f307(x60891,x60892,x60893)),f307(x60891,f333(f80(x60891),x60893),f333(f80(x60891),x60892))) % 191.49/191.40 [6090]~P81(x60901)+E(f333(f312(x60901,x60901,f80(x60901)),f304(x60901,x60902,x60903)),f304(x60901,f333(f80(x60901),x60903),f333(f80(x60901),x60902))) % 191.49/191.40 [6147]E(f175(x61471,f333(f333(f152(x61471),x61472),f118(x61471)),x61473),f333(f333(f152(x61471),x61472),f118(x61471)))+~P4(f333(f333(f335(a880),f2(a880)),x61473)) % 191.49/191.40 [6156]~P81(x61561)+E(f333(f312(x61561,x61561,f80(x61561)),f306(x61561,x61562,x61563)),f333(f303(x61561,f333(f80(x61561),x61563)),f333(f80(x61561),x61562))) % 191.49/191.40 [6176]~P61(x61761)+E(f46(x61761,f333(f80(x61761),f46(x61761,x61762,x61763)),x61763),f46(x61761,f333(f80(x61761),x61762),x61763)) % 191.49/191.40 [6275]~P4(f333(f63(f889(x62752,x62751)),x62753))+P4(f333(f63(x62751),f333(f259(x62752,x62751),x62753))) % 191.49/191.40 [6276]~P4(f333(f63(f889(x62761,x62762)),x62763))+P4(f333(f63(x62761),f333(f261(x62761,x62762),x62763))) % 191.49/191.40 [6282]~P110(x62821)+E(f333(f333(f106(f890(x62821,a874)),f307(x62821,x62822,x62823)),f333(f257(x62821),x62823)),f194(f890(x62821,a874))) % 191.49/191.40 [6283]~P110(x62831)+E(f333(f333(f106(f890(x62831,a874)),f306(x62831,x62832,x62833)),f333(f305(x62831),x62833)),f194(f890(x62831,a874))) % 191.49/191.40 [6284]~P110(x62841)+E(f333(f333(f106(f890(x62841,a874)),f304(x62841,x62842,x62843)),f333(f305(x62841),x62843)),f194(f890(x62841,a874))) % 191.49/191.40 [6347]E(f333(f333(f166(x63471),x63472),f582(x63472,x63473,x63471)),x63473)+~P4(f333(f333(f335(x63471),x63473),f333(f173(x63471),x63472))) % 191.49/191.40 [6488]E(x64881,f118(x64882))+~E(f333(f333(f333(f189(f881(x64882),f881(x64882)),x64883),f169(x64882)),x64881),f118(x64882)) % 191.49/191.40 [6587]~P4(f333(f63(f889(x65872,x65871)),x65873))+P4(f333(f63(f889(x65871,x65872)),f333(f288(x65872,x65871),x65873))) % 191.49/191.40 [6738]P55(x67381,x67382,x67383)+P4(f333(f333(f335(x67381),f767(x67383,x67382,x67381)),x67382)) % 191.49/191.40 [6739]P55(x67391,x67392,x67393)+P4(f333(f333(f335(x67391),f766(x67393,x67392,x67391)),x67392)) % 191.49/191.40 [6751]P4(f333(f321(x67511,x67512),x67513))+P4(f333(f333(x67512,f483(x67513,x67512,x67511)),x67513)) % 191.49/191.40 [6752]P4(f333(f321(x67521,x67522),x67523))+P4(f333(f333(x67522,f500(x67523,x67522,x67521)),x67523)) % 191.49/191.40 [6777]E(f333(f195(f881(x67771)),f171(x67771,x67772,x67773)),f333(f333(f3(a880),f333(f195(f881(x67771)),x67773)),f79(a880)))+~P4(f333(f333(f335(x67771),x67772),f333(f173(x67771),x67773))) % 191.49/191.40 [6815]P4(f333(f267(x68151,x68152),x68153))+P4(f333(f333(f335(x68151),f594(x68153,x68152,x68151)),x68153)) % 191.49/191.40 [6824]~P4(f333(f63(f889(x68242,x68241)),f333(f288(x68241,x68242),x68243)))+P4(f333(f63(f889(x68241,x68242)),x68243)) % 191.49/191.40 [6880]~P4(f333(f333(f335(x68801),x68802),f333(f173(x68801),f119(x68801,x68803))))+P4(f333(f333(f335(x68801),x68802),f333(f173(x68801),x68803))) % 191.49/191.40 [6885]P31(x68851,x68852,x68853)+P4(f333(f333(f335(f879(x68851)),f607(x68853,x68852,x68851)),x68853)) % 191.49/191.40 [6913]E(f333(f137(x69131,x69132),x69133),x69133)+P4(f333(f333(f335(x69131),f625(x69133,x69132,x69131)),f333(f173(x69131),x69133))) % 191.49/191.40 [6928]E(f333(f137(x69281,x69282),x69283),f118(x69281))+P4(f333(f333(f335(x69281),f624(x69283,x69282,x69281)),f333(f173(x69281),x69283))) % 191.49/191.40 [6952]P34(x69521,x69522,x69523)+P4(f333(f333(f335(x69521),f809(x69523,x69522,x69521)),f333(f173(x69521),x69523))) % 191.49/191.40 [6953]P34(x69531,x69532,x69533)+P4(f333(f333(f335(x69531),f810(x69533,x69532,x69531)),f333(f173(x69531),x69533))) % 191.49/191.40 [6954]P34(x69541,x69542,x69543)+P4(f333(f333(f335(x69541),f798(x69542,x69543,x69541)),f333(f173(x69541),x69543))) % 191.49/191.40 [6957]E(f177(x69571,x69572,x69573),x69573)+P4(f333(f333(f335(x69571),f655(x69573,x69572,x69571)),f333(f173(x69571),x69573))) % 191.49/191.40 [7038]P4(f333(f161(x70381,x70382),x70383))+P4(f333(f333(f335(x70381),f674(x70383,x70382,x70381)),f333(f173(x70381),x70383))) % 191.49/191.40 [7047]~P36(x70471,x70473,x70472)+P4(f333(f333(f335(x70471),f745(x70472,x70473,x70471)),f333(f173(x70471),x70472))) % 191.49/191.40 [7048]~P38(x70481,x70483,x70482)+P4(f333(f333(f335(x70481),f812(x70482,x70483,x70481)),f333(f173(x70481),x70482))) % 191.49/191.40 [7082]P4(f333(f333(f335(x70821),x70822),f712(x70823,x70822,x70821)))+~P4(f333(f333(f335(x70821),x70822),f41(f890(x70821,a874),x70823))) % 191.49/191.40 [7083]~P69(x70831)+E(f333(f333(f81(x70831),f333(f333(f8(a880,x70831),x70832),f333(f256(a880),x70833))),f333(x70832,x70833)),f333(f333(f8(a880,x70831),x70832),f333(f256(a880),f333(a117,x70833)))) % 191.49/191.40 [7172]~P36(x71722,x71721,x71723)+P4(f333(x71721,f333(f333(f166(x71722),x71723),f760(x71723,x71721,x71722)))) % 191.49/191.40 [7185]~P4(f333(f333(f335(x71851),x71852),f833(x71852,x71853,x71851)))+P4(f333(f333(f335(x71851),x71852),f42(f890(x71851,a874),x71853))) % 191.49/191.40 [7215]~P69(x72151)+E(f333(f333(f81(x72151),f333(f333(f8(a880,x72151),x72152),f333(f302(a880),x72153))),f333(x72152,f333(a117,x72153))),f333(f333(f8(a880,x72151),x72152),f333(f302(a880),f333(a117,x72153)))) % 191.49/191.40 [7341]P4(f333(f333(f335(f881(x73411)),x73412),f162(x73411,x73413)))+P4(f333(f333(f335(x73411),f627(x73413,x73412,x73411)),f333(f173(x73411),x73412))) % 191.49/191.40 [7357]~P4(f333(f333(f335(f881(x73571)),x73572),f162(x73571,f322(x73571,x73573))))+P4(f333(f333(f335(f881(x73571)),x73572),f322(f881(x73571),f158(x73571,x73573)))) % 191.49/191.40 [7382]~P4(f333(f333(f335(f881(x73821)),x73822),f322(f881(x73821),f158(x73821,x73823))))+P4(f333(f333(f335(f881(x73821)),x73822),f162(x73821,f322(x73821,x73823)))) % 191.49/191.40 [7418]E(f333(f333(f333(f189(f881(x74181),f881(x74181)),x74182),f169(x74181)),x74183),x74183)+~P4(f333(f333(f250(a880),f333(f195(f881(x74181)),x74183)),f79(a880))) % 191.49/191.40 [7454]E(f333(f333(f127(x74541),f787(x74542,x74543,x74541)),f333(f333(f152(x74541),x74543),f792(x74542,x74543,x74541))),x74542)+~P4(f333(f333(f335(x74541),x74543),f333(f173(x74541),x74542))) % 191.49/191.40 [7455]E(f333(f333(f127(x74551),f793(x74552,x74553,x74551)),f333(f333(f152(x74551),x74553),f794(x74552,x74553,x74551))),x74552)+~P4(f333(f333(f335(x74551),x74553),f333(f173(x74551),x74552))) % 191.49/191.40 [7456]E(f333(f333(f127(x74561),f795(x74562,x74563,x74561)),f333(f333(f152(x74561),x74563),f796(x74562,x74563,x74561))),x74562)+~P4(f333(f333(f335(x74561),x74563),f333(f173(x74561),x74562))) % 191.49/191.40 [7477]~P28(x74771,x74772,x74773,f258(f890(x74771,a874)))+P28(f881(x74771),f881(x74772),f333(f155(x74771,x74772),x74773),f258(f890(f881(x74771),a874))) % 191.49/191.40 [7622]E(x76221,f333(f333(f81(a880),f333(f333(f82(a880),f333(f262(a880,a880),x76222)),x76223)),f333(f271(a880,a880),x76222)))+~P4(f333(f49(x76221,x76223),x76222)) % 191.49/191.40 [7630]P28(x76301,x76302,x76303,f258(f890(x76301,a874)))+~P28(f881(x76301),f881(x76302),f333(f155(x76301,x76302),x76303),f258(f890(f881(x76301),a874))) % 191.49/191.40 [7668]~P4(f333(f333(f201(x76681),x76682),x76683))+P4(f333(f333(f333(f333(a203,x76681),x76682),f852(x76683,x76682,x76681)),x76683)) % 191.49/191.40 [7672]P4(f333(f333(f335(f890(x76721,a874)),f833(x76722,x76723,x76721)),x76723))+P4(f333(f333(f335(x76721),x76722),f42(f890(x76721,a874),x76723))) % 191.49/191.40 [7766]P4(f333(f333(f335(f881(x77661)),x77662),f162(x77661,x77663)))+~P4(f333(f333(f335(x77661),f627(x77663,x77662,x77661)),x77663)) % 191.49/191.40 [7863]P34(x78631,x78632,x78633)+~P4(f333(x78632,f333(f333(f166(x78631),x78633),f799(x78633,x78632,x78631)))) % 191.49/191.40 [7888]E(x78881,x78882)+~E(f333(f333(f9(x78883,f890(x78883,a874),a874),f335(x78883)),x78881),f333(f333(f9(x78883,f890(x78883,a874),a874),f335(x78883)),x78882)) % 191.49/191.40 [7894]~P4(f333(f333(f335(f889(x78941,x78941)),x78943),f260(x78941,x78942)))+P4(f333(f333(f335(x78941),f569(x78942,x78943,x78941)),x78942)) % 191.49/191.40 [7896]~P4(f333(f333(f335(x78961),x78963),f41(f890(x78961,a874),x78962)))+P4(f333(f333(f335(f890(x78961,a874)),f712(x78962,x78963,x78961)),x78962)) % 191.49/191.40 [8076]~P4(f333(f333(f335(x80761),x80762),f333(f173(x80761),f793(x80763,x80762,x80761))))+~P4(f333(f333(f335(x80761),x80762),f333(f173(x80761),x80763))) % 191.49/191.40 [8077]~P4(f333(f333(f335(x80771),x80772),f333(f173(x80771),f796(x80773,x80772,x80771))))+~P4(f333(f333(f335(x80771),x80772),f333(f173(x80771),x80773))) % 191.49/191.40 [8169]E(f333(f244(f884(f881(a329)),f881(a329),f315(x81691,x81692,f333(f333(f81(a1),x81693),f79(a1))),f242(f881(a329))),f333(x81691,x81693)),f315(x81691,x81692,x81693))+P4(f333(f333(f251(a1),x81692),x81693)) % 191.49/191.40 [8269]E(x82691,f118(x82692))+P4(f333(f333(f335(x82692),f333(f262(x82692,f889(a104,a104)),f333(f284(x82692,x82691),x82693))),f333(f173(x82692),x82691))) % 191.49/191.40 [8363]~P72(x83631)+E(f333(f143(x83631,x83631,f333(f9(x83631,x83631,x83631),f81(x83631)),x83632),f333(f170(x83631),x83633)),f333(f143(x83631,x83631,f81(x83631),x83632),x83633)) % 191.49/191.40 [8848]~P109(x88481)+E(f333(f173(x88481),f150(x88481,x88481,f7(x88481),x88482,x88483)),f333(f333(f311(x88481),x88482),f333(f173(x88481),x88483))) % 191.49/191.40 [8860]P4(f333(f333(f251(a880),f2(a880)),f771(x88601,x88602,x88603)))+~P4(f333(f333(f335(f889(x88603,x88603)),x88602),f333(f333(f290(x88603,x88603,x88603),x88601),f309(x88603,x88601)))) % 191.49/191.40 [9142]~P57(x91421,x91422)+~P4(f333(f333(f335(f889(x91421,x91421)),f333(f333(f263(x91421,x91421),x91423),x91423)),f333(f333(f290(x91421,x91421,x91421),x91422),f309(x91421,x91422)))) % 191.49/191.40 [9277]~E(f333(f333(f106(f890(f889(x92771,x92771),a874)),f333(f288(x92771,x92771),x92772)),f309(x92771,x92772)),f194(f890(f889(x92771,x92771),a874)))+~P4(f333(f333(f335(f889(x92771,x92771)),f333(f333(f263(x92771,x92771),x92773),x92773)),f333(f333(f290(x92771,x92771,x92771),x92772),f309(x92771,x92772)))) % 191.49/191.40 [9452]~P4(f333(f63(x94521),x94522))+P4(f333(f333(f250(a880),f333(f39(x94521),f333(f333(f3(f890(x94521,a874)),x94522),f333(f333(f311(x94521),x94523),f194(f890(x94521,a874)))))),f333(f39(x94521),x94522))) % 191.49/191.40 [5073]~E(x50733,f118(x50731))+E(f145(x50731,f333(f333(f152(x50731),x50732),x50733)),x50732) % 191.49/191.40 [5081]~E(x50813,f118(x50811))+E(f119(x50811,f333(f333(f152(x50811),x50812),x50813)),f118(x50811)) % 191.49/191.40 [5109]E(x51091,f118(x51092))+E(f145(x51092,f333(f333(f152(x51092),x51093),x51091)),f145(x51092,x51091)) % 191.49/191.40 [5111]E(x51111,f118(x51112))+E(f145(x51112,f333(f333(f127(x51112),x51113),x51111)),f145(x51112,x51111)) % 191.49/191.40 [5117]~E(x51173,f118(x51171))+E(f145(x51171,f333(f333(f127(x51171),x51172),x51173)),f145(x51171,x51172)) % 191.49/191.40 [5118]~E(x51183,f118(x51181))+E(f119(x51181,f333(f333(f127(x51181),x51182),x51183)),f119(x51181,x51182)) % 191.49/191.40 [5149]E(x51491,f118(x51492))+E(f333(f142(x51492),f333(f333(f127(x51492),x51491),x51493)),f333(f142(x51492),x51491)) % 191.49/191.40 [5180]~E(x51802,f118(x51801))+E(f333(f142(x51801),f333(f333(f127(x51801),x51802),x51803)),f333(f142(x51801),x51803)) % 191.49/191.40 [5235]~P6(x52351)+E(f333(f333(f115(x52351),x52352),f333(f333(f106(x52351),x52352),x52353)),x52352) % 191.49/191.40 [5236]~P6(x52361)+E(f333(f333(f106(x52361),x52362),f333(f333(f115(x52361),x52362),x52363)),x52362) % 191.49/191.40 [5237]~P109(x52371)+E(f333(f333(f248(x52371),x52372),f333(f333(f249(x52371),x52372),x52373)),x52372) % 191.49/191.40 [5238]~P109(x52381)+E(f333(f333(f249(x52381),x52382),f333(f333(f248(x52381),x52382),x52383)),x52382) % 191.49/191.40 [5258]~P60(x52581)+E(f46(x52581,f333(f333(f82(x52581),x52582),x52583),x52583),f2(x52581)) % 191.49/191.40 [5259]~P60(x52591)+E(f46(x52591,f333(f333(f82(x52591),x52592),x52593),x52592),f2(x52591)) % 191.49/191.40 [5334]~P68(x53341)+E(f333(f80(x53341),f333(f333(f3(x53341),x53342),x53343)),f333(f333(f3(x53341),x53343),x53342)) % 191.49/191.40 [5395]E(x53951,f118(x53952))+E(f119(x53952,f333(f333(f152(x53952),x53953),x53951)),f333(f333(f152(x53952),x53953),f119(x53952,x53951))) % 191.49/191.40 [5396]E(x53961,f118(x53962))+E(f119(x53962,f333(f333(f127(x53962),x53963),x53961)),f333(f333(f127(x53962),x53963),f119(x53962,x53961))) % 191.49/191.40 [5399]~P9(x53991)+E(f41(x53991,f333(f333(f311(x53991),x53992),x53993)),f333(f333(f115(x53991),x53992),f41(x53991,x53993))) % 191.49/191.40 [5400]~P9(x54001)+E(f42(x54001,f333(f333(f311(x54001),x54002),x54003)),f333(f333(f106(x54001),x54002),f42(x54001,x54003))) % 191.49/191.40 [5445]~P6(x54451)+E(f333(f333(f115(x54451),x54452),f333(f333(f115(x54451),x54452),x54453)),f333(f333(f115(x54451),x54452),x54453)) % 191.49/191.40 [5447]~P101(x54471)+E(f333(f333(f115(x54471),x54472),f333(f333(f115(x54471),x54472),x54473)),f333(f333(f115(x54471),x54472),x54473)) % 191.49/191.40 [5448]~P6(x54481)+E(f333(f333(f106(x54481),x54482),f333(f333(f106(x54481),x54482),x54483)),f333(f333(f106(x54481),x54482),x54483)) % 191.49/191.40 [5450]~P102(x54501)+E(f333(f333(f106(x54501),x54502),f333(f333(f106(x54501),x54502),x54503)),f333(f333(f106(x54501),x54502),x54503)) % 191.49/191.40 [5451]~P97(x54511)+E(f333(f333(f82(x54511),x54512),f333(f333(f82(x54511),x54512),x54513)),f333(f333(f82(x54511),x54512),x54513)) % 191.49/191.40 [5453]~P109(x54531)+E(f333(f333(f248(x54531),x54532),f333(f333(f248(x54531),x54532),x54533)),f333(f333(f248(x54531),x54532),x54533)) % 191.49/191.40 [5455]~P109(x54551)+E(f333(f333(f249(x54551),x54552),f333(f333(f249(x54551),x54552),x54553)),f333(f333(f249(x54551),x54552),x54553)) % 191.49/191.40 [5463]~P60(x54631)+E(f46(x54631,f333(f333(f81(x54631),x54632),x54633),x54633),f46(x54631,x54632,x54633)) % 191.49/191.40 [5464]~P60(x54641)+E(f46(x54641,f333(f333(f81(x54641),x54642),x54643),x54642),f46(x54641,x54643,x54642)) % 191.49/191.40 [5470]~P106(x54701)+E(f333(f333(f82(x54701),x54702),f333(f80(x54701),x54703)),f333(f80(x54701),f333(f333(f82(x54701),x54702),x54703))) % 191.49/191.40 [5471]~P63(x54711)+E(f333(f333(f291(x54711),x54712),f333(f80(x54711),x54713)),f333(f80(x54711),f333(f333(f291(x54711),x54712),x54713))) % 191.49/191.40 [5472]~P84(x54721)+E(f333(f333(f81(x54721),x54722),f333(f167(x54721),x54723)),f333(f167(x54721),f333(f333(f152(x54721),x54722),x54723))) % 191.49/191.40 [5502]~P106(x55021)+E(f333(f333(f82(x55021),f333(f80(x55021),x55022)),x55023),f333(f333(f82(x55021),x55022),f333(f80(x55021),x55023))) % 191.49/191.40 [5508]~P12(x55081,x55082,x55083)+E(f41(f890(x55081,a874),f333(f333(f62(x55081),x55082),x55083)),x55082) % 191.49/191.40 [5565]~P113(x55651)+E(f333(f333(f82(x55651),x55652),f333(f333(f264(x55651),x55652),x55653)),f333(f333(f264(x55651),x55652),f333(a117,x55653))) % 191.49/191.40 [5566]~P115(x55661)+E(f333(f333(f82(x55661),x55662),f333(f333(f264(x55661),x55662),x55663)),f333(f333(f264(x55661),x55662),f333(a117,x55663))) % 191.49/191.40 [5576]~P75(x55761)+E(f333(f333(f81(x55761),f333(f80(x55761),x55762)),f333(f333(f81(x55761),x55762),x55763)),x55763) % 191.49/191.40 [5599]~P143(x55991)+E(f333(f333(f264(x55991),f333(f105(x55991),x55992)),x55993),f333(f105(x55991),f333(f333(f264(a880),x55992),x55993))) % 191.49/191.40 [5600]~P140(x56001)+E(f333(f333(f264(x56001),f333(f107(x56001),x56002)),x56003),f333(f107(x56001),f333(f333(f264(a1),x56002),x56003))) % 191.49/191.40 [5605]~P87(x56051)+E(f333(f76(x56051),f333(f333(f3(x56051),x56052),x56053)),f333(f76(x56051),f333(f333(f3(x56051),x56053),x56052))) % 191.49/191.40 [5609]~P120(x56091)+E(f333(f333(f82(x56091),f83(x56091,x56092)),f83(x56091,x56093)),f83(x56091,f333(f333(f82(x56091),x56092),x56093))) % 191.49/191.40 [5613]E(x56131,f118(x56132))+E(f333(f333(f127(x56132),f333(f172(x56132),x56131)),x56133),f333(f172(x56132),f333(f333(f127(x56132),x56131),x56133))) % 191.49/191.40 [5618]~E(x56182,f333(a117,f333(f333(f81(a880),x56181),x56183)))+P4(f333(f333(f251(a880),x56181),x56182)) % 191.49/191.40 [5619]~P106(x56191)+E(f333(f333(f82(x56191),f333(f80(x56191),x56192)),x56193),f333(f80(x56191),f333(f333(f82(x56191),x56192),x56193))) % 191.49/191.40 [5620]~P118(x56201)+E(f333(f333(f291(x56201),f333(f80(x56201),x56202)),x56203),f333(f80(x56201),f333(f333(f291(x56201),x56202),x56203))) % 191.49/191.40 [5621]~P120(x56211)+E(f333(f333(f264(x56211),f333(f76(x56211),x56212)),x56213),f333(f76(x56211),f333(f333(f264(x56211),x56212),x56213))) % 191.49/191.40 [5719]E(f581(x57191,x57192,x57193),f585(x57191,x57192,x57193))+E(f333(f333(f106(f890(x57193,a874)),x57192),x57191),f194(f890(x57193,a874))) % 191.49/191.40 [5733]~P69(x57332)+E(f333(f333(f8(x57331,x57332),f333(f18(x57332,x57331),f2(x57332))),x57333),f2(x57332)) % 191.49/191.40 [5734]~P76(x57342)+E(f333(f333(f11(x57341,x57342),f333(f18(x57342,x57341),f79(x57342))),x57343),f79(x57342)) % 191.49/191.40 [5736]~P94(x57361)+E(f333(f333(f3(x57361),f333(f108(x57361),x57362)),f333(f108(x57361),x57363)),f333(f108(x57361),f333(f333(f3(a1),x57362),x57363))) % 191.49/191.40 [5739]~P143(x57391)+E(f333(f333(f81(x57391),f333(f105(x57391),x57392)),f333(f105(x57391),x57393)),f333(f105(x57391),f333(f333(f81(a880),x57392),x57393))) % 191.49/191.40 [5740]~P143(x57401)+E(f333(f333(f82(x57401),f333(f105(x57401),x57402)),f333(f105(x57401),x57403)),f333(f105(x57401),f333(f333(f82(a880),x57402),x57403))) % 191.49/191.40 [5741]~P140(x57411)+E(f333(f333(f3(x57411),f333(f107(x57411),x57412)),f333(f107(x57411),x57413)),f333(f107(x57411),f333(f333(f3(a1),x57412),x57413))) % 191.49/191.40 [5742]~P140(x57421)+E(f333(f333(f81(x57421),f333(f107(x57421),x57422)),f333(f107(x57421),x57423)),f333(f107(x57421),f333(f333(f81(a1),x57422),x57423))) % 191.49/191.40 [5743]~P140(x57431)+E(f333(f333(f82(x57431),f333(f107(x57431),x57432)),f333(f107(x57431),x57433)),f333(f107(x57431),f333(f333(f82(a1),x57432),x57433))) % 191.49/191.40 [5744]~P94(x57441)+E(f333(f333(f81(x57441),f333(f108(x57441),x57442)),f333(f108(x57441),x57443)),f333(f108(x57441),f333(f333(f81(a1),x57442),x57443))) % 191.49/191.40 [5745]~P94(x57451)+E(f333(f333(f82(x57451),f333(f108(x57451),x57452)),f333(f108(x57451),x57453)),f333(f108(x57451),f333(f333(f82(a1),x57452),x57453))) % 191.49/191.40 [5794]~E(x57943,x57942)+P4(f333(f333(f250(f890(x57941,a874)),x57942),x57943)) % 191.49/191.40 [5800]~E(x58002,x58003)+P4(f333(f333(f250(f890(x58001,a874)),x58002),x58003)) % 191.49/191.40 [5805]~P79(x58051)+E(f333(f333(f106(x58051),f333(f80(x58051),x58052)),f333(f80(x58051),x58053)),f333(f80(x58051),f333(f333(f115(x58051),x58052),x58053))) % 191.49/191.40 [5806]~P79(x58061)+E(f333(f333(f115(x58061),f333(f80(x58061),x58062)),f333(f80(x58061),x58063)),f333(f80(x58061),f333(f333(f106(x58061),x58062),x58063))) % 191.49/191.40 [5807]~P75(x58071)+E(f333(f333(f81(x58071),f333(f80(x58071),x58072)),f333(f80(x58071),x58073)),f333(f80(x58071),f333(f333(f81(x58071),x58073),x58072))) % 191.49/191.40 [5808]~P68(x58081)+E(f333(f333(f81(x58081),f333(f80(x58081),x58082)),f333(f80(x58081),x58083)),f333(f80(x58081),f333(f333(f81(x58081),x58082),x58083))) % 191.49/191.40 [5809]~P77(x58091)+E(f333(f333(f249(x58091),f333(f80(x58091),x58092)),f333(f80(x58091),x58093)),f333(f80(x58091),f333(f333(f248(x58091),x58092),x58093))) % 191.49/191.40 [5810]~P77(x58101)+E(f333(f333(f248(x58101),f333(f80(x58101),x58102)),f333(f80(x58101),x58103)),f333(f80(x58101),f333(f333(f249(x58101),x58102),x58103))) % 191.49/191.40 [5811]~P120(x58111)+E(f333(f333(f82(x58111),f333(f76(x58111),x58112)),f333(f76(x58111),x58113)),f333(f76(x58111),f333(f333(f82(x58111),x58112),x58113))) % 191.49/191.40 [5812]~P65(x58121)+E(f333(f333(f291(x58121),f333(f76(x58121),x58122)),f333(f76(x58121),x58123)),f333(f76(x58121),f333(f333(f291(x58121),x58122),x58123))) % 191.49/191.40 [5813]~P84(x58131)+E(f333(f333(f81(x58131),f333(f167(x58131),x58132)),f333(f167(x58131),x58133)),f333(f167(x58131),f333(f333(f127(x58131),x58132),x58133))) % 191.49/191.40 [5814]E(x58141,f194(f890(x58142,a874)))+~E(f333(f333(f115(f890(x58142,a874)),x58143),x58141),f194(f890(x58142,a874))) % 191.49/191.40 [5815]E(x58151,f194(f890(x58152,a874)))+~E(f333(f333(f115(f890(x58152,a874)),x58151),x58153),f194(f890(x58152,a874))) % 191.49/191.40 [5816]~P147(x58161,x58163,x58162)+P4(f333(x58161,f333(f333(f40(a1),x58162),x58163))) % 191.49/191.40 [5866]~P4(f333(f63(x58661),x58663))+P4(f333(f63(x58661),f333(f333(f311(x58661),x58662),x58663))) % 191.49/191.40 [5867]~P4(f333(f138(x58671),x58673))+P4(f333(f138(x58671),f333(f333(f174(x58671),x58672),x58673))) % 191.49/191.40 [5868]~P4(f333(f138(x58681),x58683))+P4(f333(f138(x58681),f333(f333(f139(x58681),x58682),x58683))) % 191.49/191.40 [5897]~P6(x58971)+P4(f333(f333(f250(x58971),x58972),f333(f333(f115(x58971),x58973),x58972))) % 191.49/191.40 [5898]~P101(x58981)+P4(f333(f333(f250(x58981),x58982),f333(f333(f115(x58981),x58983),x58982))) % 191.49/191.40 [5899]~P6(x58991)+P4(f333(f333(f250(x58991),x58992),f333(f333(f115(x58991),x58992),x58993))) % 191.49/191.40 [5900]~P101(x59001)+P4(f333(f333(f250(x59001),x59002),f333(f333(f115(x59001),x59002),x59003))) % 191.49/191.40 [5901]~P109(x59011)+P4(f333(f333(f250(x59011),x59012),f333(f333(f249(x59011),x59013),x59012))) % 191.49/191.40 [5902]~P109(x59021)+P4(f333(f333(f250(x59021),x59022),f333(f333(f249(x59021),x59022),x59023))) % 191.49/191.40 [5916]~E(x59161,f2(a880))+E(f333(f333(f40(a880),f333(f333(f82(a880),x59161),x59162)),f333(f333(f82(a880),x59161),x59163)),f2(a880)) % 191.49/191.40 [5984]P4(f333(x59841,x59842))+P4(f333(f333(f201(f33(x59841,x59843)),x59842),x59842)) % 191.49/191.40 [5999]~P94(x59991)+E(f333(f333(f3(x59991),f333(f108(x59991),x59992)),f333(f108(x59991),x59993)),f333(f108(x59991),f333(f333(f81(a1),x59992),f333(f80(a1),x59993)))) % 191.49/191.40 [6053]E(x60531,f2(a880))+E(f333(f333(f40(a880),f333(f333(f82(a880),x60531),x60532)),f333(f333(f82(a880),x60531),x60533)),f333(f333(f40(a880),x60532),x60533)) % 191.49/191.40 [6087]E(f153(x60871,f333(f333(f152(x60871),x60872),x60873)),f333(f333(f152(x60871),x60872),f153(x60871,x60873)))+P4(f333(f333(f335(x60871),x60872),f333(f173(x60871),x60873))) % 191.49/191.40 [6121]P147(x61211,x61212,x61213)+~P4(f333(x61211,f333(f333(f40(a1),x61213),x61212))) % 191.49/191.40 [6193]E(x61931,f118(x61932))+E(f333(f333(f152(x61932),f333(f142(x61932),x61931)),f333(f333(f174(x61932),x61933),f333(f172(x61932),x61931))),f333(f333(f174(x61932),f333(a117,x61933)),x61931)) % 191.49/191.40 [6200]E(f333(f333(f3(f890(x62001,a874)),x62002),x62003),x62002)+~E(f333(f333(f106(f890(x62001,a874)),x62002),x62003),f194(f890(x62001,a874))) % 191.49/191.40 [6213]E(f153(x62131,f333(f333(f152(x62131),x62132),x62133)),f153(x62131,x62133))+~P4(f333(f333(f335(x62131),x62132),f333(f173(x62131),x62133))) % 191.49/191.40 [6245]~P4(f333(f333(f251(a880),x62451),x62453))+P4(f333(f333(f251(a880),x62451),f333(f333(f81(a880),x62452),x62453))) % 191.49/191.40 [6247]~P4(f333(f333(f251(a880),x62471),x62472))+P4(f333(f333(f251(a880),x62471),f333(f333(f81(a880),x62472),x62473))) % 191.49/191.40 [6249]~P4(f333(f333(f250(a880),x62491),x62493))+P4(f333(f333(f250(a880),x62491),f333(f333(f81(a880),x62492),x62493))) % 191.49/191.40 [6251]~P4(f333(f333(f250(a880),x62511),x62512))+P4(f333(f333(f250(a880),x62511),f333(f333(f81(a880),x62512),x62513))) % 191.49/191.40 [6290]P4(f333(f63(x62901),x62902))+~P4(f333(f63(x62901),f333(f333(f311(x62901),x62903),x62902))) % 191.49/191.40 [6291]P4(f333(f138(x62911),x62912))+~P4(f333(f138(x62911),f333(f333(f152(x62911),x62913),x62912))) % 191.49/191.40 [6292]P4(f333(f138(x62921),x62922))+~P4(f333(f138(x62921),f333(f333(f127(x62921),x62923),x62922))) % 191.49/191.40 [6293]P4(f333(f138(x62931),x62932))+~P4(f333(f138(x62931),f333(f333(f127(x62931),x62932),x62933))) % 191.49/191.40 [6336]~P115(x63361)+E(f333(f333(f81(x63361),x63362),f333(f333(f82(x63361),x63363),x63362)),f333(f333(f82(x63361),f333(f333(f81(x63361),x63363),f79(x63361))),x63362)) % 191.49/191.40 [6385]~E(x63851,x63852)+~P4(f333(f333(f251(f890(x63853,a874)),x63851),x63852)) % 191.49/191.40 [6429]P4(f333(f333(f335(x64291),x64292),x64293))+P4(f333(f333(f335(x64291),x64292),f333(f80(f890(x64291,a874)),x64293))) % 191.49/191.40 [6435]E(f145(x64351,f333(f333(f139(x64351),x64352),x64353)),f145(x64351,x64353))+~P4(f333(f333(f251(a880),x64352),f333(f195(f881(x64351)),x64353))) % 191.49/191.40 [6436]E(f333(f333(f174(x64361),x64362),f119(x64361,x64363)),f333(f333(f174(x64361),x64362),x64363))+~P4(f333(f333(f251(a880),x64362),f333(f195(f881(x64361)),x64363))) % 191.49/191.40 [6490]E(f333(f333(f333(f189(f881(x64901),f881(x64901)),x64902),f169(x64901)),x64903),x64903)+~E(f46(a880,x64902,f333(f195(f881(x64901)),x64903)),f2(a880)) % 191.49/191.40 [6497]~P12(x64971,x64973,x64972)+E(f333(f333(f290(x64971,x64971,x64971),f333(f288(x64971,x64971),x64972)),x64972),x64972) % 191.49/191.40 [6536]~E(f333(f333(f115(f890(x65361,a874)),x65362),x65363),x65363)+P4(f333(f333(f250(f890(x65361,a874)),x65362),x65363)) % 191.49/191.40 [6541]~P54(x65411,x65411,x65413)+P54(x65411,x65411,f333(f333(f189(f889(x65411,x65411),a874),x65412),x65413)) % 191.49/191.40 [6543]~P4(f333(f333(f335(x65431),x65433),f333(f173(x65431),x65432)))+P4(f333(f333(f251(a880),f2(a880)),f333(f195(f881(x65431)),x65432))) % 191.49/191.40 [6569]~P87(x65691)+E(f333(f76(x65691),f333(f333(f81(x65691),f333(f76(x65691),x65692)),f333(f76(x65691),x65693))),f333(f333(f81(x65691),f333(f76(x65691),x65692)),f333(f76(x65691),x65693))) % 191.49/191.40 [6580]E(f333(f333(f40(a880),f333(f333(f82(a880),x65801),x65802)),f333(f333(f82(a880),x65801),x65803)),f333(f333(f40(a880),x65802),x65803))+~P4(f333(f333(f251(a880),f2(a880)),x65801)) % 191.49/191.40 [6628]E(x66281,x66282)+~P4(f333(f333(f333(f333(a203,a24),x66281),x66283),x66282)) % 191.49/191.40 [6717]~P4(f333(f63(x67171),x67173))+E(f333(f333(f66(x67171,f890(x67171,a874),f311(x67171)),x67172),x67173),f333(f333(f115(f890(x67171,a874)),x67173),x67172)) % 191.49/191.40 [6770]E(f333(f333(f115(f890(x67701,a874)),x67702),x67703),x67702)+~P4(f333(f333(f250(f890(x67701,a874)),x67703),x67702)) % 191.49/191.40 [6772]E(f333(f333(f115(f890(x67721,a874)),x67722),x67723),x67723)+~P4(f333(f333(f250(f890(x67721,a874)),x67722),x67723)) % 191.49/191.40 [6773]E(f333(f333(f106(f890(x67731,a874)),x67732),x67733),x67733)+~P4(f333(f333(f250(f890(x67731,a874)),x67733),x67732)) % 191.49/191.40 [6774]E(f333(f333(f106(f890(x67741,a874)),x67742),x67743),x67742)+~P4(f333(f333(f250(f890(x67741,a874)),x67742),x67743)) % 191.49/191.40 [6822]~P4(f333(f138(x68221),x68222))+E(f333(f333(f3(f890(x68221,a874)),f333(f173(x68221),x68222)),f333(f333(f311(x68221),x68223),f194(f890(x68221,a874)))),f333(f173(x68221),f171(x68221,x68223,x68222))) % 191.49/191.40 [6875]P40(x68751,x68752)+~P40(x68751,f333(f333(f189(f889(x68751,x68751),a874),x68753),x68752)) % 191.49/191.40 [6939]P4(f333(f50(x69391,x69392),f333(a52,x69393)))+~P4(f333(f50(f333(f80(a1),x69391),f333(f80(a1),x69392)),x69393)) % 191.49/191.40 [6944]E(f333(f333(f3(f890(x69441,a874)),f333(f333(f311(x69441),x69442),x69443)),f333(f333(f311(x69441),x69442),f194(f890(x69441,a874)))),x69443)+P4(f333(f333(f335(x69441),x69442),x69443)) % 191.49/191.40 [6966]E(f333(f333(f106(f890(x69661,a874)),f333(f173(x69661),x69662)),f333(f173(x69661),x69663)),f194(f890(x69661,a874)))+~P4(f333(f138(x69661),f333(f333(f127(x69661),x69662),x69663))) % 191.49/191.40 [6982]~P4(f333(f333(f335(x69821),x69822),f333(f173(x69821),x69823)))+~P4(f333(f138(x69821),f333(f333(f152(x69821),x69822),x69823))) % 191.49/191.40 [7054]P34(x70541,x70542,x70543)+P4(f333(f333(f251(a880),f799(x70543,x70542,x70541)),f333(f195(f881(x70541)),x70543))) % 191.49/191.40 [7064]E(f333(f333(f106(f890(x70641,a874)),x70642),x70643),f194(f890(x70641,a874)))+P4(f333(f333(f335(x70641),f581(x70643,x70642,x70641)),x70642)) % 191.49/191.40 [7065]E(f333(f333(f106(f890(x70651,a874)),x70652),x70653),f194(f890(x70651,a874)))+P4(f333(f333(f335(x70651),f585(x70653,x70652,x70651)),x70653)) % 191.49/191.40 [7069]E(f119(x70691,f333(f333(f174(x70691),x70692),x70693)),f333(f333(f174(x70691),f333(f333(f3(a880),x70692),f79(a880))),x70693))+~P4(f333(f333(f250(a880),x70692),f333(f195(f881(x70691)),x70693))) % 191.49/191.40 [7127]~P36(x71273,x71272,x71271)+P4(f333(f333(f251(a880),f760(x71271,x71272,x71273)),f333(f195(f881(x71273)),x71271))) % 191.49/191.40 [7145]P4(f333(f333(f251(a880),f2(a880)),x71451))+P4(f333(f333(f250(a880),f333(f333(f82(a880),x71452),x71451)),f333(f333(f82(a880),x71453),x71451))) % 191.49/191.40 [7146]P4(f333(f333(f251(a880),f2(a880)),x71461))+P4(f333(f333(f250(a880),f333(f333(f82(a880),x71461),x71462)),f333(f333(f82(a880),x71461),x71463))) % 191.49/191.40 [7149]~P4(f333(f333(f335(x71491),x71492),x71493))+~P4(f333(f333(f335(x71491),x71492),f333(f80(f890(x71491,a874)),x71493))) % 191.49/191.40 [7156]~P4(f333(f333(f251(f890(x71561,a874)),x71562),x71563))+P4(f333(f333(f250(f890(x71561,a874)),x71562),x71563)) % 191.49/191.40 [7257]~P4(f333(f333(f251(a880),x72572),x72573))+P4(f333(f333(f251(a880),f333(f333(f81(a880),x72571),x72572)),f333(f333(f81(a880),x72571),x72573))) % 191.49/191.40 [7258]~P4(f333(f333(f251(a880),x72581),x72583))+P4(f333(f333(f251(a880),f333(f333(f81(a880),x72581),x72582)),f333(f333(f81(a880),x72583),x72582))) % 191.49/191.40 [7259]~P4(f333(f333(f251(a1),x72591),x72593))+P4(f333(f333(f251(a1),f333(f333(f81(a1),x72591),x72592)),f333(f333(f81(a1),x72593),x72592))) % 191.49/191.40 [7260]~P4(f333(f333(f250(a880),x72603),x72602))+P4(f333(f333(f250(a880),f333(f333(f3(a880),x72601),x72602)),f333(f333(f3(a880),x72601),x72603))) % 191.49/191.40 [7261]~P4(f333(f333(f250(a880),x72611),x72613))+P4(f333(f333(f250(a880),f333(f333(f3(a880),x72611),x72612)),f333(f333(f3(a880),x72613),x72612))) % 191.49/191.40 [7262]~P4(f333(f333(f250(a880),x72622),x72623))+P4(f333(f333(f250(a880),f333(f333(f81(a880),x72621),x72622)),f333(f333(f81(a880),x72621),x72623))) % 191.49/191.40 [7263]~P4(f333(f333(f250(a880),x72631),x72633))+P4(f333(f333(f250(a880),f333(f333(f81(a880),x72631),x72632)),f333(f333(f81(a880),x72633),x72632))) % 191.49/191.40 [7265]~P4(f333(f333(f250(a880),x72652),x72653))+P4(f333(f333(f250(a880),f333(f333(f82(a880),x72651),x72652)),f333(f333(f82(a880),x72651),x72653))) % 191.49/191.40 [7267]~P4(f333(f333(f250(a880),x72671),x72673))+P4(f333(f333(f250(a880),f333(f333(f82(a880),x72671),x72672)),f333(f333(f82(a880),x72673),x72672))) % 191.49/191.40 [7268]~P4(f333(f333(f250(a880),x72681),x72683))+P4(f333(f333(f250(a880),f333(f333(f40(a880),x72681),x72682)),f333(f333(f40(a880),x72683),x72682))) % 191.49/191.40 [7269]~P4(f333(f333(f250(a1),x72692),x72693))+P4(f333(f333(f250(a1),f333(f333(f81(a1),x72691),x72692)),f333(f333(f81(a1),x72691),x72693))) % 191.49/191.40 [7340]E(x73401,x73402)+~P4(f333(f333(f335(x73403),x73401),f333(f333(f311(x73403),x73402),f194(f890(x73403,a874))))) % 191.49/191.40 [7342]~E(f333(f333(f106(f890(x73421,a874)),x73422),x73423),f194(f890(x73421,a874)))+P4(f333(f333(f250(f890(x73421,a874)),x73422),f333(f80(f890(x73421,a874)),x73423))) % 191.49/191.40 [7350]P4(f333(f333(f335(f890(x73501,a874)),x73502),f333(f310(x73501),x73503)))+~P4(f333(f333(f250(f890(x73501,a874)),x73502),x73503)) % 191.49/191.40 [7402]E(f333(f333(f152(x74021),f333(f333(f166(x74021),x74022),x74023)),f333(f333(f139(x74021),f333(a117,x74023)),x74022)),f333(f333(f139(x74021),x74023),x74022))+~P4(f333(f333(f251(a880),x74023),f333(f195(f881(x74021)),x74022))) % 191.49/191.40 [7429]P4(f333(f333(f335(f889(x74291,x74291)),x74292),f309(x74291,x74293)))+~P4(f333(f333(f335(f889(x74291,x74291)),x74292),x74293)) % 191.49/191.40 [7440]~P4(f333(f333(f335(f890(x74401,a874)),x74402),f333(f310(x74401),x74403)))+P4(f333(f333(f250(f890(x74401,a874)),x74402),x74403)) % 191.49/191.40 [7483]P4(f333(f333(f250(f890(x74831,a874)),x74832),f41(f890(x74831,a874),x74833)))+~P4(f333(f333(f335(f890(x74831,a874)),x74832),x74833)) % 191.49/191.40 [7508]~P140(x75081)+E(f333(f333(f82(x75081),f333(f333(f264(x75081),f333(f80(x75081),f79(x75081))),x75082)),f333(f333(f264(x75081),x75083),x75082)),f333(f333(f264(x75081),f333(f80(x75081),x75083)),x75082)) % 191.49/191.40 [7529]E(f333(f333(f166(x75291),x75292),f333(f333(f3(a880),f333(f195(f881(x75291)),x75292)),f333(a117,x75293))),f333(f333(f166(x75291),f333(f170(x75291),x75292)),x75293))+~P4(f333(f333(f251(a880),x75293),f333(f195(f881(x75291)),x75292))) % 191.49/191.40 [7546]~E(f333(f333(f106(f890(x75461,a874)),f671(x75463,x75462,x75461)),x75463),f194(f890(x75461,a874)))+E(f333(f333(f106(f890(x75461,a874)),f41(f890(x75461,a874),x75462)),x75463),f194(f890(x75461,a874))) % 191.49/191.40 [7604]~P4(f333(f333(f335(x76043),x76042),f333(f173(x76043),x76041)))+P4(f333(f333(f251(a880),f582(x76041,x76042,x76043)),f333(f195(f881(x76043)),x76041))) % 191.49/191.40 [7612]P4(f333(f333(f335(x76121),f333(f333(f166(x76121),x76122),x76123)),f333(f173(x76121),x76122)))+~P4(f333(f333(f251(a880),x76123),f333(f195(f881(x76121)),x76122))) % 191.49/191.40 [7711]~P4(f333(x77112,f662(x77113,x77112,x77111)))+E(f333(f333(f139(x77111),f333(f195(f881(x77111)),f177(x77111,x77112,x77113))),x77113),f118(x77111)) % 191.49/191.40 [7721]P4(f333(f333(f250(f890(f881(x77211),a874)),f162(x77211,x77212)),f162(x77211,x77213)))+~P4(f333(f333(f250(f890(x77211,a874)),x77212),x77213)) % 191.49/191.40 [7722]P4(f333(f333(f250(f890(f881(x77221),a874)),f161(x77221,x77222)),f161(x77221,x77223)))+~P4(f333(f333(f250(f890(x77221,a874)),x77222),x77223)) % 191.49/191.40 [7751]E(f333(f333(f106(f890(x77511,a874)),f41(f890(x77511,a874),x77512)),x77513),f194(f890(x77511,a874)))+P4(f333(f333(f335(f890(x77511,a874)),f671(x77513,x77512,x77511)),x77512)) % 191.49/191.40 [7754]~P4(f333(f333(f335(f890(x77541,a874)),x77543),x77542))+P4(f333(f333(f250(f890(x77541,a874)),f42(f890(x77541,a874),x77542)),x77543)) % 191.49/191.40 [7756]E(f333(f333(f106(f890(x77561,a874)),x77562),x77563),f194(f890(x77561,a874)))+~P4(f333(f333(f250(f890(x77561,a874)),x77562),f333(f80(f890(x77561,a874)),x77563))) % 191.49/191.40 [7805]E(f333(f333(f3(a880),f333(f333(f81(a880),f333(f167(a880),x78051)),x78052)),f333(f333(f166(a880),x78051),x78053)),f333(f167(a880),f333(f333(f160(a880,x78051),x78053),x78052)))+~P4(f333(f333(f251(a880),x78053),f333(f195(f881(a880)),x78051))) % 191.49/191.40 [7856]P4(f333(f333(f251(a880),x78561),x78562))+~P4(f333(f333(f251(a880),f333(f333(f81(a880),x78563),x78561)),f333(f333(f81(a880),x78563),x78562))) % 191.49/191.40 [7857]P4(f333(f333(f251(a880),x78571),x78572))+~P4(f333(f333(f251(a880),f333(f333(f82(a880),x78573),x78571)),f333(f333(f82(a880),x78573),x78572))) % 191.49/191.40 [7858]P4(f333(f333(f251(a880),x78581),x78582))+~P4(f333(f333(f251(a880),f333(f333(f82(a880),x78581),x78583)),f333(f333(f82(a880),x78582),x78583))) % 191.49/191.40 [7859]P4(f333(f333(f250(a880),x78591),x78592))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),x78593),x78591)),f333(f333(f81(a880),x78593),x78592))) % 191.49/191.40 [7886]P4(f333(f333(f251(a880),f2(a880)),x78861))+~P4(f333(f333(f251(a880),f333(f333(f82(a880),x78862),x78861)),f333(f333(f82(a880),x78863),x78861))) % 191.49/191.40 [7887]P4(f333(f333(f251(a880),f2(a880)),x78871))+~P4(f333(f333(f251(a880),f333(f333(f82(a880),x78871),x78872)),f333(f333(f82(a880),x78871),x78873))) % 191.49/191.40 [7955]E(f266(x79551,x79552,x79553),x79552)+~P4(f333(f333(f250(f890(x79551,a874)),x79553),f333(f333(f311(x79551),x79552),f194(f890(x79551,a874))))) % 191.49/191.40 [8012]~P4(f333(f138(x80121),x80123))+E(f333(f137(x80121,f333(f333(f10(a874,a874,x80121),a328),f333(a330,x80122))),x80123),f171(x80121,x80122,x80123)) % 191.49/191.40 [8035]E(f333(f333(f139(x80351),f333(f195(f881(x80351)),f177(x80351,x80352,x80353))),x80353),f118(x80351))+P4(f333(f333(f335(x80351),f662(x80353,x80352,x80351)),f333(f173(x80351),x80353))) % 191.49/191.40 [8040]E(f333(f333(f127(x80401),f333(f333(f174(x80401),x80402),x80403)),f333(f333(f152(x80401),f333(f333(f166(x80401),x80403),x80402)),f118(x80401))),f333(f333(f174(x80401),f333(a117,x80402)),x80403))+~P4(f333(f333(f251(a880),x80402),f333(f195(f881(x80401)),x80403))) % 191.49/191.40 [8107]E(f333(f137(x81071,f333(f333(f10(a874,a874,x81071),a328),f333(a330,x81072))),x81073),x81073)+P4(f333(f333(f335(x81071),x81072),f333(f173(x81071),x81073))) % 191.49/191.40 [8115]P4(f333(f333(f250(f890(f890(x81151,a874),a874)),f267(x81151,x81152)),f267(x81151,x81153)))+~P4(f333(f333(f250(f890(x81151,a874)),x81152),x81153)) % 191.49/191.40 [8160]~P4(f333(f138(x81601),x81603))+P4(f333(f138(x81601),f333(f333(f333(f189(f881(x81601),f881(x81601)),x81602),f169(x81601)),x81603))) % 191.49/191.40 [8165]~P4(f333(f333(f251(a880),x81652),x81653))+P4(f333(f333(f251(a880),f333(f333(f82(a880),f333(a117,x81651)),x81652)),f333(f333(f82(a880),f333(a117,x81651)),x81653))) % 191.49/191.40 [8188]P4(f333(f333(f250(f890(f890(x81881,a874),a874)),f333(f310(x81881),x81882)),f333(f310(x81881),x81883)))+~P4(f333(f333(f250(f890(x81881,a874)),x81882),x81883)) % 191.49/191.40 [8345]~P4(f333(f333(f250(f890(x83451,a874)),x83453),x83452))+P4(f333(f333(f250(f890(x83451,a874)),f333(f80(f890(x83451,a874)),x83452)),f333(f80(f890(x83451,a874)),x83453))) % 191.49/191.40 [8379]E(f333(f312(a880,a880,f333(f333(f9(a880,a880,a880),f3(a880)),x83791)),f333(f303(a880,x83792),x83793)),f333(f303(a880,f333(f333(f3(a880),x83792),x83791)),f333(f333(f3(a880),x83793),x83791)))+~P4(f333(f333(f251(a880),x83791),x83793)) % 191.49/191.40 [8402]~P84(x84021)+E(f333(f333(f81(x84021),x84022),f333(f143(x84021,x84021,f81(x84021),f2(x84021)),x84023)),f333(f143(x84021,x84021,f81(x84021),x84022),x84023)) % 191.49/191.40 [8487]~P87(x84871)+P4(f333(f333(f250(x84871),f333(f76(x84871),f333(f333(f3(x84871),x84872),x84873))),f333(f333(f81(x84871),f333(f76(x84871),x84872)),f333(f76(x84871),x84873)))) % 191.49/191.40 [8488]~P87(x84881)+P4(f333(f333(f250(x84881),f333(f76(x84881),f333(f333(f81(x84881),x84882),x84883))),f333(f333(f81(x84881),f333(f76(x84881),x84882)),f333(f76(x84881),x84883)))) % 191.49/191.40 [8498]E(f333(f333(f81(a1),f333(f333(f82(a1),x84981),f46(a1,f333(f333(f40(a1),x84982),x84981),x84983))),f46(a1,x84982,x84981)),f46(a1,x84982,f333(f333(f82(a1),x84981),x84983)))+~P4(f333(f333(f251(a1),f2(a1)),x84983)) % 191.49/191.40 [8503]E(f333(f333(f127(x85031),f333(f333(f174(x85031),x85032),x85033)),f333(f333(f152(x85031),f333(f142(x85031),f333(f333(f139(x85031),x85032),x85033))),f118(x85031))),f333(f333(f174(x85031),f333(a117,x85032)),x85033))+~P4(f333(f333(f251(a880),x85032),f333(f195(f881(x85031)),x85033))) % 191.49/191.40 [8527]E(f333(f279(x85271,f333(f333(f155(x85271,f889(a104,x85271)),f333(f263(a104,x85271),f79(a104))),x85272)),f333(a5,x85273)),f333(f333(f166(x85271),x85272),x85273))+~P4(f333(f333(f251(a880),x85273),f333(f195(f881(x85271)),x85272))) % 191.49/191.40 [8591]P4(f333(f333(f335(f889(x85911,x85911)),x85912),f333(f333(f290(x85911,x85911,x85911),x85913),f309(x85911,x85913))))+~P4(f333(f333(f335(f889(x85911,x85911)),x85912),x85913)) % 191.49/191.40 [8612]P4(f333(f333(f250(a880),x86121),x86122))+~P4(f333(f333(f250(a880),f333(f333(f82(a880),f333(a117,x86123)),x86121)),f333(f333(f82(a880),f333(a117,x86123)),x86122))) % 191.49/191.40 [8625]P4(f333(f333(f250(f890(x86251,a874)),x86252),x86253))+~P4(f333(f333(f250(f890(x86251,a874)),f333(f80(f890(x86251,a874)),x86253)),f333(f80(f890(x86251,a874)),x86252))) % 191.49/191.40 [8643]P4(f333(f138(x86431),x86432))+~P4(f333(f138(x86431),f333(f333(f333(f189(f881(x86431),f881(x86431)),x86433),f169(x86431)),x86432))) % 191.49/191.40 [8694]E(f333(f312(f889(x86941,x86942),x86942,f271(x86941,x86942)),f333(f173(f889(x86941,x86942)),x86943)),f186(x86941,x86942,f333(f178(x86941,x86942),x86943)))+~P4(f333(f138(x86941),f333(f333(f155(f889(x86941,x86942),x86941),f262(x86941,x86942)),x86943))) % 191.49/191.40 [8703]E(f333(f287(x87031,x87031,f309(x87031,x87032)),x87033),x87033)+~P4(f333(f333(f250(f890(x87031,a874)),f333(f287(x87031,x87031,x87032),x87033)),x87033)) % 191.49/191.40 [8746]~P109(x87461)+P17(x87461,f333(f137(x87461,f333(f333(f9(x87461,x87461,a874),a330),f333(x87462,x87463))),x87463)) % 191.49/191.40 [8752]~P4(f333(f333(f250(a880),x87521),x87522))+P4(f333(f333(f250(a880),x87521),f333(f143(a880,a880,f81(a880),x87522),x87523))) % 191.49/191.40 [8833]~P4(f333(f333(f335(f889(x88331,x88331)),x88332),f309(x88331,x88333)))+P4(f333(f333(f335(f889(x88331,x88331)),x88332),f333(f333(f189(f889(x88331,x88331),a874),f769(x88333,x88332,x88331)),x88333))) % 191.49/191.40 [8926]~P84(x89261)+E(f333(f333(f81(x89261),x89262),f333(f143(x89261,x89261,f333(f9(x89261,x89261,x89261),f81(x89261)),f2(x89261)),f333(f170(x89261),x89263))),f333(f143(x89261,x89261,f81(x89261),x89262),x89263)) % 191.49/191.40 [9190]P54(x91901,x91902,x91903)+P4(f333(f333(f335(f889(x91901,x91902)),f333(f333(f263(x91901,x91902),f764(x91903,x91902,x91901)),f744(x91903,x91902,x91901))),x91903)) % 191.49/191.40 [9191]P54(x91911,x91912,x91913)+P4(f333(f333(f335(f889(x91911,x91912)),f333(f333(f263(x91911,x91912),f764(x91913,x91912,x91911)),f743(x91913,x91912,x91911))),x91913)) % 191.49/191.40 [9259]~P4(f333(f333(f335(f889(x92591,x92591)),x92592),f333(f333(f290(x92591,x92591,x92591),x92593),f309(x92591,x92593))))+P4(f333(f333(f335(f889(x92591,x92591)),x92592),f333(f333(f189(f889(x92591,x92591),a874),f771(x92593,x92592,x92591)),x92593))) % 191.49/191.40 [9260]~P4(f333(x92601,f333(f333(f166(x92602),x92603),f333(f195(f881(x92602)),f177(x92602,x92601,x92603)))))+~P4(f333(f333(f251(a880),f333(f195(f881(x92602)),f177(x92602,x92601,x92603))),f333(f195(f881(x92602)),x92603))) % 191.49/191.40 [9352]~P4(f333(f333(f250(f890(x93521,a874)),x93522),x93523))+P4(f333(f333(f250(f890(x93521,a874)),f333(f333(f9(x93521,f890(x93521,a874),a874),f335(x93521)),x93522)),f333(f333(f9(x93521,f890(x93521,a874),a874),f335(x93521)),x93523))) % 191.49/191.40 [9403]~P4(f333(f333(f335(f889(f890(x94031,a874),f890(x94031,a874))),f333(f333(f263(f890(x94031,a874),f890(x94031,a874)),x94032),x94033)),f308(x94031)))+P4(f333(f333(f251(f890(x94031,a874)),x94032),x94033)) % 191.49/191.40 [9428]P55(x94281,x94282,x94283)+~P4(f333(f333(f335(f889(x94281,x94281)),f333(f333(f263(x94281,x94281),f767(x94283,x94282,x94281)),f766(x94283,x94282,x94281))),x94283)) % 191.49/191.40 [9429]P55(x94291,x94292,x94293)+~P4(f333(f333(f335(f889(x94291,x94291)),f333(f333(f263(x94291,x94291),f766(x94293,x94292,x94291)),f767(x94293,x94292,x94291))),x94293)) % 191.49/191.40 [9463]~P4(f333(f333(f335(f889(f881(x94631),f881(x94631))),f333(f333(f263(f881(x94631),f881(x94631)),x94632),x94632)),f148(x94631,x94633)))+P4(f333(f333(f335(f889(x94631,x94631)),f333(f333(f263(x94631,x94631),f639(x94632,x94633,x94631)),f639(x94632,x94633,x94631))),x94633)) % 191.49/191.40 [9529]P4(f333(f333(f250(f890(x95291,a874)),x95292),x95293))+~P4(f333(f333(f250(f890(x95291,a874)),f333(f333(f9(x95291,f890(x95291,a874),a874),f335(x95291)),x95292)),f333(f333(f9(x95291,f890(x95291,a874),a874),f335(x95291)),x95293))) % 191.49/191.40 [9616]E(f333(f333(f3(a880),f333(f333(f8(a880,a880),x96161),f333(f256(a880),x96162))),f333(f333(f8(a880,a880),x96163),f333(f256(a880),x96162))),f333(f333(f8(a880,a880),f333(f333(f20(a880,a880,a880),f333(f333(f10(a880,f890(a880,a880),a880),f3(a880)),x96161)),x96163)),f333(f256(a880),x96162)))+~P4(f333(f333(f250(a880),f333(x96163,f519(x96162,x96161,x96163))),f333(x96161,f519(x96162,x96161,x96163)))) % 191.49/191.40 [9925]E(f333(f255(f889(x99251,x99252)),f333(f272(x99251,x99252,a874),f333(f333(f9(x99251,f890(x99252,f884(x99252)),f890(x99252,a874)),f333(f333(f10(f890(f884(x99252),a874),f890(f890(x99252,f884(x99252)),f890(x99252,a874)),x99251),f10(f884(x99252),a874,x99252)),f333(f333(f10(f884(x99252),f890(f884(x99252),a874),x99251),a330),f333(f178(x99251,x99252),x99253)))),f242(x99252)))),f333(f173(f889(x99251,x99252)),x99253))+~P4(f333(f138(x99251),f333(f333(f155(f889(x99251,x99252),x99251),f262(x99251,x99252)),x99253))) % 191.49/191.40 [5653]~P75(x56531)+E(f333(f333(f3(x56531),f333(f333(f81(x56531),x56532),x56533)),x56533),x56532) % 191.49/191.40 [5654]~P75(x56541)+E(f333(f333(f81(x56541),f333(f333(f3(x56541),x56542),x56543)),x56543),x56542) % 191.49/191.40 [5874]~P75(x58741)+E(f333(f333(f81(x58741),x58742),f333(f333(f81(x58741),f333(f80(x58741),x58742)),x58743)),x58743) % 191.49/191.40 [5958]~P83(x59581)+E(f333(f333(f82(x59581),f333(f333(f264(x59581),x59582),x59583)),x59582),f333(f333(f264(x59581),x59582),f333(a117,x59583))) % 191.49/191.40 [5959]~P115(x59591)+E(f333(f333(f82(x59591),f333(f333(f264(x59591),x59592),x59593)),x59592),f333(f333(f264(x59591),x59592),f333(a117,x59593))) % 191.49/191.40 [6173]~P120(x61731)+E(f333(f76(x61731),f333(f333(f264(x61731),f333(f80(x61731),x61732)),x61733)),f333(f76(x61731),f333(f333(f264(x61731),x61732),x61733))) % 191.49/191.40 [6227]~P83(x62271)+E(f333(f333(f82(x62271),f333(f333(f264(x62271),x62272),x62273)),x62272),f333(f333(f82(x62271),x62272),f333(f333(f264(x62271),x62272),x62273))) % 191.49/191.40 [6281]E(f333(f333(f3(a104),f333(f333(f81(a104),x62811),x62812)),x62813),f283(x62811,x62812,x62813))+~P4(f333(f333(f251(a104),x62812),x62813)) % 191.49/191.40 [6301]~E(f333(f333(f139(x63011),x63013),x63012),f118(x63011))+P4(f333(f333(f250(a880),f333(f195(f881(x63011)),x63012)),x63013)) % 191.49/191.40 [6434]E(f333(f333(f82(a880),f333(f108(a880),x64341)),f333(f333(f82(a880),f333(f108(a880),x64342)),x64343)),f2(a880))+~P4(f333(f333(f251(a1),x64341),a84)) % 191.49/191.40 [6450]~P63(x64501)+E(f333(f333(f264(x64501),f333(f333(f291(x64501),f79(x64501)),x64502)),x64503),f333(f333(f291(x64501),f79(x64501)),f333(f333(f264(x64501),x64502),x64503))) % 191.49/191.40 [6521]E(f333(f333(f3(a880),f333(f333(f81(a880),x65211),x65212)),x65213),f333(f333(f3(a880),x65211),f333(f333(f3(a880),x65213),x65212)))+~P4(f333(f333(f250(a880),x65212),x65213)) % 191.49/191.40 [6523]E(f333(f333(f3(a880),f333(f333(f81(a880),x65231),x65232)),x65233),f333(f333(f81(a880),x65231),f333(f333(f3(a880),x65232),x65233)))+~P4(f333(f333(f250(a880),x65233),x65232)) % 191.49/191.40 [6560]~P6(x65601)+P4(f333(f333(f250(x65601),f333(f333(f106(x65601),x65602),x65603)),x65603)) % 191.49/191.40 [6561]~P102(x65611)+P4(f333(f333(f250(x65611),f333(f333(f106(x65611),x65612),x65613)),x65613)) % 191.49/191.40 [6562]~P6(x65621)+P4(f333(f333(f250(x65621),f333(f333(f106(x65621),x65622),x65623)),x65622)) % 191.49/191.40 [6563]~P102(x65631)+P4(f333(f333(f250(x65631),f333(f333(f106(x65631),x65632),x65633)),x65632)) % 191.49/191.40 [6564]~P109(x65641)+P4(f333(f333(f250(x65641),f333(f333(f248(x65641),x65642),x65643)),x65643)) % 191.49/191.40 [6565]~P109(x65651)+P4(f333(f333(f250(x65651),f333(f333(f248(x65651),x65652),x65653)),x65652)) % 191.49/191.40 [6579]E(f333(f333(f40(a1),f333(f333(f40(a1),x65791),x65792)),x65793),f333(f333(f40(a1),x65791),f333(f333(f82(a1),x65792),x65793)))+~P4(f333(f333(f251(a1),f2(a1)),x65793)) % 191.49/191.40 [6631]~P115(x66311)+E(f333(f333(f81(x66311),f333(f333(f82(x66311),x66312),x66313)),x66313),f333(f333(f82(x66311),f333(f333(f81(x66311),x66312),f79(x66311))),x66313)) % 191.49/191.40 [6632]~P94(x66321)+E(f333(f333(f82(x66321),f333(f80(x66321),f333(f108(x66321),x66322))),x66323),f333(f333(f82(x66321),f333(f108(x66321),f333(f80(a1),x66322))),x66323)) % 191.49/191.40 [6704]~P84(x67041)+E(f333(f167(x67041),f333(f333(f155(x67042,x67041),f333(f18(x67041,x67042),f2(x67041))),x67043)),f2(x67041)) % 191.49/191.40 [6720]E(f333(f333(f81(a880),f333(f108(a880),x67201)),f333(f333(f81(a880),f333(f108(a880),x67202)),x67203)),f333(f333(f81(a880),f333(f108(a880),x67202)),x67203))+~P4(f333(a200,f333(f108(a1),x67201))) % 191.49/191.40 [6734]~P9(x67341)+E(f41(x67341,f333(f333(f311(x67341),x67342),f333(f333(f311(x67341),x67343),f194(f890(x67341,a874))))),f333(f333(f115(x67341),x67342),x67343)) % 191.49/191.40 [6735]~P9(x67351)+E(f42(x67351,f333(f333(f311(x67351),x67352),f333(f333(f311(x67351),x67353),f194(f890(x67351,a874))))),f333(f333(f106(x67351),x67352),x67353)) % 191.49/191.41 [6758]E(f333(f333(f174(x67581),x67582),x67583),x67583)+~P4(f333(f333(f250(a880),f333(f195(f881(x67581)),x67583)),x67582)) % 191.49/191.41 [6765]E(f333(f333(f139(x67651),x67652),x67653),f118(x67651))+~P4(f333(f333(f250(a880),f333(f195(f881(x67651)),x67653)),x67652)) % 191.49/191.41 [6776]E(f333(f333(f81(a880),f333(f333(f3(a880),x67761),x67762)),x67763),f333(f333(f3(a880),f333(f333(f81(a880),x67761),x67763)),x67762))+~P4(f333(f333(f250(a880),x67762),x67761)) % 191.49/191.41 [6790]~P4(f333(f333(f251(a880),x67901),x67903))+P4(f333(f333(f251(a880),f333(f333(f3(a880),x67901),x67902)),x67903)) % 191.49/191.41 [6816]~P109(x68161)+E(f171(x68161,x68162,f333(f333(f149(x68161,x68161,f7(x68161)),x68162),x68163)),x68163) % 191.49/191.41 [6901]E(f333(f333(f3(a880),f333(f333(f81(a880),x69011),x69012)),f333(a117,x69013)),f333(f333(f3(a880),x69011),f333(a117,f333(f333(f3(a880),x69013),x69012))))+~P4(f333(f333(f250(a880),x69012),x69013)) % 191.49/191.41 [6902]~P120(x69021)+P4(f333(f333(f250(x69021),f2(x69021)),f333(f333(f264(x69021),f333(f76(x69021),x69022)),x69023))) % 191.49/191.41 [6950]P27(x69501,x69502,x69503)+~P4(f333(f333(f250(f890(f879(x69501),a874)),x69503),x69502)) % 191.49/191.41 [6993]~P4(f333(f63(x69931),x69932))+P4(f333(f63(x69931),f333(f333(f3(f890(x69931,a874)),x69932),x69933))) % 191.49/191.41 [6994]~P4(f333(f63(x69941),x69943))+P4(f333(f63(x69941),f333(f333(f106(f890(x69941,a874)),x69942),x69943))) % 191.49/191.41 [6995]~P4(f333(f63(x69951),x69952))+P4(f333(f63(x69951),f333(f333(f106(f890(x69951,a874)),x69952),x69953))) % 191.49/191.41 [7135]~P40(x71351,x71353)+P40(x71351,f333(f333(f106(f890(f889(x71351,x71351),a874)),x71352),x71353)) % 191.49/191.41 [7136]~P40(x71361,x71362)+P40(x71361,f333(f333(f106(f890(f889(x71361,x71361),a874)),x71362),x71363)) % 191.49/191.41 [7253]~P6(x72531)+E(f12(x72531,f333(f173(x72531),f333(f333(f152(x72531),x72532),x72533))),f333(f143(x72531,x72531,f115(x72531),x72532),x72533)) % 191.49/191.41 [7254]~P6(x72541)+E(f13(x72541,f333(f173(x72541),f333(f333(f152(x72541),x72542),x72543))),f333(f143(x72541,x72541,f106(x72541),x72542),x72543)) % 191.49/191.41 [7255]~P109(x72551)+E(f16(x72551,f333(f173(x72551),f333(f333(f152(x72551),x72552),x72553))),f333(f143(x72551,x72551,f248(x72551),x72552),x72553)) % 191.49/191.41 [7256]~P109(x72561)+E(f17(x72561,f333(f173(x72561),f333(f333(f152(x72561),x72562),x72563))),f333(f143(x72561,x72561,f249(x72561),x72562),x72563)) % 191.49/191.41 [7312]~P4(f333(f63(x73121),x73122))+P4(f333(f333(f250(a880),f333(f39(x73121),x73122)),f333(f39(x73121),f333(f333(f311(x73121),x73123),x73122)))) % 191.49/191.41 [7313]E(f333(f333(f115(f890(a880,a874)),f333(f303(a880,x73131),x73132)),f333(f303(a880,x73132),f333(f333(f81(a880),x73132),x73133))),f333(f303(a880,x73131),f333(f333(f81(a880),x73132),x73133)))+~P4(f333(f333(f250(a880),x73131),x73132)) % 191.49/191.41 [7321]P4(f333(f333(f251(a880),x73211),x73212))+~P4(f333(f333(f251(a880),f333(f333(f81(a880),x73211),x73213)),x73212)) % 191.49/191.41 [7324]P4(f333(f333(f250(a880),x73241),x73242))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),x73243),x73241)),x73242)) % 191.49/191.41 [7325]P4(f333(f333(f250(a880),x73251),x73252))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),x73251),x73253)),x73252)) % 191.49/191.41 [7366]~P109(x73661)+E(f14(x73661,f248(x73661),f333(f173(x73661),f333(f333(f152(x73661),x73662),x73663))),f333(f143(x73661,x73661,f248(x73661),x73662),x73663)) % 191.49/191.41 [7367]~P109(x73671)+E(f15(x73671,f249(x73671),f333(f173(x73671),f333(f333(f152(x73671),x73672),x73673))),f333(f143(x73671,x73671,f249(x73671),x73672),x73673)) % 191.49/191.41 [7371]~E(x73712,f194(f890(f889(x73711,x73711),a874)))+P4(f333(f333(f250(f890(f889(x73711,x73711),a874)),x73712),x73713)) % 191.49/191.41 [7478]E(f333(f333(f115(f890(x74781,a874)),x74782),f333(f333(f3(f890(x74781,a874)),x74783),x74782)),x74783)+~P4(f333(f333(f250(f890(x74781,a874)),x74782),x74783)) % 191.49/191.41 [7479]~P4(f333(f333(f251(a880),x74791),f333(f333(f3(a880),x74793),x74792)))+P4(f333(f333(f251(a880),f333(f333(f81(a880),x74791),x74792)),x74793)) % 191.49/191.41 [7480]~P4(f333(f333(f250(a880),x74801),f333(f333(f81(a880),x74803),x74802)))+P4(f333(f333(f250(a880),f333(f333(f3(a880),x74801),x74802)),x74803)) % 191.49/191.41 [7536]E(x75361,f118(x75362))+E(f333(f142(x75362),f333(f333(f333(f189(f881(x75362),f881(x75362)),x75363),f169(x75362)),x75361)),f333(f333(f166(x75362),x75361),f46(a880,x75363,f333(f195(f881(x75362)),x75361)))) % 191.49/191.41 [7545]E(f333(f333(f311(x75451),x75452),f333(f333(f3(f890(x75451,a874)),x75453),f333(f333(f311(x75451),x75452),f194(f890(x75451,a874))))),x75453)+~P4(f333(f333(f335(x75451),x75452),x75453)) % 191.49/191.41 [7702]P4(f333(f333(f251(a880),x77021),f333(f333(f3(a880),x77022),x77023)))+~P4(f333(f333(f251(a880),f333(f333(f81(a880),x77021),x77023)),x77022)) % 191.49/191.41 [7703]P4(f333(f333(f250(a880),x77031),f333(f333(f81(a880),x77032),x77033)))+~P4(f333(f333(f250(a880),f333(f333(f3(a880),x77031),x77033)),x77032)) % 191.49/191.41 [7725]P4(f333(f63(x77251),x77252))+~P4(f333(f63(x77251),f333(f333(f115(f890(x77251,a874)),x77253),x77252))) % 191.49/191.41 [7726]P4(f333(f63(x77261),x77262))+~P4(f333(f63(x77261),f333(f333(f115(f890(x77261,a874)),x77262),x77263))) % 191.49/191.41 [7804]~P47(x78041,x78043)+P4(f333(f333(f335(f889(x78041,x78041)),f333(f333(f263(x78041,x78041),x78042),x78042)),x78043)) % 191.49/191.41 [7930]E(f333(f333(f166(a880),f140(a880,f333(f303(a880,x79301),x79302))),x79303),f333(f333(f81(a880),x79301),x79303))+~P4(f333(f333(f251(a880),f333(f333(f81(a880),x79301),x79303)),x79302)) % 191.49/191.41 [7996]~P4(f333(f333(f201(f333(a26,x79961)),x79962),x79963))+P4(f333(f333(f201(f333(f246(a876),f333(a28,x79961))),x79962),x79963)) % 191.49/191.41 [8001]E(f333(f333(f174(a880),x80011),f140(a880,f333(f303(a880,x80012),x80013))),f140(a880,f333(f303(a880,x80012),f333(f333(f81(a880),x80012),x80011))))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),x80012),x80011)),x80013)) % 191.49/191.41 [8268]P4(f333(f333(f201(f333(a26,x82681)),x82682),x82683))+~P4(f333(f333(f201(f333(f246(a876),f333(a28,x82681))),x82682),x82683)) % 191.49/191.41 [8324]E(f333(f333(f127(x83241),f333(f333(f174(x83241),x83242),x83243)),f333(f333(f152(x83241),f333(f333(f166(x83241),x83243),x83242)),f333(f333(f139(x83241),f333(a117,x83242)),x83243))),x83243)+~P4(f333(f333(f251(a880),x83242),f333(f195(f881(x83241)),x83243))) % 191.49/191.41 [8332]P4(f333(f333(f250(f890(x83321,a874)),f321(x83321,x83322)),f321(x83321,x83323)))+~P4(f333(f333(f250(f890(x83321,f890(x83321,a874))),x83323),x83322)) % 191.49/191.41 [8334]~P55(x83341,x83342,x83343)+P55(x83341,x83342,f333(f333(f3(f890(f889(x83341,x83341),a874)),x83343),f309(x83341,f194(f890(f889(x83341,x83341),a874))))) % 191.49/191.41 [8351]P4(f333(f333(f250(f890(x83511,a874)),f322(x83511,x83512)),f322(x83511,x83513)))+~P4(f333(f333(f250(f890(f889(x83511,x83511),a874)),x83513),x83512)) % 191.49/191.41 [8358]~P125(x83581)+P4(f333(f333(f250(x83581),f2(x83581)),f333(f333(f81(x83581),f333(f333(f82(x83581),x83582),x83582)),f333(f333(f82(x83581),x83583),x83583)))) % 191.49/191.41 [8395]P4(f333(f333(f250(f890(x83951,a874)),f333(f286(x83951),x83952)),f333(f286(x83951),x83953)))+~P4(f333(f333(f250(f890(f889(x83951,x83951),a874)),x83952),x83953)) % 191.49/191.41 [8425]~P51(x84251,x84252)+~P4(f333(f333(f335(f889(x84251,x84251)),f333(f333(f263(x84251,x84251),x84253),x84253)),x84252)) % 191.49/191.41 [8427]~P40(x84271,x84272)+~P4(f333(f333(f335(f889(x84271,x84271)),f333(f333(f263(x84271,x84271),x84273),x84273)),x84272)) % 191.49/191.41 [8489]P4(f333(f333(f250(f890(x84891,a874)),f41(f890(x84891,a874),x84892)),f41(f890(x84891,a874),x84893)))+~P4(f333(f333(f250(f890(f890(x84891,a874),a874)),x84892),x84893)) % 191.49/191.41 [8490]P4(f333(f333(f250(f890(x84901,a874)),f42(f890(x84901,a874),x84902)),f42(f890(x84901,a874),x84903)))+~P4(f333(f333(f250(f890(f890(x84901,a874),a874)),x84903),x84902)) % 191.49/191.41 [8546]~P12(x85461,x85463,x85462)+P4(f333(f333(f250(f890(f889(x85461,x85461),a874)),x85462),f333(f333(f270(x85461,x85461),x85463),f333(f18(f890(x85461,a874),x85461),x85463)))) % 191.49/191.41 [8547]~P50(x85471,x85473,x85472)+P4(f333(f333(f250(f890(f889(x85471,x85471),a874)),x85472),f333(f333(f270(x85471,x85471),x85473),f333(f18(f890(x85471,a874),x85471),x85473)))) % 191.49/191.41 [8592]~P87(x85921)+P4(f333(f333(f250(x85921),f333(f333(f3(x85921),f333(f76(x85921),x85922)),f333(f76(x85921),x85923))),f333(f76(x85921),f333(f333(f3(x85921),x85923),x85922)))) % 191.49/191.41 [8593]~P87(x85931)+P4(f333(f333(f250(x85931),f333(f333(f3(x85931),f333(f76(x85931),x85932)),f333(f76(x85931),x85933))),f333(f76(x85931),f333(f333(f3(x85931),x85932),x85933)))) % 191.49/191.41 [8623]P4(f333(f333(f250(f890(f889(x86231,x86231),a874)),f309(x86231,x86232)),f309(x86231,x86233)))+~P4(f333(f333(f250(f890(f889(x86231,x86231),a874)),x86232),x86233)) % 191.49/191.41 [8769]P55(x87691,x87692,x87693)+~P55(x87691,x87692,f333(f333(f3(f890(f889(x87691,x87691),a874)),x87693),f309(x87691,f194(f890(f889(x87691,x87691),a874))))) % 191.49/191.41 [8788]P4(f333(f333(f250(f890(f889(f881(x87881),f881(x87881)),a874)),f159(x87881,x87882)),f159(x87881,x87883)))+~P4(f333(f333(f250(f890(f889(x87881,x87881),a874)),x87882),x87883)) % 191.49/191.41 [8789]P4(f333(f333(f250(f890(f889(f881(x87891),f881(x87891)),a874)),f158(x87891,x87892)),f158(x87891,x87893)))+~P4(f333(f333(f250(f890(f889(x87891,x87891),a874)),x87892),x87893)) % 191.49/191.41 [8810]~P50(x88101,x88103,x88102)+P4(f333(f333(f250(f890(f889(x88101,x88101),a874)),x88102),f333(f333(f290(x88101,x88101,x88101),f333(f288(x88101,x88101),x88102)),x88102))) % 191.49/191.41 [8861]~P4(f333(f138(x88611),x88612))+E(f333(f137(x88611,f333(f333(f9(x88611,f890(x88611,a874),a874),f335(x88611)),f333(f173(x88611),f175(x88611,x88612,x88613)))),x88612),f175(x88611,x88612,x88613)) % 191.49/191.41 [8924]E(x89241,x89242)+~P4(f333(f333(f335(f889(x89243,x89243)),f333(f333(f263(x89243,x89243),x89241),x89242)),f309(x89243,f194(f890(f889(x89243,x89243),a874))))) % 191.49/191.41 [9008]P4(f333(f333(f335(x90081),x90082),f322(x90081,x90083)))+P4(f333(f333(f335(f889(x90081,x90081)),f333(f333(f263(x90081,x90081),f694(x90083,x90082,x90081)),x90082)),x90083)) % 191.49/191.41 [9009]P4(f333(f333(f335(x90091),x90092),f322(x90091,x90093)))+P4(f333(f333(f335(f889(x90091,x90091)),f333(f333(f263(x90091,x90091),f747(x90093,x90092,x90091)),x90092)),x90093)) % 191.49/191.41 [9010]P4(f333(f333(f335(x90101),x90102),f322(x90101,x90103)))+P4(f333(f333(f335(f889(x90101,x90101)),f333(f333(f263(x90101,x90101),f756(x90103,x90102,x90101)),x90102)),x90103)) % 191.49/191.41 [9082]~P4(f333(f333(f335(f881(x90821)),x90823),f162(x90821,x90822)))+P4(f333(f161(x90821,f333(f333(f9(x90821,f890(x90821,a874),a874),f335(x90821)),x90822)),x90823)) % 191.49/191.41 [9109]P4(f333(x91093,x91092))+E(f333(f255(x91091),f333(f333(f20(x91091,a874,a874),f333(f333(f10(a874,f890(a874,a874),x91091),a331),f333(a330,x91092))),x91093)),f194(f890(x91091,a874))) % 191.49/191.41 [9133]~P87(x91331)+P4(f333(f333(f250(x91331),f333(f76(x91331),f333(f333(f3(x91331),f333(f76(x91331),x91332)),f333(f76(x91331),x91333)))),f333(f76(x91331),f333(f333(f3(x91331),x91332),x91333)))) % 191.49/191.41 [9149]~P4(f333(x91493,x91492))+E(f333(f255(x91491),f333(f333(f20(x91491,a874,a874),f333(f333(f10(a874,f890(a874,a874),x91491),a331),f333(a330,x91492))),x91493)),f333(f333(f311(x91491),x91492),f194(f890(x91491,a874)))) % 191.49/191.41 [9156]~P4(f333(f333(f335(f890(x91561,a874)),x91563),f333(f310(x91561),x91562)))+P4(f333(f267(x91561,f333(f333(f9(x91561,f890(x91561,a874),a874),f335(x91561)),x91562)),x91563)) % 191.49/191.41 [9189]P40(x91891,x91892)+P4(f333(f333(f335(f889(x91891,x91891)),f333(f333(f263(x91891,x91891),f333(f702(x91892,x91891),f333(a117,x91893))),f333(f702(x91892,x91891),x91893))),x91892)) % 191.49/191.41 [9331]P4(f333(f333(f335(f881(x93311)),x93312),f162(x93311,x93313)))+~P4(f333(f161(x93311,f333(f333(f9(x93311,f890(x93311,a874),a874),f335(x93311)),x93313)),x93312)) % 191.49/191.41 [9344]P4(f333(f333(f335(f890(x93441,a874)),x93442),f333(f310(x93441),x93443)))+~P4(f333(f267(x93441,f333(f333(f9(x93441,f890(x93441,a874),a874),f335(x93441)),x93443)),x93442)) % 191.49/191.41 [9399]P4(f333(f333(f335(x93991),f333(f279(x93991,x93992),x93993)),f333(f173(x93991),f333(f333(f155(f889(a104,x93991),x93991),f271(a104,x93991)),x93992))))+~P4(f333(f333(f251(a104),x93993),f333(f167(a104),f333(f333(f155(f889(a104,x93991),a104),f262(a104,x93991)),x93992)))) % 191.49/191.41 [9445]P4(f333(f333(f250(f890(f889(f881(x94451),f881(x94451)),a874)),f159(x94451,x94452)),f333(f333(f270(f881(x94451),f881(x94451)),f162(x94451,x94453)),f333(f18(f890(f881(x94451),a874),f881(x94451)),f162(x94451,x94453)))))+~P4(f333(f333(f250(f890(f889(x94451,x94451),a874)),x94452),f333(f333(f270(x94451,x94451),x94453),f333(f18(f890(x94451,a874),x94451),x94453)))) % 191.49/191.41 [9466]P4(f333(f333(f335(x94661),f333(f262(x94661,f889(a104,a104)),f333(f277(x94661,x94662),x94663))),f333(f173(x94661),f333(f333(f155(f889(a104,x94661),x94661),f271(a104,x94661)),x94662))))+~P4(f333(f333(f251(a104),f2(a104)),f333(f167(a104),f333(f333(f155(f889(a104,x94661),a104),f262(a104,x94661)),x94662)))) % 191.49/191.41 [9492]~P4(f333(f333(f250(f890(f889(x94921,x94921),a874)),x94922),f333(f333(f270(x94921,x94921),x94923),f333(f18(f890(x94921,a874),x94921),x94923))))+P4(f333(f333(f250(f890(f889(x94921,x94921),a874)),f333(f333(f290(x94921,x94921,x94921),x94922),f309(x94921,x94922))),f333(f333(f270(x94921,x94921),x94923),f333(f18(f890(x94921,a874),x94921),x94923)))) % 191.49/191.41 [9822]~P40(x98221,x98222)+~P4(f333(f333(f335(f889(x98221,x98221)),f333(f333(f263(x98221,x98221),f333(x98223,f333(a117,f703(x98222,x98221,x98223)))),f333(x98223,f703(x98222,x98221,x98223)))),x98222)) % 191.49/191.41 [9823]~P40(x98231,x98232)+~P4(f333(f333(f335(f889(x98231,x98231)),f333(f333(f263(x98231,x98231),f333(x98233,f333(a117,f761(x98233,x98232,x98231)))),f333(x98233,f761(x98233,x98232,x98231)))),x98232)) % 191.49/191.41 [10051]P4(f333(f333(f250(f890(f889(f890(x100511,a874),f890(x100511,a874)),a874)),f333(f333(f290(f890(x100511,a874),f890(x100511,a874),f890(x100511,a874)),f324(x100511,x100512)),f333(f333(f115(f890(f889(f890(x100511,a874),f890(x100511,a874)),a874)),f324(x100511,x100513)),f333(f333(f311(f889(f890(x100511,a874),f890(x100511,a874))),f333(f333(f263(f890(x100511,a874),f890(x100511,a874)),f194(f890(x100511,a874))),f194(f890(x100511,a874)))),f194(f890(f889(f890(x100511,a874),f890(x100511,a874)),a874)))))),f324(x100511,x100512)))+~P4(f333(f333(f250(f890(f889(x100511,x100511),a874)),f333(f333(f290(x100511,x100511,x100511),x100512),x100513)),x100512)) % 191.49/191.41 [10052]P4(f333(f333(f250(f890(f889(f890(x100521,a874),f890(x100521,a874)),a874)),f333(f333(f290(f890(x100521,a874),f890(x100521,a874),f890(x100521,a874)),f325(x100521,x100522)),f333(f333(f115(f890(f889(f890(x100521,a874),f890(x100521,a874)),a874)),f325(x100521,x100523)),f333(f333(f311(f889(f890(x100521,a874),f890(x100521,a874))),f333(f333(f263(f890(x100521,a874),f890(x100521,a874)),f194(f890(x100521,a874))),f194(f890(x100521,a874)))),f194(f890(f889(f890(x100521,a874),f890(x100521,a874)),a874)))))),f325(x100521,x100522)))+~P4(f333(f333(f250(f890(f889(x100521,x100521),a874)),f333(f333(f290(x100521,x100521,x100521),x100522),x100523)),x100522)) % 191.49/191.41 [7252]~P4(f333(f333(f250(a880),x72522),x72521))+E(f333(f333(f3(a880),f333(a117,f333(f333(f3(a880),x72521),x72522))),x72523),f333(f333(f3(a880),f333(a117,x72521)),f333(f333(f81(a880),x72522),x72523))) % 191.49/191.41 [7286]~P60(x72861)+E(f333(f333(f81(x72861),f46(x72861,x72862,x72863)),f333(f333(f82(x72861),f333(f333(f40(x72861),x72862),x72863)),x72863)),x72862) % 191.49/191.41 [7484]E(f333(f333(f82(a880),f333(f108(a880),x74841)),f333(f333(f82(a880),f333(f108(a880),x74842)),x74843)),f333(f333(f82(a880),f333(f108(a880),f333(f333(f82(a1),x74841),x74842))),x74843))+P4(f333(f333(f251(a1),x74841),a84)) % 191.49/191.41 [7939]~P4(f333(f333(f250(a880),x79393),x79392))+P4(f333(f333(f250(a880),x79391),f333(f333(f3(a880),f333(f333(f81(a880),x79392),x79391)),x79393))) % 191.49/191.41 [8150]~P4(f333(f333(f250(a880),x81501),x81502))+E(f333(f333(f127(a880),f140(a880,f333(f303(a880,x81501),x81502))),f140(a880,f333(f303(a880,x81502),f333(f333(f81(a880),x81502),x81503)))),f140(a880,f333(f303(a880,x81501),f333(f333(f81(a880),x81502),x81503)))) % 191.49/191.41 [8399]~P4(f333(f63(x83991),x83992))+E(f333(a117,f333(f39(x83991),f333(f333(f3(f890(x83991,a874)),x83992),f333(f333(f311(x83991),x83993),f194(f890(x83991,a874)))))),f333(f39(x83991),f333(f333(f311(x83991),x83993),x83992))) % 191.49/191.41 [8451]~P4(f333(f63(x84511),x84512))+E(f333(f333(f81(a880),f79(a880)),f333(f39(x84511),f333(f333(f3(f890(x84511,a874)),x84512),f333(f333(f311(x84511),x84513),f194(f890(x84511,a874)))))),f333(f39(x84511),f333(f333(f311(x84511),x84513),x84512))) % 191.49/191.41 [8632]E(f333(f333(f3(a880),f333(f39(x86321),x86322)),f333(f39(x86321),f333(f333(f106(f890(x86321,a874)),x86322),x86323))),f333(f39(x86321),f333(f333(f3(f890(x86321,a874)),x86322),x86323)))+~P4(f333(f63(x86321),f333(f333(f106(f890(x86321,a874)),x86322),x86323))) % 191.49/191.41 [8856]~P10(f333(x88562,f511(x88562,x88563,x88561)))+E(f333(f105(a1),f333(f333(f8(x88561,a880),f333(f333(f10(a1,a880,x88561),a109),x88562)),x88563)),f333(f333(f8(x88561,a1),x88562),x88563)) % 191.49/191.41 [8857]~P10(f333(x88572,f512(x88572,x88573,x88571)))+E(f333(f105(a1),f333(f333(f11(x88571,a880),f333(f333(f10(a1,a880,x88571),a109),x88572)),x88573)),f333(f333(f11(x88571,a1),x88572),x88573)) % 191.49/191.41 [8906]~P4(f333(f63(x89061),x89063))+P4(f333(f333(f250(a880),f333(f333(f3(a880),f333(f39(x89061),x89062)),f333(f39(x89061),x89063))),f333(f39(x89061),f333(f333(f3(f890(x89061,a874)),x89062),x89063)))) % 191.49/191.41 [8932]P4(f333(f333(f335(x89321),f511(x89322,x89323,x89321)),x89323))+E(f333(f105(a1),f333(f333(f8(x89321,a880),f333(f333(f10(a1,a880,x89321),a109),x89322)),x89323)),f333(f333(f8(x89321,a1),x89322),x89323)) % 191.49/191.41 [8933]P4(f333(f333(f335(x89331),f512(x89332,x89333,x89331)),x89333))+E(f333(f105(a1),f333(f333(f11(x89331,a880),f333(f333(f10(a1,a880,x89331),a109),x89332)),x89333)),f333(f333(f11(x89331,a1),x89332),x89333)) % 191.49/191.41 [9000]E(f86(x90001,f333(f333(f9(x90001,f890(x90001,a874),a874),f335(x90001)),f333(f333(f3(f890(x90001,a874)),x90002),f333(f333(f311(x90001),x90003),f194(f890(x90001,a874)))))),f266(x90001,x90003,x90002))+P4(f333(f333(f250(f890(x90001,a874)),x90002),f333(f333(f311(x90001),x90003),f194(f890(x90001,a874))))) % 191.49/191.41 [9345]E(f333(f333(f155(f881(x93451),x93451),f333(f333(f9(f881(x93451),a880,x93451),f166(x93451)),x93452)),f333(f137(f881(x93451),f333(f333(f10(a880,a874,f881(x93451)),f333(f251(a880),x93452)),f195(f881(x93451)))),x93453)),f333(f333(f166(f881(x93451)),f180(x93451,x93453)),x93452))+~P4(f333(f333(f251(a880),x93452),f333(f195(f881(f881(x93451))),f180(x93451,x93453)))) % 191.49/191.41 [9414]E(f333(f137(x94141,x94142),x94143),f177(x94141,x94142,x94143))+P4(f333(f333(f335(x94141),f672(x94143,x94142,x94141)),f333(f173(x94141),f333(f333(f139(x94141),f333(f195(f881(x94141)),f177(x94141,x94142,x94143))),x94143)))) % 191.49/191.41 [9567]E(f333(f333(f139(x95671),f333(f195(f881(x95671)),f177(x95671,x95672,x95673))),x95673),f118(x95671))+~P4(f333(x95672,f333(f142(x95671),f333(f333(f139(x95671),f333(f195(f881(x95671)),f177(x95671,x95672,x95673))),x95673)))) % 191.49/191.41 [9672]~P4(f333(f333(f335(f889(x96721,x96721)),x96722),f309(x96721,x96723)))+P4(f333(f333(f335(f889(x96721,x96721)),x96722),f333(f333(f44(a880,f890(f889(x96721,x96721),a874)),f258(f890(a880,a874))),f333(f333(f9(a880,f890(f889(x96721,x96721),a874),f890(f889(x96721,x96721),a874)),f189(f889(x96721,x96721),a874)),x96723)))) % 191.49/191.41 [9729]~P4(f333(f333(f250(f890(x97291,a874)),f333(f333(f44(a880,f890(x97291,a874)),f333(f303(a880,f2(a880)),f550(x97293,x97292,x97291))),x97292)),x97293))+P4(f333(f333(f250(f890(x97291,a874)),f333(f333(f44(a880,f890(x97291,a874)),f258(f890(a880,a874))),x97292)),x97293)) % 191.49/191.41 [9801]~P4(f333(f333(f251(a1),f2(a1)),x98013))+P4(f333(f333(f251(a1),x98011),f333(f333(f81(a1),x98012),f333(f333(f82(a1),f333(f333(f81(a1),f333(f76(a1),f333(f333(f3(a1),x98012),x98011))),f79(a1))),x98013)))) % 191.49/191.41 [9809]~P40(x98091,f333(f333(f115(f890(f889(x98091,x98091),a874)),x98092),x98093))+P40(x98091,f333(f333(f115(f890(f889(x98091,x98091),a874)),f333(f333(f115(f890(f889(x98091,x98091),a874)),f333(f333(f290(x98091,x98091,x98091),x98092),x98092)),f333(f333(f290(x98091,x98091,x98091),x98093),x98092))),x98093)) % 191.49/191.41 [9885]P40(x98851,f333(f333(f115(f890(f889(x98851,x98851),a874)),x98852),x98853))+~P40(x98851,f333(f333(f115(f890(f889(x98851,x98851),a874)),f333(f333(f115(f890(f889(x98851,x98851),a874)),f333(f333(f290(x98851,x98851,x98851),x98852),x98852)),f333(f333(f290(x98851,x98851,x98851),x98853),x98852))),x98853)) % 191.49/191.41 [9420]~P140(x94201)+E(f333(f107(x94201),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x94202),x94203)),f194(f890(f889(a880,a880),a874)))))),f333(f333(f3(x94201),f333(f105(x94201),x94202)),f333(f105(x94201),x94203))) % 191.49/191.41 [9516]P4(f333(x95163,x95162))+E(f333(f255(x95161),f333(f333(f20(x95161,a874,a874),f333(f333(f10(a874,f890(a874,a874),x95161),a331),f333(f333(f9(x95161,x95161,a874),a330),x95162))),x95163)),f194(f890(x95161,a874))) % 191.49/191.41 [9518]~P4(f333(x95183,x95182))+E(f333(f255(x95181),f333(f333(f20(x95181,a874,a874),f333(f333(f10(a874,f890(a874,a874),x95181),a331),f333(f333(f9(x95181,x95181,a874),a330),x95182))),x95183)),f333(f333(f311(x95181),x95182),f194(f890(x95181,a874)))) % 191.49/191.41 [9877]~P4(f333(f63(x98771),x98773))+E(f333(f333(f66(x98771,f890(x98771,a874),f333(f333(f10(f890(x98771,a874),f890(f890(x98771,a874),f890(x98771,a874)),x98771),f333(f9(f890(x98771,a874),f890(x98771,a874),f890(x98771,a874)),f3(f890(x98771,a874)))),f333(f333(f9(x98771,f890(x98771,a874),f890(x98771,a874)),f311(x98771)),f194(f890(x98771,a874))))),x98772),x98773),f333(f333(f3(f890(x98771,a874)),x98772),x98773)) % 191.49/191.41 [9908]~P4(f333(f333(f251(a1),f2(a1)),x99083))+P4(f333(f333(f251(a1),f333(f333(f3(a1),x99081),f333(f333(f82(a1),f333(f333(f81(a1),f333(f76(a1),f333(f333(f3(a1),x99081),x99082))),f79(a1))),x99083))),x99082)) % 191.49/191.41 [10143]~P4(f333(f333(f335(x101431),x101433),f322(x101431,x101432)))+P4(f333(f321(x101431,f333(f333(f9(x101431,f890(f889(x101431,x101431),a874),f890(x101431,a874)),f333(f333(f10(f890(x101431,f890(f890(f889(x101431,x101431),a874),a874)),f890(f890(f889(x101431,x101431),a874),f890(x101431,a874)),x101431),f9(x101431,f890(f889(x101431,x101431),a874),a874)),f333(f333(f10(f890(x101431,f889(x101431,x101431)),f890(x101431,f890(f890(f889(x101431,x101431),a874),a874)),x101431),f333(f10(f889(x101431,x101431),f890(f890(f889(x101431,x101431),a874),a874),x101431),f335(f889(x101431,x101431)))),f263(x101431,x101431)))),x101432)),x101433)) % 191.49/191.41 [10156]P4(f333(f333(f335(x101561),x101562),f322(x101561,x101563)))+~P4(f333(f321(x101561,f333(f333(f9(x101561,f890(f889(x101561,x101561),a874),f890(x101561,a874)),f333(f333(f10(f890(x101561,f890(f890(f889(x101561,x101561),a874),a874)),f890(f890(f889(x101561,x101561),a874),f890(x101561,a874)),x101561),f9(x101561,f890(f889(x101561,x101561),a874),a874)),f333(f333(f10(f890(x101561,f889(x101561,x101561)),f890(x101561,f890(f890(f889(x101561,x101561),a874),a874)),x101561),f333(f10(f889(x101561,x101561),f890(f890(f889(x101561,x101561),a874),a874),x101561),f335(f889(x101561,x101561)))),f263(x101561,x101561)))),x101563)),x101562)) % 191.49/191.41 [9727]~P4(f333(f63(x97271),f333(f255(x97271),x97273)))+P4(f333(f63(x97271),f333(f255(x97271),f333(f333(f20(x97271,a874,a874),f333(f333(f10(a874,f890(a874,a874),x97271),a331),x97272)),x97273)))) % 191.49/191.41 [9728]~P4(f333(f63(x97281),f333(f255(x97281),x97282)))+P4(f333(f63(x97281),f333(f255(x97281),f333(f333(f20(x97281,a874,a874),f333(f333(f10(a874,f890(a874,a874),x97281),a331),x97282)),x97283)))) % 191.49/191.41 [9840]P4(f333(f63(x98401),f333(f255(x98401),x98402)))+~P4(f333(f63(x98401),f333(f255(x98401),f333(f333(f20(x98401,a874,a874),f333(f333(f10(a874,f890(a874,a874),x98401),a332),x98403)),x98402)))) % 191.49/191.41 [9841]P4(f333(f63(x98411),f333(f255(x98411),x98412)))+~P4(f333(f63(x98411),f333(f255(x98411),f333(f333(f20(x98411,a874,a874),f333(f333(f10(a874,f890(a874,a874),x98411),a332),x98412)),x98413)))) % 191.49/191.41 [10107]~P4(f333(f63(x101071),x101072))+P4(f333(f63(f881(x101071)),f333(f255(f881(x101071)),f333(f333(f20(f881(x101071),a874,a874),f333(f333(f10(a874,f890(a874,a874),f881(x101071)),a331),f333(f333(f9(f881(x101071),f890(x101071,a874),a874),f333(f333(f10(f890(x101071,a874),f890(f890(x101071,a874),a874),f881(x101071)),f250(f890(x101071,a874))),f173(x101071))),x101072))),f333(f333(f9(f881(x101071),a880,a874),f333(f333(f10(a880,f890(a880,a874),f881(x101071)),a330),f195(f881(x101071)))),x101073))))) % 191.49/191.41 [10108]~P4(f333(f63(x101081),x101082))+P4(f333(f63(f881(x101081)),f333(f255(f881(x101081)),f333(f333(f20(f881(x101081),a874,a874),f333(f333(f10(a874,f890(a874,a874),f881(x101081)),a331),f333(f333(f9(f881(x101081),f890(x101081,a874),a874),f333(f333(f10(f890(x101081,a874),f890(f890(x101081,a874),a874),f881(x101081)),f250(f890(x101081,a874))),f173(x101081))),x101082))),f333(f333(f9(f881(x101081),a880,a874),f333(f333(f10(a880,f890(a880,a874),f881(x101081)),f250(a880)),f195(f881(x101081)))),x101083))))) % 191.49/191.41 [9386]~P94(x93861)+E(f333(f333(f264(x93861),x93862),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x93863)),x93863)),a102))),f333(f333(f89(x93861,x93861),f333(f333(f264(x93861),x93862),f333(f108(a880),x93863))),f333(f333(f20(x93861,x93861,x93861),f82(x93861)),f7(x93861)))) % 191.49/191.41 [10076]~P115(x100761)+E(f333(f333(f264(x100761),x100762),f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x100763)),f333(f333(f82(x100761),f333(f333(f264(x100761),x100762),x100763)),f333(f333(f264(x100761),x100762),x100763))) % 191.49/191.41 [10088]~P83(x100881)+E(f333(f333(f264(x100881),f333(f333(f264(x100881),x100882),x100883)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f333(f264(x100881),x100882),f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x100883))) % 191.49/191.41 [10122]~P140(x101221)+E(f333(f333(f264(x101221),f333(f80(x101221),x101222)),f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101223)),f333(f333(f264(x101221),x101222),f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101223))) % 191.49/191.41 [10180]~P120(x101801)+P4(f333(f333(f250(x101801),f2(x101801)),f333(f333(f81(x101801),f333(f333(f264(x101801),x101802),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101801),x101803),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))))) % 191.49/191.41 [10130]~P115(x101301)+E(f333(f333(f264(x101301),x101302),f333(a117,f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101303))),f333(f333(f82(x101301),x101302),f333(f333(f82(x101301),f333(f333(f264(x101301),x101302),x101303)),f333(f333(f264(x101301),x101302),x101303)))) % 191.49/191.41 [10149]~P83(x101491)+E(f333(f333(f82(x101491),x101492),f333(f333(f264(x101491),f333(f333(f264(x101491),x101492),x101493)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101491),x101492),f333(a117,f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101493)))) % 191.49/191.41 [10162]~P120(x101621)+P4(f333(f333(f250(x101621),f2(x101621)),f333(f333(f264(x101621),x101622),f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101623)))) % 191.49/191.41 [10199]~P94(x101991)+E(f333(f333(f3(x101991),f333(f333(f81(x101991),f333(f333(f264(x101991),x101992),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101991),x101993),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))),f333(f333(f82(x101991),f333(f333(f82(x101991),f333(f108(x101991),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101992)),x101993)),f333(f333(f264(x101991),f333(f333(f3(x101991),x101992),x101993)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.41 [10200]~P94(x102001)+E(f333(f333(f81(x102001),f333(f333(f81(x102001),f333(f333(f264(x102001),x102002),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x102001),x102003),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))),f333(f333(f82(x102001),f333(f333(f82(x102001),f333(f108(x102001),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x102002)),x102003)),f333(f333(f264(x102001),f333(f333(f81(x102001),x102002),x102003)),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.41 [10227]~P30(x102271,x102272,x102273)+P4(f99(x102271,a874,f333(f333(f10(f890(a876,f890(f890(x102271,f890(a875,a874)),f890(x102271,a874))),f890(a876,f890(f890(x102271,f890(a875,a874)),a874)),f890(x102271,f890(a875,a874))),f333(f10(f890(f890(x102271,f890(a875,a874)),f890(x102271,a874)),f890(f890(x102271,f890(a875,a874)),a874),a876),f333(f10(f890(x102271,a874),a874,f890(x102271,f890(a875,a874))),f88(x102271)))),f333(f333(f10(f890(a876,f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874)))),f890(a876,f890(f890(x102271,f890(a875,a874)),f890(x102271,a874))),f890(x102271,f890(a875,a874))),f333(f10(f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),f890(f890(x102271,f890(a875,a874)),f890(x102271,a874)),a876),f333(f10(f890(x102271,f890(a875,a874)),f890(x102271,a874),f890(x102271,f890(a875,a874))),f333(f10(f890(a875,a874),a874,x102271),f88(a875))))),f333(f333(f9(f890(x102271,f890(a875,a874)),f890(a876,f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874)))),f890(a876,f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))))),f333(f333(f10(f890(f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874)))),f890(f890(a876,f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874)))),f890(a876,f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))))),f890(x102271,f890(a875,a874))),f10(f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),a876)),f333(f333(f10(f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),f890(f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874)))),f890(x102271,f890(a875,a874))),f10(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874)))),f333(f333(f10(f890(x102271,f890(f890(a875,a874),f890(a875,a874))),f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),f890(x102271,f890(a875,a874))),f20(x102271,f890(a875,a874),f890(a875,a874))),f333(f333(f10(f890(x102271,f890(a875,f890(a874,a874))),f890(x102271,f890(f890(a875,a874),f890(a875,a874))),f890(x102271,f890(a875,a874))),f333(f10(f890(a875,f890(a874,a874)),f890(f890(a875,a874),f890(a875,a874)),x102271),f20(a875,a874,a874))),f333(f10(f890(a875,a874),f890(a875,f890(a874,a874)),x102271),f333(f10(a874,f890(a874,a874),a875),a336))))))),f333(f333(f10(f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,f890(a875,a874)))),f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),a876),f333(f10(f890(x102271,f890(a875,f890(a875,a874))),f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,a874))),f333(f10(f890(a875,f890(a875,a874)),f890(a875,a874),x102271),f333(f10(f890(a875,a874),a874,a875),f88(a875))))),f333(f333(f10(f890(f890(a875,a874),f890(a875,f890(a875,a874))),f890(f890(x102271,f890(a875,a874)),f890(x102271,f890(a875,f890(a875,a874)))),a876),f10(f890(a875,a874),f890(a875,f890(a875,a874)),x102271)),f333(f333(f10(f890(a875,f890(f890(a875,a874),f890(a875,a874))),f890(f890(a875,a874),f890(a875,f890(a875,a874))),a876),f9(a875,f890(a875,a874),f890(a875,a874))),f333(f333(f10(f890(a875,f890(a875,f890(a874,a874))),f890(a875,f890(f890(a875,a874),f890(a875,a874))),a876),f333(f10(f890(a875,f890(a874,a874)),f890(f890(a875,a874),f890(a875,a874)),a875),f20(a875,a874,a874))),f333(f333(f10(f890(a875,f890(a875,a874)),f890(a875,f890(a875,f890(a874,a874))),a876),f333(f10(f890(a875,a874),f890(a875,f890(a874,a874)),a875),f333(f10(a874,f890(a874,a874),a875),a336))),f333(f333(f9(a876,a880,f890(a875,f890(a875,a874))),f333(f333(f10(f890(a875,f890(a880,f890(a875,a874))),f890(a880,f890(a875,f890(a875,a874))),a876),f9(a875,a880,f890(a875,a874))),a203)),x102272))))))))),x102273)) % 191.49/191.41 [10229]P30(x102291,x102292,x102293)+~P4(f99(x102291,a874,f333(f333(f10(f890(a876,f890(f890(x102291,f890(a875,a874)),f890(x102291,a874))),f890(a876,f890(f890(x102291,f890(a875,a874)),a874)),f890(x102291,f890(a875,a874))),f333(f10(f890(f890(x102291,f890(a875,a874)),f890(x102291,a874)),f890(f890(x102291,f890(a875,a874)),a874),a876),f333(f10(f890(x102291,a874),a874,f890(x102291,f890(a875,a874))),f88(x102291)))),f333(f333(f10(f890(a876,f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874)))),f890(a876,f890(f890(x102291,f890(a875,a874)),f890(x102291,a874))),f890(x102291,f890(a875,a874))),f333(f10(f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),f890(f890(x102291,f890(a875,a874)),f890(x102291,a874)),a876),f333(f10(f890(x102291,f890(a875,a874)),f890(x102291,a874),f890(x102291,f890(a875,a874))),f333(f10(f890(a875,a874),a874,x102291),f88(a875))))),f333(f333(f9(f890(x102291,f890(a875,a874)),f890(a876,f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874)))),f890(a876,f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))))),f333(f333(f10(f890(f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874)))),f890(f890(a876,f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874)))),f890(a876,f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))))),f890(x102291,f890(a875,a874))),f10(f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),a876)),f333(f333(f10(f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),f890(f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874)))),f890(x102291,f890(a875,a874))),f10(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874)))),f333(f333(f10(f890(x102291,f890(f890(a875,a874),f890(a875,a874))),f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),f890(x102291,f890(a875,a874))),f20(x102291,f890(a875,a874),f890(a875,a874))),f333(f333(f10(f890(x102291,f890(a875,f890(a874,a874))),f890(x102291,f890(f890(a875,a874),f890(a875,a874))),f890(x102291,f890(a875,a874))),f333(f10(f890(a875,f890(a874,a874)),f890(f890(a875,a874),f890(a875,a874)),x102291),f20(a875,a874,a874))),f333(f10(f890(a875,a874),f890(a875,f890(a874,a874)),x102291),f333(f10(a874,f890(a874,a874),a875),a336))))))),f333(f333(f10(f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,f890(a875,a874)))),f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),a876),f333(f10(f890(x102291,f890(a875,f890(a875,a874))),f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,a874))),f333(f10(f890(a875,f890(a875,a874)),f890(a875,a874),x102291),f333(f10(f890(a875,a874),a874,a875),f88(a875))))),f333(f333(f10(f890(f890(a875,a874),f890(a875,f890(a875,a874))),f890(f890(x102291,f890(a875,a874)),f890(x102291,f890(a875,f890(a875,a874)))),a876),f10(f890(a875,a874),f890(a875,f890(a875,a874)),x102291)),f333(f333(f10(f890(a875,f890(f890(a875,a874),f890(a875,a874))),f890(f890(a875,a874),f890(a875,f890(a875,a874))),a876),f9(a875,f890(a875,a874),f890(a875,a874))),f333(f333(f10(f890(a875,f890(a875,f890(a874,a874))),f890(a875,f890(f890(a875,a874),f890(a875,a874))),a876),f333(f10(f890(a875,f890(a874,a874)),f890(f890(a875,a874),f890(a875,a874)),a875),f20(a875,a874,a874))),f333(f333(f10(f890(a875,f890(a875,a874)),f890(a875,f890(a875,f890(a874,a874))),a876),f333(f10(f890(a875,a874),f890(a875,f890(a874,a874)),a875),f333(f10(a874,f890(a874,a874),a875),a336))),f333(f333(f9(a876,a880,f890(a875,f890(a875,a874))),f333(f333(f10(f890(a875,f890(a880,f890(a875,a874))),f890(a880,f890(a875,f890(a875,a874))),a876),f9(a875,a880,f890(a875,a874))),a203)),x102292))))))))),x102293)) % 191.49/191.41 [4707]E(x47071,x47072)+~E(f34(x47073,x47071),f34(x47074,x47072)) % 191.49/191.41 [4708]E(x47081,x47082)+~E(f34(x47081,x47083),f34(x47082,x47084)) % 191.49/191.41 [4709]E(x47091,x47092)+~E(f33(x47093,x47091),f33(x47094,x47092)) % 191.49/191.41 [4710]E(x47101,x47102)+~E(f33(x47101,x47103),f33(x47102,x47104)) % 191.49/191.41 [7745]P28(x77451,x77452,x77453,x77454)+~E(f834(x77454,x77453,x77452,x77451),f835(x77454,x77453,x77452,x77451)) % 191.49/191.41 [8033]P37(x80331,x80332,x80333,x80334,f118(x80332))+~E(x80334,f118(x80331)) % 191.49/191.41 [8034]P37(x80341,x80342,x80343,f118(x80341),x80344)+~E(x80344,f118(x80342)) % 191.49/191.41 [8253]~P28(x82531,f884(x82532),x82534,f184(x82531,x82532,x82534))+P28(x82531,f884(x82532),f185(x82531,x82532,x82533,x82534),f184(x82531,x82532,x82534)) % 191.49/191.41 [8465]~P28(x84651,f884(x84652),f185(x84651,x84652,x84654,x84653),f184(x84651,x84652,x84653))+P28(x84651,f884(x84652),x84653,f184(x84651,x84652,x84653)) % 191.49/191.41 [8582]~P37(x85822,x85823,x85824,x85821,f118(x85823))+E(x85821,f118(x85822)) % 191.49/191.41 [8583]~P37(x85833,x85832,x85834,f118(x85833),x85831)+E(x85831,f118(x85832)) % 191.49/191.41 [5077]~P20(x50773,x50771,x50774)+E(f333(f333(x50771,x50772),x50772),x50772) % 191.49/191.41 [5368]~E(x53684,f194(f890(x53681,a874)))+E(f333(f312(x53681,x53682,x53683),x53684),f194(f890(x53682,a874))) % 191.49/191.41 [5634]~E(f333(f312(x56342,x56343,x56344),x56341),f194(f890(x56343,a874)))+E(x56341,f194(f890(x56342,a874))) % 191.49/191.41 [5917]~P109(x59172)+E(f333(f333(f149(x59171,x59172,x59173),x59174),f118(x59171)),f333(f333(f152(x59171),x59174),f118(x59171))) % 191.49/191.41 [5954]E(f333(x59541,x59542),f197(x59543))+P4(f333(f333(f335(x59544),x59542),f184(x59544,x59543,x59541))) % 191.49/191.41 [6274]~E(x62741,f194(f890(x62742,a874)))+~P4(f333(f64(x62742,x62743,x62741),x62744)) % 191.49/191.41 [6296]~P58(x62961,x62963,x62964,x62962)+P4(f333(f63(x62961),x62962)) % 191.49/191.41 [6297]~P58(x62971,x62973,x62972,x62974)+P4(f333(f63(x62971),x62972)) % 191.49/191.41 [6302]~P58(x63022,x63023,x63024,x63021)+~E(x63021,f194(f890(x63022,a874))) % 191.49/191.41 [6333]~P110(x63331)+E(f333(f333(f106(f890(x63331,a874)),f333(f303(x63331,x63332),x63333)),f304(x63331,x63333,x63334)),f194(f890(x63331,a874))) % 191.49/191.41 [6358]~P4(f333(f333(x63583,x63584),x63582))+P4(f333(f333(f335(x63581),x63582),f294(x63581,x63583,x63584))) % 191.49/191.41 [6359]~P4(f333(f333(x63593,x63594),x63592))+P4(f333(f333(f335(x63591),x63592),f295(x63591,x63593,x63594))) % 191.49/191.41 [6360]~P4(f333(f333(x63603,x63602),x63604))+P4(f333(f333(f335(x63601),x63602),f296(x63601,x63603,x63604))) % 191.49/191.41 [6361]~P4(f333(f333(x63613,x63612),x63614))+P4(f333(f333(f335(x63611),x63612),f299(x63611,x63613,x63614))) % 191.49/191.41 [6501]~P110(x65011)+E(f333(f333(f106(f890(x65011,a874)),f307(x65011,x65012,x65013)),f304(x65011,x65013,x65014)),f194(f890(x65011,a874))) % 191.49/191.41 [6502]~P110(x65021)+E(f333(f333(f106(f890(x65021,a874)),f306(x65021,x65022,x65023)),f307(x65021,x65023,x65024)),f194(f890(x65021,a874))) % 191.49/191.41 [6503]~P110(x65031)+E(f333(f333(f106(f890(x65031,a874)),f306(x65031,x65032,x65033)),f306(x65031,x65033,x65034)),f194(f890(x65031,a874))) % 191.49/191.41 [6504]~P110(x65041)+E(f333(f333(f106(f890(x65041,a874)),f304(x65041,x65042,x65043)),f307(x65041,x65043,x65044)),f194(f890(x65041,a874))) % 191.49/191.41 [6505]~P110(x65051)+E(f333(f333(f106(f890(x65051,a874)),f304(x65051,x65052,x65053)),f306(x65051,x65053,x65054)),f194(f890(x65051,a874))) % 191.49/191.41 [6539]P4(f333(f333(x65391,x65392),f699(x65392,x65391)))+~P4(f333(f268(x65393,x65394,x65391),x65392)) % 191.49/191.41 [6588]~E(f333(x65881,x65882),f197(x65883))+~P4(f333(f333(f335(x65884),x65882),f184(x65884,x65883,x65881))) % 191.49/191.41 [6617]~P109(x66172)+E(f333(f173(x66171),f151(x66171,x66172,x66173,x66174)),f333(f173(x66171),x66174)) % 191.49/191.41 [6669]~P143(x66691)+E(f196(x66691,x66692,f333(a117,x66693),x66694),f196(x66691,x66692,x66693,f333(x66692,x66694))) % 191.49/191.41 [6729]~P4(f333(f333(f335(x67294),x67293),f294(x67294,x67291,x67292)))+P4(f333(f333(x67291,x67292),x67293)) % 191.49/191.41 [6730]~P4(f333(f333(f335(x67304),x67303),f295(x67304,x67301,x67302)))+P4(f333(f333(x67301,x67302),x67303)) % 191.49/191.41 [6731]~P4(f333(f333(f335(x67314),x67312),f296(x67314,x67311,x67313)))+P4(f333(f333(x67311,x67312),x67313)) % 191.49/191.41 [6732]~P4(f333(f333(f335(x67324),x67322),f299(x67324,x67321,x67323)))+P4(f333(f333(x67321,x67322),x67323)) % 191.49/191.41 [6803]E(f333(f39(f888(x68031,x68032)),f320(x68031,x68032,x68033,x68034)),f2(a880))+P4(f333(f63(x68032),x68034)) % 191.49/191.41 [6804]E(f333(f39(f888(x68041,x68042)),f320(x68041,x68042,x68043,x68044)),f2(a880))+P4(f333(f63(x68041),x68043)) % 191.49/191.41 [6897]E(f333(f242(x68971),f375(x68972,x68971,x68973)),f333(x68972,x68973))+~P4(f333(f333(f335(x68974),x68973),f184(x68974,x68971,x68972))) % 191.49/191.41 [7002]~P18(x70024,x70021,x70022)+E(f333(f74(x70021,x70021,x70021,f333(x70022,x70023)),f333(x70022,x70023)),f333(x70022,x70023)) % 191.49/191.41 [7784]~P4(f333(x77841,x77844))+P4(f333(x77841,f97(x77842,a880,x77843,x77841))) % 191.49/191.41 [7864]~E(x78642,x78643)+P4(f333(f333(f335(f889(x78641,x78641)),f333(f333(f263(x78641,x78641),x78642),x78643)),f309(x78641,x78644))) % 191.49/191.41 [7893]~P28(x78931,x78932,x78933,f258(f890(x78931,a874)))+E(f333(f78(x78931,x78932,f258(f890(x78931,a874)),x78933),f333(x78933,x78934)),x78934) % 191.49/191.41 [7979]~P4(f333(f333(f335(f881(x79791)),f333(f333(f152(x79791),x79794),x79792)),f162(x79791,x79793)))+P4(f333(f333(f335(f881(x79791)),x79792),f162(x79791,x79793))) % 191.49/191.41 [7980]~P4(f333(f333(f335(f881(x79801)),f333(f333(f127(x79801),x79804),x79802)),f162(x79801,x79803)))+P4(f333(f333(f335(f881(x79801)),x79802),f162(x79801,x79803))) % 191.49/191.41 [7981]~P4(f333(f333(f335(f881(x79811)),f333(f333(f127(x79811),x79812),x79814)),f162(x79811,x79813)))+P4(f333(f333(f335(f881(x79811)),x79812),f162(x79811,x79813))) % 191.49/191.41 [7997]~P109(x79971)+P17(x79971,f333(f333(f155(x79972,x79971),x79973),f151(x79972,x79971,x79973,x79974))) % 191.49/191.41 [8100]P28(x81004,x81003,x81001,x81002)+E(f333(x81001,f834(x81002,x81001,x81003,x81004)),f333(x81001,f835(x81002,x81001,x81003,x81004))) % 191.49/191.41 [8114]E(f185(x81141,x81142,x81143,x81144),f185(x81141,x81142,x81144,x81143))+~E(f333(f333(f106(f890(x81141,a874)),f184(x81141,x81142,x81143)),f184(x81141,x81142,x81144)),f194(f890(x81141,a874))) % 191.49/191.41 [8217]~P28(x82172,x82171,x82174,x82173)+P28(x82171,x82172,f78(x82172,x82171,x82173,x82174),f333(f312(x82172,x82171,x82174),x82173)) % 191.49/191.41 [8349]P40(f889(x83492,x83494),f285(x83492,x83494,x83491,x83493))+P4(f333(x83491,f706(x83492,x83493,x83494,x83491))) % 191.49/191.41 [8472]E(x84721,x84722)+~P4(f333(f333(f335(f889(x84723,x84723)),f333(f333(f263(x84723,x84723),x84721),x84722)),f260(x84723,x84724))) % 191.49/191.41 [8538]~P4(f333(f63(f888(x85383,x85381)),f320(x85383,x85381,x85384,x85382)))+P4(f333(f63(x85381),x85382)) % 191.49/191.41 [8539]~P4(f333(f63(f888(x85391,x85393)),f320(x85391,x85393,x85392,x85394)))+P4(f333(f63(x85391),x85392)) % 191.49/191.41 [8705]P40(f889(x87051,x87052),f285(x87051,x87052,x87053,x87054))+~P40(x87052,f333(x87054,f706(x87051,x87054,x87052,x87053))) % 191.49/191.41 [9264]E(f333(f333(f160(x92641,x92642),f609(x92643,x92644,x92642,x92641)),f610(x92643,x92644,x92642,x92641)),x92644)+~P4(f333(f333(f335(f889(f881(x92641),f881(x92641))),f333(f333(f263(f881(x92641),f881(x92641)),x92642),x92644)),f158(x92641,x92643))) % 191.49/191.41 [9265]~P4(f333(x92653,x92654))+P4(f333(f333(f250(a880),f333(x92651,f97(x92652,a880,x92651,x92653))),f333(x92651,x92654))) % 191.49/191.41 [9274]~P4(f333(f333(f335(f889(f881(x92741),f881(x92741))),f333(f333(f263(f881(x92741),f881(x92741)),x92742),x92743)),f146(x92741,x92744)))+P4(f333(f333(f335(f889(f881(x92741),f881(x92741))),f333(f333(f263(f881(x92741),f881(x92741)),x92742),x92743)),f148(x92741,x92744))) % 191.49/191.41 [9383]P4(f333(f63(x93831),x93832))+~P4(f333(f333(f335(f889(f890(x93831,a874),f890(x93831,a874))),f333(f333(f263(f890(x93831,a874),f890(x93831,a874)),x93833),x93832)),f325(x93831,x93834))) % 191.49/191.41 [9384]P4(f333(f63(x93841),x93842))+~P4(f333(f333(f335(f889(f890(x93841,a874),f890(x93841,a874))),f333(f333(f263(f890(x93841,a874),f890(x93841,a874)),x93842),x93843)),f325(x93841,x93844))) % 191.49/191.41 [9385]~E(x93851,f194(f890(x93852,a874)))+~P4(f333(f333(f335(f889(f890(x93852,a874),f890(x93852,a874))),f333(f333(f263(f890(x93852,a874),f890(x93852,a874)),x93853),x93851)),f325(x93852,x93854))) % 191.49/191.41 [10032]P15(x100321,x100322,x100323,x100324)+~P4(f333(f333(f272(x100321,x100321,a874),f333(f333(f9(x100321,f890(x100321,x100322),f890(x100321,a874)),f333(f333(f10(f890(x100322,a874),f890(f890(x100321,x100322),f890(x100321,a874)),x100321),f10(x100322,a874,x100321)),f333(f333(f10(x100322,f890(x100322,a874),x100321),a330),x100324))),x100324)),f603(x100324,x100323,x100322,x100321))) % 191.49/191.41 [4978]~E(x49784,f118(x49781))+E(f333(f333(f155(x49781,x49782),x49783),x49784),f118(x49782)) % 191.49/191.41 [4979]~E(x49794,f197(x49791))+E(f333(f333(f208(x49791,x49792),x49793),x49794),f197(x49792)) % 191.49/191.41 [4980]~E(x49802,f118(x49801))+E(f333(f333(f160(x49801,x49802),x49803),x49804),f118(x49801)) % 191.49/191.41 [5215]E(x52151,f197(x52152))+~E(f333(f333(f208(x52152,x52153),x52154),x52151),f197(x52153)) % 191.49/191.41 [5216]E(x52161,f118(x52162))+~E(f333(f333(f155(x52162,x52163),x52164),x52161),f118(x52163)) % 191.49/191.41 [5217]E(x52171,f118(x52172))+~E(f333(f333(f160(x52172,x52171),x52173),x52174),f118(x52172)) % 191.49/191.41 [5250]E(x52501,x52502)+~E(f333(f333(f127(x52503),x52504),x52501),f333(f333(f127(x52503),x52504),x52502)) % 191.49/191.41 [5251]E(x52511,x52512)+~E(f333(f333(f127(x52513),x52511),x52514),f333(f333(f127(x52513),x52512),x52514)) % 191.49/191.41 [5405]P4(f333(x54053,x54052))+E(f171(x54051,x54052,f333(f137(x54051,x54053),x54054)),f333(f137(x54051,x54053),x54054)) % 191.49/191.41 [5408]~P4(f333(x54082,x54083))+P36(x54081,x54082,f333(f333(f152(x54081),x54083),x54084)) % 191.49/191.41 [5417]E(x54171,x54172)+~E(f140(a880,f333(f303(a880,x54171),x54173)),f333(f333(f152(a880),x54172),x54174)) % 191.49/191.41 [5465]~P29(x54652,x54653)+P29(x54651,f333(f333(f75(x54652,x54651),x54653),x54654)) % 191.49/191.41 [5466]~P40(x54662,x54663)+P40(x54661,f333(f333(f289(x54662,x54661),x54663),x54664)) % 191.49/191.41 [5588]~P36(x55881,x55882,x55884)+P36(x55881,x55882,f333(f333(f152(x55881),x55883),x55884)) % 191.49/191.41 [5589]~P36(x55891,x55892,x55894)+P36(x55891,x55892,f333(f333(f127(x55891),x55893),x55894)) % 191.49/191.41 [5590]~P36(x55901,x55902,x55903)+P36(x55901,x55902,f333(f333(f127(x55901),x55903),x55904)) % 191.49/191.41 [5677]~E(x56771,f118(x56772))+~E(f333(f333(f127(x56772),x56773),f333(f333(f152(x56772),x56774),f118(x56772))),x56771) % 191.49/191.41 [5702]~P34(x57023,x57021,f333(f333(f152(x57023),x57022),x57024))+P4(f333(x57021,x57022)) % 191.49/191.41 [5712]E(f145(x57121,x57122),x57123)+~E(f333(f333(f127(x57121),x57124),f333(f333(f152(x57121),x57123),f118(x57121))),x57122) % 191.49/191.41 [5713]E(f119(x57131,x57132),x57133)+~E(f333(f333(f127(x57131),x57133),f333(f333(f152(x57131),x57134),f118(x57131))),x57132) % 191.49/191.41 [5822]~E(f140(a880,f333(f303(a880,x58221),x58222)),f333(f333(f152(a880),x58223),x58224))+P4(f333(f333(f251(a880),x58221),x58222)) % 191.49/191.41 [5830]P34(x58301,x58302,x58303)+~P34(x58301,x58302,f333(f333(f152(x58301),x58304),x58303)) % 191.49/191.41 [5831]P34(x58311,x58312,x58313)+~P34(x58311,x58312,f333(f333(f127(x58311),x58314),x58313)) % 191.49/191.41 [5832]P34(x58321,x58322,x58323)+~P34(x58321,x58322,f333(f333(f127(x58321),x58323),x58324)) % 191.49/191.41 [6021]E(x60211,f333(f333(f127(x60212),f333(f170(x60212),x60213)),f333(f333(f152(x60212),x60214),f118(x60212))))+~E(f333(f170(x60212),x60211),f333(f333(f152(x60212),x60214),x60213)) % 191.49/191.41 [6195]~P110(x61951)+E(f333(f333(f106(f890(x61951,a874)),f333(f303(x61951,x61952),x61953)),f333(f303(x61951,x61953),x61954)),f194(f890(x61951,a874))) % 191.49/191.41 [6232]~P69(x62321)+E(f333(f167(x62321),f333(f333(f155(a1,x62321),x62322),f179(x62323,x62324))),f333(f333(f8(a1,x62321),x62322),f333(f173(a1),f179(x62323,x62324)))) % 191.49/191.41 [6233]~P69(x62331)+E(f333(f333(f8(a1,x62331),x62332),f333(f173(a1),f179(x62333,x62334))),f333(f167(x62331),f333(f333(f155(a1,x62331),x62332),f179(x62333,x62334)))) % 191.49/191.41 [6373]~E(x63732,f333(f333(f127(x63731),f333(f170(x63731),x63734)),f333(f333(f152(x63731),x63733),f118(x63731))))+E(f333(f170(x63731),x63732),f333(f333(f152(x63731),x63733),x63734)) % 191.49/191.41 [6389]~P22(x63892,x63893,x63894,x63891)+E(f333(x63891,f194(f890(x63892,a874))),f35(x63893)) % 191.49/191.41 [6415]~P110(x64151)+E(f333(f333(f106(f890(x64151,a874)),f307(x64151,x64152,x64153)),f333(f303(x64151,x64153),x64154)),f194(f890(x64151,a874))) % 191.49/191.41 [6618]E(x66181,f194(f890(x66182,a874)))+~E(f320(x66183,x66182,x66184,x66181),f194(f890(f888(x66183,x66182),a874))) % 191.49/191.41 [6619]E(x66191,f194(f890(x66192,a874)))+~E(f320(x66192,x66193,x66191,x66194),f194(f890(f888(x66192,x66193),a874))) % 191.49/191.41 [6688]~P109(x66882)+E(f333(f195(f881(x66881)),f151(x66881,x66882,x66883,x66884)),f333(f195(f881(x66881)),x66884)) % 191.49/191.41 [6700]~P4(f333(f269(x67003,x67004,x67001),x67002))+P4(f333(f333(x67001,f700(x67002,x67001)),x67002)) % 191.49/191.41 [6740]~P4(f333(f63(x67402),x67404))+P4(f333(f63(x67401),f333(f312(x67402,x67401,x67403),x67404))) % 191.49/191.41 [6962]~P28(x69622,x69621,x69623,x69624)+E(f333(f39(x69621),f333(f312(x69622,x69621,x69623),x69624)),f333(f39(x69622),x69624)) % 191.49/191.41 [6981]E(f333(f312(x69811,x69812,x69813),f333(f313(x69811,x69812,x69813),x69814)),x69814)+~E(f333(f312(x69811,x69812,x69813),f258(f890(x69811,a874))),f258(f890(x69812,a874))) % 191.49/191.41 [7380]~P28(x73801,x73802,x73803,f258(f890(x73801,a874)))+E(f333(f313(x73801,x73802,x73803),f333(f312(x73801,x73802,x73803),x73804)),x73804) % 191.49/191.41 [7705]P4(f333(x77051,x77052))+~P4(f333(f333(f335(x77053),x77052),f333(f173(x77053),f177(x77053,x77051,x77054)))) % 191.49/191.41 [7816]~P4(f333(f333(f335(f881(x78161)),f333(f333(f152(x78161),x78162),x78164)),f162(x78161,x78163)))+P4(f333(f333(f335(x78161),x78162),x78163)) % 191.49/191.41 [7935]~P4(f333(f333(f335(x79351),x79352),f333(f173(x79351),f171(x79351,x79354,x79353))))+P4(f333(f333(f335(x79351),x79352),f333(f173(x79351),x79353))) % 191.49/191.41 [7937]~P4(f333(f333(f335(x79371),x79372),f333(f173(x79371),f175(x79371,x79373,x79374))))+P4(f333(f333(f335(x79371),x79372),f333(f173(x79371),x79373))) % 191.49/191.41 [7938]~P4(f333(f333(f335(x79381),x79382),f333(f173(x79381),f177(x79381,x79384,x79383))))+P4(f333(f333(f335(x79381),x79382),f333(f173(x79381),x79383))) % 191.49/191.41 [7947]E(f333(f195(f881(x79471)),x79472),x79473)+~P4(f333(f333(f335(f881(x79471)),x79472),f333(f173(f881(x79471)),f56(x79471,x79473,x79474)))) % 191.49/191.41 [8051]P4(f333(x80513,x80512))+E(f333(f137(x80511,f333(f333(f10(a874,a874,x80511),a328),f333(a330,x80512))),f333(f137(x80511,x80513),x80514)),f333(f137(x80511,x80513),x80514)) % 191.49/191.41 [8167]E(f333(f333(f166(x81671),f177(x81671,x81672,x81673)),x81674),f333(f333(f166(x81671),x81673),x81674))+~P4(f333(f333(f251(a880),x81674),f333(f195(f881(x81671)),f177(x81671,x81672,x81673)))) % 191.49/191.41 [8251]~P69(x82511)+E(f333(f333(f8(a880,x82511),f333(f333(f10(a880,x82511,a880),x82512),a117)),f333(f303(a880,x82513),x82514)),f333(f333(f8(a880,x82511),x82512),f333(f303(a880,f333(a117,x82513)),f333(a117,x82514)))) % 191.49/191.41 [8260]~P69(x82601)+E(f333(f333(f8(a880,x82601),f333(f333(f10(a880,x82601,a880),x82602),a117)),f304(a880,x82603,x82604)),f333(f333(f8(a880,x82601),x82602),f304(a880,f333(a117,x82603),f333(a117,x82604)))) % 191.49/191.41 [8389]~P28(x83891,x83893,x83894,f258(f890(x83891,a874)))+P28(x83891,f890(x83892,x83893),f333(f333(f10(x83893,f890(x83892,x83893),x83891),f18(x83893,x83892)),x83894),f258(f890(x83891,a874))) % 191.49/191.41 [8478]~P28(x84782,x84781,x84784,x84783)+E(f333(f312(x84781,x84782,f78(x84782,x84781,x84783,x84784)),f333(f312(x84782,x84781,x84784),x84783)),x84783) % 191.49/191.41 [8540]~P4(f333(f333(f335(f889(x85401,x85401)),f333(f333(f263(x85401,x85401),x85402),x85404)),f260(x85401,x85403)))+P4(f333(f333(f335(x85401),x85402),x85403)) % 191.49/191.41 [8628]E(f333(f333(f333(f73(x86281,f884(x86282)),f333(f18(f884(x86282),x86281),f197(x86282))),x86283),f333(f242(x86282),f493(x86283,x86284,x86282,x86281))),x86284)+~E(f184(x86281,x86282,x86284),f333(f333(f311(x86281),x86283),f194(f890(x86281,a874)))) % 191.49/191.41 [8741]~E(f333(f333(f8(x87411,a880),x87414),x87413),f333(a117,x87412))+P4(f333(f333(f335(x87411),f370(x87412,x87413,x87414,x87411)),x87413)) % 191.49/191.41 [8761]~E(f333(f333(f8(x87614,a880),x87611),x87613),f333(a117,x87612))+P4(f333(f333(f251(a880),f2(a880)),f333(x87611,f370(x87612,x87613,x87611,x87614)))) % 191.49/191.41 [8772]~P4(f333(f63(x87722),x87724))+P4(f333(f333(f250(a880),f333(f39(x87721),f333(f312(x87722,x87721,x87723),x87724))),f333(f39(x87722),x87724))) % 191.49/191.41 [8773]E(f333(f333(f263(x87731,x87732),f801(x87733,x87734,x87732,x87731)),f802(x87733,x87734,x87732,x87731)),x87734)+~P4(f333(f333(f335(f889(x87731,x87732)),x87734),f333(f288(x87732,x87731),x87733))) % 191.49/191.41 [8782]P28(x87821,x87822,x87823,x87824)+P4(f333(f333(f335(x87821),f834(x87824,x87823,x87822,x87821)),x87824)) % 191.49/191.41 [8783]P28(x87831,x87832,x87833,x87834)+P4(f333(f333(f335(x87831),f835(x87834,x87833,x87832,x87831)),x87834)) % 191.49/191.41 [8847]P15(x88471,x88472,x88473,x88474)+P4(f333(f333(f335(f889(x88471,x88471)),f603(x88474,x88473,x88472,x88471)),x88473)) % 191.49/191.41 [8910]P4(f333(x89101,x89102))+~P4(f333(x89101,f333(f333(f263(x89103,x89104),f498(x89104,x89103,x89101)),f499(x89104,x89103,x89101)))) % 191.49/191.41 [8929]E(f333(f195(f881(x89291)),x89292),f333(f195(f881(x89291)),x89293))+~P4(f333(f333(f335(f889(f881(x89291),f881(x89291))),f333(f333(f263(f881(x89291),f881(x89291)),x89292),x89293)),f159(x89291,x89294))) % 191.49/191.41 [8930]E(f333(f195(f881(x89301)),x89302),f333(f195(f881(x89301)),x89303))+~P4(f333(f333(f335(f889(f881(x89301),f881(x89301))),f333(f333(f263(f881(x89301),f881(x89301)),x89302),x89303)),f146(x89301,x89304))) % 191.49/191.41 [8931]E(f333(f195(f881(x89311)),x89312),f333(f195(f881(x89311)),x89313))+~P4(f333(f333(f335(f889(f881(x89311),f881(x89311))),f333(f333(f263(f881(x89311),f881(x89311)),x89312),x89313)),f158(x89311,x89314))) % 191.49/191.41 [9004]P4(f333(f333(f250(a880),f156(x90041,x90042,x90043)),f156(x90041,x90044,x90043)))+P4(f333(f333(f335(x90041),f644(x90044,x90042,x90043,x90041)),f333(f173(x90041),x90043))) % 191.49/191.41 [9007]E(f333(f195(f881(x90071)),x90072),f333(f195(f881(x90071)),x90073))+~P4(f333(f333(f335(f889(f881(x90071),f881(x90071))),f333(f333(f263(f881(x90071),f881(x90071)),x90072),x90073)),f309(f881(x90071),f158(x90071,x90074)))) % 191.49/191.41 [9236]~P28(x92361,x92362,x92363,x92364)+~P4(f333(f333(f251(a880),f333(f39(x92362),f333(f312(x92361,x92362,x92363),x92364))),f333(f39(x92361),x92364))) % 191.49/191.41 [9290]~P4(f333(f333(f335(f889(f881(x92901),f881(x92901))),f333(f333(f263(f881(x92901),f881(x92901)),x92902),x92903)),f158(x92901,x92904)))+P4(f333(f333(f335(f889(f881(x92901),f881(x92901))),f333(f333(f263(f881(x92901),f881(x92901)),x92902),x92903)),f159(x92901,f309(x92901,x92904)))) % 191.49/191.41 [9294]~P4(f333(f333(f335(f889(f881(x92941),f881(x92941))),f333(f333(f263(f881(x92941),f881(x92941)),x92942),x92943)),f159(x92941,x92944)))+P4(f333(f333(f335(f889(f881(x92941),f881(x92941))),f333(f333(f263(f881(x92941),f881(x92941)),x92942),x92943)),f309(f881(x92941),f158(x92941,x92944)))) % 191.49/191.41 [9306]P4(f333(f333(f335(f889(x93061,x93061)),f333(f333(f263(x93061,x93061),x93062),x93063)),f309(x93061,x93064)))+~P4(f333(f333(f335(f889(x93061,x93061)),f333(f333(f263(x93061,x93061),x93062),x93063)),f333(f333(f290(x93061,x93061,x93061),x93064),f309(x93061,x93064)))) % 191.49/191.41 [9493]E(f333(f333(f127(x94931),f612(x94932,x94933,x94934,x94931)),f333(f333(f152(x94931),f613(x94932,x94933,x94934,x94931)),f618(x94932,x94933,x94934,x94931))),x94934)+~P4(f333(f333(f335(f889(f881(x94931),f881(x94931))),f333(f333(f263(f881(x94931),f881(x94931)),x94934),x94933)),f158(x94931,x94932))) % 191.49/191.41 [9494]E(f333(f333(f127(x94941),f612(x94942,x94943,x94944,x94941)),f333(f333(f152(x94941),f614(x94942,x94943,x94944,x94941)),f618(x94942,x94943,x94944,x94941))),x94943)+~P4(f333(f333(f335(f889(f881(x94941),f881(x94941))),f333(f333(f263(f881(x94941),f881(x94941)),x94944),x94943)),f158(x94941,x94942))) % 191.49/191.41 [9574]P4(f333(f333(f335(f889(x95741,x95741)),f333(f333(f263(x95741,x95741),x95742),f791(x95743,x95744,x95742,x95741))),f309(x95741,x95743)))+~P4(f333(f333(f335(f889(x95741,x95741)),f333(f333(f263(x95741,x95741),x95742),x95744)),f333(f333(f290(x95741,x95741,x95741),x95743),f309(x95741,x95743)))) % 191.49/191.41 [9657]P4(f333(f333(f250(a880),f156(x96571,x96572,x96573)),f156(x96571,x96574,x96573)))+~P4(f333(f333(f251(a880),f333(x96572,f644(x96574,x96572,x96573,x96571))),f333(x96574,f644(x96574,x96572,x96573,x96571)))) % 191.49/191.41 [9723]P4(f333(f333(f335(f889(x97231,x97231)),f333(f333(f263(x97231,x97231),f789(x97232,x97233,x97234,x97231)),x97233)),f309(x97231,x97232)))+~P4(f333(f333(f335(f889(x97231,x97231)),f333(f333(f263(x97231,x97231),x97234),x97233)),f333(f333(f290(x97231,x97231,x97231),x97232),f309(x97231,x97232)))) % 191.49/191.41 [5231]~E(x52312,x52313)+E(f171(x52311,x52312,f333(f333(f152(x52311),x52313),x52314)),x52314) % 191.49/191.41 [5360]P4(f333(x53602,x53603))+E(f177(x53601,x53602,f333(f333(f152(x53601),x53603),x53604)),f118(x53601)) % 191.49/191.41 [5429]~P80(x54292)+E(f333(f333(f80(f890(x54291,x54292)),x54293),x54294),f333(f80(x54292),f333(x54293,x54294))) % 191.49/191.41 [5441]~E(x54412,f2(a880))+E(f333(f333(f139(x54411),x54412),f333(f333(f152(x54411),x54413),x54414)),f333(f333(f152(x54411),x54413),x54414)) % 191.49/191.41 [5442]P4(f333(x54422,x54423))+E(f333(f137(x54421,x54422),f333(f333(f152(x54421),x54423),x54424)),f333(f137(x54421,x54422),x54424)) % 191.49/191.41 [5571]~E(x55712,x55714)+P4(f333(f333(f333(f311(x55711),x55712),x55713),x55714)) % 191.49/191.41 [5579]E(x55791,f118(x55792))+E(f145(x55793,f333(f333(f155(x55792,x55793),x55794),x55791)),f333(x55794,f145(x55792,x55791))) % 191.49/191.41 [5593]~E(x55931,f65(x55932,x55934))+E(f333(x55931,f333(f333(f311(x55932),x55933),f194(f890(x55932,a874)))),x55933) % 191.49/191.41 [5629]E(x56291,f118(x56292))+E(f333(f142(x56293),f333(f333(f155(x56292,x56293),x56294),x56291)),f333(x56294,f333(f142(x56292),x56291))) % 191.49/191.41 [5731]~P4(f333(x57313,x57314))+P4(f333(f333(f333(f311(x57311),x57312),x57313),x57314)) % 191.49/191.41 [5847]~P21(x58472,x58474,x58471)+E(f333(x58471,f333(f333(f311(x58472),x58473),f194(f890(x58472,a874)))),x58473) % 191.49/191.41 [5871]~E(x58712,x58713)+P4(f333(f333(f335(x58711),x58712),f333(f333(f311(x58711),x58713),x58714))) % 191.49/191.41 [5875]~P6(x58751)+E(f333(f333(f115(x58751),x58752),f333(f333(f115(x58751),x58753),x58754)),f333(f333(f115(x58751),x58753),f333(f333(f115(x58751),x58752),x58754))) % 191.49/191.41 [5877]~P101(x58771)+E(f333(f333(f115(x58771),x58772),f333(f333(f115(x58771),x58773),x58774)),f333(f333(f115(x58771),x58773),f333(f333(f115(x58771),x58772),x58774))) % 191.49/191.41 [5878]~P6(x58781)+E(f333(f333(f106(x58781),x58782),f333(f333(f106(x58781),x58783),x58784)),f333(f333(f106(x58781),x58783),f333(f333(f106(x58781),x58782),x58784))) % 191.49/191.41 [5880]~P102(x58801)+E(f333(f333(f106(x58801),x58802),f333(f333(f106(x58801),x58803),x58804)),f333(f333(f106(x58801),x58803),f333(f333(f106(x58801),x58802),x58804))) % 191.49/191.41 [5881]~P115(x58811)+E(f333(f333(f81(x58811),x58812),f333(f333(f81(x58811),x58813),x58814)),f333(f333(f81(x58811),x58813),f333(f333(f81(x58811),x58812),x58814))) % 191.49/191.41 [5882]~P115(x58821)+E(f333(f333(f82(x58821),x58822),f333(f333(f82(x58821),x58823),x58824)),f333(f333(f82(x58821),x58823),f333(f333(f82(x58821),x58822),x58824))) % 191.49/191.41 [5884]~P109(x58841)+E(f333(f333(f248(x58841),x58842),f333(f333(f248(x58841),x58843),x58844)),f333(f333(f248(x58841),x58843),f333(f333(f248(x58841),x58842),x58844))) % 191.49/191.41 [5886]~P109(x58861)+E(f333(f333(f249(x58861),x58862),f333(f333(f249(x58861),x58863),x58864)),f333(f333(f249(x58861),x58863),f333(f333(f249(x58861),x58862),x58864))) % 191.49/191.41 [5891]E(x58911,x58912)+E(f171(x58913,x58911,f333(f333(f152(x58913),x58912),x58914)),f333(f333(f152(x58913),x58912),f171(x58913,x58911,x58914))) % 191.49/191.41 [5904]~P4(f333(x59042,x59043))+E(f333(f137(x59041,x59042),f333(f333(f152(x59041),x59043),x59044)),f333(f333(f152(x59041),x59043),f333(f137(x59041,x59042),x59044))) % 191.49/191.41 [6041]~P4(f333(x60412,x60413))+E(f177(x60411,x60412,f333(f333(f152(x60411),x60413),x60414)),f333(f333(f152(x60411),x60413),f177(x60411,x60412,x60414))) % 191.49/191.41 [6092]P27(x60921,x60922,x60923)+~P27(x60921,x60922,f333(f333(f311(f879(x60921)),x60924),x60923)) % 191.49/191.41 [6105]E(x61051,f194(f890(x61052,a874)))+E(f333(f333(f43(x61052,f890(x61053,a874)),x61051),f333(f18(f890(x61053,a874),x61052),x61054)),x61054) % 191.49/191.41 [6106]E(x61061,f194(f890(x61062,a874)))+E(f333(f333(f44(x61062,f890(x61063,a874)),x61061),f333(f18(f890(x61063,a874),x61062),x61064)),x61064) % 191.49/191.41 [6115]~E(x61154,f194(f890(x61152,a874)))+E(f333(f333(f270(x61151,x61152),x61153),f333(f18(f890(x61152,a874),x61151),x61154)),f194(f890(f889(x61151,x61152),a874))) % 191.49/191.41 [6116]~E(x61163,f194(f890(x61161,a874)))+E(f333(f333(f270(x61161,x61162),x61163),f333(f18(f890(x61162,a874),x61161),x61164)),f194(f890(f889(x61161,x61162),a874))) % 191.49/191.41 [6164]E(x61641,f2(a880))+E(f333(f333(f139(x61642),x61641),f333(f333(f152(x61642),x61643),x61644)),f333(f333(f139(x61642),f333(f333(f3(a880),x61641),f79(a880))),x61644)) % 191.49/191.41 [6189]E(x61891,f194(f890(x61892,a874)))+E(f333(f312(x61892,x61893,f333(f18(x61893,x61892),x61894)),x61891),f333(f333(f311(x61893),x61894),f194(f890(x61893,a874)))) % 191.49/191.41 [6192]E(f333(f313(x61921,x61922,f333(f18(x61922,x61921),x61923)),x61924),f194(f890(x61921,a874)))+P4(f333(f333(f335(x61922),x61923),x61924)) % 191.49/191.41 [6258]~E(x62583,f194(f890(x62581,a874)))+E(f333(f333(f43(x62581,f890(x62582,a874)),x62583),f333(f18(f890(x62582,a874),x62581),x62584)),f258(f890(x62582,a874))) % 191.49/191.41 [6259]~E(x62593,f194(f890(x62591,a874)))+E(f333(f333(f44(x62591,f890(x62592,a874)),x62593),f333(f18(f890(x62592,a874),x62591),x62594)),f194(f890(x62592,a874))) % 191.49/191.41 [6261]~P60(x62611)+E(f46(x62611,f333(f333(f82(x62611),x62612),x62613),f333(f333(f82(x62611),x62612),x62614)),f333(f333(f82(x62611),x62612),f46(x62611,x62613,x62614))) % 191.49/191.41 [6425]E(f333(f313(x64251,x64252,f333(f18(x64252,x64251),x64253)),x64254),f258(f890(x64251,a874)))+~P4(f333(f333(f335(x64252),x64253),x64254)) % 191.49/191.41 [6448]~P4(f333(f333(f335(x64481),x64482),x64484))+P4(f333(f333(f335(x64481),x64482),f333(f333(f311(x64481),x64483),x64484))) % 191.49/191.41 [6453]P4(f333(x64531,x64532))+~P4(f333(f161(x64533,x64531),f333(f333(f152(x64533),x64532),x64534))) % 191.49/191.41 [6462]~E(x64623,f333(f333(f3(a880),f333(f195(f881(x64621)),x64622)),f79(a880)))+E(f119(x64621,f333(f333(f160(x64621,x64622),x64623),x64624)),f119(x64621,x64622)) % 191.49/191.41 [6480]~P109(x64801)+E(f333(f333(f106(f890(x64801,a874)),f333(f302(x64801),x64802)),f304(x64801,x64803,x64804)),f304(x64801,x64803,f333(f333(f248(x64801),x64802),x64804))) % 191.49/191.41 [6481]~P109(x64811)+E(f333(f333(f106(f890(x64811,a874)),f333(f257(x64811),x64812)),f304(x64811,x64813,x64814)),f304(x64811,f333(f333(f249(x64811),x64812),x64813),x64814)) % 191.49/191.41 [6496]E(f333(f333(f106(f890(x64961,a874)),x64962),f333(f333(f311(x64961),x64963),x64964)),f333(f333(f106(f890(x64961,a874)),x64962),x64964))+P4(f333(f333(f335(x64961),x64963),x64962)) % 191.49/191.41 [6508]E(f171(x65081,x65082,f333(f333(f127(x65081),x65083),x65084)),f333(f333(f127(x65081),x65083),f171(x65081,x65082,x65084)))+P4(f333(f333(f335(x65081),x65082),f333(f173(x65081),x65083))) % 191.49/191.41 [6512]~P83(x65121)+E(f333(f333(f82(x65121),f333(f333(f264(x65121),x65122),x65123)),f333(f333(f264(x65121),x65122),x65124)),f333(f333(f264(x65121),x65122),f333(f333(f81(a880),x65123),x65124))) % 191.49/191.41 [6513]~P115(x65131)+E(f333(f333(f82(x65131),f333(f333(f264(x65131),x65132),x65133)),f333(f333(f264(x65131),x65132),x65134)),f333(f333(f264(x65131),x65132),f333(f333(f81(a880),x65133),x65134))) % 191.49/191.41 [6546]~P99(x65461)+E(f333(f333(f106(x65461),f333(f333(f115(x65461),x65462),x65463)),f333(f333(f115(x65461),x65462),x65464)),f333(f333(f115(x65461),x65462),f333(f333(f106(x65461),x65463),x65464))) % 191.49/191.41 [6547]~P99(x65471)+E(f333(f333(f115(x65471),f333(f333(f106(x65471),x65472),x65473)),f333(f333(f106(x65471),x65472),x65474)),f333(f333(f106(x65471),x65472),f333(f333(f115(x65471),x65473),x65474))) % 191.49/191.41 [6548]~P115(x65481)+E(f333(f333(f81(x65481),f333(f333(f82(x65481),x65482),x65483)),f333(f333(f82(x65481),x65482),x65484)),f333(f333(f82(x65481),x65482),f333(f333(f81(x65481),x65483),x65484))) % 191.49/191.41 [6549]~P109(x65491)+E(f333(f333(f249(x65491),f333(f333(f248(x65491),x65492),x65493)),f333(f333(f248(x65491),x65492),x65494)),f333(f333(f248(x65491),x65492),f333(f333(f249(x65491),x65493),x65494))) % 191.49/191.41 [6550]~P109(x65501)+E(f333(f333(f248(x65501),f333(f333(f249(x65501),x65502),x65503)),f333(f333(f249(x65501),x65502),x65504)),f333(f333(f249(x65501),x65502),f333(f333(f248(x65501),x65503),x65504))) % 191.49/191.41 [6582]~P60(x65821)+E(f46(x65821,f333(f333(f82(x65821),x65822),x65823),f333(f333(f82(x65821),x65824),x65823)),f333(f333(f82(x65821),f46(x65821,x65822,x65824)),x65823)) % 191.49/191.41 [6585]~E(f333(f195(f881(x65851)),x65853),f333(f195(f881(x65852)),x65854))+E(f333(f333(f155(f889(x65851,x65852),x65852),f271(x65851,x65852)),f333(f333(f182(x65851,x65852),x65853),x65854)),x65854) % 191.49/191.41 [6586]~E(f333(f195(f881(x65861)),x65863),f333(f195(f881(x65862)),x65864))+E(f333(f333(f155(f889(x65861,x65862),x65861),f262(x65861,x65862)),f333(f333(f182(x65861,x65862),x65863),x65864)),x65863) % 191.49/191.41 [6592]P4(f333(f161(x65921,x65922),x65923))+~P4(f333(f161(x65921,x65922),f333(f333(f152(x65921),x65924),x65923))) % 191.49/191.41 [6593]P4(f333(f161(x65931,x65932),x65933))+~P4(f333(f161(x65931,x65932),f333(f333(f127(x65931),x65934),x65933))) % 191.49/191.41 [6594]P4(f333(f161(x65941,x65942),x65943))+~P4(f333(f161(x65941,x65942),f333(f333(f127(x65941),x65943),x65944))) % 191.49/191.41 [6599]~P61(x65991)+E(f46(x65991,f333(f333(f3(x65991),x65992),f46(x65991,x65993,x65994)),x65994),f46(x65991,f333(f333(f3(x65991),x65992),x65993),x65994)) % 191.49/191.41 [6601]~P60(x66011)+E(f46(x66011,f333(f333(f82(x66011),x66012),f46(x66011,x66013,x66014)),x66014),f46(x66011,f333(f333(f82(x66011),x66012),x66013),x66014)) % 191.49/191.41 [6602]~P60(x66021)+E(f46(x66021,f333(f333(f81(x66021),x66022),f46(x66021,x66023,x66024)),x66024),f46(x66021,f333(f333(f81(x66021),x66022),x66023),x66024)) % 191.49/191.41 [6682]~P109(x66821)+E(f333(f333(f106(f890(x66821,a874)),f304(x66821,x66822,x66823)),f333(f302(x66821),x66824)),f304(x66821,x66822,f333(f333(f248(x66821),x66823),x66824))) % 191.49/191.41 [6683]~P109(x66831)+E(f333(f333(f106(f890(x66831,a874)),f304(x66831,x66832,x66833)),f333(f257(x66831),x66834)),f304(x66831,f333(f333(f249(x66831),x66832),x66834),x66833)) % 191.49/191.41 [6686]~E(f333(f195(f881(x66861)),x66863),f333(f195(f881(x66862)),x66864))+E(f333(f333(f182(x66861,x66862),f333(f170(x66861),x66863)),f333(f170(x66862),x66864)),f333(f170(f889(x66861,x66862)),f333(f333(f182(x66861,x66862),x66863),x66864))) % 191.49/191.41 [6696]E(x66961,f333(f333(f3(a880),f333(f195(f881(x66962)),x66963)),f79(a880)))+E(f119(x66962,f333(f333(f160(x66962,x66963),x66961),x66964)),f333(f333(f160(x66962,f119(x66962,x66963)),x66961),x66964)) % 191.49/191.41 [6711]~P4(f333(f138(x67112),x67114))+P4(f333(f138(f889(x67111,x67112)),f333(f333(f182(x67111,x67112),x67113),x67114))) % 191.49/191.41 [6712]~P4(f333(f138(x67121),x67123))+P4(f333(f138(f889(x67121,x67122)),f333(f333(f182(x67121,x67122),x67123),x67124))) % 191.49/191.41 [6965]E(f333(f333(f40(a880),x69651),x69652),x69653)+~P4(f333(f49(x69651,x69652),f333(f333(f263(a880,a880),x69653),x69654))) % 191.49/191.41 [6989]E(f46(a880,x69891,x69892),x69893)+~P4(f333(f49(x69891,x69892),f333(f333(f263(a880,a880),x69894),x69893))) % 191.49/191.41 [6992]P4(f333(f138(x69921),x69922))+~P4(f333(f138(x69923),f333(f333(f155(x69921,x69923),x69924),x69922))) % 191.49/191.41 [7000]~P27(x70001,x70002,f333(f333(f311(f879(x70001)),x70003),x70004))+P27(x70001,x70002,f333(f333(f311(f879(x70001)),x70003),f194(f890(f879(x70001),a874)))) % 191.49/191.41 [7006]P4(f333(f333(f201(x70061),x70062),x70063))+~P4(f333(f333(f333(f333(a203,x70061),x70062),x70064),x70063)) % 191.49/191.41 [7077]E(f171(x70771,x70772,f333(f333(f127(x70771),x70773),x70774)),f333(f333(f127(x70771),f171(x70771,x70772,x70773)),x70774))+~P4(f333(f333(f335(x70771),x70772),f333(f173(x70771),x70773))) % 191.49/191.41 [7167]~P61(x71671)+E(f46(x71671,f333(f333(f3(x71671),f46(x71671,x71672,x71673)),x71674),x71673),f46(x71671,f333(f333(f3(x71671),x71672),x71674),x71673)) % 191.49/191.41 [7170]~P60(x71701)+E(f46(x71701,f333(f333(f81(x71701),f46(x71701,x71702,x71703)),x71704),x71703),f46(x71701,f333(f333(f81(x71701),x71702),x71704),x71703)) % 191.49/191.41 [7171]~P60(x71711)+E(f46(x71711,f333(f333(f82(x71711),f46(x71711,x71712,x71713)),x71714),x71713),f46(x71711,f333(f333(f82(x71711),x71712),x71714),x71713)) % 191.49/191.41 [7352]~E(x73521,f333(f333(f152(x73522),x73523),x73524))+~P4(f333(f333(f250(a880),f333(f195(f881(x73522)),x73521)),f333(f195(f881(x73522)),x73524))) % 191.49/191.41 [7426]~E(f333(f178(x74261,x74262),x74263),f333(f178(x74261,x74262),x74264))+E(f333(f312(f889(x74261,x74262),x74261,f262(x74261,x74262)),f333(f173(f889(x74261,x74262)),x74263)),f333(f312(f889(x74261,x74262),x74261,f262(x74261,x74262)),f333(f173(f889(x74261,x74262)),x74264))) % 191.49/191.41 [7556]P28(x75561,x75562,x75563,f333(f173(x75561),x75564))+~P4(f333(f138(x75562),f333(f333(f155(x75561,x75562),x75563),x75564))) % 191.49/191.41 [7628]~P4(f333(f333(f250(f890(x76281,a874)),x76282),x76284))+P4(f333(f333(f250(f890(x76281,a874)),x76282),f333(f333(f311(x76281),x76283),x76284))) % 191.49/191.41 [7661]~P61(x76611)+E(f46(x76611,f333(f333(f3(x76611),f46(x76611,x76612,x76613)),f46(x76611,x76614,x76613)),x76613),f46(x76611,f333(f333(f3(x76611),x76612),x76614),x76613)) % 191.49/191.41 [7662]~P60(x76621)+E(f46(x76621,f333(f333(f81(x76621),f46(x76621,x76622,x76623)),f46(x76621,x76624,x76623)),x76623),f46(x76621,f333(f333(f81(x76621),x76622),x76624),x76623)) % 191.49/191.41 [7663]~P60(x76631)+E(f46(x76631,f333(f333(f82(x76631),f46(x76631,x76632,x76633)),f46(x76631,x76634,x76633)),x76633),f46(x76631,f333(f333(f82(x76631),x76632),x76634),x76633)) % 191.49/191.41 [7761]P4(f333(f333(f333(f333(a203,x77611),x77612),f333(a117,x77613)),x77614))+~P4(f333(f333(f333(f333(a203,x77611),x77612),x77613),x77614)) % 191.49/191.41 [7770]~E(f333(x77704,f527(x77704,x77703,x77701,x77702)),f194(f890(x77702,a874)))+E(f333(f333(f44(x77701,f890(x77702,a874)),x77703),x77704),f194(f890(x77702,a874))) % 191.49/191.41 [7771]~E(f333(x77714,f502(x77714,x77713,x77711,x77712)),f258(f890(x77712,a874)))+E(f333(f333(f43(x77711,f890(x77712,a874)),x77713),x77714),f258(f890(x77712,a874))) % 191.49/191.41 [7772]~E(f333(x77724,f503(x77724,x77723,x77722,x77721)),f258(f890(x77722,a874)))+E(f333(f333(f43(x77721,f890(x77722,a874)),x77723),x77724),f258(f890(x77722,a874))) % 191.49/191.41 [7773]~E(f333(x77734,f528(x77734,x77733,x77732,x77731)),f194(f890(x77732,a874)))+E(f333(f333(f44(x77731,f890(x77732,a874)),x77733),x77734),f194(f890(x77732,a874))) % 191.49/191.41 [8168]P4(f333(x81681,x81682))+~P4(f333(f333(f335(x81683),x81682),f333(f333(f106(f890(x81683,a874)),x81684),f333(f255(x81683),x81681)))) % 191.49/191.41 [8206]~P4(f333(f333(f250(f890(x82061,a874)),x82063),x82064))+P4(f333(f333(f250(f890(x82061,a874)),f333(f333(f311(x82061),x82062),x82063)),f333(f333(f311(x82061),x82062),x82064))) % 191.49/191.41 [8370]P4(f333(f333(f201(x83701),x83702),f369(x83703,x83702,x83704,x83701)))+~P4(f333(f333(f201(f34(x83701,x83704)),x83702),x83703)) % 191.49/191.41 [8371]P4(f333(f333(f201(x83711),x83712),f389(x83713,x83712,x83714,x83711)))+~P4(f333(f333(f201(f34(x83711,x83714)),x83712),x83713)) % 191.49/191.41 [8380]P4(f333(x83802,x83803))+E(f333(f333(f139(x83801),f333(f195(f881(x83801)),f177(x83801,x83802,f333(f333(f152(x83801),x83803),x83804)))),f333(f333(f152(x83801),x83803),x83804)),f333(f333(f152(x83801),x83803),x83804)) % 191.49/191.41 [8492]~P4(f333(f333(f251(a880),f333(x84924,x84922)),f333(x84924,x84923)))+P4(f333(f333(f335(f889(x84921,x84921)),f333(f333(f263(x84921,x84921),x84922),x84923)),f333(f333(f289(a880,x84921),a254),x84924))) % 191.49/191.41 [8585]~P4(f333(x85852,f737(x85854,x85852,x85853,x85851)))+E(f177(x85851,x85852,f333(f333(f127(x85851),x85853),x85854)),f333(f333(f127(x85851),x85853),f177(x85851,x85852,x85854))) % 191.49/191.41 [8648]P28(f881(x86481),f881(x86482),f333(f155(x86481,x86482),x86483),x86484)+~P28(x86481,x86482,x86483,f41(f890(x86481,a874),f333(f312(f881(x86481),f890(x86481,a874),f173(x86481)),x86484))) % 191.49/191.41 [8713]~P4(f333(x87132,x87133))+E(f333(f333(f139(x87131),f333(f195(f881(x87131)),f177(x87131,x87132,f333(f333(f152(x87131),x87133),x87134)))),f333(f333(f152(x87131),x87133),x87134)),f333(f333(f139(x87131),f333(f195(f881(x87131)),f177(x87131,x87132,x87134))),x87134)) % 191.49/191.41 [8753]~E(x87532,x87533)+E(f333(f137(x87531,f333(f333(f10(a874,a874,x87531),a328),f333(a330,x87532))),f333(f333(f152(x87531),x87533),x87534)),f333(f137(x87531,f333(f333(f10(a874,a874,x87531),a328),f333(a330,x87532))),x87534)) % 191.49/191.41 [8762]E(f333(f333(f44(x87621,f890(x87622,a874)),x87623),x87624),f194(f890(x87622,a874)))+P4(f333(f333(f335(x87621),f527(x87624,x87623,x87621,x87622)),x87623)) % 191.49/191.41 [8763]E(f333(f333(f43(x87631,f890(x87632,a874)),x87633),x87634),f258(f890(x87632,a874)))+P4(f333(f333(f335(x87631),f502(x87634,x87633,x87631,x87632)),x87633)) % 191.49/191.41 [8764]E(f333(f333(f43(x87641,f890(x87642,a874)),x87643),x87644),f258(f890(x87642,a874)))+P4(f333(f333(f335(x87641),f503(x87644,x87643,x87642,x87641)),x87643)) % 191.49/191.41 [8765]E(f333(f333(f44(x87651,f890(x87652,a874)),x87653),x87654),f194(f890(x87652,a874)))+P4(f333(f333(f335(x87651),f528(x87654,x87653,x87652,x87651)),x87653)) % 191.49/191.41 [8804]P4(f333(f333(f251(a880),f333(x88041,x88042)),f333(x88041,x88043)))+~P4(f333(f333(f335(f889(x88044,x88044)),f333(f333(f263(x88044,x88044),x88042),x88043)),f333(f333(f289(a880,x88044),a254),x88041))) % 191.49/191.41 [8826]E(f177(x88261,x88262,f333(f333(f127(x88261),x88263),x88264)),f333(f333(f127(x88261),x88263),f177(x88261,x88262,x88264)))+P4(f333(f333(f335(x88261),f737(x88264,x88262,x88263,x88261)),f333(f173(x88261),x88263))) % 191.49/191.41 [8864]P4(f333(f333(f201(x88641),f369(x88642,x88643,x88641,x88644)),x88642))+~P4(f333(f333(f201(f34(x88644,x88641)),x88643),x88642)) % 191.49/191.41 [8865]P4(f333(f333(f201(x88651),f389(x88652,x88653,x88651,x88654)),x88652))+~P4(f333(f333(f201(f34(x88654,x88651)),x88653),x88652)) % 191.49/191.41 [8993]P4(f333(f333(f335(x89931),f558(x89932,x89933,x89934,x89931)),x89933))+~P4(f333(f333(f335(f890(x89931,a874)),x89934),f333(f333(f62(x89931),x89933),x89932))) % 191.49/191.41 [8996]E(x89961,x89962)+~P4(f333(f333(f335(f889(x89963,x89963)),f333(f333(f263(x89963,x89963),x89961),x89962)),f333(f333(f189(f889(x89963,x89963),a874),f2(a880)),x89964))) % 191.49/191.41 [9061]E(f333(f287(x90611,x90611,x90612),f333(f333(f311(x90611),f558(x90612,x90613,x90614,x90611)),f194(f890(x90611,a874)))),x90614)+~P4(f333(f333(f335(f890(x90611,a874)),x90614),f333(f333(f62(x90611),x90613),x90612))) % 191.49/191.41 [9066]~P4(f333(f333(f335(f889(x90661,x90661)),f333(f333(f263(x90661,x90661),x90663),x90662)),f309(x90661,x90664)))+P4(f333(f333(f335(f889(x90661,x90661)),f333(f333(f263(x90661,x90661),x90662),x90663)),f309(x90661,f333(f288(x90661,x90661),x90664)))) % 191.49/191.41 [9078]~P60(x90781)+E(f333(f333(f81(x90781),f333(f333(f81(x90781),f333(f333(f82(x90781),x90782),f333(f333(f40(x90781),x90783),x90782))),f46(x90781,x90783,x90782))),x90784),f333(f333(f81(x90781),x90783),x90784)) % 191.49/191.41 [9093]~P4(f333(f333(f335(x90931),x90933),x90934))+P4(f333(f333(f335(f890(x90931,a874)),f333(f287(x90931,x90931,x90932),f333(f333(f311(x90931),x90933),f194(f890(x90931,a874))))),f333(f333(f62(x90931),x90934),x90932))) % 191.49/191.41 [9105]P4(f333(f333(f335(f889(x91051,x91051)),f333(f333(f263(x91051,x91051),x91052),x91053)),f309(x91051,x91054)))+~P4(f333(f333(f335(f889(x91051,x91051)),f333(f333(f263(x91051,x91051),x91053),x91052)),f309(x91051,f333(f288(x91051,x91051),x91054)))) % 191.49/191.41 [9200]E(f333(f333(f160(x92001,f333(f170(x92001),x92002)),f333(f333(f3(a880),f333(f333(f3(a880),f333(f195(f881(x92001)),x92002)),x92003)),f79(a880))),x92004),f333(f170(x92001),f333(f333(f160(x92001,x92002),x92003),x92004)))+~P4(f333(f333(f251(a880),x92003),f333(f195(f881(x92001)),x92002))) % 191.49/191.41 [9203]~P4(f333(x92032,f730(x92034,x92032,x92033,x92031)))+E(f333(f333(f139(x92031),f333(f195(f881(x92031)),f177(x92031,x92032,f333(f333(f127(x92031),x92033),x92034)))),f333(f333(f127(x92031),x92033),x92034)),f333(f333(f139(x92031),f333(f195(f881(x92031)),f177(x92031,x92032,x92034))),x92034)) % 191.49/191.41 [9242]~P28(x92422,x92421,x92423,f258(f890(x92422,a874)))+P4(f333(f333(f250(f890(x92421,a874)),f333(f312(x92422,x92421,x92423),f333(f80(f890(x92422,a874)),x92424))),f333(f80(f890(x92421,a874)),f333(f312(x92422,x92421,x92423),x92424)))) % 191.49/191.41 [9255]~P9(x92551)+E(f333(f143(x92551,x92552,f333(f9(x92552,x92551,x92551),f333(f333(f10(x92551,f890(x92551,x92551),x92552),f106(x92551)),x92553)),f258(x92551)),x92554),f333(f333(f43(x92552,x92551),f333(f173(x92552),x92554)),x92553)) % 191.49/191.41 [9256]~P9(x92561)+E(f333(f143(x92561,x92562,f333(f9(x92562,x92561,x92561),f333(f333(f10(x92561,f890(x92561,x92561),x92562),f115(x92561)),x92563)),f194(x92561)),x92564),f333(f333(f44(x92562,x92561),f333(f173(x92562),x92564)),x92563)) % 191.49/191.41 [9270]E(f333(f333(f139(x92701),f333(f195(f881(x92701)),f177(x92701,x92702,f333(f333(f127(x92701),x92703),x92704)))),f333(f333(f127(x92701),x92703),x92704)),f333(f333(f139(x92701),f333(f195(f881(x92701)),f177(x92701,x92702,x92704))),x92704))+P4(f333(f333(f335(x92701),f730(x92704,x92702,x92703,x92701)),f333(f173(x92701),x92703))) % 191.49/191.41 [9339]~P4(f333(f333(f335(f889(f881(x93394),f881(x93394))),f333(f333(f263(f881(x93394),f881(x93394)),x93393),x93392)),f158(x93394,x93391)))+P4(f333(f333(f251(a880),f609(x93391,x93392,x93393,x93394)),f333(f195(f881(x93394)),x93393))) % 191.49/191.41 [9340]~P60(x93401)+E(f333(f333(f81(x93401),f333(f333(f81(x93401),f333(f333(f82(x93401),f333(f333(f40(x93401),x93402),x93403)),x93403)),f46(x93401,x93402,x93403))),x93404),f333(f333(f81(x93401),x93402),x93404)) % 191.49/191.41 [9373]~P4(f333(f333(f335(f889(f881(x93731),f881(x93731))),f333(f333(f263(f881(x93731),f881(x93731)),x93732),x93733)),f333(f288(f881(x93731),f881(x93731)),f158(x93731,x93734))))+P4(f333(f333(f335(f889(f881(x93731),f881(x93731))),f333(f333(f263(f881(x93731),f881(x93731)),x93732),x93733)),f158(x93731,f333(f288(x93731,x93731),x93734)))) % 191.49/191.41 [9374]P4(f333(f333(f335(f889(f881(x93741),f881(x93741))),f333(f333(f263(f881(x93741),f881(x93741)),x93742),x93743)),f333(f288(f881(x93741),f881(x93741)),f158(x93741,x93744))))+~P4(f333(f333(f335(f889(f881(x93741),f881(x93741))),f333(f333(f263(f881(x93741),f881(x93741)),x93742),x93743)),f158(x93741,f333(f288(x93741,x93741),x93744)))) % 191.49/191.41 [9401]~P4(f333(f333(f335(x94011),x94013),f333(f261(x94011,x94012),x94014)))+P4(f333(f333(f335(f889(x94011,x94012)),f333(f333(f263(x94011,x94012),x94013),f713(x94014,x94012,x94013,x94011))),x94014)) % 191.49/191.41 [9402]~P4(f333(f333(f335(x94021),x94023),f333(f261(x94021,x94022),x94024)))+P4(f333(f333(f335(f889(x94021,x94022)),f333(f333(f263(x94021,x94022),x94023),f715(x94024,x94022,x94023,x94021))),x94024)) % 191.49/191.41 [9524]~P4(f333(f63(f884(x95241)),f333(f312(x95242,f884(x95241),x95243),f258(f890(x95242,a874)))))+P4(f333(f63(f884(x95241)),f333(f312(x95242,f884(x95241),f185(x95242,x95241,x95243,f333(f178(x95242,x95241),x95244))),f258(f890(x95242,a874))))) % 191.49/191.41 [9569]~P4(f333(f333(f335(f889(x95691,x95691)),f333(f333(f263(x95691,x95691),x95692),x95694)),f333(f333(f290(x95691,x95691,x95691),x95693),f309(x95691,x95693))))+P4(f333(f333(f335(f889(x95691,x95691)),f333(f333(f263(x95691,x95691),x95692),f789(x95693,x95694,x95692,x95691))),x95693)) % 191.49/191.41 [9762]~P4(f333(f333(f335(f889(x97622,x97621)),x97624),f333(f288(x97621,x97622),x97623)))+P4(f333(f333(f335(f889(x97621,x97622)),f333(f333(f263(x97621,x97622),f802(x97623,x97624,x97621,x97622)),f801(x97623,x97624,x97621,x97622))),x97623)) % 191.49/191.41 [9793]~P4(f333(f333(f335(f889(f881(x97931),f881(x97931))),f333(f333(f263(f881(x97931),f881(x97931)),x97934),x97933)),f158(x97931,x97932)))+P4(f333(f333(f335(f889(x97931,x97931)),f333(f333(f263(x97931,x97931),f613(x97932,x97933,x97934,x97931)),f614(x97932,x97933,x97934,x97931))),x97932)) % 191.49/191.41 [9879]~P4(f333(f333(f335(f889(f881(x98791),f881(x98791))),f333(f333(f263(f881(x98791),f881(x98791)),x98792),x98794)),f158(x98791,x98793)))+P4(f333(f333(f335(f889(x98791,x98791)),f333(f333(f263(x98791,x98791),f333(f333(f166(x98791),x98792),f609(x98793,x98794,x98792,x98791))),f610(x98793,x98794,x98792,x98791))),x98793)) % 191.49/191.41 [9900]~P4(f333(f63(x99002),x99004))+E(f333(f333(f333(f67(f890(x99001,a874),x99002,f115(f890(x99001,a874))),f333(f333(f9(x99002,f890(x99001,a874),f890(x99001,a874)),f333(f333(f10(x99001,f890(f890(x99001,a874),f890(x99001,a874)),x99002),f311(x99001)),x99003)),f194(f890(x99001,a874)))),f194(f890(x99001,a874))),x99004),f333(f312(x99002,x99001,x99003),x99004)) % 191.49/191.41 [9980]~P28(x99801,x99802,x99803,f258(f890(x99801,a874)))+P4(f333(f333(f250(f890(x99801,a874)),f333(f313(x99801,x99802,x99803),f333(f333(f311(x99802),x99804),f194(f890(x99802,a874))))),f333(f333(f311(x99801),f86(x99801,f333(f333(f9(x99801,x99802,a874),f333(f333(f10(x99802,f890(x99802,a874),x99801),a330),x99803)),x99804))),f194(f890(x99801,a874))))) % 191.49/191.41 [5638]~E(f333(f333(f127(x56381),x56382),x56384),x56383)+E(f333(f333(f174(x56381),f333(f195(f881(x56381)),x56382)),x56383),x56382) % 191.49/191.41 [5639]~E(f333(f333(f127(x56392),x56393),x56391),x56394)+E(x56391,f333(f333(f139(x56392),f333(f195(f881(x56392)),x56393)),x56394)) % 191.49/191.41 [5650]~E(x56504,f2(a880))+E(f333(f333(f166(x56501),f333(f333(f152(x56501),x56502),x56503)),x56504),x56502) % 191.49/191.41 [6177]~P115(x61771)+E(f333(f333(f264(x61771),f333(f333(f264(x61771),x61772),x61773)),x61774),f333(f333(f264(x61771),x61772),f333(f333(f82(a880),x61773),x61774))) % 191.49/191.41 [6178]~P83(x61781)+E(f333(f333(f264(x61781),f333(f333(f264(x61781),x61782),x61783)),x61784),f333(f333(f264(x61781),x61782),f333(f333(f82(a880),x61783),x61784))) % 191.49/191.41 [6190]E(x61901,f2(a880))+E(f333(f333(f166(x61902),f333(f333(f152(x61902),x61903),x61904)),x61901),f333(f333(f166(x61902),x61904),f333(f333(f3(a880),x61901),f79(a880)))) % 191.49/191.41 [6216]~P118(x62161)+E(f333(f333(f291(x62161),f333(f333(f82(x62161),x62162),x62163)),x62164),f333(f333(f82(x62161),x62162),f333(f333(f291(x62161),x62163),x62164))) % 191.49/191.41 [6217]~P6(x62171)+E(f333(f333(f115(x62171),f333(f333(f115(x62171),x62172),x62173)),x62174),f333(f333(f115(x62171),x62172),f333(f333(f115(x62171),x62173),x62174))) % 191.49/191.41 [6219]~P101(x62191)+E(f333(f333(f115(x62191),f333(f333(f115(x62191),x62192),x62193)),x62194),f333(f333(f115(x62191),x62192),f333(f333(f115(x62191),x62193),x62194))) % 191.49/191.41 [6220]~P6(x62201)+E(f333(f333(f106(x62201),f333(f333(f106(x62201),x62202),x62203)),x62204),f333(f333(f106(x62201),x62202),f333(f333(f106(x62201),x62203),x62204))) % 191.49/191.41 [6222]~P102(x62221)+E(f333(f333(f106(x62221),f333(f333(f106(x62221),x62222),x62223)),x62224),f333(f333(f106(x62221),x62222),f333(f333(f106(x62221),x62223),x62224))) % 191.49/191.41 [6223]~P72(x62231)+E(f333(f333(f81(x62231),f333(f333(f81(x62231),x62232),x62233)),x62234),f333(f333(f81(x62231),x62232),f333(f333(f81(x62231),x62233),x62234))) % 191.49/191.41 [6224]~P115(x62241)+E(f333(f333(f81(x62241),f333(f333(f81(x62241),x62242),x62243)),x62244),f333(f333(f81(x62241),x62242),f333(f333(f81(x62241),x62243),x62244))) % 191.49/191.41 [6225]~P115(x62251)+E(f333(f333(f82(x62251),f333(f333(f82(x62251),x62252),x62253)),x62254),f333(f333(f82(x62251),x62252),f333(f333(f82(x62251),x62253),x62254))) % 191.49/191.41 [6226]~P73(x62261)+E(f333(f333(f82(x62261),f333(f333(f82(x62261),x62262),x62263)),x62264),f333(f333(f82(x62261),x62262),f333(f333(f82(x62261),x62263),x62264))) % 191.49/191.41 [6229]~P109(x62291)+E(f333(f333(f248(x62291),f333(f333(f248(x62291),x62292),x62293)),x62294),f333(f333(f248(x62291),x62292),f333(f333(f248(x62291),x62293),x62294))) % 191.49/191.41 [6231]~P109(x62311)+E(f333(f333(f249(x62311),f333(f333(f249(x62311),x62312),x62313)),x62314),f333(f333(f249(x62311),x62312),f333(f333(f249(x62311),x62313),x62314))) % 191.49/191.41 [6242]~P60(x62421)+E(f46(x62421,f333(f333(f81(x62421),x62422),f333(f333(f82(x62421),x62423),x62424)),x62424),f46(x62421,x62422,x62424)) % 191.49/191.41 [6243]~P60(x62431)+E(f46(x62431,f333(f333(f81(x62431),x62432),f333(f333(f82(x62431),x62433),x62434)),x62433),f46(x62431,x62432,x62433)) % 191.49/191.41 [6374]E(f333(f333(f166(x63741),f333(f333(f174(x63741),x63742),x63743)),x63744),f333(f333(f166(x63741),x63743),x63744))+~P4(f333(f333(f251(a880),x63744),x63742)) % 191.49/191.41 [6544]~P115(x65441)+E(f333(f333(f81(x65441),f333(f333(f81(x65441),x65442),x65443)),x65444),f333(f333(f81(x65441),f333(f333(f81(x65441),x65442),x65444)),x65443)) % 191.49/191.41 [6545]~P115(x65451)+E(f333(f333(f82(x65451),f333(f333(f82(x65451),x65452),x65453)),x65454),f333(f333(f82(x65451),f333(f333(f82(x65451),x65452),x65454)),x65453)) % 191.49/191.41 [6605]~P143(x66052)+E(f333(f333(f8(x66051,x66052),f333(f18(x66052,x66051),x66053)),x66054),f333(f333(f82(x66052),f333(f105(x66052),f333(f39(x66051),x66054))),x66053)) % 191.49/191.41 [6768]E(f333(f333(f106(f890(x67681,a874)),f333(f333(f311(x67681),x67682),x67683)),x67684),f333(f333(f106(f890(x67681,a874)),x67683),x67684))+P4(f333(f333(f335(x67681),x67682),x67684)) % 191.49/191.41 [6834]~P99(x68341)+E(f333(f333(f106(x68341),f333(f333(f115(x68341),x68342),x68343)),f333(f333(f115(x68341),x68344),x68343)),f333(f333(f115(x68341),f333(f333(f106(x68341),x68342),x68344)),x68343)) % 191.49/191.41 [6835]~P81(x68351)+E(f333(f333(f248(x68351),f333(f333(f3(x68351),x68352),x68353)),f333(f333(f3(x68351),x68354),x68353)),f333(f333(f3(x68351),f333(f333(f248(x68351),x68352),x68354)),x68353)) % 191.49/191.41 [6836]~P81(x68361)+E(f333(f333(f249(x68361),f333(f333(f3(x68361),x68362),x68363)),f333(f333(f3(x68361),x68364),x68363)),f333(f333(f3(x68361),f333(f333(f249(x68361),x68362),x68364)),x68363)) % 191.49/191.41 [6837]~P99(x68371)+E(f333(f333(f115(x68371),f333(f333(f106(x68371),x68372),x68373)),f333(f333(f106(x68371),x68374),x68373)),f333(f333(f106(x68371),f333(f333(f115(x68371),x68372),x68374)),x68373)) % 191.49/191.41 [6838]~P85(x68381)+E(f333(f333(f248(x68381),f333(f333(f81(x68381),x68382),x68383)),f333(f333(f81(x68381),x68384),x68383)),f333(f333(f81(x68381),f333(f333(f248(x68381),x68382),x68384)),x68383)) % 191.49/191.41 [6839]~P85(x68391)+E(f333(f333(f249(x68391),f333(f333(f81(x68391),x68392),x68393)),f333(f333(f81(x68391),x68394),x68393)),f333(f333(f81(x68391),f333(f333(f249(x68391),x68392),x68394)),x68393)) % 191.49/191.41 [6841]~P116(x68411)+E(f333(f333(f81(x68411),f333(f333(f82(x68411),x68412),x68413)),f333(f333(f82(x68411),x68414),x68413)),f333(f333(f82(x68411),f333(f333(f81(x68411),x68412),x68414)),x68413)) % 191.49/191.41 [6842]~P118(x68421)+E(f333(f333(f3(x68421),f333(f333(f291(x68421),x68422),x68423)),f333(f333(f291(x68421),x68424),x68423)),f333(f333(f291(x68421),f333(f333(f3(x68421),x68422),x68424)),x68423)) % 191.49/191.41 [6843]~P118(x68431)+E(f333(f333(f81(x68431),f333(f333(f291(x68431),x68432),x68433)),f333(f333(f291(x68431),x68434),x68433)),f333(f333(f291(x68431),f333(f333(f81(x68431),x68432),x68434)),x68433)) % 191.49/191.41 [6844]~P115(x68441)+E(f333(f333(f82(x68441),f333(f333(f264(x68441),x68442),x68443)),f333(f333(f264(x68441),x68444),x68443)),f333(f333(f264(x68441),f333(f333(f82(x68441),x68442),x68444)),x68443)) % 191.49/191.41 [6845]~P76(x68451)+E(f333(f333(f82(x68451),f333(f333(f264(x68451),x68452),x68453)),f333(f333(f264(x68451),x68454),x68453)),f333(f333(f264(x68451),f333(f333(f82(x68451),x68452),x68454)),x68453)) % 191.49/191.41 [6846]~P63(x68461)+E(f333(f333(f291(x68461),f333(f333(f264(x68461),x68462),x68463)),f333(f333(f264(x68461),x68464),x68463)),f333(f333(f264(x68461),f333(f333(f291(x68461),x68462),x68464)),x68463)) % 191.49/191.41 [6847]~P109(x68471)+E(f333(f333(f249(x68471),f333(f333(f248(x68471),x68472),x68473)),f333(f333(f248(x68471),x68474),x68473)),f333(f333(f248(x68471),f333(f333(f249(x68471),x68472),x68474)),x68473)) % 191.49/191.41 [6848]~P109(x68481)+E(f333(f333(f248(x68481),f333(f333(f249(x68481),x68482),x68483)),f333(f333(f249(x68481),x68484),x68483)),f333(f333(f249(x68481),f333(f333(f248(x68481),x68482),x68484)),x68483)) % 191.49/191.41 [6849]~P115(x68491)+E(f333(f333(f81(x68491),f333(f333(f82(x68491),x68492),x68493)),f333(f333(f82(x68491),x68494),x68493)),f333(f333(f82(x68491),f333(f333(f81(x68491),x68492),x68494)),x68493)) % 191.49/191.41 [6881]E(f333(f333(f160(x68811,x68812),x68813),x68814),x68812)+~P4(f333(f333(f250(a880),f333(f195(f881(x68811)),x68812)),x68813)) % 191.49/191.41 [6904]~P4(f333(x69043,x69044))+P4(f333(f333(f333(f115(f890(x69041,a874)),x69042),x69043),x69044)) % 191.49/191.41 [6906]~P4(f333(x69062,x69064))+P4(f333(f333(f333(f115(f890(x69061,a874)),x69062),x69063),x69064)) % 191.49/191.41 [6927]E(f333(f333(f166(x69271),f333(f333(f127(x69271),x69272),x69273)),x69274),f333(f333(f166(x69271),x69272),x69274))+~P4(f333(f333(f251(a880),x69274),f333(f195(f881(x69271)),x69272))) % 191.49/191.41 [6937]E(f333(f333(f3(f890(x69371,a874)),f333(f333(f311(x69371),x69372),x69373)),x69374),f333(f333(f3(f890(x69371,a874)),x69373),x69374))+~P4(f333(f333(f335(x69371),x69372),x69374)) % 191.49/191.41 [6979]~E(f140(a880,f333(f303(a880,x69791),x69792)),f333(f333(f152(a880),x69794),x69793))+E(f140(a880,f333(f303(a880,f333(f333(f81(a880),x69791),f79(a880))),x69792)),x69793) % 191.49/191.41 [7052]E(x70521,f2(a880))+E(f333(f333(f152(x70522),x70523),f333(f333(f174(x70522),f333(f333(f3(a880),x70521),f79(a880))),x70524)),f333(f333(f174(x70522),x70521),f333(f333(f152(x70522),x70523),x70524))) % 191.49/191.41 [7151]E(f333(f333(f166(x71511),x71512),f333(f333(f3(a880),x71513),f333(f195(f881(x71511)),x71514))),f333(f333(f166(x71511),f333(f333(f127(x71511),x71514),x71512)),x71513))+P4(f333(f333(f251(a880),x71513),f333(f195(f881(x71511)),x71514))) % 191.49/191.41 [7181]E(f333(f333(f106(f890(x71811,a874)),x71812),f333(f333(f311(x71811),x71813),x71814)),f333(f333(f311(x71811),x71813),f333(f333(f106(f890(x71811,a874)),x71812),x71814)))+~P4(f333(f333(f335(x71811),x71813),x71812)) % 191.49/191.41 [7216]E(f333(f333(f166(x72161),f333(f333(f160(x72161,x72162),x72163),x72164)),x72163),x72164)+~P4(f333(f333(f251(a880),x72163),f333(f195(f881(x72161)),x72162))) % 191.49/191.41 [7237]E(x72371,f194(f890(x72372,a874)))+E(f333(f312(f889(x72373,x72372),x72373,f262(x72373,x72372)),f333(f333(f270(x72373,x72372),x72374),f333(f18(f890(x72372,a874),x72373),x72371))),x72374) % 191.49/191.41 [7238]E(x72381,f194(f890(x72382,a874)))+E(f333(f312(f889(x72382,x72383),x72383,f271(x72382,x72383)),f333(f333(f270(x72382,x72383),x72381),f333(f18(f890(x72383,a874),x72382),x72384))),x72384) % 191.49/191.41 [7303]E(f333(f333(f3(f890(x73031,a874)),f333(f333(f311(x73031),x73032),x73033)),x73034),f333(f333(f311(x73031),x73032),f333(f333(f3(f890(x73031,a874)),x73033),x73034)))+P4(f333(f333(f335(x73031),x73032),x73034)) % 191.49/191.41 [7328]P4(f333(x73281,x73282))+P4(f333(f333(f333(f333(a203,f33(x73281,x73283)),x73282),x73284),x73282)) % 191.49/191.41 [7335]~E(x73354,f194(f890(x73352,a874)))+E(f333(f312(f889(x73351,x73352),x73351,f262(x73351,x73352)),f333(f333(f270(x73351,x73352),x73353),f333(f18(f890(x73352,a874),x73351),x73354))),f194(f890(x73351,a874))) % 191.49/191.41 [7336]~E(x73363,f194(f890(x73361,a874)))+E(f333(f312(f889(x73361,x73362),x73362,f271(x73361,x73362)),f333(f333(f270(x73361,x73362),x73363),f333(f18(f890(x73362,a874),x73361),x73364))),f194(f890(x73362,a874))) % 191.49/191.41 [7391]~P4(f333(f333(f335(x73911),x73912),x73914))+P4(f333(f333(f335(x73911),x73912),f333(f333(f115(f890(x73911,a874)),x73913),x73914))) % 191.49/191.41 [7394]~P4(f333(f333(f335(x73941),x73942),x73943))+P4(f333(f333(f335(x73941),x73942),f333(f333(f115(f890(x73941,a874)),x73943),x73944))) % 191.49/191.41 [7413]E(f333(f333(f106(f890(x74131,a874)),f333(f333(f311(x74131),x74132),x74133)),x74134),f333(f333(f311(x74131),x74132),f333(f333(f106(f890(x74131,a874)),x74133),x74134)))+~P4(f333(f333(f335(x74131),x74132),x74134)) % 191.49/191.41 [7683]P4(f333(x76831,x76832))+~P4(f333(f333(f333(f106(f890(x76833,a874)),x76834),x76831),x76832)) % 191.49/191.41 [7684]P4(f333(x76841,x76842))+~P4(f333(f333(f333(f106(f890(x76843,a874)),x76841),x76844),x76842)) % 191.49/191.41 [7687]E(f333(f333(f8(x76871,a880),x76872),f333(f333(f3(f890(x76871,a874)),x76873),f333(f333(f311(x76871),x76874),f194(f890(x76871,a874))))),f333(f333(f8(x76871,a880),x76872),x76873))+P4(f333(f333(f335(x76871),x76874),x76873)) % 191.49/191.41 [7693]~P69(x76931)+E(f333(f167(x76931),f333(f333(f155(a880,x76931),x76932),f140(a880,f333(f303(a880,x76933),x76934)))),f333(f333(f8(a880,x76931),x76932),f333(f173(a880),f140(a880,f333(f303(a880,x76933),x76934))))) % 191.49/191.41 [7694]~P69(x76941)+E(f333(f333(f8(a880,x76941),x76942),f333(f173(a880),f140(a880,f333(f303(a880,x76943),x76944)))),f333(f167(x76941),f333(f333(f155(a880,x76941),x76942),f140(a880,f333(f303(a880,x76943),x76944))))) % 191.49/191.41 [7808]~E(x78083,x78084)+P4(f333(f64(x78081,x78082,f333(f333(f311(x78081),x78083),f194(f890(x78081,a874)))),x78084)) % 191.49/191.41 [7901]P4(f333(f333(f335(x79011),x79012),f333(f173(x79011),x79013)))+~P4(f333(f333(f335(x79011),x79012),f333(f173(x79011),f333(f333(f174(x79011),x79014),x79013)))) % 191.49/191.41 [7902]P4(f333(f333(f335(x79021),x79022),f333(f173(x79021),x79023)))+~P4(f333(f333(f335(x79021),x79022),f333(f173(x79021),f333(f333(f139(x79021),x79024),x79023)))) % 191.49/191.41 [7969]P4(f333(f333(f335(x79691),x79692),x79693))+~P4(f333(f333(f335(x79691),x79692),f333(f333(f3(f890(x79691,a874)),x79693),x79694))) % 191.49/191.41 [7971]P4(f333(f333(f335(x79711),x79712),x79713))+~P4(f333(f333(f335(x79711),x79712),f333(f333(f106(f890(x79711,a874)),x79714),x79713))) % 191.49/191.41 [7974]P4(f333(f333(f335(x79741),x79742),x79743))+~P4(f333(f333(f335(x79741),x79742),f333(f333(f106(f890(x79741,a874)),x79743),x79744))) % 191.49/191.41 [7992]E(f333(f333(f127(x79921),f333(f333(f174(x79921),x79922),x79923)),f333(f333(f152(x79921),x79924),f333(f333(f139(x79921),f333(a117,x79922)),x79923))),f333(f333(f160(x79921,x79923),x79922),x79924))+~P4(f333(f333(f251(a880),x79922),f333(f195(f881(x79921)),x79923))) % 191.49/191.41 [8017]P4(f333(f333(f335(x80171),x80172),x80173))+~P4(f333(f333(f250(f890(x80171,a874)),f333(f333(f311(x80171),x80172),x80174)),x80173)) % 191.49/191.41 [8056]~P4(f333(f333(f335(x80561),x80562),x80563))+~P4(f333(f333(f335(x80561),x80562),f333(f333(f3(f890(x80561,a874)),x80564),x80563))) % 191.49/191.41 [8088]~P4(f333(f333(f251(a880),x80884),f333(f195(f881(x80881)),x80883)))+P4(f333(f333(f335(x80881),x80882),f333(f173(x80881),f333(f333(f160(x80881,x80883),x80884),x80882)))) % 191.49/191.41 [8145]E(f333(f333(f166(x81451),f333(f333(f139(x81451),x81452),x81453)),x81454),f333(f333(f166(x81451),x81453),f333(f333(f81(a880),x81452),x81454)))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),x81452),x81454)),f333(f195(f881(x81451)),x81453))) % 191.49/191.41 [8155]~P143(x81552)+E(f333(f333(f8(x81551,x81552),f333(f333(f10(a880,x81552,x81551),f105(x81552)),x81553)),x81554),f333(f105(x81552),f333(f333(f8(x81551,a880),x81553),x81554))) % 191.49/191.41 [8156]~P140(x81562)+E(f333(f333(f8(x81561,x81562),f333(f333(f10(a1,x81562,x81561),f107(x81562)),x81563)),x81564),f333(f107(x81562),f333(f333(f8(x81561,a1),x81563),x81564))) % 191.49/191.41 [8208]~P66(x82082)+E(f333(f333(f11(x82081,x82082),f333(f333(f10(x82082,x82082,x82081),f76(x82082)),x82083)),x82084),f333(f76(x82082),f333(f333(f11(x82081,x82082),x82083),x82084))) % 191.49/191.41 [8209]~P68(x82092)+E(f333(f333(f8(x82091,x82092),f333(f333(f10(x82092,x82092,x82091),f80(x82092)),x82093)),x82094),f333(f80(x82092),f333(f333(f8(x82091,x82092),x82093),x82094))) % 191.49/191.41 [8211]E(f333(f333(f8(x82111,a880),x82112),f333(f333(f3(f890(x82111,a874)),x82113),f333(f333(f311(x82111),x82114),f194(f890(x82111,a874))))),f333(f333(f3(a880),f333(f333(f8(x82111,a880),x82112),x82113)),f333(x82112,x82114)))+~P4(f333(f333(f335(x82111),x82114),x82113)) % 191.49/191.41 [8230]P4(f333(f333(f250(f890(x82301,a874)),x82302),x82303))+~P4(f333(f333(f250(f890(x82301,a874)),f333(f333(f311(x82301),x82304),x82302)),x82303)) % 191.49/191.41 [8434]E(f333(a117,f869(x84341,x84342,x84343,x84344)),x84342)+~P4(f333(f333(f333(f333(a203,f333(a26,x84344)),x84343),x84342),x84341)) % 191.49/191.41 [8436]E(f333(f333(f178(x84361,x84362),x84363),x84364),f197(x84362))+P4(f333(f333(f335(x84361),x84364),f333(f312(f889(x84361,x84362),x84361,f262(x84361,x84362)),f333(f173(f889(x84361,x84362)),x84363)))) % 191.49/191.41 [8438]P40(x84381,x84382)+~P40(x84381,f333(f333(f311(f889(x84381,x84381)),f333(f333(f263(x84381,x84381),x84383),x84384)),x84382)) % 191.49/191.41 [8439]P57(x84391,x84392)+~P57(x84391,f333(f333(f311(f889(x84391,x84391)),f333(f333(f263(x84391,x84391),x84393),x84394)),x84392)) % 191.49/191.41 [8448]~P109(x84481)+E(f333(f333(f149(x84481,x84481,f7(x84481)),x84482),f333(f333(f149(x84481,x84481,f7(x84481)),x84483),x84484)),f333(f333(f149(x84481,x84481,f7(x84481)),x84483),f333(f333(f149(x84481,x84481,f7(x84481)),x84482),x84484))) % 191.49/191.41 [8458]E(x84581,x84582)+~P4(f333(f64(x84583,x84584,f333(f333(f311(x84583),x84581),f194(f890(x84583,a874)))),x84582)) % 191.49/191.41 [8468]E(f333(f333(f127(x84681),f333(f333(f174(x84681),x84682),x84683)),f333(f333(f174(x84681),x84684),f333(f333(f139(x84681),x84682),x84683))),f333(f333(f174(x84681),f333(f333(f81(a880),x84682),x84684)),x84683))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),x84682),x84684)),f333(f195(f881(x84681)),x84683))) % 191.49/191.41 [8505]P4(f333(f63(x85051),x85052))+~E(x85052,f333(f312(a880,x85051,x85053),f333(f255(a880),f333(f333(f9(a880,a880,a874),f251(a880)),x85054)))) % 191.49/191.41 [8530]~P91(x85301)+E(f333(f143(x85301,x85301,f81(x85301),f333(f333(f81(x85301),x85302),x85303)),x85304),f333(f333(f81(x85301),x85302),f333(f143(x85301,x85301,f81(x85301),x85303),x85304))) % 191.49/191.41 [8563]P4(f333(f333(f250(f890(x85631,a874)),f333(f261(x85631,x85632),x85633)),f333(f261(x85631,x85632),x85634)))+~P4(f333(f333(f250(f890(f889(x85631,x85632),a874)),x85633),x85634)) % 191.49/191.41 [8576]~P4(f333(f333(f250(a880),x85762),x85764))+P4(f333(f333(f250(f890(x85761,a874)),f333(f173(x85761),f333(f333(f174(x85761),x85762),x85763))),f333(f173(x85761),f333(f333(f174(x85761),x85764),x85763)))) % 191.49/191.41 [8577]~P4(f333(f333(f250(a880),x85774),x85772))+P4(f333(f333(f250(f890(x85771,a874)),f333(f173(x85771),f333(f333(f139(x85771),x85772),x85773))),f333(f173(x85771),f333(f333(f139(x85771),x85774),x85773)))) % 191.49/191.41 [8630]~P4(f333(f63(x86301),f333(f333(f3(f890(x86301,a874)),x86302),x86304)))+P4(f333(f63(x86301),f333(f333(f3(f890(x86301,a874)),x86302),f333(f333(f311(x86301),x86303),x86304)))) % 191.49/191.41 [8659]P4(f333(f333(f335(f889(x86591,x86591)),x86592),f309(x86591,x86593)))+~P4(f333(f333(f335(f889(x86591,x86591)),x86592),f333(f333(f189(f889(x86591,x86591),a874),x86594),x86593))) % 191.49/191.41 [8729]~P4(f333(f63(x87291),f333(f333(f3(f890(x87291,a874)),x87292),f333(f333(f311(x87291),x87294),x87293))))+P4(f333(f63(x87291),f333(f333(f3(f890(x87291,a874)),x87292),x87293))) % 191.49/191.41 [8888]~E(f333(f333(f178(x88881,x88882),x88883),x88884),f197(x88882))+~P4(f333(f333(f335(x88881),x88884),f333(f312(f889(x88881,x88882),x88881,f262(x88881,x88882)),f333(f173(f889(x88881,x88882)),x88883)))) % 191.49/191.41 [8953]~P6(x89531)+P4(f333(f333(f250(x89531),f333(f333(f115(x89531),x89532),f333(f333(f106(x89531),x89533),x89534))),f333(f333(f106(x89531),f333(f333(f115(x89531),x89532),x89533)),f333(f333(f115(x89531),x89532),x89534)))) % 191.49/191.41 [8954]~P109(x89541)+P4(f333(f333(f250(x89541),f333(f333(f249(x89541),x89542),f333(f333(f248(x89541),x89543),x89544))),f333(f333(f248(x89541),f333(f333(f249(x89541),x89542),x89543)),f333(f333(f249(x89541),x89542),x89544)))) % 191.49/191.41 [9084]E(x90841,x90842)+~P4(f333(f333(f335(f889(x90843,x90843)),f333(f333(f263(x90843,x90843),x90841),x90842)),f333(f173(f889(x90843,x90843)),f333(f333(f182(x90843,x90843),x90844),x90844)))) % 191.49/191.41 [9119]~P4(f333(f333(f335(f889(x91191,x91191)),f333(f333(f263(x91191,x91191),x91193),x91192)),f309(x91191,x91194)))+~P40(x91191,f333(f333(f311(f889(x91191,x91191)),f333(f333(f263(x91191,x91191),x91192),x91193)),x91194)) % 191.49/191.41 [9120]~P4(f333(f333(f335(f889(x91201,x91201)),f333(f333(f263(x91201,x91201),x91203),x91202)),f309(x91201,x91204)))+~P57(x91201,f333(f333(f311(f889(x91201,x91201)),f333(f333(f263(x91201,x91201),x91202),x91203)),x91204)) % 191.49/191.41 [9132]E(x91321,x91322)+E(f333(f137(x91323,f333(f333(f10(a874,a874,x91323),a328),f333(a330,x91321))),f333(f333(f152(x91323),x91322),x91324)),f333(f333(f152(x91323),x91322),f333(f137(x91323,f333(f333(f10(a874,a874,x91323),a328),f333(a330,x91321))),x91324))) % 191.49/191.41 [9178]~P6(x91781)+P4(f333(f333(f250(x91781),f333(f333(f115(x91781),f333(f333(f106(x91781),x91782),x91783)),f333(f333(f106(x91781),x91782),x91784))),f333(f333(f106(x91781),x91782),f333(f333(f115(x91781),x91783),x91784)))) % 191.49/191.41 [9179]~P109(x91791)+P4(f333(f333(f250(x91791),f333(f333(f249(x91791),f333(f333(f248(x91791),x91792),x91793)),f333(f333(f248(x91791),x91792),x91794))),f333(f333(f248(x91791),x91792),f333(f333(f249(x91791),x91793),x91794)))) % 191.49/191.41 [9251]~E(f333(f312(x92512,x92511,x92513),f258(f890(x92512,a874))),f258(f890(x92511,a874)))+P4(f333(f333(f250(f890(x92511,a874)),f333(f80(f890(x92511,a874)),f333(f312(x92512,x92511,x92513),x92514))),f333(f312(x92512,x92511,x92513),f333(f80(f890(x92512,a874)),x92514)))) % 191.49/191.41 [9332]P4(f333(f333(f333(f333(a203,f333(f246(a876),f333(a28,x93321))),x93322),f869(x93323,x93324,x93322,x93321)),x93323))+~P4(f333(f333(f333(f333(a203,f333(a26,x93321)),x93322),x93324),x93323)) % 191.49/191.41 [9590]P4(f333(f333(f335(f889(x95901,x95901)),f333(f333(f263(x95901,x95901),x95902),x95903)),f333(f288(x95901,x95901),f333(f333(f290(x95901,x95901,x95901),x95904),f309(x95901,x95904)))))+~P4(f333(f333(f335(f889(x95901,x95901)),f333(f333(f263(x95901,x95901),x95902),x95903)),f333(f333(f290(x95901,x95901,x95901),f333(f288(x95901,x95901),x95904)),f309(x95901,f333(f288(x95901,x95901),x95904))))) % 191.49/191.41 [9592]~P4(f333(f333(f335(f889(x95921,x95921)),f333(f333(f263(x95921,x95921),x95922),x95923)),f333(f288(x95921,x95921),f333(f333(f290(x95921,x95921,x95921),x95924),f309(x95921,x95924)))))+P4(f333(f333(f335(f889(x95921,x95921)),f333(f333(f263(x95921,x95921),x95922),x95923)),f333(f333(f290(x95921,x95921,x95921),f333(f288(x95921,x95921),x95924)),f309(x95921,f333(f288(x95921,x95921),x95924))))) % 191.49/191.41 [9613]~P4(f333(f333(f335(x96132),x96134),f333(f259(x96131,x96132),x96133)))+P4(f333(f333(f335(f889(x96131,x96132)),f333(f333(f263(x96131,x96132),f710(x96133,x96131,x96134,x96132)),x96134)),x96133)) % 191.49/191.41 [9614]~P4(f333(f333(f335(x96142),x96144),f333(f259(x96141,x96142),x96143)))+P4(f333(f333(f335(f889(x96141,x96142)),f333(f333(f263(x96141,x96142),f711(x96143,x96141,x96144,x96142)),x96144)),x96143)) % 191.49/191.41 [9645]~P4(f333(f333(f335(x96451),x96454),f333(f333(f115(f890(x96451,a874)),x96452),x96453)))+P4(f333(f333(f333(f115(f890(x96451,a874)),f333(f333(f9(x96451,f890(x96451,a874),a874),f335(x96451)),x96452)),f333(f333(f9(x96451,f890(x96451,a874),a874),f335(x96451)),x96453)),x96454)) % 191.49/191.41 [9646]~P4(f333(f333(f335(x96461),x96464),f333(f333(f106(f890(x96461,a874)),x96462),x96463)))+P4(f333(f333(f333(f106(f890(x96461,a874)),f333(f333(f9(x96461,f890(x96461,a874),a874),f335(x96461)),x96462)),f333(f333(f9(x96461,f890(x96461,a874),a874),f335(x96461)),x96463)),x96464)) % 191.49/191.41 [9721]~P4(f333(f333(f335(f889(x97211,x97211)),f333(f333(f263(x97211,x97211),x97214),x97213)),f333(f333(f290(x97211,x97211,x97211),x97212),f309(x97211,x97212))))+P4(f333(f333(f335(f889(x97211,x97211)),f333(f333(f263(x97211,x97211),f791(x97212,x97213,x97214,x97211)),x97213)),x97212)) % 191.49/191.41 [9777]P4(f333(f333(f335(x97771),x97772),f333(f333(f115(f890(x97771,a874)),x97773),x97774)))+~P4(f333(f333(f333(f115(f890(x97771,a874)),f333(f333(f9(x97771,f890(x97771,a874),a874),f335(x97771)),x97773)),f333(f333(f9(x97771,f890(x97771,a874),a874),f335(x97771)),x97774)),x97772)) % 191.49/191.41 [9778]P4(f333(f333(f335(x97781),x97782),f333(f333(f106(f890(x97781,a874)),x97783),x97784)))+~P4(f333(f333(f333(f106(f890(x97781,a874)),f333(f333(f9(x97781,f890(x97781,a874),a874),f335(x97781)),x97783)),f333(f333(f9(x97781,f890(x97781,a874),a874),f335(x97781)),x97784)),x97782)) % 191.49/191.41 [10035]P35(x100351,f333(f333(f9(x100351,f890(f889(x100351,x100351),a874),f890(x100351,a874)),f333(f333(f10(f890(x100351,f890(f890(f889(x100351,x100351),a874),a874)),f890(f890(f889(x100351,x100351),a874),f890(x100351,a874)),x100351),f9(x100351,f890(f889(x100351,x100351),a874),a874)),f333(f333(f10(f890(x100351,f889(x100351,x100351)),f890(x100351,f890(f890(f889(x100351,x100351),a874),a874)),x100351),f333(f10(f889(x100351,x100351),f890(f890(f889(x100351,x100351),a874),a874),x100351),f335(f889(x100351,x100351)))),f263(x100351,x100351)))),x100352),x100353,x100354)+~P4(f333(f333(f335(f889(f881(x100351),f881(x100351))),f333(f333(f263(f881(x100351),f881(x100351)),x100353),x100354)),f159(x100351,x100352))) % 191.49/191.41 [10039]P58(x100391,f333(f333(f9(x100391,f890(f889(x100391,x100391),a874),f890(x100391,a874)),f333(f333(f10(f890(x100391,f890(f890(f889(x100391,x100391),a874),a874)),f890(f890(f889(x100391,x100391),a874),f890(x100391,a874)),x100391),f9(x100391,f890(f889(x100391,x100391),a874),a874)),f333(f333(f10(f890(x100391,f889(x100391,x100391)),f890(x100391,f890(f890(f889(x100391,x100391),a874),a874)),x100391),f333(f10(f889(x100391,x100391),f890(f890(f889(x100391,x100391),a874),a874),x100391),f335(f889(x100391,x100391)))),f263(x100391,x100391)))),x100392),x100393,x100394)+~P4(f333(f333(f335(f889(f890(x100391,a874),f890(x100391,a874))),f333(f333(f263(f890(x100391,a874),f890(x100391,a874)),x100393),x100394)),f325(x100391,x100392))) % 191.49/191.41 [10064]E(x100641,x100642)+~E(f333(f333(f9(x100643,f890(f889(x100643,x100644),a874),f890(x100644,a874)),f333(f333(f10(f890(x100644,f890(f890(f889(x100643,x100644),a874),a874)),f890(f890(f889(x100643,x100644),a874),f890(x100644,a874)),x100643),f9(x100644,f890(f889(x100643,x100644),a874),a874)),f333(f333(f10(f890(x100644,f889(x100643,x100644)),f890(x100644,f890(f890(f889(x100643,x100644),a874),a874)),x100643),f333(f10(f889(x100643,x100644),f890(f890(f889(x100643,x100644),a874),a874),x100644),f335(f889(x100643,x100644)))),f263(x100643,x100644)))),x100641),f333(f333(f9(x100643,f890(f889(x100643,x100644),a874),f890(x100644,a874)),f333(f333(f10(f890(x100644,f890(f890(f889(x100643,x100644),a874),a874)),f890(f890(f889(x100643,x100644),a874),f890(x100644,a874)),x100643),f9(x100644,f890(f889(x100643,x100644),a874),a874)),f333(f333(f10(f890(x100644,f889(x100643,x100644)),f890(x100644,f890(f890(f889(x100643,x100644),a874),a874)),x100643),f333(f10(f889(x100643,x100644),f890(f890(f889(x100643,x100644),a874),a874),x100644),f335(f889(x100643,x100644)))),f263(x100643,x100644)))),x100642)) % 191.49/191.41 [10068]~P35(x100681,f333(f333(f9(x100681,f890(f889(x100681,x100681),a874),f890(x100681,a874)),f333(f333(f10(f890(x100681,f890(f890(f889(x100681,x100681),a874),a874)),f890(f890(f889(x100681,x100681),a874),f890(x100681,a874)),x100681),f9(x100681,f890(f889(x100681,x100681),a874),a874)),f333(f333(f10(f890(x100681,f889(x100681,x100681)),f890(x100681,f890(f890(f889(x100681,x100681),a874),a874)),x100681),f333(f10(f889(x100681,x100681),f890(f890(f889(x100681,x100681),a874),a874),x100681),f335(f889(x100681,x100681)))),f263(x100681,x100681)))),x100684),x100682,x100683)+P4(f333(f333(f335(f889(f881(x100681),f881(x100681))),f333(f333(f263(f881(x100681),f881(x100681)),x100682),x100683)),f159(x100681,x100684))) % 191.49/191.41 [10069]~P58(x100691,f333(f333(f9(x100691,f890(f889(x100691,x100691),a874),f890(x100691,a874)),f333(f333(f10(f890(x100691,f890(f890(f889(x100691,x100691),a874),a874)),f890(f890(f889(x100691,x100691),a874),f890(x100691,a874)),x100691),f9(x100691,f890(f889(x100691,x100691),a874),a874)),f333(f333(f10(f890(x100691,f889(x100691,x100691)),f890(x100691,f890(f890(f889(x100691,x100691),a874),a874)),x100691),f333(f10(f889(x100691,x100691),f890(f890(f889(x100691,x100691),a874),a874),x100691),f335(f889(x100691,x100691)))),f263(x100691,x100691)))),x100694),x100692,x100693)+P4(f333(f333(f335(f889(f890(x100691,a874),f890(x100691,a874))),f333(f333(f263(f890(x100691,a874),f890(x100691,a874)),x100692),x100693)),f325(x100691,x100694))) % 191.49/191.41 [7465]~P94(x74651)+E(f333(f333(f81(x74651),f333(f108(x74651),x74652)),f333(f333(f3(x74651),f333(f108(x74651),x74653)),x74654)),f333(f333(f3(x74651),f333(f108(x74651),f333(f333(f81(a1),x74652),x74653))),x74654)) % 191.49/191.41 [7466]~P94(x74661)+E(f333(f333(f81(x74661),f333(f108(x74661),x74662)),f333(f333(f81(x74661),f333(f108(x74661),x74663)),x74664)),f333(f333(f81(x74661),f333(f108(x74661),f333(f333(f81(a1),x74662),x74663))),x74664)) % 191.49/191.41 [7467]~P94(x74671)+E(f333(f333(f82(x74671),f333(f108(x74671),x74672)),f333(f333(f82(x74671),f333(f108(x74671),x74673)),x74674)),f333(f333(f82(x74671),f333(f108(x74671),f333(f333(f82(a1),x74672),x74673))),x74674)) % 191.49/191.41 [7509]~P143(x75091)+E(f333(f167(x75091),f333(f333(f155(x75092,x75091),f333(f18(x75091,x75092),x75093)),x75094)),f333(f333(f82(x75091),f333(f105(x75091),f333(f195(f881(x75092)),x75094))),x75093)) % 191.49/191.41 [7738]E(f333(f279(x77381,f333(f333(f152(f889(a104,x77381)),x77382),x77383)),x77384),f333(f271(a104,x77381),x77382))+~P4(f333(f333(f251(a104),x77384),f333(f262(a104,x77381),x77382))) % 191.49/191.41 [7786]~P94(x77861)+E(f333(f333(f81(x77861),f333(f108(x77861),x77862)),f333(f333(f3(x77861),x77863),f333(f108(x77861),x77864))),f333(f333(f81(x77861),f333(f108(x77861),f333(f333(f81(a1),x77862),f333(f80(a1),x77864)))),x77863)) % 191.49/191.41 [7909]E(f333(f279(x79091,x79092),f333(f333(f3(a104),x79093),f333(f262(a104,x79091),x79094))),f333(f279(x79091,f333(f333(f152(f889(a104,x79091)),x79094),x79092)),x79093))+P4(f333(f333(f251(a104),x79093),f333(f262(a104,x79091),x79094))) % 191.49/191.41 [8353]~P4(f333(f333(f335(x83531),x83532),f333(f173(x83531),f119(x83531,x83534))))+P4(f333(f333(f335(x83531),x83532),f333(f173(x83531),f119(x83531,f333(f333(f127(x83531),x83533),x83534))))) % 191.49/191.41 [8354]~P4(f333(f333(f335(x83541),x83542),f333(f173(x83541),f119(x83541,x83543))))+P4(f333(f333(f335(x83541),x83542),f333(f173(x83541),f119(x83541,f333(f333(f127(x83541),x83543),x83544))))) % 191.49/191.41 [8375]E(f333(f333(f115(f890(x83751,a874)),f333(f333(f106(f890(x83751,a874)),x83752),x83753)),x83754),f333(f333(f106(f890(x83751,a874)),x83752),f333(f333(f115(f890(x83751,a874)),x83753),x83754)))+~P4(f333(f333(f250(f890(x83751,a874)),x83754),x83752)) % 191.49/191.41 [8670]~E(f333(f333(f115(f890(x86701,a874)),f333(f333(f106(f890(x86701,a874)),x86703),x86704)),x86702),f333(f333(f106(f890(x86701,a874)),x86703),f333(f333(f115(f890(x86701,a874)),x86704),x86702)))+P4(f333(f333(f250(f890(x86701,a874)),x86702),x86703)) % 191.49/191.41 [8959]~P4(f333(f333(f250(f890(x89591,a874)),x89592),f333(f333(f115(f890(x89591,a874)),x89593),x89594)))+P4(f333(f333(f250(f890(x89591,a874)),f333(f333(f3(f890(x89591,a874)),x89592),x89593)),x89594)) % 191.49/191.41 [9017]~P4(f333(f333(f333(f333(a203,f333(a26,x90171)),x90172),f333(a117,x90173)),x90174))+P4(f333(f333(f333(f333(a203,f333(f246(a876),f333(a28,x90171))),x90172),x90173),x90174)) % 191.49/191.41 [9063]P4(f333(f333(f250(f890(x90631,a874)),x90632),f333(f333(f115(f890(x90631,a874)),x90633),x90634)))+~P4(f333(f333(f250(f890(x90631,a874)),f333(f333(f3(f890(x90631,a874)),x90632),x90633)),x90634)) % 191.49/191.41 [9118]P4(f333(f333(f333(f333(a203,f333(a26,x91181)),x91182),f333(a117,x91183)),x91184))+~P4(f333(f333(f333(f333(a203,f333(f246(a876),f333(a28,x91181))),x91182),x91183),x91184)) % 191.49/191.41 [9159]~P87(x91591)+E(f333(f76(x91591),f333(f333(f8(x91592,x91591),f333(f333(f10(x91591,x91591,x91592),f76(x91591)),x91593)),x91594)),f333(f333(f8(x91592,x91591),f333(f333(f10(x91591,x91591,x91592),f76(x91591)),x91593)),x91594)) % 191.49/191.41 [9330]~P87(x93301)+P4(f333(f333(f250(x93301),f2(x93301)),f333(f333(f8(x93302,x93301),f333(f333(f10(x93301,x93301,x93302),f76(x93301)),x93303)),x93304))) % 191.49/191.41 [9335]~P68(x93351)+E(f333(f167(x93351),f333(f333(f155(x93352,x93351),f333(f74(x93351,x93351,x93352,f80(x93351)),x93353)),x93354)),f333(f80(x93351),f333(f167(x93351),f333(f333(f155(x93352,x93351),x93353),x93354)))) % 191.49/191.41 [9465]~P87(x94651)+P4(f333(f333(f250(x94651),f333(f76(x94651),f333(f333(f8(x94652,x94651),x94653),x94654))),f333(f333(f8(x94652,x94651),f333(f333(f10(x94651,x94651,x94652),f76(x94651)),x94653)),x94654))) % 191.49/191.41 [9509]~E(f333(f333(f81(a880),x95091),x95094),f333(f333(f81(a880),x95093),x95092))+P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),f333(f333(f263(a880,a880),x95091),x95092)),f333(f333(f263(a880,a880),x95093),x95094))),a113)) % 191.49/191.41 [9510]~P4(f333(f333(f251(a880),x95101),x95103))+P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),f333(f333(f263(a880,a880),x95101),x95102)),f333(f333(f263(a880,a880),x95103),x95104))),a36)) % 191.49/191.41 [9511]~P4(f333(f333(f251(a880),x95111),x95113))+P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),f333(f333(f263(a880,a880),x95111),x95112)),f333(f333(f263(a880,a880),x95113),x95114))),a71)) % 191.49/191.41 [9668]E(f333(f333(f81(a880),x96681),x96682),f333(f333(f81(a880),x96683),x96684))+~P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),f333(f333(f263(a880,a880),x96681),x96684)),f333(f333(f263(a880,a880),x96683),x96682))),a113)) % 191.49/191.41 [9695]E(f333(f333(f166(x96951),f333(f333(f139(x96951),f333(f195(f881(x96951)),f177(x96951,x96952,x96953))),x96953)),x96954),f333(f333(f166(x96951),x96953),f333(f333(f81(a880),x96954),f333(f195(f881(x96951)),f177(x96951,x96952,x96953)))))+~P4(f333(f333(f251(a880),x96954),f333(f195(f881(x96951)),f333(f333(f139(x96951),f333(f195(f881(x96951)),f177(x96951,x96952,x96953))),x96953)))) % 191.49/191.41 [9712]~P4(f333(f333(f335(x97122),x97124),f333(f333(f43(x97121,f890(x97122,a874)),f258(f890(x97121,a874))),x97123)))+P4(f333(f333(f333(f43(x97121,f890(x97122,a874)),f258(f890(x97121,a874))),f333(f333(f10(f890(x97122,a874),f890(x97122,a874),x97121),f333(f9(x97122,f890(x97122,a874),a874),f335(x97122))),x97123)),x97124)) % 191.49/191.41 [9713]~P4(f333(f333(f335(x97132),x97134),f333(f333(f44(x97131,f890(x97132,a874)),f258(f890(x97131,a874))),x97133)))+P4(f333(f333(f333(f44(x97131,f890(x97132,a874)),f258(f890(x97131,a874))),f333(f333(f10(f890(x97132,a874),f890(x97132,a874),x97131),f333(f9(x97132,f890(x97132,a874),a874),f335(x97132))),x97133)),x97134)) % 191.49/191.41 [9806]~P4(f333(f50(x98061,x98062),f333(f333(f263(a1,a1),x98064),x98063)))+P4(f333(f50(f333(f80(a1),x98061),x98062),f333(f333(f263(a1,a1),f333(f333(f333(f101(a1),f333(f333(a330,x98063),f2(a1))),f333(f80(a1),x98064)),f333(f333(f3(a1),f333(f80(a1),x98064)),f79(a1)))),f333(f333(f333(f101(a1),f333(f333(a330,x98063),f2(a1))),f2(a1)),f333(f333(f3(a1),x98062),x98063))))) % 191.49/191.41 [9814]P4(f333(f333(f335(x98141),x98142),f333(f333(f43(x98143,f890(x98141,a874)),f258(f890(x98143,a874))),x98144)))+~P4(f333(f333(f333(f43(x98143,f890(x98141,a874)),f258(f890(x98143,a874))),f333(f333(f10(f890(x98141,a874),f890(x98141,a874),x98143),f333(f9(x98141,f890(x98141,a874),a874),f335(x98141))),x98144)),x98142)) % 191.49/191.41 [9815]P4(f333(f333(f335(x98151),x98152),f333(f333(f44(x98153,f890(x98151,a874)),f258(f890(x98153,a874))),x98154)))+~P4(f333(f333(f333(f44(x98153,f890(x98151,a874)),f258(f890(x98153,a874))),f333(f333(f10(f890(x98151,a874),f890(x98151,a874),x98153),f333(f9(x98151,f890(x98151,a874),a874),f335(x98151))),x98154)),x98152)) % 191.49/191.41 [9826]E(f333(f333(f44(a880,f890(x98261,a874)),f258(f890(a880,a874))),x98262),f333(f333(f44(a880,f890(x98261,a874)),f258(f890(a880,a874))),x98263))+~E(f333(f333(f44(a880,f890(x98261,a874)),f333(f303(a880,f2(a880)),f551(x98262,x98264,x98263,x98261))),x98263),f333(f333(f44(a880,f890(x98261,a874)),f333(f303(a880,f2(a880)),f333(f333(f81(a880),f551(x98262,x98264,x98263,x98261)),x98264))),x98262)) % 191.49/191.41 [10154]~P4(f333(f333(f250(f890(f889(x101541,x101542),a874)),x101543),x101544))+P4(f333(f333(f250(f890(x101541,f890(x101542,a874))),f333(f333(f9(x101541,f890(f889(x101541,x101542),a874),f890(x101542,a874)),f333(f333(f10(f890(x101542,f890(f890(f889(x101541,x101542),a874),a874)),f890(f890(f889(x101541,x101542),a874),f890(x101542,a874)),x101541),f9(x101542,f890(f889(x101541,x101542),a874),a874)),f333(f333(f10(f890(x101542,f889(x101541,x101542)),f890(x101542,f890(f890(f889(x101541,x101542),a874),a874)),x101541),f333(f10(f889(x101541,x101542),f890(f890(f889(x101541,x101542),a874),a874),x101542),f335(f889(x101541,x101542)))),f263(x101541,x101542)))),x101543)),f333(f333(f9(x101541,f890(f889(x101541,x101542),a874),f890(x101542,a874)),f333(f333(f10(f890(x101542,f890(f890(f889(x101541,x101542),a874),a874)),f890(f890(f889(x101541,x101542),a874),f890(x101542,a874)),x101541),f9(x101542,f890(f889(x101541,x101542),a874),a874)),f333(f333(f10(f890(x101542,f889(x101541,x101542)),f890(x101542,f890(f890(f889(x101541,x101542),a874),a874)),x101541),f333(f10(f889(x101541,x101542),f890(f890(f889(x101541,x101542),a874),a874),x101542),f335(f889(x101541,x101542)))),f263(x101541,x101542)))),x101544))) % 191.49/191.41 [10177]P4(f333(f333(f250(f890(f889(x101771,x101772),a874)),x101773),x101774))+~P4(f333(f333(f250(f890(x101771,f890(x101772,a874))),f333(f333(f9(x101771,f890(f889(x101771,x101772),a874),f890(x101772,a874)),f333(f333(f10(f890(x101772,f890(f890(f889(x101771,x101772),a874),a874)),f890(f890(f889(x101771,x101772),a874),f890(x101772,a874)),x101771),f9(x101772,f890(f889(x101771,x101772),a874),a874)),f333(f333(f10(f890(x101772,f889(x101771,x101772)),f890(x101772,f890(f890(f889(x101771,x101772),a874),a874)),x101771),f333(f10(f889(x101771,x101772),f890(f890(f889(x101771,x101772),a874),a874),x101772),f335(f889(x101771,x101772)))),f263(x101771,x101772)))),x101773)),f333(f333(f9(x101771,f890(f889(x101771,x101772),a874),f890(x101772,a874)),f333(f333(f10(f890(x101772,f890(f890(f889(x101771,x101772),a874),a874)),f890(f890(f889(x101771,x101772),a874),f890(x101772,a874)),x101771),f9(x101772,f890(f889(x101771,x101772),a874),a874)),f333(f333(f10(f890(x101772,f889(x101771,x101772)),f890(x101772,f890(f890(f889(x101771,x101772),a874),a874)),x101771),f333(f10(f889(x101771,x101772),f890(f890(f889(x101771,x101772),a874),a874),x101772),f335(f889(x101771,x101772)))),f263(x101771,x101772)))),x101774))) % 191.49/191.41 [9206]~P4(f333(f333(f335(f889(x92061,x92061)),x92062),f309(x92061,x92064)))+P4(f333(f333(f335(f889(x92061,x92061)),x92062),f309(x92061,f333(f333(f115(f890(f889(x92061,x92061),a874)),x92063),x92064)))) % 191.49/191.41 [9207]~P4(f333(f333(f335(f889(x92071,x92071)),x92072),f309(x92071,x92073)))+P4(f333(f333(f335(f889(x92071,x92071)),x92072),f309(x92071,f333(f333(f115(f890(f889(x92071,x92071),a874)),x92073),x92074)))) % 191.49/191.41 [9575]~E(f333(f173(x95751),x95754),f184(x95751,x95752,x95753))+E(f333(f178(x95751,x95752),f333(f333(f155(x95751,f889(x95751,x95752)),f333(f333(f20(x95751,x95752,f889(x95751,x95752)),f263(x95751,x95752)),f333(f333(f10(f884(x95752),x95752,x95751),f246(x95752)),x95753))),x95754)),x95753) % 191.49/191.41 [9912]~P4(f333(f333(f251(a880),f333(f333(f81(a880),x99121),x99124)),f333(f333(f81(a880),x99123),x99122)))+P4(f333(f333(f251(a1),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x99121),x99122)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x99123),x99124)),f194(f890(f889(a880,a880),a874))))))) % 191.49/191.41 [9913]~P4(f333(f333(f250(a880),f333(f333(f81(a880),x99131),x99134)),f333(f333(f81(a880),x99133),x99132)))+P4(f333(f333(f250(a1),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x99131),x99132)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x99133),x99134)),f194(f890(f889(a880,a880),a874))))))) % 191.49/191.41 [9978]P4(f333(f333(f251(a880),f333(f333(f81(a880),x99781),x99782)),f333(f333(f81(a880),x99783),x99784)))+~P4(f333(f333(f251(a1),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x99781),x99784)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x99783),x99782)),f194(f890(f889(a880,a880),a874))))))) % 191.49/191.41 [9979]P4(f333(f333(f250(a880),f333(f333(f81(a880),x99791),x99792)),f333(f333(f81(a880),x99793),x99794)))+~P4(f333(f333(f250(a1),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x99791),x99794)),f194(f890(f889(a880,a880),a874)))))),f333(a90,f333(f287(f889(a880,a880),f889(a880,a880),a113),f333(f333(f311(f889(a880,a880)),f333(f333(f263(a880,a880),x99793),x99792)),f194(f890(f889(a880,a880),a874))))))) % 191.49/191.41 [10022]P4(f333(f333(f250(f890(x100221,a874)),f333(f333(f44(a880,f890(x100221,a874)),f258(f890(a880,a874))),x100222)),f333(f333(f44(a880,f890(x100221,a874)),f258(f890(a880,a874))),x100223)))+~P4(f333(f333(f250(f890(x100221,a874)),f333(f333(f44(a880,f890(x100221,a874)),f333(f303(a880,f2(a880)),f548(x100223,x100224,x100222,x100221))),x100222)),f333(f333(f44(a880,f890(x100221,a874)),f333(f303(a880,f2(a880)),f333(f333(f81(a880),f548(x100223,x100224,x100222,x100221)),x100224))),x100223))) % 191.49/191.41 [10144]~P4(f333(f333(f335(x101442),x101444),f333(f259(x101441,x101442),x101443)))+P4(f333(f269(x101441,x101442,f333(f333(f9(x101441,f890(f889(x101441,x101442),a874),f890(x101442,a874)),f333(f333(f10(f890(x101442,f890(f890(f889(x101441,x101442),a874),a874)),f890(f890(f889(x101441,x101442),a874),f890(x101442,a874)),x101441),f9(x101442,f890(f889(x101441,x101442),a874),a874)),f333(f333(f10(f890(x101442,f889(x101441,x101442)),f890(x101442,f890(f890(f889(x101441,x101442),a874),a874)),x101441),f333(f10(f889(x101441,x101442),f890(f890(f889(x101441,x101442),a874),a874),x101442),f335(f889(x101441,x101442)))),f263(x101441,x101442)))),x101443)),x101444)) % 191.49/191.41 [10145]~P4(f333(f333(f335(x101451),x101454),f333(f261(x101451,x101452),x101453)))+P4(f333(f268(x101451,x101452,f333(f333(f9(x101451,f890(f889(x101451,x101452),a874),f890(x101452,a874)),f333(f333(f10(f890(x101452,f890(f890(f889(x101451,x101452),a874),a874)),f890(f890(f889(x101451,x101452),a874),f890(x101452,a874)),x101451),f9(x101452,f890(f889(x101451,x101452),a874),a874)),f333(f333(f10(f890(x101452,f889(x101451,x101452)),f890(x101452,f890(f890(f889(x101451,x101452),a874),a874)),x101451),f333(f10(f889(x101451,x101452),f890(f890(f889(x101451,x101452),a874),a874),x101452),f335(f889(x101451,x101452)))),f263(x101451,x101452)))),x101453)),x101454)) % 191.49/191.41 [10157]P4(f333(f333(f335(x101571),x101572),f333(f259(x101573,x101571),x101574)))+~P4(f333(f269(x101573,x101571,f333(f333(f9(x101573,f890(f889(x101573,x101571),a874),f890(x101571,a874)),f333(f333(f10(f890(x101571,f890(f890(f889(x101573,x101571),a874),a874)),f890(f890(f889(x101573,x101571),a874),f890(x101571,a874)),x101573),f9(x101571,f890(f889(x101573,x101571),a874),a874)),f333(f333(f10(f890(x101571,f889(x101573,x101571)),f890(x101571,f890(f890(f889(x101573,x101571),a874),a874)),x101573),f333(f10(f889(x101573,x101571),f890(f890(f889(x101573,x101571),a874),a874),x101571),f335(f889(x101573,x101571)))),f263(x101573,x101571)))),x101574)),x101572)) % 191.49/191.41 [10158]P4(f333(f333(f335(x101581),x101582),f333(f261(x101581,x101583),x101584)))+~P4(f333(f268(x101581,x101583,f333(f333(f9(x101581,f890(f889(x101581,x101583),a874),f890(x101583,a874)),f333(f333(f10(f890(x101583,f890(f890(f889(x101581,x101583),a874),a874)),f890(f890(f889(x101581,x101583),a874),f890(x101583,a874)),x101581),f9(x101583,f890(f889(x101581,x101583),a874),a874)),f333(f333(f10(f890(x101583,f889(x101581,x101583)),f890(x101583,f890(f890(f889(x101581,x101583),a874),a874)),x101581),f333(f10(f889(x101581,x101583),f890(f890(f889(x101581,x101583),a874),a874),x101583),f335(f889(x101581,x101583)))),f263(x101581,x101583)))),x101584)),x101582)) % 191.49/191.41 [9836]P4(f333(f161(x98361,x98362),x98363))+~P4(f333(f161(x98361,f333(f333(f20(x98361,a874,a874),f333(f333(f10(a874,f890(a874,a874),x98361),a331),x98364)),x98362)),x98363)) % 191.49/191.41 [9837]P4(f333(f161(x98371,x98372),x98373))+~P4(f333(f161(x98371,f333(f333(f20(x98371,a874,a874),f333(f333(f10(a874,f890(a874,a874),x98371),a331),x98372)),x98374)),x98373)) % 191.49/191.41 [9914]~P115(x99141)+E(f333(f333(f82(x99141),f333(f333(f81(x99141),f79(x99141)),f79(x99141))),f333(f333(f8(a880,x99141),f333(f333(f10(x99141,x99141,a880),f333(f81(x99141),x99142)),f333(f333(f9(a880,x99141,x99141),f333(f333(f10(x99141,f890(x99141,x99141),a880),f82(x99141)),f105(x99141))),x99143))),f333(f256(a880),x99144))),f333(f333(f82(x99141),f333(f105(x99141),x99144)),f333(f333(f81(x99141),x99142),f333(f333(f81(x99141),x99142),f333(f333(f82(x99141),f333(f105(x99141),f333(f333(f3(a880),x99144),f79(a880)))),x99143))))) % 191.49/191.41 [10042]P4(f333(x100421,f705(x100422,x100423,x100424,x100421)))+P40(x100422,f333(f255(f889(x100422,x100422)),f333(f272(x100422,x100422,a874),f333(f333(f10(f890(x100422,a874),f890(x100422,a874),x100422),f333(f20(x100422,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100422),a331),x100421))),f333(f333(f9(x100422,f890(x100422,x100422),f890(x100422,a874)),f333(f333(f10(f890(x100422,a874),f890(f890(x100422,x100422),f890(x100422,a874)),x100422),f10(x100422,a874,x100422)),a330)),x100423))))) % 191.49/191.41 [10053]~P4(f333(f333(f251(a880),f333(x100534,f333(x100533,f705(x100531,x100533,x100534,x100532)))),f333(x100534,f705(x100531,x100533,x100534,x100532))))+P40(x100531,f333(f255(f889(x100531,x100531)),f333(f272(x100531,x100531,a874),f333(f333(f10(f890(x100531,a874),f890(x100531,a874),x100531),f333(f20(x100531,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100531),a331),x100532))),f333(f333(f9(x100531,f890(x100531,x100531),f890(x100531,a874)),f333(f333(f10(f890(x100531,a874),f890(f890(x100531,x100531),f890(x100531,a874)),x100531),f10(x100531,a874,x100531)),a330)),x100533))))) % 191.49/191.41 [10193]~P4(f333(f333(f335(f889(x101931,x101931)),f333(f333(f263(x101931,x101931),x101933),x101934)),f333(f333(f115(f890(f889(x101931,x101931),a874)),x101932),f309(x101931,f194(f890(f889(x101931,x101931),a874))))))+P4(f333(f333(f333(f333(f115(f890(x101931,f890(x101931,a874))),f333(f333(f9(x101931,f890(f889(x101931,x101931),a874),f890(x101931,a874)),f333(f333(f10(f890(x101931,f890(f890(f889(x101931,x101931),a874),a874)),f890(f890(f889(x101931,x101931),a874),f890(x101931,a874)),x101931),f9(x101931,f890(f889(x101931,x101931),a874),a874)),f333(f333(f10(f890(x101931,f889(x101931,x101931)),f890(x101931,f890(f890(f889(x101931,x101931),a874),a874)),x101931),f333(f10(f889(x101931,x101931),f890(f890(f889(x101931,x101931),a874),a874),x101931),f335(f889(x101931,x101931)))),f263(x101931,x101931)))),x101932)),a330),x101933),x101934)) % 191.49/191.41 [10207]P4(f333(f333(f335(f889(x102071,x102071)),f333(f333(f263(x102071,x102071),x102072),x102073)),f333(f333(f115(f890(f889(x102071,x102071),a874)),x102074),f309(x102071,f194(f890(f889(x102071,x102071),a874))))))+~P4(f333(f333(f333(f333(f115(f890(x102071,f890(x102071,a874))),f333(f333(f9(x102071,f890(f889(x102071,x102071),a874),f890(x102071,a874)),f333(f333(f10(f890(x102071,f890(f890(f889(x102071,x102071),a874),a874)),f890(f890(f889(x102071,x102071),a874),f890(x102071,a874)),x102071),f9(x102071,f890(f889(x102071,x102071),a874),a874)),f333(f333(f10(f890(x102071,f889(x102071,x102071)),f890(x102071,f890(f890(f889(x102071,x102071),a874),a874)),x102071),f333(f10(f889(x102071,x102071),f890(f890(f889(x102071,x102071),a874),a874),x102071),f335(f889(x102071,x102071)))),f263(x102071,x102071)))),x102074)),a330),x102072),x102073)) % 191.49/191.41 [10030]~P111(x100303)+E(f91(x100301,f333(f333(f20(x100301,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100301),a331),x100302)),f333(f333(f10(f890(x100301,a874),a874,x100301),f88(x100301)),f333(f333(f10(f890(x100301,a874),f890(x100301,a874),x100301),f333(f20(x100301,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100301),a336),x100302))),f333(f333(f10(x100303,f890(x100301,a874),x100301),f333(f9(x100301,x100303,a874),f333(f333(f10(x100303,f890(x100303,a874),x100301),f250(x100303)),x100304))),x100304))))),f333(f94(x100301,x100303,x100304),x100302)) % 191.49/191.41 [10067]~P111(x100673)+E(f91(x100671,f333(f333(f20(x100671,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100671),a331),x100672)),f333(f333(f10(f890(x100671,a874),a874,x100671),f88(x100671)),f333(f333(f10(f890(x100671,a874),f890(x100671,a874),x100671),f333(f20(x100671,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100671),a336),x100672))),f333(f333(f9(x100671,f890(x100671,x100673),f890(x100671,a874)),f333(f333(f10(f890(x100673,a874),f890(f890(x100671,x100673),f890(x100671,a874)),x100671),f10(x100673,a874,x100671)),f333(f333(f10(x100673,f890(x100673,a874),x100671),f250(x100673)),x100674))),x100674))))),f97(x100671,x100673,x100674,x100672)) % 191.49/191.41 [10142]E(f333(f333(f152(f881(x101421)),f333(f333(f152(x101421),x101422),f333(f143(f881(x101421),f881(x101421),f127(x101421),f118(x101421)),f333(f333(f155(f881(x101421),f881(x101421)),f157(f881(x101421),x101421,f118(x101421),f333(f333(f10(f881(x101421),f890(f881(x101421),f881(x101421)),x101421),f18(f881(x101421),f881(x101421))),f333(f333(f9(x101421,f881(x101421),f881(x101421)),f152(x101421)),f118(x101421))))),x101423)))),f180(x101421,f333(f333(f152(f881(x101421)),x101424),f333(f143(f881(f881(x101421)),f881(f881(x101421)),f127(f881(x101421)),f118(f881(x101421))),f333(f333(f155(f881(x101421),f881(f881(x101421))),f157(f881(f881(x101421)),x101421,f118(f881(x101421)),f333(f18(f890(f881(x101421),f881(f881(x101421))),x101421),f333(f333(f9(f881(x101421),f881(f881(x101421)),f881(f881(x101421))),f152(f881(x101421))),f118(f881(x101421)))))),x101423))))),f180(x101421,f333(f333(f152(f881(x101421)),f333(f333(f152(x101421),x101422),x101424)),x101423)))+~P4(f333(f321(f881(f881(x101421)),f181(x101421)),f333(f333(f152(f881(x101421)),f333(f333(f152(x101421),x101422),x101424)),x101423))) % 191.49/191.41 [10192]~P4(f333(f63(x101922),f333(f255(x101922),x101924)))+P4(f333(f63(x101921),f333(f255(x101921),f333(f333(f10(f890(x101922,a874),a874,x101921),f87(x101922)),f333(f333(f9(x101921,f890(x101922,a874),f890(x101922,a874)),f333(f333(f10(f890(x101922,f890(a874,a874)),f890(f890(x101922,a874),f890(x101922,a874)),x101921),f20(x101922,a874,a874)),f333(f333(f10(f890(x101922,a874),f890(x101922,f890(a874,a874)),x101921),f333(f10(a874,f890(a874,a874),x101922),a331)),f333(f333(f9(x101921,f890(x101922,x101921),f890(x101922,a874)),f333(f333(f10(f890(x101921,a874),f890(f890(x101922,x101921),f890(x101922,a874)),x101921),f10(x101921,a874,x101922)),a330)),x101923)))),x101924))))) % 191.49/191.41 [5289]E(x52891,x52892)+~E(f129(x52893,x52894,x52891),f129(x52893,x52895,x52892)) % 191.49/191.41 [5290]E(x52901,x52902)+~E(f129(x52903,x52901,x52904),f129(x52903,x52902,x52905)) % 191.49/191.41 [5663]E(f333(f333(f311(x56631),x56632),f184(x56631,x56633,x56634)),f184(x56631,x56633,x56634))+~E(f333(x56634,x56632),f333(f242(x56633),x56635)) % 191.49/191.41 [6071]P4(f333(f269(x60711,x60712,x60713),x60714))+~P4(f333(f333(x60713,x60715),x60714)) % 191.49/191.41 [6073]P4(f333(f268(x60731,x60732,x60733),x60734))+~P4(f333(f333(x60733,x60734),x60735)) % 191.49/191.41 [6076]~E(f333(x60764,x60762),f333(f242(x60763),x60765))+P4(f333(f333(f335(x60761),x60762),f184(x60761,x60763,x60764))) % 191.49/191.41 [6077]~E(f333(x60774,x60775),f333(f242(x60771),x60772))+P4(f333(f333(f335(x60771),x60772),f186(x60773,x60771,x60774))) % 191.49/191.41 [6534]~E(x65345,f2(a104))+E(f333(f207(x65341,x65342,x65343,x65344),x65345),f120(x65342)) % 191.49/191.41 [6535]~E(x65355,f2(a104))+E(f333(f205(x65351,x65352,x65353,x65354),x65355),f130(x65352)) % 191.49/191.41 [6671]~E(x66713,f2(a104))+E(f333(f282(x66711,x66712,x66713,x66714),x66715),f333(f263(x66711,x66712),x66715)) % 191.49/191.41 [6743]~E(f333(x67434,x67435),f197(x67432))+E(f333(f244(f884(x67431),x67432,f197(x67431),x67433),f333(x67434,x67435)),f197(x67431)) % 191.49/191.41 [7347]E(f333(x73471,x73472),f197(x73473))+~E(f333(f185(x73474,x73473,x73475,x73471),x73472),f197(x73473)) % 191.49/191.41 [7348]E(f333(x73481,x73482),f197(x73483))+~E(f333(f185(x73484,x73483,x73481,x73485),x73482),f197(x73483)) % 191.49/191.41 [7383]E(f333(f185(x73831,x73832,x73833,x73834),x73835),f333(x73833,x73835))+P4(f333(f333(f335(x73831),x73835),f184(x73831,x73832,x73834))) % 191.49/191.41 [7384]E(f333(f185(x73841,x73842,x73843,x73844),x73845),f333(x73844,x73845))+P4(f333(f333(f335(x73841),x73845),f184(x73841,x73842,x73843))) % 191.49/191.41 [7698]~P23(x76984,x76981,x76982,x76985)+E(f333(f74(x76981,x76981,x76981,f333(x76982,x76983)),f333(x76982,x76983)),f333(x76982,x76983)) % 191.49/191.41 [7743]E(f333(f185(x77431,x77432,x77433,x77434),x77435),f333(x77434,x77435))+~P4(f333(f333(f335(x77431),x77435),f184(x77431,x77432,x77434))) % 191.49/191.41 [8089]~P19(x80895,x80891,x80892)+E(f333(f74(x80891,x80891,x80891,f333(x80892,x80893)),f333(x80892,x80894)),f333(f74(x80891,x80891,x80891,f333(x80892,x80894)),f333(x80892,x80893))) % 191.49/191.41 [8414]P4(f333(f333(f335(f889(x84141,x84141)),f333(f333(f263(x84141,x84141),x84142),x84143)),f327(x84141,x84144,x84145)))+~P4(f333(f333(f251(a880),f333(x84144,x84142)),f333(x84144,x84143))) % 191.49/191.41 [8516]~P4(f333(f333(f335(x85164),x85163),f297(x85164,x85161,x85162,x85165)))+P4(f333(f333(x85161,x85162),x85163)) % 191.49/191.41 [8517]~P4(f333(f333(f335(x85174),x85173),f300(x85174,x85171,x85172,x85175)))+P4(f333(f333(x85171,x85172),x85173)) % 191.49/191.41 [8518]~P4(f333(f333(f335(x85184),x85182),f297(x85184,x85181,x85185,x85183)))+P4(f333(f333(x85181,x85182),x85183)) % 191.49/191.41 [8519]~P4(f333(f333(f335(x85194),x85192),f300(x85194,x85191,x85195,x85193)))+P4(f333(f333(x85191,x85192),x85193)) % 191.49/191.41 [8649]~P56(x86492,x86491,x86495,x86493,x86494)+E(f333(f312(x86491,x86492,x86493),x86494),f258(f890(x86492,a874))) % 191.49/191.41 [9074]~P37(x90741,x90742,x90743,x90744,x90745)+P37(x90741,x90742,x90743,f333(f170(x90741),x90744),f333(f170(x90742),x90745)) % 191.49/191.41 [9076]~P37(x90761,x90762,x90763,f333(f170(x90761),x90764),x90765)+P37(x90761,x90762,x90763,x90764,f333(f170(x90762),x90765)) % 191.49/191.41 [9077]~P37(x90771,x90772,x90773,x90774,f333(f170(x90772),x90775))+P37(x90771,x90772,x90773,f333(f170(x90771),x90774),x90775) % 191.49/191.41 [9083]P37(x90831,x90832,x90833,x90834,x90835)+~P37(x90831,x90832,x90833,f333(f170(x90831),x90834),f333(f170(x90832),x90835)) % 191.49/191.41 [9495]P4(f333(f333(f335(f889(f881(x94951),f881(x94951))),f333(f333(f263(f881(x94951),f881(x94951)),f333(f333(f152(x94951),x94952),x94953)),f333(f333(f152(x94951),x94952),x94954))),f158(x94951,x94955)))+~P4(f333(f333(f335(f889(f881(x94951),f881(x94951))),f333(f333(f263(f881(x94951),f881(x94951)),x94953),x94954)),f158(x94951,x94955))) % 191.49/191.41 [9496]P4(f333(f333(f335(f889(f881(x94961),f881(x94961))),f333(f333(f263(f881(x94961),f881(x94961)),f333(f333(f127(x94961),x94962),x94963)),f333(f333(f127(x94961),x94962),x94964))),f148(x94961,x94965)))+~P4(f333(f333(f335(f889(f881(x94961),f881(x94961))),f333(f333(f263(f881(x94961),f881(x94961)),x94963),x94964)),f148(x94961,x94965))) % 191.49/191.41 [9702]E(f333(f333(f152(x97021),f593(x97022,x97023,x97024,x97025,x97021)),f596(x97022,x97023,x97024,x97025,x97021)),x97025)+~P4(f333(f333(f335(f889(f881(x97021),f881(x97021))),f333(f333(f263(f881(x97021),f881(x97021)),x97025),f333(f333(f152(x97021),x97024),x97023))),f159(x97021,x97022))) % 191.49/191.41 [9724]E(f333(f333(f152(x97241),f597(x97242,x97243,x97244,x97245,x97241)),f598(x97242,x97243,x97244,x97245,x97241)),x97243)+~P4(f333(f333(f335(f889(f881(x97241),f881(x97241))),f333(f333(f263(f881(x97241),f881(x97241)),f333(f333(f152(x97241),x97245),x97244)),x97243)),f159(x97241,x97242))) % 191.49/191.41 [9890]~P4(f333(f333(f335(f889(f881(x98901),f881(x98901))),f333(f333(f263(f881(x98901),f881(x98901)),f333(f333(f152(x98901),x98905),x98902)),x98904)),f159(x98901,x98903)))+P4(f333(f333(f335(f889(f881(x98901),f881(x98901))),f333(f333(f263(f881(x98901),f881(x98901)),x98902),f598(x98903,x98904,x98902,x98905,x98901))),f159(x98901,x98903))) % 191.49/191.41 [9949]~P4(f333(f333(f335(f889(f881(x99491),f881(x99491))),f333(f333(f263(f881(x99491),f881(x99491)),x99495),f333(f333(f152(x99491),x99494),x99493))),f159(x99491,x99492)))+P4(f333(f333(f335(f889(f881(x99491),f881(x99491))),f333(f333(f263(f881(x99491),f881(x99491)),f596(x99492,x99493,x99494,x99495,x99491)),x99493)),f159(x99491,x99492))) % 191.49/191.41 [10116]P4(f333(f333(f335(f889(x101161,x101161)),f333(f333(f263(x101161,x101161),f333(x101162,f333(f333(f81(a880),x101163),x101164))),f333(x101162,x101163))),f309(x101161,x101165)))+~P4(f333(f333(f335(f889(x101161,x101161)),f333(f333(f263(x101161,x101161),f333(x101162,f333(a117,f765(x101164,x101163,x101165,x101162,x101161)))),f333(x101162,f765(x101164,x101163,x101165,x101162,x101161)))),f309(x101161,x101165))) % 191.49/191.41 [5252]E(x52521,x52522)+~E(f333(f333(f152(x52523),x52524),x52521),f333(f333(f152(x52523),x52525),x52522)) % 191.49/191.41 [5253]E(x52531,x52532)+~E(f333(f333(f152(x52533),x52531),x52534),f333(f333(f152(x52533),x52532),x52535)) % 191.49/191.41 [5306]P4(f333(x53061,x53062))+~E(f333(f137(x53063,x53061),x53064),f333(f333(f152(x53063),x53062),x53065)) % 191.49/191.41 [5307]P4(f333(x53071,x53072))+~E(f333(f333(f152(x53073),x53072),x53074),f333(f137(x53073,x53071),x53075)) % 191.49/191.41 [5462]~E(f333(f333(f139(x54621),x54623),x54622),f333(f333(f152(x54621),x54624),x54625))+E(f333(f333(f166(x54621),x54622),x54623),x54624) % 191.49/191.41 [5592]~P18(x55924,x55925,x55921)+E(f333(f333(x55921,x55922),f333(f333(x55921,x55922),x55923)),f333(f333(x55921,x55922),x55923)) % 191.49/191.41 [6129]~E(x61294,f2(a104))+E(f333(f333(f122(x61291,x61292,x61293),x61294),x61295),f333(f333(f263(f881(x61292),x61291),f118(x61292)),x61295)) % 191.49/191.41 [6199]~P109(x61992)+~E(f333(f333(f149(x61991,x61992,x61993),x61994),x61995),f118(x61991)) % 191.49/191.41 [6571]E(x65711,x65712)+~E(f333(f333(f127(x65713),x65714),f333(f333(f152(x65713),x65711),f118(x65713))),f333(f333(f127(x65713),x65715),f333(f333(f152(x65713),x65712),f118(x65713)))) % 191.49/191.41 [6572]E(x65721,x65722)+~E(f333(f333(f127(x65723),x65721),f333(f333(f152(x65723),x65724),f118(x65723))),f333(f333(f127(x65723),x65722),f333(f333(f152(x65723),x65725),f118(x65723)))) % 191.49/191.41 [6818]E(f333(f188(x68181,x68182,x68183,x68184),x68185),f197(x68182))+P4(f333(f333(f335(x68181),x68185),x68184)) % 191.49/191.41 [6879]E(f333(f333(f311(x68791),f333(x68792,x68793)),f333(f312(x68794,x68791,x68792),x68795)),f333(f312(x68794,x68791,x68792),x68795))+~P4(f333(f333(f335(x68794),x68793),x68795)) % 191.49/191.41 [6886]~P4(f333(x68864,f333(x68863,x68865)))+P4(f333(f333(f313(x68861,x68862,x68863),x68864),x68865)) % 191.49/191.41 [6983]~E(f333(f312(x69831,x69832,x69833),x69834),x69835)+E(f333(f312(f890(x69831,a874),f890(x69832,a874),f312(x69831,x69832,x69833)),f333(f310(x69831),x69834)),f333(f310(x69832),x69835)) % 191.49/191.41 [7015]E(f333(f188(x70151,x70152,x70153,x70154),x70155),f333(x70153,x70155))+~P4(f333(f333(f335(x70151),x70155),x70154)) % 191.49/191.41 [7311]P28(x73111,x73112,x73113,x73114)+~P28(x73111,x73112,x73113,f333(f333(f311(x73111),x73115),x73114)) % 191.49/191.41 [7373]P4(f333(x73731,x73732))+~P4(f333(f333(f96(x73733,x73734,x73731),x73735),x73732)) % 191.49/191.41 [7417]~P4(f333(f333(f335(x74174),x74173),x74175))+P4(f333(f333(f335(x74171),f333(x74172,x74173)),f333(f312(x74174,x74171,x74172),x74175))) % 191.49/191.41 [7441]~P109(x74412)+E(f151(x74411,x74412,x74413,f333(f137(x74411,x74414),x74415)),f333(f137(x74411,x74414),f151(x74411,x74412,x74413,x74415))) % 191.49/191.41 [7474]P4(f333(x74741,f333(x74742,x74743)))+~P4(f333(f333(f313(x74744,x74745,x74742),x74741),x74743)) % 191.49/191.41 [7475]P4(f333(f333(x74751,x74752),x74753))+~P4(f333(f333(f96(x74754,x74751,x74755),x74752),x74753)) % 191.49/191.41 [7538]~P4(f333(f333(f335(x75383),f333(x75384,x75382)),x75385))+P4(f333(f333(f335(x75381),x75382),f333(f313(x75381,x75383,x75384),x75385))) % 191.49/191.41 [7924]~P4(f333(f333(f335(x79245),x79243),f333(f313(x79245,x79241,x79242),x79244)))+P4(f333(f333(f335(x79241),f333(x79242,x79243)),x79244)) % 191.49/191.41 [8157]~E(x81573,f333(f333(f333(f73(x81571,f884(x81572)),f333(f18(f884(x81572),x81571),f197(x81572))),x81574),f333(f242(x81572),x81575)))+E(f184(x81571,x81572,x81573),f333(f333(f311(x81571),x81574),f194(f890(x81571,a874)))) % 191.49/191.41 [8235]~P19(x82352,x82351,x82353)+E(f333(f143(x82351,x82352,f333(f9(x82352,x82351,x82351),x82353),x82354),f153(x82352,x82355)),f333(f333(f66(x82352,x82351,x82353),x82354),f333(f173(x82352),x82355))) % 191.49/191.41 [8254]E(f333(x82541,f725(x82542,x82541,x82543,x82544)),x82544)+~P4(f333(f333(f335(x82545),x82544),f333(f312(x82543,x82545,x82541),x82542))) % 191.49/191.41 [8562]~E(x85622,f333(f333(f152(x85621),x85624),x85625))+P4(f333(f333(f335(f889(f881(x85621),f881(x85621))),f333(f333(f263(f881(x85621),f881(x85621)),f118(x85621)),x85622)),f148(x85621,x85623))) % 191.49/191.41 [8615]~P37(x86151,x86153,x86155,x86152,x86154)+E(f333(f195(f881(x86151)),x86152),f333(f195(f881(x86153)),x86154)) % 191.49/191.41 [8624]P4(f333(f333(f250(f890(x86241,a874)),f333(f333(f43(x86242,f890(x86241,a874)),x86243),x86244)),f333(x86244,x86245)))+~P4(f333(f333(f335(x86242),x86245),x86243)) % 191.49/191.41 [8664]~P56(x86641,x86642,x86643,x86645,x86644)+E(f333(f312(x86641,x86642,x86643),f258(f890(x86641,a874))),x86644) % 191.49/191.41 [8873]E(f333(f333(f333(f73(x88731,f884(x88732)),f188(x88731,x88732,x88733,x88734)),x88735),f197(x88732)),f188(x88731,x88732,x88733,x88734))+P4(f333(f333(f335(x88731),x88735),x88734)) % 191.49/191.41 [8878]E(f333(f137(x88781,x88782),f748(x88783,x88784,x88785,x88782,x88781)),x88783)+~E(f333(f137(x88781,x88782),x88785),f333(f333(f152(x88781),x88784),x88783)) % 191.49/191.41 [8879]E(f333(f137(x88791,x88792),f750(x88793,x88792,x88794,x88795,x88791)),x88794)+~E(f333(f333(f152(x88791),x88795),x88794),f333(f137(x88791,x88792),x88793)) % 191.49/191.41 [8880]E(f333(x88801,f557(x88802,x88803,x88801,x88804,x88805)),x88802)+~E(f333(f333(f208(x88805,x88804),x88801),x88803),f333(f242(x88804),x88802)) % 191.49/191.41 [8884]E(f333(f242(x88841),f557(x88842,x88843,x88844,x88845,x88841)),x88843)+~E(f333(f333(f208(x88841,x88845),x88844),x88843),f333(f242(x88845),x88842)) % 191.49/191.41 [8980]E(f333(f195(f881(x89801)),x89802),x89803)+~P4(f333(f333(f335(f889(f881(x89801),f881(x89801))),f333(f333(f263(f881(x89801),f881(x89801)),x89804),x89802)),f333(f144(x89801,x89805),x89803))) % 191.49/191.41 [8981]E(f333(f195(f881(x89811)),x89812),x89813)+~P4(f333(f333(f335(f889(f881(x89811),f881(x89811))),f333(f333(f263(f881(x89811),f881(x89811)),x89812),x89814)),f333(f144(x89811,x89815),x89813))) % 191.49/191.41 [9041]P4(f333(f333(f335(x90411),f725(x90412,x90413,x90411,x90414)),x90412))+~P4(f333(f333(f335(x90415),x90414),f333(f312(x90411,x90415,x90413),x90412))) % 191.49/191.41 [9204]E(f333(f312(x92041,x92042,x92043),f350(x92044,x92043,x92041,x92045,x92042)),x92045)+~P4(f333(f333(f250(f890(x92042,a874)),x92045),f333(f312(x92041,x92042,x92043),x92044))) % 191.49/191.41 [9456]E(f333(x94561,f652(x94562,x94561,x94563,x94564,x94565)),f333(f242(x94565),x94564))+~P4(f333(f333(f335(x94565),x94564),f186(x94563,x94565,f188(x94563,x94565,x94561,x94562)))) % 191.49/191.41 [9517]P4(f333(f333(f335(f889(f881(x95171),f881(x95171))),f333(f333(f263(f881(x95171),f881(x95171)),f333(f333(f152(x95171),x95172),x95173)),f333(f333(f152(x95171),x95172),x95174))),f309(f881(x95171),f158(x95171,x95175))))+~P4(f333(f333(f335(f889(f881(x95171),f881(x95171))),f333(f333(f263(f881(x95171),f881(x95171)),x95173),x95174)),f309(f881(x95171),f158(x95171,x95175)))) % 191.49/191.41 [9548]~E(f333(x95483,f559(x95485,x95484,x95483,x95482,x95481)),f333(x95485,f559(x95485,x95484,x95483,x95482,x95481)))+E(f333(f333(f155(x95481,x95482),x95483),x95484),f333(f333(f155(x95481,x95482),x95485),x95484)) % 191.49/191.41 [9634]~E(f333(f137(x96341,x96345),x96344),f333(f333(f152(x96341),x96343),x96342))+E(f333(f333(f127(x96341),f749(x96342,x96343,x96344,x96345,x96341)),f333(f333(f152(x96341),x96343),f748(x96342,x96343,x96344,x96345,x96341))),x96344) % 191.49/191.41 [9635]~E(f333(f333(f152(x96351),x96355),x96354),f333(f137(x96351,x96353),x96352))+E(f333(f333(f127(x96351),f751(x96352,x96353,x96354,x96355,x96351)),f333(f333(f152(x96351),x96355),f750(x96352,x96353,x96354,x96355,x96351))),x96352) % 191.49/191.41 [9641]E(f333(f333(f155(x96411,x96412),x96413),x96414),f333(f333(f155(x96411,x96412),x96415),x96414))+P4(f333(f333(f335(x96411),f559(x96413,x96414,x96415,x96412,x96411)),f333(f173(x96411),x96414))) % 191.49/191.41 [9669]~P4(f333(f333(f335(x96695),x96694),f333(f287(x96691,x96695,x96693),x96692)))+P4(f333(f333(f335(x96691),f549(x96692,x96693,x96691,x96694,x96695)),x96692)) % 191.49/191.41 [9670]~P4(f333(f333(f335(x96705),x96704),f333(f287(x96701,x96705,x96703),x96702)))+P4(f333(f333(f335(x96701),f577(x96702,x96703,x96701,x96704,x96705)),x96702)) % 191.49/191.41 [9696]~P4(f333(f333(f250(f890(x96965,a874)),x96964),f333(f312(x96961,x96965,x96963),x96962)))+P4(f333(f333(f250(f890(x96961,a874)),f350(x96962,x96963,x96961,x96964,x96965)),x96962)) % 191.49/191.41 [9752]~P4(f333(f333(f335(x97525),x97524),f186(x97521,x97525,f188(x97521,x97525,x97523,x97522))))+P4(f333(f333(f335(x97521),f652(x97522,x97523,x97521,x97524,x97525)),x97522)) % 191.49/191.41 [10160]E(x101601,f2(a104))+E(f333(f244(f889(f881(x101602),x101603),f889(x101602,x101603),f333(f333(f263(f881(x101602),x101603),f118(x101602)),x101604),f333(f272(x101602,x101603,f889(f881(x101602),x101603)),f333(f333(f9(x101602,f890(x101603,f889(f881(x101602),x101603)),f890(x101603,f889(f881(x101602),x101603))),f333(f333(f10(f890(f889(f881(x101602),x101603),f889(f881(x101602),x101603)),f890(f890(x101603,f889(f881(x101602),x101603)),f890(x101603,f889(f881(x101602),x101603))),x101602),f10(f889(f881(x101602),x101603),f889(f881(x101602),x101603),x101603)),f333(f333(f10(f890(f881(x101602),f890(x101603,f889(f881(x101602),x101603))),f890(f889(f881(x101602),x101603),f889(f881(x101602),x101603)),x101602),f272(f881(x101602),x101603,f889(f881(x101602),x101603))),f333(f333(f10(f890(f881(x101602),f881(x101602)),f890(f881(x101602),f890(x101603,f889(f881(x101602),x101603))),x101602),f333(f10(f881(x101602),f890(x101603,f889(f881(x101602),x101603)),f881(x101602)),f263(f881(x101602),x101603))),f152(x101602))))),f333(f122(x101603,x101602,x101605),f333(f333(f3(a104),x101601),f79(a104)))))),f333(x101605,x101604)),f333(f333(f122(x101603,x101602,x101605),x101601),x101604)) % 191.49/191.41 [5475]~E(f333(x54753,x54754),x54755)+E(f333(f333(f333(f73(x54751,x54752),x54753),x54754),x54755),x54753) % 191.49/191.41 [5915]E(f333(x59151,x59152),x59153)+~E(f333(f333(f333(f73(x59154,x59155),x59151),x59152),x59153),x59151) % 191.49/191.41 [6010]E(x60101,x60102)+~E(f333(f271(x60103,x60104),f333(f333(f263(x60103,x60104),x60105),x60101)),x60102) % 191.49/191.41 [6011]E(x60111,x60112)+~E(f333(f262(x60113,x60114),f333(f333(f263(x60113,x60114),x60111),x60115)),x60112) % 191.49/191.41 [6273]~E(x62733,f333(f333(f127(x62731),x62734),f333(f333(f152(x62731),x62732),x62735)))+P4(f333(f333(f335(x62731),x62732),f333(f173(x62731),x62733))) % 191.49/191.41 [6658]E(f333(f312(x66581,x66582,f333(f18(x66582,x66581),x66583)),x66584),f333(f333(f311(x66582),x66583),f194(f890(x66582,a874))))+~P4(f333(f333(f335(x66581),x66585),x66584)) % 191.49/191.41 [6728]E(f333(f333(f115(f890(x67281,a874)),f333(f173(x67281),x67282)),f333(f173(x67281),x67283)),f333(f173(x67281),x67284))+~E(f168(x67281,x67285,x67284),f333(f333(f263(f881(x67281),f881(x67281)),x67282),x67283)) % 191.49/191.41 [6821]~P109(x68212)+E(f333(f195(f881(x68211)),f333(f333(f149(x68211,x68212,x68213),x68214),x68215)),f333(a117,f333(f195(f881(x68211)),x68215))) % 191.49/191.41 [6833]~P109(x68332)+E(f333(f173(x68331),f333(f333(f149(x68331,x68332,x68333),x68334),x68335)),f333(f333(f311(x68331),x68334),f333(f173(x68331),x68335))) % 191.49/191.41 [7105]~P115(x71051)+E(f333(f333(f81(x71051),f333(f333(f81(x71051),x71052),x71053)),f333(f333(f81(x71051),x71054),x71055)),f333(f333(f81(x71051),f333(f333(f81(x71051),x71052),x71054)),f333(f333(f81(x71051),x71053),x71055))) % 191.49/191.41 [7106]~P115(x71061)+E(f333(f333(f82(x71061),f333(f333(f82(x71061),x71062),x71063)),f333(f333(f82(x71061),x71064),x71065)),f333(f333(f82(x71061),f333(f333(f82(x71061),x71062),x71064)),f333(f333(f82(x71061),x71063),x71065))) % 191.49/191.41 [7107]~P63(x71071)+E(f333(f333(f291(x71071),f333(f333(f82(x71071),x71072),x71073)),f333(f333(f82(x71071),x71074),x71075)),f333(f333(f82(x71071),f333(f333(f291(x71071),x71072),x71074)),f333(f333(f291(x71071),x71073),x71075))) % 191.49/191.41 [7121]~P109(x71211)+E(f307(x71211,f333(f333(f249(x71211),x71212),x71213),f333(f333(f248(x71211),x71214),x71215)),f333(f333(f106(f890(x71211,a874)),f307(x71211,x71212,x71214)),f307(x71211,x71213,x71215))) % 191.49/191.41 [7122]~P109(x71221)+E(f306(x71221,f333(f333(f249(x71221),x71222),x71223),f333(f333(f248(x71221),x71224),x71225)),f333(f333(f106(f890(x71221,a874)),f306(x71221,x71222,x71224)),f306(x71221,x71223,x71225))) % 191.49/191.41 [7123]~P109(x71231)+E(f304(x71231,f333(f333(f249(x71231),x71232),x71233),f333(f333(f248(x71231),x71234),x71235)),f333(f333(f106(f890(x71231,a874)),f304(x71231,x71232,x71234)),f304(x71231,x71233,x71235))) % 191.49/191.41 [7124]~P109(x71241)+E(f333(f333(f106(f890(x71241,a874)),f333(f303(x71241,x71242),x71243)),f333(f303(x71241,x71244),x71245)),f333(f303(x71241,f333(f333(f249(x71241),x71242),x71244)),f333(f333(f248(x71241),x71243),x71245))) % 191.49/191.41 [7239]~P4(f333(x72391,f484(x72393,x72392,x72391)))+P4(f333(x72391,f333(f333(f263(x72392,x72393),x72394),x72395))) % 191.49/191.41 [7317]~E(f333(x73173,x73174),f197(x73172))+E(f186(x73171,x73172,f333(f333(f333(f73(x73171,f884(x73172)),x73173),x73174),f333(f242(x73172),x73175))),f333(f333(f311(x73172),x73175),f186(x73171,x73172,x73173))) % 191.49/191.41 [7338]~E(x73382,f333(x73384,x73385))+P4(f333(f333(f335(x73381),x73382),f333(f312(x73383,x73381,x73384),f258(f890(x73383,a874))))) % 191.49/191.41 [7395]~E(f333(x73953,x73954),f197(x73952))+E(f333(f333(f3(f890(x73951,a874)),f184(x73951,x73952,x73953)),f333(f333(f311(x73951),x73954),x73955)),f333(f333(f3(f890(x73951,a874)),f184(x73951,x73952,x73953)),x73955)) % 191.49/191.41 [7414]~P19(x74143,x74142,x74144)+P19(x74141,x74142,f333(f333(f10(x74143,f890(x74142,x74142),x74141),x74144),x74145)) % 191.49/191.41 [7415]~P18(x74153,x74152,x74154)+P18(x74151,x74152,f333(f333(f10(x74153,f890(x74152,x74152),x74151),x74154),x74155)) % 191.49/191.41 [7553]~P28(x75531,x75532,x75533,x75534)+P28(x75531,x75532,x75533,f333(f333(f3(f890(x75531,a874)),x75534),x75535)) % 191.49/191.41 [7707]~P4(f333(f333(x77073,x77074),x77075))+P4(f333(f333(f272(x77071,x77072,a874),x77073),f333(f333(f263(x77071,x77072),x77074),x77075))) % 191.49/191.41 [7822]~P4(f333(x78222,x78224))+~E(f333(f333(f139(x78221),f333(f195(f881(x78221)),f177(x78221,x78222,x78223))),x78223),f333(f333(f152(x78221),x78224),x78225)) % 191.49/191.41 [7842]P28(x78421,x78422,x78423,x78424)+~P28(x78421,x78422,x78423,f333(f333(f115(f890(x78421,a874)),x78425),x78424)) % 191.49/191.41 [7843]P28(x78431,x78432,x78433,x78434)+~P28(x78431,x78432,x78433,f333(f333(f115(f890(x78431,a874)),x78434),x78435)) % 191.49/191.41 [7885]~P109(x78852)+E(f333(f333(f149(x78851,x78852,x78853),x78854),f151(x78851,x78852,x78853,x78855)),f151(x78851,x78852,x78853,f333(f333(f152(x78851),x78854),x78855))) % 191.49/191.41 [8044]~P30(x80441,f333(a117,x80442),f333(f333(f333(f93(x80441),x80443),f333(a26,x80444)),x80445))+P30(x80441,x80442,f333(f333(f333(f93(x80441),x80443),f333(f246(a876),f333(a28,x80444))),x80445)) % 191.49/191.41 [8184]P30(x81841,f333(a117,x81842),f333(f333(f333(f93(x81841),x81843),f333(a26,x81844)),x81845))+~P30(x81841,x81842,f333(f333(f333(f93(x81841),x81843),f333(f246(a876),f333(a28,x81844))),x81845)) % 191.49/191.41 [8212]~P18(x82122,x82121,x82123)+E(f333(f143(x82121,x82122,f333(f9(x82122,x82121,x82121),x82123),x82124),x82125),f333(f333(f66(x82122,x82121,x82123),x82124),f333(f173(x82122),x82125))) % 191.49/191.41 [8240]~E(f333(f333(f139(x82401),f333(f195(f881(x82401)),f177(x82401,x82402,x82403))),x82403),f333(f333(f152(x82401),x82404),x82405))+E(f333(f333(f127(x82401),f177(x82401,x82402,x82403)),f333(f333(f152(x82401),x82404),x82405)),x82403) % 191.49/191.41 [8264]P4(f333(f333(x82641,x82642),x82643))+~P4(f333(f333(f272(x82644,x82645,a874),x82641),f333(f333(f263(x82644,x82645),x82642),x82643))) % 191.49/191.41 [8323]~E(f333(f333(f178(x83231,x83232),x83235),x83233),f333(f242(x83232),x83234))+P4(f333(f333(f335(f889(x83231,x83232)),f333(f333(f263(x83231,x83232),x83233),x83234)),f333(f173(f889(x83231,x83232)),x83235))) % 191.49/191.41 [8718]P4(f333(f333(f250(f890(x87181,a874)),f333(f313(x87181,x87182,x87183),x87184)),f333(f313(x87181,x87182,x87183),x87185)))+~P4(f333(f333(f250(f890(x87182,a874)),x87184),x87185)) % 191.49/191.41 [8719]P4(f333(f333(f250(f890(x87191,a874)),f333(f312(x87192,x87191,x87193),x87194)),f333(f312(x87192,x87191,x87193),x87195)))+~P4(f333(f333(f250(f890(x87192,a874)),x87194),x87195)) % 191.49/191.41 [8797]E(x87971,f2(a104))+E(f333(f333(f274(x87972,x87973,x87972,f889(x87973,x87972)),f333(x87974,x87975)),f282(x87973,x87972,f333(f333(f3(a104),x87971),f79(a104)),x87974)),f333(f282(x87973,x87972,x87971,x87974),x87975)) % 191.49/191.41 [9110]P30(x91101,x91102,f333(f333(f333(f93(x91101),x91103),x91104),x91105))+P4(f333(f333(x91103,f853(x91105,x91104,x91103,x91102)),f855(x91105,x91104,x91103,x91102))) % 191.49/191.41 [9316]E(f333(f242(x93161),f563(x93162,x93163,x93164,x93161,x93165)),f333(f333(f178(x93165,x93161),x93162),x93164))+~P4(f333(f333(f335(f889(x93165,x93161)),f333(f333(f263(x93165,x93161),x93164),x93163)),f333(f173(f889(x93165,x93161)),x93162))) % 191.49/191.41 [9365]P30(x93651,x93652,f333(f333(f333(f93(x93651),x93653),x93654),x93655))+~P4(f333(f333(x93655,f853(x93655,x93654,x93653,x93652)),f856(x93655,x93654,x93653,x93652))) % 191.49/191.41 [9417]P30(x94171,x94172,f333(f333(f333(f93(x94171),x94173),x94174),x94175))+P4(f333(f333(f333(f333(a203,x94174),f855(x94175,x94174,x94173,x94172)),x94172),f856(x94175,x94174,x94173,x94172))) % 191.49/191.41 [9421]~P27(x94211,x94212,f333(f333(f311(f879(x94211)),f333(f333(f333(f93(x94211),x94213),f333(f246(a876),f333(a28,x94214))),x94215)),f194(f890(f879(x94211),a874))))+P27(x94211,x94212,f333(f333(f311(f879(x94211)),f333(f333(f333(f93(x94211),x94213),f333(a26,x94214)),x94215)),f194(f890(f879(x94211),a874)))) % 191.49/191.41 [9447]~P4(f333(f63(x94473),f333(f312(x94472,x94473,x94475),f258(f890(x94472,a874)))))+P4(f333(f63(x94471),f333(f312(x94472,x94471,f333(f333(f10(x94473,x94471,x94472),x94474),x94475)),f258(f890(x94472,a874))))) % 191.49/191.41 [9469]P4(f333(f333(f250(f890(f890(x94691,a874),a874)),f333(f312(f890(x94692,a874),f890(x94691,a874),f312(x94692,x94691,x94693)),f333(f310(x94692),x94694))),f333(f310(x94691),x94695)))+~P4(f333(f333(f250(f890(x94691,a874)),f333(f312(x94692,x94691,x94693),x94694)),x94695)) % 191.49/191.41 [9486]~P4(f333(f63(f884(x94861)),f333(f312(x94862,f884(x94861),x94863),f258(f890(x94862,a874)))))+P4(f333(f63(f884(x94861)),f333(f312(x94862,f884(x94861),f333(f333(f333(f73(x94862,f884(x94861)),x94863),x94864),f333(f242(x94861),x94865))),f258(f890(x94862,a874))))) % 191.49/191.41 [9557]E(x95571,x95572)+~P4(f333(f68(x95573,x95574,x95575,x95571,f194(f890(x95573,a874))),x95572)) % 191.49/191.41 [9570]E(f333(f333(f263(x95701,x95702),f687(x95703,x95704,x95705,x95702,x95701)),f690(x95703,x95704,x95705,x95702,x95701)),x95705)+~P4(f333(f333(f335(f889(x95701,x95702)),x95705),f333(f333(f270(x95701,x95702),x95704),x95703))) % 191.49/191.41 [9674]P4(f333(f333(f335(x96741),f687(x96742,x96743,x96744,x96745,x96741)),x96743))+~P4(f333(f333(f335(f889(x96741,x96745)),x96744),f333(f333(f270(x96741,x96745),x96743),x96742))) % 191.49/191.41 [9797]P27(x97975,x97974,f333(f333(f311(f879(x97975)),f333(f333(f333(f93(x97975),x97971),x97973),x97972)),f194(f890(f879(x97975),a874))))+P4(f333(f333(x97971,f692(x97972,x97973,x97974,x97975,x97971)),f693(x97972,x97973,x97974,x97975,x97971))) % 191.49/191.41 [9849]P4(f333(f333(f335(x98491),f690(x98492,x98493,x98494,x98491,x98495)),f333(x98492,f687(x98492,x98493,x98494,x98491,x98495))))+~P4(f333(f333(f335(f889(x98495,x98491)),x98494),f333(f333(f270(x98495,x98491),x98493),x98492))) % 191.49/191.41 [9867]P4(f333(f333(f335(f889(x98671,x98671)),f333(f333(f263(x98671,x98671),x98672),f782(x98673,x98674,x98675,x98672,x98671))),x98673))+~P4(f333(f333(f335(f889(x98671,x98671)),f333(f333(f263(x98671,x98671),x98672),x98675)),f333(f333(f189(f889(x98671,x98671),a874),f333(a117,x98674)),x98673))) % 191.49/191.41 [9868]P4(f333(f333(f335(f889(x98681,x98681)),f333(f333(f263(x98681,x98681),x98682),f790(x98683,x98684,x98685,x98682,x98681))),x98683))+~P4(f333(f333(f335(f889(x98681,x98681)),f333(f333(f263(x98681,x98681),x98682),x98685)),f333(f333(f189(f889(x98681,x98681),a874),f333(a117,x98684)),x98683))) % 191.49/191.41 [9886]~P4(f333(f333(f335(f889(f881(x98861),f881(x98861))),f333(f333(f263(f881(x98861),f881(x98861)),f333(f333(f152(x98861),x98862),x98865)),x98864)),f159(x98861,x98863)))+P4(f333(f333(f335(f889(x98861,x98861)),f333(f333(f263(x98861,x98861),x98862),f597(x98863,x98864,x98865,x98862,x98861))),x98863)) % 191.49/191.41 [9888]~P27(x98881,x98882,f333(f333(f311(f879(x98881)),f333(f333(f333(f93(x98881),f96(x98881,x98883,x98884)),x98885),x98883)),f194(f890(f879(x98881),a874))))+P27(x98881,x98882,f333(f333(f311(f879(x98881)),f333(f333(f333(f93(x98881),x98883),f33(x98884,x98885)),f96(x98881,x98883,f333(f74(a874,a874,a875,a328),x98884)))),f194(f890(f879(x98881),a874)))) % 191.49/191.41 [9889]~P31(x98891,x98892,f333(f333(f311(f879(x98891)),f333(f333(f333(f93(x98891),f96(x98891,x98893,x98894)),x98895),x98893)),f194(f890(f879(x98891),a874))))+P31(x98891,x98892,f333(f333(f311(f879(x98891)),f333(f333(f333(f93(x98891),x98893),f33(x98894,x98895)),f96(x98891,x98893,f333(f74(a874,a874,a875,a328),x98894)))),f194(f890(f879(x98891),a874)))) % 191.49/191.41 [10161]P27(x101611,x101612,f333(f333(f311(f879(x101611)),f333(f333(f333(f93(x101611),x101613),x101614),x101615)),f194(f890(f879(x101611),a874))))+~P27(x101611,x101612,f333(f333(f311(f879(x101611)),f333(f333(f333(f93(x101611),f333(f18(f890(a875,a874),x101611),f333(f333(f9(a875,a875,a874),a330),f693(x101615,x101614,x101612,x101611,x101613)))),x101614),f333(f18(f890(a875,a874),x101611),f333(x101615,f692(x101615,x101614,x101612,x101611,x101613))))),f194(f890(f879(x101611),a874)))) % 191.49/191.41 [6344]P4(f333(x63442,x63444))+E(f177(x63441,x63442,f333(f333(f127(x63441),x63443),f333(f333(f152(x63441),x63444),x63445))),f177(x63441,x63442,x63443)) % 191.49/191.41 [6394]~P6(x63942)+E(f333(f333(f333(f115(f890(x63941,x63942)),x63943),x63944),x63945),f333(f333(f115(x63942),f333(x63943,x63945)),f333(x63944,x63945))) % 191.49/191.41 [6396]~P67(x63962)+E(f333(f333(f333(f3(f890(x63961,x63962)),x63963),x63964),x63965),f333(f333(f3(x63962),f333(x63963,x63965)),f333(x63964,x63965))) % 191.49/191.41 [6398]~P6(x63982)+E(f333(f333(f333(f106(f890(x63981,x63982)),x63983),x63984),x63985),f333(f333(f106(x63982),f333(x63983,x63985)),f333(x63984,x63985))) % 191.49/191.41 [6416]E(x64161,x64162)+E(f333(f333(f166(x64163),f333(f333(f160(x64163,x64164),x64161),x64165)),x64162),f333(f333(f166(x64163),x64164),x64162)) % 191.49/191.41 [6676]~E(x66764,f194(f890(x66763,a874)))+E(f333(f333(f115(f890(x66761,a874)),x66762),f333(f333(f44(x66763,f890(x66761,a874)),x66764),x66765)),x66762) % 191.49/191.41 [6677]~E(x66774,f194(f890(x66773,a874)))+E(f333(f333(f3(f890(x66771,a874)),x66772),f333(f333(f44(x66773,f890(x66771,a874)),x66774),x66775)),x66772) % 191.49/191.41 [6678]~E(x66784,f194(f890(x66783,a874)))+E(f333(f333(f106(f890(x66781,a874)),x66782),f333(f333(f43(x66783,f890(x66781,a874)),x66784),x66785)),x66782) % 191.49/191.41 [6692]~E(x66924,f194(f890(x66923,a874)))+E(f333(f333(f311(x66921),x66922),f333(f333(f44(x66923,f890(x66921,a874)),x66924),x66925)),f333(f333(f311(x66921),x66922),f194(f890(x66921,a874)))) % 191.49/191.41 [7463]E(f333(f333(f166(x74631),f333(f333(f155(x74632,x74631),x74633),x74634)),x74635),f333(x74633,f333(f333(f166(x74632),x74634),x74635)))+~P4(f333(f333(f251(a880),x74635),f333(f195(f881(x74632)),x74634))) % 191.49/191.41 [7526]E(f333(f333(f115(f890(x75261,a874)),f333(x75262,x75263)),f333(f333(f44(x75264,f890(x75261,a874)),x75265),x75262)),f333(f333(f44(x75264,f890(x75261,a874)),x75265),x75262))+~P4(f333(f333(f335(x75264),x75263),x75265)) % 191.49/191.41 [7527]E(f333(f333(f106(f890(x75271,a874)),f333(x75272,x75273)),f333(f333(f43(x75274,f890(x75271,a874)),x75275),x75272)),f333(f333(f43(x75274,f890(x75271,a874)),x75275),x75272))+~P4(f333(f333(f335(x75274),x75273),x75275)) % 191.49/191.41 [8129]~E(x81293,f194(f890(x81291,a874)))+E(f333(f333(f44(x81291,f890(x81292,a874)),x81293),f333(f333(f10(f890(x81292,a874),f890(x81292,a874),x81291),f333(f311(x81292),x81294)),x81295)),f194(f890(x81292,a874))) % 191.49/191.41 [8135]~P4(f333(f333(f335(x81354),x81353),x81355))+P4(f333(f333(f250(f890(x81351,a874)),f333(x81352,x81353)),f333(f333(f44(x81354,f890(x81351,a874)),x81355),x81352))) % 191.49/191.41 [8263]~E(f333(x82634,x82632),x82635)+P4(f333(f333(f335(x82631),x82632),f333(f313(x82631,x82633,x82634),f333(f333(f311(x82633),x82635),f194(f890(x82633,a874)))))) % 191.49/191.41 [8309]~P54(x83091,x83092,f333(f288(x83092,x83091),x83093))+E(f333(f333(f106(f890(x83091,a874)),f333(f287(x83092,x83091,x83093),x83094)),f333(f287(x83092,x83091,x83093),x83095)),f333(f287(x83092,x83091,x83093),f333(f333(f106(f890(x83092,a874)),x83094),x83095))) % 191.49/191.41 [8384]E(x83841,f2(a104))+E(f333(f123(x83842,x83843,f333(x83844,f333(f333(f3(a104),x83841),f79(a104)))),f333(f333(f9(x83842,a104,f882(x83843)),x83845),x83841)),f333(f207(x83842,x83843,x83844,x83845),x83841)) % 191.49/191.41 [8424]E(x84241,f194(f890(x84242,a874)))+E(f333(f333(f44(x84242,f890(x84243,a874)),x84241),f333(f333(f10(f890(x84243,a874),f890(x84243,a874),x84242),f333(f311(x84243),x84244)),x84245)),f333(f333(f311(x84243),x84244),f333(f333(f44(x84242,f890(x84243,a874)),x84241),x84245))) % 191.49/191.41 [8479]~P28(x84792,x84791,x84793,f258(f890(x84792,a874)))+E(f333(f333(f3(f890(x84791,a874)),f333(f312(x84792,x84791,x84793),x84794)),f333(f312(x84792,x84791,x84793),x84795)),f333(f312(x84792,x84791,x84793),f333(f333(f3(f890(x84792,a874)),x84794),x84795))) % 191.49/191.41 [8480]~P28(x84802,x84801,x84803,f258(f890(x84802,a874)))+E(f333(f333(f106(f890(x84801,a874)),f333(f312(x84802,x84801,x84803),x84804)),f333(f312(x84802,x84801,x84803),x84805)),f333(f312(x84802,x84801,x84803),f333(f333(f106(f890(x84802,a874)),x84804),x84805))) % 191.49/191.41 [8548]~P4(f333(f333(f69(x85481,x85482,x85485),x85483),x85484))+P4(f333(f333(f335(f889(x85481,x85482)),f333(f333(f263(x85481,x85482),x85483),x85484)),x85485)) % 191.49/191.41 [8579]P4(f333(f333(f335(x85791),x85792),f333(f259(x85793,x85791),x85794)))+~P4(f333(f333(f335(f889(x85793,x85791)),f333(f333(f263(x85793,x85791),x85795),x85792)),x85794)) % 191.49/191.41 [8581]P4(f333(f333(f335(x85811),x85812),f333(f261(x85811,x85813),x85814)))+~P4(f333(f333(f335(f889(x85811,x85813)),f333(f333(f263(x85811,x85813),x85812),x85815)),x85814)) % 191.49/191.41 [8704]P4(f333(f333(f69(x87041,x87042,x87043),x87044),x87045))+~P4(f333(f333(f335(f889(x87041,x87042)),f333(f333(f263(x87041,x87042),x87044),x87045)),x87043)) % 191.49/191.41 [8734]E(f333(x87341,x87342),x87343)+~P4(f333(f333(f335(x87344),x87342),f333(f313(x87344,x87345,x87341),f333(f333(f311(x87345),x87343),f194(f890(x87345,a874)))))) % 191.49/191.41 [8977]P4(f333(f333(f335(f889(x89771,x89772)),f333(f333(f263(x89771,x89772),x89773),x89774)),f333(f288(x89772,x89771),x89775)))+~P4(f333(f333(f335(f889(x89772,x89771)),f333(f333(f263(x89772,x89771),x89774),x89773)),x89775)) % 191.49/191.41 [8995]~P4(f333(f333(x89951,x89955),x89954))+P4(f333(f333(x89951,f333(f271(x89952,x89953),f333(f333(f263(x89952,x89953),x89954),x89955))),f333(f262(x89952,x89953),f333(f333(f263(x89952,x89953),x89954),x89955)))) % 191.49/191.41 [9025]~P4(f333(f333(f335(f889(x90252,x90251)),f333(f333(f263(x90252,x90251),x90254),x90253)),f333(f288(x90251,x90252),x90255)))+P4(f333(f333(f335(f889(x90251,x90252)),f333(f333(f263(x90251,x90252),x90253),x90254)),x90255)) % 191.49/191.41 [9048]~P4(f333(f333(f335(f889(x90483,x90481)),f333(f333(f263(x90483,x90481),x90485),x90482)),x90484))+P4(f333(f333(f335(x90481),x90482),f333(f287(x90483,x90481,x90484),f333(f333(f311(x90483),x90485),f194(f890(x90483,a874)))))) % 191.49/191.41 [9091]P4(f333(f333(f335(f889(x90911,x90912)),f333(f333(f263(x90911,x90912),x90913),x90914)),x90915))+~P4(f333(f333(f335(x90912),x90914),f333(f287(x90911,x90912,x90915),f333(f333(f311(x90911),x90913),f194(f890(x90911,a874)))))) % 191.49/191.41 [9113]E(f333(f333(f333(f73(x91131,f884(x91132)),f188(x91131,x91132,x91133,x91134)),x91135),f197(x91132)),f188(x91131,x91132,x91133,f333(f333(f3(f890(x91131,a874)),x91134),f333(f333(f311(x91131),x91135),f194(f890(x91131,a874))))))+~P4(f333(f333(f335(x91131),x91135),x91134)) % 191.49/191.41 [9186]~P69(x91861)+E(f333(f333(f8(a880,x91861),x91862),f304(a880,f333(f333(f81(a880),x91863),x91864),f333(f333(f81(a880),x91865),x91864))),f333(f333(f8(a880,x91861),f333(f333(f10(a880,x91861,a880),x91862),f333(f333(f9(a880,a880,a880),f81(a880)),x91864))),f304(a880,x91863,x91865))) % 191.49/191.41 [9208]~P69(x92081)+E(f333(f333(f8(a880,x92081),x92082),f333(f303(a880,f333(f333(f81(a880),x92083),x92084)),f333(f333(f81(a880),x92085),x92084))),f333(f333(f8(a880,x92081),f333(f333(f10(a880,x92081,a880),x92082),f333(f333(f9(a880,a880,a880),f81(a880)),x92084))),f333(f303(a880,x92083),x92085))) % 191.49/191.41 [9261]~P28(x92611,x92612,x92613,f258(f890(x92611,a874)))+E(f333(f333(f155(x92611,x92612),x92613),f333(f137(x92611,f333(f333(f10(a874,a874,x92611),a328),f333(a330,x92614))),x92615)),f333(f137(x92612,f333(f333(f10(a874,a874,x92612),a328),f333(a330,f333(x92613,x92614)))),f333(f333(f155(x92611,x92612),x92613),x92615))) % 191.49/191.41 [9282]~P28(x92821,x92822,x92823,f333(f333(f311(x92821),x92824),f333(f173(x92821),x92825)))+E(f333(f333(f155(x92821,x92822),x92823),f333(f137(x92821,f333(f333(f10(a874,a874,x92821),a328),f333(a330,x92824))),x92825)),f333(f137(x92822,f333(f333(f10(a874,a874,x92822),a328),f333(a330,f333(x92823,x92824)))),f333(f333(f155(x92821,x92822),x92823),x92825))) % 191.49/191.41 [9434]P4(f333(f333(f335(f889(f881(x94341),f881(x94341))),f333(f333(f263(f881(x94341),f881(x94341)),f333(f333(f152(x94341),x94342),x94343)),f333(f333(f152(x94341),x94344),x94343))),f158(x94341,x94345)))+~P4(f333(f333(f335(f889(x94341,x94341)),f333(f333(f263(x94341,x94341),x94342),x94344)),x94345)) % 191.49/191.41 [9474]P4(f333(f333(f333(f333(a203,x94741),x94742),x94743),f858(x94744,x94743,x94742,x94745,x94741)))+~P4(f333(f333(f333(f333(a203,f34(x94741,x94745)),x94742),x94743),x94744)) % 191.49/191.41 [9555]P27(x95551,x95552,f333(f333(f311(f879(x95551)),f333(f333(f333(f93(x95551),x95553),f333(a26,x95554)),x95555)),f194(f890(f879(x95551),a874))))+~P27(x95551,f333(f333(f311(f879(x95551)),f333(f333(f333(f93(x95551),x95553),f333(a26,x95554)),x95555)),x95552),f333(f333(f311(f879(x95551)),f333(f333(f333(f93(x95551),x95553),f333(f246(a876),f333(a28,x95554))),x95555)),f194(f890(f879(x95551),a874)))) % 191.49/191.41 [9565]E(f333(f333(f311(x95651),f818(x95652,x95653,x95654,x95655,x95651)),f825(x95652,x95653,x95654,x95655,x95651)),f333(f333(f311(x95651),x95654),x95653))+~P4(f333(f64(x95651,x95655,f333(f333(f311(x95651),x95654),x95653)),x95652)) % 191.49/191.41 [9566]E(f333(f333(f311(x95661),f826(x95662,x95663,x95664,x95665,x95661)),f827(x95662,x95663,x95664,x95665,x95661)),f333(f333(f311(x95661),x95664),x95663))+~P4(f333(f64(x95661,x95665,f333(f333(f311(x95661),x95664),x95663)),x95662)) % 191.49/191.41 [9660]P4(f333(f333(f335(x96601),f530(x96602,x96603,x96604,x96605,x96601)),x96604))+P4(f333(f333(f333(f43(x96601,f890(x96605,a874)),x96604),x96603),x96602)) % 191.49/191.41 [9665]P4(f333(f333(f335(x96651),f522(x96652,x96653,x96651,x96654,x96655)),x96653))+P4(f333(f333(f335(x96655),x96654),f333(f333(f43(x96651,f890(x96655,a874)),x96653),x96652))) % 191.49/191.41 [9673]P4(f333(f333(f335(x96731),f526(x96732,x96733,x96731,x96734,x96735)),x96733))+P4(f333(f333(f250(f890(x96735,a874)),x96734),f333(f333(f43(x96731,f890(x96735,a874)),x96733),x96732))) % 191.49/191.41 [9675]P4(f333(f333(x96751,f544(x96752,x96751,x96753,x96754,x96755)),x96752))+~P4(f333(f333(f333(f44(x96755,f890(x96754,a874)),x96753),x96751),x96752)) % 191.49/191.41 [9678]P4(f333(f333(f335(x96781),f544(x96782,x96783,x96784,x96785,x96781)),x96784))+~P4(f333(f333(f333(f44(x96781,f890(x96785,a874)),x96784),x96783),x96782)) % 191.49/191.41 [9689]P4(f333(f333(f335(x96891),f538(x96892,x96893,x96891,x96894,x96895)),x96893))+~P4(f333(f333(f335(x96895),x96894),f333(f333(f44(x96891,f890(x96895,a874)),x96893),x96892))) % 191.49/191.41 [9694]P4(f333(f333(f335(x96941),x96942),f333(x96943,f538(x96943,x96944,x96945,x96942,x96941))))+~P4(f333(f333(f335(x96941),x96942),f333(f333(f44(x96945,f890(x96941,a874)),x96944),x96943))) % 191.49/191.41 [9802]~P4(f333(f333(x98024,f530(x98025,x98024,x98023,x98022,x98021)),x98025))+P4(f333(f333(f333(f43(x98021,f890(x98022,a874)),x98023),x98024),x98025)) % 191.49/191.41 [9805]~P4(f333(f333(f335(x98051),x98052),f333(x98055,f522(x98055,x98054,x98053,x98052,x98051))))+P4(f333(f333(f335(x98051),x98052),f333(f333(f43(x98053,f890(x98051,a874)),x98054),x98055))) % 191.49/191.41 [9807]~P4(f333(f333(f250(f890(x98071,a874)),x98072),f333(x98075,f526(x98075,x98074,x98073,x98072,x98071))))+P4(f333(f333(f250(f890(x98071,a874)),x98072),f333(f333(f43(x98073,f890(x98071,a874)),x98074),x98075))) % 191.49/191.41 [9853]P4(f333(f333(f333(f333(a203,x98531),f858(x98532,x98533,x98534,x98531,x98535)),x98533),x98532))+~P4(f333(f333(f333(f333(a203,f34(x98535,x98531)),x98534),x98533),x98532)) % 191.49/191.41 [9871]~P4(f333(f333(f335(x98711),f818(x98715,x98714,x98713,x98712,x98711)),f825(x98715,x98714,x98713,x98712,x98711)))+~P4(f333(f64(x98711,x98712,f333(f333(f311(x98711),x98713),x98714)),x98715)) % 191.49/191.41 [9872]~P4(f333(f333(f335(x98721),f826(x98725,x98724,x98723,x98722,x98721)),f827(x98725,x98724,x98723,x98722,x98721)))+~P4(f333(f64(x98721,x98722,f333(f333(f311(x98721),x98723),x98724)),x98725)) % 191.49/191.41 [9873]~P4(f333(f333(f335(f889(x98731,x98731)),f333(f333(f263(x98731,x98731),x98732),x98735)),f333(f333(f189(f889(x98731,x98731),a874),f333(a117,x98734)),x98733)))+P4(f333(f333(f335(f889(x98731,x98731)),f333(f333(f263(x98731,x98731),x98732),f783(x98733,x98734,x98735,x98732,x98731))),f333(f333(f189(f889(x98731,x98731),a874),x98734),x98733))) % 191.49/191.41 [9880]P4(f333(f68(x98801,x98801,x98802,f818(x98803,x98804,x98805,x98802,x98801),f825(x98803,x98804,x98805,x98802,x98801)),x98803))+~P4(f333(f64(x98801,x98802,f333(f333(f311(x98801),x98805),x98804)),x98803)) % 191.49/191.41 [9881]P4(f333(f68(x98811,x98811,x98812,f826(x98813,x98814,x98815,x98812,x98811),f827(x98813,x98814,x98815,x98812,x98811)),x98813))+~P4(f333(f64(x98811,x98812,f333(f333(f311(x98811),x98815),x98814)),x98813)) % 191.49/191.41 [9892]~P109(x98921)+P17(x98921,f333(f333(f155(x98922,x98921),x98923),f333(f137(x98922,f333(f333(f9(x98922,x98921,a874),f333(f333(f10(x98921,f890(x98921,a874),x98922),a330),x98923)),f333(x98924,x98925))),x98925))) % 191.49/191.41 [9928]~P4(f333(f333(f335(x99282),x99285),f333(f287(x99281,x99282,x99284),x99283)))+P4(f333(f333(f335(f889(x99281,x99282)),f333(f333(f263(x99281,x99282),f549(x99283,x99284,x99281,x99285,x99282)),x99285)),x99284)) % 191.49/191.41 [9929]~P4(f333(f333(f335(x99292),x99295),f333(f287(x99291,x99292,x99294),x99293)))+P4(f333(f333(f335(f889(x99291,x99292)),f333(f333(f263(x99291,x99292),f577(x99293,x99294,x99291,x99295,x99292)),x99295)),x99294)) % 191.49/191.41 [9934]~P4(f333(f333(f335(f889(x99341,x99341)),f333(f333(f263(x99341,x99341),x99345),x99344)),f333(f333(f189(f889(x99341,x99341),a874),f333(a117,x99343)),x99342)))+P4(f333(f333(f335(f889(x99341,x99341)),f333(f333(f263(x99341,x99341),f783(x99342,x99343,x99344,x99345,x99341)),x99344)),x99342)) % 191.49/191.41 [9946]~P4(f333(f333(f335(f889(x99461,x99461)),f333(f333(f263(x99461,x99461),x99465),x99464)),f333(f333(f189(f889(x99461,x99461),a874),f333(a117,x99463)),x99462)))+P4(f333(f333(f335(f889(x99461,x99461)),f333(f333(f263(x99461,x99461),f782(x99462,x99463,x99464,x99465,x99461)),x99464)),f333(f333(f189(f889(x99461,x99461),a874),x99463),x99462))) % 191.49/191.41 [9947]~P4(f333(f333(f335(f889(x99471,x99471)),f333(f333(f263(x99471,x99471),x99475),x99474)),f333(f333(f189(f889(x99471,x99471),a874),f333(a117,x99473)),x99472)))+P4(f333(f333(f335(f889(x99471,x99471)),f333(f333(f263(x99471,x99471),f790(x99472,x99473,x99474,x99475,x99471)),x99474)),f333(f333(f189(f889(x99471,x99471),a874),x99473),x99472))) % 191.49/191.41 [9948]~P4(f333(f333(f335(f889(f881(x99481),f881(x99481))),f333(f333(f263(f881(x99481),f881(x99481)),x99485),f333(f333(f152(x99481),x99484),x99483))),f159(x99481,x99482)))+P4(f333(f333(f335(f889(x99481,x99481)),f333(f333(f263(x99481,x99481),f593(x99482,x99483,x99484,x99485,x99481)),x99484)),x99482)) % 191.49/191.41 [7068]E(x70681,f197(x70682))+E(f184(x70683,x70682,f333(f333(f333(f73(x70683,f884(x70682)),x70684),x70685),x70681)),f333(f333(f311(x70683),x70685),f184(x70683,x70682,x70684))) % 191.49/191.41 [7547]~E(x75473,f194(f890(x75472,a874)))+E(f333(f333(f115(f890(x75471,a874)),f333(f333(f44(x75472,f890(x75471,a874)),x75473),x75474)),x75475),x75475) % 191.49/191.41 [7548]~E(x75483,f194(f890(x75482,a874)))+E(f333(f333(f106(f890(x75481,a874)),f333(f333(f43(x75482,f890(x75481,a874)),x75483),x75484)),x75485),x75485) % 191.49/191.41 [7900]~E(x79005,f197(x79002))+E(f184(x79001,x79002,f333(f333(f333(f73(x79001,f884(x79002)),x79003),x79004),x79005)),f333(f333(f3(f890(x79001,a874)),f184(x79001,x79002,x79003)),f333(f333(f311(x79001),x79004),f194(f890(x79001,a874))))) % 191.49/191.41 [7963]~E(x79633,f194(f890(x79632,a874)))+E(f333(f333(f3(f890(x79631,a874)),f333(f333(f43(x79632,f890(x79631,a874)),x79633),x79634)),x79635),f333(f333(f3(f890(x79631,a874)),f258(f890(x79631,a874))),x79635)) % 191.49/191.41 [8099]E(f333(f333(f160(x80991,f333(f333(f127(x80991),x80992),x80993)),x80994),x80995),f333(f333(f127(x80991),f333(f333(f160(x80991,x80992),x80994),x80995)),x80993))+~P4(f333(f333(f251(a880),x80994),f333(f195(f881(x80991)),x80992))) % 191.49/191.41 [8216]P4(f333(f333(f335(x82161),x82165),f333(f173(x82161),x82163)))+E(f333(f333(f178(x82161,x82162),f333(f333(f182(x82161,x82162),x82163),f333(f333(f155(x82161,x82162),x82164),x82163))),x82165),f197(x82162)) % 191.49/191.41 [8333]~P4(f333(f333(f335(x83331),x83335),f333(f173(x83331),x83333)))+E(f333(f333(f178(x83331,x83332),f333(f333(f182(x83331,x83332),x83333),f333(f333(f155(x83331,x83332),x83334),x83333))),x83335),f333(f242(x83332),f333(x83334,x83335))) % 191.49/191.41 [8374]E(f333(f333(f166(x83741),f333(f333(f155(a880,x83741),x83742),f140(a880,f333(f303(a880,x83743),x83744)))),x83745),f333(x83742,f333(f333(f81(a880),x83743),x83745)))+~P4(f333(f333(f251(a880),x83745),f333(f333(f3(a880),x83744),x83743))) % 191.49/191.41 [8390]E(x83901,f2(a104))+E(f125(x83902,x83903,f333(x83904,f333(f333(f3(a104),x83901),f79(a104))),f333(f333(f9(x83902,a104,f882(f884(x83903))),x83905),x83901)),f333(f205(x83902,x83903,x83904,x83905),x83901)) % 191.49/191.41 [8411]~E(x84113,f194(f890(x84111,a874)))+E(f333(f333(f43(x84111,f890(x84112,a874)),x84113),f333(f333(f10(f890(x84112,a874),f890(x84112,a874),x84111),f333(f3(f890(x84112,a874)),x84114)),x84115)),f258(f890(x84112,a874))) % 191.49/191.41 [8412]~E(x84123,f194(f890(x84121,a874)))+E(f333(f333(f43(x84121,f890(x84122,a874)),x84123),f333(f333(f10(f890(x84122,a874),f890(x84122,a874),x84121),f333(f106(f890(x84122,a874)),x84124)),x84125)),f258(f890(x84122,a874))) % 191.49/191.41 [8413]~E(x84133,f194(f890(x84131,a874)))+E(f333(f333(f44(x84131,f890(x84132,a874)),x84133),f333(f333(f10(f890(x84132,a874),f890(x84132,a874),x84131),f333(f115(f890(x84132,a874)),x84134)),x84135)),f194(f890(x84132,a874))) % 191.49/191.41 [8418]~P144(x84182)+E(f333(f333(f8(x84181,x84182),f333(f333(f10(x84182,x84182,x84181),f333(f82(x84182),x84183)),x84184)),x84185),f333(f333(f82(x84182),x84183),f333(f333(f8(x84181,x84182),x84184),x84185))) % 191.49/191.41 [8690]E(x86901,f194(f890(x86902,a874)))+E(f333(f333(f43(x86902,f890(x86903,a874)),x86901),f333(f333(f10(f890(x86903,a874),f890(x86903,a874),x86902),f333(f3(f890(x86903,a874)),x86904)),x86905)),f333(f333(f3(f890(x86903,a874)),x86904),f333(f333(f44(x86902,f890(x86903,a874)),x86901),x86905))) % 191.49/191.41 [8691]E(x86911,f194(f890(x86912,a874)))+E(f333(f333(f43(x86912,f890(x86913,a874)),x86911),f333(f333(f10(f890(x86913,a874),f890(x86913,a874),x86912),f333(f106(f890(x86913,a874)),x86914)),x86915)),f333(f333(f106(f890(x86913,a874)),x86914),f333(f333(f43(x86912,f890(x86913,a874)),x86911),x86915))) % 191.49/191.41 [8692]E(x86921,f194(f890(x86922,a874)))+E(f333(f333(f44(x86922,f890(x86923,a874)),x86921),f333(f333(f10(f890(x86923,a874),f890(x86923,a874),x86922),f333(f115(f890(x86923,a874)),x86924)),x86925)),f333(f333(f115(f890(x86923,a874)),x86924),f333(f333(f44(x86922,f890(x86923,a874)),x86921),x86925))) % 191.49/191.41 [8893]~P4(f333(f333(f251(a880),f333(x88934,x88932)),f333(x88934,x88933)))+P4(f333(f333(f335(f889(x88931,x88931)),f333(f333(f263(x88931,x88931),x88932),x88933)),f154(x88931,f333(f333(f152(f890(x88931,a880)),x88934),x88935)))) % 191.49/191.41 [9153]~P28(x91532,x91531,x91533,f333(f333(f115(f890(x91532,a874)),x91534),x91535))+E(f333(f333(f106(f890(x91531,a874)),f333(f312(x91532,x91531,x91533),f333(f333(f3(f890(x91532,a874)),x91534),x91535))),f333(f312(x91532,x91531,x91533),f333(f333(f3(f890(x91532,a874)),x91535),x91534))),f194(f890(x91531,a874))) % 191.49/191.41 [9432]~P4(f333(f333(f250(f890(x94323,a874)),f333(f287(x94321,x94323,x94324),x94322)),x94325))+P4(f333(f333(f250(f890(x94321,a874)),x94322),f333(f80(f890(x94321,a874)),f333(f287(x94323,x94321,f333(f288(x94321,x94323),x94324)),f333(f80(f890(x94323,a874)),x94325))))) % 191.49/191.41 [9455]~P28(x94551,x94552,x94553,f333(f333(f311(x94551),x94554),x94555))+~P4(f333(f333(f335(x94552),f333(x94553,x94554)),f333(f312(x94551,x94552,x94553),f333(f333(f3(f890(x94551,a874)),x94555),f333(f333(f311(x94551),x94554),f194(f890(x94551,a874))))))) % 191.49/191.41 [9521]P4(f333(f333(f250(f890(x95211,a874)),f333(f287(x95212,x95211,x95213),x95214)),x95215))+~P4(f333(f333(f250(f890(x95212,a874)),x95214),f333(f80(f890(x95212,a874)),f333(f287(x95211,x95212,f333(f288(x95212,x95211),x95213)),f333(f80(f890(x95211,a874)),x95215))))) % 191.49/191.41 [9601]~P87(x96011)+P4(f333(f333(f250(x96011),f333(f76(x96011),f333(f333(f3(x96011),f333(f333(f81(x96011),x96012),x96013)),f333(f333(f81(x96011),x96014),x96015)))),f333(f333(f81(x96011),f333(f76(x96011),f333(f333(f3(x96011),x96012),x96014))),f333(f76(x96011),f333(f333(f3(x96011),x96013),x96015))))) % 191.49/191.41 [9709]P4(f333(f333(f335(x97091),f539(x97092,x97093,x97094,x97091,x97095)),x97094))+P4(f333(f333(f250(f890(x97095,a874)),f333(f333(f44(x97091,f890(x97095,a874)),x97094),x97093)),x97092)) % 191.49/191.41 [9910]~P4(f333(f333(f250(f890(x99101,a874)),f333(x99104,f539(x99105,x99104,x99103,x99102,x99101))),x99105))+P4(f333(f333(f250(f890(x99101,a874)),f333(f333(f44(x99102,f890(x99101,a874)),x99103),x99104)),x99105)) % 191.49/191.41 [8529]E(f333(f333(f127(x85291),x85292),f333(f333(f160(x85291,x85293),f333(f333(f3(a880),x85294),f333(f195(f881(x85291)),x85292))),x85295)),f333(f333(f160(x85291,f333(f333(f127(x85291),x85292),x85293)),x85294),x85295))+P4(f333(f333(f251(a880),x85294),f333(f195(f881(x85291)),x85292))) % 191.49/191.41 [8556]~P138(x85561)+E(f333(f333(f81(x85561),f333(f333(f82(x85561),x85562),x85563)),f333(f333(f81(x85561),f333(f333(f82(x85561),x85564),x85563)),x85565)),f333(f333(f81(x85561),f333(f333(f82(x85561),f333(f333(f81(x85561),x85562),x85564)),x85563)),x85565)) % 191.49/191.41 [9102]~P144(x91021)+E(f333(f167(x91021),f333(f333(f155(x91022,x91021),f333(f333(f10(x91021,x91021,x91022),f333(f82(x91021),x91023)),x91024)),x91025)),f333(f333(f82(x91021),x91023),f333(f167(x91021),f333(f333(f155(x91022,x91021),x91024),x91025)))) % 191.49/191.41 [9281]E(f333(f195(f881(x92811)),f333(f333(f174(x92811),f333(f333(f248(a880),f333(f195(f881(x92811)),x92812)),f333(f195(f881(x92813)),x92814))),x92812)),f333(f195(f881(x92813)),f333(f333(f174(x92813),f333(f333(f248(a880),f333(f195(f881(x92811)),x92812)),f333(f195(f881(x92813)),x92814))),x92814)))+P4(f333(x92815,f333(f333(f182(x92811,x92813),x92812),x92814))) % 191.49/191.41 [9532]~P144(x95322)+E(f333(f333(f8(x95321,x95322),f333(f333(f9(x95321,x95322,x95322),f333(f333(f10(x95322,f890(x95322,x95322),x95321),f82(x95322)),x95323)),x95324)),x95325),f333(f333(f82(x95322),f333(f333(f8(x95321,x95322),x95323),x95325)),x95324)) % 191.49/191.41 [9533]~P64(x95332)+E(f333(f333(f8(x95331,x95332),f333(f333(f9(x95331,x95332,x95332),f333(f333(f10(x95332,f890(x95332,x95332),x95331),f291(x95332)),x95333)),x95334)),x95335),f333(f333(f291(x95332),f333(f333(f8(x95331,x95332),x95333),x95335)),x95334)) % 191.49/191.41 [9540]~P68(x95402)+E(f333(f333(f8(x95401,x95402),f333(f333(f20(x95401,x95402,x95402),f333(f333(f10(x95402,f890(x95402,x95402),x95401),f3(x95402)),x95403)),x95404)),x95405),f333(f333(f3(x95402),f333(f333(f8(x95401,x95402),x95403),x95405)),f333(f333(f8(x95401,x95402),x95404),x95405))) % 191.49/191.41 [9541]~P69(x95412)+E(f333(f333(f8(x95411,x95412),f333(f333(f20(x95411,x95412,x95412),f333(f333(f10(x95412,f890(x95412,x95412),x95411),f81(x95412)),x95413)),x95414)),x95415),f333(f333(f81(x95412),f333(f333(f8(x95411,x95412),x95413),x95415)),f333(f333(f8(x95411,x95412),x95414),x95415))) % 191.49/191.41 [9542]~P76(x95422)+E(f333(f333(f11(x95421,x95422),f333(f333(f20(x95421,x95422,x95422),f333(f333(f10(x95422,f890(x95422,x95422),x95421),f82(x95422)),x95423)),x95424)),x95425),f333(f333(f82(x95422),f333(f333(f11(x95421,x95422),x95423),x95425)),f333(f333(f11(x95421,x95422),x95424),x95425))) % 191.49/191.41 [9578]~E(x95783,f194(f890(x95781,a874)))+E(f333(f333(f43(x95781,f890(x95782,a874)),x95783),f333(f333(f9(x95781,f890(x95782,a874),f890(x95782,a874)),f333(f333(f10(f890(x95782,a874),f890(f890(x95782,a874),f890(x95782,a874)),x95781),f3(f890(x95782,a874))),x95784)),x95785)),f258(f890(x95782,a874))) % 191.49/191.41 [9579]~E(x95793,f194(f890(x95791,a874)))+E(f333(f333(f43(x95791,f890(x95792,a874)),x95793),f333(f333(f9(x95791,f890(x95792,a874),f890(x95792,a874)),f333(f333(f10(f890(x95792,a874),f890(f890(x95792,a874),f890(x95792,a874)),x95791),f106(f890(x95792,a874))),x95794)),x95795)),f258(f890(x95792,a874))) % 191.49/191.41 [9580]~E(x95803,f194(f890(x95801,a874)))+E(f333(f333(f44(x95801,f890(x95802,a874)),x95803),f333(f333(f9(x95801,f890(x95802,a874),f890(x95802,a874)),f333(f333(f10(f890(x95802,a874),f890(f890(x95802,a874),f890(x95802,a874)),x95801),f115(f890(x95802,a874))),x95804)),x95805)),f194(f890(x95802,a874))) % 191.49/191.41 [9609]E(x96091,f194(f890(x96092,a874)))+E(f333(f333(f43(x96092,f890(x96093,a874)),x96091),f333(f333(f9(x96092,f890(x96093,a874),f890(x96093,a874)),f333(f333(f10(f890(x96093,a874),f890(f890(x96093,a874),f890(x96093,a874)),x96092),f3(f890(x96093,a874))),x96094)),x96095)),f333(f333(f3(f890(x96093,a874)),f333(f333(f43(x96092,f890(x96093,a874)),x96091),x96094)),x96095)) % 191.49/191.41 [9610]E(x96101,f194(f890(x96102,a874)))+E(f333(f333(f43(x96102,f890(x96103,a874)),x96101),f333(f333(f9(x96102,f890(x96103,a874),f890(x96103,a874)),f333(f333(f10(f890(x96103,a874),f890(f890(x96103,a874),f890(x96103,a874)),x96102),f106(f890(x96103,a874))),x96104)),x96105)),f333(f333(f106(f890(x96103,a874)),f333(f333(f43(x96102,f890(x96103,a874)),x96101),x96104)),x96105)) % 191.49/191.41 [9611]E(x96111,f194(f890(x96112,a874)))+E(f333(f333(f44(x96112,f890(x96113,a874)),x96111),f333(f333(f9(x96112,f890(x96113,a874),f890(x96113,a874)),f333(f333(f10(f890(x96113,a874),f890(f890(x96113,a874),f890(x96113,a874)),x96112),f115(f890(x96113,a874))),x96114)),x96115)),f333(f333(f115(f890(x96113,a874)),f333(f333(f44(x96112,f890(x96113,a874)),x96111),x96114)),x96115)) % 191.49/191.41 [9160]~P4(f333(f333(f250(a880),x91601),x91604))+E(f333(f333(f3(a880),f333(f333(f81(a880),f333(f333(f82(a880),x91601),x91602)),x91603)),f333(f333(f81(a880),f333(f333(f82(a880),x91604),x91602)),x91605)),f333(f333(f3(a880),x91603),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x91604),x91601)),x91602)),x91605))) % 191.49/191.41 [9780]~P144(x97801)+E(f333(f167(x97801),f333(f333(f155(x97802,x97801),f333(f333(f9(x97802,x97801,x97801),f333(f333(f10(x97801,f890(x97801,x97801),x97802),f82(x97801)),x97803)),x97804)),x97805)),f333(f333(f82(x97801),f333(f167(x97801),f333(f333(f155(x97802,x97801),x97803),x97805))),x97804)) % 191.49/191.41 [9790]~P68(x97901)+E(f333(f167(x97901),f333(f333(f155(x97902,x97901),f333(f333(f20(x97902,x97901,x97901),f333(f333(f10(x97901,f890(x97901,x97901),x97902),f3(x97901)),x97903)),x97904)),x97905)),f333(f333(f3(x97901),f333(f167(x97901),f333(f333(f155(x97902,x97901),x97903),x97905))),f333(f167(x97901),f333(f333(f155(x97902,x97901),x97904),x97905)))) % 191.49/191.41 [9791]~P69(x97911)+E(f333(f167(x97911),f333(f333(f155(x97912,x97911),f333(f333(f20(x97912,x97911,x97911),f333(f333(f10(x97911,f890(x97911,x97911),x97912),f81(x97911)),x97913)),x97914)),x97915)),f333(f333(f81(x97911),f333(f167(x97911),f333(f333(f155(x97912,x97911),x97913),x97915))),f333(f167(x97911),f333(f333(f155(x97912,x97911),x97914),x97915)))) % 191.49/191.41 [9920]P4(f333(x99201,f333(f333(f182(x99202,x99203),x99204),x99205)))+~P4(f333(x99201,f333(f333(f182(x99202,x99203),f333(f333(f174(x99202),f333(f333(f248(a880),f333(f195(f881(x99202)),x99204)),f333(f195(f881(x99203)),x99205))),x99204)),f333(f333(f174(x99203),f333(f333(f248(a880),f333(f195(f881(x99202)),x99204)),f333(f195(f881(x99203)),x99205))),x99205)))) % 191.49/191.41 [9400]~P4(f333(f333(f250(a880),x94004),x94001))+E(f333(f333(f3(a880),f333(f333(f81(a880),f333(f333(f82(a880),x94001),x94002)),x94003)),f333(f333(f81(a880),f333(f333(f82(a880),x94004),x94002)),x94005)),f333(f333(f3(a880),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x94001),x94004)),x94002)),x94003)),x94005)) % 191.49/191.41 [10197]P27(x101971,x101972,f333(f312(a877,f879(x101971),f333(f333(f20(a877,f890(x101971,f890(a875,a874)),f879(x101971)),f333(f333(f20(a877,a876,f890(f890(x101971,f890(a875,a874)),f879(x101971))),f333(f333(f10(f890(x101971,f890(a875,a874)),f890(a876,f890(f890(x101971,f890(a875,a874)),f879(x101971))),a877),f93(x101971)),x101973)),a26)),x101974)),x101975))+~P27(x101971,f333(f333(f115(f890(f879(x101971),a874)),x101972),f333(f312(a877,f879(x101971),f333(f333(f20(a877,f890(x101971,f890(a875,a874)),f879(x101971)),f333(f333(f20(a877,a876,f890(f890(x101971,f890(a875,a874)),f879(x101971))),f333(f333(f10(f890(x101971,f890(a875,a874)),f890(a876,f890(f890(x101971,f890(a875,a874)),f879(x101971))),a877),f93(x101971)),x101973)),a26)),x101974)),x101975)),f333(f312(a877,f879(x101971),f333(f333(f20(a877,f890(x101971,f890(a875,a874)),f879(x101971)),f333(f333(f20(a877,a876,f890(f890(x101971,f890(a875,a874)),f879(x101971))),f333(f333(f10(f890(x101971,f890(a875,a874)),f890(a876,f890(f890(x101971,f890(a875,a874)),f879(x101971))),a877),f93(x101971)),x101973)),f333(f333(f10(f884(a876),a876,a877),f246(a876)),a28))),x101974)),x101975)) % 191.49/191.41 [10198]P31(x101981,x101982,f333(f312(a877,f879(x101981),f333(f333(f20(a877,f890(x101981,f890(a875,a874)),f879(x101981)),f333(f333(f20(a877,a876,f890(f890(x101981,f890(a875,a874)),f879(x101981))),f333(f333(f10(f890(x101981,f890(a875,a874)),f890(a876,f890(f890(x101981,f890(a875,a874)),f879(x101981))),a877),f93(x101981)),x101983)),a26)),x101984)),x101985))+~P31(x101981,f333(f333(f115(f890(f879(x101981),a874)),x101982),f333(f312(a877,f879(x101981),f333(f333(f20(a877,f890(x101981,f890(a875,a874)),f879(x101981)),f333(f333(f20(a877,a876,f890(f890(x101981,f890(a875,a874)),f879(x101981))),f333(f333(f10(f890(x101981,f890(a875,a874)),f890(a876,f890(f890(x101981,f890(a875,a874)),f879(x101981))),a877),f93(x101981)),x101983)),a26)),x101984)),x101985)),f333(f312(a877,f879(x101981),f333(f333(f20(a877,f890(x101981,f890(a875,a874)),f879(x101981)),f333(f333(f20(a877,a876,f890(f890(x101981,f890(a875,a874)),f879(x101981))),f333(f333(f10(f890(x101981,f890(a875,a874)),f890(a876,f890(f890(x101981,f890(a875,a874)),f879(x101981))),a877),f93(x101981)),x101983)),f333(f333(f10(f884(a876),a876,a877),f246(a876)),a28))),x101984)),x101985)) % 191.49/191.41 [5280]E(x52801,x52802)+~E(f29(x52803,x52804,x52801),f29(x52805,x52806,x52802)) % 191.49/191.41 [5281]E(x52811,x52812)+~E(f29(x52813,x52811,x52814),f29(x52815,x52812,x52816)) % 191.49/191.41 [5282]E(x52821,x52822)+~E(f29(x52821,x52823,x52824),f29(x52822,x52825,x52826)) % 191.49/191.41 [5283]E(x52831,x52832)+~E(f31(x52833,x52834,x52831),f31(x52835,x52836,x52832)) % 191.49/191.41 [5284]E(x52841,x52842)+~E(f31(x52843,x52841,x52844),f31(x52845,x52842,x52846)) % 191.49/191.41 [5285]E(x52851,x52852)+~E(f31(x52851,x52853,x52854),f31(x52852,x52855,x52856)) % 191.49/191.41 [5286]E(x52861,x52862)+~E(f30(x52863,x52864,x52861),f30(x52865,x52866,x52862)) % 191.49/191.41 [5287]E(x52871,x52872)+~E(f30(x52873,x52871,x52874),f30(x52875,x52872,x52876)) % 191.49/191.41 [5288]E(x52881,x52882)+~E(f30(x52881,x52883,x52884),f30(x52882,x52885,x52886)) % 191.49/191.41 [7247]E(x72471,x72472)+~E(f230(x72473,x72474,x72475,x72471),f230(x72473,x72474,x72476,x72472)) % 191.49/191.41 [7248]E(x72481,x72482)+~E(f230(x72483,x72484,x72481,x72485),f230(x72483,x72484,x72482,x72486)) % 191.49/191.41 [6719]E(f333(f185(x67191,x67192,x67193,x67194),x67195),f333(f242(x67192),x67196))+~E(f333(x67194,x67195),f333(f242(x67192),x67196)) % 191.49/191.41 [6853]E(f333(f244(f884(x68531),x68532,f197(x68531),x68533),f333(x68534,x68535)),f333(x68533,x68536))+~E(f333(x68534,x68535),f333(f242(x68532),x68536)) % 191.49/191.41 [8356]~P22(x83565,x83561,x83562,x83566)+E(f333(f74(x83561,x83561,x83561,f333(x83562,x83563)),f333(x83562,x83564)),f333(f74(x83561,x83561,x83561,f333(x83562,x83564)),f333(x83562,x83563))) % 191.49/191.41 [8595]~P56(x85954,x85955,x85952,x85951,x85956)+E(f333(x85951,f333(x85952,x85953)),x85953) % 191.49/191.41 [8733]P28(x87331,x87332,x87333,x87334)+~P28(x87331,x87335,f333(f74(x87332,x87335,x87331,x87336),x87333),x87334) % 191.49/191.41 [8825]~P28(x88254,x88252,f333(f74(x88251,x88252,x88254,x88253),x88255),x88256)+P28(x88251,x88252,x88253,f333(f312(x88254,x88251,x88255),x88256)) % 191.49/191.41 [9543]P4(f333(f63(x95431),x95432))+~P4(f333(f68(x95431,x95433,x95434,x95435,x95432),x95436)) % 191.49/191.41 [9551]~P4(f333(f333(f335(x95514),x95513),f301(x95514,x95515,x95511,x95512,x95516)))+P4(f333(f333(x95511,x95512),x95513)) % 191.49/191.41 [9552]~P4(f333(f333(f335(x95524),x95523),f298(x95524,x95521,x95525,x95522,x95526)))+P4(f333(f333(x95521,x95522),x95523)) % 191.49/191.41 [9553]~P4(f333(f333(f335(x95534),x95532),f301(x95534,x95531,x95535,x95536,x95533)))+P4(f333(f333(x95531,x95532),x95533)) % 191.49/191.41 [9554]~P4(f333(f333(f335(x95544),x95542),f298(x95544,x95545,x95541,x95546,x95543)))+P4(f333(f333(x95541,x95542),x95543)) % 191.49/191.41 [5783]E(x57831,x57832)+~E(f333(f333(f263(x57833,x57834),x57835),x57831),f333(f333(f263(x57833,x57834),x57836),x57832)) % 191.49/191.41 [5785]E(x57851,x57852)+~E(f333(f333(f263(x57853,x57854),x57851),x57855),f333(f333(f263(x57853,x57854),x57852),x57856)) % 191.49/191.41 [5909]~P19(x59095,x59096,x59091)+E(f333(f333(x59091,x59092),f333(f333(x59091,x59093),x59094)),f333(f333(x59091,x59093),f333(f333(x59091,x59092),x59094))) % 191.49/191.41 [7305]~P35(x73054,x73051,f333(f333(f152(x73054),x73052),x73055),f333(f333(f152(x73054),x73053),x73056))+P4(f333(f333(x73051,x73052),x73053)) % 191.49/191.41 [7658]P35(x76581,x76582,x76583,x76584)+~P35(x76581,x76582,f333(f333(f152(x76581),x76585),x76583),f333(f333(f152(x76581),x76586),x76584)) % 191.49/191.41 [8681]~P56(x86815,x86811,x86812,x86816,x86814)+P4(f333(f333(f335(x86811),f333(x86812,x86813)),x86814)) % 191.49/191.41 [8853]E(f333(f77(x88531,x88532,x88533,x88534,x88535),x88536),f333(x88533,x88536))+P4(f333(f333(f335(x88531),x88536),x88535)) % 191.49/191.41 [8876]~E(x88763,f333(f333(f152(x88761),x88765),x88766))+P4(f333(f333(f335(f889(f881(x88761),f881(x88761))),f333(f333(f263(f881(x88761),f881(x88761)),x88762),f333(f333(f127(x88761),x88762),x88763))),f148(x88761,x88764))) % 191.49/191.41 [8883]E(f333(f77(x88831,x88832,x88833,x88834,x88835),x88836),f333(x88834,x88836))+~P4(f333(f333(f335(x88831),x88836),x88835)) % 191.49/191.41 [8889]E(f333(f187(x88891,x88892,x88893,x88894,x88895),x88896),f333(x88893,x88896))+P4(f333(f333(f335(x88891),x88896),f333(f173(x88891),x88894))) % 191.49/191.41 [9106]~P37(x91061,x91062,x91063,x91065,x91066)+P37(x91061,x91062,x91063,f333(f333(f174(x91061),x91064),x91065),f333(f333(f174(x91062),x91064),x91066)) % 191.49/191.41 [9107]~P37(x91071,x91072,x91073,x91075,x91076)+P37(x91071,x91072,x91073,f333(f333(f139(x91071),x91074),x91075),f333(f333(f139(x91072),x91074),x91076)) % 191.49/191.41 [9621]~P26(x96214,x96212,x96215,x96213,x96216,x96211)+E(f333(x96211,f194(f890(x96212,a874))),x96213) % 191.49/191.41 [9874]~E(f333(x98744,f333(f262(x98741,x98743),x98745)),f333(x98746,f333(f262(x98741,x98743),x98745)))+E(f333(f273(x98741,x98742,x98743,x98743,x98744,f35(x98743)),x98745),f333(f273(x98741,x98742,x98743,x98743,x98746,f35(x98743)),x98745)) % 191.49/191.41 [9875]~E(f333(x98754,f333(f271(x98751,x98752),x98755)),f333(x98756,f333(f271(x98751,x98752),x98755)))+E(f333(f273(x98751,x98751,x98752,x98753,f35(x98751),x98754),x98755),f333(f273(x98751,x98751,x98752,x98753,f35(x98751),x98756),x98755)) % 191.49/191.41 [9917]~E(f333(f273(x99172,x99176,x99173,x99173,x99171,f35(x99173)),x99174),f333(f273(x99172,x99176,x99173,x99173,x99175,f35(x99173)),x99174))+E(f333(x99171,f333(f262(x99172,x99173),x99174)),f333(x99175,f333(f262(x99172,x99173),x99174))) % 191.49/191.41 [9918]~E(f333(f273(x99182,x99182,x99183,x99186,f35(x99182),x99181),x99184),f333(f273(x99182,x99182,x99183,x99186,f35(x99182),x99185),x99184))+E(f333(x99181,f333(f271(x99182,x99183),x99184)),f333(x99185,f333(f271(x99182,x99183),x99184))) % 191.49/191.41 [8777]P4(f333(f333(f335(x87771),x87772),x87773))+~P4(f333(f333(f335(f889(x87771,x87774)),f333(f333(f263(x87771,x87774),x87772),x87775)),f333(f333(f270(x87771,x87774),x87773),x87776))) % 191.49/191.41 [8792]P4(f333(f333(f335(x87921),x87922),f333(x87923,x87924)))+~P4(f333(f333(f335(f889(x87925,x87921)),f333(f333(f263(x87925,x87921),x87924),x87922)),f333(f333(f270(x87925,x87921),x87926),x87923))) % 191.49/191.41 [8886]~E(f333(f195(f881(x88861)),x88864),f333(f195(f881(x88862)),x88865))+E(f187(x88861,x88862,x88863,x88864,f333(f333(f127(x88862),x88865),x88866)),f187(x88861,x88862,x88863,x88864,x88865)) % 191.49/191.41 [8887]~E(f333(f195(f881(x88871)),x88874),f333(f195(f881(x88872)),x88876))+E(f187(x88871,x88872,x88873,f333(f333(f127(x88871),x88874),x88875),x88876),f187(x88871,x88872,x88873,x88874,x88876)) % 191.49/191.41 [9129]P4(f333(f333(f335(x91291),x91294),f184(x91291,x91292,x91296)))+E(f185(x91291,x91292,f333(f333(f333(f73(x91291,f884(x91292)),x91293),x91294),f333(f242(x91292),x91295)),x91296),f333(f333(f333(f73(x91291,f884(x91292)),f185(x91291,x91292,x91293,x91296)),x91294),f333(f242(x91292),x91295))) % 191.49/191.41 [9229]P4(f333(f333(f335(f889(x92291,x92291)),f333(f333(f263(x92291,x92291),f333(x92292,x92293)),f333(x92292,x92294))),x92295))+~P4(f333(f333(f335(f889(x92296,x92296)),f333(f333(f263(x92296,x92296),x92293),x92294)),f333(f333(f289(x92291,x92296),x92295),x92292))) % 191.49/191.41 [9249]~P4(f333(f333(f335(f889(x92494,x92494)),f333(f333(f263(x92494,x92494),f333(x92496,x92492)),f333(x92496,x92493))),x92495))+P4(f333(f333(f335(f889(x92491,x92491)),f333(f333(f263(x92491,x92491),x92492),x92493)),f333(f333(f289(x92494,x92491),x92495),x92496))) % 191.49/191.41 [9919]E(f333(f333(f263(x99191,x99192),f806(x99193,x99194,x99195,x99196,x99192,x99191)),f808(x99193,x99194,x99195,x99196,x99192,x99191)),x99196)+~P4(f333(f333(f335(f889(x99191,x99192)),x99196),f333(f333(f290(x99191,x99195,x99192),x99194),x99193))) % 191.49/191.41 [10114]~P4(f333(f333(f335(f889(x101141,x101146)),x101145),f333(f333(f290(x101141,x101142,x101146),x101144),x101143)))+P4(f333(f333(f335(f889(x101141,x101142)),f333(f333(f263(x101141,x101142),f806(x101143,x101144,x101142,x101145,x101146,x101141)),f807(x101143,x101144,x101142,x101145,x101146,x101141))),x101144)) % 191.49/191.41 [10115]~P4(f333(f333(f335(f889(x101156,x101152)),x101155),f333(f333(f290(x101156,x101151,x101152),x101154),x101153)))+P4(f333(f333(f335(f889(x101151,x101152)),f333(f333(f263(x101151,x101152),f807(x101153,x101154,x101151,x101155,x101152,x101156)),f808(x101153,x101154,x101151,x101155,x101152,x101156))),x101153)) % 191.49/191.41 [6187]~E(x61876,x61874)+E(f333(f333(f333(f333(f73(x61871,x61872),x61873),x61874),x61875),x61876),x61875) % 191.49/191.41 [6236]E(x62361,x62362)+E(f333(f333(f333(f333(f73(x62363,x62364),x62365),x62362),x62366),x62361),f333(x62365,x62361)) % 191.49/191.41 [7727]~P9(x77272)+E(f333(f333(f43(x77271,x77272),x77273),f333(f333(f9(x77271,x77274,x77272),x77275),x77276)),f333(f333(f333(f43(x77271,f890(x77274,x77272)),x77273),x77275),x77276)) % 191.49/191.41 [7728]~P9(x77282)+E(f333(f333(f44(x77281,x77282),x77283),f333(f333(f9(x77281,x77284,x77282),x77285),x77286)),f333(f333(f333(f44(x77281,f890(x77284,x77282)),x77283),x77285),x77286)) % 191.49/191.41 [8507]E(f333(f333(f44(x85071,f890(x85072,a874)),x85073),f333(f333(f10(f890(x85072,a874),f890(x85072,a874),x85071),f333(f311(x85072),x85074)),x85075)),f333(f333(f311(x85072),x85074),f333(f333(f44(x85071,f890(x85072,a874)),x85073),x85075)))+~P4(f333(f333(f335(x85071),x85076),x85073)) % 191.49/191.41 [8938]~P9(x89382)+E(f333(f333(f43(x89381,x89382),x89383),f333(f333(f10(f890(x89384,x89382),x89382,x89381),f333(f43(x89384,x89382),x89385)),f333(f9(x89384,x89381,x89382),x89386))),f333(f333(f43(x89384,x89382),x89385),f333(f333(f10(f890(x89381,x89382),x89382,x89384),f333(f43(x89381,x89382),x89383)),x89386))) % 191.49/191.41 [8939]~P9(x89392)+E(f333(f333(f44(x89391,x89392),x89393),f333(f333(f10(f890(x89394,x89392),x89392,x89391),f333(f44(x89394,x89392),x89395)),f333(f9(x89394,x89391,x89392),x89396))),f333(f333(f44(x89394,x89392),x89395),f333(f333(f10(f890(x89391,x89392),x89392,x89394),f333(f44(x89391,x89392),x89393)),x89396))) % 191.49/191.41 [9139]P4(f333(f333(f335(x91391),x91392),f333(f173(x91391),x91393)))+~P4(f333(f333(f335(f889(x91394,x91391)),f333(f333(f263(x91394,x91391),x91395),x91392)),f333(f173(f889(x91394,x91391)),f333(f333(f182(x91394,x91391),x91396),x91393)))) % 191.49/191.41 [9140]P4(f333(f333(f335(x91401),x91402),f333(f173(x91401),x91403)))+~P4(f333(f333(f335(f889(x91401,x91404)),f333(f333(f263(x91401,x91404),x91402),x91405)),f333(f173(f889(x91401,x91404)),f333(f333(f182(x91401,x91404),x91403),x91406)))) % 191.49/191.41 [9243]P4(f333(f333(f250(f890(x92431,a874)),f333(f287(x92432,x92431,x92433),x92434)),x92435))+~P4(f333(f333(f250(f890(f889(x92432,x92431),a874)),x92433),f333(f333(f270(x92432,x92431),x92436),f333(f18(f890(x92431,a874),x92432),x92435)))) % 191.49/191.41 [9433]P4(f333(f333(f335(f889(f881(x94331),f881(x94331))),f333(f333(f263(f881(x94331),f881(x94331)),f333(f333(f152(x94331),x94332),x94333)),f333(f333(f152(x94331),x94334),x94335))),f148(x94331,x94336)))+~P4(f333(f333(f335(f889(x94331,x94331)),f333(f333(f263(x94331,x94331),x94332),x94334)),x94336)) % 191.49/191.41 [9916]E(f333(f333(f263(x99161,x99162),f732(x99163,x99164,x99165,x99162,x99161,x99166)),f735(x99163,x99164,x99165,x99162,x99161,x99166)),x99166)+P4(f333(f333(f335(x99165),x99164),f333(f333(f272(x99161,x99162,f890(x99165,a874)),x99163),x99166))) % 191.49/191.41 [9921]E(f333(f333(f263(x99211,x99212),f733(x99213,x99214,x99212,x99211,x99215,x99216)),f734(x99213,x99214,x99212,x99211,x99215,x99216)),x99213)+~P4(f333(f333(f335(x99216),x99215),f333(f333(f272(x99211,x99212,f890(x99216,a874)),x99214),x99213))) % 191.49/191.41 [10063]P4(f333(f333(f335(x100631),x100632),f333(f333(x100633,f733(x100634,x100633,x100635,x100636,x100632,x100631)),f734(x100634,x100633,x100635,x100636,x100632,x100631))))+~P4(f333(f333(f335(x100631),x100632),f333(f333(f272(x100636,x100635,f890(x100631,a874)),x100633),x100634))) % 191.49/191.41 [10090]~P4(f333(f333(f335(x100901),x100902),f333(f333(x100905,f732(x100905,x100902,x100901,x100904,x100903,x100906)),f735(x100905,x100902,x100901,x100904,x100903,x100906))))+P4(f333(f333(f335(x100901),x100902),f333(f333(f272(x100903,x100904,f890(x100901,a874)),x100905),x100906))) % 191.49/191.41 [7851]P4(f333(f333(f335(x78511),x78514),x78516))+E(f188(x78511,x78512,f333(f333(f333(f73(x78511,f884(x78512)),x78513),x78514),x78515),x78516),f188(x78511,x78512,x78513,x78516)) % 191.49/191.41 [7918]P4(f333(f333(f335(x79181),x79184),x79186))+E(f333(f312(x79181,x79182,f333(f333(f333(f73(x79181,x79182),x79183),x79184),x79185)),x79186),f333(f312(x79181,x79182,x79183),x79186)) % 191.49/191.41 [7946]P4(f333(f333(f335(x79461),x79464),f333(f173(x79461),x79466)))+E(f333(f333(f155(x79461,x79462),f333(f333(f333(f73(x79461,x79462),x79463),x79464),x79465)),x79466),f333(f333(f155(x79461,x79462),x79463),x79466)) % 191.49/191.41 [8401]E(x84011,x84012)+E(f333(f333(f160(x84013,f333(f333(f160(x84013,x84014),x84011),x84015)),x84012),x84016),f333(f333(f160(x84013,f333(f333(f160(x84013,x84014),x84012),x84016)),x84011),x84015)) % 191.49/191.41 [8944]~P4(f333(f333(f335(x89443),x89446),x89445))+E(f333(f333(f311(x89441),x89442),f333(f312(x89443,x89441,x89444),f333(f333(f3(f890(x89443,a874)),x89445),f333(f333(f311(x89443),x89446),f194(f890(x89443,a874)))))),f333(f312(x89443,x89441,f333(f333(f333(f73(x89443,x89441),x89444),x89446),x89442)),x89445)) % 191.49/191.41 [9731]E(f187(x97311,x97312,x97313,f333(f333(f127(x97311),x97314),f333(f333(f152(x97311),x97315),f118(x97311))),x97316),f333(f333(f333(f73(x97311,f884(x97312)),f187(x97311,x97312,x97313,x97314,x97316)),x97315),f333(f242(x97312),f333(f333(f166(x97312),x97316),f333(f195(f881(x97311)),x97314)))))+~P4(f333(f333(f251(a880),f333(f195(f881(x97311)),x97314)),f333(f195(f881(x97312)),x97316))) % 191.49/191.41 [8721]~E(x87213,x87216)+E(f333(f333(f178(x87211,x87212),f333(f333(f152(f889(x87211,x87212)),f333(f333(f263(x87211,x87212),x87213),x87214)),x87215)),x87216),f333(f242(x87212),x87214)) % 191.49/191.41 [8749]E(x87491,x87492)+E(f333(f333(f178(x87493,x87494),f333(f333(f152(f889(x87493,x87494)),f333(f333(f263(x87493,x87494),x87491),x87495)),x87496)),x87492),f333(f333(f178(x87493,x87494),x87496),x87492)) % 191.49/191.41 [9019]~P4(f333(f333(x90194,x90195),x90196))+P4(f333(f333(f333(f333(f115(f890(x90191,f890(x90192,a874))),x90193),x90194),x90195),x90196)) % 191.49/191.41 [9021]~P4(f333(f333(x90213,x90215),x90216))+P4(f333(f333(f333(f333(f115(f890(x90211,f890(x90212,a874))),x90213),x90214),x90215),x90216)) % 191.49/191.41 [9303]P4(f333(f333(x93031,x93032),x93033))+~P4(f333(f333(f333(f333(f106(f890(x93034,f890(x93035,a874))),x93036),x93031),x93032),x93033)) % 191.49/191.41 [9304]P4(f333(f333(x93041,x93042),x93043))+~P4(f333(f333(f333(f333(f106(f890(x93044,f890(x93045,a874))),x93041),x93046),x93042),x93043)) % 191.49/191.41 [9765]~P69(x97652)+E(f333(f333(f8(x97651,x97652),f333(f333(f9(x97651,f890(x97653,a874),x97652),f333(f333(f10(f890(x97653,x97652),f890(f890(x97653,a874),x97652),x97651),f8(x97653,x97652)),x97654)),x97655)),x97656),f333(f333(f8(f889(x97651,x97653),x97652),f333(f272(x97651,x97653,x97652),x97654)),f333(f333(f270(x97651,x97653),x97656),f333(f18(f890(x97653,a874),x97651),x97655)))) % 191.49/191.41 [9766]~P76(x97662)+E(f333(f333(f11(x97661,x97662),f333(f333(f9(x97661,f890(x97663,a874),x97662),f333(f333(f10(f890(x97663,x97662),f890(f890(x97663,a874),x97662),x97661),f11(x97663,x97662)),x97664)),x97665)),x97666),f333(f333(f11(f889(x97661,x97663),x97662),f333(f272(x97661,x97663,x97662),x97664)),f333(f333(f270(x97661,x97663),x97666),f333(f18(f890(x97663,a874),x97661),x97665)))) % 191.49/191.41 [9901]~P69(x99012)+E(f333(f333(f8(x99011,x99012),f333(f333(f9(x99011,f890(x99013,a874),x99012),f333(f333(f10(f890(x99013,x99012),f890(f890(x99013,a874),x99012),x99011),f8(x99013,x99012)),f333(f9(x99013,x99011,x99012),x99014))),x99015)),x99016),f333(f333(f8(x99013,x99012),f333(f333(f9(x99013,f890(x99011,a874),x99012),f333(f333(f10(f890(x99011,x99012),f890(f890(x99011,a874),x99012),x99013),f8(x99011,x99012)),x99014)),x99016)),x99015)) % 191.49/191.41 [9589]~P4(f333(f333(f335(x95891),x95895),x95894))+E(f333(f333(f333(f73(x95891,f884(x95892)),f188(x95891,x95892,x95893,f333(f333(f3(f890(x95891,a874)),x95894),f333(f333(f311(x95891),x95895),f194(f890(x95891,a874)))))),x95895),x95896),f188(x95891,x95892,f333(f333(f333(f73(x95891,f884(x95892)),x95893),x95895),x95896),x95894)) % 191.49/191.41 [10205]~P4(f333(f333(f335(f889(x102051,x102052)),f333(f333(f263(x102051,x102052),x102055),x102056)),f333(f333(f115(f890(f889(x102051,x102052),a874)),x102053),x102054)))+P4(f333(f333(f333(f333(f115(f890(x102051,f890(x102052,a874))),f333(f333(f9(x102051,f890(f889(x102051,x102052),a874),f890(x102052,a874)),f333(f333(f10(f890(x102052,f890(f890(f889(x102051,x102052),a874),a874)),f890(f890(f889(x102051,x102052),a874),f890(x102052,a874)),x102051),f9(x102052,f890(f889(x102051,x102052),a874),a874)),f333(f333(f10(f890(x102052,f889(x102051,x102052)),f890(x102052,f890(f890(f889(x102051,x102052),a874),a874)),x102051),f333(f10(f889(x102051,x102052),f890(f890(f889(x102051,x102052),a874),a874),x102052),f335(f889(x102051,x102052)))),f263(x102051,x102052)))),x102053)),f333(f333(f9(x102051,f890(f889(x102051,x102052),a874),f890(x102052,a874)),f333(f333(f10(f890(x102052,f890(f890(f889(x102051,x102052),a874),a874)),f890(f890(f889(x102051,x102052),a874),f890(x102052,a874)),x102051),f9(x102052,f890(f889(x102051,x102052),a874),a874)),f333(f333(f10(f890(x102052,f889(x102051,x102052)),f890(x102052,f890(f890(f889(x102051,x102052),a874),a874)),x102051),f333(f10(f889(x102051,x102052),f890(f890(f889(x102051,x102052),a874),a874),x102052),f335(f889(x102051,x102052)))),f263(x102051,x102052)))),x102054)),x102055),x102056)) % 191.49/191.41 [10206]~P4(f333(f333(f335(f889(x102061,x102062)),f333(f333(f263(x102061,x102062),x102065),x102066)),f333(f333(f106(f890(f889(x102061,x102062),a874)),x102063),x102064)))+P4(f333(f333(f333(f333(f106(f890(x102061,f890(x102062,a874))),f333(f333(f9(x102061,f890(f889(x102061,x102062),a874),f890(x102062,a874)),f333(f333(f10(f890(x102062,f890(f890(f889(x102061,x102062),a874),a874)),f890(f890(f889(x102061,x102062),a874),f890(x102062,a874)),x102061),f9(x102062,f890(f889(x102061,x102062),a874),a874)),f333(f333(f10(f890(x102062,f889(x102061,x102062)),f890(x102062,f890(f890(f889(x102061,x102062),a874),a874)),x102061),f333(f10(f889(x102061,x102062),f890(f890(f889(x102061,x102062),a874),a874),x102062),f335(f889(x102061,x102062)))),f263(x102061,x102062)))),x102063)),f333(f333(f9(x102061,f890(f889(x102061,x102062),a874),f890(x102062,a874)),f333(f333(f10(f890(x102062,f890(f890(f889(x102061,x102062),a874),a874)),f890(f890(f889(x102061,x102062),a874),f890(x102062,a874)),x102061),f9(x102062,f890(f889(x102061,x102062),a874),a874)),f333(f333(f10(f890(x102062,f889(x102061,x102062)),f890(x102062,f890(f890(f889(x102061,x102062),a874),a874)),x102061),f333(f10(f889(x102061,x102062),f890(f890(f889(x102061,x102062),a874),a874),x102062),f335(f889(x102061,x102062)))),f263(x102061,x102062)))),x102064)),x102065),x102066)) % 191.49/191.41 [10215]P4(f333(f333(f335(f889(x102151,x102152)),f333(f333(f263(x102151,x102152),x102153),x102154)),f333(f333(f115(f890(f889(x102151,x102152),a874)),x102155),x102156)))+~P4(f333(f333(f333(f333(f115(f890(x102151,f890(x102152,a874))),f333(f333(f9(x102151,f890(f889(x102151,x102152),a874),f890(x102152,a874)),f333(f333(f10(f890(x102152,f890(f890(f889(x102151,x102152),a874),a874)),f890(f890(f889(x102151,x102152),a874),f890(x102152,a874)),x102151),f9(x102152,f890(f889(x102151,x102152),a874),a874)),f333(f333(f10(f890(x102152,f889(x102151,x102152)),f890(x102152,f890(f890(f889(x102151,x102152),a874),a874)),x102151),f333(f10(f889(x102151,x102152),f890(f890(f889(x102151,x102152),a874),a874),x102152),f335(f889(x102151,x102152)))),f263(x102151,x102152)))),x102155)),f333(f333(f9(x102151,f890(f889(x102151,x102152),a874),f890(x102152,a874)),f333(f333(f10(f890(x102152,f890(f890(f889(x102151,x102152),a874),a874)),f890(f890(f889(x102151,x102152),a874),f890(x102152,a874)),x102151),f9(x102152,f890(f889(x102151,x102152),a874),a874)),f333(f333(f10(f890(x102152,f889(x102151,x102152)),f890(x102152,f890(f890(f889(x102151,x102152),a874),a874)),x102151),f333(f10(f889(x102151,x102152),f890(f890(f889(x102151,x102152),a874),a874),x102152),f335(f889(x102151,x102152)))),f263(x102151,x102152)))),x102156)),x102153),x102154)) % 191.49/191.41 [10216]P4(f333(f333(f335(f889(x102161,x102162)),f333(f333(f263(x102161,x102162),x102163),x102164)),f333(f333(f106(f890(f889(x102161,x102162),a874)),x102165),x102166)))+~P4(f333(f333(f333(f333(f106(f890(x102161,f890(x102162,a874))),f333(f333(f9(x102161,f890(f889(x102161,x102162),a874),f890(x102162,a874)),f333(f333(f10(f890(x102162,f890(f890(f889(x102161,x102162),a874),a874)),f890(f890(f889(x102161,x102162),a874),f890(x102162,a874)),x102161),f9(x102162,f890(f889(x102161,x102162),a874),a874)),f333(f333(f10(f890(x102162,f889(x102161,x102162)),f890(x102162,f890(f890(f889(x102161,x102162),a874),a874)),x102161),f333(f10(f889(x102161,x102162),f890(f890(f889(x102161,x102162),a874),a874),x102162),f335(f889(x102161,x102162)))),f263(x102161,x102162)))),x102165)),f333(f333(f9(x102161,f890(f889(x102161,x102162),a874),f890(x102162,a874)),f333(f333(f10(f890(x102162,f890(f890(f889(x102161,x102162),a874),a874)),f890(f890(f889(x102161,x102162),a874),f890(x102162,a874)),x102161),f9(x102162,f890(f889(x102161,x102162),a874),a874)),f333(f333(f10(f890(x102162,f889(x102161,x102162)),f890(x102162,f890(f890(f889(x102161,x102162),a874),a874)),x102161),f333(f10(f889(x102161,x102162),f890(f890(f889(x102161,x102162),a874),a874),x102162),f335(f889(x102161,x102162)))),f263(x102161,x102162)))),x102166)),x102163),x102164)) % 191.49/191.41 [10194]~P4(f333(f333(f335(f889(x101942,x101943)),f333(f333(f263(x101942,x101943),x101945),x101946)),f333(f333(f43(x101941,f890(f889(x101942,x101943),a874)),f258(f890(x101941,a874))),x101944)))+P4(f333(f333(f333(f333(f43(x101941,f890(x101942,f890(x101943,a874))),f258(f890(x101941,a874))),f333(f333(f10(f890(f889(x101942,x101943),a874),f890(x101942,f890(x101943,a874)),x101941),f333(f9(x101942,f890(f889(x101942,x101943),a874),f890(x101943,a874)),f333(f333(f10(f890(x101943,f890(f890(f889(x101942,x101943),a874),a874)),f890(f890(f889(x101942,x101943),a874),f890(x101943,a874)),x101942),f9(x101943,f890(f889(x101942,x101943),a874),a874)),f333(f333(f10(f890(x101943,f889(x101942,x101943)),f890(x101943,f890(f890(f889(x101942,x101943),a874),a874)),x101942),f333(f10(f889(x101942,x101943),f890(f890(f889(x101942,x101943),a874),a874),x101943),f335(f889(x101942,x101943)))),f263(x101942,x101943))))),x101944)),x101945),x101946)) % 191.49/191.41 [10195]~P4(f333(f333(f335(f889(x101952,x101953)),f333(f333(f263(x101952,x101953),x101955),x101956)),f333(f333(f44(x101951,f890(f889(x101952,x101953),a874)),f258(f890(x101951,a874))),x101954)))+P4(f333(f333(f333(f333(f44(x101951,f890(x101952,f890(x101953,a874))),f258(f890(x101951,a874))),f333(f333(f10(f890(f889(x101952,x101953),a874),f890(x101952,f890(x101953,a874)),x101951),f333(f9(x101952,f890(f889(x101952,x101953),a874),f890(x101953,a874)),f333(f333(f10(f890(x101953,f890(f890(f889(x101952,x101953),a874),a874)),f890(f890(f889(x101952,x101953),a874),f890(x101953,a874)),x101952),f9(x101953,f890(f889(x101952,x101953),a874),a874)),f333(f333(f10(f890(x101953,f889(x101952,x101953)),f890(x101953,f890(f890(f889(x101952,x101953),a874),a874)),x101952),f333(f10(f889(x101952,x101953),f890(f890(f889(x101952,x101953),a874),a874),x101953),f335(f889(x101952,x101953)))),f263(x101952,x101953))))),x101954)),x101955),x101956)) % 191.49/191.41 [10208]P4(f333(f333(f335(f889(x102081,x102082)),f333(f333(f263(x102081,x102082),x102083),x102084)),f333(f333(f43(x102085,f890(f889(x102081,x102082),a874)),f258(f890(x102085,a874))),x102086)))+~P4(f333(f333(f333(f333(f43(x102085,f890(x102081,f890(x102082,a874))),f258(f890(x102085,a874))),f333(f333(f10(f890(f889(x102081,x102082),a874),f890(x102081,f890(x102082,a874)),x102085),f333(f9(x102081,f890(f889(x102081,x102082),a874),f890(x102082,a874)),f333(f333(f10(f890(x102082,f890(f890(f889(x102081,x102082),a874),a874)),f890(f890(f889(x102081,x102082),a874),f890(x102082,a874)),x102081),f9(x102082,f890(f889(x102081,x102082),a874),a874)),f333(f333(f10(f890(x102082,f889(x102081,x102082)),f890(x102082,f890(f890(f889(x102081,x102082),a874),a874)),x102081),f333(f10(f889(x102081,x102082),f890(f890(f889(x102081,x102082),a874),a874),x102082),f335(f889(x102081,x102082)))),f263(x102081,x102082))))),x102086)),x102083),x102084)) % 191.49/191.41 [10209]P4(f333(f333(f335(f889(x102091,x102092)),f333(f333(f263(x102091,x102092),x102093),x102094)),f333(f333(f44(x102095,f890(f889(x102091,x102092),a874)),f258(f890(x102095,a874))),x102096)))+~P4(f333(f333(f333(f333(f44(x102095,f890(x102091,f890(x102092,a874))),f258(f890(x102095,a874))),f333(f333(f10(f890(f889(x102091,x102092),a874),f890(x102091,f890(x102092,a874)),x102095),f333(f9(x102091,f890(f889(x102091,x102092),a874),f890(x102092,a874)),f333(f333(f10(f890(x102092,f890(f890(f889(x102091,x102092),a874),a874)),f890(f890(f889(x102091,x102092),a874),f890(x102092,a874)),x102091),f9(x102092,f890(f889(x102091,x102092),a874),a874)),f333(f333(f10(f890(x102092,f889(x102091,x102092)),f890(x102092,f890(f890(f889(x102091,x102092),a874),a874)),x102091),f333(f10(f889(x102091,x102092),f890(f890(f889(x102091,x102092),a874),a874),x102092),f335(f889(x102091,x102092)))),f263(x102091,x102092))))),x102096)),x102093),x102094)) % 191.49/191.41 [7410]E(f333(x74101,f333(x74102,x74103)),f333(x74104,x74103))+~E(f333(f74(x74105,x74106,x74107,x74101),x74102),x74104) % 191.49/191.41 [9620]~P25(x96203,x96204,x96201,x96205,x96206,x96207)+E(f333(f333(x96201,x96202),x96202),x96202) % 191.49/191.41 [9967]~P53(x99675,x99676,x99677,x99671,x99674,x99672,x99673)+P4(f333(f333(x99671,x99672),f704(x99673,x99672,x99674,x99671))) % 191.49/191.41 [9983]~E(f333(f244(f884(x99837),x99831,f197(x99837),x99835),f333(x99834,x99833)),f333(f242(x99837),x99832))+E(f333(f242(x99831),f509(x99832,x99833,x99834,x99835,x99836,x99837,x99831)),f333(x99834,x99833)) % 191.49/191.41 [9984]~E(f333(f244(f884(x99846),x99847,f197(x99846),x99841),f333(x99844,x99843)),f333(f242(x99846),x99842))+E(f333(x99841,f509(x99842,x99843,x99844,x99841,x99845,x99846,x99847)),f333(f242(x99846),x99842)) % 191.49/191.41 [6012]~E(f333(f333(f155(x60121,x60125),x60126),x60122),f333(f333(f155(x60123,x60125),x60127),x60124))+E(f333(f195(f881(x60121)),x60122),f333(f195(f881(x60123)),x60124)) % 191.49/191.41 [7485]E(x74851,x74852)+~E(f333(f333(f333(f73(x74853,f884(x74854)),x74855),x74856),f333(f242(x74854),x74851)),f333(f333(f333(f73(x74853,f884(x74854)),x74857),x74856),f333(f242(x74854),x74852))) % 191.49/191.41 [8444]E(f333(x84441,f333(x84442,x84443)),f333(x84444,x84443))+~E(f333(f74(x84445,x84446,x84447,x84441),x84442),f333(f74(x84446,x84446,x84447,f35(x84446)),x84444)) % 191.49/191.41 [8766]~P37(x87664,x87665,x87661,f333(f333(f152(x87664),x87662),x87666),f333(f333(f152(x87665),x87663),x87667))+P4(f333(f333(x87661,x87662),x87663)) % 191.49/191.41 [9148]P37(x91481,x91482,x91483,x91484,x91485)+~P37(x91481,x91482,x91483,f333(f333(f152(x91481),x91486),x91484),f333(f333(f152(x91482),x91487),x91485)) % 191.49/191.41 [9972]~P53(x99725,x99726,x99727,x99724,x99721,x99723,x99722)+P4(f333(f333(x99721,f704(x99722,x99723,x99721,x99724)),x99722)) % 191.49/191.41 [6056]E(x60561,x60562)+~E(f333(f333(f333(f93(x60563),x60564),x60565),x60561),f333(f333(f333(f93(x60563),x60566),x60567),x60562)) % 191.49/191.41 [6057]E(x60571,x60572)+~E(f333(f333(f333(f93(x60573),x60574),x60571),x60575),f333(f333(f333(f93(x60573),x60576),x60572),x60577)) % 191.49/191.41 [6058]E(x60581,x60582)+~E(f333(f333(f333(f93(x60583),x60581),x60584),x60585),f333(f333(f333(f93(x60583),x60582),x60586),x60587)) % 191.49/191.41 [8891]~P23(x88916,x88911,x88913,x88917)+E(f333(f74(x88911,x88911,x88912,f333(x88913,x88914)),f333(f74(x88911,x88911,x88912,f333(x88913,x88914)),x88915)),f333(f74(x88911,x88911,x88912,f333(x88913,x88914)),x88915)) % 191.49/191.41 [9252]~P37(x92523,x92522,x92524,f333(f333(f155(x92521,x92523),x92525),x92526),x92527)+P37(x92521,x92522,f333(f333(f10(x92523,f890(x92522,a874),x92521),x92524),x92525),x92526,x92527) % 191.49/191.41 [9278]P37(x92781,x92782,x92783,f333(f333(f155(x92784,x92781),x92785),x92786),x92787)+~P37(x92784,x92782,f333(f333(f10(x92781,f890(x92782,a874),x92784),x92783),x92785),x92786,x92787) % 191.49/191.41 [9711]E(f187(x97111,x97112,f333(f333(f333(f73(x97111,f884(x97112)),x97113),x97114),f333(f242(x97112),x97115)),x97116,x97117),f333(f333(f333(f73(x97111,f884(x97112)),f187(x97111,x97112,x97113,x97116,x97117)),x97114),f333(f242(x97112),x97115)))+P4(f333(f333(f335(x97111),x97114),f333(f173(x97111),x97116))) % 191.49/191.41 [8890]~P4(f333(f333(f335(x88901),x88902),f333(f333(x88905,x88906),x88907)))+P4(f333(f333(f335(x88901),x88902),f333(f333(f272(x88903,x88904,f890(x88901,a874)),x88905),f333(f333(f263(x88903,x88904),x88906),x88907)))) % 191.49/191.41 [9174]P4(f333(f333(f333(x91741,x91742),x91743),x91744))+~P4(f333(f333(f333(f272(x91745,x91746,f890(x91747,a874)),x91741),f333(f333(f263(x91745,x91746),x91742),x91743)),x91744)) % 191.49/191.41 [9317]P4(f333(f333(f335(x93171),f333(f333(x93172,x93173),x93174)),f333(f312(f889(x93175,x93176),x93171,f333(f272(x93175,x93176,x93171),x93172)),x93177)))+~P4(f333(f333(f335(f889(x93175,x93176)),f333(f333(f263(x93175,x93176),x93173),x93174)),x93177)) % 191.49/191.41 [9671]P4(f333(f333(f335(f889(f881(x96711),f881(x96711))),f333(f333(f263(f881(x96711),f881(x96711)),f333(f333(f127(x96711),x96712),f333(f333(f152(x96711),x96713),x96714))),f333(f333(f127(x96711),x96712),f333(f333(f152(x96711),x96715),x96716)))),f148(x96711,x96717)))+~P4(f333(f333(f335(f889(x96711,x96711)),f333(f333(f263(x96711,x96711),x96713),x96715)),x96717)) % 191.49/191.41 [9733]~P37(x97331,x97333,x97334,x97336,f333(f333(f155(x97332,x97333),x97335),x97337))+P37(x97331,x97332,f333(f333(f9(x97331,f890(x97332,x97333),f890(x97332,a874)),f333(f333(f10(f890(x97333,a874),f890(f890(x97332,x97333),f890(x97332,a874)),x97331),f10(x97333,a874,x97332)),x97334)),x97335),x97336,x97337) % 191.49/191.41 [9827]P37(x98271,x98272,x98273,x98274,f333(f333(f155(x98275,x98272),x98276),x98277))+~P37(x98271,x98275,f333(f333(f9(x98271,f890(x98275,x98272),f890(x98275,a874)),f333(f333(f10(f890(x98272,a874),f890(f890(x98275,x98272),f890(x98275,a874)),x98271),f10(x98272,a874,x98275)),x98273)),x98276),x98274,x98277) % 191.49/191.41 [10089]P53(x100891,x100892,x100893,f333(f333(f9(x100891,f890(f889(x100891,x100892),a874),f890(x100892,a874)),f333(f333(f10(f890(x100892,f890(f890(f889(x100891,x100892),a874),a874)),f890(f890(f889(x100891,x100892),a874),f890(x100892,a874)),x100891),f9(x100892,f890(f889(x100891,x100892),a874),a874)),f333(f333(f10(f890(x100892,f889(x100891,x100892)),f890(x100892,f890(f890(f889(x100891,x100892),a874),a874)),x100891),f333(f10(f889(x100891,x100892),f890(f890(f889(x100891,x100892),a874),a874),x100892),f335(f889(x100891,x100892)))),f263(x100891,x100892)))),x100894),f333(f333(f9(x100892,f890(f889(x100892,x100893),a874),f890(x100893,a874)),f333(f333(f10(f890(x100893,f890(f890(f889(x100892,x100893),a874),a874)),f890(f890(f889(x100892,x100893),a874),f890(x100893,a874)),x100892),f9(x100893,f890(f889(x100892,x100893),a874),a874)),f333(f333(f10(f890(x100893,f889(x100892,x100893)),f890(x100893,f890(f890(f889(x100892,x100893),a874),a874)),x100892),f333(f10(f889(x100892,x100893),f890(f890(f889(x100892,x100893),a874),a874),x100893),f335(f889(x100892,x100893)))),f263(x100892,x100893)))),x100895),x100896,x100897)+~P4(f333(f333(f335(f889(x100891,x100893)),f333(f333(f263(x100891,x100893),x100896),x100897)),f333(f333(f290(x100891,x100892,x100893),x100894),x100895))) % 191.49/191.41 [10141]~P53(x101411,x101415,x101412,f333(f333(f9(x101411,f890(f889(x101411,x101415),a874),f890(x101415,a874)),f333(f333(f10(f890(x101415,f890(f890(f889(x101411,x101415),a874),a874)),f890(f890(f889(x101411,x101415),a874),f890(x101415,a874)),x101411),f9(x101415,f890(f889(x101411,x101415),a874),a874)),f333(f333(f10(f890(x101415,f889(x101411,x101415)),f890(x101415,f890(f890(f889(x101411,x101415),a874),a874)),x101411),f333(f10(f889(x101411,x101415),f890(f890(f889(x101411,x101415),a874),a874),x101415),f335(f889(x101411,x101415)))),f263(x101411,x101415)))),x101416),f333(f333(f9(x101415,f890(f889(x101415,x101412),a874),f890(x101412,a874)),f333(f333(f10(f890(x101412,f890(f890(f889(x101415,x101412),a874),a874)),f890(f890(f889(x101415,x101412),a874),f890(x101412,a874)),x101415),f9(x101412,f890(f889(x101415,x101412),a874),a874)),f333(f333(f10(f890(x101412,f889(x101415,x101412)),f890(x101412,f890(f890(f889(x101415,x101412),a874),a874)),x101415),f333(f10(f889(x101415,x101412),f890(f890(f889(x101415,x101412),a874),a874),x101412),f335(f889(x101415,x101412)))),f263(x101415,x101412)))),x101417),x101413,x101414)+P4(f333(f333(f335(f889(x101411,x101412)),f333(f333(f263(x101411,x101412),x101413),x101414)),f333(f333(f290(x101411,x101415,x101412),x101416),x101417))) % 191.49/191.41 [9166]E(x91661,x91662)+E(f333(f333(f333(f73(x91663,x91664),f333(f333(f333(f73(x91663,x91664),x91665),x91661),x91666)),x91662),x91667),f333(f333(f333(f73(x91663,x91664),f333(f333(f333(f73(x91663,x91664),x91665),x91662),x91667)),x91661),x91666)) % 191.49/191.41 [9407]E(f187(x94071,x94072,f333(f333(f333(f73(x94071,f884(x94072)),x94073),x94074),f333(f242(x94072),x94075)),x94076,x94077),f187(x94071,x94072,x94073,x94076,x94077))+~P4(f333(f333(f335(x94071),x94074),f333(f173(x94071),f333(f333(f174(x94071),f333(f195(f881(x94072)),x94077)),x94076)))) % 191.49/191.41 [9749]E(f187(x97491,x97492,f333(f333(f333(f73(x97491,f884(x97492)),x97493),x97494),f333(f242(x97492),x97495)),x97496,x97497),f333(f333(f333(f73(x97491,f884(x97492)),f187(x97491,x97492,x97493,x97496,x97497)),x97494),f333(f242(x97492),x97495)))+P4(f333(f333(f335(x97491),x97494),f333(f173(x97491),f333(f333(f174(x97491),f333(f195(f881(x97492)),x97497)),x97496)))) % 191.49/191.41 [10102]P4(f333(f333(f335(x101021),f532(x101022,x101023,x101024,x101025,x101026,x101027,x101021)),x101025))+P4(f333(f333(f333(f333(f43(x101021,f890(x101027,f890(x101026,a874))),x101025),x101024),x101023),x101022)) % 191.49/191.41 [10103]P4(f333(f333(f335(x101031),f545(x101032,x101033,x101034,x101035,x101036,x101037,x101031)),x101035))+~P4(f333(f333(f333(f333(f44(x101031,f890(x101037,f890(x101036,a874))),x101035),x101034),x101033),x101032)) % 191.49/191.41 [10150]P4(f333(f333(f333(x101501,f545(x101502,x101503,x101501,x101504,x101505,x101506,x101507)),x101503),x101502))+~P4(f333(f333(f333(f333(f44(x101507,f890(x101506,f890(x101505,a874))),x101504),x101501),x101503),x101502)) % 191.49/191.41 [10170]~P4(f333(f333(f333(x101705,f532(x101707,x101706,x101705,x101704,x101703,x101702,x101701)),x101706),x101707))+P4(f333(f333(f333(f333(f43(x101701,f890(x101702,f890(x101703,a874))),x101704),x101705),x101706),x101707)) % 191.49/191.41 [10111]~P144(x101112)+E(f333(f333(f8(x101111,x101112),f333(f333(f9(x101111,f890(x101113,a874),x101112),f333(f333(f10(f890(x101113,x101112),f890(f890(x101113,a874),x101112),x101111),f8(x101113,x101112)),f333(f333(f9(x101111,f890(x101113,x101112),f890(x101113,x101112)),f333(f333(f10(f890(x101112,x101112),f890(f890(x101113,x101112),f890(x101113,x101112)),x101111),f10(x101112,x101112,x101113)),f333(f333(f10(x101112,f890(x101112,x101112),x101111),f82(x101112)),x101114))),x101115))),x101116)),x101117),f333(f333(f82(x101112),f333(f333(f8(x101111,x101112),x101114),x101117)),f333(f333(f8(x101113,x101112),x101115),x101116))) % 191.49/191.41 [9205]~P22(x92057,x92051,x92053,x92058)+E(f333(f74(x92051,x92051,x92052,f333(x92053,x92054)),f333(f74(x92051,x92051,x92052,f333(x92053,x92055)),x92056)),f333(f74(x92051,x92051,x92052,f333(x92053,x92055)),f333(f74(x92051,x92051,x92052,f333(x92053,x92054)),x92056))) % 191.49/191.41 [10201]E(f333(f333(f263(x102011,x102012),f333(x102013,f620(x102014,x102015,x102013,x102016,x102017,x102018,x102012,x102011))),f333(x102015,f621(x102014,x102015,x102013,x102016,x102017,x102018,x102012,x102011))),x102018)+~P4(f333(f333(f335(f889(x102011,x102012)),x102018),f333(f312(f889(x102017,x102016),f889(x102011,x102012),f273(x102017,x102011,x102016,x102012,x102013,x102015)),x102014))) % 191.49/191.41 [10222]~P4(f333(f333(f335(f889(x102228,x102227)),x102226),f333(f312(f889(x102221,x102222),f889(x102228,x102227),f273(x102221,x102228,x102222,x102227,x102225,x102224)),x102223)))+P4(f333(f333(f335(f889(x102221,x102222)),f333(f333(f263(x102221,x102222),f620(x102223,x102224,x102225,x102222,x102221,x102226,x102227,x102228)),f621(x102223,x102224,x102225,x102222,x102221,x102226,x102227,x102228))),x102223)) % 191.49/191.41 [9661]P4(f333(f333(f335(f889(f889(x96611,x96612),f889(x96611,x96612))),f333(f333(f263(f889(x96611,x96612),f889(x96611,x96612)),f333(f333(f263(x96611,x96612),x96613),x96614)),f333(f333(f263(x96611,x96612),x96615),x96616))),f326(x96611,x96612,x96617,x96618)))+~P4(f333(f333(f335(f889(x96611,x96611)),f333(f333(f263(x96611,x96611),x96613),x96615)),x96617)) % 191.49/191.41 [10188]E(f333(f143(x101881,x101882,f333(f9(x101882,x101881,x101881),x101883),f333(x101884,x101885)),x101886),f333(x101884,f333(f143(x101887,x101882,f333(f9(x101882,x101887,x101887),x101888),x101885),x101886)))+P4(f333(f333(f335(x101882),f714(x101885,x101888,x101884,x101883,x101887,x101881,x101886,x101882)),f333(f173(x101882),x101886))) % 191.49/191.41 [10211]~E(f333(f74(x102111,x102111,x102117,f333(x102113,f714(x102115,x102118,x102114,x102113,x102117,x102111,x102116,x102112))),x102114),f333(f74(x102117,x102111,x102117,x102114),f333(x102118,f714(x102115,x102118,x102114,x102113,x102117,x102111,x102116,x102112))))+E(f333(f143(x102111,x102112,f333(f9(x102112,x102111,x102111),x102113),f333(x102114,x102115)),x102116),f333(x102114,f333(f143(x102117,x102112,f333(f9(x102112,x102117,x102117),x102118),x102115),x102116))) % 191.49/191.41 [8450]E(f333(x84501,f333(x84502,x84503)),f333(x84504,f333(x84505,x84503)))+~E(f333(f74(x84506,x84507,x84508,x84501),x84502),f333(f74(x84509,x84507,x84508,x84504),x84505)) % 191.49/191.41 [10036]P4(f333(f333(f335(f889(x100361,x100362)),f333(f333(f263(x100361,x100362),f333(x100363,x100364)),f333(x100365,x100366))),f333(f312(f889(x100367,x100368),f889(x100361,x100362),f273(x100367,x100361,x100368,x100362,x100363,x100365)),x100369)))+~P4(f333(f333(f335(f889(x100367,x100368)),f333(f333(f263(x100367,x100368),x100364),x100366)),x100369)) % 191.49/191.41 [8714]~E(f333(x87144,f333(x87145,x87146)),f333(x87149,f333(x871410,x871411)))+E(f333(f333(f74(x87141,x87142,x87143,x87144),x87145),x87146),f333(f333(f74(x87147,x87142,x87148,x87149),x871410),x871411)) % 191.49/191.41 [4613]~P102(x46131)+~P109(x46131)+E(f106(x46131),f248(x46131)) % 191.49/191.41 [4614]~P101(x46141)+~P109(x46141)+E(f115(x46141),f249(x46141)) % 191.49/191.41 [4857]~P120(x48571)+~P94(x48571)+E(f333(f76(x48571),f333(f108(x48571),a102)),f79(x48571)) % 191.49/191.41 [5130]E(x51301,f2(a1))+E(f83(a1,x51301),f333(f80(a1),f79(a1)))+P4(f333(f333(f251(a1),f2(a1)),x51301)) % 191.49/191.41 [5346]E(x53461,f2(a1))+E(f83(a1,x53461),f79(a1))+~P4(f333(f333(f251(a1),f2(a1)),x53461)) % 191.49/191.41 [7309]~P42(x73091)+P4(f333(f63(a1),x73091))+~P4(f333(f63(a880),f333(f312(a1,a880,a109),x73091))) % 191.49/191.41 [8553]~P1(a5000)+~P4(f333(f333(f335(f889(a877,a876)),x85531),f333(f173(f889(a877,a876)),a27)))+P4(f333(f333(f272(a877,a876,a874),f333(f18(f890(a876,a874),a877),a25)),x85531)) % 191.49/191.41 [9619]E(x96191,f194(f890(f889(a880,a880),a874)))+~P4(f333(f63(f889(a880,a880)),x96191))+P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),f194(f890(f889(a880,a880),a874))),x96191)),a38)) % 191.49/191.41 [10061]E(x100611,f2(a880))+E(x100611,f333(a117,f2(a880)))+~P4(f333(f333(f251(a880),x100611),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.41 [10183]E(x101831,f2(a104))+E(f333(f333(f81(a1),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(a22,f333(f333(f40(a104),x101831),f333(f108(a104),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))))),f79(a1)),f333(a22,x101831))+E(f46(a104,x101831,f333(f108(a104),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f2(a104)) % 191.49/191.41 [10118]E(x101181,f2(a104))+~E(f46(a104,x101181,f333(f108(a104),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f2(a104))+E(f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(a22,f333(f333(f40(a104),x101181),f333(f108(a104),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))),f333(a22,x101181)) % 191.49/191.41 [4688]~P57(x46881,x46882)+P45(x46881,x46882)+~P46(a874) % 191.49/191.41 [4625]~P143(x46251)+P33(x46251,x46252)+~E(x46252,f2(x46251)) % 191.49/191.41 [4626]~P109(x46261)+P17(x46261,x46262)+~E(x46262,f118(x46261)) % 191.49/191.41 [4635]~P120(x46351)+~E(x46352,f2(x46351))+E(f83(x46351,x46352),f2(x46351)) % 191.49/191.41 [4636]~P90(x46361)+~E(x46362,f2(x46361))+E(f83(x46361,x46362),f2(x46361)) % 191.49/191.41 [4644]~P143(x46442)+~P33(x46442,x46441)+E(x46441,f2(x46442)) % 191.49/191.41 [4678]~P120(x46782)+~E(f83(x46782,x46781),f2(x46782))+E(x46781,f2(x46782)) % 191.49/191.41 [4695]~P8(x46952)+~P8(x46951)+P8(f890(x46951,x46952)) % 191.49/191.41 [4696]~P8(x46962)+~P8(x46961)+P8(f888(x46961,x46962)) % 191.49/191.41 [4697]~P8(x46972)+~P8(x46971)+P8(f889(x46971,x46972)) % 191.49/191.41 [4698]~P10(x46982)+~P10(x46981)+P10(f202(x46981,x46982)) % 191.49/191.41 [4699]~P145(x46992)+~P145(x46991)+P145(f889(x46991,x46992)) % 191.49/191.41 [4700]~P62(x47002)+~P62(x47001)+P62(f890(x47001,x47002)) % 191.49/191.41 [4701]~P62(x47012)+~P62(x47011)+P62(f888(x47011,x47012)) % 191.49/191.41 [4702]~P62(x47022)+~P62(x47021)+P62(f889(x47021,x47022)) % 191.49/191.41 [4703]~P62(x47031)+~P96(x47032)+P96(f890(x47031,x47032)) % 191.49/191.41 [4704]~P104(x47042)+~P104(x47041)+P104(f889(x47041,x47042)) % 191.49/191.41 [4828]~P109(x48281)+~P17(x48281,x48282)+P17(x48281,f153(x48281,x48282)) % 191.49/191.41 [5063]~P10(x50632)+~P10(x50631)+P10(f46(a1,x50631,x50632)) % 191.49/191.41 [4646]~P77(x46461)+~E(x46462,f2(x46461))+E(f333(f80(x46461),x46462),x46462) % 191.49/191.41 [4650]~P140(x46501)+~E(x46502,f2(a1))+E(f333(f107(x46501),x46502),f2(x46501)) % 191.49/191.41 [4651]~P93(x46511)+~E(x46512,f2(a1))+E(f333(f107(x46511),x46512),f2(x46511)) % 191.49/191.41 [4675]~P75(x46751)+~E(f2(x46751),x46752)+E(f333(f80(x46751),x46752),f2(x46751)) % 191.49/191.41 [4676]~P75(x46761)+~E(x46762,f2(x46761))+E(f333(f80(x46761),x46762),f2(x46761)) % 191.49/191.41 [4677]~P87(x46771)+~E(x46772,f2(x46771))+E(f333(f76(x46771),x46772),f2(x46771)) % 191.49/191.41 [4706]~P77(x47062)+E(x47061,f2(x47062))+~E(f333(f80(x47062),x47061),x47061) % 191.49/191.41 [4712]E(x47121,f333(a109,x47122))+~E(x47121,f2(a880))+~E(x47122,f333(f105(a1),x47121)) % 191.49/191.41 [4713]E(f333(a109,x47131),x47132)+~E(x47132,f2(a880))+~E(x47131,f333(f105(a1),x47132)) % 191.49/191.41 [4715]~P93(x47152)+E(x47151,f2(a1))+~E(f333(f107(x47152),x47151),f2(x47152)) % 191.49/191.41 [4720]~P75(x47202)+E(x47201,f2(x47202))+~E(f333(f80(x47202),x47201),f2(x47202)) % 191.49/191.41 [4721]~P87(x47212)+E(x47211,f2(x47212))+~E(f333(f76(x47212),x47211),f2(x47212)) % 191.49/191.41 [4722]~P75(x47221)+E(f2(x47221),x47222)+~E(f333(f80(x47221),x47222),f2(x47221)) % 191.49/191.41 [4860]~P1(a5000)+~E(f333(a28,x48602),f333(f242(a876),x48601))+P4(f333(a25,x48601)) % 191.49/191.41 [4902]~P109(x49021)+~P17(x49021,x49022)+P17(x49021,f333(f172(x49021),x49022)) % 191.49/191.41 [4928]~P4(x49282)+~P4(x49281)+P4(f333(f333(a331,x49281),x49282)) % 191.49/191.41 [4960]~E(f79(a880),f2(a880))+E(f333(f39(x49601),x49602),f2(a880))+~P4(f333(f63(x49601),x49602)) % 191.49/191.41 [4993]~P113(x49931)+~P144(x49931)+E(f333(f333(f264(x49931),f2(x49931)),f333(a117,x49932)),f2(x49931)) % 191.49/191.41 [5031]~P109(x50311)+P17(x50311,f140(x50311,x50312))+~P4(f333(f63(x50311),x50312)) % 191.49/191.41 [5032]~P109(x50321)+P17(x50321,f723(x50322,x50321))+~P4(f333(f63(x50321),x50322)) % 191.49/191.41 [5053]~P109(x50531)+E(f333(f173(x50531),f140(x50531,x50532)),x50532)+~P4(f333(f63(x50531),x50532)) % 191.49/191.41 [5054]~P109(x50541)+E(f333(f173(x50541),f723(x50542,x50541)),x50542)+~P4(f333(f63(x50541),x50542)) % 191.49/191.41 [5083]P4(x50831)+P4(x50832)+~P4(f333(f333(a332,x50832),x50831)) % 191.49/191.41 [5095]E(x50951,f194(f890(x50952,a874)))+~E(f333(f39(x50952),x50951),f2(a880))+~P4(f333(f63(x50952),x50951)) % 191.49/191.41 [5100]P4(x51001)+~P4(x51002)+~P4(f333(f333(a336,x51002),x51001)) % 191.49/191.41 [5147]~P74(x51471)+E(f333(f76(x51471),x51472),x51472)+P4(f333(f333(f251(x51471),x51472),f2(x51471))) % 191.49/191.41 [5218]~P62(x52182)+~P4(f333(f59(x52182),x52181))+P4(f333(x52181,f646(x52181,x52182))) % 191.49/191.41 [5219]~P62(x52192)+~P4(f333(f59(x52192),x52191))+P4(f333(x52191,f667(x52191,x52192))) % 191.49/191.41 [5247]~P4(f333(a25,x52472))+~P4(f333(a25,x52471))+P4(f333(a25,f34(x52471,x52472))) % 191.49/191.41 [5256]E(x52561,f118(x52562))+P4(f333(f138(x52562),f119(x52562,x52561)))+~P4(f333(f138(x52562),x52561)) % 191.49/191.41 [5261]~P109(x52611)+~P4(f333(f63(x52611),x52612))+P4(f333(f138(x52611),f140(x52611,x52612))) % 191.49/191.41 [5262]~P109(x52621)+~P4(f333(f63(x52621),x52622))+P4(f333(f138(x52621),f723(x52622,x52621))) % 191.49/191.41 [5268]~P140(x52681)+E(f333(f105(x52681),f333(a109,x52682)),f333(f107(x52681),x52682))+P4(f333(f333(f251(a1),x52682),f2(a1))) % 191.49/191.41 [5298]P11(x52982,x52981)+E(f333(x52981,f568(x52981)),f333(x52981,f574(x52981)))+P4(f333(f333(x52981,f568(x52981)),f574(x52981))) % 191.49/191.41 [5312]E(f333(f105(a1),f405(x53121,x53122)),x53121)+P4(f333(x53122,f333(a109,x53121)))+~P4(f333(x53122,f2(a880))) % 191.49/191.41 [5324]~P62(x53241)+~P4(f333(x53242,f668(x53242,x53241)))+P4(f333(f60(x53241),x53242)) % 191.49/191.41 [5325]~P62(x53251)+~P4(f333(x53252,f669(x53252,x53251)))+P4(f333(f60(x53251),x53252)) % 191.49/191.41 [5339]~P62(x53392)+~P38(x53392,x53391,f57(x53392))+P4(f333(x53391,f741(x53391,x53392))) % 191.49/191.41 [5355]~P120(x53551)+~E(f83(x53551,x53552),f333(f80(x53551),f79(x53551)))+P4(f333(f333(f251(x53551),x53552),f2(x53551))) % 191.49/191.41 [5431]~E(x54312,f2(a1))+E(f225(x54311,x54312),f333(f333(f263(a1,a1),f2(a1)),f79(a1)))+P4(f333(f333(f251(a1),x54312),f2(a1))) % 191.49/191.41 [5432]~E(x54321,f2(a1))+E(f225(x54321,x54322),f333(f333(f263(a1,a1),f2(a1)),f79(a1)))+P4(f333(f333(f251(a1),x54322),f2(a1))) % 191.49/191.41 [5484]E(f333(f105(a1),f405(x54841,x54842)),x54841)+P4(f333(x54842,f333(a109,x54841)))+P4(f333(f333(f251(a1),x54841),f2(a1))) % 191.49/191.41 [5545]~P120(x55451)+E(f83(x55451,x55452),f333(f80(x55451),f79(x55451)))+~P4(f333(f333(f251(x55451),x55452),f2(x55451))) % 191.49/191.41 [5546]~P87(x55461)+E(f333(f76(x55461),x55462),f333(f80(x55461),x55462))+~P4(f333(f333(f251(x55461),x55462),f2(x55461))) % 191.49/191.41 [5547]~P87(x55471)+E(f333(f76(x55471),x55472),f333(f80(x55471),x55472))+~P4(f333(f333(f250(x55471),x55472),f2(x55471))) % 191.49/191.41 [5548]~P74(x55481)+E(f333(f76(x55481),x55482),f333(f80(x55481),x55482))+~P4(f333(f333(f251(x55481),x55482),f2(x55481))) % 191.49/191.41 [5644]~P4(f333(x56441,f405(x56442,x56441)))+P4(f333(x56441,f333(a109,x56442)))+~P4(f333(x56441,f2(a880))) % 191.49/191.41 [5651]E(x56511,f2(a880))+E(f333(a117,f843(x56512,x56511)),x56511)+~P4(f333(f333(f251(a880),x56511),f333(a117,x56512))) % 191.49/191.41 [5655]P11(x56551,x56552)+~E(f333(x56552,f568(x56552)),f333(x56552,f574(x56552)))+~P4(f333(f333(x56552,f568(x56552)),f574(x56552))) % 191.49/191.41 [5675]~P109(x56751)+P17(x56751,x56752)+P4(f333(f333(f250(a880),f647(x56752,x56751)),f648(x56752,x56751))) % 191.49/191.41 [5676]~P109(x56761)+P17(x56761,x56762)+P4(f333(f333(f250(a880),f654(x56762,x56761)),f664(x56762,x56761))) % 191.49/191.41 [5763]~P87(x57631)+~E(x57632,f2(x57631))+P4(f333(f333(f250(x57631),f333(f76(x57631),x57632)),f2(x57631))) % 191.49/191.41 [5842]~P62(x58422)+~P62(x58421)+E(f61(x58421,x58422,f57(x58421),f57(x58422)),f57(f889(x58421,x58422))) % 191.49/191.41 [5846]~P4(f333(x58461,f405(x58462,x58461)))+P4(f333(x58461,f333(a109,x58462)))+P4(f333(f333(f251(a1),x58462),f2(a1))) % 191.49/191.41 [5869]~P4(f333(x58691,f333(a109,x58692)))+P4(f333(x58691,f2(a880)))+~P4(f333(f333(f251(a1),x58692),f2(a1))) % 191.49/191.41 [6208]~P120(x62081)+~P4(f333(f333(f251(x62081),x62082),f2(x62081)))+P4(f333(f333(f251(x62081),f83(x62081,x62082)),f2(x62081))) % 191.49/191.41 [6321]~P120(x63211)+P4(f333(f333(f251(x63211),f333(f107(x63211),x63212)),f2(x63211)))+~P4(f333(f333(f251(a1),x63212),f2(a1))) % 191.49/191.41 [6322]~P120(x63221)+P4(f333(f333(f250(x63221),f333(f107(x63221),x63222)),f2(x63221)))+~P4(f333(f333(f250(a1),x63222),f2(a1))) % 191.49/191.41 [6329]~P87(x63292)+E(x63291,f2(x63292))+~P4(f333(f333(f250(x63292),f333(f76(x63292),x63291)),f2(x63292))) % 191.49/191.41 [6405]~P140(x64051)+~P4(f333(f333(f335(x64051),x64052),f114(x64051)))+P4(f333(f333(f335(x64051),f333(f80(x64051),x64052)),f114(x64051))) % 191.49/191.41 [6437]~P120(x64371)+~P4(f333(f333(f251(x64371),f83(x64371,x64372)),f2(x64371)))+P4(f333(f333(f251(x64371),x64372),f2(x64371))) % 191.49/191.41 [6603]~P120(x66032)+~P4(f333(f333(f251(x66032),f333(f107(x66032),x66031)),f2(x66032)))+P4(f333(f333(f251(a1),x66031),f2(a1))) % 191.49/191.41 [6604]~P120(x66042)+~P4(f333(f333(f250(x66042),f333(f107(x66042),x66041)),f2(x66042)))+P4(f333(f333(f250(a1),x66041),f2(a1))) % 191.49/191.41 [7098]~P120(x70981)+~P4(f333(f333(f251(x70981),x70982),f2(x70981)))+P4(f333(f333(f251(x70981),f333(f333(f81(x70981),x70982),x70982)),f2(x70981))) % 191.49/191.41 [7099]~P77(x70991)+~P4(f333(f333(f251(x70991),x70992),f2(x70991)))+P4(f333(f333(f251(x70991),f333(f333(f81(x70991),x70992),x70992)),f2(x70991))) % 191.49/191.41 [7100]~P77(x71001)+~P4(f333(f333(f250(x71001),x71002),f2(x71001)))+P4(f333(f333(f250(x71001),f333(f333(f81(x71001),x71002),x71002)),f2(x71001))) % 191.49/191.41 [7652]~P120(x76521)+~P4(f333(f333(f251(x76521),f333(f333(f81(x76521),x76522),x76522)),f2(x76521)))+P4(f333(f333(f251(x76521),x76522),f2(x76521))) % 191.49/191.41 [7653]~P77(x76531)+~P4(f333(f333(f251(x76531),f333(f333(f81(x76531),x76532),x76532)),f2(x76531)))+P4(f333(f333(f251(x76531),x76532),f2(x76531))) % 191.49/191.41 [7654]~P77(x76541)+~P4(f333(f333(f250(x76541),f333(f333(f81(x76541),x76542),x76542)),f2(x76541)))+P4(f333(f333(f250(x76541),x76542),f2(x76541))) % 191.49/191.41 [4760]~E(x47602,f2(a880))+~E(x47601,f2(a880))+E(f333(f333(f81(a880),x47601),x47602),f2(a880)) % 191.49/191.41 [4761]~E(x47612,f79(a880))+~E(x47611,f79(a880))+E(f333(f333(f82(a880),x47611),x47612),f79(a880)) % 191.49/191.41 [4762]~E(x47622,f79(a1))+~E(x47621,f79(a1))+E(f333(f333(f82(a1),x47621),x47622),f79(a1)) % 191.49/191.41 [4814]~P118(x48142)+E(x48141,f2(x48142))+E(f333(f333(f291(x48142),x48141),x48141),f79(x48142)) % 191.49/191.41 [4815]~P60(x48152)+E(x48151,f2(x48152))+E(f333(f333(f40(x48152),x48151),x48151),f79(x48152)) % 191.49/191.41 [4816]~P119(x48162)+E(x48161,f2(x48162))+E(f333(f333(f291(x48162),x48161),x48161),f79(x48162)) % 191.49/191.41 [4833]~P77(x48331)+~E(x48332,f2(x48331))+E(f333(f333(f81(x48331),x48332),x48332),f2(x48331)) % 191.49/191.41 [4836]~P139(x48361)+~E(x48362,f79(x48361))+E(f333(f333(f82(x48361),x48362),x48362),f79(x48361)) % 191.49/191.41 [4837]~P119(x48371)+~E(x48372,f2(x48371))+E(f333(f333(f291(x48371),x48372),x48372),f2(x48371)) % 191.49/191.41 [4881]~E(x48812,f2(a880))+~E(x48811,f2(a880))+E(f333(f80(a1),f333(f105(a1),x48811)),f333(f105(a1),x48812)) % 191.49/191.41 [4899]E(x48991,f79(a880))+E(x48992,f2(a880))+~E(f333(f333(f82(a880),x48992),x48991),x48992) % 191.49/191.41 [4909]E(x49091,f2(a880))+E(x49092,f2(a880))+~E(f333(f333(f82(a880),x49092),x49091),f2(a880)) % 191.49/191.41 [4937]~E(x49372,f2(a880))+~E(x49371,f333(a117,f2(a880)))+E(f333(f333(f81(a880),x49371),x49372),f333(a117,f2(a880))) % 191.49/191.41 [4938]~E(x49381,f2(a880))+~E(x49382,f333(a117,f2(a880)))+E(f333(f333(f81(a880),x49381),x49382),f333(a117,f2(a880))) % 191.49/191.41 [4943]E(x49431,f79(a1))+E(x49432,f333(f108(a1),a102))+~E(f333(f333(f82(a1),x49431),x49432),f79(a1)) % 191.49/191.41 [4944]E(x49441,f79(a1))+E(x49442,f333(f108(a1),a102))+~E(f333(f333(f82(a1),x49442),x49441),f79(a1)) % 191.49/191.41 [4945]E(x49451,f79(a1))+E(x49451,f333(f108(a1),a102))+~E(f333(f333(f82(a1),x49452),x49451),f79(a1)) % 191.49/191.41 [4947]E(x49471,f79(a1))+E(x49471,f333(f108(a1),a102))+~E(f333(f333(f82(a1),x49471),x49472),f79(a1)) % 191.49/191.41 [4964]~P77(x49642)+E(x49641,f2(x49642))+~E(f333(f333(f81(x49642),x49641),x49641),f2(x49642)) % 191.49/191.41 [4970]~E(x49701,f333(f108(a1),a102))+~E(x49702,f333(f108(a1),a102))+E(f333(f333(f82(a1),x49701),x49702),f79(a1)) % 191.49/191.41 [4982]E(x49821,f2(a880))+E(x49822,f2(a880))+~E(f333(f333(f81(a880),x49822),x49821),f333(a117,f2(a880))) % 191.49/191.41 [4992]~P63(x49921)+~P94(x49921)+E(f333(f333(f291(x49921),x49922),f333(f108(x49921),a84)),f2(x49921)) % 191.49/191.41 [4998]~P139(x49981)+~E(x49982,f333(f80(x49981),f79(x49981)))+E(f333(f333(f82(x49981),x49982),x49982),f79(x49981)) % 191.49/191.41 [5003]~P10(x50032)+~P10(x50031)+P10(f333(f333(f81(a1),x50031),x50032)) % 191.49/191.41 [5004]~P10(x50042)+~P10(x50041)+P10(f333(f333(f82(a1),x50041),x50042)) % 191.49/191.41 [5005]~P10(x50052)+~P10(x50051)+P10(f333(f333(f40(a1),x50051),x50052)) % 191.49/191.41 [5007]~E(x50072,f2(a1))+E(x50071,f2(a1))+E(f47(x50071,x50072),f333(f333(f263(a1,a1),f2(a1)),x50071)) % 191.49/191.41 [5029]~E(x50292,f333(a117,f2(a880)))+~E(x50291,f333(a117,f2(a880)))+E(f333(f333(f82(a880),x50291),x50292),f333(a117,f2(a880))) % 191.49/191.41 [5044]E(x50441,f2(a880))+E(x50442,f333(a117,f2(a880)))+~E(f333(f333(f264(a880),x50442),x50441),f333(a117,f2(a880))) % 191.49/191.41 [5045]E(x50451,f2(a880))+E(x50451,f333(a117,f2(a880)))+~E(f333(f333(f81(a880),x50452),x50451),f333(a117,f2(a880))) % 191.49/191.41 [5046]E(x50461,f2(a880))+E(x50461,f333(a117,f2(a880)))+~E(f333(f333(f81(a880),x50461),x50462),f333(a117,f2(a880))) % 191.49/191.41 [5055]~P63(x50551)+~P94(x50551)+E(f333(f333(f291(x50551),x50552),f333(f108(x50551),a102)),f333(f80(x50551),x50552)) % 191.49/191.41 [5075]E(x50751,f333(a109,x50752))+~E(x50751,f2(a880))+P4(f333(f333(f250(a1),f2(a1)),x50752)) % 191.49/191.41 [5076]E(f333(a109,x50761),x50762)+~E(x50762,f2(a880))+P4(f333(f333(f250(a1),f2(a1)),x50761)) % 191.49/191.41 [5091]E(x50911,f333(a117,f2(a880)))+E(x50912,f333(a117,f2(a880)))+~E(f333(f333(f81(a880),x50911),x50912),f333(a117,f2(a880))) % 191.49/191.41 [5101]~E(x51011,f333(a109,x51012))+E(x51011,f2(a880))+P4(f333(f333(f250(a1),f2(a1)),x51012)) % 191.49/191.41 [5102]~E(f333(a109,x51022),x51021)+E(x51021,f2(a880))+P4(f333(f333(f250(a1),f2(a1)),x51022)) % 191.49/191.41 [5124]~P6(x51241)+E(f333(f65(x51241,f115(x51241)),x51242),f12(x51241,x51242))+~P4(f333(f63(x51241),x51242)) % 191.49/191.41 [5125]~P6(x51251)+E(f333(f65(x51251,f106(x51251)),x51252),f13(x51251,x51252))+~P4(f333(f63(x51251),x51252)) % 191.49/191.41 [5126]~P109(x51261)+E(f333(f65(x51261,f248(x51261)),x51262),f16(x51261,x51262))+~P4(f333(f63(x51261),x51262)) % 191.49/191.41 [5127]~P109(x51271)+E(f333(f65(x51271,f249(x51271)),x51272),f17(x51271,x51272))+~P4(f333(f63(x51271),x51272)) % 191.49/191.41 [5129]~P62(x51291)+~P4(f333(x51292,f197(x51291)))+P4(f333(f59(f884(x51291)),x51292)) % 191.49/191.41 [5211]~P62(x52112)+P4(f333(x52111,f197(x52112)))+~P4(f333(f60(f884(x52112)),x52111)) % 191.49/191.41 [5212]E(x52121,x52122)+~E(f333(f333(f3(a880),x52122),x52121),f2(a880))+~E(f333(f333(f3(a880),x52121),x52122),f2(a880)) % 191.49/191.41 [5226]P10(x52261)+~P42(x52262)+~P4(f333(f333(f335(a1),x52261),x52262)) % 191.49/191.41 [5257]~P120(x52571)+~E(f83(x52571,x52572),f79(x52571))+P4(f333(f333(f251(x52571),f2(x52571)),x52572)) % 191.49/191.41 [5269]~P94(x52691)+E(f333(f105(x52691),f333(f108(a880),x52692)),f333(f108(x52691),x52692))+P4(f333(a200,f333(f108(a1),x52692))) % 191.49/191.41 [5275]~P45(x52751,x52752)+P46(a874)+P4(f333(f63(f889(x52751,x52751)),x52752)) % 191.49/191.41 [5348]~P109(x53481)+E(f333(f65(x53481,f248(x53481)),x53482),f14(x53481,f248(x53481),x53482))+~P4(f333(f63(x53481),x53482)) % 191.49/191.41 [5349]~P109(x53491)+E(f333(f65(x53491,f249(x53491)),x53492),f15(x53491,f249(x53491),x53492))+~P4(f333(f63(x53491),x53492)) % 191.49/191.41 [5362]E(x53621,x53622)+P4(f333(f333(f251(a880),x53622),x53621))+P4(f333(f333(f251(a880),x53621),x53622)) % 191.49/191.41 [5363]E(x53631,x53632)+P4(f333(f333(f251(a1),x53632),x53631))+P4(f333(f333(f251(a1),x53631),x53632)) % 191.49/191.41 [5418]~P94(x54181)+E(f333(f105(x54181),f333(f108(a880),x54182)),f2(x54181))+~P4(f333(a200,f333(f108(a1),x54182))) % 191.49/191.41 [5421]~E(x54212,f333(a109,x54211))+E(x54211,f333(f105(a1),x54212))+~P4(f333(f333(f250(a1),f2(a1)),x54211)) % 191.49/191.41 [5422]~E(f333(a109,x54221),x54222)+E(x54221,f333(f105(a1),x54222))+~P4(f333(f333(f250(a1),f2(a1)),x54221)) % 191.49/191.41 [5423]~E(x54231,f333(a109,x54232))+E(f333(f105(a1),x54231),x54232)+~P4(f333(f333(f250(a1),f2(a1)),x54232)) % 191.49/191.41 [5433]E(x54331,f333(a109,x54332))+~E(x54332,f333(f105(a1),x54331))+~P4(f333(f333(f250(a1),f2(a1)),x54332)) % 191.49/191.41 [5434]E(f333(a109,x54341),x54342)+~E(x54341,f333(f105(a1),x54342))+~P4(f333(f333(f250(a1),f2(a1)),x54341)) % 191.49/191.41 [5473]~P87(x54732)+E(x54731,f2(x54732))+P4(f333(f333(f251(x54732),f2(x54732)),f333(f76(x54732),x54731))) % 191.49/191.41 [5538]~P120(x55381)+E(f83(x55381,x55382),f79(x55381))+~P4(f333(f333(f251(x55381),f2(x55381)),x55382)) % 191.49/191.41 [5542]~P94(x55421)+E(f333(f105(x55421),f333(f108(a880),x55422)),f2(x55421))+P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x55422))) % 191.49/191.41 [5549]~P87(x55491)+E(f333(f76(x55491),x55492),x55492)+~P4(f333(f333(f251(x55491),f2(x55491)),x55492)) % 191.49/191.41 [5550]~P87(x55501)+E(f333(f76(x55501),x55502),x55502)+~P4(f333(f333(f250(x55501),f2(x55501)),x55502)) % 191.49/191.41 [5557]E(x55571,f2(a880))+~E(f140(a880,f333(f303(a880,x55572),x55571)),f118(a880))+P4(f333(f333(f250(a880),x55571),x55572)) % 191.49/191.41 [5567]~P69(x55671)+E(f333(f333(f8(x55671,x55671),f7(x55671)),f333(f173(x55671),x55672)),f333(f167(x55671),x55672))+~P4(f333(f138(x55671),x55672)) % 191.49/191.41 [5570]~P140(x55701)+E(f333(f105(x55701),f333(a109,x55702)),f333(f107(x55701),x55702))+~P4(f333(f333(f250(a1),f2(a1)),x55702)) % 191.49/191.41 [5597]E(x55971,x55972)+P4(f333(f333(f251(a880),x55971),x55972))+~P4(f333(f333(f250(a880),x55971),x55972)) % 191.49/191.41 [5598]E(x55981,x55982)+P4(f333(f333(f251(a1),x55981),x55982))+~P4(f333(f333(f250(a1),x55981),x55982)) % 191.49/191.41 [5601]E(x56011,f79(a1))+~E(f333(f333(f82(a1),x56012),x56011),f79(a1))+~P4(f333(f333(f251(a1),f2(a1)),x56012)) % 191.49/191.41 [5602]E(x56021,f79(a1))+~E(f333(f333(f82(a1),x56021),x56022),f79(a1))+~P4(f333(f333(f251(a1),f2(a1)),x56021)) % 191.49/191.41 [5641]~P42(x56412)+P4(f333(f333(f250(a1),f2(a1)),x56411))+~P4(f333(f333(f335(a1),x56411),x56412)) % 191.49/191.41 [5660]~P57(x56601,x56602)+P40(x56601,x56602)+~P4(f333(f63(f889(x56601,x56601)),x56602)) % 191.49/191.41 [5662]~P57(x56621,x56622)+P45(x56621,x56622)+~P4(f333(f63(f889(x56621,x56621)),x56622)) % 191.49/191.41 [5706]E(x57061,f194(f890(x57062,a874)))+~P4(f333(f63(x57062),x57061))+P4(f333(f333(f251(a880),f2(a880)),f333(f39(x57062),x57061))) % 191.49/191.41 [5732]~P4(f333(x57321,x57322))+P4(f333(x57321,f2(a880)))+P4(f333(f333(f251(a880),f373(x57322,x57321)),x57322)) % 191.49/191.41 [5757]E(x57571,f2(a880))+~E(f333(f167(a880),x57572),f2(a880))+~P4(f333(f333(f335(a880),x57571),f333(f173(a880),x57572))) % 191.49/191.41 [5823]E(x58231,x58232)+~P4(f333(f333(f250(a880),x58232),x58231))+~P4(f333(f333(f250(a880),x58231),x58232)) % 191.49/191.41 [5824]E(x58241,x58242)+~P4(f333(f333(f250(a1),x58242),x58241))+~P4(f333(f333(f250(a1),x58241),x58242)) % 191.49/191.41 [5825]E(f333(f39(x58251),x58252),f2(a880))+~P4(f333(f63(x58251),x58252))+P4(f333(f333(f335(x58251),f374(x58252,x58251)),x58252)) % 191.49/191.41 [5834]E(f51(x58341,x58342),f47(x58341,x58342))+P4(f333(f333(f250(a1),f2(a1)),x58341))+~P4(f333(f333(f251(a1),f2(a1)),x58342)) % 191.49/191.41 [5858]~P4(f333(x58581,f397(x58581)))+P4(f333(x58581,f333(a109,x58582)))+~P4(f333(f333(f250(a1),f2(a1)),x58582)) % 191.49/191.41 [5860]P4(f333(f333(f251(a880),x58601),f372(x58602)))+~P4(f333(f63(a880),x58602))+~P4(f333(f333(f335(a880),x58601),x58602)) % 191.49/191.41 [5861]P4(f333(f333(f250(a880),x58611),f363(x58612)))+~P4(f333(f63(a880),x58612))+~P4(f333(f333(f335(a880),x58611),x58612)) % 191.49/191.41 [5890]E(x58901,x58902)+~P4(f333(f333(f251(a880),x58901),f333(a117,x58902)))+P4(f333(f333(f251(a880),x58901),x58902)) % 191.49/191.41 [5924]E(x59241,f333(a117,x59242))+~P4(f333(f333(f250(a880),x59241),f333(a117,x59242)))+P4(f333(f333(f250(a880),x59241),x59242)) % 191.49/191.41 [5936]P4(f333(x59361,f404(x59361)))+~P4(f333(x59361,f333(a109,x59362)))+~P4(f333(f333(f250(a1),f2(a1)),x59362)) % 191.49/191.41 [5950]~P4(f333(x59501,x59502))+~P4(f333(f333(f250(a1),f2(a1)),x59502))+P4(f333(x59501,f333(f105(a1),f387(x59501)))) % 191.49/191.41 [5965]~P87(x59652)+~E(x59651,f2(x59652))+~P4(f333(f333(f251(x59652),f2(x59652)),f333(f76(x59652),x59651))) % 191.49/191.41 [5992]~P57(x59921,x59922)+P40(x59921,f333(f288(x59921,x59921),x59922))+~P4(f333(f63(f889(x59921,x59921)),x59922)) % 191.49/191.41 [6000]~P94(x60001)+E(f333(f105(x60001),f333(f108(a880),x60002)),f333(f108(x60001),x60002))+~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x60002))) % 191.49/191.41 [6004]E(f333(a117,x60041),x60042)+~P4(f333(f333(f251(a880),x60041),x60042))+P4(f333(f333(f251(a880),f333(a117,x60041)),x60042)) % 191.49/191.41 [6016]E(f333(f333(f40(a1),x60161),x60162),f2(a1))+~P4(f333(f333(f250(a1),x60161),f2(a1)))+~P4(f333(f333(f251(a1),x60162),x60161)) % 191.49/191.41 [6029]E(f46(a1,x60291,x60292),x60291)+~P4(f333(f333(f250(a1),x60291),f2(a1)))+~P4(f333(f333(f251(a1),x60292),x60291)) % 191.49/191.41 [6042]E(f48(x60421,x60422),f47(x60421,x60422))+~P4(f333(f333(f250(a1),f2(a1)),x60421))+~P4(f333(f333(f250(a1),f2(a1)),x60422)) % 191.49/191.41 [6050]E(f333(f333(f40(a1),x60501),x60502),f2(a1))+~P4(f333(f333(f250(a1),f2(a1)),x60501))+~P4(f333(f333(f251(a1),x60501),x60502)) % 191.49/191.41 [6062]E(f46(a880,f333(f108(a880),x60621),f333(f108(a880),x60622)),f333(f108(a880),x60621))+P4(f333(a200,f333(f108(a1),x60621)))+~P4(f333(a200,f333(f108(a1),x60622))) % 191.49/191.41 [6064]E(f46(a1,x60641,x60642),x60641)+~P4(f333(f333(f250(a1),f2(a1)),x60641))+~P4(f333(f333(f251(a1),x60641),x60642)) % 191.49/191.41 [6065]E(x60651,x60652)+~P4(f333(f333(f251(a880),x60651),f333(a117,x60652)))+~P4(f333(f333(f250(a880),x60652),x60651)) % 191.49/191.41 [6082]~P120(x60821)+~P4(f333(f333(f251(x60821),x60822),f2(x60821)))+P4(f333(f333(f251(x60821),x60822),f333(f80(x60821),x60822))) % 191.49/191.41 [6083]~P77(x60831)+~P4(f333(f333(f250(x60831),x60832),f2(x60831)))+P4(f333(f333(f250(x60831),x60832),f333(f80(x60831),x60832))) % 191.49/191.41 [6093]~P9(x60931)+E(f333(f333(f66(x60931,x60931,f115(x60931)),f194(x60931)),x60932),f41(x60931,x60932))+~P4(f333(f63(x60931),x60932)) % 191.49/191.41 [6094]~P9(x60941)+E(f333(f333(f66(x60941,x60941,f106(x60941)),f258(x60941)),x60942),f42(x60941,x60942))+~P4(f333(f63(x60941),x60942)) % 191.49/191.41 [6108]~P123(x61081)+~P4(f333(f333(f251(a880),f2(a880)),x61082))+P4(f333(f333(f251(x61081),f2(x61081)),f333(f105(x61081),x61082))) % 191.49/191.41 [6109]~P120(x61091)+~P4(f333(f333(f251(a1),f2(a1)),x61092))+P4(f333(f333(f251(x61091),f2(x61091)),f333(f107(x61091),x61092))) % 191.49/191.41 [6110]~P120(x61101)+~P4(f333(f333(f250(a1),f2(a1)),x61102))+P4(f333(f333(f250(x61101),f2(x61101)),f333(f107(x61101),x61102))) % 191.49/191.41 [6113]~P10(x61132)+~P10(x61131)+E(f333(f312(a880,a1,f105(a1)),f304(a880,f333(a109,x61131),f333(a109,x61132))),f304(a1,x61131,x61132)) % 191.49/191.41 [6119]P4(f333(x61191,x61192))+~P4(f333(f333(f250(a1),f2(a1)),x61192))+~P4(f333(x61191,f333(f105(a1),f388(x61191)))) % 191.49/191.41 [6144]E(f333(f333(f81(a880),f333(f108(a880),x61441)),f333(f108(a880),x61442)),f333(f108(a880),x61441))+P4(f333(f333(f251(a1),x61441),a84))+~P4(f333(f333(f251(a1),x61442),a84)) % 191.49/191.41 [6150]~P120(x61501)+P4(f333(f333(f251(x61501),f2(x61501)),f83(x61501,x61502)))+~P4(f333(f333(f251(x61501),f2(x61501)),x61502)) % 191.49/191.41 [6161]~P81(x61611)+~P4(f333(f333(f251(x61611),x61612),f2(x61611)))+P4(f333(f333(f251(x61611),f2(x61611)),f333(f80(x61611),x61612))) % 191.49/191.41 [6162]~P81(x61621)+~P4(f333(f333(f250(x61621),x61622),f2(x61621)))+P4(f333(f333(f250(x61621),f2(x61621)),f333(f80(x61621),x61622))) % 191.49/191.41 [6165]E(x61651,f258(f890(x61652,a874)))+~E(f333(f39(x61652),x61651),f333(f39(x61652),f258(f890(x61652,a874))))+~P4(f333(f63(x61652),f258(f890(x61652,a874)))) % 191.49/191.41 [6201]~P120(x62011)+P4(f333(f333(f251(x62011),x62012),f2(x62011)))+~P4(f333(f333(f251(x62011),x62012),f333(f80(x62011),x62012))) % 191.49/191.41 [6202]~P77(x62021)+P4(f333(f333(f250(x62021),x62022),f2(x62021)))+~P4(f333(f333(f250(x62021),x62022),f333(f80(x62021),x62022))) % 191.49/191.41 [6210]~P94(x62101)+P4(f333(f333(f335(x62101),f333(f108(x62101),x62102)),f192(x62101)))+~P4(f333(f333(f250(a1),a84),x62102)) % 191.49/191.41 [6241]E(x62411,f2(a880))+~P4(f333(f333(f251(a880),x62411),f333(a117,x62412)))+P4(f333(f333(f251(a880),f843(x62412,x62411)),x62412)) % 191.49/191.41 [6263]~P120(x62631)+~P4(f333(f333(f251(x62631),f2(x62631)),f83(x62631,x62632)))+P4(f333(f333(f251(x62631),f2(x62631)),x62632)) % 191.49/191.41 [6265]~E(f333(f108(a880),x62652),f333(f108(a880),x62651))+P4(f333(f333(f250(a1),f333(f108(a1),x62651)),f2(a1)))+~P4(f333(a200,f333(f108(a1),x62652))) % 191.49/191.41 [6295]E(f333(f262(a1,a1),f51(x62951,x62952)),f333(f333(f40(a1),x62951),x62952))+~P4(f333(f333(f251(a1),x62951),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x62952)) % 191.49/191.41 [6327]E(f333(f271(a1,a1),f51(x63271,x63272)),f46(a1,x63271,x63272))+~P4(f333(f333(f251(a1),x63271),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x63272)) % 191.49/191.41 [6330]~P123(x63302)+~P4(f333(f333(f251(x63302),f2(x63302)),f333(f105(x63302),x63301)))+P4(f333(f333(f251(a880),f2(a880)),x63301)) % 191.49/191.41 [6331]~P120(x63312)+~P4(f333(f333(f251(x63312),f2(x63312)),f333(f107(x63312),x63311)))+P4(f333(f333(f251(a1),f2(a1)),x63311)) % 191.49/191.41 [6332]~P120(x63322)+~P4(f333(f333(f250(x63322),f2(x63322)),f333(f107(x63322),x63321)))+P4(f333(f333(f250(a1),f2(a1)),x63321)) % 191.49/191.41 [6335]E(f333(f262(a1,a1),f48(x63351,x63352)),f333(f333(f40(a1),x63351),x63352))+~P4(f333(f333(f251(a1),f2(a1)),x63351))+~P4(f333(f333(f250(a1),f2(a1)),x63352)) % 191.49/191.41 [6348]E(f333(f271(a1,a1),f48(x63481,x63482)),f46(a1,x63481,x63482))+~P4(f333(f333(f251(a1),f2(a1)),x63481))+~P4(f333(f333(f250(a1),f2(a1)),x63482)) % 191.49/191.41 [6365]~P81(x63651)+P4(f333(f333(f251(x63651),x63652),f2(x63651)))+~P4(f333(f333(f251(x63651),f2(x63651)),f333(f80(x63651),x63652))) % 191.49/191.41 [6366]~P81(x63661)+P4(f333(f333(f250(x63661),x63662),f2(x63661)))+~P4(f333(f333(f250(x63661),f2(x63661)),f333(f80(x63661),x63662))) % 191.49/191.41 [6392]P4(f333(f50(x63921,x63922),f51(x63921,x63922)))+~P4(f333(f333(f251(a1),x63921),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x63922)) % 191.49/191.41 [6417]P4(f333(f50(x64171,x64172),f48(x64171,x64172)))+~P4(f333(f333(f251(a1),f2(a1)),x64172))+~P4(f333(f333(f250(a1),f2(a1)),x64171)) % 191.49/191.41 [6460]~P81(x64601)+P4(f333(f333(f251(x64601),f333(f80(x64601),x64602)),f2(x64601)))+~P4(f333(f333(f251(x64601),f2(x64601)),x64602)) % 191.49/191.41 [6461]~P81(x64611)+P4(f333(f333(f250(x64611),f333(f80(x64611),x64612)),f2(x64611)))+~P4(f333(f333(f250(x64611),f2(x64611)),x64612)) % 191.49/191.41 [6477]E(f333(f333(f3(a880),f333(a109,x64771)),f333(a109,x64772)),f333(a109,f202(x64771,x64772)))+~P4(f333(f333(f250(a1),f2(a1)),x64772))+~P4(f333(f333(f250(a1),f2(a1)),x64771)) % 191.49/191.41 [6494]P4(f333(f333(f250(a1),f2(a1)),f202(x64941,x64942)))+~P4(f333(f333(f250(a1),f2(a1)),x64942))+~P4(f333(f333(f250(a1),f2(a1)),x64941)) % 191.49/191.41 [6526]~P4(f333(x65261,x65262))+P4(f333(x65261,f2(a880)))+P4(f333(x65261,f333(f333(f81(a880),f373(x65262,x65261)),f79(a880)))) % 191.49/191.41 [6610]E(f333(f108(a880),x66101),f333(f108(a880),x66102))+~P4(f333(f333(f250(a1),f333(f108(a1),x66102)),f2(a1)))+~P4(f333(a200,f333(f108(a1),x66101))) % 191.49/191.41 [6620]~E(x66201,f2(a880))+~E(f615(x66202,x66201),f2(a880))+E(f333(f143(a880,a880,f81(a880),x66201),x66202),f2(a880)) % 191.49/191.41 [6646]~P4(f333(f63(x66461),f681(x66462,x66461)))+~P4(f333(f63(f890(x66461,a874)),x66462))+P4(f333(f63(x66461),f41(f890(x66461,a874),x66462))) % 191.49/191.41 [6652]E(x66521,x66522)+P4(f333(f333(f251(a1),x66521),x66522))+~P4(f333(f333(f251(a1),x66521),f333(f333(f81(a1),x66522),f79(a1)))) % 191.49/191.41 [6654]P4(f333(f333(f251(a880),f333(a109,x66541)),f333(a109,x66542)))+~P4(f333(f333(f251(a1),f2(a1)),x66542))+~P4(f333(f333(f251(a1),x66541),x66542)) % 191.49/191.41 [6655]P4(f333(f333(f251(a880),f333(a109,x66551)),f333(a109,x66552)))+~P4(f333(f333(f250(a1),f2(a1)),x66551))+~P4(f333(f333(f251(a1),x66551),x66552)) % 191.49/191.41 [6656]P4(f333(f333(f250(a880),f333(a109,x66561)),f333(a109,x66562)))+~P4(f333(f333(f251(a1),f2(a1)),x66561))+~P4(f333(f333(f250(a1),x66561),x66562)) % 191.49/191.41 [6657]P4(f333(f333(f250(a880),f333(a109,x66571)),f333(a109,x66572)))+~P4(f333(f333(f250(a1),f2(a1)),x66572))+~P4(f333(f333(f250(a1),x66571),x66572)) % 191.49/191.41 [6668]E(f46(a880,f333(a109,x66681),f333(a109,x66682)),f333(a109,f46(a1,x66681,x66682)))+~P4(f333(f333(f250(a1),f2(a1)),x66682))+~P4(f333(f333(f250(a1),f2(a1)),x66681)) % 191.49/191.41 [6690]~P81(x66901)+~P4(f333(f333(f251(x66901),f333(f80(x66901),x66902)),f2(x66901)))+P4(f333(f333(f251(x66901),f2(x66901)),x66902)) % 191.49/191.41 [6691]~P81(x66911)+~P4(f333(f333(f250(x66911),f333(f80(x66911),x66912)),f2(x66911)))+P4(f333(f333(f250(x66911),f2(x66911)),x66912)) % 191.49/191.41 [6706]~P4(f333(f333(f251(a1),a84),x67062))+~P4(f333(f333(f251(a1),x67061),x67062))+P4(f333(f333(f251(a880),f333(f108(a880),x67061)),f333(f108(a880),x67062))) % 191.49/191.41 [6791]~P4(f333(f333(f250(a1),f2(a1)),x67911))+P4(f333(f333(f251(a880),f333(a109,x67911)),x67912))+~P4(f333(f333(f251(a1),x67911),f333(f105(a1),x67912))) % 191.49/191.41 [6807]E(x68071,f2(a1))+E(f46(a1,x68072,x68071),f2(a1))+E(f333(f333(f3(a1),f333(f80(a1),f333(f333(f40(a1),x68072),x68071))),f79(a1)),f333(f333(f40(a1),x68072),f333(f80(a1),x68071))) % 191.49/191.41 [6820]~P4(f333(f333(f250(a1),f2(a1)),x68201))+~P4(f333(f333(f251(a880),f333(a109,x68201)),x68202))+P4(f333(f333(f251(a1),x68201),f333(f105(a1),x68202))) % 191.49/191.41 [6857]~P4(f333(f333(f250(a880),f333(a109,x68571)),f333(a109,x68572)))+~P4(f333(f333(f251(a1),f2(a1)),x68571))+P4(f333(f333(f250(a1),x68571),x68572)) % 191.49/191.41 [6858]~P4(f333(f333(f250(a880),f333(a109,x68581)),f333(a109,x68582)))+~P4(f333(f333(f250(a1),f2(a1)),x68582))+P4(f333(f333(f250(a1),x68581),x68582)) % 191.49/191.41 [6884]P4(f333(f333(f250(a1),x68841),x68842))+~P4(f333(f333(f250(a880),f333(f108(a880),x68841)),f333(f108(a880),x68842)))+P4(f333(f333(f250(a1),x68841),a84)) % 191.49/191.41 [6909]P4(f333(f333(f250(a1),f2(a1)),f46(a1,x69091,x69092)))+~P4(f333(f333(f250(a1),f2(a1)),x69092))+~P4(f333(f333(f250(a1),f2(a1)),x69091)) % 191.49/191.41 [7010]P4(f333(f333(f251(a1),a84),x70101))+~P4(f333(f333(f251(a1),x70102),x70101))+~P4(f333(f333(f251(a880),f333(f108(a880),x70102)),f333(f108(a880),x70101))) % 191.49/191.41 [7061]E(f333(f333(f263(a1,a1),f333(f333(f40(a1),x70611),x70612)),f46(a1,x70611,x70612)),f51(x70611,x70612))+~P4(f333(f333(f251(a1),x70611),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x70612)) % 191.49/191.41 [7081]E(f333(f333(f263(a1,a1),f333(f333(f40(a1),x70811),x70812)),f46(a1,x70811,x70812)),f48(x70811,x70812))+~P4(f333(f333(f250(a1),f2(a1)),x70812))+~P4(f333(f333(f250(a1),f2(a1)),x70811)) % 191.49/191.41 [7132]~P97(x71322)+E(x71321,f118(x71322))+E(f333(f143(x71322,x71322,f82(x71322),f333(f142(x71322),x71321)),f333(f172(x71322),x71321)),f333(f65(x71322,f82(x71322)),f333(f173(x71322),x71321))) % 191.49/191.41 [7244]~E(x72441,f2(a880))+E(f333(f143(a880,a880,f81(a880),x72441),x72442),f2(a880))+P4(f333(f333(f335(a880),f615(x72442,x72441)),f333(f173(a880),x72442))) % 191.49/191.41 [7288]~P4(f333(f333(f251(a1),x72882),f2(a1)))+P4(f333(f333(f251(a1),f333(f333(f40(a1),x72881),x72882)),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x72881)) % 191.49/191.41 [7290]~P4(f333(f333(f251(a1),x72901),f2(a1)))+P4(f333(f333(f251(a1),f333(f333(f40(a1),x72901),x72902)),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x72902)) % 191.49/191.41 [7291]~P4(f333(f333(f251(a1),x72912),f2(a1)))+P4(f333(f333(f250(a1),f333(f333(f40(a1),x72911),x72912)),f2(a1)))+~P4(f333(f333(f250(a1),f2(a1)),x72911)) % 191.49/191.41 [7292]~P4(f333(f333(f250(a1),x72921),f2(a1)))+P4(f333(f333(f250(a1),f333(f333(f40(a1),x72921),x72922)),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x72922)) % 191.49/191.41 [7299]P4(f333(f333(f335(f890(x72991,a874)),f681(x72992,x72991)),x72992))+~P4(f333(f63(f890(x72991,a874)),x72992))+P4(f333(f63(x72991),f41(f890(x72991,a874),x72992))) % 191.49/191.41 [7388]P28(x73881,x73881,x73882,f258(f890(x73881,a874)))+~E(f333(f312(x73881,x73881,x73882),f258(f890(x73881,a874))),f258(f890(x73881,a874)))+~P4(f333(f63(x73881),f258(f890(x73881,a874)))) % 191.49/191.41 [7513]~P28(x75131,x75131,x75132,f258(f890(x75131,a874)))+E(f333(f312(x75131,x75131,x75132),f258(f890(x75131,a874))),f258(f890(x75131,a874)))+~P4(f333(f63(x75131),f258(f890(x75131,a874)))) % 191.49/191.41 [7646]E(f333(f333(f40(a1),x76461),x76462),f333(f108(a1),a102))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),x76461),x76462)),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x76461)) % 191.49/191.41 [7704]~P4(f333(f333(f251(a1),x77042),f2(a1)))+~P4(f333(f333(f251(a1),f333(f333(f40(a1),x77041),x77042)),f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x77041)) % 191.49/191.41 [7709]E(f333(f333(f81(a1),x77091),x77092),f46(a1,x77091,x77092))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),x77091),x77092)),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x77091)) % 191.49/191.41 [7712]P4(f333(f333(f251(a1),x77121),f2(a1)))+~P4(f333(f333(f251(a1),f333(f333(f40(a1),x77121),x77122)),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x77122)) % 191.49/191.41 [8102]~P62(x81021)+~P4(f333(f60(f884(x81021)),x81022))+P4(f333(f60(x81021),f333(f333(f10(f884(x81021),a874,x81021),x81022),f242(x81021)))) % 191.49/191.41 [8408]~P109(x84081)+P17(x84081,x84082)+~P4(f333(f333(f250(x84081),f333(f333(f166(x84081),x84082),f647(x84082,x84081))),f333(f333(f166(x84081),x84082),f648(x84082,x84081)))) % 191.49/191.41 [8409]~P109(x84091)+P17(x84091,x84092)+~P4(f333(f333(f250(x84091),f333(f333(f166(x84091),x84092),f654(x84092,x84091))),f333(f333(f166(x84091),x84092),f664(x84092,x84091)))) % 191.49/191.41 [8566]~P62(x85661)+P4(f333(f59(f884(x85661)),x85662))+~P4(f333(f59(x85661),f333(f333(f10(f884(x85661),a874,x85661),x85662),f242(x85661)))) % 191.49/191.41 [9746]~P62(x97461)+~P62(x97462)+E(f333(f333(f155(f881(x97461),f890(x97462,x97461)),f333(f333(f10(f890(x97462,f884(x97461)),f890(x97462,x97461),f881(x97461)),f74(f884(x97461),x97461,x97462,f246(x97461))),f333(f333(f10(f881(f889(x97462,x97461)),f890(x97462,f884(x97461)),f881(x97461)),f178(x97462,x97461)),f333(f182(x97462,x97461),f57(x97462))))),f56(x97461,f333(f195(f881(x97462)),f57(x97462)),f57(x97461))),f57(f890(x97462,x97461))) % 191.49/191.41 [5699]E(x56991,f2(a1))+~E(f46(a1,x56992,x56991),f2(a1))+E(f333(f333(f40(a1),x56992),f333(f80(a1),x56991)),f333(f80(a1),f333(f333(f40(a1),x56992),x56991))) % 191.49/191.41 [5717]~P42(x57172)+~P42(x57171)+P42(f333(f333(f115(f890(a1,a874)),x57171),x57172)) % 191.49/191.41 [5718]~P42(x57182)+~P42(x57181)+P42(f333(f333(f106(f890(a1,a874)),x57181),x57182)) % 191.49/191.41 [5735]~P63(x57351)+~P94(x57351)+E(f333(f80(x57351),f333(f333(f291(x57351),f79(x57351)),x57352)),f333(f333(f291(x57351),f333(f108(x57351),a102)),x57352)) % 191.49/191.41 [5850]E(x58501,f2(a1))+~E(f46(a1,x58502,x58501),f2(a1))+E(f333(f333(f40(a1),f333(f80(a1),x58502)),x58501),f333(f80(a1),f333(f333(f40(a1),x58502),x58501))) % 191.49/191.41 [5986]~P109(x59861)+P17(x59861,x59862)+P4(f333(f333(f251(a880),f648(x59862,x59861)),f333(f195(f881(x59861)),x59862))) % 191.49/191.41 [5987]~P109(x59871)+P17(x59871,x59872)+P4(f333(f333(f251(a880),f664(x59872,x59871)),f333(f195(f881(x59871)),x59872))) % 191.49/191.41 [6140]~P94(x61401)+~E(f333(f108(x61401),x61402),f2(x61401))+P33(x61401,f333(f108(x61401),f333(f333(f81(a1),x61402),f333(f80(a1),a84)))) % 191.49/191.41 [6141]~P94(x61411)+~E(f333(f108(x61411),x61412),f2(x61411))+P33(x61411,f333(f108(x61411),f333(f333(f81(a1),a84),f333(f80(a1),x61412)))) % 191.49/191.41 [6143]E(f333(a52,f48(f333(f80(a1),x61431),f333(f80(a1),x61432))),f47(x61431,x61432))+P4(f333(f333(f251(a1),f2(a1)),x61432))+P4(f333(f333(f250(a1),f2(a1)),x61431)) % 191.49/191.41 [6271]~E(x62712,f2(a880))+~E(x62711,f2(a880))+P4(f333(f333(f250(a1),f333(f105(a1),x62711)),f333(f80(a1),f333(f105(a1),x62712)))) % 191.49/191.41 [6299]E(f333(f333(f81(a880),f333(f108(a880),x62991)),f333(f108(a880),x62992)),f333(f108(a880),f333(f333(f81(a1),x62991),x62992)))+P4(f333(f333(f251(a1),x62991),a84))+P4(f333(f333(f251(a1),x62992),a84)) % 191.49/191.41 [6426]~P77(x64261)+~P4(f333(f333(f251(x64261),f2(x64261)),x64262))+P4(f333(f333(f251(x64261),f333(f80(x64261),x64262)),x64262)) % 191.49/191.41 [6427]~P77(x64271)+~P4(f333(f333(f250(x64271),f2(x64271)),x64272))+P4(f333(f333(f250(x64271),f333(f80(x64271),x64272)),x64272)) % 191.49/191.41 [6596]E(f333(f333(f3(a880),f333(a109,x65961)),f333(a109,x65962)),f333(a109,f333(f333(f3(a1),x65961),x65962)))+~P4(f333(f333(f250(a1),f2(a1)),x65962))+~P4(f333(f333(f250(a1),x65962),x65961)) % 191.49/191.41 [6629]E(f333(a109,f46(a1,f333(f108(a1),x66291),f333(f108(a1),x66292))),f46(a880,f333(f108(a880),x66291),f333(f108(a880),x66292)))+P4(f333(a200,f333(f108(a1),x66291)))+P4(f333(a200,f333(f108(a1),x66292))) % 191.49/191.41 [6647]~P77(x66471)+P4(f333(f333(f251(x66471),f2(x66471)),x66472))+~P4(f333(f333(f251(x66471),f333(f80(x66471),x66472)),x66472)) % 191.49/191.41 [6648]~P77(x66481)+P4(f333(f333(f250(x66481),f2(x66481)),x66482))+~P4(f333(f333(f250(x66481),f333(f80(x66481),x66482)),x66482)) % 191.49/191.41 [6659]~P77(x66591)+~P4(f333(f333(f251(x66591),f2(x66591)),x66592))+P4(f333(f333(f251(x66591),f2(x66591)),f333(f333(f81(x66591),x66592),x66592))) % 191.49/191.41 [6662]~P77(x66621)+~P4(f333(f333(f250(x66621),f2(x66621)),x66622))+P4(f333(f333(f250(x66621),f2(x66621)),f333(f333(f81(x66621),x66622),x66622))) % 191.49/191.41 [6673]E(f333(f333(f81(a880),f333(a109,x66731)),f333(a109,x66732)),f333(a109,f333(f333(f81(a1),x66731),x66732)))+~P4(f333(f333(f250(a1),f2(a1)),x66732))+~P4(f333(f333(f250(a1),f2(a1)),x66731)) % 191.49/191.41 [6685]E(x66851,f2(a880))+P4(f333(f333(f251(a880),f2(a880)),x66852))+~P4(f333(f333(f251(a880),f2(a880)),f333(f333(f264(a880),x66852),x66851))) % 191.49/191.41 [6715]~P94(x67151)+E(f333(f108(x67151),x67152),f2(x67151))+~P33(x67151,f333(f108(x67151),f333(f333(f81(a1),a84),f333(f80(a1),x67152)))) % 191.49/191.41 [6716]~P94(x67161)+E(f333(f108(x67161),x67162),f2(x67161))+~P33(x67161,f333(f108(x67161),f333(f333(f81(a1),x67162),f333(f80(a1),a84)))) % 191.49/191.41 [6769]~P4(f333(f63(x67691),x67692))+~P4(f333(f63(x67691),f258(f890(x67691,a874))))+P4(f333(f63(x67691),f333(f80(f890(x67691,a874)),x67692))) % 191.49/191.41 [6792]~P4(f333(f333(f251(a1),f2(a1)),x67922))+~P4(f333(f333(f250(a1),x67922),x67921))+P4(f333(f333(f251(a1),f2(a1)),f333(f333(f40(a1),x67921),x67922))) % 191.49/191.41 [6793]~P4(f333(f333(f251(a1),x67932),f2(a1)))+~P4(f333(f333(f250(a1),x67931),f2(a1)))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f40(a1),x67931),x67932))) % 191.49/191.41 [6828]~P4(f333(f333(f251(a880),f2(a880)),x68282))+~P4(f333(f333(f251(a880),f2(a880)),x68281))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f82(a880),x68281),x68282))) % 191.49/191.41 [6829]~P4(f333(f333(f250(a1),f2(a1)),x68292))+~P4(f333(f333(f250(a1),f2(a1)),x68291))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f81(a1),x68291),x68292))) % 191.49/191.41 [6830]~P4(f333(f333(f250(a1),f2(a1)),x68302))+~P4(f333(f333(f250(a1),f2(a1)),x68301))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f82(a1),x68301),x68302))) % 191.49/191.41 [6831]~P4(f333(f333(f251(a1),f2(a1)),x68312))+~P4(f333(f333(f250(a1),f2(a1)),x68311))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f40(a1),x68311),x68312))) % 191.49/191.41 [6832]~P4(f333(f333(f250(a1),f2(a1)),x68322))+~P4(f333(f333(f250(a1),f2(a1)),x68321))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f40(a1),x68321),x68322))) % 191.49/191.41 [6894]E(x68941,f2(a1))+E(f46(a1,x68942,x68941),f2(a1))+E(f333(f333(f3(a1),f333(f80(a1),f333(f333(f40(a1),x68942),x68941))),f79(a1)),f333(f333(f40(a1),f333(f80(a1),x68942)),x68941)) % 191.49/191.41 [6951]P4(f333(f333(f251(a880),f2(a880)),x69511))+P4(f333(f333(f251(a880),f2(a880)),x69512))+~P4(f333(f333(f251(a880),f2(a880)),f333(f333(f81(a880),x69512),x69511))) % 191.49/191.41 [6955]~P77(x69551)+P4(f333(f333(f251(x69551),f2(x69551)),x69552))+~P4(f333(f333(f251(x69551),f2(x69551)),f333(f333(f81(x69551),x69552),x69552))) % 191.49/191.41 [6956]~P77(x69561)+P4(f333(f333(f250(x69561),f2(x69561)),x69562))+~P4(f333(f333(f250(x69561),f2(x69561)),f333(f333(f81(x69561),x69562),x69562))) % 191.49/191.41 [7011]~P4(f333(f63(x70111),x70112))+P4(f333(f63(x70111),f258(f890(x70111,a874))))+~P4(f333(f63(x70111),f333(f80(f890(x70111,a874)),x70112))) % 191.49/191.41 [7073]P4(f333(f333(f250(a1),x70731),f2(a1)))+~P4(f333(f333(f251(a1),x70732),f2(a1)))+~P4(f333(f333(f250(a1),f2(a1)),f333(f333(f40(a1),x70731),x70732))) % 191.49/191.41 [7079]~P4(f333(f333(f251(a1),f2(a1)),x70791))+P4(f333(f333(f250(a1),x70791),x70792))+~P4(f333(f333(f251(a1),f2(a1)),f333(f333(f40(a1),x70792),x70791))) % 191.49/191.41 [7080]~P4(f333(f333(f250(a1),f2(a1)),x70802))+P4(f333(f333(f250(a1),x70801),x70802))+~P4(f333(f333(f251(a1),f2(a1)),f333(f333(f40(a1),x70802),x70801))) % 191.49/191.41 [7109]P4(f333(f333(f251(a1),f2(a1)),x71091))+~P4(f333(f333(f250(a1),f2(a1)),x71092))+~P4(f333(f333(f251(a1),f2(a1)),f333(f333(f40(a1),x71092),x71091))) % 191.49/191.41 [7110]P4(f333(f333(f250(a1),f2(a1)),x71101))+~P4(f333(f333(f251(a1),f2(a1)),x71102))+~P4(f333(f333(f250(a1),f2(a1)),f333(f333(f40(a1),x71101),x71102))) % 191.49/191.41 [7543]~P4(f333(f63(x75432),f258(f890(x75432,a874))))+~P4(f333(f63(x75431),f258(f890(x75431,a874))))+P4(f333(f63(f888(x75431,x75432)),f258(f890(f888(x75431,x75432),a874)))) % 191.49/191.41 [7544]~P4(f333(f63(x75442),f258(f890(x75442,a874))))+~P4(f333(f63(x75441),f258(f890(x75441,a874))))+P4(f333(f63(f889(x75441,x75442)),f258(f890(f889(x75441,x75442),a874)))) % 191.49/191.41 [7610]~P4(f333(f333(f251(a880),f333(a117,f2(a880))),x76101))+~P4(f333(f333(f251(a880),f333(a117,f2(a880))),x76102))+P4(f333(f333(f251(a880),x76101),f333(f333(f82(a880),x76102),x76101))) % 191.49/191.41 [7611]~P4(f333(f333(f251(a880),f333(a117,f2(a880))),x76111))+~P4(f333(f333(f251(a880),f333(a117,f2(a880))),x76112))+P4(f333(f333(f251(a880),x76111),f333(f333(f82(a880),x76111),x76112))) % 191.49/191.41 [7645]E(f333(f39(x76451),f258(f890(x76451,a874))),f333(a117,f2(a880)))+P4(f333(f63(x76452),f258(f890(x76452,a874))))+~P4(f333(f63(f890(x76452,x76451)),f258(f890(f890(x76452,x76451),a874)))) % 191.49/191.41 [7774]~P4(f333(f333(f251(a880),f333(a117,f2(a880))),x77742))+~P4(f333(f333(f251(a880),f333(a117,f2(a880))),x77741))+P4(f333(f333(f251(a880),f333(a117,f2(a880))),f333(f333(f82(a880),x77741),x77742))) % 191.49/191.41 [7775]~P4(f333(f333(f250(a880),f333(a117,f2(a880))),x77751))+~P4(f333(f333(f250(a880),f333(a117,f2(a880))),x77752))+P4(f333(f333(f250(a880),f333(a117,f2(a880))),f333(f333(f82(a880),x77751),x77752))) % 191.49/191.41 [8461]E(x84611,f118(x84612))+~P4(f333(f138(x84612),x84611))+E(f177(x84612,f333(f333(f10(a874,a874,x84612),a328),f333(f333(f9(x84612,x84612,a874),a330),f145(x84612,x84611))),x84611),f119(x84612,x84611)) % 191.49/191.41 [8558]~P42(x85582)+~P42(x85581)+E(f333(f312(a880,a1,f105(a1)),f333(f333(f115(f890(a880,a874)),f333(f312(a1,a880,a109),x85581)),f333(f312(a1,a880,a109),x85582))),f333(f333(f115(f890(a1,a874)),x85581),x85582)) % 191.49/191.41 [8559]~P42(x85592)+~P42(x85591)+E(f333(f312(a880,a1,f105(a1)),f333(f333(f106(f890(a880,a874)),f333(f312(a1,a880,a109),x85591)),f333(f312(a1,a880,a109),x85592))),f333(f333(f106(f890(a1,a874)),x85591),x85592)) % 191.49/191.41 [9269]~P94(x92691)+~E(f333(f108(x92691),x92692),f79(x92691))+P33(x92691,f333(f108(x92691),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),f333(f80(a1),x92692)))) % 191.49/191.41 [9487]~P94(x94871)+E(f333(f108(x94871),x94872),f79(x94871))+~P33(x94871,f333(f108(x94871),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),f333(f80(a1),x94872)))) % 191.49/191.41 [10219]E(x102191,f2(a1))+E(x102192,f2(a1))+E(f333(f273(a1,a1,a1,a1,f35(a1),f333(f82(a1),f83(a1,x102192))),f333(f333(f333(f101(f889(a1,a1)),f333(f333(a330,f83(a1,x102191)),f83(a1,x102192))),f54(x102191,x102192)),f333(f333(f272(a1,a1,f889(a1,a1)),f333(f333(f20(a1,f890(a1,f889(a1,a1)),f890(a1,f889(a1,a1))),f333(f333(f10(f890(a1,f890(f889(a1,a1),f889(a1,a1))),f890(f890(a1,f889(a1,a1)),f890(a1,f889(a1,a1))),a1),f20(a1,f889(a1,a1),f889(a1,a1))),f333(f333(f10(f889(a1,a1),f890(a1,f890(f889(a1,a1),f889(a1,a1))),a1),f333(f9(a1,f889(a1,a1),f890(f889(a1,a1),f889(a1,a1))),f333(f333(f10(a874,f890(f889(a1,a1),f890(f889(a1,a1),f889(a1,a1))),a1),f101(f889(a1,a1))),f333(f333(f9(a1,a1,a874),a330),f2(a1))))),f333(f333(f9(a1,a1,f889(a1,a1)),f333(f333(f10(a1,f890(a1,f889(a1,a1)),a1),f263(a1,a1)),f80(a1))),f2(a1))))),f333(f333(f9(a1,f890(a1,a1),f890(a1,f889(a1,a1))),f333(f333(f10(f890(a1,f889(a1,a1)),f890(f890(a1,a1),f890(a1,f889(a1,a1))),a1),f10(a1,f889(a1,a1),a1)),f333(f333(f10(a1,f890(a1,f889(a1,a1)),a1),f263(a1,a1)),f333(f333(f9(a1,a1,a1),f333(f333(f10(a1,f890(a1,a1),a1),f3(a1)),f80(a1))),f79(a1))))),f333(f3(a1),f333(f76(a1),x102192))))),f54(x102191,x102192)))),f47(x102191,x102192)) % 191.49/191.41 [10220]E(x102201,f2(a1))+E(x102202,f2(a1))+E(f333(f273(a1,a1,a1,a1,f35(a1),f333(f82(a1),f83(a1,x102202))),f333(f333(f333(f101(f889(a1,a1)),f333(f333(a332,f333(f333(a331,f333(f333(f251(a1),f2(a1)),x102202)),f333(f333(f250(a1),f2(a1)),x102201))),f333(f333(a331,f333(f333(f251(a1),x102202),f2(a1))),f333(f333(f251(a1),x102201),f2(a1))))),f54(x102201,x102202)),f333(f333(f272(a1,a1,f889(a1,a1)),f333(f333(f20(a1,f890(a1,f889(a1,a1)),f890(a1,f889(a1,a1))),f333(f333(f10(f890(a1,f890(f889(a1,a1),f889(a1,a1))),f890(f890(a1,f889(a1,a1)),f890(a1,f889(a1,a1))),a1),f20(a1,f889(a1,a1),f889(a1,a1))),f333(f333(f10(f889(a1,a1),f890(a1,f890(f889(a1,a1),f889(a1,a1))),a1),f333(f9(a1,f889(a1,a1),f890(f889(a1,a1),f889(a1,a1))),f333(f333(f10(a874,f890(f889(a1,a1),f890(f889(a1,a1),f889(a1,a1))),a1),f101(f889(a1,a1))),f333(f333(f9(a1,a1,a874),a330),f2(a1))))),f333(f333(f9(a1,a1,f889(a1,a1)),f333(f333(f10(a1,f890(a1,f889(a1,a1)),a1),f263(a1,a1)),f80(a1))),f2(a1))))),f333(f333(f9(a1,f890(a1,a1),f890(a1,f889(a1,a1))),f333(f333(f10(f890(a1,f889(a1,a1)),f890(f890(a1,a1),f890(a1,f889(a1,a1))),a1),f10(a1,f889(a1,a1),a1)),f333(f333(f10(a1,f890(a1,f889(a1,a1)),a1),f263(a1,a1)),f333(f333(f9(a1,a1,a1),f333(f333(f10(a1,f890(a1,a1),a1),f3(a1)),f80(a1))),f79(a1))))),f333(f3(a1),f333(f76(a1),x102202))))),f54(x102201,x102202)))),f47(x102201,x102202)) % 191.49/191.41 [10221]~P32(a5000)+P27(a875,x102211,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),x102212),f201(x102212))),f194(f890(f879(a875),a874))))+~P27(a875,x102211,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),f333(f333(f10(f890(a875,f890(a875,a874)),f890(a875,a874),a875),f333(f10(f890(a875,a874),a874,a875),f88(a875))),f333(f333(f10(f890(a875,a874),f890(a875,f890(a875,a874)),a875),f333(f9(a875,f890(a875,a874),f890(a875,a874)),f333(f333(f10(f890(a875,f890(a874,a874)),f890(f890(a875,a874),f890(a875,a874)),a875),f20(a875,a874,a874)),f333(f333(f10(f890(a875,a874),f890(a875,f890(a874,a874)),a875),f333(f10(a874,f890(a874,a874),a875),a336)),f201(x102212))))),a330))),x102212),a330)),f194(f890(f879(a875),a874)))) % 191.49/191.41 [5725]~P120(x57251)+~P94(x57251)+E(f333(f76(x57251),f333(f333(f264(x57251),f333(f108(x57251),a102)),x57252)),f79(x57251)) % 191.49/191.41 [6211]~P140(x62111)+~P4(f333(f333(f251(a1),x62112),f2(a1)))+E(f333(f80(x62111),f333(f105(x62111),f333(a109,f333(f80(a1),x62112)))),f333(f107(x62111),x62112)) % 191.49/191.41 [6410]P4(f333(f333(f250(a104),x64101),f79(a104)))+E(f333(f333(f81(a104),f79(a104)),f281(x64101,f333(f333(f40(a104),x64102),x64101))),f281(x64101,x64102))+P4(f333(f333(f251(a104),x64102),x64101)) % 191.49/191.41 [6996]~P93(x69961)+~P4(f333(f333(f335(x69961),x69962),f114(x69961)))+~E(f333(f333(f81(x69961),f333(f333(f81(x69961),f79(x69961)),x69962)),x69962),f2(x69961)) % 191.49/191.41 [7111]~P4(f333(f333(f251(a1),x71111),f2(a1)))+~P4(f333(f333(f250(a1),x71112),f2(a1)))+E(f333(f262(a1,a1),f333(a52,f48(f333(f80(a1),x71111),f333(f80(a1),x71112)))),f333(f333(f40(a1),x71111),x71112)) % 191.49/191.41 [7128]~P4(f333(f333(f251(a1),x71281),f2(a1)))+~P4(f333(f333(f250(a1),x71282),f2(a1)))+E(f333(f271(a1,a1),f333(a52,f48(f333(f80(a1),x71281),f333(f80(a1),x71282)))),f46(a1,x71281,x71282)) % 191.49/191.41 [7134]~P4(f333(f333(f251(a1),x71342),f2(a1)))+E(f333(f262(a1,a1),f333(a52,f51(f333(f80(a1),x71341),f333(f80(a1),x71342)))),f333(f333(f40(a1),x71341),x71342))+~P4(f333(f333(f251(a1),f2(a1)),x71341)) % 191.49/191.41 [7152]~P4(f333(f333(f251(a1),x71522),f2(a1)))+E(f333(f271(a1,a1),f333(a52,f51(f333(f80(a1),x71521),f333(f80(a1),x71522)))),f46(a1,x71521,x71522))+~P4(f333(f333(f251(a1),f2(a1)),x71521)) % 191.49/191.41 [7205]E(f333(f333(f40(a1),f333(f333(f264(a1),x72051),x72052)),x72051),f333(f333(f264(a1),x72051),f333(f333(f3(a880),x72052),f333(a117,f2(a880)))))+~P4(f333(f333(f251(a880),f2(a880)),x72052))+~P4(f333(f333(f251(a1),f2(a1)),x72051)) % 191.49/191.41 [7296]~P4(f333(f333(f251(a880),f2(a880)),x72961))+~P4(f333(f333(f251(a880),f2(a880)),x72962))+P4(f333(f333(f251(a880),f333(f333(f3(a880),x72961),x72962)),x72961)) % 191.49/191.41 [7297]~P4(f333(f333(f251(a880),f2(a880)),x72971))+~P4(f333(f333(f251(a880),f79(a880)),x72972))+P4(f333(f333(f251(a880),f333(f333(f40(a880),x72971),x72972)),x72971)) % 191.49/191.41 [7298]~P4(f333(f333(f251(a1),f2(a1)),x72981))+~P4(f333(f333(f251(a1),f79(a1)),x72982))+P4(f333(f333(f251(a1),f333(f333(f40(a1),x72981),x72982)),x72981)) % 191.49/191.41 [7438]E(x74381,f2(a880))+~E(x74382,f2(a1))+~P4(f333(f333(f251(a1),f2(a1)),f333(f333(f264(a1),f333(f76(a1),x74382)),x74381))) % 191.49/191.41 [7854]~E(x78542,f118(f881(x78541)))+E(f333(f195(f881(f881(x78541))),f180(x78541,x78542)),f2(a880))+~P17(a880,f333(f170(a880),f333(f333(f155(f881(x78541),a880),f195(f881(x78541))),x78542))) % 191.49/191.41 [8101]P4(f333(x81011,x81012))+~P4(f333(x81011,f333(a111,f716(x81011,x81012))))+~P4(f333(f333(f335(f890(f889(a880,a880),a874)),x81012),a103)) % 191.49/191.41 [8121]E(x81211,f118(f881(x81212)))+E(f333(f195(f881(x81212)),f333(f333(f166(f881(x81212)),x81211),f2(a880))),f333(f195(f881(f881(x81212))),f180(x81212,x81211)))+~P17(a880,f333(f170(a880),f333(f333(f155(f881(x81212),a880),f195(f881(x81212))),x81211))) % 191.49/191.41 [8812]~P4(f333(f63(x88121),f333(f255(x88121),x88122)))+~P4(f333(f63(x88121),f258(f890(x88121,a874))))+P4(f333(f63(x88121),f333(f255(x88121),f333(f333(f10(a874,a874,x88121),a328),x88122)))) % 191.49/191.41 [8877]E(f333(f333(f263(a880,a880),f333(a117,f333(f333(f40(a880),f333(f333(f3(a880),x88771),x88772)),x88772))),f46(a880,f333(f333(f3(a880),x88771),x88772),x88772)),f86(f889(a880,a880),f49(x88771,x88772)))+~P4(f333(f333(f251(a880),f2(a880)),x88772))+~P4(f333(f333(f250(a880),x88772),x88771)) % 191.49/191.41 [9164]~P4(f333(f63(x91641),f333(f255(x91641),x91642)))+P4(f333(f63(x91641),f258(f890(x91641,a874))))+~P4(f333(f63(x91641),f333(f255(x91641),f333(f333(f10(a874,a874,x91641),a328),x91642)))) % 191.49/191.41 [9911]P29(x99111,x99112)+~P40(x99111,f333(f262(f890(f889(x99111,x99111),a874),f890(f889(x99111,x99111),a874)),x99112))+~P4(f333(f333(f250(f890(f889(x99111,x99111),a874)),f333(f333(f290(x99111,x99111,x99111),f333(f262(f890(f889(x99111,x99111),a874),f890(f889(x99111,x99111),a874)),x99112)),f333(f271(f890(f889(x99111,x99111),a874),f890(f889(x99111,x99111),a874)),x99112))),f333(f262(f890(f889(x99111,x99111),a874),f890(f889(x99111,x99111),a874)),x99112))) % 191.49/191.41 [7231]~P4(f333(f333(f251(a880),f2(a880)),x72312))+P4(f333(f333(f251(a880),x72311),x72312))+E(f333(a117,f333(f333(f40(a880),f333(f333(f3(a880),x72311),x72312)),x72312)),f333(f333(f40(a880),x72311),x72312)) % 191.49/191.41 [7358]~P4(f333(f333(f251(a880),f2(a880)),x73582))+~P4(f333(f333(f250(a880),x73582),x73581))+E(f333(a117,f333(f333(f40(a880),f333(f333(f3(a880),x73581),x73582)),x73582)),f333(f333(f40(a880),x73581),x73582)) % 191.49/191.41 [8437]~P94(x84371)+~P93(x84371)+~P33(x84371,f333(f108(x84371),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x84372)),x84372))) % 191.49/191.41 [9060]E(x90601,f2(a880))+E(f333(f333(f272(a880,a880,f889(a880,a880)),f333(f333(f10(a880,f890(a880,f889(a880,a880)),a880),f263(a880,a880)),a117)),f86(f889(a880,a880),f49(f333(f333(f3(a880),x90602),x90601),x90601))),f86(f889(a880,a880),f49(x90602,x90601)))+P4(f333(f333(f251(a880),x90602),x90601)) % 191.49/191.41 [9508]P4(f333(x95082,f803(x95082,x95081)))+P4(f333(x95081,f803(x95082,x95081)))+E(f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),x95081)),f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),x95082))) % 191.49/191.41 [9512]~P4(f333(x95122,f803(x95122,x95121)))+~P4(f333(x95121,f803(x95122,x95121)))+E(f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),x95121)),f333(f255(a1),f333(f333(f20(a1,a874,a874),f333(f333(f10(a874,f890(a874,a874),a1),a331),f333(f250(a1),f2(a1)))),x95122))) % 191.49/191.41 [7811]~P64(x78111)+~P94(x78111)+E(f333(f333(f291(x78111),x78112),f333(f108(x78111),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),x78112) % 191.49/191.41 [9268]~P94(x92681)+~E(f333(f108(x92681),x92682),f79(x92681))+P33(x92681,f333(f108(x92681),f333(f333(f81(a1),x92682),f333(f80(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))))) % 191.49/191.41 [9488]~P94(x94881)+E(f333(f108(x94881),x94882),f79(x94881))+~P33(x94881,f333(f108(x94881),f333(f333(f81(a1),x94882),f333(f80(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))))) % 191.49/191.41 [9935]~P139(x99351)+~E(x99352,f79(x99351))+E(f333(f333(f264(x99351),x99352),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f79(x99351)) % 191.49/191.41 [9936]~P139(x99361)+~E(x99362,f2(x99361))+E(f333(f333(f264(x99361),x99362),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f2(x99361)) % 191.49/191.41 [9939]~P139(x99391)+~E(x99392,f333(f80(x99391),f79(x99391)))+E(f333(f333(f264(x99391),x99392),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f79(x99391)) % 191.49/191.41 [10074]~P120(x100742)+E(x100741,f2(x100742))+P4(f333(f333(f251(x100742),f2(x100742)),f333(f333(f264(x100742),x100741),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.41 [10112]~P120(x101122)+~E(x101121,f2(x101122))+~P4(f333(f333(f251(x101122),f2(x101122)),f333(f333(f264(x101122),x101121),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.41 [10124]P4(f333(f333(f250(a1),x101241),f2(a1)))+P4(f333(f333(f251(a1),x101242),x101241))+E(f333(f45(x101241),f48(x101242,f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101241))),f48(x101242,x101241)) % 191.49/191.41 [10125]~P4(f333(f333(f251(a1),f2(a1)),x101251))+P4(f333(f333(f251(a1),x101252),x101251))+E(f333(f45(x101251),f48(x101252,f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101251))),f48(x101252,x101251)) % 191.49/191.41 [10126]P4(f333(f333(f250(a1),x101261),f2(a1)))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f81(a1),x101262),x101261)))+E(f333(f45(x101261),f51(x101262,f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101261))),f51(x101262,x101261)) % 191.49/191.41 [10127]~P4(f333(f333(f251(a1),f2(a1)),x101271))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f81(a1),x101272),x101271)))+E(f333(f45(x101271),f51(x101272,f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101271))),f51(x101272,x101271)) % 191.49/191.41 [10128]~P143(x101281)+~P4(f333(f333(f250(a1),f2(a1)),x101282))+E(f333(f105(x101281),f333(a109,f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x101282))),f333(f333(f81(x101281),f333(f105(x101281),f333(a109,x101282))),f333(f105(x101281),f333(a109,x101282)))) % 191.49/191.41 [5064]~P146(x50641,x50643,x50642)+~E(x50643,f2(a1))+P4(f333(x50641,x50642)) % 191.49/191.41 [5184]~P109(x51841)+~P17(x51841,x51843)+P17(x51841,f171(x51841,x51842,x51843)) % 191.49/191.41 [5185]~P109(x51851)+~P17(x51851,x51853)+P17(x51851,f177(x51851,x51852,x51853)) % 191.49/191.41 [4771]~P75(x47712)+~E(x47713,f333(f80(x47712),x47711))+E(x47711,f333(f80(x47712),x47713)) % 191.49/191.41 [4773]~P75(x47731)+~E(f333(f80(x47731),x47733),x47732)+E(f333(f80(x47731),x47732),x47733) % 191.49/191.41 [4847]~P79(x48473)+E(x48471,x48472)+~E(f333(f80(x48473),x48471),f333(f80(x48473),x48472)) % 191.49/191.41 [4848]~P75(x48483)+E(x48481,x48482)+~E(f333(f80(x48483),x48481),f333(f80(x48483),x48482)) % 191.49/191.41 [4849]~P103(x48493)+E(x48491,x48492)+~E(f333(f105(x48493),x48491),f333(f105(x48493),x48492)) % 191.49/191.41 [4850]~P93(x48503)+E(x48501,x48502)+~E(f333(f107(x48503),x48501),f333(f107(x48503),x48502)) % 191.49/191.41 [4851]~P109(x48513)+E(x48511,x48512)+~E(f333(f256(x48513),x48511),f333(f256(x48513),x48512)) % 191.49/191.41 [4852]~P109(x48523)+E(x48521,x48522)+~E(f333(f302(x48523),x48521),f333(f302(x48523),x48522)) % 191.49/191.41 [4853]~P109(x48533)+E(x48531,x48532)+~E(f333(f305(x48533),x48531),f333(f305(x48533),x48532)) % 191.49/191.41 [4854]~P109(x48543)+E(x48541,x48542)+~E(f333(f257(x48543),x48541),f333(f257(x48543),x48542)) % 191.49/191.41 [4951]~P62(x49511)+~P4(f333(x49512,x49513))+P4(f333(f59(x49511),x49512)) % 191.49/191.41 [4984]~P62(x49843)+P4(f333(x49841,x49842))+~P4(f333(f60(x49843),x49841)) % 191.49/191.41 [5082]~P147(x50821,x50822,x50823)+~E(x50822,f2(a1))+P4(f333(x50821,f2(a1))) % 191.49/191.41 [5119]~E(x51191,f2(a880))+E(f739(x51191,x51192,x51193),f194(f890(x51193,a874)))+~E(f333(f39(x51193),x51192),f333(a117,x51191)) % 191.49/191.41 [5274]~E(x52742,f2(a880))+E(f333(f262(a880,a880),x52741),f2(a880))+~P4(f333(f49(x52743,x52742),x52741)) % 191.49/191.41 [5321]P4(f333(x53211,x53212))+~E(x53213,f333(f105(a1),x53212))+~P4(f333(x53211,f333(a109,x53213))) % 191.49/191.41 [5789]~E(x57893,f2(a880))+~P4(f333(x57891,x57892))+P4(f333(x57891,f46(a880,x57892,x57893))) % 191.49/191.41 [5920]~P4(f333(a25,x59203))+~P4(f333(a25,x59202))+P4(f333(a25,f31(x59201,x59202,x59203))) % 191.49/191.41 [5951]~P62(x59513)+~P13(x59513,x59511,x59512)+P4(f333(x59511,f665(x59512,x59511,x59513))) % 191.49/191.41 [6013]~P104(x60132)+~P104(x60131)+E(f133(x60131,x60132,f136(x60131,x60133),f136(x60132,x60133)),f136(f889(x60131,x60132),x60133)) % 191.49/191.41 [6194]~E(x61943,f2(a880))+P4(f333(x61941,x61942))+~P4(f333(x61941,f46(a880,x61942,x61943))) % 191.49/191.41 [6339]~P62(x63391)+P14(x63391,x63392,x63393)+~P4(f333(x63392,f666(x63393,x63392,x63391))) % 191.49/191.41 [6854]E(x68541,f2(a880))+~P4(f333(x68542,f410(x68541,x68543,x68542)))+P4(f333(x68542,f46(a880,x68543,x68541))) % 191.49/191.41 [6961]~P9(x69611)+~P4(f333(f333(f250(x69611),x69612),f346(x69613,x69612,x69611)))+P4(f333(f333(f250(x69611),x69612),f42(x69611,x69613))) % 191.49/191.41 [6963]~P4(f333(x69631,x69632))+~P4(f333(x69631,f410(x69633,x69632,x69631)))+P4(f333(x69631,f46(a880,x69632,x69633))) % 191.49/191.41 [7067]E(x70671,f118(x70672))+E(f333(f333(f152(x70672),f626(x70673,x70671,x70672)),f642(x70673,x70671,x70672)),x70671)+~P4(f333(f333(f335(f881(x70672)),x70671),f162(x70672,x70673))) % 191.49/191.41 [7097]~P140(x70971)+~P4(f333(f333(f335(x70971),x70972),f114(x70971)))+P4(f333(f333(f335(x70971),f333(f333(f264(x70971),x70972),x70973)),f114(x70971))) % 191.49/191.41 [7407]P40(x74071,x74072)+~P4(f333(f333(f335(x74071),x74073),f785(x74072,x74071)))+P4(f333(f333(f335(x74071),f800(x74072,x74071,x74073)),f785(x74072,x74071))) % 191.49/191.41 [7671]E(x76711,f118(x76712))+~P4(f333(f333(f335(f881(x76712)),x76711),f162(x76712,x76713)))+P4(f333(f333(f335(f881(x76712)),f642(x76713,x76711,x76712)),f162(x76712,x76713))) % 191.49/191.41 [7723]E(x77231,f2(a880))+E(f333(f333(f81(a880),f333(f333(f82(a880),x77231),f411(x77231,x77232,x77233))),f410(x77231,x77232,x77233)),x77232)+P4(f333(x77233,f46(a880,x77232,x77231))) % 191.49/191.41 [7769]~P4(f333(x77693,x77692))+E(f333(f333(f81(a880),f333(f333(f82(a880),x77691),f411(x77691,x77692,x77693))),f410(x77691,x77692,x77693)),x77692)+P4(f333(x77693,f46(a880,x77692,x77691))) % 191.49/191.41 [7905]P4(f333(f333(f251(a1),x79051),f398(x79052,x79053,x79051)))+P4(f333(f333(x79053,f333(f333(f40(a1),x79052),x79051)),f46(a1,x79052,x79051)))+~P4(f333(f333(f251(a1),x79051),f2(a1))) % 191.49/191.41 [8183]P4(f333(f333(x81832,f333(f333(f40(a1),x81831),x81833)),f46(a1,x81831,x81833)))+~P4(f333(f333(f251(a1),x81833),f2(a1)))+P4(f333(f333(f250(a1),f398(x81831,x81832,x81833)),f2(a1))) % 191.49/191.41 [8359]E(f333(f333(f81(a1),f333(f333(f82(a1),x83591),f399(x83592,x83593,x83591))),f398(x83592,x83593,x83591)),x83592)+P4(f333(f333(x83593,f333(f333(f40(a1),x83592),x83591)),f46(a1,x83592,x83591)))+~P4(f333(f333(f251(a1),x83591),f2(a1))) % 191.49/191.41 [8602]~P4(f333(f333(x86021,f399(x86022,x86021,x86023)),f398(x86022,x86021,x86023)))+P4(f333(f333(x86021,f333(f333(f40(a1),x86022),x86023)),f46(a1,x86022,x86023)))+~P4(f333(f333(f251(a1),x86023),f2(a1))) % 191.49/191.41 [8823]~P109(x88231)+~P17(x88231,x88233)+P17(x88231,f150(x88231,x88231,f7(x88231),x88232,x88233)) % 191.49/191.41 [9327]~P124(x93272)+E(x93271,f2(x93272))+~P4(f333(f333(f250(x93272),f333(f333(f81(x93272),f333(f333(f82(x93272),x93273),x93273)),f333(f333(f82(x93272),x93271),x93271))),f2(x93272))) % 191.49/191.41 [9328]~P124(x93282)+E(x93281,f2(x93282))+~P4(f333(f333(f250(x93282),f333(f333(f81(x93282),f333(f333(f82(x93282),x93281),x93281)),f333(f333(f82(x93282),x93283),x93283))),f2(x93282))) % 191.49/191.41 [10210]~P120(x102101)+~P4(f333(f333(f251(x102101),x102102),f2(x102101)))+P4(f333(f333(f251(x102101),f333(f333(f264(x102101),x102102),f333(a117,f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x102103)))),f2(x102101))) % 191.49/191.41 [10213]~P120(x102132)+E(x102131,f2(x102132))+~P4(f333(f333(f250(x102132),f333(f333(f81(x102132),f333(f333(f264(x102132),x102133),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x102132),x102131),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))),f2(x102132))) % 191.49/191.41 [10214]~P120(x102142)+E(x102141,f2(x102142))+~P4(f333(f333(f250(x102142),f333(f333(f81(x102142),f333(f333(f264(x102142),x102141),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x102142),x102143),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))),f2(x102142))) % 191.49/191.41 [4803]~E(x48032,x48033)+~P68(x48031)+E(f333(f333(f3(x48031),x48032),x48033),f2(x48031)) % 191.49/191.41 [4804]~E(x48042,x48043)+~P75(x48041)+E(f333(f333(f3(x48041),x48042),x48043),f2(x48041)) % 191.49/191.41 [4817]~P137(x48171)+~E(x48173,f2(x48171))+E(f333(f333(f81(x48171),x48172),x48173),x48172) % 191.49/191.41 [4834]~P141(x48341)+~E(x48343,f2(x48341))+E(f333(f333(f82(x48341),x48342),x48343),f2(x48341)) % 191.49/191.41 [4835]~P141(x48351)+~E(x48352,f2(x48351))+E(f333(f333(f82(x48351),x48352),x48353),f2(x48351)) % 191.49/191.41 [4856]~E(x48563,f118(x48561))+~E(x48562,f118(x48561))+E(f333(f333(f127(x48561),x48562),x48563),f118(x48561)) % 191.49/191.41 [4941]~P137(x49412)+E(x49411,f2(x49412))+~E(f333(f333(f81(x49412),x49413),x49411),x49413) % 191.49/191.41 [4942]~P75(x49421)+~E(x49422,f333(f80(x49421),x49423))+E(f333(f333(f81(x49421),x49422),x49423),f2(x49421)) % 191.49/191.41 [4949]E(x49491,f118(x49492))+E(x49493,f2(a880))+~E(f333(f333(f174(x49492),x49493),x49491),f118(x49492)) % 191.49/191.41 [4955]~P68(x49553)+E(x49551,x49552)+~E(f333(f333(f3(x49553),x49551),x49552),f2(x49553)) % 191.49/191.41 [4956]~P75(x49563)+E(x49561,x49562)+~E(f333(f333(f3(x49563),x49561),x49562),f2(x49563)) % 191.49/191.41 [4965]~P139(x49652)+E(x49651,f2(x49652))+~E(f333(f333(f264(x49652),x49651),x49653),f2(x49652)) % 191.49/191.41 [4966]~P7(x49662)+E(x49661,f194(x49662))+~E(f333(f333(f115(x49662),x49663),x49661),f194(x49662)) % 191.49/191.41 [4967]~P7(x49672)+E(x49671,f194(x49672))+~E(f333(f333(f115(x49672),x49671),x49673),f194(x49672)) % 191.49/191.41 [4968]~P100(x49682)+E(x49681,f258(x49682))+~E(f333(f333(f106(x49682),x49683),x49681),f258(x49682)) % 191.49/191.41 [4969]~P100(x49692)+E(x49691,f258(x49692))+~E(f333(f333(f106(x49692),x49691),x49693),f258(x49692)) % 191.49/191.41 [5035]~P75(x50352)+E(x50351,f333(f80(x50352),x50353))+~E(f333(f333(f81(x50352),x50351),x50353),f2(x50352)) % 191.49/191.41 [5036]~P75(x50361)+E(f333(f80(x50361),x50362),x50363)+~E(f333(f333(f81(x50361),x50362),x50363),f2(x50361)) % 191.49/191.41 [5038]~E(x50382,x50383)+~P108(x50381)+P4(f333(f333(f250(x50381),x50382),x50383)) % 191.49/191.41 [5040]~E(x50402,x50403)+~P110(x50401)+P4(f333(f333(f250(x50401),x50402),x50403)) % 191.49/191.41 [5041]~E(x50412,x50413)+~P96(x50411)+P4(f333(f333(f92(x50411),x50412),x50413)) % 191.49/191.41 [5135]~P117(x51351)+~E(x51352,f333(f80(x51351),x51353))+E(f333(f333(f82(x51351),x51352),x51352),f333(f333(f82(x51351),x51353),x51353)) % 191.49/191.41 [5143]~P109(x51431)+~P17(x51431,x51433)+P17(x51431,f333(f333(f174(x51431),x51432),x51433)) % 191.49/191.41 [5144]~P109(x51441)+~P17(x51441,x51443)+P17(x51441,f333(f333(f139(x51441),x51442),x51443)) % 191.49/191.41 [5182]E(x51821,x51822)+E(x51823,f2(a880))+~E(f333(f333(f82(a880),x51823),x51821),f333(f333(f82(a880),x51823),x51822)) % 191.49/191.41 [5183]E(x51831,x51832)+E(x51833,f2(a880))+~E(f333(f333(f82(a880),x51831),x51833),f333(f333(f82(a880),x51832),x51833)) % 191.49/191.41 [5265]~E(x52652,x52653)+~P110(x52651)+E(f304(x52651,x52652,x52653),f333(f333(f311(x52651),x52652),f194(f890(x52651,a874)))) % 191.49/191.41 [5309]E(x53091,x53092)+~P96(x53093)+~P4(f333(f333(f92(x53093),x53091),x53092)) % 191.49/191.41 [5319]~E(x53191,x53192)+~P109(x53193)+~P4(f333(f333(f251(x53193),x53191),x53192)) % 191.49/191.41 [5320]~E(x53201,x53202)+~P110(x53203)+~P4(f333(f333(f251(x53203),x53201),x53202)) % 191.49/191.41 [5330]~P110(x53301)+E(f333(f303(x53301,x53302),x53303),f194(f890(x53301,a874)))+P4(f333(f333(f251(x53301),x53302),x53303)) % 191.49/191.41 [5376]~P110(x53761)+E(f306(x53761,x53762,x53763),f194(f890(x53761,a874)))+P4(f333(f333(f251(x53761),x53762),x53763)) % 191.49/191.41 [5377]~P110(x53771)+E(f304(x53771,x53772,x53773),f194(f890(x53771,a874)))+P4(f333(f333(f250(x53771),x53772),x53773)) % 191.49/191.41 [5378]~P110(x53781)+E(f194(f890(x53781,a874)),f306(x53781,x53782,x53783))+P4(f333(f333(f251(x53781),x53782),x53783)) % 191.49/191.41 [5379]~P110(x53791)+E(f194(f890(x53791,a874)),f304(x53791,x53792,x53793))+P4(f333(f333(f250(x53791),x53792),x53793)) % 191.49/191.41 [5387]~P101(x53871)+~E(f333(f333(f115(x53871),x53872),x53873),x53873)+P4(f333(f333(f250(x53871),x53872),x53873)) % 191.49/191.41 [5388]~P102(x53881)+~E(f333(f333(f106(x53881),x53882),x53883),x53882)+P4(f333(f333(f250(x53881),x53882),x53883)) % 191.49/191.41 [5389]~P109(x53891)+~E(f333(f333(f248(x53891),x53892),x53893),x53892)+P4(f333(f333(f250(x53891),x53892),x53893)) % 191.49/191.41 [5390]~P109(x53901)+~E(f333(f333(f249(x53901),x53902),x53903),x53903)+P4(f333(f333(f250(x53901),x53902),x53903)) % 191.49/191.41 [5410]~P109(x54101)+P17(x54101,x54102)+~P17(x54101,f333(f333(f152(x54101),x54103),x54102)) % 191.49/191.41 [5411]~P109(x54111)+P17(x54111,x54112)+~P17(x54111,f333(f333(f127(x54111),x54113),x54112)) % 191.49/191.41 [5412]~P109(x54121)+P17(x54121,x54122)+~P17(x54121,f333(f333(f127(x54121),x54122),x54123)) % 191.49/191.41 [5480]~P109(x54801)+P4(f333(f333(f250(x54801),x54803),x54802))+P4(f333(f333(f251(x54801),x54802),x54803)) % 191.49/191.41 [5482]~P109(x54821)+P4(f333(f333(f250(x54821),x54823),x54822))+P4(f333(f333(f250(x54821),x54822),x54823)) % 191.49/191.41 [5518]~P101(x55181)+E(f333(f333(f115(x55181),x55182),x55183),x55182)+~P4(f333(f333(f250(x55181),x55183),x55182)) % 191.49/191.41 [5520]~P101(x55201)+E(f333(f333(f115(x55201),x55202),x55203),x55203)+~P4(f333(f333(f250(x55201),x55202),x55203)) % 191.49/191.41 [5521]~P102(x55211)+E(f333(f333(f106(x55211),x55212),x55213),x55213)+~P4(f333(f333(f250(x55211),x55213),x55212)) % 191.49/191.41 [5523]~P102(x55231)+E(f333(f333(f106(x55231),x55232),x55233),x55232)+~P4(f333(f333(f250(x55231),x55232),x55233)) % 191.49/191.41 [5524]~P109(x55241)+E(f333(f333(f248(x55241),x55242),x55243),x55243)+~P4(f333(f333(f250(x55241),x55243),x55242)) % 191.49/191.41 [5526]~P109(x55261)+E(f333(f333(f248(x55261),x55262),x55263),x55262)+~P4(f333(f333(f250(x55261),x55262),x55263)) % 191.49/191.41 [5527]~P109(x55271)+E(f333(f333(f249(x55271),x55272),x55273),x55272)+~P4(f333(f333(f250(x55271),x55273),x55272)) % 191.49/191.41 [5529]~P109(x55291)+E(f333(f333(f249(x55291),x55292),x55293),x55293)+~P4(f333(f333(f250(x55291),x55292),x55293)) % 191.49/191.41 [5536]~P118(x55362)+E(x55361,f2(x55362))+E(f333(f333(f291(x55362),f333(f80(x55362),x55363)),f333(f80(x55362),x55361)),f333(f333(f291(x55362),x55363),x55361)) % 191.49/191.41 [5581]~P110(x55811)+E(f333(f303(x55811,x55812),x55813),f194(f890(x55811,a874)))+~P4(f333(f333(f250(x55811),x55813),x55812)) % 191.49/191.41 [5614]~P110(x56141)+E(f307(x56141,x56142,x56143),f194(f890(x56141,a874)))+~P4(f333(f333(f250(x56141),x56143),x56142)) % 191.49/191.41 [5615]~P110(x56151)+E(f306(x56151,x56152,x56153),f194(f890(x56151,a874)))+~P4(f333(f333(f250(x56151),x56153),x56152)) % 191.49/191.41 [5616]~P110(x56161)+E(f304(x56161,x56162,x56163),f194(f890(x56161,a874)))+~P4(f333(f333(f251(x56161),x56163),x56162)) % 191.49/191.41 [5667]~E(f333(f333(f3(a880),x56671),x56673),x56672)+E(x56671,f333(f333(f81(a880),x56672),x56673))+~P4(f333(f333(f250(a880),x56673),x56671)) % 191.49/191.41 [5668]~E(x56681,f333(f333(f81(a880),x56683),x56682))+E(f333(f333(f3(a880),x56681),x56682),x56683)+~P4(f333(f333(f250(a880),x56682),x56681)) % 191.49/191.41 [5714]~P4(f333(x57141,x57143))+P4(f333(x57141,f413(x57141,x57142)))+~P4(f333(f333(f250(a880),x57143),x57142)) % 191.49/191.41 [5715]~P4(f333(x57151,x57153))+P4(f333(x57151,f423(x57151,x57152)))+~P4(f333(f333(f251(a880),x57153),x57152)) % 191.49/191.41 [5723]~P110(x57231)+~E(f333(f303(x57231,x57232),x57233),f194(f890(x57231,a874)))+~P4(f333(f333(f251(x57231),x57232),x57233)) % 191.49/191.41 [5727]~P108(x57271)+~P4(f333(f333(f251(x57271),x57272),x57273))+P4(f333(f333(f250(x57271),x57272),x57273)) % 191.49/191.41 [5729]~P110(x57291)+~P4(f333(f333(f251(x57291),x57292),x57293))+P4(f333(f333(f250(x57291),x57292),x57293)) % 191.49/191.41 [5837]~P110(x58371)+~E(f306(x58371,x58372,x58373),f194(f890(x58371,a874)))+~P4(f333(f333(f251(x58371),x58372),x58373)) % 191.49/191.41 [5838]~P110(x58381)+~E(f304(x58381,x58382,x58383),f194(f890(x58381,a874)))+~P4(f333(f333(f250(x58381),x58382),x58383)) % 191.49/191.41 [5839]~P110(x58391)+~E(f194(f890(x58391,a874)),f306(x58391,x58392,x58393))+~P4(f333(f333(f251(x58391),x58392),x58393)) % 191.49/191.41 [5840]~P110(x58401)+~E(f194(f890(x58401,a874)),f304(x58401,x58402,x58403))+~P4(f333(f333(f250(x58401),x58402),x58403)) % 191.49/191.41 [5848]P4(f333(x58481,x58482))+~P4(f333(x58481,f414(x58481,x58483)))+~P4(f333(f333(f250(a880),x58482),x58483)) % 191.49/191.41 [5849]P4(f333(x58491,x58492))+~P4(f333(x58491,f424(x58491,x58493)))+~P4(f333(f333(f251(a880),x58492),x58493)) % 191.49/191.41 [5857]~E(x58571,f333(a117,x58573))+P4(f333(f333(f251(a880),x58571),f333(a117,x58572)))+~P4(f333(f333(f251(a880),x58573),x58572)) % 191.49/191.41 [5873]E(x58731,x58732)+~E(f333(f333(f82(a880),x58733),x58731),f333(f333(f82(a880),x58733),x58732))+~P4(f333(f333(f251(a880),f2(a880)),x58733)) % 191.49/191.41 [5931]E(f333(x59311,f859(x59311,x59312,x59313)),f79(a880))+~E(f333(f333(f8(x59313,a880),x59311),x59312),f79(a880))+~P4(f333(f63(x59313),x59312)) % 191.49/191.41 [5942]~P9(x59421)+P4(f333(f333(f250(x59421),x59422),f41(x59421,x59423)))+~P4(f333(f333(f335(x59421),x59422),x59423)) % 191.49/191.41 [5972]~P108(x59721)+~P4(f333(f333(f251(x59721),x59723),x59722))+~P4(f333(f333(f251(x59721),x59722),x59723)) % 191.49/191.41 [5973]~P108(x59731)+~P4(f333(f333(f250(x59731),x59733),x59732))+~P4(f333(f333(f251(x59731),x59732),x59733)) % 191.49/191.41 [5974]~P109(x59741)+~P4(f333(f333(f251(x59741),x59743),x59742))+~P4(f333(f333(f251(x59741),x59742),x59743)) % 191.49/191.41 [5977]~P109(x59771)+~P4(f333(f333(f250(x59771),x59773),x59772))+~P4(f333(f333(f251(x59771),x59772),x59773)) % 191.49/191.41 [5978]~P110(x59781)+~P4(f333(f333(f251(x59781),x59783),x59782))+~P4(f333(f333(f251(x59781),x59782),x59783)) % 191.49/191.41 [6007]~E(f333(x60072,f860(x60072,x60073,x60071)),f2(a880))+E(f333(f333(f8(x60071,a880),x60072),x60073),f2(a880))+~P4(f333(f63(x60071),x60073)) % 191.49/191.41 [6008]~E(f333(x60082,f832(x60082,x60083,x60081)),f79(a880))+E(f333(f333(f11(x60081,a880),x60082),x60083),f79(a880))+~P4(f333(f63(x60081),x60083)) % 191.49/191.41 [6022]~P111(x60221)+~P4(f333(f333(f251(x60221),x60223),x60222))+P4(f333(f333(f335(x60221),x60222),f333(f305(x60221),x60223))) % 191.49/191.41 [6023]~P111(x60231)+~P4(f333(f333(f250(x60231),x60233),x60232))+P4(f333(f333(f335(x60231),x60232),f333(f257(x60231),x60233))) % 191.49/191.41 [6024]~P111(x60241)+~P4(f333(f333(f251(x60241),x60242),x60243))+P4(f333(f333(f335(x60241),x60242),f333(f256(x60241),x60243))) % 191.49/191.41 [6025]~P111(x60251)+~P4(f333(f333(f250(x60251),x60252),x60253))+P4(f333(f333(f335(x60251),x60252),f333(f302(x60251),x60253))) % 191.49/191.41 [6037]E(f333(x60371,f861(x60371,x60372,x60373)),f333(a117,f2(a880)))+~E(f333(f333(f8(x60373,a880),x60371),x60372),f333(a117,f2(a880)))+~P4(f333(f63(x60373),x60372)) % 191.49/191.41 [6120]~P9(x61201)+~P4(f333(f333(f335(x61201),x61203),x61202))+P4(f333(f333(f250(x61201),f42(x61201,x61202)),x61203)) % 191.49/191.41 [6137]~P4(f333(f333(f250(a880),x61371),x61373))+P4(f333(f333(f250(a880),x61371),x61372))+~P4(f333(f333(f250(a880),x61373),x61372)) % 191.49/191.41 [6138]~P4(f333(f333(f250(a1),x61381),x61383))+P4(f333(f333(f250(a1),x61381),x61382))+~P4(f333(f333(f250(a1),x61383),x61382)) % 191.49/191.41 [6157]~P111(x61571)+~P4(f333(f333(f335(x61571),x61573),f333(f305(x61571),x61572)))+P4(f333(f333(f251(x61571),x61572),x61573)) % 191.49/191.41 [6158]~P111(x61581)+~P4(f333(f333(f335(x61581),x61582),f333(f256(x61581),x61583)))+P4(f333(f333(f251(x61581),x61582),x61583)) % 191.49/191.41 [6159]~P111(x61591)+~P4(f333(f333(f335(x61591),x61593),f333(f257(x61591),x61592)))+P4(f333(f333(f250(x61591),x61592),x61593)) % 191.49/191.41 [6160]~P111(x61601)+~P4(f333(f333(f335(x61601),x61602),f333(f302(x61601),x61603)))+P4(f333(f333(f250(x61601),x61602),x61603)) % 191.49/191.41 [6277]P4(f333(x62771,x62772))+~P4(f333(x62771,f599(x62771)))+~P4(f333(f333(f335(x62773),x62772),f258(f890(x62773,a874)))) % 191.49/191.41 [6375]~P65(x63751)+P4(f333(f333(f251(x63751),f2(x63751)),f364(x63753,x63752,x63751)))+P4(f333(f333(f250(x63751),x63752),x63753)) % 191.49/191.41 [6376]~P66(x63761)+P4(f333(f333(f251(x63761),f2(x63761)),f451(x63763,x63762,x63761)))+P4(f333(f333(f250(x63761),x63762),x63763)) % 191.49/191.41 [6443]~P81(x64431)+~P4(f333(f333(f251(x64431),x64433),f333(f80(x64431),x64432)))+P4(f333(f333(f251(x64431),x64432),f333(f80(x64431),x64433))) % 191.49/191.41 [6445]~P81(x64451)+~P4(f333(f333(f250(x64451),x64453),f333(f80(x64451),x64452)))+P4(f333(f333(f250(x64451),x64452),f333(f80(x64451),x64453))) % 191.49/191.41 [6457]~P4(f333(f333(f251(a880),x64571),x64573))+~P4(f333(f333(f251(a880),x64573),x64572))+P4(f333(f333(f251(a880),f333(a117,x64571)),x64572)) % 191.49/191.41 [6483]~P120(x64831)+P4(f333(f333(f251(x64831),f333(f107(x64831),x64832)),f333(f107(x64831),x64833)))+~P4(f333(f333(f251(a1),x64832),x64833)) % 191.49/191.41 [6484]~P123(x64841)+P4(f333(f333(f251(x64841),f333(f105(x64841),x64842)),f333(f105(x64841),x64843)))+~P4(f333(f333(f251(a880),x64842),x64843)) % 191.49/191.41 [6485]~P123(x64851)+P4(f333(f333(f250(x64851),f333(f105(x64851),x64852)),f333(f105(x64851),x64853)))+~P4(f333(f333(f250(a880),x64852),x64853)) % 191.49/191.41 [6486]~P120(x64861)+P4(f333(f333(f250(x64861),f333(f107(x64861),x64862)),f333(f107(x64861),x64863)))+~P4(f333(f333(f250(a1),x64862),x64863)) % 191.49/191.41 [6492]~P109(x64921)+E(f333(f333(f115(f890(x64921,a874)),f333(f256(x64921),x64922)),f333(f303(x64921,x64922),x64923)),f333(f256(x64921),x64923))+~P4(f333(f333(f250(x64921),x64922),x64923)) % 191.49/191.41 [6516]~P81(x65161)+~P4(f333(f333(f251(x65161),x65163),x65162))+P4(f333(f333(f251(x65161),f333(f80(x65161),x65162)),f333(f80(x65161),x65163))) % 191.49/191.41 [6518]~P79(x65181)+~P4(f333(f333(f250(x65181),x65183),x65182))+P4(f333(f333(f250(x65181),f333(f80(x65181),x65182)),f333(f80(x65181),x65183))) % 191.49/191.41 [6520]~P81(x65201)+~P4(f333(f333(f250(x65201),x65203),x65202))+P4(f333(f333(f250(x65201),f333(f80(x65201),x65202)),f333(f80(x65201),x65203))) % 191.49/191.41 [6554]~P109(x65541)+E(f333(f333(f115(f890(x65541,a874)),f333(f256(x65541),x65542)),f304(x65541,x65542,x65543)),f333(f302(x65541),x65543))+~P4(f333(f333(f250(x65541),x65542),x65543)) % 191.49/191.41 [6555]~P109(x65551)+E(f333(f333(f115(f890(x65551,a874)),f333(f302(x65551),x65552)),f307(x65551,x65552,x65553)),f333(f256(x65551),x65553))+~P4(f333(f333(f251(x65551),x65552),x65553)) % 191.49/191.41 [6556]~P109(x65561)+E(f333(f333(f115(f890(x65561,a874)),f333(f302(x65561),x65562)),f306(x65561,x65562,x65563)),f333(f302(x65561),x65563))+~P4(f333(f333(f250(x65561),x65562),x65563)) % 191.49/191.41 [6591]~P109(x65911)+E(f333(f333(f115(f890(x65911,a874)),f333(f303(x65911,x65912),x65913)),f333(f257(x65911),x65913)),f333(f257(x65911),x65912))+~P4(f333(f333(f250(x65911),x65912),x65913)) % 191.49/191.41 [6746]~P109(x67461)+E(f333(f333(f115(f890(x67461,a874)),f307(x67461,x67462,x67463)),f333(f257(x67461),x67463)),f333(f305(x67461),x67462))+~P4(f333(f333(f251(x67461),x67462),x67463)) % 191.49/191.41 [6747]~P109(x67471)+E(f333(f333(f115(f890(x67471,a874)),f306(x67471,x67472,x67473)),f333(f305(x67471),x67473)),f333(f305(x67471),x67472))+~P4(f333(f333(f250(x67471),x67472),x67473)) % 191.49/191.41 [6748]~P109(x67481)+E(f333(f333(f115(f890(x67481,a874)),f304(x67481,x67482,x67483)),f333(f305(x67481),x67483)),f333(f257(x67481),x67482))+~P4(f333(f333(f250(x67481),x67482),x67483)) % 191.49/191.41 [6760]P4(f333(x67601,x67602))+~P4(f333(f333(f250(a880),x67602),x67603))+P4(f333(f333(f335(a880),f414(x67601,x67603)),f304(a880,f2(a880),x67603))) % 191.49/191.41 [6794]E(x67941,x67942)+~E(f333(f333(f166(x67943),x67941),f575(x67943,x67942,x67941)),f333(f333(f166(x67943),x67942),f575(x67943,x67942,x67941)))+~E(f333(f195(f881(x67943)),x67941),f333(f195(f881(x67943)),x67942)) % 191.49/191.41 [6799]~E(x67993,f333(f333(f40(a880),x67991),x67992))+~P4(f333(f333(f251(a880),f2(a880)),x67992))+P4(f333(f333(f251(a880),x67991),f333(f333(f82(a880),x67992),f333(a117,x67993)))) % 191.49/191.41 [6814]~P4(f333(x68141,x68143))+~P4(f333(f333(f250(a880),x68143),x68142))+P4(f333(f333(f335(a880),f413(x68141,x68142)),f304(a880,f2(a880),x68142))) % 191.49/191.41 [6851]~P4(f333(x68511,x68513))+P4(f333(x68511,f426(x68511,x68512)))+~P4(f333(f333(f335(a880),x68513),f304(a880,f2(a880),x68512))) % 191.49/191.41 [6871]~P123(x68713)+~P4(f333(f333(f251(x68713),f333(f105(x68713),x68711)),f333(f105(x68713),x68712)))+P4(f333(f333(f251(a880),x68711),x68712)) % 191.49/191.41 [6872]~P120(x68723)+~P4(f333(f333(f251(x68723),f333(f107(x68723),x68721)),f333(f107(x68723),x68722)))+P4(f333(f333(f251(a1),x68721),x68722)) % 191.49/191.41 [6873]~P123(x68733)+~P4(f333(f333(f250(x68733),f333(f105(x68733),x68731)),f333(f105(x68733),x68732)))+P4(f333(f333(f250(a880),x68731),x68732)) % 191.49/191.41 [6874]~P120(x68743)+~P4(f333(f333(f250(x68743),f333(f107(x68743),x68741)),f333(f107(x68743),x68742)))+P4(f333(f333(f250(a1),x68741),x68742)) % 191.49/191.41 [6888]~P123(x68881)+~P4(f333(f333(f251(x68881),f79(x68881)),x68882))+P4(f333(f333(f251(x68881),f79(x68881)),f333(f333(f264(x68881),x68882),f333(a117,x68883)))) % 191.49/191.41 [6890]~P81(x68901)+~P4(f333(f333(f251(x68901),f333(f80(x68901),x68903)),f333(f80(x68901),x68902)))+P4(f333(f333(f251(x68901),x68902),x68903)) % 191.49/191.41 [6891]~P79(x68911)+~P4(f333(f333(f250(x68911),f333(f80(x68911),x68913)),f333(f80(x68911),x68912)))+P4(f333(f333(f250(x68911),x68912),x68913)) % 191.49/191.41 [6892]~P81(x68921)+~P4(f333(f333(f250(x68921),f333(f80(x68921),x68923)),f333(f80(x68921),x68922)))+P4(f333(f333(f250(x68921),x68922),x68923)) % 191.49/191.41 [6919]P4(f333(x69191,x69192))+~P4(f333(x69191,f415(x69191,x69193)))+~P4(f333(f333(f335(a880),x69192),f304(a880,f2(a880),x69193))) % 191.49/191.41 [6938]~P65(x69381)+P4(f333(f333(f251(x69381),f364(x69383,x69382,x69381)),f79(x69381)))+P4(f333(f333(f250(x69381),x69382),x69383)) % 191.49/191.41 [6958]~E(f46(a880,x69583,x69582),f46(a880,x69581,x69582))+E(f333(f333(f81(a880),x69581),f333(f333(f82(a880),x69582),f453(x69581,x69582,x69583))),x69583)+~P4(f333(f333(f250(a880),x69581),x69583)) % 191.49/191.41 [6977]E(f333(x69771,f824(x69771,x69772,x69773)),f197(x69772))+~P4(f333(f63(x69773),f184(x69773,x69772,x69771)))+P4(f333(f63(x69773),f258(f890(x69773,a874)))) % 191.49/191.41 [7018]E(f333(f333(f8(x70181,a880),x70182),x70183),f2(a880))+~P4(f333(f63(x70181),x70183))+P4(f333(f333(f335(x70181),f860(x70182,x70183,x70181)),x70183)) % 191.49/191.41 [7019]E(f333(f333(f11(x70191,a880),x70192),x70193),f79(a880))+~P4(f333(f63(x70191),x70193))+P4(f333(f333(f335(x70191),f832(x70192,x70193,x70191)),x70193)) % 191.49/191.41 [7041]~P109(x70411)+~P4(f333(f333(f251(x70411),x70412),x70413))+P4(f333(f333(f251(f890(x70411,a874)),f333(f256(x70411),x70412)),f333(f256(x70411),x70413))) % 191.49/191.41 [7042]~P109(x70421)+~P4(f333(f333(f250(x70421),x70422),x70423))+P4(f333(f333(f250(f890(x70421,a874)),f333(f256(x70421),x70422)),f333(f256(x70421),x70423))) % 191.49/191.41 [7043]~P110(x70431)+~P4(f333(f333(f250(x70431),x70432),x70433))+P4(f333(f333(f250(f890(x70431,a874)),f333(f302(x70431),x70432)),f333(f302(x70431),x70433))) % 191.49/191.41 [7044]~P109(x70441)+~P4(f333(f333(f250(x70441),x70443),x70442))+P4(f333(f333(f250(f890(x70441,a874)),f333(f305(x70441),x70442)),f333(f305(x70441),x70443))) % 191.49/191.41 [7045]~P110(x70451)+~P4(f333(f333(f250(x70451),x70453),x70452))+P4(f333(f333(f250(f890(x70451,a874)),f333(f257(x70451),x70452)),f333(f257(x70451),x70453))) % 191.49/191.41 [7053]~P9(x70531)+P4(f333(f333(f250(x70531),x70532),f42(x70531,x70533)))+P4(f333(f333(f335(x70531),f346(x70533,x70532,x70531)),x70533)) % 191.49/191.41 [7059]~P81(x70591)+P4(f333(f333(f251(x70591),f333(f333(f3(x70591),x70592),x70593)),f2(x70591)))+~P4(f333(f333(f251(x70591),x70592),x70593)) % 191.49/191.41 [7060]~P81(x70601)+P4(f333(f333(f250(x70601),f333(f333(f3(x70601),x70602),x70603)),f2(x70601)))+~P4(f333(f333(f250(x70601),x70602),x70603)) % 191.49/191.41 [7101]P4(f333(x71011,x71012))+P4(f333(f333(f250(a880),f415(x71011,x71013)),x71013))+~P4(f333(f333(f335(a880),x71012),f304(a880,f2(a880),x71013))) % 191.49/191.41 [7141]~E(f333(f333(f8(x71411,a880),x71412),x71413),f79(a880))+~P4(f333(f63(x71411),x71413))+P4(f333(f333(f335(x71411),f859(x71412,x71413,x71411)),x71413)) % 191.49/191.41 [7142]~P4(f333(x71421,x71423))+P4(f333(f333(f250(a880),f426(x71421,x71422)),x71422))+~P4(f333(f333(f335(a880),x71423),f304(a880,f2(a880),x71422))) % 191.49/191.41 [7182]~P9(x71821)+P4(f333(f333(f335(x71821),f347(x71823,x71822,x71821)),x71822))+P4(f333(f333(f250(x71821),f41(x71821,x71822)),x71823)) % 191.49/191.41 [7213]~E(f333(f333(f8(x72131,a880),x72132),x72133),f333(a117,f2(a880)))+~P4(f333(f63(x72131),x72133))+P4(f333(f333(f335(x72131),f861(x72132,x72133,x72131)),x72133)) % 191.49/191.41 [7224]E(x72241,f2(a880))+P4(f333(x72242,f46(a880,x72243,x72241)))+P4(f333(f333(f251(a880),f410(x72241,x72243,x72242)),x72241)) % 191.49/191.41 [7320]~P4(f333(x73201,x73202))+P4(f333(x73201,f46(a880,x73202,x73203)))+P4(f333(f333(f251(a880),f410(x73203,x73202,x73201)),x73203)) % 191.49/191.41 [7442]E(x74421,f118(x74422))+~P4(f333(f333(f335(f881(x74422)),x74421),f162(x74422,x74423)))+P4(f333(f333(f335(x74422),f626(x74423,x74421,x74422)),x74423)) % 191.49/191.41 [7464]~P109(x74641)+E(f333(f333(f115(f890(x74641,a874)),f333(f333(f311(x74641),x74642),f194(f890(x74641,a874)))),f307(x74641,x74642,x74643)),f333(f303(x74641,x74642),x74643))+~P4(f333(f333(f251(x74641),x74642),x74643)) % 191.49/191.41 [7487]~P109(x74871)+E(f333(f333(f115(f890(x74871,a874)),f333(f333(f311(x74871),x74872),f194(f890(x74871,a874)))),f306(x74871,x74872,x74873)),f304(x74871,x74872,x74873))+~P4(f333(f333(f250(x74871),x74872),x74873)) % 191.49/191.41 [7590]~P109(x75901)+P4(f333(f333(f251(x75901),x75902),x75903))+~P4(f333(f333(f251(f890(x75901,a874)),f333(f256(x75901),x75902)),f333(f256(x75901),x75903))) % 191.49/191.41 [7591]~P109(x75911)+P4(f333(f333(f250(x75911),x75912),x75913))+~P4(f333(f333(f250(f890(x75911,a874)),f333(f305(x75911),x75913)),f333(f305(x75911),x75912))) % 191.49/191.41 [7592]~P110(x75921)+P4(f333(f333(f250(x75921),x75922),x75923))+~P4(f333(f333(f250(f890(x75921,a874)),f333(f257(x75921),x75923)),f333(f257(x75921),x75922))) % 191.49/191.41 [7593]~P109(x75931)+P4(f333(f333(f250(x75931),x75932),x75933))+~P4(f333(f333(f250(f890(x75931,a874)),f333(f256(x75931),x75932)),f333(f256(x75931),x75933))) % 191.49/191.41 [7594]~P110(x75941)+P4(f333(f333(f250(x75941),x75942),x75943))+~P4(f333(f333(f250(f890(x75941,a874)),f333(f302(x75941),x75942)),f333(f302(x75941),x75943))) % 191.49/191.41 [7617]~P81(x76171)+~P4(f333(f333(f251(x76171),f333(f333(f3(x76171),x76172),x76173)),f2(x76171)))+P4(f333(f333(f251(x76171),x76172),x76173)) % 191.49/191.41 [7618]~P81(x76181)+~P4(f333(f333(f250(x76181),f333(f333(f3(x76181),x76182),x76183)),f2(x76181)))+P4(f333(f333(f250(x76181),x76182),x76183)) % 191.49/191.41 [7776]E(x77761,f2(a880))+~E(f333(f143(a880,a880,f81(a880),x77762),x77763),f2(a880))+~P4(f333(f333(f335(a880),x77761),f333(f173(a880),x77763))) % 191.49/191.41 [7780]~P9(x77801)+~P4(f333(f333(f250(x77801),f347(x77803,x77802,x77801)),x77803))+P4(f333(f333(f250(x77801),f41(x77801,x77802)),x77803)) % 191.49/191.41 [7927]P4(f333(f333(f250(a1),f2(a1)),f401(x79271,x79272,x79273)))+P4(f333(f333(x79272,f333(f333(f40(a1),x79271),x79273)),f46(a1,x79271,x79273)))+~P4(f333(f333(f251(a1),f2(a1)),x79273)) % 191.49/191.41 [8019]E(x80191,x80192)+~E(f333(f195(f881(x80193)),x80191),f333(f195(f881(x80193)),x80192))+~P4(f333(f333(f272(x80193,x80193,a874),a330),f602(x80193,x80191,x80192))) % 191.49/191.41 [8092]~P40(x80922,x80923)+E(x80921,f194(f890(x80922,a874)))+~P4(f333(f333(f250(f890(x80922,a874)),x80921),f333(f287(x80922,x80922,x80923),x80921))) % 191.49/191.41 [8123]~P66(x81231)+~P4(f333(f333(f250(x81231),x81232),f333(f333(f81(x81231),x81233),f451(x81233,x81232,x81231))))+P4(f333(f333(f250(x81231),x81232),x81233)) % 191.49/191.41 [8164]P50(x81641,x81642,x81643)+P4(f333(f333(f335(x81641),f616(x81643,x81642,x81641)),x81642))+P4(f333(f333(f335(f889(x81641,x81641)),f617(x81643,x81642,x81641)),x81643)) % 191.49/191.41 [8187]P4(f333(f333(x81872,f333(f333(f40(a1),x81871),x81873)),f46(a1,x81871,x81873)))+~P4(f333(f333(f251(a1),f2(a1)),x81873))+P4(f333(f333(f251(a1),f401(x81871,x81872,x81873)),x81873)) % 191.49/191.41 [8210]E(f333(f312(a880,a880,f333(f333(f9(a880,a880,a880),f3(a880)),x82101)),f333(f303(a880,x82102),x82103)),f194(f890(a880,a874)))+P4(f333(f333(f251(a880),x82101),x82103))+P4(f333(f333(f251(a880),x82102),x82103)) % 191.49/191.41 [8315]E(f333(f312(a880,a880,f333(f333(f9(a880,a880,a880),f3(a880)),x83151)),f333(f303(a880,x83152),x83153)),f333(f333(f311(a880),f2(a880)),f194(f890(a880,a874))))+P4(f333(f333(f251(a880),x83151),x83153))+~P4(f333(f333(f251(a880),x83152),x83153)) % 191.49/191.41 [8329]~P109(x83291)+E(f150(x83291,x83291,f7(x83291),x83292,x83293),x83293)+~P4(f333(f333(f335(x83291),x83292),f333(f173(x83291),x83293))) % 191.49/191.41 [8343]P28(x83431,x83431,x83432,x83433)+~P4(f333(f63(x83431),x83433))+~P4(f333(f333(f250(f890(x83431,a874)),x83433),f333(f312(x83431,x83431,x83432),x83433))) % 191.49/191.41 [8367]E(f333(f333(f81(a1),f333(f333(f82(a1),x83671),f402(x83672,x83673,x83671))),f401(x83672,x83673,x83671)),x83672)+P4(f333(f333(x83673,f333(f333(f40(a1),x83672),x83671)),f46(a1,x83672,x83671)))+~P4(f333(f333(f251(a1),f2(a1)),x83671)) % 191.49/191.41 [8608]~P4(f333(f333(x86081,f402(x86082,x86081,x86083)),f401(x86082,x86081,x86083)))+P4(f333(f333(x86081,f333(f333(f40(a1),x86082),x86083)),f46(a1,x86082,x86083)))+~P4(f333(f333(f251(a1),f2(a1)),x86083)) % 191.49/191.41 [9461]~P4(f333(f63(x94611),x94612))+~P4(f333(f333(f335(x94611),x94613),x94612))+P4(f333(f333(f251(a880),f333(f39(x94611),f333(f333(f3(f890(x94611,a874)),x94612),f333(f333(f311(x94611),x94613),f194(f890(x94611,a874)))))),f333(f39(x94611),x94612))) % 191.49/191.41 [10070]P50(x100701,x100702,x100703)+~P4(f333(f333(f272(x100701,x100701,a874),f333(f333(f9(x100701,f890(x100701,a874),f890(x100701,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x100701,a874),f890(x100701,a874)),x100701),f10(a874,a874,x100701)),f333(f333(f10(a874,f890(a874,a874),x100701),a331),f333(f333(f9(x100701,f890(x100701,a874),a874),f335(x100701)),x100702)))),f333(f333(f9(x100701,f890(x100701,a874),a874),f335(x100701)),x100702))),f617(x100703,x100702,x100701)))+P4(f333(f333(f335(x100701),f616(x100703,x100702,x100701)),x100702)) % 191.49/191.41 [5499]~P118(x54992)+E(x54991,f2(x54992))+E(f333(f333(f291(x54992),x54993),f333(f80(x54992),x54991)),f333(f80(x54992),f333(f333(f291(x54992),x54993),x54991))) % 191.49/191.41 [5630]~E(x56303,f194(f890(x56301,a874)))+~E(x56302,f194(f890(x56301,a874)))+E(f333(f333(f115(f890(x56301,a874)),x56302),x56303),f194(f890(x56301,a874))) % 191.49/191.41 [5688]~E(x56883,f2(a880))+~P4(f333(x56881,f2(a880)))+P4(f333(x56881,f333(f333(f40(a880),x56882),x56883))) % 191.49/191.41 [5829]~P66(x58292)+E(x58291,f2(x58292))+E(f333(f333(f291(x58292),f333(f76(x58292),x58293)),f333(f76(x58292),x58291)),f333(f76(x58292),f333(f333(f291(x58292),x58293),x58291))) % 191.49/191.41 [5996]~P4(f333(f63(x59961),x59963))+E(f333(f39(x59961),f333(f333(f311(x59961),x59962),x59963)),f333(a117,f333(f39(x59961),x59963)))+P4(f333(f333(f335(x59961),x59962),x59963)) % 191.49/191.41 [6069]~E(x60692,f2(a880))+P4(f333(x60691,f2(a880)))+~P4(f333(x60691,f333(f333(f40(a880),x60693),x60692))) % 191.49/191.41 [6088]~P4(f333(f63(x60881),x60883))+E(f333(f39(x60881),f333(f333(f311(x60881),x60882),x60883)),f333(f39(x60881),x60883))+~P4(f333(f333(f335(x60881),x60882),x60883)) % 191.49/191.41 [6122]~P4(f333(f63(x61221),x61223))+E(f333(f39(x61221),f333(f333(f311(x61221),x61222),x61223)),f333(f333(f81(a880),f79(a880)),f333(f39(x61221),x61223)))+P4(f333(f333(f335(x61221),x61222),x61223)) % 191.49/191.41 [6239]E(f333(f333(f81(a880),x62391),f862(x62391,x62392,x62393)),x62392)+~P4(f333(x62393,f2(a880)))+P4(f333(x62393,f333(f333(f3(a880),x62392),x62391))) % 191.49/191.41 [6240]E(f333(f333(f81(a880),x62401),f863(x62401,x62402,x62403)),x62402)+~P4(f333(x62403,f2(a880)))+P4(f333(x62403,f333(f333(f3(a880),x62402),x62401))) % 191.49/191.41 [6287]~P9(x62871)+~P4(f333(f63(x62871),x62873))+E(f333(f333(f66(x62871,x62871,f115(x62871)),x62872),x62873),f333(f333(f115(x62871),x62872),f41(x62871,x62873))) % 191.49/191.41 [6288]~P9(x62881)+~P4(f333(f63(x62881),x62883))+E(f333(f333(f66(x62881,x62881,f106(x62881)),x62882),x62883),f333(f333(f106(x62881),x62882),f42(x62881,x62883))) % 191.49/191.41 [6294]~P94(x62941)+~E(f333(f108(x62941),x62942),f333(f108(x62941),x62943))+P33(x62941,f333(f108(x62941),f333(f333(f81(a1),x62942),f333(f80(a1),x62943)))) % 191.49/191.41 [6300]~P140(x63001)+E(f333(f333(f3(x63001),f333(f105(x63001),x63002)),f333(f105(x63001),x63003)),f333(f105(x63001),f333(f333(f3(a880),x63002),x63003)))+~P4(f333(f333(f250(a880),x63003),x63002)) % 191.49/191.41 [6386]E(f333(f333(f81(a880),x63861),f862(x63861,x63862,x63863)),x63862)+P4(f333(f333(f251(a880),x63862),x63861))+P4(f333(x63863,f333(f333(f3(a880),x63862),x63861))) % 191.49/191.41 [6387]E(f333(f333(f81(a880),x63871),f863(x63871,x63872,x63873)),x63872)+P4(f333(f333(f251(a880),x63872),x63871))+P4(f333(x63873,f333(f333(f3(a880),x63872),x63871))) % 191.49/191.41 [6402]~P120(x64021)+E(f333(f333(f82(x64021),f333(f76(x64021),x64022)),x64023),f333(f76(x64021),f333(f333(f82(x64021),x64022),x64023)))+~P4(f333(f333(f250(x64021),f2(x64021)),x64023)) % 191.49/191.41 [6403]~P65(x64031)+E(f333(f333(f291(x64031),f333(f76(x64031),x64032)),x64033),f333(f76(x64031),f333(f333(f291(x64031),x64032),x64033)))+~P4(f333(f333(f251(x64031),f2(x64031)),x64033)) % 191.49/191.41 [6411]~P6(x64111)+~P4(f333(f63(x64111),x64113))+E(f333(f333(f66(x64111,x64111,f115(x64111)),x64112),x64113),f12(x64111,f333(f333(f311(x64111),x64112),x64113))) % 191.49/191.41 [6412]~P6(x64121)+~P4(f333(f63(x64121),x64123))+E(f333(f333(f66(x64121,x64121,f106(x64121)),x64122),x64123),f13(x64121,f333(f333(f311(x64121),x64122),x64123))) % 191.49/191.41 [6413]~P109(x64131)+~P4(f333(f63(x64131),x64133))+E(f333(f333(f66(x64131,x64131,f248(x64131)),x64132),x64133),f16(x64131,f333(f333(f311(x64131),x64132),x64133))) % 191.49/191.41 [6414]~P109(x64141)+~P4(f333(f63(x64141),x64143))+E(f333(f333(f66(x64141,x64141,f249(x64141)),x64142),x64143),f17(x64141,f333(f333(f311(x64141),x64142),x64143))) % 191.49/191.41 [6459]E(x64591,f118(x64592))+~E(f180(x64592,x64593),f118(f881(x64592)))+~P4(f333(f333(f335(f881(x64592)),x64591),f333(f173(f881(x64592)),x64593))) % 191.49/191.41 [6500]~P4(f333(f138(x65001),x65003))+P4(f333(f333(f335(x65001),x65002),f333(f173(x65001),x65003)))+P4(f333(f138(x65001),f333(f333(f152(x65001),x65002),x65003))) % 191.49/191.41 [6511]~P97(x65111)+~P4(f333(f63(x65111),x65113))+E(f333(f65(x65111,f82(x65111)),f333(f333(f311(x65111),x65112),x65113)),f333(f333(f66(x65111,x65111,f82(x65111)),x65112),x65113)) % 191.49/191.41 [6530]~P109(x65301)+~P4(f333(f63(x65301),x65303))+E(f14(x65301,f248(x65301),f333(f333(f311(x65301),x65302),x65303)),f333(f333(f66(x65301,x65301,f248(x65301)),x65302),x65303)) % 191.49/191.41 [6531]~P109(x65311)+~P4(f333(f63(x65311),x65313))+E(f15(x65311,f249(x65311),f333(f333(f311(x65311),x65312),x65313)),f333(f333(f66(x65311,x65311,f249(x65311)),x65312),x65313)) % 191.49/191.41 [6533]P4(f333(x65331,f2(a880)))+~P4(f333(f333(f251(a880),x65332),x65333))+~P4(f333(x65331,f333(f333(f3(a880),x65332),x65333))) % 191.49/191.41 [6551]~P120(x65511)+P4(f333(f333(f251(x65511),x65512),x65513))+~P4(f333(f333(f251(x65511),f333(f76(x65511),x65512)),x65513)) % 191.49/191.41 [6553]~P87(x65531)+P4(f333(f333(f250(x65531),x65532),x65533))+~P4(f333(f333(f250(x65531),f333(f76(x65531),x65532)),x65533)) % 191.49/191.41 [6570]E(x65701,f118(x65702))+E(f333(f142(x65702),f333(f333(f139(x65702),x65703),x65701)),f333(f333(f166(x65702),x65701),x65703))+~P4(f333(f333(f251(a880),x65703),f333(f195(f881(x65702)),x65701))) % 191.49/191.41 [6622]~P4(f333(x66221,x66223))+P4(f333(x66221,f427(x66221,x66222)))+~P4(f333(f333(f335(a880),x66223),f333(f303(a880,f2(a880)),x66222))) % 191.49/191.41 [6644]P4(f333(x66441,x66442))+~P4(f333(f333(f251(a880),x66442),x66443))+P4(f333(f333(f335(a880),f424(x66441,x66443)),f333(f303(a880,f2(a880)),x66443))) % 191.49/191.41 [6660]~P123(x66601)+~P4(f333(f333(f251(x66601),f2(x66601)),x66602))+P4(f333(f333(f251(x66601),f2(x66601)),f333(f333(f264(x66601),x66602),x66603))) % 191.49/191.41 [6661]~P123(x66611)+~P4(f333(f333(f250(x66611),f79(x66611)),x66612))+P4(f333(f333(f250(x66611),f79(x66611)),f333(f333(f264(x66611),x66612),x66613))) % 191.49/191.41 [6663]~P123(x66631)+~P4(f333(f333(f250(x66631),f2(x66631)),x66632))+P4(f333(f333(f250(x66631),f2(x66631)),f333(f333(f264(x66631),x66632),x66633))) % 191.49/191.41 [6687]~P4(f333(x66871,x66873))+~P4(f333(f333(f251(a880),x66873),x66872))+P4(f333(f333(f335(a880),f423(x66871,x66872)),f333(f303(a880,f2(a880)),x66872))) % 191.49/191.41 [6694]P4(f333(f63(x66941),x66942))+~P4(f333(f63(x66941),x66943))+~P4(f333(f333(f250(f890(x66941,a874)),x66942),x66943)) % 191.49/191.41 [6702]P4(f333(x67021,x67022))+~P4(f333(x67021,f425(x67021,x67023)))+~P4(f333(f333(f335(a880),x67022),f333(f303(a880,f2(a880)),x67023))) % 191.49/191.41 [6713]E(x67131,f2(a880))+P4(f333(x67132,f409(x67131,x67133,x67132)))+~P4(f333(x67132,f333(f333(f40(a880),x67133),x67131))) % 191.49/191.41 [6721]~P124(x67212)+E(x67211,f2(x67212))+~E(f333(f333(f81(x67212),f333(f333(f82(x67212),x67213),x67213)),f333(f333(f82(x67212),x67211),x67211)),f2(x67212)) % 191.49/191.41 [6722]~P124(x67222)+E(x67221,f2(x67222))+~E(f333(f333(f81(x67222),f333(f333(f82(x67222),x67221),x67221)),f333(f333(f82(x67222),x67223),x67223)),f2(x67222)) % 191.49/191.41 [6761]E(x67611,f2(a880))+~P4(f333(x67612,f406(x67611,x67613,x67612)))+P4(f333(x67612,f333(f333(f40(a880),x67613),x67611))) % 191.49/191.41 [6766]~P109(x67661)+~P17(x67661,x67663)+P17(x67661,f333(f333(f149(x67661,x67661,f7(x67661)),x67662),x67663)) % 191.49/191.41 [6808]P4(f333(x68081,f409(x68082,x68083,x68081)))+P4(f333(x68081,f2(a880)))+~P4(f333(x68081,f333(f333(f40(a880),x68083),x68082))) % 191.49/191.41 [6813]~P94(x68131)+E(f333(f108(x68131),x68132),f333(f108(x68131),x68133))+~P33(x68131,f333(f108(x68131),f333(f333(f81(a1),x68132),f333(f80(a1),x68133)))) % 191.49/191.41 [6877]E(x68771,f2(a1))+E(x68772,f2(a1))+~P4(f333(f50(x68772,x68772),f333(f333(f263(a1,a1),x68773),x68771))) % 191.49/191.41 [6878]E(x68781,f79(a1))+E(x68782,f2(a1))+~P4(f333(f50(x68782,x68782),f333(f333(f263(a1,a1),x68781),x68783))) % 191.49/191.41 [6889]P4(f333(x68891,x68892))+P4(f333(f333(f251(a880),f425(x68891,x68893)),x68893))+~P4(f333(f333(f335(a880),x68892),f333(f303(a880,f2(a880)),x68893))) % 191.49/191.41 [6914]~P4(f333(x69141,f862(x69143,x69142,x69141)))+~P4(f333(x69141,f2(a880)))+P4(f333(x69141,f333(f333(f3(a880),x69142),x69143))) % 191.49/191.41 [6915]~P4(f333(x69151,f863(x69153,x69152,x69151)))+~P4(f333(x69151,f2(a880)))+P4(f333(x69151,f333(f333(f3(a880),x69152),x69153))) % 191.49/191.41 [6916]~P4(f333(x69161,f406(x69163,x69162,x69161)))+~P4(f333(x69161,f2(a880)))+P4(f333(x69161,f333(f333(f40(a880),x69162),x69163))) % 191.49/191.41 [6934]~P4(f333(x69341,x69343))+P4(f333(f333(f251(a880),f427(x69341,x69342)),x69342))+~P4(f333(f333(f335(a880),x69343),f333(f303(a880,f2(a880)),x69342))) % 191.49/191.41 [6935]E(f333(f333(f3(a880),f333(f333(f3(a880),x69351),x69352)),f333(f333(f3(a880),x69353),x69352)),f333(f333(f3(a880),x69351),x69353))+~P4(f333(f333(f250(a880),x69352),x69351))+~P4(f333(f333(f250(a880),x69352),x69353)) % 191.49/191.41 [6971]~P81(x69711)+~P4(f333(f333(f251(x69711),f333(f80(x69711),x69713)),x69712))+P4(f333(f333(f251(x69711),f333(f80(x69711),x69712)),x69713)) % 191.49/191.41 [6972]~P120(x69721)+~P4(f333(f333(f251(x69721),f333(f76(x69721),x69722)),x69723))+P4(f333(f333(f251(x69721),f333(f80(x69721),x69722)),x69723)) % 191.49/191.41 [6974]~P81(x69741)+~P4(f333(f333(f250(x69741),f333(f80(x69741),x69743)),x69742))+P4(f333(f333(f250(x69741),f333(f80(x69741),x69742)),x69743)) % 191.49/191.41 [6976]~P87(x69761)+~P4(f333(f333(f250(x69761),f333(f76(x69761),x69762)),x69763))+P4(f333(f333(f250(x69761),f333(f80(x69761),x69762)),x69763)) % 191.49/191.41 [7012]~P4(f333(x70123,f862(x70122,x70121,x70123)))+P4(f333(f333(f251(a880),x70121),x70122))+P4(f333(x70123,f333(f333(f3(a880),x70121),x70122))) % 191.49/191.41 [7013]~P4(f333(x70133,f863(x70132,x70131,x70133)))+P4(f333(f333(f251(a880),x70131),x70132))+P4(f333(x70133,f333(f333(f3(a880),x70131),x70132))) % 191.49/191.41 [7063]~E(f701(x70633,x70632,x70631),f683(x70633,x70632,x70631))+E(f333(f333(f106(f890(x70631,a874)),x70632),f41(f890(x70631,a874),x70633)),f194(f890(x70631,a874)))+P4(f333(f333(f335(f890(x70631,a874)),x70632),x70633)) % 191.49/191.41 [7071]~P4(f333(f63(x70711),x70713))+P4(f333(f63(x70711),f42(f890(x70711,a874),x70712)))+~P4(f333(f333(f335(f890(x70711,a874)),x70713),x70712)) % 191.49/191.41 [7130]~P109(x71301)+E(f333(f333(f115(f890(x71301,a874)),f333(f303(x71301,x71302),x71303)),f333(f333(f311(x71301),x71303),f194(f890(x71301,a874)))),f304(x71301,x71302,x71303))+~P4(f333(f333(f250(x71301),x71302),x71303)) % 191.49/191.41 [7131]E(x71311,f2(a880))+P4(f333(f333(f251(a880),f407(x71311,x71313,x71312)),x71311))+P4(f333(x71312,f333(f333(f40(a880),x71313),x71311))) % 191.49/191.41 [7166]E(x71661,x71662)+~P4(f333(f333(f250(f890(x71663,a874)),x71661),x71662))+P4(f333(f333(f251(f890(x71663,a874)),x71661),x71662)) % 191.49/191.41 [7179]E(x71791,x71792)+~E(f333(f195(f881(x71793)),x71791),f333(f195(f881(x71793)),x71792))+P4(f333(f333(f251(a880),f575(x71793,x71791,x71792)),f333(f195(f881(x71793)),x71792))) % 191.49/191.41 [7225]P12(x72251,x72252,x72253)+~E(f333(f261(x72251,x72251),x72253),x72252)+~E(f333(f333(f290(x72251,x72251,x72251),f333(f288(x72251,x72251),x72253)),x72253),x72253) % 191.49/191.41 [7295]~P4(f333(x72951,f2(a880)))+P4(f333(f333(f251(a880),f407(x72953,x72952,x72951)),x72953))+P4(f333(x72951,f333(f333(f40(a880),x72952),x72953))) % 191.49/191.41 [7304]~P109(x73041)+E(f333(f333(f115(f890(x73041,a874)),f307(x73041,x73042,x73043)),f333(f333(f311(x73041),x73043),f194(f890(x73041,a874)))),f306(x73041,x73042,x73043))+~P4(f333(f333(f251(x73041),x73042),x73043)) % 191.49/191.41 [7396]~P4(f333(f63(x73961),x73963))+P4(f333(f333(f251(a880),f333(f39(x73961),x73962)),f333(f39(x73961),x73963)))+~P4(f333(f333(f251(f890(x73961,a874)),x73962),x73963)) % 191.49/191.41 [7397]~P4(f333(f63(x73971),x73973))+P4(f333(f333(f250(a880),f333(f39(x73971),x73972)),f333(f39(x73971),x73973)))+~P4(f333(f333(f250(f890(x73971,a874)),x73972),x73973)) % 191.49/191.41 [7435]~P4(f333(x74353,x74352))+P4(f333(f333(f201(x74351),x74352),f485(x74352,x74351,x74353)))+~P4(f333(f333(f201(f33(x74353,x74351)),x74352),x74352)) % 191.49/191.41 [7531]E(x75311,x75312)+~P4(f333(f333(f250(f890(x75313,a874)),x75312),x75311))+~P4(f333(f333(f250(f890(x75313,a874)),x75311),x75312)) % 191.49/191.41 [7534]~P109(x75341)+P17(x75341,x75342)+~P17(x75341,f333(f333(f149(x75341,x75341,f7(x75341)),x75343),x75342)) % 191.49/191.41 [7597]~P4(f333(f333(f251(a880),x75973),x75972))+~P4(f333(f333(f251(a880),x75973),x75971))+P4(f333(f333(f251(a880),f333(f333(f3(a880),x75971),x75972)),f333(f333(f3(a880),x75971),x75973))) % 191.49/191.41 [7598]~P4(f333(f333(f251(a880),x75981),x75983))+~P4(f333(f333(f250(a880),x75982),x75981))+P4(f333(f333(f251(a880),f333(f333(f3(a880),x75981),x75982)),f333(f333(f3(a880),x75983),x75982))) % 191.49/191.41 [7615]~P4(f333(f333(f251(a1),x76152),f2(a1)))+~P4(f333(f333(f250(a1),x76153),x76151))+P4(f333(f333(f250(a1),f333(f333(f40(a1),x76151),x76152)),f333(f333(f40(a1),x76153),x76152))) % 191.49/191.41 [7635]~P4(f333(f333(f251(a880),f2(a880)),x76352))+~P4(f333(f333(f251(a880),x76351),x76353))+P4(f333(f333(f251(a880),f333(f333(f82(a880),x76351),x76352)),f333(f333(f82(a880),x76353),x76352))) % 191.49/191.41 [7636]~P4(f333(f333(f251(a880),f2(a880)),x76361))+~P4(f333(f333(f251(a880),x76362),x76363))+P4(f333(f333(f251(a880),f333(f333(f82(a880),x76361),x76362)),f333(f333(f82(a880),x76361),x76363))) % 191.49/191.41 [7637]~P4(f333(f333(f251(a1),f2(a1)),x76371))+~P4(f333(f333(f251(a1),x76372),x76373))+P4(f333(f333(f251(a1),f333(f333(f82(a1),x76371),x76372)),f333(f333(f82(a1),x76371),x76373))) % 191.49/191.41 [7639]~P4(f333(f333(f251(a880),f2(a880)),x76393))+~P4(f333(f333(f250(a880),x76393),x76392))+P4(f333(f333(f250(a880),f333(f333(f40(a880),x76391),x76392)),f333(f333(f40(a880),x76391),x76393))) % 191.49/191.41 [7640]~P4(f333(f333(f251(a1),f2(a1)),x76402))+~P4(f333(f333(f250(a1),x76401),x76403))+P4(f333(f333(f250(a1),f333(f333(f40(a1),x76401),x76402)),f333(f333(f40(a1),x76403),x76402))) % 191.49/191.41 [7688]E(x76881,f2(a880))+E(f333(f333(f81(a880),f333(f333(f82(a880),x76881),f406(x76881,x76882,x76883))),f407(x76881,x76882,x76883)),x76882)+P4(f333(x76883,f333(f333(f40(a880),x76882),x76881))) % 191.49/191.41 [7748]E(f333(f333(f81(a880),f333(f333(f82(a880),x77481),f406(x77481,x77482,x77483))),f407(x77481,x77482,x77483)),x77482)+~P4(f333(x77483,f2(a880)))+P4(f333(x77483,f333(f333(f40(a880),x77482),x77481))) % 191.49/191.41 [7767]~P4(f333(f63(x77671),x77673))+P4(f333(f333(f335(x77671),f868(x77672,x77673,x77671)),x77673))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f11(x77671,a880),x77672),x77673))) % 191.49/191.41 [7768]~P4(f333(f63(x77681),x77683))+P4(f333(f333(f335(x77681),f348(x77682,x77683,x77681)),x77683))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f11(x77681,a880),x77682),x77683))) % 191.49/191.41 [8058]E(x80581,f194(f890(x80582,a874)))+E(x80581,f333(f333(f311(x80582),x80583),f194(f890(x80582,a874))))+~P4(f333(f333(f250(f890(x80582,a874)),x80581),f333(f333(f311(x80582),x80583),f194(f890(x80582,a874))))) % 191.49/191.41 [8074]~P62(x80741)+P14(x80741,x80742,x80743)+P4(f333(f333(f335(f881(x80741)),f666(x80743,x80742,x80741)),f333(f173(f881(x80741)),f56(x80741,x80743,f57(x80741))))) % 191.49/191.41 [8094]~P4(f333(f333(f251(a880),f2(a880)),x80943))+P4(f333(f333(f251(a880),x80941),x80942))+~P4(f333(f333(f251(a880),f333(f333(f264(a880),x80943),x80941)),f333(f333(f264(a880),x80943),x80942))) % 191.49/191.41 [8096]~P4(f333(f333(f251(a880),f2(a880)),x80963))+P4(f333(f333(f250(a880),x80961),x80962))+~P4(f333(f333(f250(a880),f333(f333(f82(a880),x80963),x80961)),f333(f333(f82(a880),x80963),x80962))) % 191.49/191.41 [8097]~P4(f333(f333(f251(a880),f2(a880)),x80973))+P4(f333(f333(f250(a880),x80971),x80972))+~P4(f333(f333(f250(a880),f333(f333(f82(a880),x80971),x80973)),f333(f333(f82(a880),x80972),x80973))) % 191.49/191.41 [8125]~P62(x81251)+~P13(x81251,x81253,x81252)+P4(f333(f333(f335(f881(x81251)),f665(x81252,x81253,x81251)),f333(f173(f881(x81251)),f56(x81251,x81252,f57(x81251))))) % 191.49/191.41 [8133]~P4(f333(x81331,x81333))+P4(f333(f333(f201(f33(x81331,x81332)),f485(x81333,x81332,x81331)),x81333))+~P4(f333(f333(f201(f33(x81331,x81332)),x81333),x81333)) % 191.49/191.41 [8142]~E(f333(f333(f106(f890(x81421,a874)),f683(x81423,x81422,x81421)),f701(x81423,x81422,x81421)),f194(f890(x81421,a874)))+E(f333(f333(f106(f890(x81421,a874)),x81422),f41(f890(x81421,a874),x81423)),f194(f890(x81421,a874)))+P4(f333(f333(f335(f890(x81421,a874)),x81422),x81423)) % 191.49/191.41 [8159]E(x81591,f118(x81592))+~E(f333(f143(f881(x81592),f881(x81592),f127(x81592),f118(x81592)),x81593),f118(x81592))+~P4(f333(f333(f335(f881(x81592)),x81591),f333(f173(f881(x81592)),x81593))) % 191.49/191.41 [8215]E(x82151,f194(f890(f890(x82152,a874),a874)))+P4(f333(f333(f335(f890(x82152,a874)),f368(x82153,x82151,x82152)),x82151))+P4(f333(f333(f250(f890(x82152,a874)),f42(f890(x82152,a874),x82151)),x82153)) % 191.49/191.41 [8221]~P69(x82211)+~P76(x82211)+E(f333(f333(f8(a1,x82211),f333(f333(f10(a880,x82211,a1),x82212),a109)),f333(f312(a880,a1,f105(a1)),x82213)),f333(f333(f8(a880,x82211),x82212),x82213)) % 191.49/191.41 [8222]~P69(x82221)+~P76(x82221)+E(f333(f333(f11(a1,x82221),f333(f333(f10(a880,x82221,a1),x82222),a109)),f333(f312(a880,a1,f105(a1)),x82223)),f333(f333(f11(a880,x82221),x82222),x82223)) % 191.49/191.41 [8261]~P4(f333(f63(x82611),x82613))+~P4(f333(f333(f251(a880),f2(a880)),f333(x82612,f868(x82612,x82613,x82611))))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f11(x82611,a880),x82612),x82613))) % 191.49/191.41 [8262]~P4(f333(f63(x82621),x82623))+~P4(f333(f333(f251(a880),f2(a880)),f333(x82622,f348(x82622,x82623,x82621))))+P4(f333(f333(f251(a880),f2(a880)),f333(f333(f11(x82621,a880),x82622),x82623))) % 191.49/191.41 [8297]~P64(x82972)+E(x82971,f79(x82972))+E(f333(f333(f291(x82972),f333(f333(f3(x82972),f333(f333(f264(x82972),x82971),x82973)),f79(x82972))),f333(f333(f3(x82972),x82971),f79(x82972))),f333(f333(f8(a880,x82972),f333(f264(x82972),x82971)),f333(f303(a880,f2(a880)),x82973))) % 191.49/191.41 [8352]E(x83521,f2(a880))+~P4(f333(x83523,f333(f333(f40(a880),x83522),x83521)))+P4(f333(f333(f251(a880),x83522),f333(f333(f82(a880),x83521),f333(a117,f409(x83521,x83522,x83523))))) % 191.49/191.41 [8372]P4(f333(x83721,f2(a880)))+~P4(f333(x83721,f333(f333(f40(a880),x83722),x83723)))+P4(f333(f333(f251(a880),x83722),f333(f333(f82(a880),x83723),f333(a117,f409(x83723,x83722,x83721))))) % 191.49/191.41 [8410]E(x84101,f2(a880))+~P4(f333(x84103,f333(f333(f40(a880),x84102),x84101)))+P4(f333(f333(f250(a880),f333(f333(f82(a880),x84101),f409(x84101,x84102,x84103))),x84102)) % 191.49/191.41 [8452]P4(f333(x84521,f2(a880)))+~P4(f333(x84521,f333(f333(f40(a880),x84523),x84522)))+P4(f333(f333(f250(a880),f333(f333(f82(a880),x84522),f409(x84522,x84523,x84521))),x84523)) % 191.49/191.41 [8455]~P109(x84551)+E(f333(f333(f149(x84551,x84551,f7(x84551)),x84552),x84553),f150(x84551,x84551,f7(x84551),x84552,x84553))+P4(f333(f333(f335(x84551),x84552),f333(f173(x84551),x84553))) % 191.49/191.41 [8491]~E(f333(x84913,f727(x84912,x84913,x84911)),f333(x84913,f729(x84912,x84913,x84911)))+~P59(x84911,f333(x84913,f728(x84912,x84913,x84911)))+P59(x84911,f333(f333(f44(x84912,f890(x84911,f890(x84911,a874))),f258(f890(x84912,a874))),x84913)) % 191.49/191.41 [8499]E(x84991,f194(f890(f890(x84992,a874),a874)))+~P4(f333(f333(f250(f890(x84992,a874)),f368(x84993,x84991,x84992)),x84993))+P4(f333(f333(f250(f890(x84992,a874)),f42(f890(x84992,a874),x84991)),x84993)) % 191.49/191.41 [8561]~P66(x85611)+~P4(f333(f333(f251(x85611),x85612),x85613))+P4(f333(f333(f251(x85611),x85612),f333(f333(f291(x85611),f333(f333(f81(x85611),x85612),x85613)),f333(f333(f81(x85611),f79(x85611)),f79(x85611))))) % 191.49/191.41 [8616]~P4(f333(f333(x86161,f505(x86161,x86163,x86162)),f506(x86161,x86163,x86162)))+P4(f333(f333(x86161,x86162),x86163))+~P4(f333(f321(f889(a1,a1),a53),f333(f333(f263(a1,a1),x86162),x86163))) % 191.49/191.41 [8617]~P4(f333(f333(x86171,f507(x86171,x86173,x86172)),f508(x86171,x86173,x86172)))+P4(f333(f333(x86171,x86172),x86173))+~P4(f333(f321(f889(a1,a1),a58),f333(f333(f263(a1,a1),x86172),x86173))) % 191.49/191.41 [8618]~P4(f333(f333(x86181,f510(x86181,x86183,x86182)),f513(x86181,x86183,x86182)))+P4(f333(f333(x86181,x86182),x86183))+~P4(f333(f321(f889(a1,a1),a231),f333(f333(f263(a1,a1),x86182),x86183))) % 191.49/191.41 [8619]~P4(f333(f333(x86191,f514(x86191,x86193,x86192)),f516(x86191,x86193,x86192)))+P4(f333(f333(x86191,x86192),x86193))+~P4(f333(f321(f889(a880,a880),a229),f333(f333(f263(a880,a880),x86192),x86193))) % 191.49/191.41 [8620]~P4(f333(f333(x86201,f586(x86201,x86203,x86202)),f588(x86201,x86203,x86202)))+P4(f333(f333(x86201,x86202),x86203))+~P4(f333(f321(f889(a1,a1),a183),f333(f333(f263(a1,a1),x86202),x86203))) % 191.49/191.41 [8867]P4(f333(f333(x88671,x88672),x88673))+P4(f333(f321(f889(a880,a880),a229),f333(f333(f263(a880,a880),f514(x88671,x88673,x88672)),f516(x88671,x88673,x88672))))+~P4(f333(f321(f889(a880,a880),a229),f333(f333(f263(a880,a880),x88672),x88673))) % 191.49/191.41 [8868]P4(f333(f333(x88681,x88682),x88683))+P4(f333(f321(f889(a1,a1),a53),f333(f333(f263(a1,a1),f505(x88681,x88683,x88682)),f506(x88681,x88683,x88682))))+~P4(f333(f321(f889(a1,a1),a53),f333(f333(f263(a1,a1),x88682),x88683))) % 191.49/191.41 [8869]P4(f333(f333(x88691,x88692),x88693))+P4(f333(f321(f889(a1,a1),a58),f333(f333(f263(a1,a1),f507(x88691,x88693,x88692)),f508(x88691,x88693,x88692))))+~P4(f333(f321(f889(a1,a1),a58),f333(f333(f263(a1,a1),x88692),x88693))) % 191.49/191.41 [8870]P4(f333(f333(x88701,x88702),x88703))+P4(f333(f321(f889(a1,a1),a231),f333(f333(f263(a1,a1),f510(x88701,x88703,x88702)),f513(x88701,x88703,x88702))))+~P4(f333(f321(f889(a1,a1),a231),f333(f333(f263(a1,a1),x88702),x88703))) % 191.49/191.41 [8871]P4(f333(f333(x88711,x88712),x88713))+P4(f333(f321(f889(a1,a1),a183),f333(f333(f263(a1,a1),f586(x88711,x88713,x88712)),f588(x88711,x88713,x88712))))+~P4(f333(f321(f889(a1,a1),a183),f333(f333(f263(a1,a1),x88712),x88713))) % 191.49/191.41 [9209]~P4(f333(f63(x92091),x92093))+P4(f333(f333(f335(f889(f890(x92091,a874),f890(x92091,a874))),f333(f333(f263(f890(x92091,a874),f890(x92091,a874)),x92092),x92093)),f308(x92091)))+~P4(f333(f333(f251(f890(x92091,a874)),x92092),x92093)) % 191.49/191.41 [9288]~P59(x92881,f333(x92883,f728(x92882,x92883,x92881)))+P59(x92881,f333(f333(f44(x92882,f890(x92881,f890(x92881,a874))),f258(f890(x92882,a874))),x92883))+~E(f333(f333(f106(f890(x92881,a874)),f268(x92881,x92881,f333(x92883,f727(x92882,x92883,x92881)))),f269(x92881,x92881,f333(x92883,f729(x92882,x92883,x92881)))),f194(f890(x92881,a874))) % 191.49/191.41 [9359]~P31(a875,f194(f890(f879(a875),a874)),f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),x93591),x93592),x93593)),f194(f890(f879(a875),a874))))+~P27(a875,f194(f890(f879(a875),a874)),f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),x93592),f201(x93592))),f194(f890(f879(a875),a874))))+P27(a875,f194(f890(f879(a875),a874)),f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),x93591),x93592),x93593)),f194(f890(f879(a875),a874)))) % 191.49/191.41 [9479]P50(x94791,x94792,x94793)+P4(f333(f333(f335(f889(x94791,x94791)),f617(x94793,x94792,x94791)),x94793))+~P4(f333(f333(f335(f889(x94791,x94791)),f333(f333(f263(x94791,x94791),f616(x94793,x94792,x94791)),f616(x94793,x94792,x94791))),x94793)) % 191.49/191.41 [10080]P50(x100801,x100802,x100803)+~P4(f333(f333(f272(x100801,x100801,a874),f333(f333(f9(x100801,f890(x100801,a874),f890(x100801,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x100801,a874),f890(x100801,a874)),x100801),f10(a874,a874,x100801)),f333(f333(f10(a874,f890(a874,a874),x100801),a331),f333(f333(f9(x100801,f890(x100801,a874),a874),f335(x100801)),x100802)))),f333(f333(f9(x100801,f890(x100801,a874),a874),f335(x100801)),x100802))),f617(x100803,x100802,x100801)))+~P4(f333(f333(f335(f889(x100801,x100801)),f333(f333(f263(x100801,x100801),f616(x100803,x100802,x100801)),f616(x100803,x100802,x100801))),x100803)) % 191.49/191.41 [5669]~P60(x56692)+E(x56691,f2(x56692))+E(f333(f333(f40(x56692),f333(f333(f82(x56692),x56693),x56691)),x56691),x56693) % 191.49/191.41 [5670]~P60(x56702)+E(x56701,f2(x56702))+E(f333(f333(f40(x56702),f333(f333(f82(x56702),x56701),x56703)),x56701),x56703) % 191.49/191.41 [6458]~P69(x64581)+~E(f333(x64582,f2(a880)),f2(x64581))+E(f333(f333(f8(a880,x64581),x64582),f333(f303(a880,f333(a117,f2(a880))),x64583)),f333(f333(f8(a880,x64581),x64582),f333(f303(a880,f2(a880)),x64583))) % 191.49/191.41 [6583]~P60(x65832)+E(x65831,f2(x65832))+E(f333(f333(f40(x65832),f333(f333(f81(x65832),x65833),x65831)),x65831),f333(f333(f81(x65832),f333(f333(f40(x65832),x65833),x65831)),f79(x65832))) % 191.49/191.41 [6584]~P60(x65842)+E(x65841,f2(x65842))+E(f333(f333(f40(x65842),f333(f333(f81(x65842),x65841),x65843)),x65841),f333(f333(f81(x65842),f333(f333(f40(x65842),x65843),x65841)),f79(x65842))) % 191.49/191.41 [6797]~P4(f333(x67973,f2(a1)))+P4(f333(f333(f250(a880),x67971),x67972))+P4(f333(x67973,f333(f105(a1),f333(f333(f3(a880),x67972),x67971)))) % 191.49/191.41 [6895]P4(f333(f333(f250(a880),x68952),x68951))+P4(f333(f333(f251(a880),x68951),x68952))+P4(f333(x68953,f333(f105(a1),f333(f333(f3(a880),x68951),x68952)))) % 191.49/191.41 [6969]E(f333(f333(f81(a880),f333(f108(a880),x69691)),f333(f333(f81(a880),f333(f108(a880),x69692)),x69693)),f333(f333(f81(a880),f333(f108(a880),x69691)),x69693))+P4(f333(a200,f333(f108(a1),x69691)))+~P4(f333(a200,f333(f108(a1),x69692))) % 191.49/191.41 [7050]~E(x70502,f333(f333(f40(a880),x70503),x70501))+~P4(f333(f333(f251(a880),f2(a880)),x70501))+P4(f333(f333(f250(a880),f333(f333(f82(a880),x70501),x70502)),x70503)) % 191.49/191.41 [7163]~P4(f333(f63(x71631),x71633))+~P4(f333(f63(x71631),x71632))+P4(f333(f63(x71631),f333(f333(f115(f890(x71631,a874)),x71632),x71633))) % 191.49/191.41 [7448]~P109(x74481)+~P4(f333(f63(x74481),x74482))+E(f140(x74481,f333(f333(f3(f890(x74481,a874)),x74482),f333(f333(f311(x74481),x74483),f194(f890(x74481,a874))))),f171(x74481,x74483,f140(x74481,x74482))) % 191.49/191.41 [7511]P4(f333(x75111,f2(a1)))+~P4(f333(f333(f251(a880),x75112),x75113))+~P4(f333(x75111,f333(f105(a1),f333(f333(f3(a880),x75112),x75113)))) % 191.49/191.41 [7528]~P4(f333(f63(x75281),x75282))+E(f333(f39(x75281),f333(f333(f3(f890(x75281,a874)),x75282),f333(f333(f311(x75281),x75283),f194(f890(x75281,a874))))),f333(f39(x75281),x75282))+P4(f333(f333(f335(x75281),x75283),x75282)) % 191.49/191.41 [7655]~P123(x76551)+~P4(f333(f333(f251(x76551),f79(x76551)),x76552))+P4(f333(f333(f251(x76551),f79(x76551)),f333(f333(f82(x76551),x76552),f333(f333(f264(x76551),x76552),x76553)))) % 191.49/191.41 [7699]~P4(f333(f63(x76991),x76993))+E(f333(f333(f3(a880),f333(f39(x76991),x76992)),f333(f39(x76991),x76993)),f333(f39(x76991),f333(f333(f3(f890(x76991,a874)),x76992),x76993)))+~P4(f333(f333(f250(f890(x76991,a874)),x76993),x76992)) % 191.49/191.41 [7757]~P4(f333(f333(f250(a880),x77572),x77573))+~P4(f333(f333(f250(a880),x77571),f333(f333(f3(a880),x77573),x77572)))+P4(f333(f333(f250(a880),f333(f333(f81(a880),x77571),x77572)),x77573)) % 191.49/191.41 [7812]P4(f333(f63(x78121),x78122))+~P4(f333(f63(x78121),x78123))+~P4(f333(f63(x78121),f333(f333(f3(f890(x78121,a874)),x78122),x78123))) % 191.49/191.41 [7818]~P4(f333(f63(x78181),x78182))+E(f333(f39(x78181),f333(f333(f3(f890(x78181,a874)),x78182),f333(f333(f311(x78181),x78183),f194(f890(x78181,a874))))),f333(f333(f3(a880),f333(f39(x78181),x78182)),f79(a880)))+~P4(f333(f333(f335(x78181),x78183),x78182)) % 191.49/191.41 [7889]P59(x78891,x78892)+~P59(x78891,x78893)+~P4(f333(f333(f250(f890(x78891,f890(x78891,a874))),x78892),x78893)) % 191.49/191.41 [7926]~P4(f333(f333(f250(a880),x79263),x79262))+P4(f333(f333(f250(a880),x79261),f333(f333(f3(a880),x79262),x79263)))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),x79261),x79263)),x79262)) % 191.49/191.41 [7944]P40(x79441,x79442)+~P40(x79441,x79443)+~P4(f333(f333(f250(f890(f889(x79441,x79441),a874)),x79442),x79443)) % 191.49/191.41 [7945]P57(x79451,x79452)+~P57(x79451,x79453)+~P4(f333(f333(f250(f890(f889(x79451,x79451),a874)),x79452),x79453)) % 191.49/191.41 [8195]~P123(x81951)+~P4(f333(f333(f251(x81951),f79(x81951)),x81952))+P4(f333(f333(f251(x81951),f333(f333(f264(x81951),x81952),x81953)),f333(f333(f82(x81951),x81952),f333(f333(f264(x81951),x81952),x81953)))) % 191.49/191.41 [8281]~P4(f333(x82811,f2(a1)))+~P4(f333(x82811,f333(f333(f3(a1),f333(f105(a1),x82812)),f333(f105(a1),x82813))))+P4(f333(x82811,f333(f105(a1),f333(f333(f3(a880),x82812),x82813)))) % 191.49/191.41 [8294]~P4(f333(f333(f250(a880),x82943),x82942))+P4(f333(x82941,f333(f333(f3(a1),f333(f105(a1),x82942)),f333(f105(a1),x82943))))+~P4(f333(x82941,f333(f105(a1),f333(f333(f3(a880),x82942),x82943)))) % 191.49/191.41 [8312]P4(f333(f333(f251(a880),x83121),x83122))+~P4(f333(x83123,f333(f333(f3(a1),f333(f105(a1),x83121)),f333(f105(a1),x83122))))+P4(f333(x83123,f333(f105(a1),f333(f333(f3(a880),x83121),x83122)))) % 191.49/191.41 [8364]~P124(x83642)+E(x83641,f2(x83642))+P4(f333(f333(f251(x83642),f2(x83642)),f333(f333(f81(x83642),f333(f333(f82(x83642),x83643),x83643)),f333(f333(f82(x83642),x83641),x83641)))) % 191.49/191.41 [8365]~P124(x83652)+E(x83651,f2(x83652))+P4(f333(f333(f251(x83652),f2(x83652)),f333(f333(f81(x83652),f333(f333(f82(x83652),x83651),x83651)),f333(f333(f82(x83652),x83653),x83653)))) % 191.49/191.41 [8473]~P4(f333(f333(f251(a880),f2(a880)),x84731))+~P4(f333(f333(f251(a1),x84732),x84733))+P4(f333(f333(f251(a1),f333(f333(f82(a1),f333(f105(a1),x84731)),x84732)),f333(f333(f82(a1),f333(f105(a1),x84731)),x84733))) % 191.49/191.41 [8531]E(f333(f333(f106(f890(x85311,a874)),x85312),f41(f890(x85311,a874),x85313)),f194(f890(x85311,a874)))+P4(f333(f333(f335(f890(x85311,a874)),x85312),x85313))+P4(f333(f333(f335(f890(x85311,a874)),f683(x85313,x85312,x85311)),f333(f333(f311(f890(x85311,a874)),x85312),x85313))) % 191.49/191.41 [8532]E(f333(f333(f106(f890(x85321,a874)),x85322),f41(f890(x85321,a874),x85323)),f194(f890(x85321,a874)))+P4(f333(f333(f335(f890(x85321,a874)),x85322),x85323))+P4(f333(f333(f335(f890(x85321,a874)),f701(x85323,x85322,x85321)),f333(f333(f311(f890(x85321,a874)),x85322),x85323))) % 191.49/191.41 [8560]E(x85601,x85602)+~E(f333(f195(f881(x85603)),x85601),f333(f195(f881(x85603)),x85602))+P4(f333(f333(f335(f889(x85603,x85603)),f602(x85603,x85601,x85602)),f333(f173(f889(x85603,x85603)),f333(f333(f182(x85603,x85603),x85602),x85601)))) % 191.49/191.41 [8781]E(f309(x87811,x87812),f309(x87811,x87813))+~P4(f333(f333(f250(f890(f889(x87811,x87811),a874)),x87813),f309(x87811,x87812)))+~P4(f333(f333(f250(f890(f889(x87811,x87811),a874)),x87812),x87813)) % 191.49/191.41 [8844]~P50(x88441,f258(f890(x88441,a874)),x88443)+P4(f333(f333(f250(f890(f889(f881(x88441),f881(x88441)),a874)),f158(x88441,x88442)),f159(x88441,x88443)))+~P4(f333(f333(f250(f890(f889(x88441,x88441),a874)),x88442),x88443)) % 191.49/191.41 [9043]P40(x90431,x90432)+~P4(f333(f333(f335(x90431),x90433),f785(x90432,x90431)))+P4(f333(f333(f335(f889(x90431,x90431)),f333(f333(f263(x90431,x90431),f800(x90432,x90431,x90433)),x90433)),x90432)) % 191.49/191.41 [9070]~P4(f333(f63(x90701),x90702))+P4(f333(f63(f890(x90701,a874)),f333(f333(f62(x90701),x90702),x90703)))+~P4(f333(f333(f250(f890(f889(x90701,x90701),a874)),x90703),f333(f333(f270(x90701,x90701),x90702),f333(f18(f890(x90701,a874),x90701),x90702)))) % 191.49/191.41 [9111]P50(x91111,x91112,x91113)+P4(f333(f333(f335(x91111),f622(x91113,x91112,x91111)),x91112))+~P4(f333(f333(f250(f890(f889(x91111,x91111),a874)),x91113),f333(f333(f270(x91111,x91111),x91112),f333(f18(f890(x91111,a874),x91111),x91112)))) % 191.49/191.41 [9112]P50(x91121,x91122,x91123)+P4(f333(f333(f335(x91121),f629(x91122,x91123,x91121)),x91122))+~P4(f333(f333(f250(f890(f889(x91121,x91121),a874)),x91123),f333(f333(f270(x91121,x91121),x91122),f333(f18(f890(x91121,a874),x91121),x91122)))) % 191.49/191.41 [9152]~P66(x91521)+~P4(f333(f333(f251(x91521),x91522),x91523))+P4(f333(f333(f251(x91521),f333(f333(f291(x91521),f333(f333(f81(x91521),x91522),x91523)),f333(f333(f81(x91521),f79(x91521)),f79(x91521)))),x91523)) % 191.49/191.41 [9181]~P65(x91811)+P4(f333(f333(f250(x91811),x91812),x91813))+~P4(f333(f333(f250(x91811),f333(f333(f82(x91811),f364(x91813,x91812,x91811)),x91812)),x91813)) % 191.49/191.41 [9318]E(f333(f195(f881(f881(x93181))),f333(f137(f881(x93181),f333(f333(f10(a880,a874,f881(x93181)),f333(f251(a880),x93182)),f195(f881(x93181)))),f180(x93181,x93183))),f333(f195(f881(x93181)),f333(f333(f166(f881(x93181)),x93183),x93182)))+~P17(a880,f333(f170(a880),f333(f333(f155(f881(x93181),a880),f195(f881(x93181))),x93183)))+~P4(f333(f333(f251(a880),x93182),f333(f195(f881(f881(x93181))),x93183))) % 191.49/191.41 [9424]~P40(x94241,x94242)+P29(x94241,f333(f333(f263(f890(f889(x94241,x94241),a874),f890(f889(x94241,x94241),a874)),x94242),x94243))+~P4(f333(f333(f250(f890(f889(x94241,x94241),a874)),f333(f333(f290(x94241,x94241,x94241),x94242),x94243)),x94242)) % 191.49/191.41 [9431]E(f333(f333(f155(f881(x94311),x94311),f333(f333(f9(f881(x94311),a880,x94311),f166(x94311)),x94312)),f333(f137(f881(x94311),f333(f333(f10(a880,a874,f881(x94311)),f333(f251(a880),x94312)),f195(f881(x94311)))),f180(x94311,x94313))),f333(f333(f166(f881(x94311)),x94313),x94312))+~P17(a880,f333(f170(a880),f333(f333(f155(f881(x94311),a880),f195(f881(x94311))),x94313)))+~P4(f333(f333(f251(a880),x94312),f333(f195(f881(f881(x94311))),x94313))) % 191.49/191.41 [9576]P50(x95761,x95762,x95763)+~P4(f333(f333(f335(f889(x95761,x95761)),f333(f333(f263(x95761,x95761),f622(x95763,x95762,x95761)),f622(x95763,x95762,x95761))),x95763))+~P4(f333(f333(f250(f890(f889(x95761,x95761),a874)),x95763),f333(f333(f270(x95761,x95761),x95762),f333(f18(f890(x95761,a874),x95761),x95762)))) % 191.49/191.41 [9577]P50(x95771,x95772,x95773)+~P4(f333(f333(f335(f889(x95771,x95771)),f333(f333(f263(x95771,x95771),f629(x95772,x95773,x95771)),f629(x95772,x95773,x95771))),x95773))+~P4(f333(f333(f250(f890(f889(x95771,x95771),a874)),x95773),f333(f333(f270(x95771,x95771),x95772),f333(f18(f890(x95771,a874),x95771),x95772)))) % 191.49/191.41 [9776]~P140(x97761)+~P122(x97761)+E(f333(f333(f291(x97761),f333(f107(x97761),f333(f333(f74(f889(a1,a1),a1,x97762,f262(a1,a1)),f222(x97762)),x97763))),f333(f107(x97761),f333(f333(f74(f889(a1,a1),a1,x97762,f271(a1,a1)),f222(x97762)),x97763))),f232(x97762,x97761,x97763)) % 191.49/191.41 [9955]~E(x99553,f2(a880))+~E(f333(f195(f881(x99551)),f333(f333(f166(f881(x99551)),x99552),f658(x99553,x99551,x99552))),x99553)+E(f333(f333(f155(a880,f881(x99551)),f333(f333(f9(a880,f881(a880),f881(x99551)),f333(f333(f10(f890(a880,x99551),f890(f881(a880),f881(x99551)),a880),f155(a880,x99551)),f333(f9(a880,a880,x99551),f333(f333(f10(f881(x99551),f890(a880,x99551),a880),f166(x99551)),f333(f166(f881(x99551)),x99552))))),f140(a880,f333(f303(a880,f2(a880)),f333(f195(f881(f881(x99551))),x99552))))),f140(a880,f333(f303(a880,f2(a880)),x99553))),f180(x99551,x99552)) % 191.49/191.41 [9956]E(x99561,f118(f881(x99562)))+~E(f333(f195(f881(x99562)),f333(f333(f166(f881(x99562)),x99561),f658(x99563,x99562,x99561))),x99563)+E(f333(f333(f155(a880,f881(x99562)),f333(f333(f9(a880,f881(a880),f881(x99562)),f333(f333(f10(f890(a880,x99562),f890(f881(a880),f881(x99562)),a880),f155(a880,x99562)),f333(f9(a880,a880,x99562),f333(f333(f10(f881(x99562),f890(a880,x99562),a880),f166(x99562)),f333(f166(f881(x99562)),x99561))))),f140(a880,f333(f303(a880,f2(a880)),f333(f195(f881(f881(x99562))),x99561))))),f140(a880,f333(f303(a880,f2(a880)),x99563))),f180(x99562,x99561)) % 191.49/191.41 [9957]~E(x99573,f2(a880))+E(f333(f333(f155(a880,f881(x99571)),f333(f333(f9(a880,f881(a880),f881(x99571)),f333(f333(f10(f890(a880,x99571),f890(f881(a880),f881(x99571)),a880),f155(a880,x99571)),f333(f9(a880,a880,x99571),f333(f333(f10(f881(x99571),f890(a880,x99571),a880),f166(x99571)),f333(f166(f881(x99571)),x99572))))),f140(a880,f333(f303(a880,f2(a880)),f333(f195(f881(f881(x99571))),x99572))))),f140(a880,f333(f303(a880,f2(a880)),x99573))),f180(x99571,x99572))+P4(f333(f333(f251(a880),f658(x99573,x99571,x99572)),f333(f195(f881(f881(x99571))),x99572))) % 191.49/191.41 [9958]E(x99581,f118(f881(x99582)))+E(f333(f333(f155(a880,f881(x99582)),f333(f333(f9(a880,f881(a880),f881(x99582)),f333(f333(f10(f890(a880,x99582),f890(f881(a880),f881(x99582)),a880),f155(a880,x99582)),f333(f9(a880,a880,x99582),f333(f333(f10(f881(x99582),f890(a880,x99582),a880),f166(x99582)),f333(f166(f881(x99582)),x99581))))),f140(a880,f333(f303(a880,f2(a880)),f333(f195(f881(f881(x99582))),x99581))))),f140(a880,f333(f303(a880,f2(a880)),x99583))),f180(x99582,x99581))+P4(f333(f333(f251(a880),f658(x99583,x99582,x99581)),f333(f195(f881(f881(x99582))),x99581))) % 191.49/191.41 [7696]E(f333(f333(f81(a880),f333(f108(a880),x76961)),f333(f333(f81(a880),f333(f108(a880),x76962)),x76963)),f333(f333(f81(a880),f333(f108(a880),f333(f333(f81(a1),x76961),x76962))),x76963))+P4(f333(a200,f333(f108(a1),x76961)))+P4(f333(a200,f333(f108(a1),x76962))) % 191.49/191.41 [8464]~P4(f333(f63(x84641),x84642))+~P4(f333(f333(f335(x84641),x84643),x84642))+E(f333(a117,f333(f39(x84641),f333(f333(f3(f890(x84641,a874)),x84642),f333(f333(f311(x84641),x84643),f194(f890(x84641,a874)))))),f333(f39(x84641),x84642)) % 191.49/191.41 [8481]~P4(f333(f63(x84811),x84812))+~P4(f333(f333(f335(x84811),x84813),x84812))+E(f333(f333(f81(a880),f79(a880)),f333(f39(x84811),f333(f333(f3(f890(x84811,a874)),x84812),f333(f333(f311(x84811),x84813),f194(f890(x84811,a874)))))),f333(f39(x84811),x84812)) % 191.49/191.41 [8568]~P109(x85681)+~P4(f333(f63(x85681),x85683))+E(f333(f333(f149(x85681,x85681,f7(x85681)),x85682),f140(x85681,f333(f333(f3(f890(x85681,a874)),x85683),f333(f333(f311(x85681),x85682),f194(f890(x85681,a874)))))),f140(x85681,f333(f333(f311(x85681),x85682),x85683))) % 191.49/191.41 [8710]~P4(f333(f63(x87101),x87103))+~P4(f333(f63(x87101),x87102))+E(f333(f333(f81(a880),f333(f39(x87101),f333(f333(f115(f890(x87101,a874)),x87102),x87103))),f333(f39(x87101),f333(f333(f106(f890(x87101,a874)),x87102),x87103))),f333(f333(f81(a880),f333(f39(x87101),x87102)),f333(f39(x87101),x87103))) % 191.49/191.41 [9915]~P28(x99151,f890(f890(x99151,a874),a874),f333(f333(f9(x99151,f890(f889(x99151,x99151),a874),f890(f890(x99151,a874),a874)),f333(f333(f10(f890(x99151,a874),f890(f890(f889(x99151,x99151),a874),f890(f890(x99151,a874),a874)),x99151),f62(x99151)),f333(f333(f9(x99151,f890(x99151,a874),f890(x99151,a874)),f311(x99151)),f194(f890(x99151,a874))))),x99153),x99152)+~P4(f333(f63(x99151),x99152))+E(f333(f39(f890(x99151,a874)),f333(f333(f62(x99151),x99152),x99153)),f333(f39(x99151),x99152)) % 191.49/191.41 [8105]~P94(x81051)+P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x81053)))+E(f333(f333(f264(x81051),x81052),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x81053)),x81053))),f79(x81051)) % 191.49/191.41 [9415]~P94(x94151)+~P4(f333(f333(f250(a1),f2(a1)),f333(f108(a1),x94153)))+E(f333(f333(f264(x94151),x94152),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x94153)),x94153))),f333(f333(f89(x94151,x94151),f333(f333(f264(x94151),x94152),f333(f108(a880),x94153))),f333(f333(f20(x94151,x94151,x94151),f333(f333(f10(x94151,f890(x94151,x94151),x94151),f82(x94151)),f333(f82(x94151),x94152))),f7(x94151)))) % 191.49/191.41 [9833]~P4(f333(f138(x98331),x98333))+~P4(f333(f333(f335(x98331),x98332),f333(f173(x98331),x98333)))+E(f333(f333(f139(x98331),f333(f195(f881(x98331)),f177(x98331,f333(f333(f10(a874,a874,x98331),a328),f333(f333(f9(x98331,x98331,a874),a330),x98332)),f333(f170(x98331),x98333)))),f333(f170(x98331),x98333)),f333(f333(f152(x98331),x98332),f333(f170(x98331),f177(x98331,f333(f333(f10(a874,a874,x98331),a328),f333(f333(f9(x98331,x98331,a874),a330),x98332)),x98333)))) % 191.49/191.41 [9898]P4(f333(f333(f250(f890(f889(x98981,x98981),a874)),f309(x98981,x98982)),x98983))+~P4(f333(f333(f250(f890(f889(x98981,x98981),a874)),f309(x98981,f194(f890(f889(x98981,x98981),a874)))),x98983))+~P4(f333(f333(f250(f890(f889(x98981,x98981),a874)),f333(f333(f290(x98981,x98981,x98981),f333(f333(f106(f890(f889(x98981,x98981),a874)),f309(x98981,x98982)),x98983)),x98982)),x98983)) % 191.49/191.41 [9740]~P4(f333(f63(x97401),f333(f255(x97401),x97403)))+~P4(f333(f63(x97401),f333(f255(x97401),x97402)))+P4(f333(f63(x97401),f333(f255(x97401),f333(f333(f20(x97401,a874,a874),f333(f333(f10(a874,f890(a874,a874),x97401),a332),x97402)),x97403)))) % 191.49/191.41 [10018]P4(f333(f333(f250(f890(f889(x100181,x100181),a874)),f333(f333(f290(x100181,x100181,x100181),x100182),f309(x100181,x100182))),x100183))+~P4(f333(f333(f250(f890(f889(x100181,x100181),a874)),x100182),x100183))+~P4(f333(f333(f250(f890(f889(x100181,x100181),a874)),f333(f333(f290(x100181,x100181,x100181),f333(f333(f106(f890(f889(x100181,x100181),a874)),f333(f333(f290(x100181,x100181,x100181),x100182),f309(x100181,x100182))),x100183)),x100182)),x100183)) % 191.49/191.41 [9977]~P4(f333(f138(x99771),x99773))+~P4(f333(f333(f335(x99771),x99772),f333(f173(x99771),x99773)))+E(f333(f170(x99771),f333(f172(x99771),f333(f333(f139(x99771),f333(f195(f881(x99771)),f177(x99771,f333(f333(f10(a874,a874,x99771),a328),f333(f333(f9(x99771,x99771,a874),a330),x99772)),x99773))),x99773))),f177(x99771,f333(f333(f10(a874,a874,x99771),a328),f333(f333(f9(x99771,x99771,a874),a330),x99772)),f333(f170(x99771),x99773))) % 191.49/191.41 [10147]~P120(x101472)+E(x101471,f2(x101472))+~E(f333(f333(f81(x101472),f333(f333(f264(x101472),x101473),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101472),x101471),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f2(x101472)) % 191.49/191.41 [10148]~P120(x101482)+E(x101481,f2(x101482))+~E(f333(f333(f81(x101482),f333(f333(f264(x101482),x101481),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101482),x101483),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f2(x101482)) % 191.49/191.41 [10181]~P120(x101812)+E(x101811,f2(x101812))+P4(f333(f333(f251(x101812),f2(x101812)),f333(f333(f81(x101812),f333(f333(f264(x101812),x101813),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101812),x101811),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))))) % 191.49/191.41 [10182]~P120(x101822)+E(x101821,f2(x101822))+P4(f333(f333(f251(x101822),f2(x101822)),f333(f333(f81(x101822),f333(f333(f264(x101822),x101821),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101822),x101823),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))))) % 191.49/191.41 [10203]~P120(x102031)+P4(f333(f333(f250(x102031),f2(x102031)),x102032))+~P4(f333(f333(f250(x102031),f2(x102031)),f333(f333(f264(x102031),x102032),f333(a117,f333(f333(f82(a880),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),x102033))))) % 191.49/191.41 [5510]~P27(x55101,x55104,x55103)+P27(x55101,x55102,x55103)+~P27(x55101,x55102,x55104) % 191.49/191.41 [4975]~E(x49752,f91(x49753,x49751))+P4(f333(x49751,x49752))+~P4(f333(x49751,x49754)) % 191.49/191.41 [6714]~P40(x67142,x67144)+~P40(x67141,x67143)+P40(f889(x67141,x67142),f326(x67141,x67142,x67143,x67144)) % 191.49/191.41 [5153]~P11(x51534,x51531)+~E(f333(x51531,x51532),f333(x51531,x51533))+P4(f333(f333(x51531,x51532),x51533)) % 191.49/191.41 [5328]~P11(x53284,x53281)+E(f333(x53281,x53282),f333(x53281,x53283))+~P4(f333(f333(x53281,x53282),x53283)) % 191.49/191.41 [5419]~P21(x54193,x54194,x54191)+E(f333(x54191,x54192),f333(f65(x54193,x54194),x54192))+~P4(f333(f63(x54193),x54192)) % 191.49/191.41 [5420]~P2(x54203,x54204,x54201)+E(f333(x54201,x54202),f333(f65(x54203,x54204),x54202))+~P4(f333(f63(x54203),x54202)) % 191.49/191.41 [5543]~P11(x55434,x55431)+~P4(f333(f333(x55431,x55433),x55432))+P4(f333(f333(x55431,x55432),x55433)) % 191.49/191.41 [5612]E(x56121,x56122)+~E(f333(f262(x56123,x56124),x56121),f333(f262(x56123,x56124),x56122))+~E(f333(f271(x56123,x56124),x56121),f333(f271(x56123,x56124),x56122)) % 191.49/191.41 [5637]E(x56371,x56372)+~P4(f333(f49(x56373,x56374),x56372))+~P4(f333(f49(x56373,x56374),x56371)) % 191.49/191.41 [5828]~P69(x58282)+E(f240(x58281,x58282,x58283,x58284),f2(x58282))+P4(f333(f63(x58281),x58284)) % 191.49/191.41 [5964]~P4(f333(f321(x59641,x59642),x59644))+P4(f333(f321(x59641,x59642),x59643))+~P4(f333(f333(x59642,x59643),x59644)) % 191.49/191.41 [7884]~P109(x78842)+~P4(f333(f138(x78841),x78844))+P4(f333(f138(x78841),f151(x78841,x78842,x78843,x78844))) % 191.49/191.41 [8112]~P4(f333(f63(x81122),x81124))+~P4(f333(f63(x81121),x81123))+P4(f333(f63(f888(x81121,x81122)),f320(x81121,x81122,x81123,x81124))) % 191.49/191.41 [8113]~P4(f333(f138(x81132),x81134))+~P4(f333(f138(x81131),x81133))+P4(f333(f138(f889(x81131,x81132)),f61(x81131,x81132,x81133,x81134))) % 191.49/191.41 [8117]P4(f333(f333(f335(f881(x81171)),f333(f333(f127(x81171),x81172),x81173)),f162(x81171,x81174)))+~P4(f333(f333(f335(f881(x81171)),x81173),f162(x81171,x81174)))+~P4(f333(f333(f335(f881(x81171)),x81172),f162(x81171,x81174))) % 191.49/191.41 [8431]P4(f333(x84311,x84312))+~E(x84313,f333(f242(x84314),x84312))+~P4(f333(x84311,f400(x84312,x84311,x84313,x84314))) % 191.49/191.41 [8443]~P109(x84433)+~P4(f333(f138(x84431),f151(x84431,x84433,x84434,x84432)))+P4(f333(f138(x84431),x84432)) % 191.49/191.41 [8701]~P4(f333(f333(f335(f889(x87011,x87011)),f333(f333(f263(x87011,x87011),x87012),x87014)),f309(x87011,x87013)))+P4(f333(f333(f335(x87011),x87012),f322(x87011,x87013)))+~P4(f333(f333(f335(x87011),x87014),f322(x87011,x87013))) % 191.49/191.41 [8722]~E(x87224,f333(f242(x87223),x87222))+P4(f333(x87221,x87222))+P4(f333(f333(f335(x87223),f400(x87222,x87221,x87224,x87223)),f241(x87223,x87224))) % 191.49/191.41 [5138]~P69(x51382)+E(f333(f333(f8(x51381,x51382),x51383),x51384),f2(x51382))+P4(f333(f63(x51381),x51384)) % 191.49/191.41 [5141]~P76(x51412)+E(f333(f333(f11(x51411,x51412),x51413),x51414),f79(x51412))+P4(f333(f63(x51411),x51414)) % 191.49/191.41 [5292]~P70(x52923)+E(x52921,x52922)+~E(f333(f333(f81(x52923),x52924),x52921),f333(f333(f81(x52923),x52924),x52922)) % 191.49/191.41 [5293]~P71(x52933)+E(x52931,x52932)+~E(f333(f333(f81(x52933),x52934),x52931),f333(f333(f81(x52933),x52934),x52932)) % 191.49/191.41 [5295]~P70(x52953)+E(x52951,x52952)+~E(f333(f333(f81(x52953),x52951),x52954),f333(f333(f81(x52953),x52952),x52954)) % 191.49/191.41 [5415]~P9(x54153)+E(x54151,f194(f890(x54152,a874)))+E(f333(f333(f43(x54152,x54153),x54151),f333(f18(x54153,x54152),x54154)),x54154) % 191.49/191.41 [5416]~P9(x54163)+E(x54161,f194(f890(x54162,a874)))+E(f333(f333(f44(x54162,x54163),x54161),f333(f18(x54163,x54162),x54164)),x54164) % 191.49/191.41 [5625]~P110(x56253)+E(x56251,x56252)+~E(f304(x56253,x56254,x56251),f333(f333(f311(x56253),x56252),f194(f890(x56253,a874)))) % 191.49/191.41 [5626]~P110(x56263)+E(x56261,x56262)+~E(f304(x56263,x56261,x56262),f333(f333(f311(x56263),x56264),f194(f890(x56263,a874)))) % 191.49/191.41 [5686]~P38(x56863,x56861,x56864)+P38(x56863,x56861,f333(f333(f152(x56863),x56862),x56864))+P4(f333(x56861,x56862)) % 191.49/191.41 [5788]~P34(x57881,x57882,x57884)+~P4(f333(x57882,x57883))+P34(x57881,x57882,f333(f333(f152(x57881),x57883),x57884)) % 191.49/191.41 [5921]P4(f333(x59211,x59212))+~P4(f333(f267(x59213,x59211),x59214))+~P4(f333(f333(f335(x59213),x59212),x59214)) % 191.49/191.41 [5930]~P34(x59301,x59302,x59304)+~P34(x59301,x59302,x59303)+P34(x59301,x59302,f333(f333(f127(x59301),x59303),x59304)) % 191.49/191.41 [5939]P36(x59391,x59392,x59393)+~P36(x59391,x59392,f333(f333(f152(x59391),x59394),x59393))+P4(f333(x59392,x59394)) % 191.49/191.41 [5940]P38(x59401,x59402,x59403)+~P38(x59401,x59402,f333(f333(f152(x59401),x59404),x59403))+P4(f333(x59402,x59404)) % 191.49/191.41 [5953]E(x59531,x59532)+~P4(f333(f333(f201(x59533),x59534),x59532))+~P4(f333(f333(f201(x59533),x59534),x59531)) % 191.49/191.41 [6019]P36(x60191,x60192,x60193)+P36(x60191,x60192,x60194)+~P36(x60191,x60192,f333(f333(f127(x60191),x60194),x60193)) % 191.49/191.41 [6038]~P69(x60381)+E(f333(f333(f8(a880,x60381),x60382),f333(f303(a880,x60383),f333(a117,x60384))),f2(x60381))+~P4(f333(f333(f251(a880),x60384),x60383)) % 191.49/191.41 [6043]~P61(x60431)+~E(f46(x60431,x60432,x60433),f46(x60431,x60434,x60433))+E(f46(x60431,f333(f80(x60431),x60432),x60433),f46(x60431,f333(f80(x60431),x60434),x60433)) % 191.49/191.41 [6111]P4(f333(x61111,x61112))+~E(f333(f137(x61113,x61111),x61114),x61114)+~P4(f333(f333(f335(x61113),x61112),f333(f173(x61113),x61114))) % 191.49/191.41 [6130]~E(f333(f333(f81(a880),x61303),x61302),f333(f333(f81(a880),x61301),x61304))+~P4(f333(f333(f251(a880),x61303),x61304))+P4(f333(f333(f251(a880),x61301),x61302)) % 191.49/191.41 [6134]P36(x61341,x61342,x61343)+~P4(f333(x61342,x61344))+~P4(f333(f333(f335(x61341),x61344),f333(f173(x61341),x61343))) % 191.49/191.41 [6172]~P34(x61723,x61721,x61724)+P4(f333(x61721,x61722))+~P4(f333(f333(f335(x61723),x61722),f333(f173(x61723),x61724))) % 191.49/191.41 [6174]~E(f333(f137(x61741,x61742),x61743),f118(x61741))+~P4(f333(x61742,x61744))+~P4(f333(f333(f335(x61741),x61744),f333(f173(x61741),x61743))) % 191.49/191.41 [6175]~E(f177(x61753,x61751,x61754),x61754)+P4(f333(x61751,x61752))+~P4(f333(f333(f335(x61753),x61752),f333(f173(x61753),x61754))) % 191.49/191.41 [6205]~E(x62054,f194(f890(x62052,a874)))+~E(x62053,f194(f890(x62051,a874)))+E(f320(x62051,x62052,x62053,x62054),f194(f890(f888(x62051,x62052),a874))) % 191.49/191.41 [6346]P4(f333(x63461,x63462))+~P4(f333(f161(x63463,x63461),x63464))+~P4(f333(f333(f335(x63463),x63462),f333(f173(x63463),x63464))) % 191.49/191.41 [6612]~P69(x66121)+E(f333(f333(f8(a880,x66121),x66122),f304(a880,x66123,f333(a117,x66124))),f2(x66121))+~P4(f333(f333(f251(a880),f333(a117,x66124)),x66123)) % 191.49/191.41 [6753]~P109(x67531)+E(f333(f333(f3(f890(x67531,a874)),f333(f303(x67531,x67532),x67533)),f333(f303(x67531,x67532),x67534)),f333(f303(x67531,x67534),x67533))+~P4(f333(f333(f250(x67531),x67532),x67534)) % 191.49/191.41 [7095]~P4(f333(f333(f335(f881(x70951)),x70954),f162(x70951,x70953)))+P4(f333(f333(f335(x70951),x70952),x70953))+~P4(f333(f333(f335(x70951),x70952),f333(f173(x70951),x70954))) % 191.49/191.41 [7102]~P40(x71021,x71022)+P4(f333(f333(f335(x71021),f786(x71022,x71021,x71023)),x71023))+~P4(f333(f333(f335(x71021),x71024),x71023)) % 191.49/191.41 [7158]~P69(x71581)+E(f333(f333(f333(f67(x71581,x71582,f81(x71581)),x71583),f2(x71581)),x71584),f333(f333(f8(x71582,x71581),x71583),x71584))+~P4(f333(f63(x71582),x71584)) % 191.49/191.41 [7160]~P76(x71601)+E(f333(f333(f333(f67(x71601,x71602,f82(x71601)),x71603),f79(x71601)),x71604),f333(f333(f11(x71602,x71601),x71603),x71604))+~P4(f333(f63(x71602),x71604)) % 191.49/191.41 [7188]P28(x71881,x71882,x71883,x71884)+~E(f333(f39(x71882),f333(f312(x71881,x71882,x71883),x71884)),f333(f39(x71881),x71884))+~P4(f333(f63(x71881),x71884)) % 191.49/191.41 [7364]~P69(x73641)+E(f333(f333(f81(x73641),f333(x73642,x73643)),f333(f333(f8(a880,x73641),x73642),f306(a880,x73643,x73644))),f333(f333(f8(a880,x73641),x73642),f304(a880,x73643,x73644)))+~P4(f333(f333(f250(a880),x73643),x73644)) % 191.49/191.41 [7374]~P69(x73741)+~P28(x73742,x73741,x73743,x73744)+E(f333(f333(f8(x73741,x73741),f35(x73741)),f333(f312(x73742,x73741,x73743),x73744)),f333(f333(f8(x73742,x73741),x73743),x73744)) % 191.49/191.41 [7375]~P76(x73751)+~P28(x73752,x73751,x73753,x73754)+E(f333(f333(f11(x73751,x73751),f35(x73751)),f333(f312(x73752,x73751,x73753),x73754)),f333(f333(f11(x73752,x73751),x73753),x73754)) % 191.49/191.41 [7428]E(f333(f39(f888(x74281,x74282)),f320(x74281,x74282,x74283,x74284)),f333(f333(f81(a880),f333(f39(x74281),x74283)),f333(f39(x74282),x74284)))+~P4(f333(f63(x74282),x74284))+~P4(f333(f63(x74281),x74283)) % 191.49/191.41 [7512]E(x75121,x75122)+P4(f333(f333(f335(x75123),x75121),f333(f173(x75123),f171(x75123,x75122,x75124))))+~P4(f333(f333(f335(x75123),x75121),f333(f173(x75123),x75124))) % 191.49/191.41 [7732]~P69(x77321)+E(f333(f333(f81(x77321),f333(f333(f8(a880,x77321),x77322),f333(f303(a880,x77323),x77324))),f333(x77322,x77324)),f333(f333(f8(a880,x77321),x77322),f333(f303(a880,x77323),f333(a117,x77324))))+P4(f333(f333(f251(a880),x77324),x77323)) % 191.49/191.41 [7788]~P28(x77881,x77882,x77883,f258(f890(x77881,a874)))+~P4(f333(f63(x77882),x77884))+P4(f333(f63(x77881),f333(f313(x77881,x77882,x77883),x77884))) % 191.49/191.41 [7897]P4(f333(f333(f335(f881(x78971)),f333(f333(f152(x78971),x78972),x78973)),f162(x78971,x78974)))+~P4(f333(f333(f335(f881(x78971)),x78973),f162(x78971,x78974)))+~P4(f333(f333(f335(x78971),x78972),x78974)) % 191.49/191.41 [7982]~E(f333(f312(x79823,x79821,x79824),f258(f890(x79823,a874))),f258(f890(x79821,a874)))+P4(f333(f63(x79821),x79822))+~P4(f333(f63(x79823),f333(f313(x79823,x79821,x79824),x79822))) % 191.49/191.41 [8083]~P28(x80831,x80833,x80834,x80832)+P4(f333(f63(x80831),x80832))+~P4(f333(f63(x80833),f333(f312(x80831,x80833,x80834),x80832))) % 191.49/191.41 [8104]~E(x81042,x81043)+P4(f333(f333(f335(f889(x81041,x81041)),f333(f333(f263(x81041,x81041),x81042),x81043)),f260(x81041,x81044)))+~P4(f333(f333(f335(x81041),x81042),x81044)) % 191.49/191.41 [8144]~P69(x81441)+E(f333(f333(f81(x81441),f333(f333(f8(a880,x81441),x81442),f304(a880,x81443,x81444))),f333(x81442,f333(a117,x81444))),f333(f333(f8(a880,x81441),x81442),f304(a880,x81443,f333(a117,x81444))))+P4(f333(f333(f251(a880),f333(a117,x81444)),x81443)) % 191.49/191.41 [8207]P4(f333(x82071,x82072))+~P4(f333(x82071,f333(f333(f166(x82073),x82074),f579(x82071,x82074,x82073))))+~P4(f333(f333(f335(x82073),x82072),f333(f173(x82073),x82074))) % 191.49/191.41 [8342]~P4(f333(f333(f335(x83421),x83422),f322(x83421,x83424)))+P4(f333(f333(f335(f881(x83421)),f333(f333(f152(x83421),x83422),x83423)),f322(f881(x83421),f158(x83421,x83424))))+~P4(f333(f333(f335(f881(x83421)),x83423),f322(f881(x83421),f158(x83421,x83424)))) % 191.49/191.41 [8355]~P28(x83552,x83553,x83554,f847(x83554,x83553,x83552,x83551))+P28(x83552,x83553,x83554,f42(f890(x83552,a874),x83551))+E(x83551,f194(f890(f890(x83552,a874),a874))) % 191.49/191.41 [8629]E(x86291,x86292)+~P4(f333(f333(f335(f889(x86293,x86293)),f333(f333(f263(x86293,x86293),x86291),x86292)),f309(x86293,x86294)))+P4(f333(f333(f335(x86293),x86291),f333(f261(x86293,x86293),x86294))) % 191.49/191.41 [8905]P28(x89052,x89053,x89054,f42(f890(x89052,a874),x89051))+E(x89051,f194(f890(f890(x89052,a874),a874)))+P4(f333(f333(f335(f890(x89052,a874)),f847(x89054,x89053,x89052,x89051)),x89051)) % 191.49/191.41 [9036]P4(f333(f63(x90361),x90362))+~P4(f333(f63(x90364),f333(f312(x90361,x90364,x90363),x90362)))+P4(f333(f333(f335(x90361),f719(x90363,x90364,x90362,x90361)),x90362)) % 191.49/191.41 [9127]~P9(x91272)+E(f333(f333(f66(x91271,x91272,f333(f333(f10(x91272,f890(x91272,x91272),x91271),f106(x91272)),x91273)),f258(x91272)),x91274),f333(f333(f43(x91271,x91272),x91274),x91273))+~P4(f333(f63(x91271),x91274)) % 191.49/191.41 [9128]~P9(x91282)+E(f333(f333(f66(x91281,x91282,f333(f333(f10(x91282,f890(x91282,x91282),x91281),f115(x91282)),x91283)),f194(x91282)),x91284),f333(f333(f44(x91281,x91282),x91284),x91283))+~P4(f333(f63(x91281),x91284)) % 191.49/191.41 [9212]P4(f333(x92121,x92122))+~P4(f333(x92121,f333(f333(f166(x92123),x92124),f686(x92122,x92121,x92124,x92123))))+~P4(f333(f333(f335(x92123),x92122),f333(f173(x92123),x92124))) % 191.49/191.41 [9232]E(x92321,x92322)+~P4(f333(f333(f335(f889(x92323,x92323)),f333(f333(f263(x92323,x92323),x92321),x92322)),f309(x92323,x92324)))+P4(f333(f333(f335(f889(x92323,x92323)),f333(f333(f263(x92323,x92323),x92321),x92322)),f333(f333(f290(x92323,x92323,x92323),x92324),f309(x92323,x92324)))) % 191.49/191.41 [9289]~E(f333(f195(f881(x92891)),x92892),f333(f195(f881(x92891)),x92893))+~P4(f333(f333(f335(f889(f881(x92891),f881(x92891))),f333(f333(f263(f881(x92891),f881(x92891)),x92892),x92893)),f148(x92891,x92894)))+P4(f333(f333(f335(f889(f881(x92891),f881(x92891))),f333(f333(f263(f881(x92891),f881(x92891)),x92892),x92893)),f146(x92891,x92894))) % 191.49/191.41 [9525]P34(x95251,f333(f333(f20(x95251,a874,a874),f333(f333(f10(a874,f890(a874,a874),x95251),a332),f333(f333(f10(a874,a874,x95251),a328),x95252))),f333(a330,x95253)),x95254)+~P4(f333(x95252,x95253))+~P38(x95251,x95252,f333(f333(f152(x95251),x95253),x95254)) % 191.49/191.41 [9697]~P34(x96971,f333(f333(f20(x96971,a874,a874),f333(f333(f10(a874,f890(a874,a874),x96971),a332),f333(f333(f10(a874,a874,x96971),a328),x96972))),f333(a330,x96973)),x96974)+~P4(f333(x96972,x96973))+P38(x96971,x96972,f333(f333(f152(x96971),x96973),x96974)) % 191.49/191.41 [9701]~P38(x97011,x97012,x97014)+~P34(x97011,f333(f333(f20(x97011,a874,a874),f333(f333(f10(a874,f890(a874,a874),x97011),a332),f333(f333(f10(a874,a874,x97011),a328),x97012))),f333(a330,x97013)),x97014)+P38(x97011,x97012,f333(f333(f152(x97011),x97013),x97014)) % 191.49/191.41 [9743]~P68(x97431)+E(f333(f333(f8(a880,x97431),f333(f333(f20(a880,x97431,x97431),f333(f333(f10(x97431,f890(x97431,x97431),a880),f3(x97431)),x97432)),f333(f333(f10(a880,x97431,a880),x97432),f333(f333(f9(a880,a880,a880),f81(a880)),f79(a880))))),f304(a880,x97433,x97434)),f2(x97431))+P4(f333(f333(f250(a880),x97433),x97434)) % 191.49/191.41 [9971]~P40(x99712,x99714)+~P28(x99712,x99711,x99713,f258(f890(x99712,a874)))+P40(x99711,f333(f312(f889(x99712,x99712),f889(x99711,x99711),f273(x99712,x99711,x99712,x99711,x99713,x99713)),x99714)) % 191.49/191.41 [10159]~E(f333(f195(f881(x101591)),x101593),f333(f195(f881(x101591)),x101592))+P4(f333(f333(f335(f889(f881(x101591),f881(x101591))),f333(f333(f263(f881(x101591),f881(x101591)),x101592),x101593)),f159(x101591,x101594)))+~P4(f333(f333(f272(x101591,x101591,a874),f333(f333(f9(x101591,f890(f889(x101591,x101591),a874),f890(x101591,a874)),f333(f333(f10(f890(x101591,f890(f890(f889(x101591,x101591),a874),a874)),f890(f890(f889(x101591,x101591),a874),f890(x101591,a874)),x101591),f9(x101591,f890(f889(x101591,x101591),a874),a874)),f333(f333(f10(f890(x101591,f889(x101591,x101591)),f890(x101591,f890(f890(f889(x101591,x101591),a874),a874)),x101591),f333(f10(f889(x101591,x101591),f890(f890(f889(x101591,x101591),a874),a874),x101591),f335(f889(x101591,x101591)))),f263(x101591,x101591)))),x101594)),f595(x101594,x101593,x101592,x101591))) % 191.49/191.41 [6003]~E(x60034,x60032)+P4(f333(x60031,x60032))+P4(f333(f333(f201(f33(x60031,x60033)),x60032),x60034)) % 191.49/191.41 [6095]~P60(x60951)+~E(x60952,f2(x60951))+E(f333(f333(f40(x60951),f333(f333(f82(x60951),x60952),x60953)),f333(f333(f82(x60951),x60952),x60954)),f2(x60951)) % 191.49/191.41 [6133]E(x61331,f118(x61332))+E(x61333,f333(f333(f3(a880),f333(f195(f881(x61332)),x61331)),f79(a880)))+E(f145(x61332,f333(f333(f160(x61332,x61331),x61333),x61334)),f145(x61332,x61331)) % 191.49/191.41 [6163]E(x61631,x61632)+P4(f333(x61633,x61632))+~P4(f333(f333(f333(f311(x61634),x61631),x61633),x61632)) % 191.49/191.41 [6179]~P69(x61791)+~P4(f333(f138(x61792),x61794))+E(f333(f167(x61791),f333(f333(f155(x61792,x61791),x61793),x61794)),f333(f333(f8(x61792,x61791),x61793),f333(f173(x61792),x61794))) % 191.49/191.41 [6198]~P76(x61982)+~P4(f333(f63(x61981),x61984))+E(f333(f333(f11(x61981,x61982),f333(f18(x61982,x61981),x61983)),x61984),f333(f333(f264(x61982),x61983),f333(f39(x61981),x61984))) % 191.49/191.41 [6252]~P63(x62522)+E(x62521,f2(x62522))+E(f333(f333(f291(x62522),f333(f333(f82(x62522),x62523),x62521)),f333(f333(f82(x62522),x62524),x62521)),f333(f333(f291(x62522),x62523),x62524)) % 191.49/191.41 [6253]~P63(x62532)+E(x62531,f2(x62532))+E(f333(f333(f291(x62532),f333(f333(f82(x62532),x62531),x62533)),f333(f333(f82(x62532),x62531),x62534)),f333(f333(f291(x62532),x62533),x62534)) % 191.49/191.41 [6254]~P60(x62542)+E(x62541,f2(x62542))+E(f333(f333(f40(x62542),f333(f333(f82(x62542),x62543),x62541)),f333(f333(f82(x62542),x62544),x62541)),f333(f333(f40(x62542),x62543),x62544)) % 191.49/191.41 [6256]~P60(x62562)+E(x62561,f2(x62562))+E(f333(f333(f40(x62562),f333(f333(f82(x62562),x62561),x62563)),f333(f333(f82(x62562),x62561),x62564)),f333(f333(f40(x62562),x62563),x62564)) % 191.49/191.41 [6318]P4(f333(x63181,x63182))+~E(x63183,f333(f333(f81(a880),x63184),x63182))+~P4(f333(x63181,f333(f333(f3(a880),x63183),x63184))) % 191.49/191.41 [6399]P31(x63991,x63992,x63993)+P30(x63991,f600(x63993,x63992,x63991),x63994)+~P4(f333(f333(f335(f879(x63991)),x63994),x63992)) % 191.49/191.41 [6401]~P4(f333(x64012,x64013))+~P4(f333(f161(x64011,x64012),x64014))+P4(f333(f161(x64011,x64012),f333(f333(f152(x64011),x64013),x64014))) % 191.49/191.41 [6441]E(x64411,f118(x64412))+~E(x64413,f333(f333(f3(a880),f333(f195(f881(x64412)),x64411)),f79(a880)))+E(f145(x64412,f333(f333(f160(x64412,x64411),x64413),x64414)),x64414) % 191.49/191.41 [6463]~P101(x64631)+~P4(f333(f333(f251(x64631),x64632),x64634))+P4(f333(f333(f251(x64631),x64632),f333(f333(f115(x64631),x64633),x64634))) % 191.49/191.41 [6464]~P101(x64641)+~P4(f333(f333(f251(x64641),x64642),x64643))+P4(f333(f333(f251(x64641),x64642),f333(f333(f115(x64641),x64643),x64644))) % 191.49/191.41 [6466]~P109(x64661)+~P4(f333(f333(f251(x64661),x64662),x64664))+P4(f333(f333(f251(x64661),x64662),f333(f333(f249(x64661),x64663),x64664))) % 191.49/191.41 [6468]~P109(x64681)+~P4(f333(f333(f251(x64681),x64682),x64683))+P4(f333(f333(f251(x64681),x64682),f333(f333(f249(x64681),x64683),x64684))) % 191.49/191.41 [6469]~P101(x64691)+~P4(f333(f333(f250(x64691),x64692),x64694))+P4(f333(f333(f250(x64691),x64692),f333(f333(f115(x64691),x64693),x64694))) % 191.49/191.41 [6470]~P101(x64701)+~P4(f333(f333(f250(x64701),x64702),x64703))+P4(f333(f333(f250(x64701),x64702),f333(f333(f115(x64701),x64703),x64704))) % 191.49/191.41 [6472]~P109(x64721)+~P4(f333(f333(f250(x64721),x64722),x64724))+P4(f333(f333(f250(x64721),x64722),f333(f333(f249(x64721),x64723),x64724))) % 191.49/191.41 [6474]~P109(x64741)+~P4(f333(f333(f250(x64741),x64742),x64743))+P4(f333(f333(f250(x64741),x64742),f333(f333(f249(x64741),x64743),x64744))) % 191.49/191.41 [6557]~E(f333(f333(f166(x65571),x65572),x65573),x65574)+E(f333(f333(f160(x65571,x65572),x65573),x65574),x65572)+~P4(f333(f333(f251(a880),x65573),f333(f195(f881(x65571)),x65572))) % 191.49/191.41 [6574]E(x65741,x65742)+P4(f333(x65743,x65741))+~P4(f333(f333(f201(f33(x65743,x65744)),x65741),x65742)) % 191.49/191.41 [6598]P4(f333(x65981,x65982))+~P4(f333(x65983,x65982))+~P4(f333(f333(f250(f890(x65984,a874)),x65983),x65981)) % 191.49/191.41 [6630]~E(f333(f333(f160(x66301,x66302),x66303),x66304),x66302)+E(f333(f333(f166(x66301),x66302),x66303),x66304)+~P4(f333(f333(f251(a880),x66303),f333(f195(f881(x66301)),x66302))) % 191.49/191.41 [6645]~P4(f333(f161(x66451,x66452),x66454))+~P4(f333(f161(x66451,x66452),x66453))+P4(f333(f161(x66451,x66452),f333(f333(f127(x66451),x66453),x66454))) % 191.49/191.41 [6741]P30(x67411,x67412,x67413)+~P30(x67411,f333(a117,x67412),f604(x67412,x67414,x67411))+~P4(f333(f333(f335(f879(x67411)),x67413),x67414)) % 191.49/191.41 [6750]E(x67501,f194(f890(x67502,a874)))+E(x67503,f194(f890(x67504,a874)))+~E(f333(f333(f270(x67504,x67502),x67503),f333(f18(f890(x67502,a874),x67504),x67501)),f194(f890(f889(x67504,x67502),a874))) % 191.49/191.41 [6763]E(x67631,x67632)+P4(f333(f333(f335(x67633),x67631),x67634))+~P4(f333(f333(f335(x67633),x67631),f333(f333(f311(x67633),x67632),x67634))) % 191.49/191.41 [6779]~P109(x67791)+P4(f333(f333(f251(x67791),x67792),x67793))+~P4(f333(f333(f251(x67791),x67792),f333(f333(f248(x67791),x67794),x67793))) % 191.49/191.41 [6780]~P109(x67801)+P4(f333(f333(f251(x67801),x67802),x67803))+~P4(f333(f333(f251(x67801),x67802),f333(f333(f248(x67801),x67803),x67804))) % 191.49/191.41 [6782]~P102(x67821)+P4(f333(f333(f250(x67821),x67822),x67823))+~P4(f333(f333(f250(x67821),x67822),f333(f333(f106(x67821),x67824),x67823))) % 191.49/191.41 [6784]~P102(x67841)+P4(f333(f333(f250(x67841),x67842),x67843))+~P4(f333(f333(f250(x67841),x67842),f333(f333(f106(x67841),x67843),x67844))) % 191.49/191.41 [6786]~P109(x67861)+P4(f333(f333(f250(x67861),x67862),x67863))+~P4(f333(f333(f250(x67861),x67862),f333(f333(f248(x67861),x67864),x67863))) % 191.49/191.41 [6788]~P109(x67881)+P4(f333(f333(f250(x67881),x67882),x67883))+~P4(f333(f333(f250(x67881),x67882),f333(f333(f248(x67881),x67883),x67884))) % 191.49/191.41 [6809]~E(f333(f333(f166(x68091),x68093),x68094),x68092)+P4(f333(f333(f335(x68091),x68092),f333(f173(x68091),x68093)))+~P4(f333(f333(f251(a880),x68094),f333(f195(f881(x68091)),x68093))) % 191.49/191.41 [6819]~P109(x68191)+~P17(x68191,f333(f333(f152(x68191),x68192),f333(f333(f152(x68191),x68193),x68194)))+P4(f333(f333(f250(x68191),x68192),x68193)) % 191.49/191.41 [6959]~P34(x69592,x69591,x69593)+P4(f333(x69591,f333(f333(f166(x69592),x69593),x69594)))+~P4(f333(f333(f251(a880),x69594),f333(f195(f881(x69592)),x69593))) % 191.49/191.41 [6978]E(x69781,f2(a1))+E(f333(f333(f40(a1),x69782),x69781),x69783)+~P4(f333(f50(x69782,x69781),f333(f333(f263(a1,a1),x69783),x69784))) % 191.49/191.41 [6999]E(f46(a1,x69992,x69991),x69993)+E(x69991,f2(a1))+~P4(f333(f50(x69992,x69991),f333(f333(f263(a1,a1),x69994),x69993))) % 191.49/191.41 [7116]P4(f333(f333(f335(x71161),x71162),x71163))+~P4(f333(f333(f335(x71161),x71162),x71164))+~P4(f333(f333(f251(f890(x71161,a874)),x71164),x71163)) % 191.49/191.41 [7120]P4(f333(f333(f335(x71201),x71202),x71203))+~P4(f333(f333(f335(x71201),x71202),x71204))+~P4(f333(f333(f250(f890(x71201,a874)),x71204),x71203)) % 191.49/191.41 [7228]P36(x72281,x72282,x72283)+~P4(f333(x72282,f333(f333(f166(x72281),x72283),x72284)))+~P4(f333(f333(f251(a880),x72284),f333(f195(f881(x72281)),x72283))) % 191.49/191.41 [7330]~P111(x73302)+~P4(f333(f333(f251(f890(x73301,x73302)),x73303),x73304))+P4(f333(f333(f250(f890(x73301,x73302)),x73303),x73304)) % 191.49/191.41 [7416]~P27(x74161,x74162,x74164)+P27(x74161,x74162,f333(f333(f311(f879(x74161)),x74163),x74164))+~P27(x74161,x74162,f333(f333(f311(f879(x74161)),x74163),f194(f890(f879(x74161),a874)))) % 191.49/191.41 [7461]~P4(f333(f333(f335(x74611),x74612),x74614))+P4(f333(f333(f335(x74611),x74612),f41(f890(x74611,a874),x74613)))+~P4(f333(f333(f335(f890(x74611,a874)),x74614),x74613)) % 191.49/191.41 [7473]P30(x74731,x74732,x74733)+P4(f333(f333(f335(f879(x74731)),f604(x74732,x74734,x74731)),x74734))+~P4(f333(f333(f335(f879(x74731)),x74733),x74734)) % 191.49/191.41 [7490]~P85(x74901)+~P4(f333(f333(f251(x74901),x74903),x74904))+P4(f333(f333(f251(x74901),f333(f333(f81(x74901),x74902),x74903)),f333(f333(f81(x74901),x74902),x74904))) % 191.49/191.41 [7491]~P88(x74911)+~P4(f333(f333(f251(x74911),x74913),x74914))+P4(f333(f333(f251(x74911),f333(f333(f81(x74911),x74912),x74913)),f333(f333(f81(x74911),x74912),x74914))) % 191.49/191.41 [7492]~P85(x74921)+~P4(f333(f333(f251(x74921),x74922),x74924))+P4(f333(f333(f251(x74921),f333(f333(f81(x74921),x74922),x74923)),f333(f333(f81(x74921),x74924),x74923))) % 191.49/191.41 [7493]~P88(x74931)+~P4(f333(f333(f251(x74931),x74932),x74934))+P4(f333(f333(f251(x74931),f333(f333(f81(x74931),x74932),x74933)),f333(f333(f81(x74931),x74934),x74933))) % 191.49/191.41 [7494]~P85(x74941)+~P4(f333(f333(f250(x74941),x74943),x74944))+P4(f333(f333(f250(x74941),f333(f333(f81(x74941),x74942),x74943)),f333(f333(f81(x74941),x74942),x74944))) % 191.49/191.41 [7495]~P86(x74951)+~P4(f333(f333(f250(x74951),x74953),x74954))+P4(f333(f333(f250(x74951),f333(f333(f81(x74951),x74952),x74953)),f333(f333(f81(x74951),x74952),x74954))) % 191.49/191.41 [7496]~P85(x74961)+~P4(f333(f333(f250(x74961),x74962),x74964))+P4(f333(f333(f250(x74961),f333(f333(f81(x74961),x74962),x74963)),f333(f333(f81(x74961),x74964),x74963))) % 191.49/191.41 [7497]~P86(x74971)+~P4(f333(f333(f250(x74971),x74972),x74974))+P4(f333(f333(f250(x74971),f333(f333(f81(x74971),x74972),x74973)),f333(f333(f81(x74971),x74974),x74973))) % 191.49/191.41 [7506]~P106(x75061)+~P95(x75061)+E(f333(f333(f3(x75061),f333(f333(f82(x75061),x75062),f333(f108(x75061),x75063))),f333(f333(f82(x75061),x75064),f333(f108(x75061),x75063))),f333(f333(f82(x75061),f333(f333(f3(x75061),x75062),x75064)),f333(f108(x75061),x75063))) % 191.49/191.41 [7507]~P138(x75071)+~P95(x75071)+E(f333(f333(f81(x75071),f333(f333(f82(x75071),x75072),f333(f108(x75071),x75073))),f333(f333(f82(x75071),x75074),f333(f108(x75071),x75073))),f333(f333(f82(x75071),f333(f333(f81(x75071),x75072),x75074)),f333(f108(x75071),x75073))) % 191.49/191.41 [7542]~P69(x75421)+E(f333(f333(f81(x75421),f333(x75422,x75423)),f333(f333(f8(a880,x75421),x75422),f304(a880,f333(a117,x75423),x75424))),f333(f333(f8(a880,x75421),x75422),f304(a880,x75423,x75424)))+~P4(f333(f333(f250(a880),x75423),x75424)) % 191.49/191.41 [7552]~P28(x75522,x75521,x75523,f333(f173(x75522),x75524))+~P4(f333(f138(x75522),x75524))+P4(f333(f138(x75521),f333(f333(f155(x75522,x75521),x75523),x75524))) % 191.49/191.41 [7599]~P4(f333(f333(f251(a880),x75992),x75994))+~P4(f333(f333(f251(a880),x75991),x75993))+P4(f333(f333(f251(a880),f333(f333(f81(a880),x75991),x75992)),f333(f333(f81(a880),x75993),x75994))) % 191.49/191.41 [7600]~P4(f333(f333(f251(a1),x76001),x76003))+~P4(f333(f333(f250(a1),x76002),x76004))+P4(f333(f333(f251(a1),f333(f333(f81(a1),x76001),x76002)),f333(f333(f81(a1),x76003),x76004))) % 191.49/191.41 [7601]~P4(f333(f333(f250(a880),x76012),x76014))+~P4(f333(f333(f250(a880),x76011),x76013))+P4(f333(f333(f250(a880),f333(f333(f81(a880),x76011),x76012)),f333(f333(f81(a880),x76013),x76014))) % 191.49/191.41 [7602]~P4(f333(f333(f250(a880),x76022),x76024))+~P4(f333(f333(f250(a880),x76021),x76023))+P4(f333(f333(f250(a880),f333(f333(f82(a880),x76021),x76022)),f333(f333(f82(a880),x76023),x76024))) % 191.49/191.41 [7650]P4(f333(f333(f335(x76501),x76502),x76503))+~P4(f333(f333(f335(x76501),x76502),f42(f890(x76501,a874),x76504)))+~P4(f333(f333(f335(f890(x76501,a874)),x76503),x76504)) % 191.49/191.41 [7665]~P4(f333(x76651,f578(x76651,x76653,x76652)))+P4(f333(x76651,f333(f333(f166(x76652),x76653),x76654)))+~P4(f333(f333(f251(a880),x76654),f333(f195(f881(x76652)),x76653))) % 191.49/191.41 [7670]P4(f333(x76701,x76702))+~P4(f333(f333(f335(x76704),x76702),f333(f173(x76704),x76703)))+P4(f333(f333(f251(a880),f579(x76701,x76703,x76704)),f333(f195(f881(x76704)),x76703))) % 191.49/191.41 [7689]~P4(f333(f333(f201(x76892),x76893),x76894))+~P4(f333(f333(f201(f33(x76891,x76892)),x76894),x76893))+P4(f333(f333(f201(f33(x76891,x76892)),x76893),x76893)) % 191.49/191.41 [7718]~P111(x77181)+~P4(f333(f333(f250(f890(x77182,x77181)),x77184),x77183))+~P4(f333(f333(f251(f890(x77182,x77181)),x77183),x77184)) % 191.49/191.41 [7765]~P4(f333(x77654,x77652))+~P4(f333(f333(f335(x77651),x77652),x77653))+P4(f333(f333(f335(x77651),x77652),f333(f333(f106(f890(x77651,a874)),x77653),f333(f255(x77651),x77654)))) % 191.49/191.41 [7906]~P4(f333(f333(f335(x79061),x79063),x79064))+~P4(f333(f333(f251(f890(x79061,a874)),x79062),x79064))+P4(f333(f333(f251(f890(x79061,a874)),x79062),f333(f333(f311(x79061),x79063),x79064))) % 191.49/191.41 [7908]E(f333(f333(f106(f890(x79081,a874)),x79082),x79083),f194(f890(x79081,a874)))+~E(f333(f333(f106(f890(x79081,a874)),f41(f890(x79081,a874),x79084)),x79083),f194(f890(x79081,a874)))+~P4(f333(f333(f335(f890(x79081,a874)),x79082),x79084)) % 191.49/191.41 [7978]P4(f333(f333(f335(x79781),x79782),x79783))+~P4(f333(f333(f250(f890(x79781,a874)),x79783),f333(f333(f311(x79781),x79782),x79784)))+P4(f333(f333(f250(f890(x79781,a874)),x79783),x79784)) % 191.49/191.41 [8000]P4(f333(f333(f335(x80002),f578(x80001,x80003,x80002)),f333(f173(x80002),x80003)))+P4(f333(x80001,f333(f333(f166(x80002),x80003),x80004)))+~P4(f333(f333(f251(a880),x80004),f333(f195(f881(x80002)),x80003))) % 191.49/191.41 [8008]~P4(f333(f333(f251(f890(x80081,a874)),x80082),x80084))+P4(f333(f333(f251(f890(x80081,a874)),x80082),x80083))+~P4(f333(f333(f251(f890(x80081,a874)),x80084),x80083)) % 191.49/191.41 [8009]~P4(f333(f333(f250(f890(x80091,a874)),x80092),x80094))+P4(f333(f333(f251(f890(x80091,a874)),x80092),x80093))+~P4(f333(f333(f251(f890(x80091,a874)),x80094),x80093)) % 191.49/191.41 [8010]~P4(f333(f333(f250(f890(x80101,a874)),x80104),x80103))+~P4(f333(f333(f251(f890(x80101,a874)),x80102),x80104))+P4(f333(f333(f251(f890(x80101,a874)),x80102),x80103)) % 191.49/191.41 [8011]~P4(f333(f333(f250(f890(x80111,a874)),x80112),x80114))+P4(f333(f333(f250(f890(x80111,a874)),x80112),x80113))+~P4(f333(f333(f250(f890(x80111,a874)),x80114),x80113)) % 191.49/191.41 [8057]~P4(f333(f333(f335(x80571),x80574),x80573))+~P4(f333(f333(f251(f890(x80571,a874)),x80572),f333(f333(f311(x80571),x80574),x80573)))+P4(f333(f333(f251(f890(x80571,a874)),x80572),x80573)) % 191.49/191.41 [8067]~P85(x80671)+P4(f333(f333(f251(x80671),x80672),x80673))+~P4(f333(f333(f251(x80671),f333(f333(f81(x80671),x80674),x80672)),f333(f333(f81(x80671),x80674),x80673))) % 191.49/191.41 [8069]~P85(x80691)+P4(f333(f333(f251(x80691),x80692),x80693))+~P4(f333(f333(f251(x80691),f333(f333(f81(x80691),x80692),x80694)),f333(f333(f81(x80691),x80693),x80694))) % 191.49/191.41 [8071]~P85(x80711)+P4(f333(f333(f250(x80711),x80712),x80713))+~P4(f333(f333(f250(x80711),f333(f333(f81(x80711),x80714),x80712)),f333(f333(f81(x80711),x80714),x80713))) % 191.49/191.41 [8073]~P85(x80731)+P4(f333(f333(f250(x80731),x80732),x80733))+~P4(f333(f333(f250(x80731),f333(f333(f81(x80731),x80732),x80734)),f333(f333(f81(x80731),x80733),x80734))) % 191.49/191.41 [8124]P4(f333(x81241,x81242))+~E(f333(f333(f139(x81243),f333(f195(f881(x81243)),f177(x81243,x81241,x81244))),x81244),f118(x81243))+~P4(f333(f333(f335(x81243),x81242),f333(f173(x81243),x81244))) % 191.49/191.41 [8248]P4(f333(x82481,x82482))+~P4(f333(f333(f335(x82483),x82482),f333(f173(x82483),x82484)))+P4(f333(f333(f251(a880),f333(f195(f881(x82483)),f333(f137(x82483,x82481),x82484))),f333(f195(f881(x82483)),x82484))) % 191.49/191.41 [8373]E(x83731,x83732)+P4(f333(f333(f201(x83733),x83731),f492(x83732,x83731,x83733,x83734)))+~P4(f333(f333(f201(f33(x83734,x83733)),x83731),x83732)) % 191.49/191.41 [8398]~P4(f333(x83984,x83982))+P4(f333(f333(f201(x83981),x83982),f492(x83983,x83982,x83981,x83984)))+~P4(f333(f333(f201(f33(x83984,x83981)),x83982),x83983)) % 191.49/191.41 [8712]~P4(f333(x87121,f757(x87121,x87123,x87122,x87124)))+P4(f333(x87121,f333(f333(f166(x87122),x87123),x87124)))+~P4(f333(f333(f251(a880),x87124),f333(f195(f881(x87122)),x87123))) % 191.49/191.41 [8730]~P28(x87304,x87303,x87301,f258(f890(x87304,a874)))+E(f333(x87301,f836(x87302,x87301,x87303,x87304)),x87302)+~P4(f333(f333(f335(x87303),x87302),f333(f312(x87304,x87303,x87301),f258(f890(x87304,a874))))) % 191.49/191.41 [8803]E(f177(x88031,x88032,x88033),f333(f333(f174(x88031),x88034),x88033))+P4(f333(f333(f251(a880),f675(x88032,x88033,x88031,x88034)),x88034))+P4(f333(f333(f251(a880),x88034),f333(f195(f881(x88031)),x88033))) % 191.49/191.41 [8806]E(f177(x88061,x88062,x88063),f333(f333(f174(x88061),x88064),x88063))+P4(f333(f333(f251(a880),f675(x88062,x88063,x88061,x88064)),x88064))+P4(f333(x88062,f333(f333(f166(x88061),x88063),x88064))) % 191.49/191.41 [8837]P4(f333(x88371,x88372))+~P4(f333(f333(f335(x88374),x88372),f333(f173(x88374),x88373)))+P4(f333(f333(f251(a880),f686(x88372,x88371,x88373,x88374)),f333(f195(f881(x88374)),x88373))) % 191.49/191.41 [8840]E(f177(x88401,x88402,x88403),f333(f333(f174(x88401),x88404),x88403))+P4(f333(f333(f251(a880),x88404),f333(f195(f881(x88401)),x88403)))+P4(f333(f333(f251(a880),f675(x88402,x88403,x88401,x88404)),f333(f195(f881(x88401)),x88403))) % 191.49/191.41 [8846]E(f177(x88461,x88462,x88463),f333(f333(f174(x88461),x88464),x88463))+P4(f333(x88462,f333(f333(f166(x88461),x88463),x88464)))+P4(f333(f333(f251(a880),f675(x88462,x88463,x88461,x88464)),f333(f195(f881(x88461)),x88463))) % 191.49/191.41 [8874]~P123(x88744)+P4(f333(f333(f335(x88741),f380(x88742,x88743,x88741,x88744)),x88743))+P4(f333(f333(f251(x88744),f2(x88744)),f333(f333(f11(x88741,x88744),x88742),x88743))) % 191.49/191.41 [8875]~P123(x88754)+P4(f333(f333(f335(x88751),f385(x88752,x88753,x88751,x88754)),x88753))+P4(f333(f333(f250(x88754),f2(x88754)),f333(f333(f11(x88751,x88754),x88752),x88753))) % 191.49/191.41 [8907]~P4(f333(f63(x89071),x89074))+P4(f333(f333(f335(x89071),f628(x89072,x89073,x89074,x89071)),x89074))+P4(f333(f63(f889(x89071,x89073)),f333(f333(f270(x89071,x89073),x89074),x89072))) % 191.49/191.41 [8941]P4(f333(f333(f335(x89412),f757(x89411,x89413,x89412,x89414)),f333(f173(x89412),x89413)))+P4(f333(x89411,f333(f333(f166(x89412),x89413),x89414)))+~P4(f333(f333(f251(a880),x89414),f333(f195(f881(x89412)),x89413))) % 191.49/191.41 [8956]E(x89561,x89562)+P4(f333(f333(f201(f33(x89563,x89564)),f492(x89561,x89562,x89564,x89563)),x89561))+~P4(f333(f333(f201(f33(x89563,x89564)),x89562),x89561)) % 191.49/191.41 [8975]~P4(f333(x89751,x89754))+P4(f333(f333(f201(f33(x89751,x89752)),f492(x89753,x89754,x89752,x89751)),x89753))+~P4(f333(f333(f201(f33(x89751,x89752)),x89754),x89753)) % 191.49/191.41 [9057]P4(f333(f333(f250(a880),x90574),f333(f195(f881(x90572)),f177(x90572,x90573,x90571))))+P4(f333(f333(f251(a880),f676(x90571,x90572,x90573,x90574)),x90574))+~P4(f333(f333(f250(a880),x90574),f333(f195(f881(x90572)),x90571))) % 191.49/191.41 [9171]~E(f333(f333(f178(x91711,x91712),x91713),f720(x91714,x91713,x91712,x91711)),f333(f333(f178(x91711,x91712),x91714),f720(x91714,x91713,x91712,x91711)))+E(f333(f178(x91711,x91712),x91713),f333(f178(x91711,x91712),x91714))+~E(f333(f173(x91711),f333(f333(f155(f889(x91711,x91712),x91711),f262(x91711,x91712)),x91713)),f333(f173(x91711),f333(f333(f155(f889(x91711,x91712),x91711),f262(x91711,x91712)),x91714))) % 191.49/191.41 [9215]E(f177(x92151,x92152,x92153),f333(f333(f174(x92151),x92154),x92153))+~P4(f333(x92152,f333(f333(f166(x92151),x92153),f675(x92152,x92153,x92151,x92154))))+P4(f333(f333(f251(a880),x92154),f333(f195(f881(x92151)),x92153))) % 191.49/191.41 [9219]E(f177(x92191,x92192,x92193),f333(f333(f174(x92191),x92194),x92193))+~P4(f333(x92192,f333(f333(f166(x92191),x92193),f675(x92192,x92193,x92191,x92194))))+P4(f333(x92192,f333(f333(f166(x92191),x92193),x92194))) % 191.49/191.41 [9226]~P4(f333(f63(x92261),x92263))+~P4(f333(f63(x92262),f333(x92264,f628(x92264,x92262,x92263,x92261))))+P4(f333(f63(f889(x92261,x92262)),f333(f333(f270(x92261,x92262),x92263),x92264))) % 191.49/191.41 [9234]~P123(x92341)+~P4(f333(f333(f251(x92341),f2(x92341)),f333(x92343,f380(x92343,x92344,x92342,x92341))))+P4(f333(f333(f251(x92341),f2(x92341)),f333(f333(f11(x92342,x92341),x92343),x92344))) % 191.49/191.41 [9235]~P123(x92351)+~P4(f333(f333(f250(x92351),f2(x92351)),f333(x92353,f385(x92353,x92354,x92352,x92351))))+P4(f333(f333(f250(x92351),f2(x92351)),f333(f333(f11(x92352,x92351),x92353),x92354))) % 191.49/191.41 [9241]~E(f333(f195(f881(x92414)),x92412),f333(f195(f881(x92414)),x92413))+P4(f333(f333(f335(f889(f881(x92414),f881(x92414))),f333(f333(f263(f881(x92414),f881(x92414)),x92413),x92412)),f159(x92414,x92411)))+P4(f333(f333(f251(a880),f587(x92411,x92412,x92413,x92414)),f333(f195(f881(x92414)),x92413))) % 191.49/191.41 [9298]~P4(f333(x92983,f333(f333(f166(x92982),x92984),f676(x92984,x92982,x92983,x92981))))+P4(f333(f333(f250(a880),x92981),f333(f195(f881(x92982)),f177(x92982,x92983,x92984))))+~P4(f333(f333(f250(a880),x92981),f333(f195(f881(x92982)),x92984))) % 191.49/191.41 [9380]E(f333(f333(f174(x93801),f611(x93802,x93803,x93804,x93801)),x93803),f333(f333(f174(x93801),f611(x93802,x93803,x93804,x93801)),x93804))+~P4(f333(f333(f335(f889(f881(x93801),f881(x93801))),f333(f333(f263(f881(x93801),f881(x93801)),x93804),x93803)),f148(x93801,x93802)))+P4(f333(f333(f251(a880),f333(f195(f881(x93801)),x93804)),f333(f195(f881(x93801)),x93803))) % 191.49/191.41 [9427]~P4(f333(f333(f251(a880),f2(a880)),x94273))+~P4(f333(f333(f251(a880),x94274),x94271))+P4(f333(f333(f251(a880),f333(f333(f81(a880),f333(f333(f82(a880),x94271),f46(a880,x94272,x94273))),x94274)),f333(f333(f82(a880),x94271),x94273))) % 191.49/191.41 [9643]~P111(x96432)+~P4(f333(f333(f250(x96432),f333(x96433,f351(x96434,x96433,x96431,x96432))),f333(x96434,f351(x96434,x96433,x96431,x96432))))+P4(f333(f333(f250(f890(x96431,x96432)),x96433),x96434)) % 191.49/191.41 [9750]~P68(x97501)+E(f333(f333(f8(a880,x97501),f333(f333(f20(a880,x97501,x97501),f333(f333(f10(x97501,f890(x97501,x97501),a880),f3(x97501)),x97502)),f333(f333(f10(a880,x97501,a880),x97502),f333(f333(f9(a880,a880,a880),f81(a880)),f79(a880))))),f304(a880,x97503,x97504)),f333(f333(f3(x97501),f333(x97502,x97503)),f333(x97502,f333(f333(f81(a880),x97504),f79(a880)))))+~P4(f333(f333(f250(a880),x97503),x97504)) % 191.49/191.41 [6812]E(f333(f333(f127(x68121),x68122),x68123),x68124)+~E(x68123,f333(f333(f139(x68121),f333(f195(f881(x68121)),x68122)),x68124))+~E(f333(f333(f174(x68121),f333(f195(f881(x68121)),x68122)),x68124),x68122) % 191.49/191.41 [6866]~P64(x68662)+E(x68661,f2(x68662))+E(f333(f333(f291(x68662),f333(f333(f264(x68662),x68663),x68664)),f333(f333(f264(x68662),x68661),x68664)),f333(f333(f264(x68662),f333(f333(f291(x68662),x68663),x68661)),x68664)) % 191.49/191.41 [7001]~E(f333(f195(f881(x70011)),x70013),f333(f195(f881(x70012)),x70014))+~P4(f333(f138(x70011),x70013))+E(f184(x70011,x70012,f333(f178(x70011,x70012),f333(f333(f182(x70011,x70012),x70013),x70014))),f333(f173(x70011),x70013)) % 191.49/191.41 [7020]~P102(x70201)+~P4(f333(f333(f251(x70201),x70203),x70204))+P4(f333(f333(f251(x70201),f333(f333(f106(x70201),x70202),x70203)),x70204)) % 191.49/191.41 [7021]~P102(x70211)+~P4(f333(f333(f251(x70211),x70212),x70214))+P4(f333(f333(f251(x70211),f333(f333(f106(x70211),x70212),x70213)),x70214)) % 191.49/191.41 [7023]~P109(x70231)+~P4(f333(f333(f251(x70231),x70233),x70234))+P4(f333(f333(f251(x70231),f333(f333(f248(x70231),x70232),x70233)),x70234)) % 191.49/191.41 [7025]~P109(x70251)+~P4(f333(f333(f251(x70251),x70252),x70254))+P4(f333(f333(f251(x70251),f333(f333(f248(x70251),x70252),x70253)),x70254)) % 191.49/191.41 [7026]~P102(x70261)+~P4(f333(f333(f250(x70261),x70263),x70264))+P4(f333(f333(f250(x70261),f333(f333(f106(x70261),x70262),x70263)),x70264)) % 191.49/191.41 [7027]~P102(x70271)+~P4(f333(f333(f250(x70271),x70272),x70274))+P4(f333(f333(f250(x70271),f333(f333(f106(x70271),x70272),x70273)),x70274)) % 191.49/191.41 [7029]~P109(x70291)+~P4(f333(f333(f250(x70291),x70293),x70294))+P4(f333(f333(f250(x70291),f333(f333(f248(x70291),x70292),x70293)),x70294)) % 191.49/191.41 [7031]~P109(x70311)+~P4(f333(f333(f250(x70311),x70312),x70314))+P4(f333(f333(f250(x70311),f333(f333(f248(x70311),x70312),x70313)),x70314)) % 191.49/191.41 [7051]~P4(f333(x70513,x70514))+~P4(f333(x70512,x70514))+P4(f333(f333(f333(f106(f890(x70511,a874)),x70512),x70513),x70514)) % 191.49/191.41 [7174]P27(x71741,x71742,x71743)+~P27(x71741,x71744,x71743)+~P4(f333(f333(f250(f890(f879(x71741),a874)),x71744),x71742)) % 191.49/191.41 [7175]P27(x71751,x71752,x71753)+~P27(x71751,x71752,x71754)+~P4(f333(f333(f250(f890(f879(x71751),a874)),x71753),x71754)) % 191.49/191.41 [7532]~P69(x75321)+E(f333(f333(f81(x75321),f333(x75322,x75323)),f333(f333(f8(a880,x75321),x75322),f333(f303(a880,f333(a117,x75323)),x75324))),f333(f333(f8(a880,x75321),x75322),f333(f303(a880,x75323),x75324)))+~P4(f333(f333(f251(a880),x75323),x75324)) % 191.49/191.41 [7559]~P109(x75591)+P4(f333(f333(f251(x75591),x75592),x75593))+~P4(f333(f333(f251(x75591),f333(f333(f249(x75591),x75594),x75592)),x75593)) % 191.49/191.41 [7560]~P109(x75601)+P4(f333(f333(f251(x75601),x75602),x75603))+~P4(f333(f333(f251(x75601),f333(f333(f249(x75601),x75602),x75604)),x75603)) % 191.49/191.41 [7562]~P101(x75621)+P4(f333(f333(f250(x75621),x75622),x75623))+~P4(f333(f333(f250(x75621),f333(f333(f115(x75621),x75624),x75622)),x75623)) % 191.49/191.41 [7564]~P101(x75641)+P4(f333(f333(f250(x75641),x75642),x75643))+~P4(f333(f333(f250(x75641),f333(f333(f115(x75641),x75642),x75644)),x75643)) % 191.49/191.41 [7566]~P109(x75661)+P4(f333(f333(f250(x75661),x75662),x75663))+~P4(f333(f333(f250(x75661),f333(f333(f249(x75661),x75664),x75662)),x75663)) % 191.49/191.41 [7568]~P109(x75681)+P4(f333(f333(f250(x75681),x75682),x75683))+~P4(f333(f333(f250(x75681),f333(f333(f249(x75681),x75682),x75684)),x75683)) % 191.49/191.41 [7642]~P4(f333(f333(f335(x76421),x76422),x76424))+P4(f333(f333(f335(x76421),x76422),x76423))+P4(f333(f333(f335(x76421),x76422),f333(f333(f3(f890(x76421,a874)),x76424),x76423))) % 191.49/191.41 [7724]P4(f333(x77241,x77242))+P4(f333(x77243,x77242))+~P4(f333(f333(f333(f115(f890(x77244,a874)),x77243),x77241),x77242)) % 191.49/191.41 [7734]~P4(f333(f333(f335(x77341),x77342),x77344))+~P4(f333(f333(f335(x77341),x77342),x77343))+P4(f333(f333(f335(x77341),x77342),f333(f333(f106(f890(x77341,a874)),x77343),x77344))) % 191.49/191.41 [7789]~P101(x77891)+~P4(f333(f63(x77891),x77894))+E(f333(f333(f66(x77891,x77891,f115(x77891)),x77892),f333(f333(f311(x77891),x77893),x77894)),f333(f333(f115(x77891),x77893),f333(f333(f66(x77891,x77891,f115(x77891)),x77892),x77894))) % 191.49/191.41 [7790]~P102(x77901)+~P4(f333(f63(x77901),x77904))+E(f333(f333(f66(x77901,x77901,f106(x77901)),x77902),f333(f333(f311(x77901),x77903),x77904)),f333(f333(f106(x77901),x77903),f333(f333(f66(x77901,x77901,f106(x77901)),x77902),x77904))) % 191.49/191.41 [7791]~P109(x77911)+~P4(f333(f63(x77911),x77914))+E(f333(f333(f66(x77911,x77911,f248(x77911)),x77912),f333(f333(f311(x77911),x77913),x77914)),f333(f333(f248(x77911),x77913),f333(f333(f66(x77911,x77911,f248(x77911)),x77912),x77914))) % 191.49/191.41 [7792]~P109(x77921)+~P4(f333(f63(x77921),x77924))+E(f333(f333(f66(x77921,x77921,f249(x77921)),x77922),f333(f333(f311(x77921),x77923),x77924)),f333(f333(f249(x77921),x77923),f333(f333(f66(x77921,x77921,f249(x77921)),x77922),x77924))) % 191.49/191.41 [7793]~P106(x77931)+~P95(x77931)+E(f333(f333(f3(x77931),f333(f333(f82(x77931),f333(f108(x77931),x77932)),x77933)),f333(f333(f82(x77931),f333(f108(x77931),x77932)),x77934)),f333(f333(f82(x77931),f333(f108(x77931),x77932)),f333(f333(f3(x77931),x77933),x77934))) % 191.49/191.41 [7794]~P138(x77941)+~P95(x77941)+E(f333(f333(f81(x77941),f333(f333(f82(x77941),f333(f108(x77941),x77942)),x77943)),f333(f333(f82(x77941),f333(f108(x77941),x77942)),x77944)),f333(f333(f82(x77941),f333(f108(x77941),x77942)),f333(f333(f81(x77941),x77943),x77944))) % 191.49/191.41 [7904]E(x79041,x79042)+P4(f333(f333(f335(x79043),x79041),f333(f173(x79043),x79044)))+~P4(f333(f333(f335(x79043),x79041),f333(f173(x79043),f333(f333(f152(x79043),x79042),x79044)))) % 191.49/191.41 [7925]~P62(x79251)+~E(f333(f195(f881(x79252)),x79253),f333(f195(f881(x79251)),f57(x79251)))+E(f333(f333(f178(x79251,x79252),f333(f333(f182(x79251,x79252),f57(x79251)),x79253)),x79254),f333(f242(x79252),f673(x79254,x79253,x79252,x79251))) % 191.49/191.41 [8080]P54(x80801,x80802,x80803)+~P54(x80801,x80802,x80804)+~P4(f333(f333(f250(f890(f889(x80801,x80802),a874)),x80803),x80804)) % 191.49/191.41 [8127]P4(f333(f333(f335(x81271),x81272),x81273))+P4(f333(f333(f335(x81271),x81272),x81274))+~P4(f333(f333(f335(x81271),x81272),f333(f333(f115(f890(x81271,a874)),x81274),x81273))) % 191.49/191.41 [8138]~P50(x81381,x81384,x81383)+~P4(f333(f333(f335(x81381),x81382),x81384))+P4(f333(f333(f335(f889(x81381,x81381)),f333(f333(f263(x81381,x81381),x81382),x81382)),x81383)) % 191.49/191.41 [8153]~P4(f333(f63(x81532),x81534))+~P4(f333(f63(x81531),x81533))+P4(f333(f63(f889(x81531,x81532)),f333(f333(f270(x81531,x81532),x81533),f333(f18(f890(x81532,a874),x81531),x81534)))) % 191.49/191.41 [8154]~P4(f333(f333(f335(x81541),x81542),x81544))+~P4(f333(f333(f250(f890(x81541,a874)),x81543),x81544))+P4(f333(f333(f250(f890(x81541,a874)),f333(f333(f311(x81541),x81542),x81543)),x81544)) % 191.49/191.41 [8162]~P76(x81622)+~P143(x81622)+E(f333(f333(f11(x81621,x81622),f333(f333(f10(a880,x81622,x81621),f105(x81622)),x81623)),x81624),f333(f105(x81622),f333(f333(f11(x81621,a880),x81623),x81624))) % 191.49/191.41 [8163]~P76(x81632)+~P140(x81632)+E(f333(f333(f11(x81631,x81632),f333(f333(f10(a1,x81632,x81631),f107(x81632)),x81633)),x81634),f333(f107(x81632),f333(f333(f11(x81631,a1),x81633),x81634))) % 191.49/191.41 [8190]E(f333(f333(f3(f890(x81901,a874)),x81902),f333(f333(f3(f890(x81901,a874)),x81903),x81904)),x81904)+~P4(f333(f333(f250(f890(x81901,a874)),x81902),x81903))+~P4(f333(f333(f250(f890(x81901,a874)),x81904),x81902)) % 191.49/191.41 [8282]~P4(f333(f63(x82821),x82824))+E(f333(f333(f3(a880),f333(f333(f8(x82821,a880),x82822),x82823)),f333(f333(f8(x82821,a880),x82822),x82824)),f333(f333(f8(x82821,a880),x82822),f333(f333(f3(f890(x82821,a874)),x82823),x82824)))+~P4(f333(f333(f250(f890(x82821,a874)),x82824),x82823)) % 191.49/191.41 [8435]~P12(x84351,x84354,x84353)+~P4(f333(f333(f335(x84351),x84352),x84354))+P4(f333(f333(f335(x84351),x84352),f333(f287(x84351,x84351,x84353),f333(f333(f311(x84351),x84352),f194(f890(x84351,a874)))))) % 191.49/191.41 [8497]~P4(f333(f333(f250(f890(x84971,a874)),x84972),x84973))+~P4(f333(f333(f250(f890(x84971,a874)),x84972),x84974))+P4(f333(f333(f250(f890(x84971,a874)),x84972),f333(f333(f106(f890(x84971,a874)),x84973),x84974))) % 191.49/191.41 [8596]E(x85961,f194(f890(x85962,a874)))+P4(f333(f63(x85963),x85964))+~P4(f333(f63(f889(x85963,x85962)),f333(f333(f270(x85963,x85962),x85964),f333(f18(f890(x85962,a874),x85963),x85961)))) % 191.49/191.41 [8597]E(x85971,f194(f890(x85972,a874)))+P4(f333(f63(x85973),x85974))+~P4(f333(f63(f889(x85972,x85973)),f333(f333(f270(x85972,x85973),x85971),f333(f18(f890(x85973,a874),x85972),x85974)))) % 191.49/191.41 [8657]P4(f333(f333(f335(x86571),x86572),f322(x86571,x86573)))+~P4(f333(f333(f335(x86571),x86574),f322(x86571,x86573)))+~P4(f333(f333(f335(f889(x86571,x86571)),f333(f333(f263(x86571,x86571),x86572),x86574)),x86573)) % 191.49/191.41 [8707]~P40(x87071,x87074)+P4(f333(f333(f335(f889(x87071,x87071)),f333(f333(f263(x87071,x87071),x87073),x87072)),f309(x87071,x87074)))+P40(x87071,f333(f333(f311(f889(x87071,x87071)),f333(f333(f263(x87071,x87071),x87072),x87073)),x87074)) % 191.49/191.41 [8708]~P57(x87081,x87084)+P4(f333(f333(f335(f889(x87081,x87081)),f333(f333(f263(x87081,x87081),x87083),x87082)),f309(x87081,x87084)))+P57(x87081,f333(f333(f311(f889(x87081,x87081)),f333(f333(f263(x87081,x87081),x87082),x87083)),x87084)) % 191.49/191.41 [8786]~E(x87862,x87863)+~P4(f333(f333(f335(x87861),x87862),f333(f173(x87861),x87864)))+P4(f333(f333(f335(f889(x87861,x87861)),f333(f333(f263(x87861,x87861),x87862),x87863)),f333(f173(f889(x87861,x87861)),f333(f333(f182(x87861,x87861),x87864),x87864)))) % 191.49/191.41 [8872]~E(x88723,x88724)+P4(f333(f333(f272(x88721,x88721,a874),a330),x88722))+~P4(f333(f333(f335(f889(x88721,x88721)),x88722),f333(f173(f889(x88721,x88721)),f333(f333(f182(x88721,x88721),x88723),x88724)))) % 191.49/191.41 [8899]~P4(f333(x88994,x88992))+P4(f333(f333(f333(f333(a203,x88991),x88992),x88993),f494(x88993,x88992,x88991,x88994)))+~P4(f333(f333(f333(f333(a203,f33(x88994,x88991)),x88992),x88993),x88992)) % 191.49/191.41 [8925]P4(f333(f333(f335(f889(f881(x89251),f881(x89251))),f333(f333(f263(f881(x89251),f881(x89251)),x89252),x89253)),f148(x89251,x89254)))+~E(f333(f333(f174(x89251),f333(f195(f881(x89251)),x89252)),x89253),x89252)+~P4(f333(f333(f251(a880),f333(f195(f881(x89251)),x89252)),f333(f195(f881(x89251)),x89253))) % 191.49/191.41 [9022]~P4(f333(f63(x90221),x90224))+P4(f333(f333(f335(x90221),f536(x90222,x90223,x90224,x90221)),x90224))+P4(f333(f63(x90223),f333(f333(f44(x90221,f890(x90223,a874)),x90224),x90222))) % 191.49/191.41 [9023]~P4(f333(f63(x90231),x90234))+P4(f333(f333(f335(x90231),f726(x90232,x90233,x90234,x90231)),x90234))+P4(f333(f63(x90233),f333(f333(f44(x90231,f890(x90233,a874)),x90234),x90232))) % 191.49/191.41 [9095]P4(f333(f333(f335(f889(x90951,x90951)),x90952),f333(f333(f290(x90951,x90951,x90951),x90953),f309(x90951,x90953))))+~P4(f333(f333(f251(a880),f2(a880)),x90954))+~P4(f333(f333(f335(f889(x90951,x90951)),x90952),f333(f333(f189(f889(x90951,x90951),a874),x90954),x90953))) % 191.49/191.41 [9104]~P40(x91041,x91042)+~P4(f333(f333(f335(f889(x91041,x91041)),f333(f333(f263(x91041,x91041),x91044),x91043)),x91042))+~P4(f333(f333(f335(f889(x91041,x91041)),f333(f333(f263(x91041,x91041),x91043),x91044)),x91042)) % 191.49/191.41 [9233]~P4(f333(f63(x92331),x92334))+E(f333(f333(f8(x92331,a880),f333(f333(f10(f890(x92332,a874),a880,x92331),f39(x92332)),x92333)),x92334),f333(f39(f889(x92331,x92332)),f333(f333(f270(x92331,x92332),x92334),x92333)))+P4(f333(f333(f335(x92331),f632(x92333,x92332,x92334,x92331)),x92334)) % 191.49/191.41 [9237]~P4(f333(f138(x92371),x92372))+P4(f333(f138(x92371),f333(f333(f160(x92371,x92372),x92373),x92374)))+P4(f333(f333(f335(x92371),x92374),f333(f333(f3(f890(x92371,a874)),f333(f173(x92371),x92372)),f333(f333(f311(x92371),f333(f333(f166(x92371),x92372),x92373)),f194(f890(x92371,a874)))))) % 191.49/191.41 [9253]~P4(f333(f63(x92532),x92533))+~P4(f333(f63(x92531),f333(x92534,f536(x92534,x92531,x92533,x92532))))+P4(f333(f63(x92531),f333(f333(f44(x92532,f890(x92531,a874)),x92533),x92534))) % 191.49/191.41 [9254]~P4(f333(f63(x92542),x92543))+~P4(f333(f63(x92541),f333(x92544,f726(x92544,x92541,x92543,x92542))))+P4(f333(f63(x92541),f333(f333(f44(x92542,f890(x92541,a874)),x92543),x92544))) % 191.49/191.41 [9336]~P4(f333(f333(f335(f889(x93361,x93361)),x93362),f333(f333(f290(x93361,x93361,x93361),x93364),f309(x93361,x93364))))+P4(f333(f333(f335(f889(x93361,x93361)),x93362),f333(f333(f290(x93361,x93361,x93361),x93363),f309(x93361,x93363))))+~P4(f333(f333(f250(f890(f889(x93361,x93361),a874)),x93364),x93363)) % 191.49/191.41 [9343]E(f333(f333(f174(x93431),f611(x93434,x93433,x93432,x93431)),x93433),f333(f333(f174(x93431),f611(x93434,x93433,x93432,x93431)),x93432))+~P4(f333(f333(f335(f889(f881(x93431),f881(x93431))),f333(f333(f263(f881(x93431),f881(x93431)),x93432),x93433)),f148(x93431,x93434)))+E(f333(f333(f174(x93431),f333(f195(f881(x93431)),x93432)),x93433),x93432) % 191.49/191.41 [9364]~P4(f333(f63(x93641),x93644))+E(f333(f333(f8(x93641,a880),f333(f333(f10(f890(x93642,a874),a880,x93641),f39(x93642)),x93643)),x93644),f333(f39(f889(x93641,x93642)),f333(f333(f270(x93641,x93642),x93644),x93643)))+~P4(f333(f63(x93642),f333(x93643,f632(x93643,x93642,x93644,x93641)))) % 191.49/191.41 [9369]~E(f333(f195(f881(x93691)),x93693),f333(f195(f881(x93691)),x93692))+P4(f333(f333(f335(f889(f881(x93691),f881(x93691))),f333(f333(f263(f881(x93691),f881(x93691)),x93692),x93693)),f159(x93691,x93694)))+P4(f333(f333(f335(f889(x93691,x93691)),f595(x93694,x93693,x93692,x93691)),f333(f173(f889(x93691,x93691)),f333(f333(f182(x93691,x93691),x93692),x93693)))) % 191.49/191.41 [9437]~P4(f333(f333(f335(f889(f881(x94371),f881(x94371))),f333(f333(f263(f881(x94371),f881(x94371)),x94372),x94373)),f148(x94371,x94374)))+E(f333(f333(f174(x94371),f333(f195(f881(x94371)),x94372)),x94373),x94372)+P4(f333(f333(f251(a880),f611(x94374,x94373,x94372,x94371)),f333(f333(f248(a880),f333(f195(f881(x94371)),x94372)),f333(f195(f881(x94371)),x94373)))) % 191.49/191.41 [9438]E(f333(f178(x94381,x94382),x94383),f333(f178(x94381,x94382),x94384))+~E(f333(f173(x94381),f333(f333(f155(f889(x94381,x94382),x94381),f262(x94381,x94382)),x94383)),f333(f173(x94381),f333(f333(f155(f889(x94381,x94382),x94381),f262(x94381,x94382)),x94384)))+P4(f333(f333(f335(x94381),f720(x94383,x94384,x94382,x94381)),f333(f173(x94381),f333(f333(f155(f889(x94381,x94382),x94381),f262(x94381,x94382)),x94384)))) % 191.49/191.41 [9454]~P4(f333(x94541,x94544))+P4(f333(f333(f333(f333(a203,f33(x94541,x94542)),f494(x94543,x94544,x94542,x94541)),x94543),x94544))+~P4(f333(f333(f333(f333(a203,f33(x94541,x94542)),x94544),x94543),x94544)) % 191.49/191.41 [9459]~P4(f333(f333(f335(f889(f881(x94591),f881(x94591))),f333(f333(f263(f881(x94591),f881(x94591)),x94592),x94593)),f148(x94591,x94594)))+P4(f333(f333(f251(a880),f333(f195(f881(x94591)),x94592)),f333(f195(f881(x94591)),x94593)))+P4(f333(f333(f251(a880),f611(x94594,x94593,x94592,x94591)),f333(f333(f248(a880),f333(f195(f881(x94591)),x94592)),f333(f195(f881(x94591)),x94593)))) % 191.49/191.41 [9796]~P4(f333(f333(f333(x97961,f523(x97961,x97964,x97963,x97962)),f524(x97961,x97964,x97963,x97962)),f525(x97961,x97964,x97963,x97962)))+P4(f333(f333(f333(x97961,x97962),x97963),x97964))+~P4(f333(f321(f889(f890(a1,f884(f881(a329))),f889(a1,a1)),a319),f333(f333(f263(f890(a1,f884(f881(a329))),f889(a1,a1)),x97962),f333(f333(f263(a1,a1),x97963),x97964)))) % 191.49/191.41 [9866]P4(f333(f333(f333(x98661,x98662),x98663),x98664))+P4(f333(f321(f889(f890(a1,f884(f881(a329))),f889(a1,a1)),a319),f333(f333(f263(f890(a1,f884(f881(a329))),f889(a1,a1)),f523(x98661,x98664,x98663,x98662)),f333(f333(f263(a1,a1),f524(x98661,x98664,x98663,x98662)),f525(x98661,x98664,x98663,x98662)))))+~P4(f333(f321(f889(f890(a1,f884(f881(a329))),f889(a1,a1)),a319),f333(f333(f263(f890(a1,f884(f881(a329))),f889(a1,a1)),x98662),f333(f333(f263(a1,a1),x98663),x98664)))) % 191.49/191.41 [9903]~P4(f333(f333(f335(f889(f881(x99031),f881(x99031))),f333(f333(f263(f881(x99031),f881(x99031)),x99032),x99033)),f148(x99031,x99034)))+E(f333(f333(f174(x99031),f333(f195(f881(x99031)),x99032)),x99033),x99032)+P4(f333(f333(f335(f889(x99031,x99031)),f333(f333(f263(x99031,x99031),f333(f333(f166(x99031),x99032),f611(x99034,x99033,x99032,x99031))),f333(f333(f166(x99031),x99033),f611(x99034,x99033,x99032,x99031)))),x99034)) % 191.49/191.41 [9906]~P4(f333(f333(f335(f889(f881(x99061),f881(x99061))),f333(f333(f263(f881(x99061),f881(x99061)),x99062),x99063)),f148(x99061,x99064)))+P4(f333(f333(f251(a880),f333(f195(f881(x99061)),x99062)),f333(f195(f881(x99061)),x99063)))+P4(f333(f333(f335(f889(x99061,x99061)),f333(f333(f263(x99061,x99061),f333(f333(f166(x99061),x99062),f611(x99064,x99063,x99062,x99061))),f333(f333(f166(x99061),x99063),f611(x99064,x99063,x99062,x99061)))),x99064)) % 191.49/191.41 [9950]~E(f333(f195(f881(x99501)),x99502),f333(f195(f881(x99501)),x99503))+P4(f333(f333(f335(f889(f881(x99501),f881(x99501))),f333(f333(f263(f881(x99501),f881(x99501)),x99502),x99503)),f159(x99501,x99504)))+~P4(f333(f333(f335(f889(x99501,x99501)),f333(f333(f263(x99501,x99501),f333(f333(f166(x99501),x99502),f587(x99504,x99503,x99502,x99501))),f333(f333(f166(x99501),x99503),f587(x99504,x99503,x99502,x99501)))),x99504)) % 191.49/191.41 [10087]~P69(x100871)+~P4(f333(f63(x100872),x100874))+E(f333(f167(x100871),f333(f333(f155(x100872,x100871),x100873),f91(f881(x100872),f333(f333(f20(f881(x100872),a874,a874),f333(f333(f10(a874,f890(a874,a874),f881(x100872)),a331),f333(f333(f9(f881(x100872),f890(x100872,a874),a874),f333(f333(f10(f890(x100872,a874),f890(f890(x100872,a874),a874),f881(x100872)),a330),f173(x100872))),x100874))),f138(x100872))))),f240(x100872,x100871,x100873,x100874)) % 191.49/191.41 [7376]~P63(x73762)+E(x73761,f2(x73762))+E(f333(f333(f291(x73762),f333(f333(f81(x73762),x73763),f333(f333(f82(x73762),x73764),x73761))),x73761),f333(f333(f81(x73762),x73764),f333(f333(f291(x73762),x73763),x73761))) % 191.49/191.41 [7377]~P60(x73772)+E(x73771,f2(x73772))+E(f333(f333(f40(x73772),f333(f333(f81(x73772),x73773),f333(f333(f82(x73772),x73774),x73771))),x73771),f333(f333(f81(x73772),x73774),f333(f333(f40(x73772),x73773),x73771))) % 191.49/191.41 [7378]~P60(x73782)+E(x73781,f2(x73782))+E(f333(f333(f40(x73782),f333(f333(f81(x73782),x73783),f333(f333(f82(x73782),x73781),x73784))),x73781),f333(f333(f81(x73782),x73784),f333(f333(f40(x73782),x73783),x73781))) % 191.49/191.41 [7605]~P64(x76052)+E(x76051,f2(x76052))+E(f333(f333(f291(x76052),f333(f333(f3(x76052),x76053),f333(f333(f82(x76052),x76051),x76054))),x76051),f333(f333(f3(x76052),f333(f333(f291(x76052),x76053),x76051)),x76054)) % 191.49/191.41 [7606]~P63(x76062)+E(x76061,f2(x76062))+E(f333(f333(f291(x76062),f333(f333(f81(x76062),x76063),f333(f333(f82(x76062),x76064),x76061))),x76061),f333(f333(f81(x76062),f333(f333(f291(x76062),x76063),x76061)),x76064)) % 191.49/191.41 [7607]~P64(x76072)+E(x76071,f2(x76072))+E(f333(f333(f291(x76072),f333(f333(f81(x76072),x76073),f333(f333(f82(x76072),x76071),x76074))),x76071),f333(f333(f81(x76072),f333(f333(f291(x76072),x76073),x76071)),x76074)) % 191.49/191.41 [8310]~P4(f333(f161(x83101,x83103),x83104))+~P4(f333(f161(x83101,x83102),x83104))+P4(f333(f161(x83101,f333(f333(f106(f890(x83101,a874)),x83102),x83103)),x83104)) % 191.49/191.41 [8669]~E(f333(f333(f290(x86691,x86691,x86691),x86692),x86694),f194(f890(f889(x86691,x86691),a874)))+~E(f333(f333(f290(x86691,x86691,x86691),x86692),x86693),f194(f890(f889(x86691,x86691),a874)))+E(f333(f333(f290(x86691,x86691,x86691),x86692),f333(f333(f115(f890(f889(x86691,x86691),a874)),x86693),x86694)),f194(f890(f889(x86691,x86691),a874))) % 191.49/191.41 [8787]~P4(f333(f333(f250(f890(x87871,a874)),x87873),x87874))+~P4(f333(f333(f250(f890(x87871,a874)),x87872),x87874))+P4(f333(f333(f250(f890(x87871,a874)),f333(f333(f115(f890(x87871,a874)),x87872),x87873)),x87874)) % 191.49/191.41 [9165]~P4(f333(f63(x91651),x91654))+~P4(f333(f63(x91651),x91653))+E(f333(f333(f3(a880),f333(f333(f81(a880),f333(f333(f8(x91651,a880),x91652),x91653)),f333(f333(f8(x91651,a880),x91652),x91654))),f333(f333(f8(x91651,a880),x91652),f333(f333(f106(f890(x91651,a874)),x91653),x91654))),f333(f333(f8(x91651,a880),x91652),f333(f333(f115(f890(x91651,a874)),x91653),x91654))) % 191.49/191.41 [9250]~P4(f333(f333(f335(x92501),x92503),x92502))+~P4(f333(f333(f250(f890(x92501,a874)),x92502),f333(f333(f311(x92501),x92503),x92504)))+P4(f333(f333(f250(f890(x92501,a874)),f333(f333(f3(f890(x92501,a874)),x92502),f333(f333(f311(x92501),x92503),f194(f890(x92501,a874))))),x92504)) % 191.49/191.41 [9409]~P4(f333(f333(f335(x94091),x94093),x94092))+P4(f333(f333(f250(f890(x94091,a874)),x94092),f333(f333(f311(x94091),x94093),x94094)))+~P4(f333(f333(f250(f890(x94091,a874)),f333(f333(f3(f890(x94091,a874)),x94092),f333(f333(f311(x94091),x94093),f194(f890(x94091,a874))))),x94094)) % 191.49/191.41 [9514]~P4(f333(f333(f251(a880),x95142),x95144))+~P4(f333(f333(f250(a880),x95141),x95143))+P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),f333(f333(f263(a880,a880),x95141),x95142)),f333(f333(f263(a880,a880),x95143),x95144))),a36)) % 191.49/191.41 [9515]~P4(f333(f333(f250(a880),x95152),x95154))+~P4(f333(f333(f250(a880),x95151),x95153))+P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),f333(f333(f263(a880,a880),x95151),x95152)),f333(f333(f263(a880,a880),x95153),x95154))),a71)) % 191.49/191.41 [9831]~P4(f333(f333(f335(f881(x98311)),x98314),f162(x98311,x98313)))+~P4(f333(f333(f335(f881(x98311)),x98314),f162(x98311,x98312)))+P4(f333(f161(x98311,f333(f333(f106(f890(x98311,a874)),f333(f333(f9(x98311,f890(x98311,a874),a874),f335(x98311)),x98312)),f333(f333(f9(x98311,f890(x98311,a874),a874),f335(x98311)),x98313))),x98314)) % 191.49/191.41 [9924]~P28(x99241,f890(f890(x99241,a874),a874),f333(f333(f9(x99241,f890(f889(x99241,x99241),a874),f890(f890(x99241,a874),a874)),f333(f333(f10(f890(x99241,a874),f890(f890(f889(x99241,x99241),a874),f890(f890(x99241,a874),a874)),x99241),f62(x99241)),f333(f333(f9(x99241,f890(x99241,a874),f890(x99241,a874)),f311(x99241)),f194(f890(x99241,a874))))),x99243),x99242)+~P4(f333(f333(f335(x99241),x99244),x99242))+E(f333(f333(f3(f890(f890(x99241,a874),a874)),f333(f333(f62(x99241),x99242),x99243)),f333(f333(f62(x99241),f333(f333(f311(x99241),x99244),f194(f890(x99241,a874)))),x99243)),f333(f333(f62(x99241),f333(f333(f3(f890(x99241,a874)),x99242),f333(f333(f311(x99241),x99244),f194(f890(x99241,a874))))),x99243)) % 191.49/191.41 [10044]~P50(x100441,x100442,x100444)+~P4(f333(f333(f335(f889(x100441,x100441)),x100443),x100444))+P4(f333(f333(f272(x100441,x100441,a874),f333(f333(f9(x100441,f890(x100441,a874),f890(x100441,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x100441,a874),f890(x100441,a874)),x100441),f10(a874,a874,x100441)),f333(f333(f10(a874,f890(a874,a874),x100441),a331),f333(f333(f9(x100441,f890(x100441,a874),a874),f335(x100441)),x100442)))),f333(f333(f9(x100441,f890(x100441,a874),a874),f335(x100441)),x100442))),x100443)) % 191.49/191.41 [10056]P4(f333(f63(x100561),x100562))+~P4(f333(f63(x100563),f333(f312(x100561,x100563,x100564),x100562)))+~P4(f333(f63(x100561),f333(f255(x100561),f333(f333(f20(x100561,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100561),a331),f333(f333(f9(x100561,f890(x100561,a874),a874),f335(x100561)),x100562))),f333(f333(f9(x100561,x100563,a874),f333(f333(f10(x100563,f890(x100563,a874),x100561),a330),x100564)),f333(x100564,f719(x100564,x100563,x100562,x100561))))))) % 191.49/191.41 [8062]~P64(x80622)+E(x80621,f2(x80622))+E(f333(f333(f291(x80622),f333(f333(f3(x80622),f333(f333(f82(x80622),x80621),x80623)),x80624)),x80621),f333(f333(f3(x80622),x80623),f333(f333(f291(x80622),x80624),x80621))) % 191.49/191.41 [8063]~P64(x80632)+E(x80631,f2(x80632))+E(f333(f333(f291(x80632),f333(f333(f81(x80632),f333(f333(f82(x80632),x80631),x80633)),x80634)),x80631),f333(f333(f81(x80632),x80633),f333(f333(f291(x80632),x80634),x80631))) % 191.49/191.41 [8955]~E(f333(f333(f290(x89551,x89551,x89551),x89553),x89554),f194(f890(f889(x89551,x89551),a874)))+~E(f333(f333(f290(x89551,x89551,x89551),x89552),x89554),f194(f890(f889(x89551,x89551),a874)))+E(f333(f333(f290(x89551,x89551,x89551),f333(f333(f115(f890(f889(x89551,x89551),a874)),x89552),x89553)),x89554),f194(f890(f889(x89551,x89551),a874))) % 191.49/191.41 [9989]~P145(x99891)+~P145(x99892)+E(f333(f333(f318(x99891),f333(f333(f9(x99891,a104,f884(f881(a329))),f333(f333(f10(f890(x99892,f884(f881(a329))),f890(a104,f884(f881(a329))),x99891),f318(x99892)),f333(f333(f10(f890(x99892,f889(x99891,x99892)),f890(x99892,f884(f881(a329))),x99891),f333(f10(f889(x99891,x99892),f884(f881(a329)),x99892),x99893)),f263(x99891,x99892)))),x99894)),x99894),f333(f333(f318(f889(x99891,x99892)),x99893),x99894)) % 191.49/191.41 [9730]~P4(f333(f161(x97301,x97303),x97304))+~P4(f333(f161(x97301,x97302),x97304))+P4(f333(f161(x97301,f333(f333(f20(x97301,a874,a874),f333(f333(f10(a874,f890(a874,a874),x97301),a331),x97302)),x97303)),x97304)) % 191.49/191.41 [9981]P4(f333(x99811,f570(x99812,x99813,x99811,x99814)))+~P4(f333(f63(x99814),f333(f255(x99814),x99811)))+P4(f333(f63(x99813),f333(f255(x99813),f333(f333(f10(f890(x99814,a874),a874,x99813),f87(x99814)),f333(f333(f10(f890(x99814,a874),f890(x99814,a874),x99813),f333(f20(x99814,a874,a874),f333(f333(f10(a874,f890(a874,a874),x99814),a331),x99811))),x99812))))) % 191.49/191.41 [10003]~P4(f333(f63(x100032),f333(f255(x100032),x100033)))+~P4(f333(f63(x100031),f333(f255(x100031),f333(f333(f9(x100031,x100032,a874),x100034),f570(x100034,x100031,x100033,x100032)))))+P4(f333(f63(x100031),f333(f255(x100031),f333(f333(f10(f890(x100032,a874),a874,x100031),f87(x100032)),f333(f333(f10(f890(x100032,a874),f890(x100032,a874),x100031),f333(f20(x100032,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100032),a331),x100033))),x100034))))) % 191.49/191.41 [6538]E(x65381,x65382)+~E(f333(x65383,x65381),f333(x65383,x65382))+~P28(x65384,x65385,x65383,f258(f890(x65384,a874))) % 191.49/191.41 [6698]~E(f333(x66983,x66985),f197(x66982))+~E(f333(x66984,x66985),f197(x66982))+E(f333(f185(x66981,x66982,x66983,x66984),x66985),f197(x66982)) % 191.49/191.41 [7411]E(x74111,x74112)+~P28(x74113,x74114,x74115,f258(f890(x74113,a874)))+~E(f333(f312(x74113,x74114,x74115),x74111),f333(f312(x74113,x74114,x74115),x74112)) % 191.49/191.41 [7659]P28(x76592,x76593,f353(x76594,x76593,x76592,x76591),x76591)+~E(f333(f312(x76593,x76592,x76595),x76594),x76591)+E(x76591,f194(f890(x76592,a874))) % 191.49/191.41 [8201]~P4(f333(f333(x82013,x82012),x82015))+~P4(f333(f333(x82013,x82014),x82012))+P4(f333(f333(f335(x82011),x82012),f297(x82011,x82013,x82014,x82015))) % 191.49/191.41 [8202]~P4(f333(f333(x82023,x82022),x82025))+~P4(f333(f333(x82023,x82024),x82022))+P4(f333(f333(f335(x82021),x82022),f300(x82021,x82023,x82024,x82025))) % 191.49/191.41 [8745]~P28(x87451,x87453,x87455,f258(f890(x87451,a874)))+~P28(x87453,x87452,x87454,f258(f890(x87453,a874)))+P28(x87451,x87452,f333(f74(x87453,x87452,x87451,x87454),x87455),f258(f890(x87451,a874))) % 191.49/191.41 [9312]P4(f333(f333(f335(f889(x93121,x93121)),f333(f333(f263(x93121,x93121),x93122),x93123)),f309(x93121,x93124)))+~P4(f333(f333(f335(f889(x93121,x93121)),f333(f333(f263(x93121,x93121),x93122),x93125)),f309(x93121,x93124)))+~P4(f333(f333(f335(f889(x93121,x93121)),f333(f333(f263(x93121,x93121),x93125),x93123)),f309(x93121,x93124))) % 191.49/191.41 [9350]~P109(x93502)+~P4(f333(f138(x93501),x93505))+P4(f333(f138(x93501),f150(x93501,x93502,x93503,x93504,x93505))) % 191.49/191.41 [5381]~E(x53812,f118(x53811))+E(f333(f333(f127(x53811),x53812),x53813),f333(f333(f152(x53811),x53814),x53815))+~E(x53813,f333(f333(f152(x53811),x53814),x53815)) % 191.49/191.41 [5382]~E(x53822,f118(x53821))+E(f333(f333(f127(x53821),x53822),x53823),f333(f333(f152(x53821),x53824),x53825))+~E(f333(f333(f152(x53821),x53824),x53825),x53823) % 191.49/191.41 [6498]~E(f333(f195(f881(x64981)),x64985),f333(f195(f881(x64982)),x64984))+E(f333(f333(f155(f889(x64981,x64982),x64982),f271(x64981,x64982)),x64983),x64984)+~E(f333(f333(f182(x64981,x64982),x64985),x64984),x64983) % 191.49/191.41 [6499]~E(f333(f195(f881(x64991)),x64994),f333(f195(f881(x64992)),x64995))+E(f333(f333(f155(f889(x64991,x64992),x64991),f262(x64991,x64992)),x64993),x64994)+~E(f333(f333(f182(x64991,x64992),x64994),x64995),x64993) % 191.49/191.41 [6960]~P109(x69601)+~P17(x69601,f333(f333(f155(x69602,x69601),x69603),x69605))+P17(x69601,f333(f333(f155(x69602,x69601),x69603),f333(f137(x69602,x69604),x69605))) % 191.49/191.41 [7007]~P4(f333(x70073,x70075))+~P4(f333(f333(x70072,x70074),x70075))+P4(f333(f333(f96(x70071,x70072,x70073),x70074),x70075)) % 191.49/191.41 [7103]~P109(x71031)+P17(x71031,f333(f333(f155(x71032,x71031),x71033),f171(x71032,x71034,x71035)))+~P17(x71031,f333(f333(f155(x71032,x71031),x71033),x71035)) % 191.49/191.41 [7126]~P54(x71263,x71262,x71265)+~P54(x71261,x71263,x71264)+P54(x71261,x71262,f333(f333(f290(x71261,x71263,x71262),x71264),x71265)) % 191.49/191.41 [7218]E(x72181,x72182)+~P28(x72183,x72184,x72185,f258(f890(x72183,a874)))+~E(f333(f333(f155(x72183,x72184),x72185),x72181),f333(f333(f155(x72183,x72184),x72185),x72182)) % 191.49/191.41 [7362]~P4(f333(f333(f251(a880),x73621),f333(x73623,x73625)))+P4(f333(f333(f251(a880),x73621),f156(x73622,x73623,x73624)))+~P4(f333(f333(f335(x73622),x73625),f333(f173(x73622),x73624))) % 191.49/191.41 [7363]~P4(f333(f333(f250(a880),x73631),f333(x73633,x73635)))+P4(f333(f333(f250(a880),x73631),f156(x73632,x73633,x73634)))+~P4(f333(f333(f335(x73632),x73635),f333(f173(x73632),x73634))) % 191.49/191.41 [7762]~P110(x77621)+P4(f333(f333(f250(f890(x77621,a874)),f304(x77621,x77622,x77623)),f304(x77621,x77624,x77625)))+P4(f333(f333(f250(x77621),x77622),x77623)) % 191.49/191.41 [7787]~P9(x77871)+P4(f333(f333(f250(x77871),f333(f333(f43(x77872,x77871),x77873),x77874)),f333(x77874,x77875)))+~P4(f333(f333(f335(x77872),x77875),x77873)) % 191.49/191.41 [7855]~P28(x78551,x78552,x78554,x78553)+E(f333(f78(x78551,x78552,x78553,x78554),f333(x78554,x78555)),x78555)+~P4(f333(f333(f335(x78551),x78555),x78553)) % 191.49/191.41 [8052]~P4(f333(x80521,x80525))+P4(f333(x80521,f428(x80521,x80522,x80523,x80524)))+~P4(f333(f333(f335(x80524),x80525),x80523)) % 191.49/191.41 [8053]~P4(f333(x80531,x80535))+P4(f333(x80531,f428(x80531,x80532,x80533,x80534)))+~P4(f333(f333(f335(x80534),x80535),x80532)) % 191.49/191.41 [8151]P4(f333(f63(x81511),x81512))+~P4(f333(f63(x81513),x81514))+~P4(f333(f333(f250(f890(x81511,a874)),x81512),f333(f312(x81513,x81511,x81515),x81514))) % 191.49/191.41 [8314]E(x83141,x83142)+~P28(x83143,x83144,x83145,f333(f333(f115(f890(x83143,a874)),f333(f173(x83143),x83141)),f333(f173(x83143),x83142)))+~E(f333(f333(f155(x83143,x83144),x83145),x83141),f333(f333(f155(x83143,x83144),x83145),x83142)) % 191.49/191.41 [8366]~P110(x83661)+~P4(f333(f333(f251(f890(x83661,a874)),f304(x83661,x83664,x83665)),f304(x83661,x83662,x83663)))+P4(f333(f333(f250(x83661),x83662),x83663)) % 191.49/191.41 [8433]~P28(x84331,x84334,x84335,f258(f890(x84331,a874)))+~P4(f333(f333(f335(x84334),f333(x84335,x84332)),f333(f312(x84331,x84334,x84335),x84333)))+P4(f333(f333(f335(x84331),x84332),x84333)) % 191.49/191.41 [8509]P4(f333(x85091,x85092))+~P4(f333(x85091,f432(x85091,x85093,x85094,x85095)))+~P4(f333(f333(f335(x85095),x85092),x85094)) % 191.49/191.41 [8510]P4(f333(x85101,x85102))+~P4(f333(x85101,f432(x85101,x85103,x85104,x85105)))+~P4(f333(f333(f335(x85105),x85102),x85103)) % 191.49/191.41 [8784]~P28(x87842,x87843,x87841,x87844)+E(f333(x87841,f333(f78(x87842,x87843,x87844,x87841),x87845)),x87845)+~P4(f333(f333(f335(x87843),x87845),f333(f312(x87842,x87843,x87841),x87844))) % 191.49/191.41 [8894]E(x88941,f118(x88942))+E(f333(f333(f152(x88942),x88943),f589(x88944,x88943,x88945,x88941,x88942)),x88941)+~E(f333(f333(f127(x88942),x88941),x88945),f333(f333(f152(x88942),x88943),x88944)) % 191.49/191.41 [8895]E(x88951,f118(x88952))+E(f333(f333(f152(x88952),x88953),f590(x88954,x88951,x88955,x88953,x88952)),x88951)+~E(f333(f333(f127(x88952),x88951),x88954),f333(f333(f152(x88952),x88953),x88955)) % 191.49/191.41 [8911]E(f333(f333(f152(x89112),x89113),f589(x89114,x89113,x89111,x89115,x89112)),x89115)+~E(f333(f333(f127(x89112),x89115),x89111),f333(f333(f152(x89112),x89113),x89114))+E(x89111,f333(f333(f152(x89112),x89113),x89114)) % 191.49/191.41 [8912]E(f333(f333(f152(x89121),x89122),f590(x89124,x89125,x89123,x89122,x89121)),x89125)+~E(f333(f333(f127(x89121),x89125),x89124),f333(f333(f152(x89121),x89122),x89123))+E(f333(f333(f152(x89121),x89122),x89123),x89124) % 191.49/191.41 [8992]~E(f333(f312(x89923,x89922,x89924),f258(f890(x89923,a874))),f258(f890(x89922,a874)))+~E(f333(f312(x89921,x89923,x89925),f258(f890(x89921,a874))),f258(f890(x89923,a874)))+E(f333(f312(x89921,x89922,f333(f74(x89923,x89922,x89921,x89924),x89925)),f258(f890(x89921,a874))),f258(f890(x89922,a874))) % 191.49/191.41 [9361]E(x93611,f118(x93612))+~E(f333(f333(f127(x93612),x93611),x93613),f333(f333(f152(x93612),x93615),x93614))+E(f333(f333(f127(x93612),f590(x93613,x93611,x93614,x93615,x93612)),x93613),x93614) % 191.49/191.41 [9362]E(x93621,f118(x93622))+~E(f333(f333(f127(x93622),x93621),x93625),f333(f333(f152(x93622),x93624),x93623))+E(f333(f333(f127(x93622),f589(x93623,x93624,x93625,x93621,x93622)),x93625),x93623) % 191.49/191.41 [9370]E(f333(f333(f127(x93702),f589(x93704,x93703,x93701,x93705,x93702)),x93701),x93704)+~E(f333(f333(f127(x93702),x93705),x93701),f333(f333(f152(x93702),x93703),x93704))+E(x93701,f333(f333(f152(x93702),x93703),x93704)) % 191.49/191.41 [9371]~E(f333(f333(f127(x93711),x93715),x93714),f333(f333(f152(x93711),x93712),x93713))+E(f333(f333(f127(x93711),f590(x93714,x93715,x93713,x93712,x93711)),x93714),x93713)+E(f333(f333(f152(x93711),x93712),x93713),x93714) % 191.49/191.41 [9372]E(f333(f333(f127(x93721),x93725),f592(x93723,x93722,x93724,x93725,x93721)),x93722)+E(f333(f333(f127(x93721),x93722),f591(x93723,x93722,x93724,x93725,x93721)),x93725)+~E(f333(f333(f127(x93721),x93725),x93724),f333(f333(f127(x93721),x93722),x93723)) % 191.49/191.41 [9397]~P109(x93971)+P17(x93971,f333(f333(f155(x93972,x93971),x93973),f150(x93972,x93971,x93973,x93974,x93975)))+~P17(x93971,f333(f333(f155(x93972,x93971),x93973),x93975)) % 191.49/191.41 [9406]~P58(x94065,x94061,x94064,x94063)+P4(f333(f333(x94061,x94062),f708(x94063,x94064,x94061,x94065,x94062)))+~P4(f333(f333(f335(x94065),x94062),x94064)) % 191.49/191.41 [9526]~P4(f333(f333(f335(f889(x95261,x95261)),f333(f333(f263(x95261,x95261),x95265),x95263)),f309(x95261,x95264)))+P4(f333(f333(f335(f889(x95261,x95261)),f333(f333(f263(x95261,x95261),x95262),x95263)),f333(f333(f290(x95261,x95261,x95261),x95264),f309(x95261,x95264))))+~P4(f333(f333(f335(f889(x95261,x95261)),f333(f333(f263(x95261,x95261),x95262),x95265)),f333(f333(f290(x95261,x95261,x95261),x95264),f309(x95261,x95264)))) % 191.49/191.41 [9527]~P4(f333(f333(f335(f889(x95271,x95271)),f333(f333(f263(x95271,x95271),x95272),x95275)),f309(x95271,x95274)))+P4(f333(f333(f335(f889(x95271,x95271)),f333(f333(f263(x95271,x95271),x95272),x95273)),f333(f333(f290(x95271,x95271,x95271),x95274),f309(x95271,x95274))))+~P4(f333(f333(f335(f889(x95271,x95271)),f333(f333(f263(x95271,x95271),x95275),x95273)),f333(f333(f290(x95271,x95271,x95271),x95274),f309(x95271,x95274)))) % 191.49/191.41 [9530]P4(f333(f333(f335(f889(f881(x95301),f881(x95301))),f333(f333(f263(f881(x95301),f881(x95301)),x95302),x95303)),f159(x95301,f309(x95301,x95304))))+~P4(f333(f333(f335(f889(f881(x95301),f881(x95301))),f333(f333(f263(f881(x95301),f881(x95301)),x95302),x95305)),f159(x95301,f309(x95301,x95304))))+~P4(f333(f333(f335(f889(f881(x95301),f881(x95301))),f333(f333(f263(f881(x95301),f881(x95301)),x95305),x95303)),f159(x95301,f309(x95301,x95304)))) % 191.49/191.41 [9534]E(f333(f333(f127(x95341),x95342),f591(x95343,x95342,x95344,x95345,x95341)),x95345)+E(f333(f333(f127(x95341),f592(x95343,x95342,x95344,x95345,x95341)),x95343),x95344)+~E(f333(f333(f127(x95341),x95342),x95343),f333(f333(f127(x95341),x95345),x95344)) % 191.49/191.41 [9535]E(f333(f333(f127(x95351),x95352),f592(x95353,x95354,x95355,x95352,x95351)),x95354)+E(f333(f333(f127(x95351),f591(x95353,x95354,x95355,x95352,x95351)),x95355),x95353)+~E(f333(f333(f127(x95351),x95352),x95355),f333(f333(f127(x95351),x95354),x95353)) % 191.49/191.41 [9595]P4(f333(f333(f335(f889(x95951,x95951)),f333(f333(f263(x95951,x95951),x95952),x95953)),f333(f333(f290(x95951,x95951,x95951),x95954),f309(x95951,x95954))))+~P4(f333(f333(f335(f889(x95951,x95951)),f333(f333(f263(x95951,x95951),x95952),x95955)),f333(f333(f290(x95951,x95951,x95951),x95954),f309(x95951,x95954))))+~P4(f333(f333(f335(f889(x95951,x95951)),f333(f333(f263(x95951,x95951),x95955),x95953)),f333(f333(f290(x95951,x95951,x95951),x95954),f309(x95951,x95954)))) % 191.49/191.41 [9626]P37(x96261,x96262,x96263,x96264,x96265)+~E(f333(f195(f881(x96261)),x96264),f333(f195(f881(x96262)),x96265))+~P4(f333(f333(f272(x96261,x96262,a874),x96263),f677(x96265,x96264,x96263,x96262,x96261))) % 191.49/191.41 [9627]P37(x96271,x96272,x96273,x96274,x96275)+~E(f333(f195(f881(x96271)),x96274),f333(f195(f881(x96272)),x96275))+~P4(f333(f333(f272(x96271,x96272,a874),x96273),f688(x96273,x96275,x96274,x96272,x96271))) % 191.49/191.41 [9632]E(f333(f333(f127(x96321),f591(x96322,x96323,x96324,x96325,x96321)),x96324),x96322)+~E(f333(f333(f127(x96321),x96323),x96322),f333(f333(f127(x96321),x96325),x96324))+E(f333(f333(f127(x96321),f592(x96322,x96323,x96324,x96325,x96321)),x96322),x96324) % 191.49/191.41 [9649]~P109(x96492)+E(f333(f333(f149(x96491,x96492,x96493),x96494),x96495),f333(f333(f152(x96491),x96494),x96495))+P4(f333(f333(f335(x96491),f738(x96494,x96493,x96495,x96491,x96492)),f333(f173(x96491),x96495))) % 191.49/191.41 [9655]~P58(x96551,x96554,x96553,x96552)+~P4(f333(f333(f335(x96551),x96555),x96553))+P4(f333(f333(f335(x96551),f708(x96552,x96553,x96554,x96551,x96555)),x96552)) % 191.49/191.41 [9788]~P4(f333(f333(f335(f889(f890(x97881,a874),f890(x97881,a874))),f333(f333(f263(f890(x97881,a874),f890(x97881,a874)),x97884),x97883)),f325(x97881,x97882)))+~P4(f333(f333(f335(x97881),x97885),x97884))+P4(f333(f333(f335(x97881),f759(x97882,x97883,x97884,x97881,x97885)),x97883)) % 191.49/191.41 [9799]~P109(x97992)+E(f333(f333(f149(x97991,x97992,x97993),x97994),x97995),f333(f333(f152(x97991),x97994),x97995))+~P4(f333(f333(f250(x97992),f333(x97993,x97994)),f333(x97993,f738(x97994,x97993,x97995,x97991,x97992)))) % 191.49/191.41 [9965]P37(x99651,x99652,x99653,x99654,x99655)+~E(f333(f195(f881(x99651)),x99654),f333(f195(f881(x99652)),x99655))+~P4(f333(f333(x99653,f333(f333(f166(x99651),x99654),f689(x99655,x99654,x99653,x99652,x99651))),f333(f333(f166(x99652),x99655),f689(x99655,x99654,x99653,x99652,x99651)))) % 191.49/191.41 [9966]P37(x99661,x99662,x99663,x99664,x99665)+~E(f333(f195(f881(x99661)),x99664),f333(f195(f881(x99662)),x99665))+~P4(f333(f333(x99663,f333(f333(f166(x99661),x99664),f731(x99663,x99665,x99662,x99664,x99661))),f333(f333(f166(x99662),x99665),f731(x99663,x99665,x99662,x99664,x99661)))) % 191.49/191.41 [6566]~P20(x65662,x65665,x65661)+~P4(f333(f63(x65662),x65664))+E(f333(x65661,f333(f333(f311(x65662),x65663),x65664)),f333(f333(f66(x65662,x65662,x65665),x65663),x65664)) % 191.49/191.41 [6567]~E(x65673,x65674)+~E(x65672,x65675)+E(f333(f333(f311(x65671),x65672),f333(f333(f311(x65671),x65673),f194(f890(x65671,a874)))),f333(f333(f311(x65671),x65674),f333(f333(f311(x65671),x65675),f194(f890(x65671,a874))))) % 191.49/191.41 [6578]P4(f333(x65782,x65785))+E(f177(x65781,x65782,f333(f333(f127(x65781),x65783),x65784)),f177(x65781,x65782,x65783))+~P4(f333(f333(f335(x65781),x65785),f333(f173(x65781),x65783))) % 191.49/191.41 [6615]E(f333(x66151,x66152),f194(f890(x66153,a874)))+~E(f333(f333(f44(x66154,f890(x66153,a874)),x66155),x66151),f194(f890(x66153,a874)))+~P4(f333(f333(f335(x66154),x66152),x66155)) % 191.49/191.41 [6616]E(f333(x66161,x66162),f258(f890(x66163,a874)))+~E(f333(f333(f43(x66164,f890(x66163,a874)),x66165),x66161),f258(f890(x66163,a874)))+~P4(f333(f333(f335(x66164),x66162),x66165)) % 191.49/191.41 [6908]~P4(f333(f333(f201(x69081),x69083),x69085))+~P4(f333(f333(f201(x69082),x69085),x69084))+P4(f333(f333(f201(f34(x69081,x69082)),x69083),x69084)) % 191.49/191.41 [7113]~E(x71132,x71134)+~P137(x71131)+E(f333(f333(f81(x71131),f333(f333(f82(x71131),x71132),x71133)),f333(f333(f82(x71131),x71134),x71135)),f333(f333(f81(x71131),f333(f333(f82(x71131),x71132),x71135)),f333(f333(f82(x71131),x71134),x71133))) % 191.49/191.41 [7173]~P9(x71731)+~P4(f333(f333(f335(x71734),x71733),x71735))+P4(f333(f333(f250(x71731),f333(x71732,x71733)),f333(f333(f44(x71734,x71731),x71735),x71732))) % 191.49/191.41 [7223]~P111(x72231)+P4(f333(f333(f250(x72231),f333(x72232,x72233)),f333(x72234,x72233)))+~P4(f333(f333(f250(f890(x72235,x72231)),x72232),x72234)) % 191.49/191.41 [7331]E(x73311,x73312)+E(x73313,x73311)+~E(f333(f333(f311(x73314),x73311),f333(f333(f311(x73314),x73315),f194(f890(x73314,a874)))),f333(f333(f311(x73314),x73312),f333(f333(f311(x73314),x73313),f194(f890(x73314,a874))))) % 191.49/191.41 [7332]E(x73321,x73322)+E(x73323,x73321)+~E(f333(f333(f311(x73324),x73323),f333(f333(f311(x73324),x73322),f194(f890(x73324,a874)))),f333(f333(f311(x73324),x73325),f333(f333(f311(x73324),x73321),f194(f890(x73324,a874))))) % 191.49/191.41 [7333]E(x73331,x73332)+E(x73331,x73333)+~E(f333(f333(f311(x73334),x73333),f333(f333(f311(x73334),x73332),f194(f890(x73334,a874)))),f333(f333(f311(x73334),x73335),f333(f333(f311(x73334),x73331),f194(f890(x73334,a874))))) % 191.49/191.41 [7334]E(x73341,x73342)+E(x73341,x73343)+~E(f333(f333(f311(x73344),x73341),f333(f333(f311(x73344),x73345),f194(f890(x73344,a874)))),f333(f333(f311(x73344),x73342),f333(f333(f311(x73344),x73343),f194(f890(x73344,a874))))) % 191.49/191.41 [7860]P28(x78601,x78602,x78603,x78604)+~P28(x78601,x78602,x78603,x78605)+~P4(f333(f333(f250(f890(x78601,a874)),x78604),x78605)) % 191.49/191.41 [7867]~P4(f333(f333(f250(a880),x78675),x78673))+~P4(f333(f333(f333(f333(a203,x78671),x78672),x78675),x78674))+P4(f333(f333(f333(f333(a203,x78671),x78672),x78673),x78674)) % 191.49/191.41 [7958]P4(f333(x79581,x79582))+~P4(f333(f333(f201(x79584),x79582),x79585))+P4(f333(f333(f201(f31(x79581,x79583,x79584)),x79582),x79585)) % 191.49/191.41 [7985]~P4(f333(x79851,x79854))+~P4(f333(f333(f201(x79852),x79854),x79855))+P4(f333(f333(f201(f31(x79851,x79852,x79853)),x79854),x79855)) % 191.49/191.41 [8037]E(x80371,x80372)+~E(f333(f312(x80373,x80374,x80375),x80371),f333(f312(x80373,x80374,x80375),x80372))+~P28(x80373,x80374,x80375,f333(f333(f115(f890(x80373,a874)),x80371),x80372)) % 191.49/191.41 [8116]P4(f333(x81162,x81164))+E(f333(f333(f139(x81161),f333(f195(f881(x81161)),f177(x81161,x81162,x81163))),x81163),f333(f333(f152(x81161),x81164),x81165))+~E(f333(f333(f127(x81161),f177(x81161,x81162,x81163)),f333(f333(f152(x81161),x81164),x81165)),x81163) % 191.49/191.41 [8148]~P28(x81481,x81482,x81483,x81485)+~P28(x81481,x81482,x81483,x81484)+P28(x81481,x81482,x81483,f333(f333(f106(f890(x81481,a874)),x81484),x81485)) % 191.49/191.41 [8255]~P69(x82551)+E(f333(f333(f81(x82551),f333(x82552,x82553)),f333(f167(x82551),f333(f333(f155(x82554,x82551),x82552),f171(x82554,x82553,x82555)))),f333(f167(x82551),f333(f333(f155(x82554,x82551),x82552),x82555)))+~P4(f333(f333(f335(x82554),x82553),f333(f173(x82554),x82555))) % 191.49/191.41 [8341]~P109(x83411)+~P17(x83411,f333(f333(f155(x83412,x83411),x83413),x83415))+P17(x83411,f333(f333(f155(x83412,x83411),x83413),f333(f333(f149(x83412,x83411,x83413),x83414),x83415))) % 191.49/191.41 [8417]P4(f333(x84171,x84172))+P4(f333(f333(f201(x84173),x84172),x84174))+~P4(f333(f333(f201(f31(x84171,x84175,x84173)),x84172),x84174)) % 191.49/191.41 [8428]~P9(x84281)+P4(f333(f333(f250(x84281),f333(f333(f43(x84282,x84281),x84283),x84284)),f333(f333(f43(x84282,x84281),x84285),x84284)))+~P4(f333(f333(f250(f890(x84282,a874)),x84285),x84283)) % 191.49/191.41 [8429]~P9(x84291)+P4(f333(f333(f250(x84291),f333(f333(f44(x84292,x84291),x84293),x84294)),f333(f333(f44(x84292,x84291),x84295),x84294)))+~P4(f333(f333(f250(f890(x84292,a874)),x84293),x84295)) % 191.49/191.41 [8442]~P4(f333(x84424,x84422))+P4(f333(f333(f201(x84421),x84422),x84423))+~P4(f333(f333(f201(f31(x84424,x84421,x84425)),x84422),x84423)) % 191.49/191.41 [8466]~P109(x84663)+P4(f333(f138(x84661),x84662))+~P4(f333(f138(x84661),f333(f333(f149(x84661,x84663,x84664),x84665),x84662))) % 191.49/191.41 [8476]P4(f333(f333(f201(x84761),x84762),x84763))+P4(f333(f333(f201(x84764),x84762),x84763))+~P4(f333(f333(f201(f31(x84765,x84761,x84764)),x84762),x84763)) % 191.49/191.41 [8607]~P109(x86071)+~P4(f333(f333(f335(x86072),x86073),f333(f173(x86072),x86074)))+~P4(f333(f138(x86072),f333(f333(f149(x86072,x86071,x86075),x86073),x86074))) % 191.49/191.41 [8679]~P109(x86791)+P17(x86791,f333(f333(f155(x86792,x86791),x86793),x86794))+~P17(x86791,f333(f333(f155(x86792,x86791),x86793),f333(f333(f149(x86792,x86791,x86793),x86795),x86794))) % 191.49/191.41 [8771]~P109(x87712)+E(f333(f333(f149(x87711,x87712,x87713),x87714),x87715),f150(x87711,x87712,x87713,x87714,x87715))+P4(f333(f333(f335(x87712),f333(x87713,x87714)),f333(f312(x87711,x87712,x87713),f333(f173(x87711),x87715)))) % 191.49/191.41 [8849]~P109(x88492)+E(f150(x88491,x88492,x88493,x88494,x88495),x88495)+~P4(f333(f333(f335(x88492),f333(x88493,x88494)),f333(f312(x88491,x88492,x88493),f333(f173(x88491),x88495)))) % 191.49/191.41 [8866]~P28(x88662,x88661,x88663,x88665)+P4(f333(f333(f251(f890(x88661,a874)),f333(f312(x88662,x88661,x88663),x88664)),f333(f312(x88662,x88661,x88663),x88665)))+~P4(f333(f333(f251(f890(x88662,a874)),x88664),x88665)) % 191.49/191.41 [9029]~P28(x90291,x90292,x90293,f258(f890(x90291,a874)))+~P4(f333(f333(f250(f890(x90292,a874)),x90294),f333(f312(x90291,x90292,x90293),x90295)))+P4(f333(f333(f250(f890(x90291,a874)),f333(f313(x90291,x90292,x90293),x90294)),x90295)) % 191.49/191.41 [9047]~E(f333(f312(x90473,x90471,x90474),f258(f890(x90473,a874))),f258(f890(x90471,a874)))+P4(f333(f333(f250(f890(x90471,a874)),x90472),f333(f312(x90473,x90471,x90474),x90475)))+~P4(f333(f333(f250(f890(x90473,a874)),f333(f313(x90473,x90471,x90474),x90472)),x90475)) % 191.49/191.41 [9064]~E(f333(f242(x90642),x90644),f333(f333(f178(x90641,x90642),x90645),x90643))+~P4(f333(f138(x90641),f333(f333(f155(f889(x90641,x90642),x90641),f262(x90641,x90642)),x90645)))+P4(f333(f333(f335(f889(x90641,x90642)),f333(f333(f263(x90641,x90642),x90643),x90644)),f333(f173(f889(x90641,x90642)),x90645))) % 191.49/191.41 [9157]~P28(x91571,x91574,x91575,f258(f890(x91571,a874)))+~P4(f333(f333(f250(f890(x91574,a874)),f333(f312(x91571,x91574,x91575),x91572)),f333(f312(x91571,x91574,x91575),x91573)))+P4(f333(f333(f250(f890(x91571,a874)),x91572),x91573)) % 191.49/191.41 [9220]E(f333(f242(x92201),x92202),f333(f333(f178(x92203,x92201),x92204),x92205))+~P4(f333(f138(x92203),f333(f333(f155(f889(x92203,x92201),x92203),f262(x92203,x92201)),x92204)))+~P4(f333(f333(f335(f889(x92203,x92201)),f333(f333(f263(x92203,x92201),x92205),x92202)),f333(f173(f889(x92203,x92201)),x92204))) % 191.49/191.41 [9222]E(f333(f333(f178(x92221,x92222),x92223),x92224),f333(f242(x92222),x92225))+~P4(f333(f138(x92221),f333(f333(f155(f889(x92221,x92222),x92221),f262(x92221,x92222)),x92223)))+~P4(f333(f333(f335(f889(x92221,x92222)),f333(f333(f263(x92221,x92222),x92224),x92225)),f333(f173(f889(x92221,x92222)),x92223))) % 191.49/191.41 [9280]~P84(x92801)+~E(f333(x92803,f663(x92803,x92804,x92805,x92802,x92801)),f2(x92801))+E(f333(f167(x92801),f333(f333(f155(x92802,x92801),x92803),f333(f137(x92802,x92804),x92805))),f333(f167(x92801),f333(f333(f155(x92802,x92801),x92803),x92805))) % 191.49/191.41 [9453]~P19(x94531,x94532,x94533)+~P4(f333(f63(x94531),x94535))+P4(f333(f68(x94531,x94532,x94533,x94534,x94535),f333(f333(f66(x94531,x94532,x94533),x94534),x94535))) % 191.49/191.41 [9547]P4(f333(x95471,f804(x95472,x95471,x95473,x95474,x95475)))+~P4(f333(f333(f250(f890(x95475,a874)),x95474),x95473))+P4(f333(f333(f250(f890(x95475,a874)),f333(f333(f106(f890(x95475,a874)),x95474),f333(f255(x95475),x95471))),f333(f333(f106(f890(x95475,a874)),x95473),f333(f255(x95475),x95472)))) % 191.49/191.41 [9561]~P84(x95611)+~P4(f333(x95614,f663(x95613,x95614,x95615,x95612,x95611)))+E(f333(f167(x95611),f333(f333(f155(x95612,x95611),x95613),f333(f137(x95612,x95614),x95615))),f333(f167(x95611),f333(f333(f155(x95612,x95611),x95613),x95615))) % 191.49/191.41 [9653]~P9(x96535)+P4(f333(f333(f335(x96531),f529(x96532,x96533,x96531,x96534,x96535)),x96533))+P4(f333(f333(f250(x96535),x96534),f333(f333(f43(x96531,x96535),x96533),x96532))) % 191.49/191.41 [9656]~P84(x96561)+E(f333(f167(x96561),f333(f333(f155(x96562,x96561),x96563),f333(f137(x96562,x96564),x96565))),f333(f167(x96561),f333(f333(f155(x96562,x96561),x96563),x96565)))+P4(f333(f333(f335(x96562),f663(x96563,x96564,x96565,x96562,x96561)),f333(f173(x96562),x96565))) % 191.49/191.41 [9663]~P4(f333(x96635,f804(x96635,x96633,x96634,x96632,x96631)))+~P4(f333(f333(f250(f890(x96631,a874)),x96632),x96634))+P4(f333(f333(f250(f890(x96631,a874)),f333(f333(f106(f890(x96631,a874)),x96632),f333(f255(x96631),x96633))),f333(f333(f106(f890(x96631,a874)),x96634),f333(f255(x96631),x96635)))) % 191.49/191.41 [9698]P37(x96981,x96982,x96983,x96984,x96985)+~E(f333(f195(f881(x96982)),x96985),f333(f195(f881(x96981)),x96984))+P4(f333(f333(f251(a880),f689(x96985,x96984,x96983,x96982,x96981)),f333(f195(f881(x96981)),x96984))) % 191.49/191.41 [9699]P37(x96991,x96992,x96993,x96994,x96995)+~E(f333(f195(f881(x96992)),x96995),f333(f195(f881(x96991)),x96994))+P4(f333(f333(f251(a880),f731(x96993,x96995,x96992,x96994,x96991)),f333(f195(f881(x96991)),x96994))) % 191.49/191.41 [9732]P4(f333(f333(f335(x97321),f804(x97322,x97323,x97324,x97325,x97321)),x97325))+~P4(f333(f333(f250(f890(x97321,a874)),x97325),x97324))+P4(f333(f333(f250(f890(x97321,a874)),f333(f333(f106(f890(x97321,a874)),x97325),f333(f255(x97321),x97323))),f333(f333(f106(f890(x97321,a874)),x97324),f333(f255(x97321),x97322)))) % 191.49/191.41 [9800]~P9(x98001)+~P4(f333(f333(f250(x98001),x98002),f333(x98005,f529(x98005,x98004,x98003,x98002,x98001))))+P4(f333(f333(f250(x98001),x98002),f333(f333(f43(x98003,x98001),x98004),x98005))) % 191.49/191.41 [9829]~P76(x98291)+~P4(f333(f63(x98292),x98295))+E(f333(f333(f333(f67(x98291,x98292,f82(x98291)),f333(f333(f20(x98292,x98291,x98291),f333(f333(f10(x98291,f890(x98291,x98291),x98292),f82(x98291)),x98293)),x98294)),f79(x98291)),x98295),f333(f333(f82(x98291),f333(f333(f333(f67(x98291,x98292,f82(x98291)),x98293),f79(x98291)),x98295)),f333(f333(f333(f67(x98291,x98292,f82(x98291)),x98294),f79(x98291)),x98295))) % 191.49/191.41 [9887]~P4(f333(f333(f335(f889(f890(x98871,a874),f890(x98871,a874))),f333(f333(f263(f890(x98871,a874),f890(x98871,a874)),x98875),x98874)),f325(x98871,x98873)))+~P4(f333(f333(f335(x98871),x98872),x98875))+P4(f333(f333(f335(f889(x98871,x98871)),f333(f333(f263(x98871,x98871),x98872),f759(x98873,x98874,x98875,x98871,x98872))),x98873)) % 191.49/191.41 [9998]~P4(f333(f333(f335(f889(f881(x99981),f881(x99981))),f333(f333(f263(f881(x99981),f881(x99981)),f333(f333(f127(x99981),x99985),x99982)),f333(f333(f127(x99981),x99985),x99983))),f148(x99981,x99984)))+P4(f333(f333(f335(f889(f881(x99981),f881(x99981))),f333(f333(f263(f881(x99981),f881(x99981)),x99982),x99983)),f148(x99981,x99984)))+P4(f333(f333(f335(f889(x99981,x99981)),f333(f333(f263(x99981,x99981),f619(x99984,x99983,x99982,x99985,x99981)),f619(x99984,x99983,x99982,x99985,x99981))),x99984)) % 191.49/191.41 [7153]~E(f333(f195(f881(x71531)),x71533),f333(f195(f881(x71532)),x71534))+E(f333(f333(f178(x71531,x71532),f333(f333(f182(x71531,x71532),x71533),x71534)),x71535),f197(x71532))+P4(f333(f333(f335(x71531),x71535),f333(f173(x71531),x71533))) % 191.49/191.41 [7226]~E(x72263,x72265)+E(f333(f333(f166(x72261),f333(f333(f160(x72261,x72262),x72263),x72264)),x72265),x72264)+~P4(f333(f333(f251(a880),x72263),f333(f195(f881(x72261)),x72262))) % 191.49/191.41 [7326]~E(f333(f333(f127(x73261),x73262),x73264),f333(f333(f127(x73261),x73263),x73265))+E(f333(f333(f174(x73261),f333(f195(f881(x73261)),x73262)),x73263),x73262)+P4(f333(f333(f250(a880),f333(f195(f881(x73261)),x73263)),f333(f195(f881(x73261)),x73262))) % 191.49/191.41 [7343]~E(x73435,x73432)+P4(f333(x73431,x73432))+P4(f333(f333(f333(f333(a203,f33(x73431,x73433)),x73432),x73434),x73435)) % 191.49/191.41 [7826]~E(f333(f333(f127(x78261),x78262),x78264),f333(f333(f127(x78261),x78263),x78265))+E(f333(f333(f174(x78261),f333(f195(f881(x78261)),x78262)),x78263),x78262)+~P4(f333(f333(f250(a880),f333(f195(f881(x78261)),x78262)),f333(f195(f881(x78261)),x78263))) % 191.49/191.41 [7850]~P4(f333(f63(x78501),f333(x78504,x78505)))+~P4(f333(f333(f335(x78502),x78505),x78503))+P4(f333(f63(x78501),f333(f333(f43(x78502,f890(x78501,a874)),x78503),x78504))) % 191.49/191.41 [7898]~E(f333(f195(f881(x78981)),x78982),f333(f195(f881(x78983)),x78984))+~E(f333(f333(f178(x78981,x78983),f333(f333(f182(x78981,x78983),x78982),x78984)),x78985),f197(x78983))+~P4(f333(f333(f335(x78981),x78985),f333(f173(x78981),x78982))) % 191.49/191.41 [8021]~P50(x80211,x80213,x80215)+~P50(x80211,x80212,x80214)+P50(x80211,f333(f333(f115(f890(x80211,a874)),x80212),x80213),f333(f333(f115(f890(f889(x80211,x80211),a874)),x80214),x80215)) % 191.49/191.41 [8022]~P50(x80221,x80223,x80225)+~P50(x80221,x80222,x80224)+P50(x80221,f333(f333(f106(f890(x80221,a874)),x80222),x80223),f333(f333(f106(f890(f889(x80221,x80221),a874)),x80224),x80225)) % 191.49/191.41 [8110]E(x81101,x81102)+P4(f333(x81103,x81101))+~P4(f333(f333(f333(f333(a203,f33(x81103,x81104)),x81101),x81105),x81102)) % 191.49/191.41 [8381]E(f333(f333(f263(x83811,x83812),f333(f333(f166(x83811),x83813),x83814)),f333(f333(f166(x83812),x83815),x83814)),f333(f333(f166(f889(x83811,x83812)),f333(f333(f182(x83811,x83812),x83813),x83815)),x83814))+~P4(f333(f333(f251(a880),x83814),f333(f195(f881(x83811)),x83813)))+~P4(f333(f333(f251(a880),x83814),f333(f195(f881(x83812)),x83815))) % 191.49/191.41 [8542]~P50(x85421,x85423,x85424)+P4(f333(f333(f335(x85421),x85422),x85423))+~P4(f333(f333(f335(f889(x85421,x85421)),f333(f333(f263(x85421,x85421),x85425),x85422)),x85424)) % 191.49/191.41 [8543]~P50(x85431,x85433,x85434)+P4(f333(f333(f335(x85431),x85432),x85433))+~P4(f333(f333(f335(f889(x85431,x85431)),f333(f333(f263(x85431,x85431),x85432),x85435)),x85434)) % 191.49/191.41 [8544]~P12(x85441,x85443,x85444)+P4(f333(f333(f335(x85441),x85442),x85443))+~P4(f333(f333(f335(f889(x85441,x85441)),f333(f333(f263(x85441,x85441),x85445),x85442)),x85444)) % 191.49/191.41 [8545]~P12(x85451,x85453,x85454)+P4(f333(f333(f335(x85451),x85452),x85453))+~P4(f333(f333(f335(f889(x85451,x85451)),f333(f333(f263(x85451,x85451),x85452),x85455)),x85454)) % 191.49/191.41 [8796]~P12(x87961,x87965,x87962)+E(f333(f287(x87961,x87961,x87962),f333(f333(f311(x87961),x87963),f194(f890(x87961,a874)))),f333(f287(x87961,x87961,x87962),f333(f333(f311(x87961),x87964),f194(f890(x87961,a874)))))+~P4(f333(f333(f335(f889(x87961,x87961)),f333(f333(f263(x87961,x87961),x87963),x87964)),x87962)) % 191.49/191.41 [8881]~P4(f333(f333(f333(f333(a203,x88812),x88813),x88814),x88815))+~P4(f333(f333(f333(f333(a203,f33(x88811,x88812)),x88815),x88814),x88813))+P4(f333(f333(f333(f333(a203,f33(x88811,x88812)),x88813),x88814),x88813)) % 191.49/191.41 [8989]P4(f333(x89891,x89892))+~P4(f333(f333(f335(x89893),x89892),x89895))+P4(f333(f333(f335(x89893),f432(x89891,x89894,x89895,x89893)),f333(f333(f115(f890(x89893,a874)),x89895),x89894))) % 191.49/191.41 [8990]P4(f333(x89901,x89902))+~P4(f333(f333(f335(x89903),x89902),x89904))+P4(f333(f333(f335(x89903),f432(x89901,x89904,x89905,x89903)),f333(f333(f115(f890(x89903,a874)),x89905),x89904))) % 191.49/191.41 [8998]~P4(f333(x89982,x89985))+~P4(f333(f333(f335(x89981),x89985),x89984))+P4(f333(f333(f335(x89981),f428(x89982,x89983,x89984,x89981)),f333(f333(f115(f890(x89981,a874)),x89984),x89983))) % 191.49/191.41 [8999]~P4(f333(x89992,x89995))+~P4(f333(f333(f335(x89991),x89995),x89993))+P4(f333(f333(f335(x89991),f428(x89992,x89993,x89994,x89991)),f333(f333(f115(f890(x89991,a874)),x89994),x89993))) % 191.49/191.41 [9014]~P4(f333(f333(f250(f890(x90141,a874)),x90143),x90145))+~P4(f333(f333(f250(f890(x90141,a874)),x90142),x90144))+P4(f333(f333(f250(f890(x90141,a874)),f333(f333(f115(f890(x90141,a874)),x90142),x90143)),f333(f333(f115(f890(x90141,a874)),x90144),x90145))) % 191.49/191.41 [9015]~P4(f333(f333(f250(f890(x90151,a874)),x90155),x90153))+~P4(f333(f333(f250(f890(x90151,a874)),x90152),x90154))+P4(f333(f333(f250(f890(x90151,a874)),f333(f333(f3(f890(x90151,a874)),x90152),x90153)),f333(f333(f3(f890(x90151,a874)),x90154),x90155))) % 191.49/191.41 [9016]~P4(f333(f333(f250(f890(x90161,a874)),x90163),x90165))+~P4(f333(f333(f250(f890(x90161,a874)),x90162),x90164))+P4(f333(f333(f250(f890(x90161,a874)),f333(f333(f106(f890(x90161,a874)),x90162),x90163)),f333(f333(f106(f890(x90161,a874)),x90164),x90165))) % 191.49/191.41 [9094]~E(f333(f195(f881(x90941)),x90943),f333(f195(f881(x90942)),x90944))+E(f333(f333(f178(x90941,x90942),f333(f333(f182(x90941,x90942),x90943),x90944)),x90945),f333(f242(x90942),f576(x90945,x90944,x90942,x90943,x90941)))+~P4(f333(f333(f335(x90941),x90945),f333(f173(x90941),x90943))) % 191.49/191.41 [9099]P4(f333(f333(f335(f889(x90991,x90991)),f333(f333(f263(x90991,x90991),x90992),x90993)),f327(x90991,x90994,x90995)))+~P4(f333(f333(f250(a880),f333(x90994,x90992)),f333(x90994,x90993)))+~P4(f333(f333(f335(f889(x90991,x90991)),f333(f333(f263(x90991,x90991),x90992),x90993)),x90995)) % 191.49/191.41 [9295]P4(f333(f333(f335(f889(x92951,x92951)),f333(f333(f263(x92951,x92951),x92952),x92953)),f309(x92951,x92954)))+~P4(f333(f333(f335(f889(x92951,x92951)),f333(f333(f263(x92951,x92951),x92952),x92955)),f309(x92951,x92954)))+~P4(f333(f333(f335(f889(x92951,x92951)),f333(f333(f263(x92951,x92951),x92955),x92953)),x92954)) % 191.49/191.41 [9296]P4(f333(f333(f335(f889(x92961,x92961)),f333(f333(f263(x92961,x92961),x92962),x92963)),f309(x92961,x92964)))+~P4(f333(f333(f335(f889(x92961,x92961)),f333(f333(f263(x92961,x92961),x92965),x92963)),f309(x92961,x92964)))+~P4(f333(f333(f335(f889(x92961,x92961)),f333(f333(f263(x92961,x92961),x92962),x92965)),x92964)) % 191.49/191.41 [9390]E(x93901,x93902)+E(f333(a117,f774(x93903,x93904,x93901,x93902,x93905)),x93904)+~P4(f333(f333(f335(f889(x93905,x93905)),f333(f333(f263(x93905,x93905),x93902),x93901)),f333(f333(f189(f889(x93905,x93905),a874),x93904),x93903))) % 191.49/191.41 [9391]E(x93911,x93912)+E(f333(a117,f776(x93913,x93914,x93911,x93912,x93915)),x93914)+~P4(f333(f333(f335(f889(x93915,x93915)),f333(f333(f263(x93915,x93915),x93912),x93911)),f333(f333(f189(f889(x93915,x93915),a874),x93914),x93913))) % 191.49/191.41 [9392]E(x93921,f2(a880))+E(f333(a117,f774(x93922,x93921,x93923,x93924,x93925)),x93921)+~P4(f333(f333(f335(f889(x93925,x93925)),f333(f333(f263(x93925,x93925),x93924),x93923)),f333(f333(f189(f889(x93925,x93925),a874),x93921),x93922))) % 191.49/191.41 [9393]E(x93931,f2(a880))+E(f333(a117,f776(x93932,x93931,x93933,x93934,x93935)),x93931)+~P4(f333(f333(f335(f889(x93935,x93935)),f333(f333(f263(x93935,x93935),x93934),x93933)),f333(f333(f189(f889(x93935,x93935),a874),x93931),x93932))) % 191.49/191.41 [9405]P4(f333(f333(f335(f889(x94051,x94051)),f333(f333(f263(x94051,x94051),x94052),x94053)),f333(f333(f290(x94051,x94051,x94051),x94054),f309(x94051,x94054))))+~P4(f333(f333(f335(f889(x94051,x94051)),f333(f333(f263(x94051,x94051),x94052),x94055)),x94054))+~P4(f333(f333(f335(f889(x94051,x94051)),f333(f333(f263(x94051,x94051),x94055),x94053)),x94054)) % 191.49/191.41 [9410]~P4(f333(f333(f335(f889(x94101,x94101)),f333(f333(f263(x94101,x94101),x94102),x94105)),f309(x94101,x94104)))+P4(f333(f333(f335(f889(x94101,x94101)),f333(f333(f263(x94101,x94101),x94102),x94103)),f333(f333(f290(x94101,x94101,x94101),x94104),f309(x94101,x94104))))+~P4(f333(f333(f335(f889(x94101,x94101)),f333(f333(f263(x94101,x94101),x94105),x94103)),x94104)) % 191.49/191.41 [9449]~P12(x94491,x94495,x94492)+~P4(f333(f333(f335(f889(x94491,x94491)),f333(f333(f263(x94491,x94491),x94493),x94494)),x94492))+P4(f333(f333(f250(f890(x94491,a874)),f333(f287(x94491,x94491,x94492),f333(f333(f311(x94491),x94493),f194(f890(x94491,a874))))),f333(f287(x94491,x94491,x94492),f333(f333(f311(x94491),x94494),f194(f890(x94491,a874)))))) % 191.49/191.41 [9475]E(x94751,x94752)+P4(f333(f333(f333(f333(a203,x94753),x94751),x94754),f495(x94752,x94754,x94751,x94753,x94755)))+~P4(f333(f333(f333(f333(a203,f33(x94755,x94753)),x94751),x94754),x94752)) % 191.49/191.41 [9478]~P4(f333(x94785,x94782))+P4(f333(f333(f333(f333(a203,x94781),x94782),x94783),f495(x94784,x94783,x94782,x94781,x94785)))+~P4(f333(f333(f333(f333(a203,f33(x94785,x94781)),x94782),x94783),x94784)) % 191.49/191.41 [9519]P4(f333(f333(f335(f889(x95191,x95191)),f333(f333(f263(x95191,x95191),x95192),x95193)),f333(f333(f290(x95191,x95191,x95191),x95194),f309(x95191,x95194))))+~P4(f333(f333(f335(f889(x95191,x95191)),f333(f333(f263(x95191,x95191),x95192),x95195)),f333(f333(f290(x95191,x95191,x95191),x95194),f309(x95191,x95194))))+~P4(f333(f333(f335(f889(x95191,x95191)),f333(f333(f263(x95191,x95191),x95195),x95193)),x95194)) % 191.49/191.41 [9520]P4(f333(f333(f335(f889(x95201,x95201)),f333(f333(f263(x95201,x95201),x95202),x95203)),f333(f333(f290(x95201,x95201,x95201),x95204),f309(x95201,x95204))))+~P4(f333(f333(f335(f889(x95201,x95201)),f333(f333(f263(x95201,x95201),x95205),x95203)),f333(f333(f290(x95201,x95201,x95201),x95204),f309(x95201,x95204))))+~P4(f333(f333(f335(f889(x95201,x95201)),f333(f333(f263(x95201,x95201),x95202),x95205)),x95204)) % 191.49/191.41 [9568]~P4(f333(f68(x95681,x95681,x95684,x95682,x95683),x95685))+P4(f333(f333(f335(x95681),x95682),x95683))+P4(f333(f64(x95681,x95684,f333(f333(f311(x95681),x95682),x95683)),x95685)) % 191.49/191.41 [9615]~E(f333(f312(x96153,x96152,x96155),x96154),x96151)+E(x96151,f194(f890(x96152,a874)))+P4(f333(f333(f250(f890(x96153,a874)),f333(f312(x96152,x96153,f353(x96154,x96153,x96152,x96151)),x96151)),x96154)) % 191.49/191.41 [9666]~P9(x96665)+P4(f333(f333(f335(x96661),f541(x96662,x96663,x96664,x96661,x96665)),x96664))+P4(f333(f333(f250(x96665),f333(f333(f44(x96661,x96665),x96664),x96663)),x96662)) % 191.49/191.41 [9718]P37(x97181,x97182,x97183,x97184,x97185)+~E(f333(f195(f881(x97181)),x97184),f333(f195(f881(x97182)),x97185))+P4(f333(f333(f335(f889(x97181,x97182)),f677(x97185,x97184,x97183,x97182,x97181)),f333(f173(f889(x97181,x97182)),f333(f333(f182(x97181,x97182),x97184),x97185)))) % 191.49/191.41 [9719]P37(x97191,x97192,x97193,x97194,x97195)+~E(f333(f195(f881(x97191)),x97194),f333(f195(f881(x97192)),x97195))+P4(f333(f333(f335(f889(x97191,x97192)),f688(x97193,x97195,x97194,x97192,x97191)),f333(f173(f889(x97191,x97192)),f333(f333(f182(x97191,x97192),x97194),x97195)))) % 191.49/191.41 [9855]E(x98551,x98552)+P4(f333(f333(f333(f333(a203,f33(x98553,x98554)),f495(x98551,x98555,x98552,x98554,x98553)),x98555),x98551))+~P4(f333(f333(f333(f333(a203,f33(x98553,x98554)),x98552),x98555),x98551)) % 191.49/191.41 [9857]~P4(f333(x98571,x98575))+P4(f333(f333(f333(f333(a203,f33(x98571,x98572)),f495(x98573,x98574,x98575,x98572,x98571)),x98574),x98573))+~P4(f333(f333(f333(f333(a203,f33(x98571,x98572)),x98575),x98574),x98573)) % 191.49/191.41 [9864]E(x98641,x98642)+P4(f333(f333(f335(f889(x98643,x98643)),f333(f333(f263(x98643,x98643),x98641),f775(x98644,x98645,x98642,x98641,x98643))),x98644))+~P4(f333(f333(f335(f889(x98643,x98643)),f333(f333(f263(x98643,x98643),x98641),x98642)),f333(f333(f189(f889(x98643,x98643),a874),x98645),x98644))) % 191.49/191.41 [9865]E(x98651,f2(a880))+P4(f333(f333(f335(f889(x98652,x98652)),f333(f333(f263(x98652,x98652),x98653),f775(x98654,x98651,x98655,x98653,x98652))),x98654))+~P4(f333(f333(f335(f889(x98652,x98652)),f333(f333(f263(x98652,x98652),x98653),x98655)),f333(f333(f189(f889(x98652,x98652),a874),x98651),x98654))) % 191.49/191.41 [9907]~P9(x99071)+~P4(f333(f333(f250(x99071),f333(x99074,f541(x99075,x99074,x99073,x99072,x99071))),x99075))+P4(f333(f333(f250(x99071),f333(f333(f44(x99072,x99071),x99073),x99074)),x99075)) % 191.49/191.41 [9932]E(x99321,x99322)+P4(f333(f333(f335(f889(x99323,x99323)),f333(f333(f263(x99323,x99323),f777(x99324,x99325,x99321,x99322,x99323)),x99321)),x99324))+~P4(f333(f333(f335(f889(x99323,x99323)),f333(f333(f263(x99323,x99323),x99322),x99321)),f333(f333(f189(f889(x99323,x99323),a874),x99325),x99324))) % 191.49/191.41 [9933]E(x99331,f2(a880))+P4(f333(f333(f335(f889(x99332,x99332)),f333(f333(f263(x99332,x99332),f777(x99333,x99331,x99334,x99335,x99332)),x99334)),x99333))+~P4(f333(f333(f335(f889(x99332,x99332)),f333(f333(f263(x99332,x99332),x99335),x99334)),f333(f333(f189(f889(x99332,x99332),a874),x99331),x99333))) % 191.49/191.41 [9943]E(x99431,x99432)+P4(f333(f333(f335(f889(x99433,x99433)),f333(f333(f263(x99433,x99433),x99431),f777(x99434,x99435,x99432,x99431,x99433))),f333(f333(f189(f889(x99433,x99433),a874),f776(x99434,x99435,x99432,x99431,x99433)),x99434)))+~P4(f333(f333(f335(f889(x99433,x99433)),f333(f333(f263(x99433,x99433),x99431),x99432)),f333(f333(f189(f889(x99433,x99433),a874),x99435),x99434))) % 191.49/191.41 [9944]E(x99441,f2(a880))+P4(f333(f333(f335(f889(x99442,x99442)),f333(f333(f263(x99442,x99442),x99443),f777(x99444,x99441,x99445,x99443,x99442))),f333(f333(f189(f889(x99442,x99442),a874),f776(x99444,x99441,x99445,x99443,x99442)),x99444)))+~P4(f333(f333(f335(f889(x99442,x99442)),f333(f333(f263(x99442,x99442),x99443),x99445)),f333(f333(f189(f889(x99442,x99442),a874),x99441),x99444))) % 191.49/191.41 [9990]E(x99901,x99902)+P4(f333(f333(f335(f889(x99903,x99903)),f333(f333(f263(x99903,x99903),f775(x99904,x99905,x99901,x99902,x99903)),x99901)),f333(f333(f189(f889(x99903,x99903),a874),f774(x99904,x99905,x99901,x99902,x99903)),x99904)))+~P4(f333(f333(f335(f889(x99903,x99903)),f333(f333(f263(x99903,x99903),x99902),x99901)),f333(f333(f189(f889(x99903,x99903),a874),x99905),x99904))) % 191.49/191.41 [9991]E(x99911,f2(a880))+P4(f333(f333(f335(f889(x99912,x99912)),f333(f333(f263(x99912,x99912),f775(x99913,x99911,x99914,x99915,x99912)),x99914)),f333(f333(f189(f889(x99912,x99912),a874),f774(x99913,x99911,x99914,x99915,x99912)),x99913)))+~P4(f333(f333(f335(f889(x99912,x99912)),f333(f333(f263(x99912,x99912),x99915),x99914)),f333(f333(f189(f889(x99912,x99912),a874),x99911),x99913))) % 191.49/191.41 [10027]~P69(x100272)+~P4(f333(f63(x100271),x100275))+E(f333(f333(f8(x100271,x100272),f333(f333(f9(x100271,x100272,x100272),f333(f333(f20(x100271,x100272,f890(x100272,x100272)),f333(f333(f10(a874,f890(x100272,f890(x100272,x100272)),x100271),f101(x100272)),f333(f333(f9(x100271,f890(x100271,a874),a874),f335(x100271)),x100273))),x100274)),f2(x100272))),x100275),f333(f333(f8(x100271,x100272),x100274),f333(f333(f106(f890(x100271,a874)),x100275),x100273))) % 191.49/191.41 [8604]~P69(x86041)+~P4(f333(f63(x86044),x86045))+E(f333(f333(f81(x86041),f333(x86042,x86043)),f333(f333(f8(x86044,x86041),x86042),f333(f333(f3(f890(x86044,a874)),x86045),f333(f333(f311(x86044),x86043),f194(f890(x86044,a874)))))),f333(f333(f8(x86044,x86041),x86042),f333(f333(f311(x86044),x86043),x86045))) % 191.49/191.41 [8605]~P76(x86051)+~P4(f333(f63(x86054),x86055))+E(f333(f333(f82(x86051),f333(x86052,x86053)),f333(f333(f11(x86054,x86051),x86052),f333(f333(f3(f890(x86054,a874)),x86055),f333(f333(f311(x86054),x86053),f194(f890(x86054,a874)))))),f333(f333(f11(x86054,x86051),x86052),f333(f333(f311(x86054),x86053),x86055))) % 191.49/191.41 [8920]~P109(x89202)+~P17(x89202,f333(f170(x89202),f333(f333(f155(x89201,x89202),x89204),x89205)))+E(f333(f137(x89201,f333(f333(f10(x89202,a874,x89201),f333(f251(x89202),x89203)),x89204)),x89205),f177(x89201,f333(f333(f10(x89202,a874,x89201),f333(f251(x89202),x89203)),x89204),x89205)) % 191.49/191.41 [8945]~P69(x89451)+E(f333(f333(f81(x89451),f333(f333(f8(a880,x89451),x89452),f304(a880,x89453,x89454))),f333(f333(f8(a880,x89451),x89452),f304(a880,f333(f333(f81(a880),x89454),f79(a880)),f333(f333(f81(a880),x89454),x89455)))),f333(f333(f8(a880,x89451),x89452),f304(a880,x89453,f333(f333(f81(a880),x89454),x89455))))+~P4(f333(f333(f250(a880),x89453),f333(f333(f81(a880),x89454),f79(a880)))) % 191.49/191.41 [8946]~P4(f333(f333(f335(x89461),x89464),x89465))+~P4(f333(f333(f250(f890(x89461,a874)),f333(f173(x89461),x89462)),x89465))+P4(f333(f333(f250(f890(x89461,a874)),f333(f173(x89461),f333(f333(f160(x89461,x89462),x89463),x89464))),x89465)) % 191.49/191.41 [9167]~P9(x91672)+~P4(f333(f63(x91671),x91675))+E(f333(f333(f66(x91671,x91672,f333(f333(f10(x91672,f890(x91672,x91672),x91671),f115(x91672)),x91673)),x91674),x91675),f333(f333(f115(x91672),x91674),f333(f333(f44(x91671,x91672),x91675),x91673))) % 191.49/191.41 [9168]~P9(x91682)+~P4(f333(f63(x91681),x91685))+E(f333(f333(f66(x91681,x91682,f333(f333(f10(x91682,f890(x91682,x91682),x91681),f106(x91682)),x91683)),x91684),x91685),f333(f333(f106(x91682),x91684),f333(f333(f43(x91681,x91682),x91685),x91683))) % 191.49/191.41 [9213]E(f333(x92131,x92132),f333(x92131,x92133))+P4(f333(f333(f251(a880),f333(x92131,x92132)),f333(x92131,x92133)))+~P4(f333(f333(f335(f889(x92134,x92134)),f333(f333(f263(x92134,x92134),x92132),x92133)),f154(x92134,f333(f333(f152(f890(x92134,a880)),x92131),x92135)))) % 191.49/191.41 [9244]~E(f333(x92444,x92442),f333(x92444,x92443))+~P4(f333(f333(f335(f889(x92441,x92441)),f333(f333(f263(x92441,x92441),x92442),x92443)),f154(x92441,x92445)))+P4(f333(f333(f335(f889(x92441,x92441)),f333(f333(f263(x92441,x92441),x92442),x92443)),f154(x92441,f333(f333(f152(f890(x92441,a880)),x92444),x92445)))) % 191.49/191.41 [9266]~P28(x92661,x92662,x92663,x92665)+P28(x92661,x92662,x92663,f333(f333(f311(x92661),x92664),x92665))+P4(f333(f333(f335(x92662),f333(x92663,x92664)),f333(f312(x92661,x92662,x92663),f333(f333(f3(f890(x92661,a874)),x92665),f333(f333(f311(x92661),x92664),f194(f890(x92661,a874))))))) % 191.49/191.41 [9272]P4(f333(x92722,x92725))+~P4(f333(f333(f335(x92721),x92725),f333(f173(x92721),x92723)))+E(f333(f333(f139(x92721),f333(f195(f881(x92721)),f177(x92721,x92722,f333(f333(f127(x92721),x92723),x92724)))),f333(f333(f127(x92721),x92723),x92724)),f333(f333(f127(x92721),f333(f333(f139(x92721),f333(f195(f881(x92721)),f177(x92721,x92722,x92723))),x92723)),x92724)) % 191.49/191.41 [9276]~P4(f333(f333(f335(f889(x92761,x92761)),f333(f333(f263(x92761,x92761),x92762),x92763)),f154(x92761,x92765)))+~P4(f333(f333(f250(a880),f333(x92764,x92762)),f333(x92764,x92763)))+P4(f333(f333(f335(f889(x92761,x92761)),f333(f333(f263(x92761,x92761),x92762),x92763)),f154(x92761,f333(f333(f152(f890(x92761,a880)),x92764),x92765)))) % 191.49/191.41 [9341]P4(f333(f333(f335(f889(x93414,x93414)),f333(f333(f263(x93414,x93414),x93412),x93413)),f154(x93414,x93415)))+P4(f333(f333(f251(a880),f333(x93411,x93412)),f333(x93411,x93413)))+~P4(f333(f333(f335(f889(x93414,x93414)),f333(f333(f263(x93414,x93414),x93412),x93413)),f154(x93414,f333(f333(f152(f890(x93414,a880)),x93411),x93415)))) % 191.49/191.41 [9481]~P4(f333(f333(f335(f889(f881(x94811),f881(x94811))),f333(f333(f263(f881(x94811),f881(x94811)),x94812),x94814)),f159(x94811,x94815)))+~P4(f333(f333(f251(a880),x94813),f333(f195(f881(x94811)),x94812)))+P4(f333(f333(f335(f889(x94811,x94811)),f333(f333(f263(x94811,x94811),f333(f333(f166(x94811),x94812),x94813)),f333(f333(f166(x94811),x94814),x94813))),x94815)) % 191.49/191.41 [9751]E(x97511,f2(a1))+~P4(f333(f50(x97513,x97511),f333(f333(f263(a1,a1),x97514),x97515)))+P4(f333(f50(f333(f333(f82(a1),x97512),x97513),x97511),f333(f333(f263(a1,a1),f333(f333(f81(a1),f333(f333(f82(a1),x97512),x97514)),f333(f333(f40(a1),f333(f333(f82(a1),x97512),x97515)),x97511))),f46(a1,f333(f333(f82(a1),x97512),x97515),x97511)))) % 191.49/191.41 [9760]~P4(f333(f333(f251(a880),f2(a880)),x97603))+~P4(f333(f49(x97602,x97603),f333(f333(f263(a880,a880),x97604),x97605)))+P4(f333(f49(f333(f333(f82(a880),x97601),x97602),x97603),f333(f333(f263(a880,a880),f333(f333(f81(a880),f333(f333(f82(a880),x97601),x97604)),f333(f333(f40(a880),f333(f333(f82(a880),x97601),x97605)),x97603))),f46(a880,f333(f333(f82(a880),x97601),x97605),x97603)))) % 191.49/191.41 [10045]~P69(x100452)+~P4(f333(f63(x100451),x100454))+E(f333(f333(f8(x100451,x100452),x100453),f333(f255(x100451),f333(f333(f20(x100451,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100451),a331),f333(f333(f9(x100451,f890(x100451,a874),a874),f335(x100451)),x100454))),f333(f333(f9(x100451,f890(x100451,a874),a874),f335(x100451)),x100455)))),f333(f333(f8(x100451,x100452),f333(f333(f9(x100451,x100452,x100452),f333(f333(f20(x100451,x100452,f890(x100452,x100452)),f333(f333(f10(a874,f890(x100452,f890(x100452,x100452)),x100451),f101(x100452)),f333(f333(f9(x100451,f890(x100451,a874),a874),f335(x100451)),x100455))),x100453)),f2(x100452))),x100454)) % 191.49/191.41 [8237]~E(f333(f333(f127(x82371),x82372),x82375),f333(f333(f127(x82371),x82373),x82374))+E(f333(f333(f127(x82371),f333(f333(f139(x82371),f333(f195(f881(x82371)),x82372)),x82373)),x82374),x82375)+P4(f333(f333(f250(a880),f333(f195(f881(x82371)),x82373)),f333(f195(f881(x82371)),x82372))) % 191.49/191.41 [8432]~E(f333(f333(f127(x84322),x84323),x84321),f333(f333(f127(x84322),x84324),x84325))+E(x84321,f333(f333(f127(x84322),f333(f333(f139(x84322),f333(f195(f881(x84322)),x84323)),x84324)),x84325))+~P4(f333(f333(f250(a880),f333(f195(f881(x84322)),x84323)),f333(f195(f881(x84322)),x84324))) % 191.49/191.41 [8525]~E(f333(f333(f81(a880),f333(f333(f82(a880),x85253),x85254)),x85251),f333(f333(f81(a880),f333(f333(f82(a880),x85252),x85254)),x85255))+~P4(f333(f333(f250(a880),x85253),x85252))+E(x85251,f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x85252),x85253)),x85254)),x85255)) % 191.49/191.41 [8526]~E(f333(f333(f81(a880),f333(f333(f82(a880),x85261),x85263)),x85264),f333(f333(f81(a880),f333(f333(f82(a880),x85262),x85263)),x85265))+~P4(f333(f333(f250(a880),x85262),x85261))+E(f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x85261),x85262)),x85263)),x85264),x85265) % 191.49/191.41 [8672]E(f333(f333(f81(a880),f333(f333(f82(a880),x86721),x86722)),x86723),f333(f333(f81(a880),f333(f333(f82(a880),x86724),x86722)),x86725))+~P4(f333(f333(f250(a880),x86724),x86721))+~E(x86725,f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x86721),x86724)),x86722)),x86723)) % 191.49/191.41 [8673]E(f333(f333(f81(a880),f333(f333(f82(a880),x86731),x86732)),x86733),f333(f333(f81(a880),f333(f333(f82(a880),x86734),x86732)),x86735))+~P4(f333(f333(f250(a880),x86734),x86731))+~E(f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x86731),x86734)),x86732)),x86733),x86735) % 191.49/191.41 [9546]~P63(x95462)+~P4(f333(f63(x95461),x95465))+E(f333(f333(f11(x95461,x95462),f333(f333(f20(x95461,x95462,x95462),f333(f333(f10(x95462,f890(x95462,x95462),x95461),f291(x95462)),x95463)),x95464)),x95465),f333(f333(f291(x95462),f333(f333(f11(x95461,x95462),x95463),x95465)),f333(f333(f11(x95461,x95462),x95464),x95465))) % 191.49/191.41 [9681]~E(f778(x96815,x96814,x96813,x96812,x96811),f779(x96815,x96814,x96813,x96812,x96811))+P4(f333(f333(f335(f889(x96811,x96811)),f333(f333(f263(x96811,x96811),x96812),x96813)),f309(x96811,x96814)))+~P4(f333(f333(f335(f889(x96811,x96811)),f333(f333(f263(x96811,x96811),x96812),x96813)),f309(x96811,f333(f333(f115(f890(f889(x96811,x96811),a874)),x96814),x96815)))) % 191.49/191.41 [9682]~E(f780(x96825,x96824,x96823,x96822,x96821),f781(x96825,x96824,x96823,x96822,x96821))+P4(f333(f333(f335(f889(x96821,x96821)),f333(f333(f263(x96821,x96821),x96822),x96823)),f309(x96821,x96824)))+~P4(f333(f333(f335(f889(x96821,x96821)),f333(f333(f263(x96821,x96821),x96822),x96823)),f309(x96821,f333(f333(f115(f890(f889(x96821,x96821),a874)),x96824),x96825)))) % 191.49/191.41 [9897]P4(f333(f333(f335(f889(x98971,x98971)),f333(f333(f263(x98971,x98971),x98972),f779(x98975,x98974,x98973,x98972,x98971))),f309(x98971,x98974)))+P4(f333(f333(f335(f889(x98971,x98971)),f333(f333(f263(x98971,x98971),x98972),x98973)),f309(x98971,x98974)))+~P4(f333(f333(f335(f889(x98971,x98971)),f333(f333(f263(x98971,x98971),x98972),x98973)),f309(x98971,f333(f333(f115(f890(f889(x98971,x98971),a874)),x98974),x98975)))) % 191.49/191.41 [9962]P4(f333(f333(f335(f889(x99621,x99621)),f333(f333(f263(x99621,x99621),f781(x99625,x99624,x99623,x99622,x99621)),x99623)),f309(x99621,x99624)))+P4(f333(f333(f335(f889(x99621,x99621)),f333(f333(f263(x99621,x99621),x99622),x99623)),f309(x99621,x99624)))+~P4(f333(f333(f335(f889(x99621,x99621)),f333(f333(f263(x99621,x99621),x99622),x99623)),f309(x99621,f333(f333(f115(f890(f889(x99621,x99621),a874)),x99624),x99625)))) % 191.49/191.41 [9996]P4(f333(f333(f335(f889(x99961,x99961)),f333(f333(f263(x99961,x99961),x99962),x99963)),f309(x99961,x99964)))+P4(f333(f333(f335(f889(x99961,x99961)),f333(f333(f263(x99961,x99961),f779(x99965,x99964,x99963,x99962,x99961)),f778(x99965,x99964,x99963,x99962,x99961))),x99965))+~P4(f333(f333(f335(f889(x99961,x99961)),f333(f333(f263(x99961,x99961),x99962),x99963)),f309(x99961,f333(f333(f115(f890(f889(x99961,x99961),a874)),x99964),x99965)))) % 191.49/191.41 [9997]P4(f333(f333(f335(f889(x99971,x99971)),f333(f333(f263(x99971,x99971),x99972),x99973)),f309(x99971,x99974)))+P4(f333(f333(f335(f889(x99971,x99971)),f333(f333(f263(x99971,x99971),f780(x99975,x99974,x99973,x99972,x99971)),f781(x99975,x99974,x99973,x99972,x99971))),x99975))+~P4(f333(f333(f335(f889(x99971,x99971)),f333(f333(f263(x99971,x99971),x99972),x99973)),f309(x99971,f333(f333(f115(f890(f889(x99971,x99971),a874)),x99974),x99975)))) % 191.49/191.41 [10146]~P4(f333(f333(f335(f889(f881(x101461),f881(x101461))),f333(f333(f263(f881(x101461),f881(x101461)),x101464),x101465)),f159(x101461,x101462)))+~P4(f333(f333(f335(f889(x101461,x101461)),x101463),f333(f173(f889(x101461,x101461)),f333(f333(f182(x101461,x101461),x101464),x101465))))+P4(f333(f333(f272(x101461,x101461,a874),f333(f333(f9(x101461,f890(f889(x101461,x101461),a874),f890(x101461,a874)),f333(f333(f10(f890(x101461,f890(f890(f889(x101461,x101461),a874),a874)),f890(f890(f889(x101461,x101461),a874),f890(x101461,a874)),x101461),f9(x101461,f890(f889(x101461,x101461),a874),a874)),f333(f333(f10(f890(x101461,f889(x101461,x101461)),f890(x101461,f890(f890(f889(x101461,x101461),a874),a874)),x101461),f333(f10(f889(x101461,x101461),f890(f890(f889(x101461,x101461),a874),a874),x101461),f335(f889(x101461,x101461)))),f263(x101461,x101461)))),x101462)),x101463)) % 191.49/191.41 [9572]~P4(f333(f333(f250(a880),x95723),x95722))+~P4(f333(f333(f251(a880),f333(f333(f81(a880),f333(f333(f82(a880),x95723),x95724)),x95721)),f333(f333(f81(a880),f333(f333(f82(a880),x95722),x95724)),x95725)))+P4(f333(f333(f251(a880),x95721),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x95722),x95723)),x95724)),x95725))) % 191.49/191.41 [9573]~P4(f333(f333(f250(a880),x95733),x95732))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),f333(f333(f82(a880),x95733),x95734)),x95731)),f333(f333(f81(a880),f333(f333(f82(a880),x95732),x95734)),x95735)))+P4(f333(f333(f250(a880),x95731),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x95732),x95733)),x95734)),x95735))) % 191.49/191.41 [9599]~P4(f333(f333(f250(a880),x95991),x95994))+P4(f333(f333(f251(a880),f333(f333(f81(a880),f333(f333(f82(a880),x95991),x95992)),x95993)),f333(f333(f81(a880),f333(f333(f82(a880),x95994),x95992)),x95995)))+~P4(f333(f333(f251(a880),x95993),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x95994),x95991)),x95992)),x95995))) % 191.49/191.41 [9600]~P4(f333(f333(f250(a880),x96001),x96004))+P4(f333(f333(f250(a880),f333(f333(f81(a880),f333(f333(f82(a880),x96001),x96002)),x96003)),f333(f333(f81(a880),f333(f333(f82(a880),x96004),x96002)),x96005)))+~P4(f333(f333(f250(a880),x96003),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x96004),x96001)),x96002)),x96005))) % 191.49/191.41 [9716]~P4(f333(f333(f250(a880),x97162),x97161))+~P4(f333(f333(f251(a880),f333(f333(f81(a880),f333(f333(f82(a880),x97161),x97163)),x97164)),f333(f333(f81(a880),f333(f333(f82(a880),x97162),x97163)),x97165)))+P4(f333(f333(f251(a880),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x97161),x97162)),x97163)),x97164)),x97165)) % 191.49/191.41 [9717]~P4(f333(f333(f250(a880),x97172),x97171))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),f333(f333(f82(a880),x97171),x97173)),x97174)),f333(f333(f81(a880),f333(f333(f82(a880),x97172),x97173)),x97175)))+P4(f333(f333(f250(a880),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x97171),x97172)),x97173)),x97174)),x97175)) % 191.49/191.41 [9785]~P4(f333(f333(f250(a880),x97854),x97851))+P4(f333(f333(f251(a880),f333(f333(f81(a880),f333(f333(f82(a880),x97851),x97852)),x97853)),f333(f333(f81(a880),f333(f333(f82(a880),x97854),x97852)),x97855)))+~P4(f333(f333(f251(a880),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x97851),x97854)),x97852)),x97853)),x97855)) % 191.49/191.41 [9786]~P4(f333(f333(f250(a880),x97864),x97861))+P4(f333(f333(f250(a880),f333(f333(f81(a880),f333(f333(f82(a880),x97861),x97862)),x97863)),f333(f333(f81(a880),f333(f333(f82(a880),x97864),x97862)),x97865)))+~P4(f333(f333(f250(a880),f333(f333(f81(a880),f333(f333(f82(a880),f333(f333(f3(a880),x97861),x97864)),x97862)),x97863)),x97865)) % 191.49/191.41 [9982]~P15(x99821,x99822,x99825,x99823)+~P4(f333(f333(f335(f889(x99821,x99821)),x99824),x99825))+P4(f333(f333(f272(x99821,x99821,a874),f333(f333(f9(x99821,f890(x99821,x99822),f890(x99821,a874)),f333(f333(f10(f890(x99822,a874),f890(f890(x99821,x99822),f890(x99821,a874)),x99821),f10(x99822,a874,x99821)),f333(f333(f10(x99822,f890(x99822,a874),x99821),a330),x99823))),x99823)),x99824)) % 191.49/191.41 [6802]~E(f333(x68024,x68025),f197(x68022))+E(f333(f185(x68021,x68022,x68023,x68024),x68025),f333(f242(x68022),x68026))+~E(f333(x68023,x68025),f333(f242(x68022),x68026)) % 191.49/191.41 [6896]~E(f333(x68963,x68966),f197(x68961))+E(f333(f244(f884(x68961),x68962,f197(x68961),x68963),f333(x68964,x68965)),f197(x68961))+~E(f333(x68964,x68965),f333(f242(x68962),x68966)) % 191.49/191.41 [7472]E(f333(x74721,x74722),f197(x74723))+~E(f333(f185(x74725,x74723,x74726,x74721),x74722),f333(f242(x74723),x74724))+E(f333(x74721,x74722),f333(f242(x74723),x74724)) % 191.49/191.41 [7505]~E(f333(f185(x75056,x75053,x75055,x75051),x75052),f333(f242(x75053),x75054))+E(f333(x75051,x75052),f333(f242(x75053),x75054))+E(f333(x75055,x75052),f333(f242(x75053),x75054)) % 191.49/191.41 [8394]~P22(x83946,x83941,x83942,x83944)+E(f333(f74(x83941,x83941,x83941,f333(x83942,x83943)),f333(x83944,x83945)),f333(f74(x83941,x83941,x83941,f333(x83944,x83945)),f333(x83942,x83943)))+~P4(f333(f63(x83946),x83945)) % 191.49/191.41 [8808]~P28(x88081,x88083,x88085,x88086)+~P28(x88083,x88082,x88084,f333(f312(x88081,x88083,x88085),x88086))+P28(x88081,x88082,f333(f74(x88083,x88082,x88081,x88084),x88085),x88086) % 191.49/191.41 [9378]~P4(f333(f333(x93783,x93782),x93786))+~P4(f333(f333(x93784,x93785),x93782))+P4(f333(f333(f335(x93781),x93782),f301(x93781,x93783,x93784,x93785,x93786))) % 191.49/191.41 [9379]~P4(f333(f333(x93794,x93792),x93796))+~P4(f333(f333(x93793,x93795),x93792))+P4(f333(f333(f335(x93791),x93792),f298(x93791,x93793,x93794,x93795,x93796))) % 191.49/191.41 [9482]E(x94821,x94822)+E(x94823,x94824)+~P4(f333(f333(f335(f889(f881(x94825),f881(x94825))),f333(f333(f263(f881(x94825),f881(x94825)),f333(f333(f152(x94825),x94823),x94821)),f333(f333(f152(x94825),x94824),x94822))),f158(x94825,x94826))) % 191.49/191.41 [9497]~E(x94972,x94974)+P4(f333(f333(f335(f889(f881(x94971),f881(x94971))),f333(f333(f263(f881(x94971),f881(x94971)),f333(f333(f152(x94971),x94972),x94973)),f333(f333(f152(x94971),x94974),x94975))),f146(x94971,x94976)))+~P4(f333(f333(f335(f889(f881(x94971),f881(x94971))),f333(f333(f263(f881(x94971),f881(x94971)),x94973),x94975)),f146(x94971,x94976))) % 191.49/191.41 [9498]~E(x94982,x94984)+P4(f333(f333(f335(f889(f881(x94981),f881(x94981))),f333(f333(f263(f881(x94981),f881(x94981)),f333(f333(f152(x94981),x94982),x94983)),f333(f333(f152(x94981),x94984),x94985))),f148(x94981,x94986)))+~P4(f333(f333(f335(f889(f881(x94981),f881(x94981))),f333(f333(f263(f881(x94981),f881(x94981)),x94983),x94985)),f148(x94981,x94986))) % 191.49/191.41 [9499]~E(x94992,x94994)+P4(f333(f333(f335(f889(f881(x94991),f881(x94991))),f333(f333(f263(f881(x94991),f881(x94991)),f333(f333(f152(x94991),x94992),x94993)),f333(f333(f152(x94991),x94994),x94995))),f158(x94991,x94996)))+~P4(f333(f333(f335(f889(f881(x94991),f881(x94991))),f333(f333(f263(f881(x94991),f881(x94991)),x94993),x94995)),f158(x94991,x94996))) % 191.49/191.41 [9500]~E(x95002,x95004)+P4(f333(f333(f335(f889(f881(x95001),f881(x95001))),f333(f333(f263(f881(x95001),f881(x95001)),f333(f333(f127(x95001),x95002),x95003)),f333(f333(f127(x95001),x95004),x95005))),f158(x95001,x95006)))+~P4(f333(f333(f335(f889(f881(x95001),f881(x95001))),f333(f333(f263(f881(x95001),f881(x95001)),x95003),x95005)),f158(x95001,x95006))) % 191.49/191.41 [9501]~E(x95013,x95015)+P4(f333(f333(f335(f889(f881(x95011),f881(x95011))),f333(f333(f263(f881(x95011),f881(x95011)),f333(f333(f127(x95011),x95012),x95013)),f333(f333(f127(x95011),x95014),x95015))),f158(x95011,x95016)))+~P4(f333(f333(f335(f889(f881(x95011),f881(x95011))),f333(f333(f263(f881(x95011),f881(x95011)),x95012),x95014)),f158(x95011,x95016))) % 191.49/191.41 [9562]E(x95621,x95622)+P4(f333(f333(f335(f889(f881(x95623),f881(x95623))),f333(f333(f263(f881(x95623),f881(x95623)),x95621),x95622)),f158(x95623,x95624)))+~P4(f333(f333(f335(f889(f881(x95623),f881(x95623))),f333(f333(f263(f881(x95623),f881(x95623)),f333(f333(f152(x95623),x95625),x95621)),f333(f333(f152(x95623),x95626),x95622))),f158(x95623,x95624))) % 191.49/191.41 [9720]~E(x97203,x97205)+P4(f333(f333(f335(f889(f881(x97201),f881(x97201))),f333(f333(f263(f881(x97201),f881(x97201)),f333(f333(f127(x97201),x97202),f333(f333(f152(x97201),x97203),f118(x97201)))),f333(f333(f127(x97201),x97204),f333(f333(f152(x97201),x97205),f118(x97201))))),f158(x97201,x97206)))+~P4(f333(f333(f335(f889(f881(x97201),f881(x97201))),f333(f333(f263(f881(x97201),f881(x97201)),x97202),x97204)),f158(x97201,x97206))) % 191.49/191.41 [9741]E(f333(x97411,x97412),f197(x97413))+~E(f333(f244(f884(x97416),x97413,f197(x97416),x97414),f333(x97411,x97412)),f197(x97416))+E(f333(x97414,f496(x97412,x97411,x97414,x97415,x97416,x97413)),f197(x97416)) % 191.49/191.41 [9742]E(f333(x97421,x97422),f197(x97423))+~E(f333(f244(f884(x97426),x97423,f197(x97426),x97424),f333(x97421,x97422)),f197(x97426))+E(f333(f242(x97423),f496(x97422,x97421,x97424,x97425,x97426,x97423)),f333(x97421,x97422)) % 191.49/191.41 [9789]E(x97891,x97892)+E(x97893,x97894)+~P4(f333(f333(f335(f889(f881(x97895),f881(x97895))),f333(f333(f263(f881(x97895),f881(x97895)),f333(f333(f127(x97895),x97893),f333(f333(f152(x97895),x97891),f118(x97895)))),f333(f333(f127(x97895),x97894),f333(f333(f152(x97895),x97892),f118(x97895))))),f158(x97895,x97896))) % 191.49/191.41 [9810]E(x98101,x98102)+~P4(f333(f333(f335(f889(f881(x98103),f881(x98103))),f333(f333(f263(f881(x98103),f881(x98103)),f333(f333(f127(x98103),x98101),f333(f333(f152(x98103),x98105),f118(x98103)))),f333(f333(f127(x98103),x98102),f333(f333(f152(x98103),x98106),f118(x98103))))),f158(x98103,x98104)))+P4(f333(f333(f335(f889(f881(x98103),f881(x98103))),f333(f333(f263(f881(x98103),f881(x98103)),x98101),x98102)),f158(x98103,x98104))) % 191.49/191.41 [9850]~P4(f333(f333(f335(f889(f890(x98501,a874),f890(x98501,a874))),f333(f333(f263(f890(x98501,a874),f890(x98501,a874)),x98502),x98504)),f325(x98501,x98506)))+~P4(f333(f333(f335(f889(f890(x98501,a874),f890(x98501,a874))),f333(f333(f263(f890(x98501,a874),f890(x98501,a874)),x98503),x98505)),f325(x98501,x98506)))+P4(f333(f333(f335(f889(f890(x98501,a874),f890(x98501,a874))),f333(f333(f263(f890(x98501,a874),f890(x98501,a874)),f333(f333(f115(f890(x98501,a874)),x98502),x98503)),f333(f333(f115(f890(x98501,a874)),x98504),x98505))),f325(x98501,x98506))) % 191.49/191.41 [5266]~E(f333(x52663,x52666),x52665)+~E(x52664,f333(f242(x52661),x52666))+E(f333(f333(f208(x52661,x52662),x52663),x52664),f333(f242(x52662),x52665)) % 191.49/191.41 [5678]~E(f333(f333(f127(x56781),x56786),x56783),x56785)+E(f333(f333(f127(x56781),x56782),x56783),f333(f333(f152(x56781),x56784),x56785))+~E(x56782,f333(f333(f152(x56781),x56784),x56786)) % 191.49/191.41 [5679]~E(f333(f333(f127(x56791),x56796),x56793),x56795)+E(f333(f333(f127(x56791),x56792),x56793),f333(f333(f127(x56791),x56794),x56795))+~E(x56792,f333(f333(f127(x56791),x56794),x56796)) % 191.49/191.41 [5681]E(f333(f333(f127(x56811),x56812),x56813),f333(f333(f152(x56811),x56814),x56815))+~E(f333(f333(f152(x56811),x56814),x56816),x56812)+~E(x56815,f333(f333(f127(x56811),x56816),x56813)) % 191.49/191.41 [5683]~E(f333(f333(f127(x56831),x56832),x56836),x56834)+E(f333(f333(f127(x56831),x56832),x56833),f333(f333(f127(x56831),x56834),x56835))+~E(x56833,f333(f333(f127(x56831),x56836),x56835)) % 191.49/191.41 [6796]E(f333(x67961,x67962),f333(x67963,x67962))+~E(f333(f333(f155(x67964,x67965),x67961),x67966),f333(f333(f155(x67964,x67965),x67963),x67966))+~P4(f333(f333(f335(x67964),x67962),f333(f173(x67964),x67966))) % 191.49/191.41 [7176]~P22(x71764,x71765,x71766,x71761)+E(f333(f333(x71761,x71762),x71763),f333(f333(f66(x71764,x71765,x71766),x71763),x71762))+~P4(f333(f63(x71764),x71762)) % 191.49/191.41 [7242]~E(x72422,f333(x72424,x72426))+~P4(f333(f333(f335(x72423),x72426),x72425))+P4(f333(f333(f335(x72421),x72422),f333(f312(x72423,x72421,x72424),x72425))) % 191.49/191.41 [7243]~E(f333(x72434,x72432),x72436)+~P4(f333(f333(f335(x72433),x72436),x72435))+P4(f333(f333(f335(x72431),x72432),f333(f313(x72431,x72433,x72434),x72435))) % 191.49/191.41 [7679]~P35(x76791,x76792,x76794,x76796)+P35(x76791,x76792,f333(f333(f152(x76791),x76793),x76794),f333(f333(f152(x76791),x76795),x76796))+~P4(f333(f333(x76792,x76793),x76795)) % 191.49/191.41 [8680]~P56(x86804,x86805,x86801,x86802,x86806)+E(f333(x86801,f333(x86802,x86803)),x86803)+~P4(f333(f333(f335(x86805),x86803),x86806)) % 191.49/191.41 [9485]E(x94851,x94852)+E(f333(f195(f881(x94853)),x94854),f333(f195(f881(x94853)),x94855))+~P4(f333(f333(f335(f889(f881(x94853),f881(x94853))),f333(f333(f263(f881(x94853),f881(x94853)),f333(f333(f152(x94853),x94851),x94854)),f333(f333(f152(x94853),x94852),x94855))),f146(x94853,x94856))) % 191.49/191.41 [9558]~P19(x95581,x95582,x95583)+E(f333(f333(f66(x95581,x95582,x95583),x95584),x95585),x95586)+~P4(f333(f68(x95581,x95582,x95583,x95584,x95585),x95586)) % 191.49/191.41 [9563]E(f333(f195(f881(x95631)),x95632),f333(f195(f881(x95631)),x95633))+P4(f333(f333(f335(f889(f881(x95631),f881(x95631))),f333(f333(f263(f881(x95631),f881(x95631)),x95632),x95633)),f146(x95631,x95634)))+~P4(f333(f333(f335(f889(f881(x95631),f881(x95631))),f333(f333(f263(f881(x95631),f881(x95631)),f333(f333(f152(x95631),x95635),x95632)),f333(f333(f152(x95631),x95636),x95633))),f146(x95631,x95634))) % 191.49/191.41 [9593]~P4(f333(f333(f335(f889(x95931,x95931)),f333(f333(f263(x95931,x95931),x95932),x95934)),f309(x95931,x95936)))+P4(f333(f333(f335(f889(f881(x95931),f881(x95931))),f333(f333(f263(f881(x95931),f881(x95931)),f333(f333(f152(x95931),x95932),x95933)),f333(f333(f152(x95931),x95934),x95935))),f309(f881(x95931),f158(x95931,x95936))))+~P4(f333(f333(f335(f889(f881(x95931),f881(x95931))),f333(f333(f263(f881(x95931),f881(x95931)),x95933),x95935)),f309(f881(x95931),f158(x95931,x95936)))) % 191.49/191.41 [9794]~P4(f333(x97942,x97946))+~E(f333(f137(x97941,x97942),x97943),f333(f333(f152(x97941),x97944),x97945))+~P4(f333(f333(f335(x97941),x97946),f333(f173(x97941),f749(x97945,x97944,x97943,x97942,x97941)))) % 191.49/191.41 [9795]~P4(f333(x97954,x97956))+~E(f333(f333(f152(x97951),x97952),x97953),f333(f137(x97951,x97954),x97955))+~P4(f333(f333(f335(x97951),x97956),f333(f173(x97951),f751(x97955,x97954,x97953,x97952,x97951)))) % 191.49/191.41 [10081]~P69(x100812)+E(f333(f333(f8(x100811,x100812),f333(f333(f10(f890(x100813,a874),x100812,x100811),f333(f8(x100813,x100812),x100814)),f333(f333(f10(f890(x100813,a874),f890(x100813,a874),x100811),f255(x100813)),f333(f333(f10(f890(x100813,a874),f890(x100813,a874),x100811),f333(f20(x100813,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100813),a331),f333(f333(f9(x100813,f890(x100813,a874),a874),f335(x100813)),x100815)))),f333(f9(x100813,x100811,a874),f333(f333(f10(x100811,f890(x100811,a874),x100813),a330),x100816)))))),f333(f312(x100813,x100811,x100816),x100815)),f333(f333(f8(x100813,x100812),x100814),x100815))+~P4(f333(f63(x100813),x100815)) % 191.49/191.41 [6850]~P109(x68503)+P4(f333(x68502,x68505))+E(f333(f137(x68501,x68502),f333(f333(f149(x68501,x68503,x68504),x68505),x68506)),f333(f137(x68501,x68502),x68506)) % 191.49/191.41 [6852]P4(f333(x68521,x68522))+~E(f168(x68523,x68521,x68524),f333(f333(f263(f881(x68523),f881(x68523)),x68525),x68526))+~P4(f333(f333(f335(x68523),x68522),f333(f173(x68523),x68525))) % 191.49/191.41 [6893]~P4(f333(x68932,x68936))+~E(f168(x68931,x68932,x68933),f333(f333(f263(f881(x68931),f881(x68931)),x68934),x68935))+~P4(f333(f333(f335(x68931),x68936),f333(f173(x68931),x68935))) % 191.49/191.41 [7549]~P18(x75491,x75492,x75493)+~P4(f333(f63(x75491),x75496))+E(f333(f333(f66(x75491,x75492,x75493),x75494),f333(f333(f311(x75491),x75495),x75496)),f333(f333(f66(x75491,x75492,x75493),f333(f333(x75493,x75495),x75494)),x75496)) % 191.49/191.41 [7596]~P109(x75962)+~P4(f333(f333(f250(x75962),f333(x75963,x75964)),f333(x75963,x75965)))+E(f333(f333(f149(x75961,x75962,x75963),x75964),f333(f333(f152(x75961),x75965),x75966)),f333(f333(f152(x75961),x75964),f333(f333(f152(x75961),x75965),x75966))) % 191.49/191.41 [7710]E(x77101,x77102)+~E(f333(f333(f270(x77103,x77104),x77101),f333(f18(f890(x77104,a874),x77103),x77105)),f333(f333(f270(x77103,x77104),x77102),f333(f18(f890(x77104,a874),x77103),x77105)))+~P4(f333(f333(f335(x77104),x77106),x77105)) % 191.49/191.41 [7777]~P18(x77771,x77772,x77773)+~P4(f333(f63(x77771),x77776))+E(f333(f333(f66(x77771,x77772,x77773),x77774),f333(f333(f311(x77771),x77775),x77776)),f333(f333(x77773,x77775),f333(f333(f66(x77771,x77772,x77773),x77774),x77776))) % 191.49/191.41 [7890]~P19(x78901,x78902,x78903)+~P4(f333(f63(x78901),x78906))+E(f333(f333(f66(x78901,x78902,x78903),f333(f333(x78903,x78904),x78905)),x78906),f333(f333(x78903,x78904),f333(f333(f66(x78901,x78902,x78903),x78905),x78906))) % 191.49/191.41 [7954]~P23(x79542,x79545,x79546,x79541)+~P4(f333(f63(x79542),x79544))+E(f333(x79541,f333(f333(f311(x79542),x79543),x79544)),f333(f74(x79545,x79545,x79545,f333(x79541,x79544)),f333(x79546,x79543))) % 191.49/191.41 [7991]~P109(x79912)+P4(f333(f333(f250(x79912),f333(x79913,x79914)),f333(x79913,x79915)))+E(f333(f333(f149(x79911,x79912,x79913),x79914),f333(f333(f152(x79911),x79915),x79916)),f333(f333(f152(x79911),x79915),f333(f333(f149(x79911,x79912,x79913),x79914),x79916))) % 191.49/191.41 [8140]~E(f333(f195(f881(x81401)),x81405),f333(f195(f881(x81402)),x81406))+~E(f333(f195(f881(x81401)),x81403),f333(f195(f881(x81402)),x81404))+E(f333(f333(f127(f889(x81401,x81402)),f333(f333(f182(x81401,x81402),x81403),x81404)),f333(f333(f182(x81401,x81402),x81405),x81406)),f333(f333(f182(x81401,x81402),f333(f333(f127(x81401),x81403),x81405)),f333(f333(f127(x81402),x81404),x81406))) % 191.49/191.41 [8252]~E(x82522,f333(f312(x82523,x82521,x82524),x82526))+P4(f333(f333(f250(f890(x82521,a874)),x82522),f333(f312(x82523,x82521,x82524),x82525)))+~P4(f333(f333(f250(f890(x82523,a874)),x82526),x82525)) % 191.49/191.41 [8350]~P109(x83505)+E(f333(x83501,x83502),f333(x83501,x83503))+E(f333(f333(f149(x83504,x83505,x83501),x83502),f333(f333(f149(x83504,x83505,x83501),x83503),x83506)),f333(f333(f149(x83504,x83505,x83501),x83503),f333(f333(f149(x83504,x83505,x83501),x83502),x83506))) % 191.49/191.41 [8388]~P28(x83883,x83881,x83884,x83885)+P28(x83883,x83881,f333(f333(f333(f73(x83883,x83881),x83884),x83886),x83882),x83885)+P4(f333(f333(f335(x83881),x83882),f333(f312(x83883,x83881,x83884),x83885))) % 191.49/191.41 [8534]~P4(f333(f333(f335(x85342),x85344),f333(x85346,x85343)))+~P4(f333(f333(f335(x85341),x85343),x85345))+P4(f333(f333(f335(f889(x85341,x85342)),f333(f333(f263(x85341,x85342),x85343),x85344)),f333(f333(f270(x85341,x85342),x85345),x85346))) % 191.49/191.41 [8987]~P69(x89872)+~P28(x89874,x89871,x89875,x89876)+E(f333(f333(f8(x89871,x89872),x89873),f333(f312(x89874,x89871,x89875),x89876)),f333(f333(f8(x89874,x89872),f333(f74(x89871,x89872,x89874,x89873),x89875)),x89876)) % 191.49/191.41 [8988]~P76(x89882)+~P28(x89884,x89881,x89885,x89886)+E(f333(f333(f11(x89881,x89882),x89883),f333(f312(x89884,x89881,x89885),x89886)),f333(f333(f11(x89884,x89882),f333(f74(x89881,x89882,x89884,x89883),x89885)),x89886)) % 191.49/191.41 [9031]~P37(x90312,x90315,x90311,x90313,x90316)+P4(f333(f333(x90311,f333(f333(f166(x90312),x90313),x90314)),f333(f333(f166(x90315),x90316),x90314)))+~P4(f333(f333(f251(a880),x90314),f333(f195(f881(x90315)),x90316))) % 191.49/191.41 [9032]~P37(x90322,x90325,x90321,x90323,x90326)+P4(f333(f333(x90321,f333(f333(f166(x90322),x90323),x90324)),f333(f333(f166(x90325),x90326),x90324)))+~P4(f333(f333(f251(a880),x90324),f333(f195(f881(x90322)),x90323))) % 191.49/191.41 [9240]~P22(x92403,x92401,x92406,x92402)+~P4(f333(f63(x92403),x92404))+E(f333(f74(x92401,x92401,x92401,f333(x92402,f333(f333(f3(f890(x92403,a874)),x92404),f333(f333(f311(x92403),x92405),f194(f890(x92403,a874)))))),f333(x92406,x92405)),f333(x92402,f333(f333(f311(x92403),x92405),x92404))) % 191.49/191.41 [9878]~E(f333(f312(x98782,x98784,x98786),f258(f890(x98782,a874))),f258(f890(x98784,a874)))+~E(f333(f312(x98781,x98783,x98785),f258(f890(x98781,a874))),f258(f890(x98783,a874)))+E(f333(f312(f889(x98781,x98782),f889(x98783,x98784),f273(x98781,x98783,x98782,x98784,x98785,x98786)),f258(f890(f889(x98781,x98782),a874))),f258(f890(f889(x98783,x98784),a874))) % 191.49/191.41 [9922]~P28(x99223,x99224,x99225,f333(x99226,f721(x99226,x99225,x99224,x99223,x99222,x99221)))+P28(x99223,x99224,x99225,f333(f333(f43(x99222,f890(x99223,a874)),x99221),x99226))+E(x99221,f194(f890(x99222,a874))) % 191.49/191.41 [9970]P28(x99706,x99705,x99704,f333(f333(f43(x99702,f890(x99706,a874)),x99701),x99703))+E(x99701,f194(f890(x99702,a874)))+P4(f333(f333(f335(x99702),f721(x99703,x99704,x99705,x99706,x99702,x99701)),x99701)) % 191.49/191.41 [9974]P4(f333(f333(f335(x99741),f753(x99742,x99743,x99744,x99745,x99746,x99741)),x99746))+P4(f333(f333(f250(f890(f889(x99741,x99744),a874)),f333(f333(f270(x99741,x99744),x99746),x99743)),f333(f333(f270(x99741,x99744),x99745),x99742)))+~P4(f333(f333(f250(f890(x99741,a874)),x99746),x99745)) % 191.49/191.41 [10012]P27(x100126,x100125,f333(f333(f311(f879(x100126)),f333(f333(f333(f93(x100126),x100124),x100123),x100122)),f194(f890(f879(x100126),a874))))+~P27(x100126,x100125,f333(f333(f311(f879(x100126)),f333(f333(f333(f93(x100126),x100124),x100123),x100121)),f194(f890(f879(x100126),a874))))+P4(f333(f333(x100121,f857(x100122,x100121,x100123,x100124,x100125,x100126)),f865(x100122,x100121,x100123,x100124,x100125,x100126))) % 191.49/191.41 [10013]P27(x100136,x100135,f333(f333(f311(f879(x100136)),f333(f333(f333(f93(x100136),x100131),x100133),x100132)),f194(f890(f879(x100136),a874))))+~P27(x100136,x100135,f333(f333(f311(f879(x100136)),f333(f333(f333(f93(x100136),x100134),x100133),x100132)),f194(f890(f879(x100136),a874))))+P4(f333(f333(x100131,f873(x100131,x100132,x100133,x100134,x100135,x100136)),f359(x100131,x100132,x100133,x100134,x100135,x100136))) % 191.49/191.41 [10048]~P27(x100481,x100482,f333(f333(f311(f879(x100481)),f333(f333(f333(f93(x100481),x100483),x100484),x100486)),f194(f890(f879(x100481),a874))))+P27(x100481,x100482,f333(f333(f311(f879(x100481)),f333(f333(f333(f93(x100481),x100483),x100484),x100485)),f194(f890(f879(x100481),a874))))+~P4(f333(f333(x100485,f857(x100485,x100486,x100484,x100483,x100482,x100481)),f865(x100485,x100486,x100484,x100483,x100482,x100481))) % 191.49/191.41 [10049]~P27(x100491,x100492,f333(f333(f311(f879(x100491)),f333(f333(f333(f93(x100491),x100496),x100494),x100495)),f194(f890(f879(x100491),a874))))+P27(x100491,x100492,f333(f333(f311(f879(x100491)),f333(f333(f333(f93(x100491),x100493),x100494),x100495)),f194(f890(f879(x100491),a874))))+~P4(f333(f333(x100496,f873(x100493,x100495,x100494,x100496,x100492,x100491)),f359(x100493,x100495,x100494,x100496,x100492,x100491))) % 191.49/191.41 [10091]~P4(f333(f333(f250(f890(x100912,a874)),f333(x100914,f753(x100916,x100914,x100912,x100915,x100913,x100911))),f333(x100916,f753(x100916,x100914,x100912,x100915,x100913,x100911))))+~P4(f333(f333(f250(f890(x100911,a874)),x100913),x100915))+P4(f333(f333(f250(f890(f889(x100911,x100912),a874)),f333(f333(f270(x100911,x100912),x100913),x100914)),f333(f333(f270(x100911,x100912),x100915),x100916))) % 191.49/191.41 [7729]~P4(f333(x77291,x77295))+~P4(f333(x77296,x77294))+P4(f333(x77291,f333(f271(x77292,x77293),f333(f333(f263(x77292,x77293),x77294),x77295)))) % 191.49/191.41 [7730]~P4(f333(x77301,x77304))+~P4(f333(x77306,x77305))+P4(f333(x77301,f333(f262(x77302,x77303),f333(f333(f263(x77302,x77303),x77304),x77305)))) % 191.49/191.41 [7753]~E(f333(f195(f881(x77531)),x77533),f333(f195(f881(x77534)),x77535))+~E(f333(f333(f178(x77531,x77534),f333(f333(f182(x77531,x77534),x77533),x77535)),x77532),f333(f242(x77534),x77536))+P4(f333(f333(f335(x77531),x77532),f333(f173(x77531),x77533))) % 191.49/191.41 [7782]~P4(f333(f333(x77824,x77826),x77825))+~P4(f333(f333(f335(x77821),x77826),x77823))+P4(f333(f333(f333(f44(x77821,f890(x77822,a874)),x77823),x77824),x77825)) % 191.49/191.41 [8087]~P4(f333(f333(f335(x80871),x80872),f333(x80875,x80876)))+~P4(f333(f333(f335(x80873),x80876),x80874))+P4(f333(f333(f335(x80871),x80872),f333(f333(f44(x80873,f890(x80871,a874)),x80874),x80875))) % 191.49/191.41 [8132]P4(f333(f333(x81321,x81322),x81323))+~P4(f333(f333(x81324,x81322),x81323))+~P4(f333(f333(f250(f890(x81325,f890(x81326,a874))),x81324),x81321)) % 191.49/191.41 [8276]P4(f333(f333(x82761,x82762),x82763))+~P4(f333(f333(f335(x82764),x82762),x82765))+~P4(f333(f333(f333(f43(x82764,f890(x82766,a874)),x82765),x82761),x82763)) % 191.49/191.41 [8407]P4(f333(f333(f335(x84071),x84072),f333(x84073,x84074)))+~P4(f333(f333(f335(x84075),x84074),x84076))+~P4(f333(f333(f335(x84071),x84072),f333(f333(f43(x84075,f890(x84071,a874)),x84076),x84073))) % 191.49/191.41 [8601]~P4(f333(f333(f333(f333(a203,x86011),x86013),x86014),x86016))+~P4(f333(f333(f333(f333(a203,x86012),x86016),x86014),x86015))+P4(f333(f333(f333(f333(a203,f34(x86011,x86012)),x86013),x86014),x86015)) % 191.49/191.41 [8663]~P15(x86634,x86635,x86636,x86631)+E(f333(x86631,x86632),f333(x86631,x86633))+~P4(f333(f333(f335(f889(x86634,x86634)),f333(f333(f263(x86634,x86634),x86632),x86633)),x86636)) % 191.49/191.41 [8693]P4(f333(f333(f250(f890(x86931,a874)),x86932),f333(x86933,x86934)))+~P4(f333(f333(f335(x86935),x86934),x86936))+~P4(f333(f333(f250(f890(x86931,a874)),x86932),f333(f333(f43(x86935,f890(x86931,a874)),x86936),x86933))) % 191.49/191.41 [8723]~P54(x87233,x87234,f333(f288(x87234,x87233),x87235))+E(x87231,f194(f890(x87232,a874)))+E(f333(f333(f43(x87232,f890(x87233,a874)),x87231),f333(f333(f10(f890(x87234,a874),f890(x87233,a874),x87232),f287(x87234,x87233,x87235)),x87236)),f333(f287(x87234,x87233,x87235),f333(f333(f43(x87232,f890(x87234,a874)),x87231),x87236))) % 191.49/191.41 [8799]P4(f333(f333(f335(x87991),x87992),f333(f287(x87993,x87991,x87994),x87995)))+~P4(f333(f333(f335(x87993),x87996),x87995))+~P4(f333(f333(f335(f889(x87993,x87991)),f333(f333(f263(x87993,x87991),x87996),x87992)),x87994)) % 191.49/191.41 [8919]P4(f333(x89191,x89192))+~P4(f333(f333(f333(f333(a203,x89194),x89192),x89195),x89196))+P4(f333(f333(f333(f333(a203,f31(x89191,x89193,x89194)),x89192),x89195),x89196)) % 191.49/191.41 [8936]~P4(f333(x89361,x89364))+~P4(f333(f333(f333(f333(a203,x89362),x89364),x89365),x89366))+P4(f333(f333(f333(f333(a203,f31(x89361,x89362,x89363)),x89364),x89365),x89366)) % 191.49/191.41 [9101]P4(f333(f333(f250(f890(x91011,a874)),f333(f287(x91012,x91011,x91013),x91014)),f333(f287(x91012,x91011,x91015),x91016)))+~P4(f333(f333(f250(f890(x91012,a874)),x91014),x91016))+~P4(f333(f333(f250(f890(f889(x91012,x91011),a874)),x91013),x91015)) % 191.49/191.41 [9194]P4(f333(x91941,x91942))+P4(f333(f333(f333(f333(a203,x91943),x91942),x91944),x91945))+~P4(f333(f333(f333(f333(a203,f31(x91941,x91946,x91943)),x91942),x91944),x91945)) % 191.49/191.41 [9199]~P4(f333(x91995,x91992))+P4(f333(f333(f333(f333(a203,x91991),x91992),x91993),x91994))+~P4(f333(f333(f333(f333(a203,f31(x91995,x91991,x91996)),x91992),x91993),x91994)) % 191.49/191.41 [9247]P4(f333(f333(f333(f333(a203,x92471),x92472),x92473),x92474))+P4(f333(f333(f333(f333(a203,x92475),x92472),x92473),x92474))+~P4(f333(f333(f333(f333(a203,f31(x92476,x92471,x92475)),x92472),x92473),x92474)) % 191.49/191.41 [9297]~P4(f333(f333(f335(x92972),x92976),x92974))+~P4(f333(f333(f250(f890(x92971,a874)),x92973),x92975))+P4(f333(f333(f250(f890(f889(x92971,x92972),a874)),f333(f333(f270(x92971,x92972),x92973),f333(f18(f890(x92972,a874),x92971),x92974))),f333(f333(f270(x92971,x92972),x92975),f333(f18(f890(x92972,a874),x92971),x92974)))) % 191.49/191.41 [9305]~P37(x93051,x93052,x93053,x93055,x93056)+P4(f333(f333(f272(x93051,x93052,a874),x93053),x93054))+~P4(f333(f333(f335(f889(x93051,x93052)),x93054),f333(f173(f889(x93051,x93052)),f333(f333(f182(x93051,x93052),x93055),x93056)))) % 191.49/191.41 [9435]~E(x94353,x94355)+P4(f333(f333(f335(f889(f881(x94351),f881(x94351))),f333(f333(f263(f881(x94351),f881(x94351)),f333(f333(f152(x94351),x94352),x94353)),f333(f333(f152(x94351),x94354),x94355))),f158(x94351,x94356)))+~P4(f333(f333(f335(f889(x94351,x94351)),f333(f333(f263(x94351,x94351),x94352),x94354)),x94356)) % 191.49/191.41 [9441]~E(f333(f195(f881(x94411)),x94415),f333(f195(f881(x94412)),x94416))+E(f187(x94411,x94412,f188(x94411,x94412,x94413,f333(f333(f3(f890(x94411,a874)),x94414),f333(f173(x94411),x94415))),x94415,x94416),f188(x94411,x94412,f187(x94411,x94412,x94413,x94415,x94416),x94414))+~P4(f333(f333(f250(f890(x94411,a874)),f333(f173(x94411),x94415)),x94414)) % 191.49/191.41 [9442]~E(f333(f195(f881(x94421)),x94423),f333(f195(f881(x94421)),x94425))+P4(f333(f333(f335(f889(f881(x94421),f881(x94421))),f333(f333(f263(f881(x94421),f881(x94421)),f333(f333(f152(x94421),x94422),x94423)),f333(f333(f152(x94421),x94424),x94425))),f146(x94421,x94426)))+~P4(f333(f333(f335(f889(x94421,x94421)),f333(f333(f263(x94421,x94421),x94422),x94424)),x94426)) % 191.49/191.41 [9476]P4(f333(f333(f335(f889(x94761,x94761)),f333(f333(f263(x94761,x94761),x94762),x94763)),f333(f333(f189(f889(x94761,x94761),a874),f333(a117,x94764)),x94765)))+~P4(f333(f333(f335(f889(x94761,x94761)),f333(f333(f263(x94761,x94761),x94766),x94763)),x94765))+~P4(f333(f333(f335(f889(x94761,x94761)),f333(f333(f263(x94761,x94761),x94762),x94766)),f333(f333(f189(f889(x94761,x94761),a874),x94764),x94765))) % 191.49/191.41 [9477]P4(f333(f333(f335(f889(x94771,x94771)),f333(f333(f263(x94771,x94771),x94772),x94773)),f333(f333(f189(f889(x94771,x94771),a874),f333(a117,x94774)),x94775)))+~P4(f333(f333(f335(f889(x94771,x94771)),f333(f333(f263(x94771,x94771),x94772),x94776)),x94775))+~P4(f333(f333(f335(f889(x94771,x94771)),f333(f333(f263(x94771,x94771),x94776),x94773)),f333(f333(f189(f889(x94771,x94771),a874),x94774),x94775))) % 191.49/191.41 [9480]~P4(f333(f333(f335(x94804),x94805),x94806))+P4(f333(f333(f250(f890(x94801,a874)),x94802),x94803))+~P4(f333(f333(f250(f890(f889(x94801,x94804),a874)),f333(f333(f270(x94801,x94804),x94802),f333(f18(f890(x94804,a874),x94801),x94806))),f333(f333(f270(x94801,x94804),x94803),f333(f18(f890(x94804,a874),x94801),x94806)))) % 191.49/191.41 [9536]E(x95361,x95362)+~P4(f333(f333(f335(f889(f881(x95363),f881(x95363))),f333(f333(f263(f881(x95363),f881(x95363)),f333(f333(f152(x95363),x95361),x95365)),f333(f333(f152(x95363),x95362),x95366))),f146(x95363,x95364)))+P4(f333(f333(f335(f889(x95363,x95363)),f333(f333(f263(x95363,x95363),x95361),x95362)),x95364)) % 191.49/191.41 [9537]E(x95371,x95372)+~P4(f333(f333(f335(f889(f881(x95373),f881(x95373))),f333(f333(f263(f881(x95373),f881(x95373)),f333(f333(f152(x95373),x95371),x95375)),f333(f333(f152(x95373),x95372),x95376))),f148(x95373,x95374)))+P4(f333(f333(f335(f889(x95373,x95373)),f333(f333(f263(x95373,x95373),x95371),x95372)),x95374)) % 191.49/191.41 [9538]E(x95381,x95382)+~P4(f333(f333(f335(f889(f881(x95383),f881(x95383))),f333(f333(f263(f881(x95383),f881(x95383)),f333(f333(f152(x95383),x95381),x95385)),f333(f333(f152(x95383),x95382),x95386))),f158(x95383,x95384)))+P4(f333(f333(f335(f889(x95383,x95383)),f333(f333(f263(x95383,x95383),x95381),x95382)),x95384)) % 191.49/191.41 [9571]P4(f333(f333(f335(f889(f881(x95711),f881(x95711))),f333(f333(f263(f881(x95711),f881(x95711)),f333(f333(f152(x95711),x95712),x95713)),f333(f333(f152(x95711),x95714),x95715))),f159(x95711,x95716)))+~P4(f333(f333(f335(f889(f881(x95711),f881(x95711))),f333(f333(f263(f881(x95711),f881(x95711)),x95713),x95715)),f159(x95711,x95716)))+~P4(f333(f333(f335(f889(x95711,x95711)),f333(f333(f263(x95711,x95711),x95712),x95714)),x95716)) % 191.49/191.41 [9597]P4(f333(x95971,x95972))+~P4(f333(x95971,f546(x95971,x95973,x95974,x95975,x95976)))+~P4(f333(f333(f335(x95976),x95972),f333(f333(f44(x95975,f890(x95976,a874)),x95974),x95973))) % 191.49/191.41 [9602]~P4(f333(f333(f335(f889(f881(x96021),f881(x96021))),f333(f333(f263(f881(x96021),f881(x96021)),f333(f333(f152(x96021),x96022),x96025)),f333(f333(f152(x96021),x96023),x96026))),f146(x96021,x96024)))+P4(f333(f333(f335(f889(f881(x96021),f881(x96021))),f333(f333(f263(f881(x96021),f881(x96021)),x96025),x96026)),f146(x96021,x96024)))+P4(f333(f333(f335(f889(x96021,x96021)),f333(f333(f263(x96021,x96021),x96022),x96023)),x96024)) % 191.49/191.41 [9603]~P4(f333(f333(f335(f889(f881(x96031),f881(x96031))),f333(f333(f263(f881(x96031),f881(x96031)),f333(f333(f152(x96031),x96032),x96035)),f333(f333(f152(x96031),x96033),x96036))),f148(x96031,x96034)))+P4(f333(f333(f335(f889(f881(x96031),f881(x96031))),f333(f333(f263(f881(x96031),f881(x96031)),x96035),x96036)),f148(x96031,x96034)))+P4(f333(f333(f335(f889(x96031,x96031)),f333(f333(f263(x96031,x96031),x96032),x96033)),x96034)) % 191.49/191.41 [9604]~P4(f333(f333(f335(f889(f881(x96041),f881(x96041))),f333(f333(f263(f881(x96041),f881(x96041)),f333(f333(f152(x96041),x96042),x96045)),f333(f333(f152(x96041),x96043),x96046))),f158(x96041,x96044)))+P4(f333(f333(f335(f889(f881(x96041),f881(x96041))),f333(f333(f263(f881(x96041),f881(x96041)),x96045),x96046)),f158(x96041,x96044)))+P4(f333(f333(f335(f889(x96041,x96041)),f333(f333(f263(x96041,x96041),x96042),x96043)),x96044)) % 191.49/191.41 [9692]P4(f333(x96921,x96922))+P4(f333(f333(f335(x96923),f547(x96921,x96924,x96925,x96923,x96926)),x96925))+~P4(f333(f333(f335(x96926),x96922),f333(f333(f44(x96923,f890(x96926,a874)),x96925),x96924))) % 191.49/191.41 [9703]~E(x97032,x97034)+P4(f333(f333(f335(f889(f881(x97031),f881(x97031))),f333(f333(f263(f881(x97031),f881(x97031)),f333(f333(f127(x97031),x97032),f333(f333(f152(x97031),x97033),f118(x97031)))),f333(f333(f127(x97031),x97034),f333(f333(f152(x97031),x97035),f118(x97031))))),f158(x97031,x97036)))+~P4(f333(f333(f335(f889(x97031,x97031)),f333(f333(f263(x97031,x97031),x97033),x97035)),x97036)) % 191.49/191.41 [9804]E(x98041,x98042)+~P4(f333(f333(f335(f889(f881(x98043),f881(x98043))),f333(f333(f263(f881(x98043),f881(x98043)),f333(f333(f127(x98043),x98045),f333(f333(f152(x98043),x98041),f118(x98043)))),f333(f333(f127(x98043),x98046),f333(f333(f152(x98043),x98042),f118(x98043))))),f158(x98043,x98044)))+P4(f333(f333(f335(f889(x98043,x98043)),f333(f333(f263(x98043,x98043),x98041),x98042)),x98044)) % 191.49/191.41 [9828]~P4(f333(f333(f335(f889(f881(x98281),f881(x98281))),f333(f333(f263(f881(x98281),f881(x98281)),f333(f333(f127(x98281),x98285),f333(f333(f152(x98281),x98282),f118(x98281)))),f333(f333(f127(x98281),x98286),f333(f333(f152(x98281),x98283),f118(x98281))))),f158(x98281,x98284)))+P4(f333(f333(f335(f889(f881(x98281),f881(x98281))),f333(f333(f263(f881(x98281),f881(x98281)),x98285),x98286)),f158(x98281,x98284)))+P4(f333(f333(f335(f889(x98281,x98281)),f333(f333(f263(x98281,x98281),x98282),x98283)),x98284)) % 191.49/191.41 [9851]P4(f333(x98511,x98512))+P4(f333(f333(f335(x98513),f546(x98511,x98514,x98515,x98516,x98513)),f333(x98514,f547(x98511,x98514,x98515,x98516,x98513))))+~P4(f333(f333(f335(x98513),x98512),f333(f333(f44(x98516,f890(x98513,a874)),x98515),x98514))) % 191.49/191.41 [8815]~P19(x88153,x88154,x88151)+~P4(f333(f63(x88153),x88156))+E(f333(f333(x88151,x88152),f333(f333(f66(x88153,x88154,x88151),x88155),f333(f333(f3(f890(x88153,a874)),x88156),f333(f333(f311(x88153),x88152),f194(f890(x88153,a874)))))),f333(f333(f66(x88153,x88154,x88151),x88155),f333(f333(f311(x88153),x88152),x88156))) % 191.49/191.41 [8903]~E(f333(f333(f178(x89031,x89032),x89034),x89035),f333(f242(x89032),x89036))+~P4(f333(f333(x89033,x89035),x89036))+E(f333(f333(f178(x89031,x89032),f333(f137(f889(x89031,x89032),f333(f272(x89031,x89032,a874),x89033)),x89034)),x89035),f333(f242(x89032),x89036)) % 191.49/191.41 [9108]~P4(f333(f333(f335(x91085),x91083),x91086))+P4(f333(f333(f250(f890(x91081,a874)),f333(x91082,x91083)),x91084))+~P4(f333(f333(f250(f890(x91081,a874)),f333(f333(f44(x91085,f890(x91081,a874)),x91086),x91082)),x91084)) % 191.49/191.41 [9775]~P12(x97751,x97755,x97754)+P4(f333(f333(f335(f889(x97751,x97751)),f333(f333(f263(x97751,x97751),x97752),x97753)),x97754))+~P4(f333(f333(f335(x97751),x97756),f333(f333(f106(f890(x97751,a874)),f333(f287(x97751,x97751,x97754),f333(f333(f311(x97751),x97752),f194(f890(x97751,a874))))),f333(f287(x97751,x97751,x97754),f333(f333(f311(x97751),x97753),f194(f890(x97751,a874))))))) % 191.49/191.41 [8569]~P106(x85692)+~E(f333(f333(f81(x85692),f333(f333(f82(x85692),x85694),x85695)),x85691),f333(f333(f81(x85692),f333(f333(f82(x85692),x85693),x85695)),x85696))+E(x85691,f333(f333(f81(x85692),f333(f333(f82(x85692),f333(f333(f3(x85692),x85693),x85694)),x85695)),x85696)) % 191.49/191.41 [8570]~P106(x85701)+~E(f333(f333(f81(x85701),f333(f333(f82(x85701),x85702),x85704)),x85705),f333(f333(f81(x85701),f333(f333(f82(x85701),x85703),x85704)),x85706))+E(f333(f333(f81(x85701),f333(f333(f82(x85701),f333(f333(f3(x85701),x85702),x85703)),x85704)),x85705),x85706) % 191.49/191.41 [8726]~P106(x87261)+E(f333(f333(f81(x87261),f333(f333(f82(x87261),x87262),x87263)),x87264),f333(f333(f81(x87261),f333(f333(f82(x87261),x87265),x87263)),x87266))+~E(x87266,f333(f333(f81(x87261),f333(f333(f82(x87261),f333(f333(f3(x87261),x87262),x87265)),x87263)),x87264)) % 191.49/191.41 [8727]~P106(x87271)+E(f333(f333(f81(x87271),f333(f333(f82(x87271),x87272),x87273)),x87274),f333(f333(f81(x87271),f333(f333(f82(x87271),x87275),x87273)),x87276))+~E(f333(f333(f81(x87271),f333(f333(f82(x87271),f333(f333(f3(x87271),x87272),x87275)),x87273)),x87274),x87276) % 191.49/191.41 [9049]~P4(f333(f333(x90494,x90495),x90496))+~P4(f333(f333(x90493,x90495),x90496))+P4(f333(f333(f333(f333(f106(f890(x90491,f890(x90492,a874))),x90493),x90494),x90495),x90496)) % 191.49/191.41 [9313]P4(f333(f333(x93131,x93132),x93133))+P4(f333(f333(x93134,x93132),x93133))+~P4(f333(f333(f333(f333(f115(f890(x93135,f890(x93136,a874))),x93134),x93131),x93132),x93133)) % 191.49/191.41 [9617]~P126(x96171)+~P4(f333(f333(f251(x96171),f333(f333(f81(x96171),f333(f333(f82(x96171),x96174),x96175)),x96172)),f333(f333(f81(x96171),f333(f333(f82(x96171),x96173),x96175)),x96176)))+P4(f333(f333(f251(x96171),x96172),f333(f333(f81(x96171),f333(f333(f82(x96171),f333(f333(f3(x96171),x96173),x96174)),x96175)),x96176))) % 191.49/191.41 [9618]~P126(x96181)+~P4(f333(f333(f250(x96181),f333(f333(f81(x96181),f333(f333(f82(x96181),x96184),x96185)),x96182)),f333(f333(f81(x96181),f333(f333(f82(x96181),x96183),x96185)),x96186)))+P4(f333(f333(f250(x96181),x96182),f333(f333(f81(x96181),f333(f333(f82(x96181),f333(f333(f3(x96181),x96183),x96184)),x96185)),x96186))) % 191.49/191.41 [9647]~P126(x96471)+P4(f333(f333(f251(x96471),f333(f333(f81(x96471),f333(f333(f82(x96471),x96472),x96473)),x96474)),f333(f333(f81(x96471),f333(f333(f82(x96471),x96475),x96473)),x96476)))+~P4(f333(f333(f251(x96471),x96474),f333(f333(f81(x96471),f333(f333(f82(x96471),f333(f333(f3(x96471),x96475),x96472)),x96473)),x96476))) % 191.49/191.41 [9648]~P126(x96481)+P4(f333(f333(f250(x96481),f333(f333(f81(x96481),f333(f333(f82(x96481),x96482),x96483)),x96484)),f333(f333(f81(x96481),f333(f333(f82(x96481),x96485),x96483)),x96486)))+~P4(f333(f333(f250(x96481),x96484),f333(f333(f81(x96481),f333(f333(f82(x96481),f333(f333(f3(x96481),x96485),x96482)),x96483)),x96486))) % 191.49/191.41 [9763]~P126(x97631)+~P4(f333(f333(f251(x97631),f333(f333(f81(x97631),f333(f333(f82(x97631),x97632),x97634)),x97635)),f333(f333(f81(x97631),f333(f333(f82(x97631),x97633),x97634)),x97636)))+P4(f333(f333(f251(x97631),f333(f333(f81(x97631),f333(f333(f82(x97631),f333(f333(f3(x97631),x97632),x97633)),x97634)),x97635)),x97636)) % 191.49/191.41 [9764]~P126(x97641)+~P4(f333(f333(f250(x97641),f333(f333(f81(x97641),f333(f333(f82(x97641),x97642),x97644)),x97645)),f333(f333(f81(x97641),f333(f333(f82(x97641),x97643),x97644)),x97646)))+P4(f333(f333(f250(x97641),f333(f333(f81(x97641),f333(f333(f82(x97641),f333(f333(f3(x97641),x97642),x97643)),x97644)),x97645)),x97646)) % 191.49/191.41 [9812]~P126(x98121)+P4(f333(f333(f251(x98121),f333(f333(f81(x98121),f333(f333(f82(x98121),x98122),x98123)),x98124)),f333(f333(f81(x98121),f333(f333(f82(x98121),x98125),x98123)),x98126)))+~P4(f333(f333(f251(x98121),f333(f333(f81(x98121),f333(f333(f82(x98121),f333(f333(f3(x98121),x98122),x98125)),x98123)),x98124)),x98126)) % 191.49/191.41 [9813]~P126(x98131)+P4(f333(f333(f250(x98131),f333(f333(f81(x98131),f333(f333(f82(x98131),x98132),x98133)),x98134)),f333(f333(f81(x98131),f333(f333(f82(x98131),x98135),x98133)),x98136)))+~P4(f333(f333(f250(x98131),f333(f333(f81(x98131),f333(f333(f82(x98131),f333(f333(f3(x98131),x98132),x98135)),x98133)),x98134)),x98136)) % 191.49/191.41 [9963]~P69(x99632)+~P4(f333(f63(x99631),x99636))+E(f333(f333(f8(x99631,x99632),f333(f333(f20(x99631,x99632,x99632),f333(f333(f20(x99631,x99632,f890(x99632,x99632)),f333(f333(f10(a874,f890(x99632,f890(x99632,x99632)),x99631),f101(x99632)),x99633)),x99634)),x99635)),x99636),f333(f333(f81(x99632),f333(f333(f8(x99631,x99632),x99634),f333(f333(f106(f890(x99631,a874)),x99636),f333(f255(x99631),x99633)))),f333(f333(f8(x99631,x99632),x99635),f333(f333(f106(f890(x99631,a874)),x99636),f333(f80(f890(x99631,a874)),f333(f255(x99631),x99633)))))) % 191.49/191.41 [10023]P4(f333(f333(f335(x100232),x100234),x100236))+P4(f333(f333(f335(x100232),x100235),x100236))+E(f333(f313(x100231,x100232,f333(f333(f9(x100231,x100232,x100232),f333(f333(f9(x100231,x100232,f890(x100232,x100232)),f333(f333(f10(a874,f890(x100232,f890(x100232,x100232)),x100231),f101(x100232)),f333(f333(f9(x100231,f890(x100231,a874),a874),f335(x100231)),x100233))),x100234)),x100235)),x100236),f194(f890(x100231,a874))) % 191.49/191.41 [10024]P4(f333(f333(f335(x100242),x100245),x100246))+~P4(f333(f333(f335(x100242),x100244),x100246))+E(f333(f313(x100241,x100242,f333(f333(f9(x100241,x100242,x100242),f333(f333(f9(x100241,x100242,f890(x100242,x100242)),f333(f333(f10(a874,f890(x100242,f890(x100242,x100242)),x100241),f101(x100242)),f333(f333(f9(x100241,f890(x100241,a874),a874),f335(x100241)),x100243))),x100244)),x100245)),x100246),x100243) % 191.49/191.41 [10025]P4(f333(f333(f335(x100252),x100254),x100256))+~P4(f333(f333(f335(x100252),x100255),x100256))+E(f333(f313(x100251,x100252,f333(f333(f9(x100251,x100252,x100252),f333(f333(f9(x100251,x100252,f890(x100252,x100252)),f333(f333(f10(a874,f890(x100252,f890(x100252,x100252)),x100251),f101(x100252)),f333(f333(f9(x100251,f890(x100251,a874),a874),f335(x100251)),x100253))),x100254)),x100255)),x100256),f333(f80(f890(x100251,a874)),x100253)) % 191.49/191.41 [10026]~P4(f333(f333(f335(x100262),x100264),x100266))+~P4(f333(f333(f335(x100262),x100265),x100266))+E(f333(f313(x100261,x100262,f333(f333(f9(x100261,x100262,x100262),f333(f333(f9(x100261,x100262,f890(x100262,x100262)),f333(f333(f10(a874,f890(x100262,f890(x100262,x100262)),x100261),f101(x100262)),f333(f333(f9(x100261,f890(x100261,a874),a874),f335(x100261)),x100263))),x100264)),x100265)),x100266),f258(f890(x100261,a874))) % 191.49/191.41 [10190]P27(x101901,x101902,f333(f333(f311(f879(x101901)),f333(f333(f333(f93(x101901),f333(x101903,x101904)),f333(a26,x101904)),f333(x101905,x101904))),f194(f890(f879(x101901),a874))))+~P4(f333(f333(f335(a877),x101904),x101906))+~P27(x101901,f333(f333(f115(f890(f879(x101901),a874)),x101902),f333(f312(a877,f879(x101901),f333(f333(f20(a877,f890(x101901,f890(a875,a874)),f879(x101901)),f333(f333(f20(a877,a876,f890(f890(x101901,f890(a875,a874)),f879(x101901))),f333(f333(f10(f890(x101901,f890(a875,a874)),f890(a876,f890(f890(x101901,f890(a875,a874)),f879(x101901))),a877),f93(x101901)),x101903)),a26)),x101905)),x101906)),f333(f312(a877,f879(x101901),f333(f333(f20(a877,f890(x101901,f890(a875,a874)),f879(x101901)),f333(f333(f20(a877,a876,f890(f890(x101901,f890(a875,a874)),f879(x101901))),f333(f333(f10(f890(x101901,f890(a875,a874)),f890(a876,f890(f890(x101901,f890(a875,a874)),f879(x101901))),a877),f93(x101901)),x101903)),f333(f333(f10(f884(a876),a876,a877),f246(a876)),a28))),x101905)),x101906)) % 191.49/191.41 [8598]E(x85981,x85982)+~P56(x85984,x85985,x85983,x85986,x85987)+~E(f333(x85983,x85981),f333(x85983,x85982)) % 191.49/191.41 [7003]E(f333(f244(f884(x70031),x70032,f197(x70031),x70033),f333(x70034,x70035)),f333(f242(x70031),x70036))+~E(f333(x70034,x70035),f333(f242(x70032),x70037))+~E(f333(x70033,x70037),f333(f242(x70031),x70036)) % 191.49/191.41 [8627]~P3(x86276,x86275,x86277,x86274,x86271)+E(f333(f333(x86271,x86272),x86273),x86274)+P4(f333(f63(x86275),x86273)) % 191.49/191.41 [9462]P44(x94621,x94622,x94623,x94624,x94625,f333(f333(x94623,x94626),x94627))+~E(f333(f333(x94623,x94626),x94627),x94624)+~E(x94625,f194(f890(x94621,a874))) % 191.49/191.41 [9667]~P4(f333(x96676,x96673))+~P4(f333(f333(f335(f889(x96672,x96672)),f333(f333(f263(x96672,x96672),x96674),x96675)),f333(x96677,x96673)))+P4(f333(f333(f335(f889(f889(x96671,x96672),f889(x96671,x96672))),f333(f333(f263(f889(x96671,x96672),f889(x96671,x96672)),f333(f333(f263(x96671,x96672),x96673),x96674)),f333(f333(f263(x96671,x96672),x96673),x96675))),f285(x96671,x96672,x96676,x96677))) % 191.49/191.41 [10083]~P44(x100832,x100837,x100833,x100836,x100831,f333(f333(x100833,x100835),x100834))+E(f333(f333(x100833,f755(x100834,x100835,x100831,x100836,x100833,x100837,x100832)),f763(x100834,x100835,x100831,x100836,x100833,x100837,x100832)),f333(f333(x100833,x100835),x100834))+E(x100831,f194(f890(x100832,a874))) % 191.49/191.41 [10084]~P44(x100847,x100846,x100841,x100844,x100845,f333(f333(x100841,x100842),x100843))+E(f333(f333(x100841,f755(x100843,x100842,x100845,x100844,x100841,x100846,x100847)),f763(x100843,x100842,x100845,x100844,x100841,x100846,x100847)),f333(f333(x100841,x100842),x100843))+E(f333(f333(x100841,x100842),x100843),x100844) % 191.49/191.41 [9151]~P37(x91511,x91512,x91513,x91515,x91517)+P37(x91511,x91512,x91513,f333(f333(f152(x91511),x91514),x91515),f333(f333(f152(x91512),x91516),x91517))+~P4(f333(f333(x91513,x91514),x91516)) % 191.49/191.41 [9169]P37(x91691,x91692,x91693,x91694,x91695)+~P37(x91691,x91692,x91693,f333(f333(f127(x91691),x91696),x91694),f333(f333(f127(x91692),x91697),x91695))+~E(f333(f195(f881(x91691)),x91696),f333(f195(f881(x91692)),x91697)) % 191.49/191.41 [9170]P37(x91701,x91702,x91703,x91704,x91705)+~P37(x91701,x91702,x91703,f333(f333(f127(x91701),x91704),x91706),f333(f333(f127(x91702),x91705),x91707))+~E(f333(f195(f881(x91701)),x91704),f333(f195(f881(x91702)),x91705)) % 191.49/191.41 [9381]~P37(x93811,x93812,x93813,x93815,x93817)+~P37(x93811,x93812,x93813,x93814,x93816)+P37(x93811,x93812,x93813,f333(f333(f127(x93811),x93814),x93815),f333(f333(f127(x93812),x93816),x93817)) % 191.49/191.41 [9745]~P4(f333(f68(x97451,x97454,x97455,x97456,x97453),x97457))+P4(f333(f68(x97451,x97454,x97455,x97456,f333(f333(f311(x97451),x97452),x97453)),f333(f333(x97455,x97452),x97457)))+P4(f333(f333(f335(x97451),x97452),x97453)) % 191.49/191.41 [9876]~P28(x98763,x98761,x98764,f258(f890(x98763,a874)))+E(f333(f333(f178(x98761,x98762),f333(f333(f155(f889(x98763,x98762),f889(x98761,x98762)),f333(f272(x98763,x98762,f889(x98761,x98762)),f333(f333(f10(x98761,f890(x98762,f889(x98761,x98762)),x98763),f263(x98761,x98762)),x98764))),x98765)),f333(x98764,x98766)),f333(f242(x98762),x98767))+~E(f333(f333(f178(x98763,x98762),x98765),x98766),f333(f242(x98762),x98767)) % 191.49/191.41 [10104]~P44(x101042,x101047,x101046,x101045,x101041,f333(f333(x101046,x101044),x101043))+E(x101041,f194(f890(x101042,a874)))+P4(f333(f333(f335(x101042),f755(x101043,x101044,x101041,x101045,x101046,x101047,x101042)),x101041)) % 191.49/191.41 [10105]~P44(x101055,x101057,x101051,x101054,x101056,f333(f333(x101051,x101052),x101053))+E(f333(f333(x101051,x101052),x101053),x101054)+P4(f333(f333(f335(x101055),f755(x101053,x101052,x101056,x101054,x101051,x101057,x101055)),x101056)) % 191.49/191.41 [6795]~E(x67955,x67957)+~E(x67956,x67954)+E(f333(f333(f333(f333(f73(x67951,f884(x67952)),x67953),x67954),f333(f242(x67952),x67955)),x67956),f333(f242(x67952),x67957)) % 191.49/191.41 [6918]E(x69181,x69182)+~E(f333(x69185,x69181),f333(f242(x69184),x69187))+E(f333(f333(f333(f333(f73(x69183,f884(x69184)),x69185),x69182),f333(f242(x69184),x69186)),x69181),f333(f242(x69184),x69187)) % 191.49/191.41 [7621]E(x76211,x76212)+~E(x76213,x76214)+~E(f333(f333(f333(f333(f73(x76215,f884(x76216)),x76217),x76214),f333(f242(x76216),x76211)),x76213),f333(f242(x76216),x76212)) % 191.49/191.41 [7685]E(x76851,x76852)+E(f333(x76853,x76854),f333(f242(x76855),x76851))+~E(f333(f333(f333(f333(f73(x76856,f884(x76855)),x76853),x76857),f333(f242(x76855),x76852)),x76854),f333(f242(x76855),x76851)) % 191.49/191.41 [7686]E(x76861,x76862)+E(f333(x76863,x76861),f333(f242(x76864),x76865))+~E(f333(f333(f333(f333(f73(x76866,f884(x76864)),x76863),x76862),f333(f242(x76864),x76867)),x76861),f333(f242(x76864),x76865)) % 191.49/191.41 [8841]~P24(x88414,x88415,x88416,x88417,x88411)+~P4(f333(f63(x88415),x88413))+E(f333(f333(x88411,x88412),x88413),f333(f333(f333(f67(x88414,x88415,x88416),x88412),x88417),x88413)) % 191.49/191.41 [8842]~P3(x88424,x88425,x88426,x88427,x88421)+~P4(f333(f63(x88425),x88423))+E(f333(f333(x88421,x88422),x88423),f333(f333(f333(f67(x88424,x88425,x88426),x88422),x88427),x88423)) % 191.49/191.41 [9430]~P27(x94301,x94302,f333(f333(f311(f879(x94301)),f333(f333(f333(f93(x94301),x94303),x94304),x94307)),f194(f890(f879(x94301),a874))))+P27(x94301,x94302,f333(f333(f311(f879(x94301)),f333(f333(f333(f93(x94301),x94303),f34(x94304,x94305)),x94306)),f194(f890(f879(x94301),a874))))+~P27(x94301,x94302,f333(f333(f311(f879(x94301)),f333(f333(f333(f93(x94301),x94307),x94305),x94306)),f194(f890(f879(x94301),a874)))) % 191.49/191.41 [9642]~P26(x96423,x96424,x96425,x96427,x96426,x96421)+~P4(f333(f63(x96424),x96422))+E(f333(x96421,x96422),f333(f333(f333(f67(x96423,x96424,x96425),x96426),x96427),x96422)) % 191.49/191.41 [9808]P44(x98081,x98082,x98083,x98084,x98085,f333(f333(x98083,x98086),x98087))+~P44(x98081,x98082,x98083,x98084,f333(f333(f3(f890(x98081,a874)),x98085),f333(f333(f311(x98081),x98086),f194(f890(x98081,a874)))),x98087)+~P4(f333(f333(f335(x98081),x98086),x98085)) % 191.49/191.41 [10050]~P27(x100501,x100502,f333(f333(f311(f879(x100501)),f333(f333(f333(f93(x100501),f96(x100501,x100503,x100504)),x100505),x100507)),f194(f890(f879(x100501),a874))))+P27(x100501,x100502,f333(f333(f311(f879(x100501)),f333(f333(f333(f93(x100501),x100503),f31(x100504,x100505,x100506)),x100507)),f194(f890(f879(x100501),a874))))+~P27(x100501,x100502,f333(f333(f311(f879(x100501)),f333(f333(f333(f93(x100501),f96(x100501,x100503,f333(f74(a874,a874,a875,a328),x100504))),x100506),x100507)),f194(f890(f879(x100501),a874)))) % 191.49/191.41 [10152]~P44(x101522,x101523,x101524,x101525,x101521,f333(f333(x101524,x101527),x101526))+P44(x101522,x101523,x101524,x101525,f333(f333(f3(f890(x101522,a874)),x101521),f333(f333(f311(x101522),f755(x101526,x101527,x101521,x101525,x101524,x101523,x101522)),f194(f890(x101522,a874)))),f763(x101526,x101527,x101521,x101525,x101524,x101523,x101522))+E(x101521,f194(f890(x101522,a874))) % 191.49/191.41 [10153]~P44(x101535,x101536,x101531,x101534,x101537,f333(f333(x101531,x101532),x101533))+P44(x101535,x101536,x101531,x101534,f333(f333(f3(f890(x101535,a874)),x101537),f333(f333(f311(x101535),f755(x101533,x101532,x101537,x101534,x101531,x101536,x101535)),f194(f890(x101535,a874)))),f763(x101533,x101532,x101537,x101534,x101531,x101536,x101535))+E(f333(f333(x101531,x101532),x101533),x101534) % 191.49/191.41 [9158]E(f187(x91581,x91582,x91583,x91584,f333(f333(f160(x91582,x91585),x91586),x91587)),f187(x91581,x91582,x91583,x91584,x91585))+~P4(f333(f333(f251(a880),x91586),f333(f195(f881(x91582)),x91585)))+~P4(f333(f333(f250(a880),f333(f195(f881(x91581)),x91584)),x91586)) % 191.49/191.41 [9450]P4(f333(f333(f250(f890(f889(x94501,x94502),a874)),f333(f333(f290(x94501,x94503,x94502),x94504),x94505)),f333(f333(f290(x94501,x94503,x94502),x94506),x94507)))+~P4(f333(f333(f250(f890(f889(x94503,x94502),a874)),x94505),x94507))+~P4(f333(f333(f250(f890(f889(x94501,x94503),a874)),x94504),x94506)) % 191.49/191.41 [9818]~P4(f333(f333(f335(x98181),x98186),x98185))+P4(f333(f68(x98181,x98182,x98183,x98184,x98185),f333(f333(x98183,x98186),x98187)))+~P4(f333(f68(x98181,x98182,x98183,x98184,f333(f333(f3(f890(x98181,a874)),x98185),f333(f333(f311(x98181),x98186),f194(f890(x98181,a874))))),x98187)) % 191.49/191.41 [10228]~P144(x102281)+~P28(f889(x102282,x102283),x102281,f333(f272(x102282,x102283,x102281),f333(f333(f9(x102282,f890(x102283,x102281),f890(x102283,x102281)),f333(f333(f10(f890(x102281,x102281),f890(f890(x102283,x102281),f890(x102283,x102281)),x102282),f10(x102281,x102281,x102283)),f333(f333(f10(x102281,f890(x102281,x102281),x102282),f82(x102281)),x102284))),x102285)),f333(f333(f270(x102282,x102283),x102286),f333(f18(f890(x102283,a874),x102282),x102287)))+E(f333(f333(f8(x102281,x102281),f35(x102281)),f333(f255(x102281),f333(f333(f10(f890(x102282,a874),a874,x102281),f87(x102282)),f333(f333(f10(f890(x102282,f890(x102283,a874)),f890(x102282,a874),x102281),f333(f10(f890(x102283,a874),a874,x102282),f87(x102283))),f333(f333(f9(x102281,f890(x102282,f890(x102283,a874)),f890(x102282,f890(x102283,a874))),f333(f333(f10(f890(x102282,f890(f890(x102283,a874),f890(x102283,a874))),f890(f890(x102282,f890(x102283,a874)),f890(x102282,f890(x102283,a874))),x102281),f20(x102282,f890(x102283,a874),f890(x102283,a874))),f333(f333(f10(f890(x102282,f890(x102283,f890(a874,a874))),f890(x102282,f890(f890(x102283,a874),f890(x102283,a874))),x102281),f333(f10(f890(x102283,f890(a874,a874)),f890(f890(x102283,a874),f890(x102283,a874)),x102282),f20(x102283,a874,a874))),f333(f333(f10(f890(x102282,f890(x102283,a874)),f890(x102282,f890(x102283,f890(a874,a874))),x102281),f333(f10(f890(x102283,a874),f890(x102283,f890(a874,a874)),x102282),f333(f10(a874,f890(a874,a874),x102283),a331))),f333(f333(f9(x102281,f890(x102282,f890(x102283,x102281)),f890(x102282,f890(x102283,a874))),f333(f333(f10(f890(f890(x102283,x102281),f890(x102283,a874)),f890(f890(x102282,f890(x102283,x102281)),f890(x102282,f890(x102283,a874))),x102281),f10(f890(x102283,x102281),f890(x102283,a874),x102282)),f333(f333(f10(f890(x102281,a874),f890(f890(x102283,x102281),f890(x102283,a874)),x102281),f10(x102281,a874,x102283)),a330))),f333(f333(f9(x102282,f890(x102283,x102281),f890(x102283,x102281)),f333(f333(f10(f890(x102281,x102281),f890(f890(x102283,x102281),f890(x102283,x102281)),x102282),f10(x102281,x102281,x102283)),f333(f333(f10(x102281,f890(x102281,x102281),x102282),f82(x102281)),x102284))),x102285)))))),f333(f333(f9(x102282,f890(x102283,a874),f890(x102283,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x102283,a874),f890(x102283,a874)),x102282),f10(a874,a874,x102283)),f333(f333(f10(a874,f890(a874,a874),x102282),a331),f333(f333(f9(x102282,f890(x102282,a874),a874),f335(x102282)),x102286)))),f333(f333(f9(x102283,f890(x102283,a874),a874),f335(x102283)),x102287))))))),f333(f333(f82(x102281),f333(f333(f8(x102282,x102281),x102284),x102286)),f333(f333(f8(x102283,x102281),x102285),x102287))) % 191.49/191.41 [9905]P53(x99051,x99052,x99053,x99054,x99055,x99056,x99057)+~P4(f333(f333(x99054,x99056),x99058))+~P4(f333(f333(x99055,x99058),x99057)) % 191.49/191.41 [9217]~P22(x92178,x92171,x92173,x92175)+~P4(f333(f63(x92178),x92176))+E(f333(f74(x92171,x92171,x92172,f333(x92173,x92174)),f333(f74(x92171,x92171,x92172,f333(x92175,x92176)),x92177)),f333(f74(x92171,x92171,x92172,f333(x92175,x92176)),f333(f74(x92171,x92171,x92172,f333(x92173,x92174)),x92177))) % 191.49/191.41 [9628]~P25(x96287,x96282,x96285,x96288,x96286,x96281)+~P4(f333(f63(x96282),x96284))+E(f333(x96281,f333(f333(f311(x96282),x96283),x96284)),f333(f333(x96285,f333(x96286,x96283)),f333(x96281,x96284))) % 191.49/191.41 [9761]~P28(x97612,x97614,x97616,x97618)+~P28(x97611,x97613,x97615,x97617)+P28(f889(x97611,x97612),f889(x97613,x97614),f273(x97611,x97613,x97612,x97614,x97615,x97616),f333(f333(f270(x97611,x97612),x97617),f333(f18(f890(x97612,a874),x97611),x97618))) % 191.49/191.41 [9398]P4(f333(f333(f335(f889(x93981,x93982)),f333(f333(f263(x93981,x93982),x93983),x93984)),f333(f333(f290(x93981,x93985,x93982),x93986),x93987)))+~P4(f333(f333(f335(f889(x93981,x93985)),f333(f333(f263(x93981,x93985),x93983),x93988)),x93986))+~P4(f333(f333(f335(f889(x93985,x93982)),f333(f333(f263(x93985,x93982),x93988),x93984)),x93987)) % 191.49/191.41 [9605]~P4(f333(f333(f250(f890(f889(x96053,x96052),a874)),x96055),f333(f333(f270(x96053,x96052),x96058),f333(f18(f890(x96052,a874),x96053),x96057))))+~P4(f333(f333(f250(f890(f889(x96051,x96053),a874)),x96054),f333(f333(f270(x96051,x96053),x96056),f333(f18(f890(x96053,a874),x96051),x96058))))+P4(f333(f333(f250(f890(f889(x96051,x96052),a874)),f333(f333(f290(x96051,x96053,x96052),x96054),x96055)),f333(f333(f270(x96051,x96052),x96056),f333(f18(f890(x96052,a874),x96051),x96057)))) % 191.49/191.41 [9662]~E(x96623,x96625)+P4(f333(f333(f335(f889(f889(x96621,x96622),f889(x96621,x96622))),f333(f333(f263(f889(x96621,x96622),f889(x96621,x96622)),f333(f333(f263(x96621,x96622),x96623),x96624)),f333(f333(f263(x96621,x96622),x96625),x96626))),f326(x96621,x96622,x96627,x96628)))+~P4(f333(f333(f335(f889(x96622,x96622)),f333(f333(f263(x96622,x96622),x96624),x96626)),x96628)) % 191.49/191.41 [9787]E(x97871,x97872)+~P4(f333(f333(f335(f889(f889(x97873,x97875),f889(x97873,x97875))),f333(f333(f263(f889(x97873,x97875),f889(x97873,x97875)),f333(f333(f263(x97873,x97875),x97871),x97876)),f333(f333(f263(x97873,x97875),x97872),x97877))),f326(x97873,x97875,x97874,x97878)))+P4(f333(f333(f335(f889(x97873,x97873)),f333(f333(f263(x97873,x97873),x97871),x97872)),x97874)) % 191.49/191.41 [9803]~P4(f333(f333(f335(f889(f889(x98031,x98035),f889(x98031,x98035))),f333(f333(f263(f889(x98031,x98035),f889(x98031,x98035)),f333(f333(f263(x98031,x98035),x98032),x98036)),f333(f333(f263(x98031,x98035),x98033),x98037))),f326(x98031,x98035,x98034,x98038)))+P4(f333(f333(f335(f889(x98031,x98031)),f333(f333(f263(x98031,x98031),x98032),x98033)),x98034))+P4(f333(f333(f335(f889(x98035,x98035)),f333(f333(f263(x98035,x98035),x98036),x98037)),x98038)) % 191.49/191.41 [9693]~P26(x96937,x96935,x96931,x96938,x96932,x96934)+~P4(f333(f63(x96935),x96936))+E(f333(f333(x96931,f333(x96932,x96933)),f333(x96934,f333(f333(f3(f890(x96935,a874)),x96936),f333(f333(f311(x96935),x96933),f194(f890(x96935,a874)))))),f333(x96934,f333(f333(f311(x96935),x96933),x96936))) % 191.49/191.41 [9177]~P4(f333(f333(f333(x91775,x91778),x91776),x91777))+~P4(f333(f333(f335(x91771),x91778),x91774))+P4(f333(f333(f333(f333(f44(x91771,f890(x91772,f890(x91773,a874))),x91774),x91775),x91776),x91777)) % 191.49/191.41 [9389]P4(f333(f333(f333(x93891,x93892),x93893),x93894))+~P4(f333(f333(f335(x93895),x93892),x93896))+~P4(f333(f333(f333(f333(f43(x93895,f890(x93897,f890(x93898,a874))),x93896),x93891),x93893),x93894)) % 191.49/191.41 [9598]~P24(x95983,x95982,x95984,x95988,x95981)+~P4(f333(f63(x95982),x95987))+E(f333(f333(x95981,f333(f333(f20(x95982,x95983,x95983),f333(f333(f10(x95983,f890(x95983,x95983),x95982),x95984),x95985)),x95986)),x95987),f333(f333(x95984,f333(f333(x95981,x95985),x95987)),f333(f333(x95981,x95986),x95987))) % 191.49/191.41 [9884]~E(f333(f312(x98842,x98844,x98846),x98848),x988410)+~E(f333(f312(x98841,x98843,x98845),x98847),x98849)+E(f333(f312(f889(x98841,x98842),f889(x98843,x98844),f273(x98841,x98843,x98842,x98844,x98845,x98846)),f333(f333(f270(x98841,x98842),x98847),f333(f18(f890(x98842,a874),x98841),x98848))),f333(f333(f270(x98843,x98844),x98849),f333(f18(f890(x98844,a874),x98843),x988410))) % 191.49/191.41 [4861]~P109(x48612)+~P17(x48612,x48611)+P17(x48612,f119(x48612,x48611))+E(x48611,f118(x48612)) % 191.49/191.41 [4862]~P109(x48622)+~P17(x48622,x48621)+P17(x48622,f645(x48621,x48622))+E(x48621,f118(x48622)) % 191.49/191.41 [5093]~P9(x50932)+E(f12(x50932,x50931),f41(x50932,x50931))+E(x50931,f194(f890(x50932,a874)))+~P4(f333(f63(x50932),x50931)) % 191.49/191.41 [5094]~P9(x50942)+E(f13(x50942,x50941),f42(x50942,x50941))+E(x50941,f194(f890(x50942,a874)))+~P4(f333(f63(x50942),x50941)) % 191.49/191.41 [5254]~P109(x52542)+~P17(x52542,x52541)+E(x52541,f118(x52542))+E(f333(f333(f152(x52542),f678(x52541,x52542)),f645(x52541,x52542)),x52541) % 191.49/191.41 [6047]~P6(x60472)+E(x60471,f194(f890(x60472,a874)))+P4(f333(f333(f250(x60472),f13(x60472,x60471)),f12(x60472,x60471)))+~P4(f333(f63(x60472),x60471)) % 191.49/191.41 [6059]~P42(x60592)+~P42(x60591)+E(x60591,x60592)+~E(f333(f312(a1,a880,a109),x60591),f333(f312(a1,a880,a109),x60592)) % 191.49/191.41 [9033]~P120(x90331)+~P4(f333(f333(f335(x90331),x90332),f114(x90331)))+P4(f333(f333(f251(x90331),f333(f333(f81(x90331),f333(f333(f81(x90331),f79(x90331)),x90332)),x90332)),f2(x90331)))+~P4(f333(f333(f251(x90331),x90332),f2(x90331))) % 191.49/191.41 [9275]~P120(x92751)+~P4(f333(f333(f335(x92751),x92752),f114(x92751)))+~P4(f333(f333(f251(x92751),f333(f333(f81(x92751),f333(f333(f81(x92751),f79(x92751)),x92752)),x92752)),f2(x92751)))+P4(f333(f333(f251(x92751),x92752),f2(x92751))) % 191.49/191.41 [4917]~P113(x49172)+~P144(x49172)+E(x49171,f2(a880))+E(f333(f333(f264(x49172),f2(x49172)),x49171),f2(x49172)) % 191.49/191.41 [4921]~P113(x49211)+~P144(x49211)+~E(x49212,f2(a880))+E(f333(f333(f264(x49211),f2(x49211)),x49212),f79(x49211)) % 191.49/191.41 [5080]~P139(x50802)+E(x50801,f79(x50802))+E(x50801,f333(f80(x50802),f79(x50802)))+~E(f333(f333(f82(x50802),x50801),x50801),f79(x50802)) % 191.49/191.41 [5337]~P90(x53372)+E(x53371,f2(x53372))+E(f83(x53372,x53371),f333(f80(x53372),f79(x53372)))+P4(f333(f333(f251(x53372),f2(x53372)),x53371)) % 191.49/191.41 [5568]~P90(x55682)+E(f83(x55682,x55681),f79(x55682))+E(x55681,f2(x55682))+~P4(f333(f333(f251(x55682),f2(x55682)),x55681)) % 191.49/191.41 [5577]E(x55771,x55772)+~E(f333(f108(a880),x55771),f333(f108(a880),x55772))+P4(f333(a200,f333(f108(a1),x55772)))+P4(f333(a200,f333(f108(a1),x55771))) % 191.49/191.41 [5628]~P93(x56281)+~E(x56282,f2(x56281))+E(f333(f333(f81(x56281),x56282),x56282),f2(x56281))+~P4(f333(f333(f335(x56281),x56282),f114(x56281))) % 191.49/191.41 [5666]E(x56661,f2(a1))+~E(f333(f333(f40(a1),x56662),x56661),f2(a1))+P4(f333(f333(f251(a1),x56661),x56662))+P4(f333(f333(f251(a1),x56662),x56661)) % 191.49/191.41 [5697]E(x56971,f2(a1))+~E(f333(f333(f40(a1),x56972),x56971),f2(a1))+P4(f333(f333(f250(a1),x56972),f2(a1)))+P4(f333(f333(f251(a1),x56972),x56971)) % 191.49/191.41 [5730]E(x57301,f2(a1))+~E(f333(f333(f40(a1),x57302),x57301),f2(a1))+P4(f333(f333(f250(a1),f2(a1)),x57302))+P4(f333(f333(f251(a1),x57301),x57302)) % 191.49/191.41 [5766]~P93(x57662)+E(x57661,f2(x57662))+~E(f333(f333(f81(x57662),x57661),x57661),f2(x57662))+~P4(f333(f333(f335(x57662),x57661),f114(x57662))) % 191.49/191.41 [5826]E(f333(f108(a880),x58261),f333(f108(a880),x58262))+~E(f333(f108(a1),x58262),f2(a1))+P4(f333(a200,f333(f108(a1),x58262)))+~P4(f333(a200,f333(f108(a1),x58261))) % 191.49/191.41 [5853]~E(f333(f108(a880),x58532),f333(f108(a880),x58531))+E(f333(f108(a1),x58531),f2(a1))+P4(f333(a200,f333(f108(a1),x58531)))+~P4(f333(a200,f333(f108(a1),x58532))) % 191.49/191.41 [5862]~P109(x58622)+E(x58621,f194(f890(x58622,a874)))+~P4(f333(f63(x58622),x58621))+P4(f333(f333(f335(x58622),f16(x58622,x58621)),x58621)) % 191.49/191.41 [5863]~P109(x58632)+E(x58631,f194(f890(x58632,a874)))+~P4(f333(f63(x58632),x58631))+P4(f333(f333(f335(x58632),f17(x58632,x58631)),x58631)) % 191.49/191.41 [6027]~P120(x60271)+~P94(x60271)+P4(f333(f333(f251(x60271),f2(x60271)),f333(f108(x60271),x60272)))+~P4(f333(f333(f251(a1),a84),x60272)) % 191.49/191.41 [6028]~P120(x60281)+~P94(x60281)+P4(f333(f333(f250(x60281),f2(x60281)),f333(f108(x60281),x60282)))+~P4(f333(f333(f250(a1),a84),x60282)) % 191.49/191.41 [6046]~P120(x60461)+~P94(x60461)+E(f333(f76(x60461),f333(f108(x60461),x60462)),f333(f108(x60461),x60462))+P4(f333(f333(f251(x60461),f333(f108(x60461),x60462)),f2(x60461))) % 191.49/191.41 [6086]E(x60861,x60862)+~E(f333(a109,x60861),f333(a109,x60862))+~P4(f333(f333(f250(a1),f2(a1)),x60862))+~P4(f333(f333(f250(a1),f2(a1)),x60861)) % 191.49/191.41 [6279]~P94(x62792)+~P120(x62792)+~P4(f333(f333(f251(x62792),f2(x62792)),f333(f108(x62792),x62791)))+P4(f333(f333(f251(a1),a84),x62791)) % 191.49/191.41 [6280]~P94(x62802)+~P120(x62802)+~P4(f333(f333(f250(x62802),f2(x62802)),f333(f108(x62802),x62801)))+P4(f333(f333(f250(a1),a84),x62801)) % 191.49/191.41 [6285]~P120(x62851)+~P94(x62851)+P4(f333(f333(f251(x62851),f333(f108(x62851),x62852)),f2(x62851)))+~P4(f333(f333(f251(a1),x62852),a84)) % 191.49/191.41 [6286]~P120(x62861)+~P94(x62861)+P4(f333(f333(f250(x62861),f333(f108(x62861),x62862)),f2(x62861)))+~P4(f333(f333(f250(a1),x62862),a84)) % 191.49/191.41 [6589]~P94(x65892)+~P120(x65892)+~P4(f333(f333(f251(x65892),f333(f108(x65892),x65891)),f2(x65892)))+P4(f333(f333(f251(a1),x65891),a84)) % 191.49/191.41 [6590]~P94(x65902)+~P120(x65902)+~P4(f333(f333(f250(x65902),f333(f108(x65902),x65901)),f2(x65902)))+P4(f333(f333(f250(a1),x65901),a84)) % 191.49/191.41 [6681]~P120(x66811)+~P94(x66811)+E(f333(f76(x66811),f333(f108(x66811),x66812)),f333(f80(x66811),f333(f108(x66811),x66812)))+~P4(f333(f333(f251(x66811),f333(f108(x66811),x66812)),f2(x66811))) % 191.49/191.41 [6699]E(f333(f108(a880),x66991),f333(f108(a880),x66992))+~E(f333(f108(a1),x66992),f2(a1))+~P4(f333(f333(f250(a1),f333(f108(a1),x66991)),f2(a1)))+~P4(f333(a200,f333(f108(a1),x66991))) % 191.49/191.41 [7554]~P109(x75542)+E(x75541,f194(f890(x75542,a874)))+~P4(f333(f63(x75542),x75541))+P4(f333(f333(f250(x75542),f14(x75542,f248(x75542),x75541)),f15(x75542,f249(x75542),x75541))) % 191.49/191.41 [7866]~P42(x78662)+~P10(x78661)+P4(f333(f333(f335(a1),x78661),x78662))+~P4(f333(f333(f335(a880),f333(a109,x78661)),f333(f312(a1,a880,a109),x78662))) % 191.49/191.41 [8143]~P62(x81432)+P4(f333(x81431,f197(x81432)))+~P4(f333(f59(f884(x81432)),x81431))+P4(f333(f59(x81432),f333(f333(f10(f884(x81432),a874,x81432),x81431),f242(x81432)))) % 191.49/191.41 [8606]~P62(x86061)+~P4(f333(x86062,f197(x86061)))+P4(f333(f60(f884(x86061)),x86062))+~P4(f333(f60(x86061),f333(f333(f10(f884(x86061),a874,x86061),x86062),f242(x86061)))) % 191.49/191.41 [5859]~P140(x58592)+E(x58591,f2(a1))+E(f333(f80(x58592),f333(f107(x58592),f333(f80(a1),x58591))),f333(f107(x58592),x58591))+~P4(f333(f333(f251(a1),x58591),f2(a1))) % 191.49/191.41 [6267]~P77(x62672)+E(x62671,f194(f890(x62672,a874)))+E(f17(x62672,f333(f312(x62672,x62672,f80(x62672)),x62671)),f333(f80(x62672),f16(x62672,x62671)))+~P4(f333(f63(x62672),x62671)) % 191.49/191.41 [6268]~P77(x62682)+E(x62681,f194(f890(x62682,a874)))+E(f16(x62682,f333(f312(x62682,x62682,f80(x62682)),x62681)),f333(f80(x62682),f17(x62682,x62681)))+~P4(f333(f63(x62682),x62681)) % 191.49/191.41 [6388]E(x63881,f2(a1))+E(f333(a52,f51(f333(f80(a1),x63881),f333(f80(a1),x63882))),f47(x63881,x63882))+P4(f333(f333(f250(a1),f2(a1)),x63882))+~P4(f333(f333(f250(a1),f2(a1)),x63881)) % 191.49/191.41 [8360]~P32(a5000)+~P4(f333(a25,x83601))+P27(a875,x83602,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),x83601),f201(x83601))),f194(f890(f879(a875),a874))))+P4(f333(f333(f335(a877),f556(x83601,x83602)),f184(a877,a876,a28))) % 191.49/191.41 [8644]~P42(x86442)+~P42(x86441)+P4(f333(f333(f251(f890(a880,a874)),f333(f312(a1,a880,a109),x86441)),f333(f312(a1,a880,a109),x86442)))+~P4(f333(f333(f251(f890(a1,a874)),x86441),x86442)) % 191.49/191.41 [8859]~E(f695(x88592,x88591),f696(x88592,x88591))+~P4(f333(f138(x88591),f697(x88592,x88591)))+~P4(f333(f138(f881(x88591)),x88592))+P4(f333(f138(x88591),f333(f143(f881(x88591),f881(x88591),f127(x88591),f118(x88591)),x88592))) % 191.49/191.41 [8957]~P42(x89572)+~P42(x89571)+~P4(f333(f333(f251(f890(a880,a874)),f333(f312(a1,a880,a109),x89571)),f333(f312(a1,a880,a109),x89572)))+P4(f333(f333(f251(f890(a1,a874)),x89571),x89572)) % 191.49/191.41 [8958]~P42(x89582)+~P42(x89581)+~P4(f333(f333(f250(f890(a880,a874)),f333(f312(a1,a880,a109),x89581)),f333(f312(a1,a880,a109),x89582)))+P4(f333(f333(f250(f890(a1,a874)),x89581),x89582)) % 191.49/191.41 [8964]~E(f695(x89642,x89641),f696(x89642,x89641))+~P4(f333(f138(f881(x89641)),x89642))+P4(f333(f138(x89641),f333(f143(f881(x89641),f881(x89641),f127(x89641),f118(x89641)),x89642)))+P4(f333(f333(f335(f881(x89641)),f697(x89642,x89641)),f333(f173(f881(x89641)),x89642))) % 191.49/191.41 [9005]~P4(f333(f138(x90051),f697(x90052,x90051)))+~P4(f333(f138(f881(x90051)),x90052))+P4(f333(f138(x90051),f333(f143(f881(x90051),f881(x90051),f127(x90051),f118(x90051)),x90052)))+P4(f333(f333(f335(f881(x90051)),f696(x90052,x90051)),f333(f173(f881(x90051)),x90052))) % 191.49/191.41 [9006]~P4(f333(f138(x90061),f697(x90062,x90061)))+~P4(f333(f138(f881(x90061)),x90062))+P4(f333(f138(x90061),f333(f143(f881(x90061),f881(x90061),f127(x90061),f118(x90061)),x90062)))+P4(f333(f333(f335(f881(x90061)),f695(x90062,x90061)),f333(f173(f881(x90061)),x90062))) % 191.49/191.41 [9067]~P4(f333(f138(f881(x90671)),x90672))+P4(f333(f138(x90671),f333(f143(f881(x90671),f881(x90671),f127(x90671),f118(x90671)),x90672)))+P4(f333(f333(f335(f881(x90671)),f696(x90672,x90671)),f333(f173(f881(x90671)),x90672)))+P4(f333(f333(f335(f881(x90671)),f697(x90672,x90671)),f333(f173(f881(x90671)),x90672))) % 191.49/191.41 [9068]~P4(f333(f138(f881(x90681)),x90682))+P4(f333(f138(x90681),f333(f143(f881(x90681),f881(x90681),f127(x90681),f118(x90681)),x90682)))+P4(f333(f333(f335(f881(x90681)),f695(x90682,x90681)),f333(f173(f881(x90681)),x90682)))+P4(f333(f333(f335(f881(x90681)),f697(x90682,x90681)),f333(f173(f881(x90681)),x90682))) % 191.49/191.41 [9081]~E(f333(f333(f106(f890(x90811,a874)),f333(f173(x90811),f696(x90812,x90811))),f333(f173(x90811),f695(x90812,x90811))),f194(f890(x90811,a874)))+~P4(f333(f138(x90811),f697(x90812,x90811)))+~P4(f333(f138(f881(x90811)),x90812))+P4(f333(f138(x90811),f333(f143(f881(x90811),f881(x90811),f127(x90811),f118(x90811)),x90812))) % 191.49/191.41 [9154]~E(f333(f333(f106(f890(x91541,a874)),f333(f173(x91541),f696(x91542,x91541))),f333(f173(x91541),f695(x91542,x91541))),f194(f890(x91541,a874)))+~P4(f333(f138(f881(x91541)),x91542))+P4(f333(f138(x91541),f333(f143(f881(x91541),f881(x91541),f127(x91541),f118(x91541)),x91542)))+P4(f333(f333(f335(f881(x91541)),f697(x91542,x91541)),f333(f173(f881(x91541)),x91542))) % 191.49/191.41 [9422]E(x94221,f2(a1))+E(x94222,f2(a1))+E(f333(f333(f89(a1,f889(a1,a1)),f333(f333(a227,x94222),x94221)),f333(f333(f20(a1,a1,f889(a1,a1)),f333(f333(f10(a1,f890(a1,f889(a1,a1)),a1),f263(a1,a1)),f333(f40(a1),x94222))),f333(f40(a1),x94221))),f225(x94222,x94221))+P4(f333(f333(f251(a1),x94221),f2(a1))) % 191.49/191.41 [9491]~P32(a5000)+~P4(f333(a25,x94912))+P27(a875,x94911,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),x94912),f201(x94912))),f194(f890(f879(a875),a874))))+~P27(a875,x94911,f333(f333(f311(f879(a875)),f333(f333(f333(f93(a875),a330),f333(a26,f556(x94912,x94911))),f201(f333(a26,f556(x94912,x94911))))),f194(f890(f879(a875),a874)))) % 191.49/191.41 [8325]~P94(x83252)+~P120(x83252)+~P4(f333(f333(f251(x83252),f333(f108(x83252),x83251)),f79(x83252)))+P4(f333(f333(f251(a1),x83251),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))) % 191.49/191.41 [8326]~P94(x83262)+~P120(x83262)+~P4(f333(f333(f250(x83262),f333(f108(x83262),x83261)),f79(x83262)))+P4(f333(f333(f250(a1),x83261),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))) % 191.49/191.41 [8609]~P120(x86091)+~P94(x86091)+P4(f333(f333(f251(x86091),f333(f108(x86091),x86092)),f79(x86091)))+~P4(f333(f333(f251(a1),x86092),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))) % 191.49/191.41 [8610]~P120(x86101)+~P94(x86101)+P4(f333(f333(f250(x86101),f333(f108(x86101),x86102)),f79(x86101)))+~P4(f333(f333(f250(a1),x86102),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))) % 191.49/191.41 [8793]~P94(x87932)+~P120(x87932)+~P4(f333(f333(f251(x87932),f79(x87932)),f333(f108(x87932),x87931)))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),x87931)) % 191.49/191.41 [8794]~P94(x87942)+~P120(x87942)+~P4(f333(f333(f250(x87942),f79(x87942)),f333(f108(x87942),x87941)))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),x87941)) % 191.49/191.41 [9144]~P120(x91441)+~P94(x91441)+P4(f333(f333(f251(x91441),f79(x91441)),f333(f108(x91441),x91442)))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),x91442)) % 191.49/191.41 [9145]~P120(x91451)+~P94(x91451)+P4(f333(f333(f250(x91451),f79(x91451)),f333(f108(x91451),x91452)))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84)),x91452)) % 191.49/191.41 [9273]~P93(x92731)+~P94(x92731)+~P33(x92731,f333(f108(x92731),x92732))+P33(x92731,f333(f108(x92731),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x92732)),x92732)),a102))) % 191.49/191.41 [9489]~P93(x94891)+~P94(x94891)+P33(x94891,f333(f108(x94891),x94892))+~P33(x94891,f333(f108(x94891),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),x94892)),x94892)),a102))) % 191.49/191.41 [10000]~P139(x100002)+E(x100001,f79(x100002))+E(x100001,f333(f80(x100002),f79(x100002)))+~E(f333(f333(f264(x100002),x100001),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f79(x100002)) % 191.49/191.41 [10078]~P65(x100781)+~P94(x100781)+~P4(f333(f333(f251(x100781),f2(x100781)),x100782))+P4(f333(f333(f251(x100781),f2(x100781)),f333(f333(f291(x100781),x100782),f333(f108(x100781),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.41 [10113]~P65(x101131)+~P94(x101131)+P4(f333(f333(f251(x101131),f2(x101131)),x101132))+~P4(f333(f333(f251(x101131),f2(x101131)),f333(f333(f291(x101131),x101132),f333(f108(x101131),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.41 [10189]~P140(x101892)+E(x101891,f2(a1))+P4(f333(f333(f251(a1),x101891),f2(a1)))+E(f333(f333(f272(a1,a1,x101892),f333(f333(f9(a1,f890(a1,f890(x101892,x101892)),f890(a1,x101892)),f333(f333(f10(f890(f890(x101892,x101892),x101892),f890(f890(a1,f890(x101892,x101892)),f890(a1,x101892)),a1),f10(f890(x101892,x101892),x101892,a1)),f333(f333(f10(x101892,f890(f890(x101892,x101892),x101892),a1),f89(x101892,x101892)),f107(x101892)))),f333(f333(f9(a1,f890(x101892,x101892),f890(x101892,x101892)),f333(f333(f10(f890(x101892,f890(x101892,x101892)),f890(f890(x101892,x101892),f890(x101892,x101892)),a1),f20(x101892,x101892,x101892)),f333(f333(f9(a1,f890(x101892,x101892),f890(x101892,f890(x101892,x101892))),f333(f333(f10(f890(x101892,f890(x101892,x101892)),f890(f890(x101892,x101892),f890(x101892,f890(x101892,x101892))),a1),f10(x101892,f890(x101892,x101892),x101892)),f333(f333(f10(a874,f890(x101892,f890(x101892,x101892)),a1),f101(x101892)),f333(f333(f9(a1,a1,a874),a330),f2(a1))))),f333(f333(f20(x101892,x101892,x101892),f81(x101892)),f7(x101892))))),f333(f333(f9(x101892,x101892,x101892),f333(f333(f10(x101892,f890(x101892,x101892),x101892),f81(x101892)),f333(f333(f20(x101892,x101892,x101892),f81(x101892)),f7(x101892)))),f79(x101892))))),f47(x101891,f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f107(x101892),x101891)) % 191.49/191.41 [5249]~P62(x52493)+~P38(x52493,x52492,f57(x52493))+E(x52491,f741(x52492,x52493))+~P4(f333(x52492,x52491)) % 191.49/191.41 [5407]~P62(x54071)+P38(x54071,x54072,f57(x54071))+~E(f742(x54072,x54071,x54073),x54073)+~P4(f333(x54072,x54073)) % 191.49/191.41 [4888]~P93(x48883)+~P94(x48883)+E(x48881,x48882)+~E(f333(f108(x48883),x48881),f333(f108(x48883),x48882)) % 191.49/191.41 [6026]~P62(x60261)+P38(x60261,x60262,f57(x60261))+~P4(f333(x60262,x60263))+P4(f333(x60262,f742(x60262,x60261,x60263))) % 191.49/191.41 [6036]~P4(f333(x60361,x60362))+~P4(f333(x60361,x60363))+~P4(f333(f333(f250(a880),x60363),f373(x60362,x60361)))+P4(f333(x60361,f2(a880))) % 191.49/191.41 [6451]P147(x64512,x64511,x64513)+E(x64511,f2(a1))+P4(f333(f333(f250(a1),f2(a1)),f814(x64513,x64511,x64512)))+P4(f333(f333(f251(a1),x64511),f2(a1))) % 191.49/191.41 [6452]P146(x64522,x64521,x64523)+E(x64521,f2(a1))+P4(f333(f333(f250(a1),f2(a1)),f821(x64523,x64521,x64522)))+P4(f333(f333(f251(a1),x64521),f2(a1))) % 191.49/191.41 [6568]P146(x65681,x65682,x65683)+~P4(f333(x65681,x65683))+P4(f333(f333(f250(a1),f2(a1)),f821(x65683,x65682,x65681)))+P4(f333(f333(f251(a1),x65682),f2(a1))) % 191.49/191.41 [6595]P147(x65951,x65952,x65953)+P4(f333(f333(f250(a1),f2(a1)),f814(x65953,x65952,x65951)))+~P4(f333(x65951,f2(a1)))+P4(f333(f333(f251(a1),x65952),f2(a1))) % 191.49/191.41 [6623]P147(x66232,x66231,x66233)+E(x66231,f2(a1))+~P4(f333(x66232,f815(x66233,x66231,x66232)))+P4(f333(f333(f251(a1),x66231),f2(a1))) % 191.49/191.41 [6624]P146(x66242,x66241,x66243)+E(x66241,f2(a1))+~P4(f333(x66242,f821(x66243,x66241,x66242)))+P4(f333(f333(f251(a1),x66241),f2(a1))) % 191.49/191.41 [6724]~P9(x67241)+~P109(x67241)+~P4(f333(f333(f251(x67241),x67242),f41(x67241,x67243)))+P4(f333(f333(f251(x67241),x67242),f845(x67243,x67242,x67241))) % 191.49/191.41 [6733]P146(x67331,x67332,x67333)+~P4(f333(x67331,x67333))+~P4(f333(x67331,f821(x67333,x67332,x67331)))+P4(f333(f333(f251(a1),x67332),f2(a1))) % 191.49/191.41 [6759]P147(x67591,x67592,x67593)+~P4(f333(x67591,f815(x67593,x67592,x67591)))+~P4(f333(x67591,f2(a1)))+P4(f333(f333(f251(a1),x67592),f2(a1))) % 191.49/191.41 [7008]P147(x70082,x70081,x70083)+E(x70081,f2(a1))+P4(f333(f333(f250(a1),f2(a1)),f814(x70083,x70081,x70082)))+P4(f333(f333(f251(a1),x70081),f813(x70083,x70081,x70082))) % 191.49/191.41 [7009]P146(x70092,x70091,x70093)+E(x70091,f2(a1))+P4(f333(f333(f250(a1),f2(a1)),f821(x70093,x70091,x70092)))+P4(f333(f333(f251(a1),x70091),f820(x70093,x70091,x70092))) % 191.49/191.41 [7125]P146(x71251,x71252,x71253)+~P4(f333(x71251,x71253))+P4(f333(f333(f250(a1),f2(a1)),f821(x71253,x71252,x71251)))+P4(f333(f333(f251(a1),x71252),f820(x71253,x71252,x71251))) % 191.49/191.41 [7144]P147(x71441,x71442,x71443)+P4(f333(f333(f250(a1),f2(a1)),f814(x71443,x71442,x71441)))+P4(f333(f333(f251(a1),x71442),f813(x71443,x71442,x71441)))+~P4(f333(x71441,f2(a1))) % 191.49/191.41 [7177]P147(x71772,x71771,x71773)+E(x71771,f2(a1))+~P4(f333(x71772,f815(x71773,x71771,x71772)))+P4(f333(f333(f251(a1),x71771),f813(x71773,x71771,x71772))) % 191.49/191.41 [7178]P146(x71782,x71781,x71783)+E(x71781,f2(a1))+~P4(f333(x71782,f821(x71783,x71781,x71782)))+P4(f333(f333(f251(a1),x71781),f820(x71783,x71781,x71782))) % 191.49/191.41 [7219]P147(x72192,x72191,x72193)+E(x72191,f2(a1))+P4(f333(f333(f250(a1),f2(a1)),f814(x72193,x72191,x72192)))+~P4(f333(x72192,f819(x72193,x72191,x72192))) % 191.49/191.41 [7220]P146(x72202,x72201,x72203)+E(x72201,f2(a1))+P4(f333(f333(f250(a1),f2(a1)),f821(x72203,x72201,x72202)))+~P4(f333(x72202,f820(x72203,x72201,x72202))) % 191.49/191.41 [7306]P146(x73061,x73062,x73063)+~P4(f333(x73061,x73063))+~P4(f333(x73061,f821(x73063,x73062,x73061)))+P4(f333(f333(f251(a1),x73062),f820(x73063,x73062,x73061))) % 191.49/191.41 [7315]P147(x73151,x73152,x73153)+~P4(f333(x73151,f815(x73153,x73152,x73151)))+P4(f333(f333(f251(a1),x73152),f813(x73153,x73152,x73151)))+~P4(f333(x73151,f2(a1))) % 191.49/191.41 [7319]P146(x73191,x73192,x73193)+~P4(f333(x73191,x73193))+P4(f333(f333(f250(a1),f2(a1)),f821(x73193,x73192,x73191)))+~P4(f333(x73191,f820(x73193,x73192,x73191))) % 191.49/191.41 [7337]P147(x73371,x73372,x73373)+P4(f333(f333(f250(a1),f2(a1)),f814(x73373,x73372,x73371)))+~P4(f333(x73371,f819(x73373,x73372,x73371)))+~P4(f333(x73371,f2(a1))) % 191.49/191.41 [7360]P147(x73602,x73601,x73603)+E(x73601,f2(a1))+~P4(f333(x73602,f815(x73603,x73601,x73602)))+~P4(f333(x73602,f819(x73603,x73601,x73602))) % 191.49/191.41 [7361]P146(x73612,x73611,x73613)+E(x73611,f2(a1))+~P4(f333(x73612,f821(x73613,x73611,x73612)))+~P4(f333(x73612,f820(x73613,x73611,x73612))) % 191.49/191.41 [7453]P146(x74531,x74532,x74533)+~P4(f333(x74531,x74533))+~P4(f333(x74531,f821(x74533,x74532,x74531)))+~P4(f333(x74531,f820(x74533,x74532,x74531))) % 191.49/191.41 [7470]P147(x74701,x74702,x74703)+~P4(f333(x74701,f815(x74703,x74702,x74701)))+~P4(f333(x74701,f819(x74703,x74702,x74701)))+~P4(f333(x74701,f2(a1))) % 191.49/191.41 [7515]P147(x75152,x75151,x75153)+E(x75151,f2(a1))+P4(f333(f333(f250(a1),f2(a1)),f814(x75153,x75151,x75152)))+P4(f333(f333(f250(a1),f813(x75153,x75151,x75152)),f2(a1))) % 191.49/191.41 [7516]P146(x75162,x75161,x75163)+E(x75161,f2(a1))+P4(f333(f333(f250(a1),f2(a1)),f821(x75163,x75161,x75162)))+P4(f333(f333(f250(a1),f820(x75163,x75161,x75162)),f2(a1))) % 191.49/191.41 [7517]~P140(x75171)+~P4(f333(f333(f335(x75171),x75173),f114(x75171)))+~P4(f333(f333(f335(x75171),x75172),f114(x75171)))+P4(f333(f333(f335(x75171),f333(f333(f3(x75171),x75172),x75173)),f114(x75171))) % 191.49/191.41 [7518]~P140(x75181)+~P4(f333(f333(f335(x75181),x75183),f114(x75181)))+~P4(f333(f333(f335(x75181),x75182),f114(x75181)))+P4(f333(f333(f335(x75181),f333(f333(f81(x75181),x75182),x75183)),f114(x75181))) % 191.49/191.41 [7519]~P143(x75191)+~P4(f333(f333(f335(x75191),x75193),f192(x75191)))+~P4(f333(f333(f335(x75191),x75192),f192(x75191)))+P4(f333(f333(f335(x75191),f333(f333(f81(x75191),x75192),x75193)),f192(x75191))) % 191.49/191.41 [7520]~P140(x75201)+~P4(f333(f333(f335(x75201),x75203),f114(x75201)))+~P4(f333(f333(f335(x75201),x75202),f114(x75201)))+P4(f333(f333(f335(x75201),f333(f333(f82(x75201),x75202),x75203)),f114(x75201))) % 191.49/191.41 [7521]~P143(x75211)+~P4(f333(f333(f335(x75211),x75213),f192(x75211)))+~P4(f333(f333(f335(x75211),x75212),f192(x75211)))+P4(f333(f333(f335(x75211),f333(f333(f82(x75211),x75212),x75213)),f192(x75211))) % 191.49/191.41 [7522]~P89(x75221)+~P4(f333(f333(f251(x75221),x75223),f2(x75221)))+~P4(f333(f333(f251(x75221),x75222),f2(x75221)))+P4(f333(f333(f251(x75221),f333(f333(f81(x75221),x75222),x75223)),f2(x75221))) % 191.49/191.41 [7523]~P89(x75231)+~P4(f333(f333(f250(x75231),x75232),f2(x75231)))+~P4(f333(f333(f251(x75231),x75233),f2(x75231)))+P4(f333(f333(f251(x75231),f333(f333(f81(x75231),x75232),x75233)),f2(x75231))) % 191.49/191.41 [7524]~P89(x75241)+~P4(f333(f333(f250(x75241),x75243),f2(x75241)))+~P4(f333(f333(f251(x75241),x75242),f2(x75241)))+P4(f333(f333(f251(x75241),f333(f333(f81(x75241),x75242),x75243)),f2(x75241))) % 191.49/191.41 [7525]~P89(x75251)+~P4(f333(f333(f250(x75251),x75253),f2(x75251)))+~P4(f333(f333(f250(x75251),x75252),f2(x75251)))+P4(f333(f333(f250(x75251),f333(f333(f81(x75251),x75252),x75253)),f2(x75251))) % 191.49/191.41 [7550]P147(x75503,x75501,x75502)+E(x75501,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x75501),f815(x75502,x75501,x75503))),f814(x75502,x75501,x75503)),x75502)+P4(f333(f333(f251(a1),x75501),f2(a1))) % 191.49/191.41 [7551]P146(x75513,x75511,x75512)+E(x75511,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x75511),f822(x75512,x75511,x75513))),f821(x75512,x75511,x75513)),x75512)+P4(f333(f333(f251(a1),x75511),f2(a1))) % 191.49/191.41 [7631]P146(x76311,x76312,x76313)+~P4(f333(x76311,x76313))+P4(f333(f333(f250(a1),f2(a1)),f821(x76313,x76312,x76311)))+P4(f333(f333(f250(a1),f820(x76313,x76312,x76311)),f2(a1))) % 191.49/191.41 [7660]P147(x76601,x76602,x76603)+P4(f333(f333(f250(a1),f2(a1)),f814(x76603,x76602,x76601)))+~P4(f333(x76601,f2(a1)))+P4(f333(f333(f250(a1),f813(x76603,x76602,x76601)),f2(a1))) % 191.49/191.41 [7669]P146(x76693,x76691,x76692)+~P4(f333(x76693,x76692))+E(f333(f333(f81(a1),f333(f333(f82(a1),x76691),f822(x76692,x76691,x76693))),f821(x76692,x76691,x76693)),x76692)+P4(f333(f333(f251(a1),x76691),f2(a1))) % 191.49/191.41 [7675]P147(x76752,x76751,x76753)+E(x76751,f2(a1))+~P4(f333(x76752,f815(x76753,x76751,x76752)))+P4(f333(f333(f250(a1),f813(x76753,x76751,x76752)),f2(a1))) % 191.49/191.41 [7676]P146(x76762,x76761,x76763)+E(x76761,f2(a1))+~P4(f333(x76762,f821(x76763,x76761,x76762)))+P4(f333(f333(f250(a1),f820(x76763,x76761,x76762)),f2(a1))) % 191.49/191.41 [7680]P147(x76803,x76801,x76802)+E(f333(f333(f81(a1),f333(f333(f82(a1),x76801),f815(x76802,x76801,x76803))),f814(x76802,x76801,x76803)),x76802)+~P4(f333(x76803,f2(a1)))+P4(f333(f333(f251(a1),x76801),f2(a1))) % 191.49/191.41 [7735]P146(x77351,x77352,x77353)+~P4(f333(x77351,x77353))+~P4(f333(x77351,f821(x77353,x77352,x77351)))+P4(f333(f333(f250(a1),f820(x77353,x77352,x77351)),f2(a1))) % 191.49/191.41 [7740]P147(x77401,x77402,x77403)+~P4(f333(x77401,f815(x77403,x77402,x77401)))+~P4(f333(x77401,f2(a1)))+P4(f333(f333(f250(a1),f813(x77403,x77402,x77401)),f2(a1))) % 191.49/191.41 [7813]~P65(x78131)+~P4(f333(f333(f251(x78131),f333(f333(f291(x78131),x78133),x78132)),f2(x78131)))+P4(f333(f333(f251(x78131),x78132),f2(x78131)))+P4(f333(f333(f251(x78131),x78133),f2(x78131))) % 191.49/191.41 [7814]~P124(x78141)+~P4(f333(f333(f250(x78141),f333(f333(f82(x78141),x78143),x78142)),f2(x78141)))+P4(f333(f333(f250(x78141),x78142),f2(x78141)))+P4(f333(f333(f250(x78141),x78143),f2(x78141))) % 191.49/191.41 [7815]~P65(x78151)+~P4(f333(f333(f250(x78151),f333(f333(f291(x78151),x78153),x78152)),f2(x78151)))+P4(f333(f333(f250(x78151),x78152),f2(x78151)))+P4(f333(f333(f250(x78151),x78153),f2(x78151))) % 191.49/191.41 [7919]P147(x79193,x79191,x79192)+E(x79191,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x79191),f815(x79192,x79191,x79193))),f814(x79192,x79191,x79193)),x79192)+P4(f333(f333(f251(a1),x79191),f813(x79192,x79191,x79193))) % 191.49/191.41 [7920]P146(x79203,x79201,x79202)+E(x79201,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x79201),f822(x79202,x79201,x79203))),f821(x79202,x79201,x79203)),x79202)+P4(f333(f333(f251(a1),x79201),f820(x79202,x79201,x79203))) % 191.49/191.41 [7933]P147(x79333,x79331,x79332)+E(x79331,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x79331),f819(x79332,x79331,x79333))),f813(x79332,x79331,x79333)),x79332)+P4(f333(f333(f250(a1),f2(a1)),f814(x79332,x79331,x79333))) % 191.49/191.41 [7934]P146(x79343,x79341,x79342)+E(x79341,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x79341),f823(x79342,x79341,x79343))),f820(x79342,x79341,x79343)),x79342)+P4(f333(f333(f250(a1),f2(a1)),f821(x79342,x79341,x79343))) % 191.49/191.41 [7976]P146(x79763,x79761,x79762)+~P4(f333(x79763,x79762))+E(f333(f333(f81(a1),f333(f333(f82(a1),x79761),f822(x79762,x79761,x79763))),f821(x79762,x79761,x79763)),x79762)+P4(f333(f333(f251(a1),x79761),f820(x79762,x79761,x79763))) % 191.49/191.41 [7988]P147(x79883,x79881,x79882)+E(f333(f333(f81(a1),f333(f333(f82(a1),x79881),f815(x79882,x79881,x79883))),f814(x79882,x79881,x79883)),x79882)+P4(f333(f333(f251(a1),x79881),f813(x79882,x79881,x79883)))+~P4(f333(x79883,f2(a1))) % 191.49/191.41 [7994]P146(x79943,x79941,x79942)+~P4(f333(x79943,x79942))+E(f333(f333(f81(a1),f333(f333(f82(a1),x79941),f823(x79942,x79941,x79943))),f820(x79942,x79941,x79943)),x79942)+P4(f333(f333(f250(a1),f2(a1)),f821(x79942,x79941,x79943))) % 191.49/191.41 [8002]P147(x80023,x80021,x80022)+E(f333(f333(f81(a1),f333(f333(f82(a1),x80021),f819(x80022,x80021,x80023))),f813(x80022,x80021,x80023)),x80022)+P4(f333(f333(f250(a1),f2(a1)),f814(x80022,x80021,x80023)))+~P4(f333(x80023,f2(a1))) % 191.49/191.41 [8013]P147(x80133,x80131,x80132)+E(x80131,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x80131),f815(x80132,x80131,x80133))),f814(x80132,x80131,x80133)),x80132)+~P4(f333(x80133,f819(x80132,x80131,x80133))) % 191.49/191.41 [8014]P146(x80143,x80141,x80142)+E(x80141,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x80141),f822(x80142,x80141,x80143))),f821(x80142,x80141,x80143)),x80142)+~P4(f333(x80143,f820(x80142,x80141,x80143))) % 191.49/191.41 [8015]P147(x80153,x80151,x80152)+E(x80151,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x80151),f819(x80152,x80151,x80153))),f813(x80152,x80151,x80153)),x80152)+~P4(f333(x80153,f815(x80152,x80151,x80153))) % 191.49/191.41 [8016]P146(x80163,x80161,x80162)+E(x80161,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x80161),f823(x80162,x80161,x80163))),f820(x80162,x80161,x80163)),x80162)+~P4(f333(x80163,f821(x80162,x80161,x80163))) % 191.49/191.41 [8078]P146(x80783,x80781,x80782)+~P4(f333(x80783,x80782))+E(f333(f333(f81(a1),f333(f333(f82(a1),x80781),f822(x80782,x80781,x80783))),f821(x80782,x80781,x80783)),x80782)+~P4(f333(x80783,f820(x80782,x80781,x80783))) % 191.49/191.41 [8079]P146(x80793,x80791,x80792)+~P4(f333(x80793,x80792))+E(f333(f333(f81(a1),f333(f333(f82(a1),x80791),f823(x80792,x80791,x80793))),f820(x80792,x80791,x80793)),x80792)+~P4(f333(x80793,f821(x80792,x80791,x80793))) % 191.49/191.41 [8090]P147(x80903,x80901,x80902)+E(f333(f333(f81(a1),f333(f333(f82(a1),x80901),f815(x80902,x80901,x80903))),f814(x80902,x80901,x80903)),x80902)+~P4(f333(x80903,f819(x80902,x80901,x80903)))+~P4(f333(x80903,f2(a1))) % 191.49/191.41 [8091]P147(x80913,x80911,x80912)+E(f333(f333(f81(a1),f333(f333(f82(a1),x80911),f819(x80912,x80911,x80913))),f813(x80912,x80911,x80913)),x80912)+~P4(f333(x80913,f815(x80912,x80911,x80913)))+~P4(f333(x80913,f2(a1))) % 191.49/191.41 [8198]P147(x81983,x81981,x81982)+E(x81981,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x81981),f815(x81982,x81981,x81983))),f814(x81982,x81981,x81983)),x81982)+P4(f333(f333(f250(a1),f813(x81982,x81981,x81983)),f2(a1))) % 191.49/191.41 [8199]P146(x81993,x81991,x81992)+E(x81991,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x81991),f822(x81992,x81991,x81993))),f821(x81992,x81991,x81993)),x81992)+P4(f333(f333(f250(a1),f820(x81992,x81991,x81993)),f2(a1))) % 191.49/191.41 [8236]P146(x82363,x82361,x82362)+~P4(f333(x82363,x82362))+E(f333(f333(f81(a1),f333(f333(f82(a1),x82361),f822(x82362,x82361,x82363))),f821(x82362,x82361,x82363)),x82362)+P4(f333(f333(f250(a1),f820(x82362,x82361,x82363)),f2(a1))) % 191.49/191.41 [8241]P147(x82413,x82411,x82412)+E(f333(f333(f81(a1),f333(f333(f82(a1),x82411),f815(x82412,x82411,x82413))),f814(x82412,x82411,x82413)),x82412)+~P4(f333(x82413,f2(a1)))+P4(f333(f333(f250(a1),f813(x82412,x82411,x82413)),f2(a1))) % 191.49/191.41 [8368]P147(x83683,x83681,x83682)+E(x83681,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x83681),f819(x83682,x83681,x83683))),f813(x83682,x83681,x83683)),x83682)+E(f333(f333(f81(a1),f333(f333(f82(a1),x83681),f815(x83682,x83681,x83683))),f814(x83682,x83681,x83683)),x83682) % 191.49/191.41 [8369]P146(x83693,x83691,x83692)+E(x83691,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x83691),f823(x83692,x83691,x83693))),f820(x83692,x83691,x83693)),x83692)+E(f333(f333(f81(a1),f333(f333(f82(a1),x83691),f822(x83692,x83691,x83693))),f821(x83692,x83691,x83693)),x83692) % 191.49/191.41 [8393]P146(x83933,x83931,x83932)+~P4(f333(x83933,x83932))+E(f333(f333(f81(a1),f333(f333(f82(a1),x83931),f823(x83932,x83931,x83933))),f820(x83932,x83931,x83933)),x83932)+E(f333(f333(f81(a1),f333(f333(f82(a1),x83931),f822(x83932,x83931,x83933))),f821(x83932,x83931,x83933)),x83932) % 191.49/191.41 [8400]P147(x84003,x84001,x84002)+E(f333(f333(f81(a1),f333(f333(f82(a1),x84001),f819(x84002,x84001,x84003))),f813(x84002,x84001,x84003)),x84002)+E(f333(f333(f81(a1),f333(f333(f82(a1),x84001),f815(x84002,x84001,x84003))),f814(x84002,x84001,x84003)),x84002)+~P4(f333(x84003,f2(a1))) % 191.49/191.41 [9042]~P124(x90421)+~E(x90423,f2(x90421))+~E(x90422,f2(x90421))+P4(f333(f333(f250(x90421),f333(f333(f81(x90421),f333(f333(f82(x90421),x90422),x90422)),f333(f333(f82(x90421),x90423),x90423))),f2(x90421))) % 191.49/191.41 [10202]~P120(x102021)+~E(x102023,f2(x102021))+~E(x102022,f2(x102021))+P4(f333(f333(f250(x102021),f333(f333(f81(x102021),f333(f333(f264(x102021),x102022),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x102021),x102023),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))),f2(x102021))) % 191.49/191.41 [4838]~E(x48383,x48381)+~P118(x48382)+E(x48381,f2(x48382))+E(f333(f333(f291(x48382),x48383),x48381),f79(x48382)) % 191.49/191.41 [4889]~P7(x48891)+~E(x48893,f194(x48891))+~E(x48892,f194(x48891))+E(f333(f333(f115(x48891),x48892),x48893),f194(x48891)) % 191.49/191.41 [4890]~P100(x48901)+~E(x48903,f258(x48901))+~E(x48902,f258(x48901))+E(f333(f333(f106(x48901),x48902),x48903),f258(x48901)) % 191.49/191.41 [4976]~P118(x49763)+E(x49761,x49762)+E(x49762,f2(x49763))+~E(f333(f333(f291(x49763),x49761),x49762),f79(x49763)) % 191.49/191.41 [4995]~P127(x49952)+E(x49951,f2(x49952))+E(x49953,f2(x49952))+~E(f333(f333(f82(x49952),x49953),x49951),f2(x49952)) % 191.49/191.41 [4996]~P141(x49962)+E(x49961,f2(x49962))+E(x49963,f2(x49962))+~E(f333(f333(f82(x49962),x49963),x49961),f2(x49962)) % 191.49/191.41 [5374]~P117(x53743)+E(x53741,x53742)+E(x53741,f333(f80(x53743),x53742))+~E(f333(f333(f82(x53743),x53741),x53741),f333(f333(f82(x53743),x53742),x53742)) % 191.49/191.41 [5414]~P79(x54141)+E(f333(f80(x54141),x54142),x54143)+~E(f333(f333(f115(x54141),x54142),x54143),f258(x54141))+~E(f333(f333(f106(x54141),x54142),x54143),f194(x54141)) % 191.49/191.41 [5493]~P120(x54933)+E(x54931,x54932)+P4(f333(f333(f251(x54933),x54932),x54931))+P4(f333(f333(f251(x54933),x54931),x54932)) % 191.49/191.41 [5494]~P109(x54943)+E(x54941,x54942)+P4(f333(f333(f251(x54943),x54942),x54941))+P4(f333(f333(f251(x54943),x54941),x54942)) % 191.49/191.41 [5495]~E(x54952,x54953)+~P109(x54951)+P4(f333(f333(f250(x54951),x54952),x54953))+P4(f333(f333(f251(x54951),x54952),x54953)) % 191.49/191.41 [5746]~P110(x57463)+E(x57461,x57462)+~P4(f333(f333(f250(x57463),x57462),x57461))+P4(f333(f333(f251(x57463),x57462),x57461)) % 191.49/191.41 [5748]~P109(x57483)+E(x57481,x57482)+~P4(f333(f333(f250(x57483),x57481),x57482))+P4(f333(f333(f251(x57483),x57481),x57482)) % 191.49/191.41 [5754]~P110(x57543)+E(x57541,x57542)+~P4(f333(f333(f250(x57543),x57541),x57542))+P4(f333(f333(f251(x57543),x57541),x57542)) % 191.49/191.41 [5856]P146(x58561,x58562,x58563)+~P4(f333(x58561,x58563))+P4(f333(f333(f251(a1),x58562),f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x58562)) % 191.49/191.41 [5903]P147(x59031,x59032,x59033)+~P4(f333(x59031,f2(a1)))+P4(f333(f333(f251(a1),x59032),f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x59032)) % 191.49/191.41 [5907]~P6(x59071)+E(f333(f333(f115(x59071),x59072),f13(x59071,x59073)),x59072)+~P4(f333(f63(x59071),x59073))+~P4(f333(f333(f335(x59071),x59072),x59073)) % 191.49/191.41 [5908]~P6(x59081)+E(f333(f333(f106(x59081),x59082),f12(x59081,x59083)),x59082)+~P4(f333(f63(x59081),x59083))+~P4(f333(f333(f335(x59081),x59082),x59083)) % 191.49/191.41 [5943]~P6(x59431)+E(f333(f333(f115(x59431),x59432),f12(x59431,x59433)),f12(x59431,x59433))+~P4(f333(f63(x59431),x59433))+~P4(f333(f333(f335(x59431),x59432),x59433)) % 191.49/191.41 [5944]~P6(x59441)+E(f333(f333(f106(x59441),x59442),f13(x59441,x59443)),f13(x59441,x59443))+~P4(f333(f63(x59441),x59443))+~P4(f333(f333(f335(x59441),x59442),x59443)) % 191.49/191.41 [5945]~P109(x59451)+E(f333(f333(f248(x59451),x59452),f16(x59451,x59453)),f16(x59451,x59453))+~P4(f333(f63(x59451),x59453))+~P4(f333(f333(f335(x59451),x59452),x59453)) % 191.49/191.41 [5946]~P109(x59461)+E(f333(f333(f249(x59461),x59462),f17(x59461,x59463)),f17(x59461,x59463))+~P4(f333(f63(x59461),x59463))+~P4(f333(f333(f335(x59461),x59462),x59463)) % 191.49/191.41 [5991]E(x59911,x59912)+~P110(x59913)+~P4(f333(f333(f250(x59913),x59912),x59911))+~P4(f333(f333(f250(x59913),x59911),x59912)) % 191.49/191.41 [6131]~P108(x61311)+P4(f333(f333(f250(x61311),x61313),x61312))+~P4(f333(f333(f250(x61311),x61312),x61313))+P4(f333(f333(f251(x61311),x61312),x61313)) % 191.49/191.41 [6154]~P109(x61541)+~P4(f333(f63(x61541),x61543))+P4(f333(f333(f250(x61541),x61542),f17(x61541,x61543)))+~P4(f333(f333(f335(x61541),x61542),x61543)) % 191.49/191.41 [6203]~P109(x62031)+E(f333(f333(f248(x62031),x62032),f15(x62031,f249(x62031),x62033)),x62032)+~P4(f333(f63(x62031),x62033))+~P4(f333(f333(f335(x62031),x62032),x62033)) % 191.49/191.41 [6204]~P109(x62041)+E(f333(f333(f249(x62041),x62042),f14(x62041,f248(x62041),x62043)),x62042)+~P4(f333(f63(x62041),x62043))+~P4(f333(f333(f335(x62041),x62042),x62043)) % 191.49/191.41 [6338]E(x63381,x63382)+~E(f333(f333(f3(a880),x63381),x63383),f333(f333(f3(a880),x63382),x63383))+~P4(f333(f333(f250(a880),x63383),x63381))+~P4(f333(f333(f250(a880),x63383),x63382)) % 191.49/191.41 [6367]~P109(x63671)+~P4(f333(f63(x63671),x63672))+~P4(f333(f333(f335(x63671),x63673),x63672))+P4(f333(f333(f250(x63671),f16(x63671,x63672)),x63673)) % 191.49/191.41 [6430]P147(x64302,x64301,x64303)+E(x64301,f2(a1))+P4(f333(f333(f251(a1),x64301),f813(x64303,x64301,x64302)))+P4(f333(f333(f251(a1),f2(a1)),x64301)) % 191.49/191.41 [6431]P146(x64312,x64311,x64313)+E(x64311,f2(a1))+P4(f333(f333(f251(a1),x64311),f820(x64313,x64311,x64312)))+P4(f333(f333(f251(a1),f2(a1)),x64311)) % 191.49/191.41 [6432]~P109(x64321)+E(f333(f333(f248(x64321),x64322),f14(x64321,f248(x64321),x64323)),f14(x64321,f248(x64321),x64323))+~P4(f333(f63(x64321),x64323))+~P4(f333(f333(f335(x64321),x64322),x64323)) % 191.49/191.41 [6433]~P109(x64331)+E(f333(f333(f249(x64331),x64332),f15(x64331,f249(x64331),x64333)),f15(x64331,f249(x64331),x64333))+~P4(f333(f63(x64331),x64333))+~P4(f333(f333(f335(x64331),x64332),x64333)) % 191.49/191.41 [6439]~P4(f333(x64391,x64392))+P4(f333(x64391,f452(x64392,x64391,x64393)))+P4(f333(x64391,f2(a880)))+~P4(f333(f333(f251(a880),x64392),x64393)) % 191.49/191.41 [6493]~P4(f333(x64931,x64932))+~P4(f333(f63(x64933),x64932))+P4(f333(x64931,f608(x64931,x64932,x64933)))+P4(f333(x64931,f194(f890(x64933,a874)))) % 191.49/191.41 [6506]~P120(x65061)+~P94(x65061)+P4(f333(f333(f251(x65061),f333(f108(x65061),x65062)),f333(f108(x65061),x65063)))+~P4(f333(f333(f251(a1),x65062),x65063)) % 191.49/191.41 [6507]~P120(x65071)+~P94(x65071)+P4(f333(f333(f250(x65071),f333(f108(x65071),x65072)),f333(f108(x65071),x65073)))+~P4(f333(f333(f250(a1),x65072),x65073)) % 191.49/191.41 [6510]~P4(f333(x65101,x65103))+~P4(f333(f63(x65102),x65103))+P4(f333(f63(x65102),f608(x65101,x65103,x65102)))+P4(f333(x65101,f194(f890(x65102,a874)))) % 191.49/191.41 [6540]P146(x65401,x65402,x65403)+~P4(f333(x65401,x65403))+P4(f333(f333(f251(a1),x65402),f820(x65403,x65402,x65401)))+P4(f333(f333(f251(a1),f2(a1)),x65402)) % 191.49/191.41 [6575]P147(x65751,x65752,x65753)+P4(f333(f333(f251(a1),x65752),f813(x65753,x65752,x65751)))+~P4(f333(x65751,f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x65752)) % 191.49/191.41 [6606]~P111(x66061)+~P95(x66061)+E(f333(f333(f248(x66061),f333(f108(x66061),x66062)),f333(f108(x66061),x66063)),f333(f108(x66061),x66063))+P4(f333(f333(f250(x66061),f333(f108(x66061),x66062)),f333(f108(x66061),x66063))) % 191.49/191.41 [6607]~P111(x66071)+~P95(x66071)+E(f333(f333(f249(x66071),f333(f108(x66071),x66072)),f333(f108(x66071),x66073)),f333(f108(x66071),x66072))+P4(f333(f333(f250(x66071),f333(f108(x66071),x66072)),f333(f108(x66071),x66073))) % 191.49/191.41 [6665]P147(x66652,x66651,x66653)+E(x66651,f2(a1))+~P4(f333(x66652,f819(x66653,x66651,x66652)))+P4(f333(f333(f251(a1),f2(a1)),x66651)) % 191.49/191.41 [6666]P146(x66662,x66661,x66663)+E(x66661,f2(a1))+~P4(f333(x66662,f820(x66663,x66661,x66662)))+P4(f333(f333(f251(a1),f2(a1)),x66661)) % 191.49/191.41 [6670]P4(f333(x66701,x66702))+~P4(f333(f63(x66703),x66702))+P4(f333(x66701,f501(x66701,x66702,x66703)))+~P4(f333(x66701,f194(f890(x66703,a874)))) % 191.49/191.41 [6689]P4(f333(x66891,x66892))+P4(f333(f63(x66893),f501(x66891,x66892,x66893)))+~P4(f333(f63(x66893),x66892))+~P4(f333(x66891,f194(f890(x66893,a874)))) % 191.49/191.41 [6754]P146(x67541,x67542,x67543)+~P4(f333(x67541,x67543))+~P4(f333(x67541,f820(x67543,x67542,x67541)))+P4(f333(f333(f251(a1),f2(a1)),x67542)) % 191.49/191.41 [6778]P147(x67781,x67782,x67783)+~P4(f333(x67781,f819(x67783,x67782,x67781)))+~P4(f333(x67781,f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x67782)) % 191.49/191.41 [6882]~P94(x68823)+~P120(x68823)+~P4(f333(f333(f251(x68823),f333(f108(x68823),x68821)),f333(f108(x68823),x68822)))+P4(f333(f333(f251(a1),x68821),x68822)) % 191.49/191.41 [6883]~P94(x68833)+~P120(x68833)+~P4(f333(f333(f250(x68833),f333(f108(x68833),x68831)),f333(f108(x68833),x68832)))+P4(f333(f333(f250(a1),x68831),x68832)) % 191.49/191.41 [6910]~P109(x69101)+~P17(x69101,x69103)+P17(x69101,f333(f333(f152(x69101),x69102),x69103))+~P4(f333(f333(f250(x69101),x69102),f649(x69103,x69102,x69101))) % 191.49/191.41 [6911]~P109(x69111)+~P17(x69111,x69113)+P17(x69111,f333(f333(f152(x69111),x69112),x69113))+~P4(f333(f333(f250(x69111),x69112),f650(x69113,x69112,x69111))) % 191.49/191.42 [6912]~P109(x69121)+~P17(x69121,x69123)+P17(x69121,f333(f333(f152(x69121),x69122),x69123))+~P4(f333(f333(f250(x69121),x69122),f746(x69122,x69123,x69121))) % 191.49/191.42 [6997]P147(x69972,x69971,x69973)+E(x69971,f2(a1))+P4(f333(f333(f251(a1),x69971),f2(a1)))+P4(f333(f333(f251(a1),f814(x69973,x69971,x69972)),x69971)) % 191.49/191.42 [6998]P146(x69982,x69981,x69983)+E(x69981,f2(a1))+P4(f333(f333(f251(a1),x69981),f2(a1)))+P4(f333(f333(f251(a1),f821(x69983,x69981,x69982)),x69981)) % 191.49/191.42 [7039]P147(x70392,x70391,x70393)+E(x70391,f2(a1))+P4(f333(f333(f250(a1),f813(x70393,x70391,x70392)),f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x70391)) % 191.49/191.42 [7040]P146(x70402,x70401,x70403)+E(x70401,f2(a1))+P4(f333(f333(f250(a1),f820(x70403,x70401,x70402)),f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x70401)) % 191.49/191.42 [7062]~P109(x70621)+~P17(x70621,x70623)+E(f333(f333(f149(x70621,x70621,f7(x70621)),x70622),f171(x70621,x70622,x70623)),x70623)+~P4(f333(f333(f335(x70621),x70622),f333(f173(x70621),x70623))) % 191.49/191.42 [7108]P146(x71081,x71082,x71083)+~P4(f333(x71081,x71083))+P4(f333(f333(f251(a1),x71082),f2(a1)))+P4(f333(f333(f251(a1),f821(x71083,x71082,x71081)),x71082)) % 191.49/191.42 [7114]~P111(x71141)+~P95(x71141)+E(f333(f333(f248(x71141),f333(f108(x71141),x71142)),f333(f108(x71141),x71143)),f333(f108(x71141),x71142))+~P4(f333(f333(f250(x71141),f333(f108(x71141),x71142)),f333(f108(x71141),x71143))) % 191.49/191.42 [7115]~P111(x71151)+~P95(x71151)+E(f333(f333(f249(x71151),f333(f108(x71151),x71152)),f333(f108(x71151),x71153)),f333(f108(x71151),x71153))+~P4(f333(f333(f250(x71151),f333(f108(x71151),x71152)),f333(f108(x71151),x71153))) % 191.49/191.42 [7129]P147(x71291,x71292,x71293)+~P4(f333(x71291,f2(a1)))+P4(f333(f333(f251(a1),x71292),f2(a1)))+P4(f333(f333(f251(a1),f814(x71293,x71292,x71291)),x71292)) % 191.49/191.42 [7137]P146(x71371,x71372,x71373)+~P4(f333(x71371,x71373))+P4(f333(f333(f250(a1),f820(x71373,x71372,x71371)),f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x71372)) % 191.49/191.42 [7161]P147(x71611,x71612,x71613)+~P4(f333(x71611,f2(a1)))+P4(f333(f333(f250(a1),f813(x71613,x71612,x71611)),f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x71612)) % 191.49/191.42 [7189]~P4(f333(x71891,x71892))+P4(f333(x71891,f2(a880)))+~P4(f333(f333(f251(a880),x71892),x71893))+P4(f333(f333(f251(a880),f452(x71892,x71891,x71893)),x71893)) % 191.49/191.42 [7206]~P109(x72061)+~P17(x72061,x72063)+P17(x72061,f333(f333(f152(x72061),x72062),x72063))+P4(f333(f333(f335(x72061),f649(x72063,x72062,x72061)),f333(f173(x72061),x72063))) % 191.49/191.42 [7207]~P109(x72071)+~P17(x72071,x72073)+P17(x72071,f333(f333(f152(x72071),x72072),x72073))+P4(f333(f333(f335(x72071),f650(x72073,x72072,x72071)),f333(f173(x72071),x72073))) % 191.49/191.42 [7208]~P109(x72081)+~P17(x72081,x72083)+P17(x72081,f333(f333(f152(x72081),x72082),x72083))+P4(f333(f333(f335(x72081),f746(x72082,x72083,x72081)),f333(f173(x72081),x72083))) % 191.49/191.42 [7310]~P9(x73101)+~P109(x73101)+~P4(f333(f333(f251(x73101),x73103),f41(x73101,x73102)))+P4(f333(f333(f335(x73101),f845(x73102,x73103,x73101)),x73102)) % 191.49/191.42 [7468]~P9(x74681)+~P109(x74681)+~P4(f333(f333(f251(x74681),f42(x74681,x74683)),x74682))+P4(f333(f333(f335(x74681),f846(x74682,x74683,x74681)),x74683)) % 191.49/191.42 [7469]~P9(x74691)+~P109(x74691)+~P4(f333(f333(f251(x74691),f42(x74691,x74693)),x74692))+P4(f333(f333(f251(x74691),f846(x74692,x74693,x74691)),x74692)) % 191.49/191.42 [7481]P147(x74812,x74811,x74813)+E(x74811,f2(a1))+P4(f333(f333(f251(a1),x74811),f813(x74813,x74811,x74812)))+P4(f333(f333(f251(a1),f814(x74813,x74811,x74812)),x74811)) % 191.49/191.42 [7482]P146(x74822,x74821,x74823)+E(x74821,f2(a1))+P4(f333(f333(f251(a1),x74821),f820(x74823,x74821,x74822)))+P4(f333(f333(f251(a1),f821(x74823,x74821,x74822)),x74821)) % 191.49/191.42 [7569]P147(x75693,x75691,x75692)+E(x75691,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x75691),f819(x75692,x75691,x75693))),f813(x75692,x75691,x75693)),x75692)+P4(f333(f333(f251(a1),f2(a1)),x75691)) % 191.49/191.42 [7570]P146(x75703,x75701,x75702)+E(x75701,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x75701),f823(x75702,x75701,x75703))),f820(x75702,x75701,x75703)),x75702)+P4(f333(f333(f251(a1),f2(a1)),x75701)) % 191.49/191.42 [7572]~P129(x75721)+~P4(f333(f333(f251(x75721),x75723),f2(x75721)))+P4(f333(f333(f251(x75721),f333(f333(f82(x75721),x75722),x75723)),f2(x75721)))+~P4(f333(f333(f251(x75721),f2(x75721)),x75722)) % 191.49/191.42 [7573]~P129(x75731)+~P4(f333(f333(f251(x75731),x75732),f2(x75731)))+P4(f333(f333(f251(x75731),f333(f333(f82(x75731),x75732),x75733)),f2(x75731)))+~P4(f333(f333(f251(x75731),f2(x75731)),x75733)) % 191.49/191.42 [7574]~P66(x75741)+~P4(f333(f333(f251(x75741),x75743),f2(x75741)))+P4(f333(f333(f251(x75741),f333(f333(f291(x75741),x75742),x75743)),f2(x75741)))+~P4(f333(f333(f251(x75741),f2(x75741)),x75742)) % 191.49/191.42 [7575]~P66(x75751)+~P4(f333(f333(f251(x75751),x75752),f2(x75751)))+P4(f333(f333(f251(x75751),f333(f333(f291(x75751),x75752),x75753)),f2(x75751)))+~P4(f333(f333(f251(x75751),f2(x75751)),x75753)) % 191.49/191.42 [7576]~P65(x75761)+~P4(f333(f333(f251(x75761),x75763),f2(x75761)))+P4(f333(f333(f251(x75761),f333(f333(f291(x75761),x75762),x75763)),f2(x75761)))+~P4(f333(f333(f251(x75761),f2(x75761)),x75762)) % 191.49/191.42 [7577]~P65(x75771)+~P4(f333(f333(f251(x75771),x75772),f2(x75771)))+P4(f333(f333(f251(x75771),f333(f333(f291(x75771),x75772),x75773)),f2(x75771)))+~P4(f333(f333(f251(x75771),f2(x75771)),x75773)) % 191.49/191.42 [7579]~P124(x75791)+~P4(f333(f333(f250(x75791),x75793),f2(x75791)))+P4(f333(f333(f250(x75791),f333(f333(f82(x75791),x75792),x75793)),f2(x75791)))+~P4(f333(f333(f250(x75791),f2(x75791)),x75792)) % 191.49/191.42 [7580]~P124(x75801)+~P4(f333(f333(f250(x75801),x75802),f2(x75801)))+P4(f333(f333(f250(x75801),f333(f333(f82(x75801),x75802),x75803)),f2(x75801)))+~P4(f333(f333(f250(x75801),f2(x75801)),x75803)) % 191.49/191.42 [7582]~P133(x75821)+~P4(f333(f333(f250(x75821),x75823),f2(x75821)))+P4(f333(f333(f250(x75821),f333(f333(f82(x75821),x75822),x75823)),f2(x75821)))+~P4(f333(f333(f250(x75821),f2(x75821)),x75822)) % 191.49/191.42 [7584]~P133(x75841)+~P4(f333(f333(f250(x75841),x75842),f2(x75841)))+P4(f333(f333(f250(x75841),f333(f333(f82(x75841),x75842),x75843)),f2(x75841)))+~P4(f333(f333(f250(x75841),f2(x75841)),x75843)) % 191.49/191.42 [7585]~P66(x75851)+~P4(f333(f333(f251(x75851),x75853),f2(x75851)))+P4(f333(f333(f250(x75851),f333(f333(f291(x75851),x75852),x75853)),f2(x75851)))+~P4(f333(f333(f250(x75851),f2(x75851)),x75852)) % 191.49/191.42 [7586]~P66(x75861)+~P4(f333(f333(f250(x75861),x75862),f2(x75861)))+P4(f333(f333(f250(x75861),f333(f333(f291(x75861),x75862),x75863)),f2(x75861)))+~P4(f333(f333(f251(x75861),f2(x75861)),x75863)) % 191.49/191.42 [7587]~P65(x75871)+~P4(f333(f333(f250(x75871),x75873),f2(x75871)))+P4(f333(f333(f250(x75871),f333(f333(f291(x75871),x75872),x75873)),f2(x75871)))+~P4(f333(f333(f250(x75871),f2(x75871)),x75872)) % 191.49/191.42 [7588]~P65(x75881)+~P4(f333(f333(f250(x75881),x75882),f2(x75881)))+P4(f333(f333(f250(x75881),f333(f333(f291(x75881),x75882),x75883)),f2(x75881)))+~P4(f333(f333(f250(x75881),f2(x75881)),x75883)) % 191.49/191.42 [7603]P146(x76031,x76032,x76033)+~P4(f333(x76031,x76033))+P4(f333(f333(f251(a1),x76032),f820(x76033,x76032,x76031)))+P4(f333(f333(f251(a1),f821(x76033,x76032,x76031)),x76032)) % 191.49/191.42 [7616]P147(x76161,x76162,x76163)+P4(f333(f333(f251(a1),x76162),f813(x76163,x76162,x76161)))+~P4(f333(x76161,f2(a1)))+P4(f333(f333(f251(a1),f814(x76163,x76162,x76161)),x76162)) % 191.49/191.42 [7666]P147(x76662,x76661,x76663)+E(x76661,f2(a1))+~P4(f333(x76662,f819(x76663,x76661,x76662)))+P4(f333(f333(f251(a1),f814(x76663,x76661,x76662)),x76661)) % 191.49/191.42 [7667]P146(x76672,x76671,x76673)+E(x76671,f2(a1))+~P4(f333(x76672,f820(x76673,x76671,x76672)))+P4(f333(f333(f251(a1),f821(x76673,x76671,x76672)),x76671)) % 191.49/191.42 [7677]P146(x76773,x76771,x76772)+~P4(f333(x76773,x76772))+E(f333(f333(f81(a1),f333(f333(f82(a1),x76771),f823(x76772,x76771,x76773))),f820(x76772,x76771,x76773)),x76772)+P4(f333(f333(f251(a1),f2(a1)),x76771)) % 191.49/191.42 [7695]P147(x76953,x76951,x76952)+E(f333(f333(f81(a1),f333(f333(f82(a1),x76951),f819(x76952,x76951,x76953))),f813(x76952,x76951,x76953)),x76952)+~P4(f333(x76953,f2(a1)))+P4(f333(f333(f251(a1),f2(a1)),x76951)) % 191.49/191.42 [7720]~P4(f333(x77201,x77203))+~P4(f333(f63(x77202),x77203))+P4(f333(f333(f335(x77202),f605(x77201,x77203,x77202)),f608(x77201,x77203,x77202)))+P4(f333(x77201,f194(f890(x77202,a874)))) % 191.49/191.42 [7731]P146(x77311,x77312,x77313)+~P4(f333(x77311,x77313))+~P4(f333(x77311,f820(x77313,x77312,x77311)))+P4(f333(f333(f251(a1),f821(x77313,x77312,x77311)),x77312)) % 191.49/191.42 [7736]P147(x77361,x77362,x77363)+~P4(f333(x77361,f819(x77363,x77362,x77361)))+~P4(f333(x77361,f2(a1)))+P4(f333(f333(f251(a1),f814(x77363,x77362,x77361)),x77362)) % 191.49/191.42 [7844]~P65(x78441)+~P4(f333(f333(f251(x78441),f333(f333(f291(x78441),x78443),x78442)),f2(x78441)))+P4(f333(f333(f251(x78441),x78442),f2(x78441)))+P4(f333(f333(f251(x78441),f2(x78441)),x78442)) % 191.49/191.42 [7845]~P65(x78451)+~P4(f333(f333(f251(x78451),f333(f333(f291(x78451),x78452),x78453)),f2(x78451)))+P4(f333(f333(f251(x78451),x78452),f2(x78451)))+P4(f333(f333(f251(x78451),f2(x78451)),x78452)) % 191.49/191.42 [7846]~P124(x78461)+~P4(f333(f333(f250(x78461),f333(f333(f82(x78461),x78463),x78462)),f2(x78461)))+P4(f333(f333(f250(x78461),x78462),f2(x78461)))+P4(f333(f333(f250(x78461),f2(x78461)),x78462)) % 191.49/191.42 [7847]~P124(x78471)+~P4(f333(f333(f250(x78471),f333(f333(f82(x78471),x78472),x78473)),f2(x78471)))+P4(f333(f333(f250(x78471),x78472),f2(x78471)))+P4(f333(f333(f250(x78471),f2(x78471)),x78472)) % 191.49/191.42 [7848]~P65(x78481)+~P4(f333(f333(f250(x78481),f333(f333(f291(x78481),x78483),x78482)),f2(x78481)))+P4(f333(f333(f250(x78481),x78482),f2(x78481)))+P4(f333(f333(f250(x78481),f2(x78481)),x78482)) % 191.49/191.42 [7849]~P65(x78491)+~P4(f333(f333(f250(x78491),f333(f333(f291(x78491),x78492),x78493)),f2(x78491)))+P4(f333(f333(f250(x78491),x78492),f2(x78491)))+P4(f333(f333(f250(x78491),f2(x78491)),x78492)) % 191.49/191.42 [7868]~P65(x78681)+~P4(f333(f333(f251(x78681),f333(f333(f291(x78681),x78682),x78683)),f2(x78681)))+P4(f333(f333(f251(x78681),f2(x78681)),x78682))+P4(f333(f333(f251(x78681),f2(x78681)),x78683)) % 191.49/191.42 [7869]~P124(x78691)+~P4(f333(f333(f250(x78691),f333(f333(f82(x78691),x78692),x78693)),f2(x78691)))+P4(f333(f333(f250(x78691),f2(x78691)),x78692))+P4(f333(f333(f250(x78691),f2(x78691)),x78693)) % 191.49/191.42 [7870]~P65(x78701)+~P4(f333(f333(f250(x78701),f333(f333(f291(x78701),x78702),x78703)),f2(x78701)))+P4(f333(f333(f250(x78701),f2(x78701)),x78702))+P4(f333(f333(f250(x78701),f2(x78701)),x78703)) % 191.49/191.42 [7891]P147(x78912,x78911,x78913)+E(x78911,f2(a1))+P4(f333(f333(f250(a1),f813(x78913,x78911,x78912)),f2(a1)))+P4(f333(f333(f251(a1),f814(x78913,x78911,x78912)),x78911)) % 191.49/191.42 [7892]P146(x78922,x78921,x78923)+E(x78921,f2(a1))+P4(f333(f333(f250(a1),f820(x78923,x78921,x78922)),f2(a1)))+P4(f333(f333(f251(a1),f821(x78923,x78921,x78922)),x78921)) % 191.49/191.42 [7899]~P123(x78991)+~P4(f333(f333(f251(x78991),x78992),f79(x78991)))+P4(f333(f333(f251(x78991),f333(f333(f264(x78991),x78992),f333(a117,x78993))),f79(x78991)))+~P4(f333(f333(f251(x78991),f2(x78991)),x78992)) % 191.49/191.42 [7949]~P109(x79491)+~E(x79493,f118(x79491))+~P17(x79491,f333(f170(x79491),x79493))+E(f333(f143(x79491,x79491,f333(f9(x79491,x79491,x79491),f249(x79491)),x79492),f333(f170(x79491),x79493)),x79492) % 191.49/191.42 [7951]P146(x79511,x79512,x79513)+~P4(f333(x79511,x79513))+P4(f333(f333(f250(a1),f820(x79513,x79512,x79511)),f2(a1)))+P4(f333(f333(f251(a1),f821(x79513,x79512,x79511)),x79512)) % 191.49/191.42 [7960]P147(x79601,x79602,x79603)+~P4(f333(x79601,f2(a1)))+P4(f333(f333(f250(a1),f813(x79603,x79602,x79601)),f2(a1)))+P4(f333(f333(f251(a1),f814(x79603,x79602,x79601)),x79602)) % 191.49/191.42 [8193]P147(x81933,x81931,x81932)+E(x81931,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x81931),f819(x81932,x81931,x81933))),f813(x81932,x81931,x81933)),x81932)+P4(f333(f333(f251(a1),f814(x81932,x81931,x81933)),x81931)) % 191.49/191.42 [8194]P146(x81943,x81941,x81942)+E(x81941,f2(a1))+E(f333(f333(f81(a1),f333(f333(f82(a1),x81941),f823(x81942,x81941,x81943))),f820(x81942,x81941,x81943)),x81942)+P4(f333(f333(f251(a1),f821(x81942,x81941,x81943)),x81941)) % 191.49/191.42 [8227]P146(x82273,x82271,x82272)+~P4(f333(x82273,x82272))+E(f333(f333(f81(a1),f333(f333(f82(a1),x82271),f823(x82272,x82271,x82273))),f820(x82272,x82271,x82273)),x82272)+P4(f333(f333(f251(a1),f821(x82272,x82271,x82273)),x82271)) % 191.49/191.42 [8228]~P69(x82281)+~P76(x82281)+~P42(x82283)+E(f333(f333(f8(a880,x82281),f333(f333(f10(a1,x82281,a880),x82282),f105(a1))),f333(f312(a1,a880,a109),x82283)),f333(f333(f8(a1,x82281),x82282),x82283)) % 191.49/191.42 [8229]~P69(x82291)+~P76(x82291)+~P42(x82293)+E(f333(f333(f11(a880,x82291),f333(f333(f10(a1,x82291,a880),x82292),f105(a1))),f333(f312(a1,a880,a109),x82293)),f333(f333(f11(a1,x82291),x82292),x82293)) % 191.49/191.42 [8238]P147(x82383,x82381,x82382)+E(f333(f333(f81(a1),f333(f333(f82(a1),x82381),f819(x82382,x82381,x82383))),f813(x82382,x82381,x82383)),x82382)+~P4(f333(x82383,f2(a1)))+P4(f333(f333(f251(a1),f814(x82382,x82381,x82383)),x82381)) % 191.49/191.42 [8257]~E(x82572,f2(a880))+~E(f333(f262(a880,a880),x82573),f2(a880))+~E(x82571,f333(f333(f81(a880),f333(f333(f82(a880),f333(f262(a880,a880),x82573)),x82572)),f333(f271(a880,a880),x82573)))+P4(f333(f49(x82571,x82572),x82573)) % 191.49/191.42 [8311]P4(f333(x83111,x83112))+~P4(f333(f333(f335(x83113),f504(x83111,x83112,x83113)),f501(x83111,x83112,x83113)))+~P4(f333(f63(x83113),x83112))+~P4(f333(x83111,f194(f890(x83113,a874)))) % 191.49/191.42 [8921]P4(f333(x89211,x89212))+~P4(f333(f63(x89213),x89212))+~P4(f333(x89211,f333(f333(f311(x89213),f504(x89211,x89212,x89213)),f501(x89211,x89212,x89213))))+~P4(f333(x89211,f194(f890(x89213,a874)))) % 191.49/191.42 [9150]P4(f333(f333(f250(a1),x91501),f2(a1)))+~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f82(a1),x91502),x91501)),x91503)),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x91502))+~P4(f333(f333(f250(a1),f2(a1)),x91503)) % 191.49/191.42 [5817]~P6(x58172)+E(x58171,f194(f890(x58172,a874)))+~P4(f333(f63(x58172),x58171))+E(f12(x58172,f333(f333(f311(x58172),x58173),x58171)),f333(f333(f115(x58172),x58173),f12(x58172,x58171))) % 191.49/191.42 [5818]~P6(x58182)+E(x58181,f194(f890(x58182,a874)))+~P4(f333(f63(x58182),x58181))+E(f13(x58182,f333(f333(f311(x58182),x58183),x58181)),f333(f333(f106(x58182),x58183),f13(x58182,x58181))) % 191.49/191.42 [5819]~P109(x58192)+E(x58191,f194(f890(x58192,a874)))+~P4(f333(f63(x58192),x58191))+E(f16(x58192,f333(f333(f311(x58192),x58193),x58191)),f333(f333(f248(x58192),x58193),f16(x58192,x58191))) % 191.49/191.42 [5820]~P109(x58202)+E(x58201,f194(f890(x58202,a874)))+~P4(f333(f63(x58202),x58201))+E(f17(x58202,f333(f333(f311(x58202),x58203),x58201)),f333(f333(f249(x58202),x58203),f17(x58202,x58201))) % 191.49/191.42 [6128]~P124(x61281)+~E(x61283,f2(x61281))+~E(x61282,f2(x61281))+E(f333(f333(f81(x61281),f333(f333(f82(x61281),x61282),x61282)),f333(f333(f82(x61281),x61283),x61283)),f2(x61281)) % 191.49/191.42 [6196]~P97(x61962)+E(x61961,f194(f890(x61962,a874)))+~P4(f333(f63(x61962),x61961))+E(f333(f65(x61962,f82(x61962)),f333(f333(f311(x61962),x61963),x61961)),f333(f333(f82(x61962),x61963),f333(f65(x61962,f82(x61962)),x61961))) % 191.49/191.42 [6319]~P109(x63192)+E(x63191,f194(f890(x63192,a874)))+~P4(f333(f63(x63192),x63191))+E(f14(x63192,f248(x63192),f333(f333(f311(x63192),x63193),x63191)),f333(f333(f248(x63192),x63193),f14(x63192,f248(x63192),x63191))) % 191.49/191.42 [6320]~P109(x63202)+E(x63201,f194(f890(x63202,a874)))+~P4(f333(f63(x63202),x63201))+E(f15(x63202,f249(x63202),f333(f333(f311(x63202),x63203),x63201)),f333(f333(f249(x63202),x63203),f15(x63202,f249(x63202),x63201))) % 191.49/191.42 [6811]~P73(x68111)+~P4(f333(f63(x68111),x68113))+E(f333(f65(x68111,f82(x68111)),f333(f333(f311(x68111),x68112),x68113)),f333(f333(f66(x68111,x68111,f82(x68111)),x68112),x68113))+P4(f333(f333(f335(x68111),x68112),x68113)) % 191.49/191.42 [6887]~E(f333(f333(f81(a1),x68872),f333(f333(f82(a1),x68873),x68871)),x68873)+~P4(f333(f333(f251(a1),f2(a1)),x68873))+P4(f333(f333(f250(a1),f79(a1)),x68871))+~P4(f333(f333(f251(a1),x68872),x68873)) % 191.49/191.42 [6917]~E(f333(f333(f81(a1),x69172),f333(f333(f82(a1),x69173),x69171)),x69173)+P4(f333(f333(f250(a1),x69171),f79(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x69173))+~P4(f333(f333(f250(a1),f2(a1)),x69172)) % 191.49/191.42 [6933]E(x69331,f2(a880))+~P4(f333(f49(x69333,x69331),x69332))+~P4(f333(f333(f251(a880),f2(a880)),x69331))+P4(f333(f333(f251(a880),f333(f271(a880,a880),x69332)),x69331)) % 191.49/191.42 [6964]~P136(x69641)+~P4(f333(f333(f250(x69641),x69642),f2(x69641)))+~P4(f333(f333(f250(x69641),x69643),f2(x69641)))+E(f333(f333(f82(x69641),f333(f76(x69641),x69642)),f333(f76(x69641),x69643)),f333(f76(x69641),f333(f333(f82(x69641),x69642),x69643))) % 191.49/191.42 [7016]~P136(x70161)+~P4(f333(f333(f250(x70161),x70162),f2(x70161)))+E(f333(f333(f82(x70161),f333(f76(x70161),x70162)),f333(f76(x70161),x70163)),f333(f76(x70161),f333(f333(f82(x70161),x70162),x70163)))+~P4(f333(f333(f250(x70161),f2(x70161)),x70163)) % 191.49/191.42 [7017]~P136(x70171)+~P4(f333(f333(f250(x70171),x70173),f2(x70171)))+E(f333(f333(f82(x70171),f333(f76(x70171),x70172)),f333(f76(x70171),x70173)),f333(f76(x70171),f333(f333(f82(x70171),x70172),x70173)))+~P4(f333(f333(f250(x70171),f2(x70171)),x70172)) % 191.49/191.42 [7070]~P136(x70701)+E(f333(f333(f82(x70701),f333(f76(x70701),x70702)),f333(f76(x70701),x70703)),f333(f76(x70701),f333(f333(f82(x70701),x70702),x70703)))+~P4(f333(f333(f250(x70701),f2(x70701)),x70702))+~P4(f333(f333(f250(x70701),f2(x70701)),x70703)) % 191.49/191.42 [7086]~P124(x70861)+~P4(f333(f333(f251(x70861),x70863),f2(x70861)))+~P4(f333(f333(f251(x70861),x70862),f2(x70861)))+P4(f333(f333(f251(x70861),f2(x70861)),f333(f333(f82(x70861),x70862),x70863))) % 191.49/191.42 [7087]~P66(x70871)+~P4(f333(f333(f251(x70871),x70873),f2(x70871)))+~P4(f333(f333(f251(x70871),x70872),f2(x70871)))+P4(f333(f333(f251(x70871),f2(x70871)),f333(f333(f291(x70871),x70872),x70873))) % 191.49/191.42 [7088]~P65(x70881)+~P4(f333(f333(f251(x70881),x70883),f2(x70881)))+~P4(f333(f333(f251(x70881),x70882),f2(x70881)))+P4(f333(f333(f251(x70881),f2(x70881)),f333(f333(f291(x70881),x70882),x70883))) % 191.49/191.42 [7090]~P126(x70901)+~P4(f333(f333(f250(x70901),x70903),f2(x70901)))+~P4(f333(f333(f250(x70901),x70902),f2(x70901)))+P4(f333(f333(f250(x70901),f2(x70901)),f333(f333(f82(x70901),x70902),x70903))) % 191.49/191.42 [7091]~P124(x70911)+~P4(f333(f333(f250(x70911),x70913),f2(x70911)))+~P4(f333(f333(f250(x70911),x70912),f2(x70911)))+P4(f333(f333(f250(x70911),f2(x70911)),f333(f333(f82(x70911),x70912),x70913))) % 191.49/191.42 [7092]~P66(x70921)+~P4(f333(f333(f251(x70921),x70923),f2(x70921)))+~P4(f333(f333(f250(x70921),x70922),f2(x70921)))+P4(f333(f333(f250(x70921),f2(x70921)),f333(f333(f291(x70921),x70922),x70923))) % 191.49/191.42 [7093]~P65(x70931)+~P4(f333(f333(f250(x70931),x70933),f2(x70931)))+~P4(f333(f333(f250(x70931),x70932),f2(x70931)))+P4(f333(f333(f250(x70931),f2(x70931)),f333(f333(f291(x70931),x70932),x70933))) % 191.49/191.42 [7094]~P123(x70941)+~P4(f333(f333(f251(a880),f2(a880)),x70943))+~P4(f333(f333(f251(x70941),f79(x70941)),x70942))+P4(f333(f333(f251(x70941),f79(x70941)),f333(f333(f264(x70941),x70942),x70943))) % 191.49/191.42 [7190]~P123(x71901)+~P4(f333(f333(f251(x71901),f79(x71901)),x71903))+~P4(f333(f333(f251(x71901),f79(x71901)),x71902))+P4(f333(f333(f251(x71901),f79(x71901)),f333(f333(f82(x71901),x71902),x71903))) % 191.49/191.42 [7191]~P89(x71911)+~P4(f333(f333(f251(x71911),f2(x71911)),x71913))+~P4(f333(f333(f251(x71911),f2(x71911)),x71912))+P4(f333(f333(f251(x71911),f2(x71911)),f333(f333(f81(x71911),x71912),x71913))) % 191.49/191.42 [7194]~P129(x71941)+~P4(f333(f333(f251(x71941),f2(x71941)),x71943))+~P4(f333(f333(f251(x71941),f2(x71941)),x71942))+P4(f333(f333(f251(x71941),f2(x71941)),f333(f333(f82(x71941),x71942),x71943))) % 191.49/191.42 [7195]~P66(x71951)+~P4(f333(f333(f251(x71951),f2(x71951)),x71953))+~P4(f333(f333(f251(x71951),f2(x71951)),x71952))+P4(f333(f333(f251(x71951),f2(x71951)),f333(f333(f291(x71951),x71952),x71953))) % 191.49/191.42 [7196]~P65(x71961)+~P4(f333(f333(f251(x71961),f2(x71961)),x71963))+~P4(f333(f333(f251(x71961),f2(x71961)),x71962))+P4(f333(f333(f251(x71961),f2(x71961)),f333(f333(f291(x71961),x71962),x71963))) % 191.49/191.42 [7198]~P126(x71981)+~P4(f333(f333(f250(x71981),f2(x71981)),x71983))+~P4(f333(f333(f250(x71981),f2(x71981)),x71982))+P4(f333(f333(f250(x71981),f2(x71981)),f333(f333(f82(x71981),x71982),x71983))) % 191.49/191.42 [7199]~P124(x71991)+~P4(f333(f333(f250(x71991),f2(x71991)),x71993))+~P4(f333(f333(f250(x71991),f2(x71991)),x71992))+P4(f333(f333(f250(x71991),f2(x71991)),f333(f333(f82(x71991),x71992),x71993))) % 191.49/191.42 [7200]~P133(x72001)+~P4(f333(f333(f250(x72001),f2(x72001)),x72003))+~P4(f333(f333(f250(x72001),f2(x72001)),x72002))+P4(f333(f333(f250(x72001),f2(x72001)),f333(f333(f82(x72001),x72002),x72003))) % 191.49/191.42 [7201]~P66(x72011)+~P4(f333(f333(f251(x72011),f2(x72011)),x72013))+~P4(f333(f333(f250(x72011),f2(x72011)),x72012))+P4(f333(f333(f250(x72011),f2(x72011)),f333(f333(f291(x72011),x72012),x72013))) % 191.49/191.42 [7202]~P65(x72021)+~P4(f333(f333(f250(x72021),f2(x72021)),x72023))+~P4(f333(f333(f250(x72021),f2(x72021)),x72022))+P4(f333(f333(f250(x72021),f2(x72021)),f333(f333(f291(x72021),x72022),x72023))) % 191.49/191.42 [7270]~P6(x72701)+~P4(f333(f63(x72701),x72703))+E(f12(x72701,f333(f333(f311(x72701),x72702),x72703)),x72702)+~E(f333(f333(f3(f890(x72701,a874)),x72703),f333(f333(f311(x72701),x72702),f194(f890(x72701,a874)))),f194(f890(x72701,a874))) % 191.49/191.42 [7271]~P6(x72711)+~P4(f333(f63(x72711),x72713))+E(f13(x72711,f333(f333(f311(x72711),x72712),x72713)),x72712)+~E(f333(f333(f3(f890(x72711,a874)),x72713),f333(f333(f311(x72711),x72712),f194(f890(x72711,a874)))),f194(f890(x72711,a874))) % 191.49/191.42 [7272]~P109(x72721)+~P4(f333(f63(x72721),x72723))+E(f16(x72721,f333(f333(f311(x72721),x72722),x72723)),x72722)+~E(f333(f333(f3(f890(x72721,a874)),x72723),f333(f333(f311(x72721),x72722),f194(f890(x72721,a874)))),f194(f890(x72721,a874))) % 191.49/191.42 [7273]~P109(x72731)+~P4(f333(f63(x72731),x72733))+E(f17(x72731,f333(f333(f311(x72731),x72732),x72733)),x72732)+~E(f333(f333(f3(f890(x72731,a874)),x72733),f333(f333(f311(x72731),x72732),f194(f890(x72731,a874)))),f194(f890(x72731,a874))) % 191.49/191.42 [7274]~P65(x72741)+P4(f333(f333(f251(x72741),x72742),f2(x72741)))+P4(f333(f333(f251(x72741),f2(x72741)),x72743))+~P4(f333(f333(f251(x72741),f2(x72741)),f333(f333(f291(x72741),x72743),x72742))) % 191.49/191.42 [7275]~P65(x72751)+P4(f333(f333(f251(x72751),x72752),f2(x72751)))+P4(f333(f333(f251(x72751),f2(x72751)),x72753))+~P4(f333(f333(f251(x72751),f2(x72751)),f333(f333(f291(x72751),x72752),x72753))) % 191.49/191.42 [7276]~P65(x72761)+P4(f333(f333(f251(x72761),x72762),f2(x72761)))+P4(f333(f333(f251(x72761),f2(x72761)),x72762))+~P4(f333(f333(f251(x72761),f2(x72761)),f333(f333(f291(x72761),x72763),x72762))) % 191.49/191.42 [7277]~P65(x72771)+P4(f333(f333(f251(x72771),x72772),f2(x72771)))+P4(f333(f333(f251(x72771),f2(x72771)),x72772))+~P4(f333(f333(f251(x72771),f2(x72771)),f333(f333(f291(x72771),x72772),x72773))) % 191.49/191.42 [7278]~P124(x72781)+P4(f333(f333(f250(x72781),x72782),f2(x72781)))+P4(f333(f333(f250(x72781),f2(x72781)),x72783))+~P4(f333(f333(f250(x72781),f2(x72781)),f333(f333(f82(x72781),x72783),x72782))) % 191.49/191.42 [7279]~P124(x72791)+P4(f333(f333(f250(x72791),x72792),f2(x72791)))+P4(f333(f333(f250(x72791),f2(x72791)),x72793))+~P4(f333(f333(f250(x72791),f2(x72791)),f333(f333(f82(x72791),x72792),x72793))) % 191.49/191.42 [7280]~P65(x72801)+P4(f333(f333(f250(x72801),x72802),f2(x72801)))+P4(f333(f333(f250(x72801),f2(x72801)),x72803))+~P4(f333(f333(f250(x72801),f2(x72801)),f333(f333(f291(x72801),x72803),x72802))) % 191.49/191.42 [7281]~P65(x72811)+P4(f333(f333(f250(x72811),x72812),f2(x72811)))+P4(f333(f333(f250(x72811),f2(x72811)),x72813))+~P4(f333(f333(f250(x72811),f2(x72811)),f333(f333(f291(x72811),x72812),x72813))) % 191.49/191.42 [7282]~P124(x72821)+P4(f333(f333(f250(x72821),x72822),f2(x72821)))+P4(f333(f333(f250(x72821),f2(x72821)),x72822))+~P4(f333(f333(f250(x72821),f2(x72821)),f333(f333(f82(x72821),x72823),x72822))) % 191.49/191.42 [7283]~P124(x72831)+P4(f333(f333(f250(x72831),x72832),f2(x72831)))+P4(f333(f333(f250(x72831),f2(x72831)),x72832))+~P4(f333(f333(f250(x72831),f2(x72831)),f333(f333(f82(x72831),x72832),x72833))) % 191.49/191.42 [7284]~P65(x72841)+P4(f333(f333(f250(x72841),x72842),f2(x72841)))+P4(f333(f333(f250(x72841),f2(x72841)),x72842))+~P4(f333(f333(f250(x72841),f2(x72841)),f333(f333(f291(x72841),x72843),x72842))) % 191.49/191.42 [7285]~P65(x72851)+P4(f333(f333(f250(x72851),x72852),f2(x72851)))+P4(f333(f333(f250(x72851),f2(x72851)),x72852))+~P4(f333(f333(f250(x72851),f2(x72851)),f333(f333(f291(x72851),x72852),x72853))) % 191.49/191.42 [7368]~E(f333(f333(f106(f890(x73681,a874)),f333(f173(x73681),x73682)),f333(f173(x73681),x73683)),f194(f890(x73681,a874)))+~P4(f333(f138(x73681),x73683))+~P4(f333(f138(x73681),x73682))+P4(f333(f138(x73681),f333(f333(f127(x73681),x73682),x73683))) % 191.49/191.42 [7369]~P109(x73691)+~P4(f333(f63(x73691),x73693))+E(f14(x73691,f248(x73691),f333(f333(f311(x73691),x73692),x73693)),x73692)+~E(f333(f333(f3(f890(x73691,a874)),x73693),f333(f333(f311(x73691),x73692),f194(f890(x73691,a874)))),f194(f890(x73691,a874))) % 191.49/191.42 [7370]~P109(x73701)+~P4(f333(f63(x73701),x73703))+E(f15(x73701,f249(x73701),f333(f333(f311(x73701),x73702),x73703)),x73702)+~E(f333(f333(f3(f890(x73701,a874)),x73703),f333(f333(f311(x73701),x73702),f194(f890(x73701,a874)))),f194(f890(x73701,a874))) % 191.49/191.42 [7385]~P120(x73851)+~P4(f333(f333(f251(x73851),x73852),x73853))+~P4(f333(f333(f251(x73851),f333(f80(x73851),x73852)),x73853))+P4(f333(f333(f251(x73851),f333(f76(x73851),x73852)),x73853)) % 191.49/191.42 [7387]~P87(x73871)+~P4(f333(f333(f250(x73871),x73872),x73873))+~P4(f333(f333(f250(x73871),f333(f80(x73871),x73872)),x73873))+P4(f333(f333(f250(x73871),f333(f76(x73871),x73872)),x73873)) % 191.49/191.42 [7458]~P129(x74581)+P4(f333(f333(f251(x74581),f2(x74581)),x74582))+~P4(f333(f333(f251(x74581),f2(x74581)),x74583))+~P4(f333(f333(f251(x74581),f2(x74581)),f333(f333(f82(x74581),x74583),x74582))) % 191.49/191.42 [7459]~P129(x74591)+P4(f333(f333(f251(x74591),f2(x74591)),x74592))+~P4(f333(f333(f251(x74591),f2(x74591)),x74593))+~P4(f333(f333(f251(x74591),f2(x74591)),f333(f333(f82(x74591),x74592),x74593))) % 191.49/191.42 [7755]E(x77551,x77552)+~P4(f333(f63(x77553),x77551))+~P4(f333(f333(f250(a880),f333(f39(x77553),x77551)),f333(f39(x77553),x77552)))+~P4(f333(f333(f250(f890(x77553,a874)),x77552),x77551)) % 191.49/191.42 [7895]~P4(f333(f333(f251(a1),x78951),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x78952))+~P4(f333(f333(f250(a1),x78952),x78953))+P4(f333(f333(f250(a1),f333(f333(f40(a1),x78951),x78952)),f333(f333(f40(a1),x78951),x78953))) % 191.49/191.42 [7907]~P4(f333(f333(f251(a1),f2(a1)),x79073))+~P4(f333(f333(f250(a1),f2(a1)),x79071))+~P4(f333(f333(f250(a1),x79073),x79072))+P4(f333(f333(f250(a1),f333(f333(f40(a1),x79071),x79072)),f333(f333(f40(a1),x79071),x79073))) % 191.49/191.42 [8042]E(f333(x80421,f454(x80422,x80421,x80423)),x80422)+~P4(f333(f333(f250(a1),x80422),f333(x80421,x80423)))+P4(f333(f333(f251(a880),f455(x80422,x80421,x80423)),x80423))+~P4(f333(f333(f250(a1),f333(x80421,f2(a880))),x80422)) % 191.49/191.42 [8043]E(f333(x80431,f458(x80432,x80431,x80433)),x80432)+~P4(f333(f333(f250(a1),x80432),f333(x80431,x80433)))+P4(f333(f333(f251(a880),f459(x80432,x80431,x80433)),x80433))+~P4(f333(f333(f250(a1),f333(x80431,f2(a880))),x80432)) % 191.49/191.42 [8152]~P4(f333(f63(x81521),x81523))+~P4(f333(f333(f251(a880),f333(f39(x81521),x81522)),f333(f39(x81521),x81523)))+~P4(f333(f333(f250(f890(x81521,a874)),x81522),x81523))+P4(f333(f333(f251(f890(x81521,a874)),x81522),x81523)) % 191.49/191.42 [8181]E(f333(f333(f81(a1),f416(x81813,x81811,x81812)),f417(x81813,x81811,x81812)),x81811)+E(f333(f333(f3(a1),x81811),x81812),x81811)+~P4(f333(f333(f251(a1),f2(a1)),x81812))+~P4(f333(f333(f335(a1),f333(f333(f3(a1),x81811),f79(a1))),x81813)) % 191.49/191.42 [8182]E(f333(f333(f3(a1),f429(x81823,x81821,x81822)),f430(x81823,x81821,x81822)),x81821)+E(f333(f333(f81(a1),x81821),x81822),x81821)+~P4(f333(f333(f251(a1),f2(a1)),x81822))+~P4(f333(f333(f335(a1),f333(f333(f81(a1),x81821),f79(a1))),x81823)) % 191.49/191.42 [8233]~P4(f333(f333(f250(a880),x82333),x82331))+P4(f333(f333(f251(a880),x82331),x82332))+~P4(f333(f333(f250(a880),x82333),x82332))+~P4(f333(f333(f251(a880),f333(f333(f3(a880),x82331),x82333)),f333(f333(f3(a880),x82332),x82333))) % 191.49/191.42 [8234]~P4(f333(f333(f250(a880),x82343),x82341))+P4(f333(f333(f250(a880),x82341),x82342))+~P4(f333(f333(f250(a880),x82343),x82342))+~P4(f333(f333(f250(a880),f333(f333(f3(a880),x82341),x82343)),f333(f333(f3(a880),x82342),x82343))) % 191.49/191.42 [8250]~P109(x82502)+E(x82501,f118(x82502))+~P17(x82502,f333(f170(x82502),x82501))+E(f333(f143(x82502,x82502,f333(f9(x82502,x82502,x82502),f249(x82502)),x82503),f333(f170(x82502),x82501)),f333(f333(f249(x82502),f333(f333(f166(x82502),x82501),f2(a880))),x82503)) % 191.49/191.42 [8316]E(f333(f333(f3(a1),x83161),x83162),x83161)+~P4(f333(f333(f251(a1),f2(a1)),x83162))+P4(f333(f333(f335(a1),f416(x83163,x83161,x83162)),x83163))+~P4(f333(f333(f335(a1),f333(f333(f3(a1),x83161),f79(a1))),x83163)) % 191.49/191.42 [8317]E(f333(f333(f81(a1),x83171),x83172),x83171)+~P4(f333(f333(f251(a1),f2(a1)),x83172))+P4(f333(f333(f335(a1),f429(x83173,x83171,x83172)),x83173))+~P4(f333(f333(f335(a1),f333(f333(f81(a1),x83171),f79(a1))),x83173)) % 191.49/191.42 [8391]~P4(f333(f333(f250(a1),x83911),f333(x83912,x83913)))+P4(f333(f333(f250(a880),f454(x83911,x83912,x83913)),x83913))+P4(f333(f333(f251(a880),f455(x83911,x83912,x83913)),x83913))+~P4(f333(f333(f250(a1),f333(x83912,f2(a880))),x83911)) % 191.49/191.42 [8392]~P4(f333(f333(f250(a1),x83921),f333(x83922,x83923)))+P4(f333(f333(f250(a880),f458(x83921,x83922,x83923)),x83923))+P4(f333(f333(f251(a880),f459(x83921,x83922,x83923)),x83923))+~P4(f333(f333(f250(a1),f333(x83922,f2(a880))),x83921)) % 191.49/191.42 [8469]E(f333(f333(f3(a1),x84691),x84692),x84691)+~P4(f333(f333(f251(a1),f2(a1)),x84692))+P4(f333(f333(f335(a1),f417(x84693,x84691,x84692)),f304(a1,f79(a1),x84692)))+~P4(f333(f333(f335(a1),f333(f333(f3(a1),x84691),f79(a1))),x84693)) % 191.49/191.42 [8470]E(f333(f333(f81(a1),x84701),x84702),x84701)+~P4(f333(f333(f251(a1),f2(a1)),x84702))+P4(f333(f333(f335(a1),f430(x84703,x84701,x84702)),f304(a1,f79(a1),x84702)))+~P4(f333(f333(f335(a1),f333(f333(f81(a1),x84701),f79(a1))),x84703)) % 191.49/191.42 [8599]~P123(x85991)+~P4(f333(f333(f251(x85991),x85992),f79(x85991)))+~P4(f333(f333(f251(x85991),f2(x85991)),x85992))+P4(f333(f333(f251(x85991),f333(f333(f82(x85991),x85992),f333(f333(f264(x85991),x85992),x85993))),f333(f333(f264(x85991),x85992),x85993))) % 191.49/191.42 [8674]~P4(f333(x86741,x86742))+P4(f333(x86741,f2(a880)))+~P4(f333(f333(f251(a880),x86742),x86743))+~P4(f333(x86741,f46(a880,f333(a117,f452(x86742,x86741,x86743)),x86743))) % 191.49/191.42 [8816]E(f516(x88161,x88162,x88163),f2(a880))+P4(f333(f333(x88161,x88163),x88162))+P4(f333(f333(x88161,f516(x88161,x88162,x88163)),f46(a880,f514(x88161,x88162,x88163),f516(x88161,x88162,x88163))))+~P4(f333(f321(f889(a880,a880),a229),f333(f333(f263(a880,a880),x88163),x88162))) % 191.49/191.42 [8854]~P28(x88541,x88541,x88542,x88543)+E(f333(f312(x88541,x88541,x88542),x88543),x88543)+~P4(f333(f63(x88541),x88543))+~P4(f333(f333(f250(f890(x88541,a874)),f333(f312(x88541,x88541,x88542),x88543)),x88543)) % 191.49/191.42 [9080]P4(f333(f333(x90801,x90802),x90803))+~P4(f333(f333(f251(a1),f513(x90801,x90803,x90802)),f2(a1)))+P4(f333(f333(x90801,f333(f80(a1),f510(x90801,x90803,x90802))),f333(f80(a1),f513(x90801,x90803,x90802))))+~P4(f333(f321(f889(a1,a1),a231),f333(f333(f263(a1,a1),x90802),x90803))) % 191.49/191.42 [9279]P4(f333(f333(x92791,x92792),x92793))+P4(f333(f333(x92791,f333(f333(f81(a1),f586(x92791,x92793,x92792)),f79(a1))),f588(x92791,x92793,x92792)))+~P4(f333(f333(f250(a1),f586(x92791,x92793,x92792)),f588(x92791,x92793,x92792)))+~P4(f333(f321(f889(a1,a1),a183),f333(f333(f263(a1,a1),x92792),x92793))) % 191.49/191.42 [9725]~P62(x97252)+~P62(x97251)+~P4(f333(f59(f889(x97251,x97252)),x97253))+P4(f333(f59(x97251),f333(f333(f10(f890(x97252,a874),a874,x97251),f59(x97252)),f333(f333(f10(f890(x97252,f889(x97251,x97252)),f890(x97252,a874),x97251),f333(f10(f889(x97251,x97252),a874,x97252),x97253)),f263(x97251,x97252))))) % 191.49/191.42 [9726]~P62(x97262)+~P62(x97261)+~P4(f333(f60(f889(x97261,x97262)),x97263))+P4(f333(f60(x97261),f333(f333(f10(f890(x97262,a874),a874,x97261),f60(x97262)),f333(f333(f10(f890(x97262,f889(x97261,x97262)),f890(x97262,a874),x97261),f333(f10(f889(x97261,x97262),a874,x97262),x97263)),f263(x97261,x97262))))) % 191.49/191.42 [9838]~P62(x98382)+~P62(x98381)+P4(f333(f59(f889(x98381,x98382)),x98383))+~P4(f333(f59(x98381),f333(f333(f10(f890(x98382,a874),a874,x98381),f59(x98382)),f333(f333(f10(f890(x98382,f889(x98381,x98382)),f890(x98382,a874),x98381),f333(f10(f889(x98381,x98382),a874,x98382),x98383)),f263(x98381,x98382))))) % 191.49/191.42 [9839]~P62(x98392)+~P62(x98391)+P4(f333(f60(f889(x98391,x98392)),x98393))+~P4(f333(f60(x98391),f333(f333(f10(f890(x98392,a874),a874,x98391),f60(x98392)),f333(f333(f10(f890(x98392,f889(x98391,x98392)),f890(x98392,a874),x98391),f333(f10(f889(x98391,x98392),a874,x98392),x98393)),f263(x98391,x98392))))) % 191.49/191.42 [9987]E(f333(x99871,f454(x99872,x99871,x99873)),x99872)+~P4(f333(f333(f250(a1),x99872),f333(x99871,x99873)))+~P4(f333(f333(f250(a1),f333(f76(a1),f333(f333(f3(a1),f333(x99871,f333(f333(f81(a880),f455(x99872,x99871,x99873)),f79(a880)))),f333(x99871,f455(x99872,x99871,x99873))))),f79(a1)))+~P4(f333(f333(f250(a1),f333(x99871,f2(a880))),x99872)) % 191.49/191.42 [9988]E(f333(x99881,f458(x99882,x99881,x99883)),x99882)+~P4(f333(f333(f250(a1),x99882),f333(x99881,x99883)))+~P4(f333(f333(f250(a1),f333(f76(a1),f333(f333(f3(a1),f333(x99881,f333(f333(f81(a880),f459(x99882,x99881,x99883)),f79(a880)))),f333(x99881,f459(x99882,x99881,x99883))))),f79(a1)))+~P4(f333(f333(f250(a1),f333(x99881,f2(a880))),x99882)) % 191.49/191.42 [9992]~P4(f333(f333(f250(a1),x99921),f333(x99922,x99923)))+~P4(f333(f333(f250(a1),f333(f76(a1),f333(f333(f3(a1),f333(x99922,f333(f333(f81(a880),f455(x99921,x99922,x99923)),f79(a880)))),f333(x99922,f455(x99921,x99922,x99923))))),f79(a1)))+P4(f333(f333(f250(a880),f454(x99921,x99922,x99923)),x99923))+~P4(f333(f333(f250(a1),f333(x99922,f2(a880))),x99921)) % 191.49/191.42 [9993]~P4(f333(f333(f250(a1),x99931),f333(x99932,x99933)))+~P4(f333(f333(f250(a1),f333(f76(a1),f333(f333(f3(a1),f333(x99932,f333(f333(f81(a880),f459(x99931,x99932,x99933)),f79(a880)))),f333(x99932,f459(x99931,x99932,x99933))))),f79(a1)))+P4(f333(f333(f250(a880),f458(x99931,x99932,x99933)),x99933))+~P4(f333(f333(f250(a1),f333(x99932,f2(a880))),x99931)) % 191.49/191.42 [10046]E(x100461,x100462)+~E(f333(f143(f881(x100463),f881(x100463),f127(x100463),f118(x100463)),x100461),f333(f143(f881(x100463),f881(x100463),f127(x100463),f118(x100463)),x100462))+~E(f333(f195(f881(f881(x100463))),x100461),f333(f195(f881(f881(x100463))),x100462))+~P4(f333(f333(f272(f881(x100463),f881(x100463),a874),f333(f333(f9(f881(x100463),f890(f881(x100463),a880),f890(f881(x100463),a874)),f333(f333(f10(f890(a880,a874),f890(f890(f881(x100463),a880),f890(f881(x100463),a874)),f881(x100463)),f10(a880,a874,f881(x100463))),f333(f333(f10(a880,f890(a880,a874),f881(x100463)),a330),f195(f881(x100463))))),f195(f881(x100463)))),f659(x100462,x100461,x100463))) % 191.49/191.42 [10047]E(x100471,x100472)+~E(f333(f143(f881(x100473),f881(x100473),f127(x100473),f118(x100473)),x100471),f333(f143(f881(x100473),f881(x100473),f127(x100473),f118(x100473)),x100472))+~E(f333(f195(f881(f881(x100473))),x100471),f333(f195(f881(f881(x100473))),x100472))+~P4(f333(f333(f272(f881(x100473),f881(x100473),a874),f333(f333(f9(f881(x100473),f890(f881(x100473),a880),f890(f881(x100473),a874)),f333(f333(f10(f890(a880,a874),f890(f890(f881(x100473),a880),f890(f881(x100473),a874)),f881(x100473)),f10(a880,a874,f881(x100473))),f333(f333(f10(a880,f890(a880,a874),f881(x100473)),a330),f195(f881(x100473))))),f195(f881(x100473)))),f660(x100471,x100472,x100473))) % 191.49/191.42 [6800]~E(f79(a880),f2(a880))+~P4(f333(f63(x68001),x68003))+~P4(f333(f63(x68001),x68002))+E(f333(f333(f81(a880),f333(f39(x68001),x68002)),f333(f39(x68001),x68003)),f333(f39(x68001),f333(f333(f115(f890(x68001,a874)),x68002),x68003))) % 191.49/191.42 [7209]~P102(x72091)+~P4(f333(f63(x72091),x72092))+~P4(f333(f333(f335(x72091),x72093),x72092))+P4(f333(f333(f250(x72091),f333(f65(x72091,f106(x72091)),x72092)),x72093)) % 191.49/191.42 [7210]~P109(x72101)+~P4(f333(f63(x72101),x72102))+~P4(f333(f333(f335(x72101),x72103),x72102))+P4(f333(f333(f250(x72101),f333(f65(x72101,f248(x72101)),x72102)),x72103)) % 191.49/191.42 [7452]~P4(f333(f63(x74521),x74523))+~P4(f333(f63(x74521),x74522))+~E(f333(f333(f106(f890(x74521,a874)),x74522),x74523),f194(f890(x74521,a874)))+E(f333(f333(f81(a880),f333(f39(x74521),x74522)),f333(f39(x74521),x74523)),f333(f39(x74521),f333(f333(f115(f890(x74521,a874)),x74522),x74523))) % 191.49/191.42 [8239]~P40(x82391,x82393)+~P40(x82391,x82392)+~E(f333(f333(f106(f890(x82391,a874)),f333(f261(x82391,x82391),x82392)),f333(f259(x82391,x82391),x82393)),f194(f890(x82391,a874)))+P40(x82391,f333(f333(f115(f890(f889(x82391,x82391),a874)),x82392),x82393)) % 191.49/191.42 [8328]E(x83281,f333(f333(f40(a880),x83282),x83283))+~P4(f333(f333(f251(a880),f2(a880)),x83283))+~P4(f333(f333(f251(a880),x83282),f333(f333(f82(a880),x83283),f333(a117,x83281))))+~P4(f333(f333(f250(a880),f333(f333(f82(a880),x83283),x83281)),x83282)) % 191.49/191.42 [8467]~P4(f333(f63(x84671),x84672))+~P4(f333(f63(x84671),x84673))+E(f333(f333(f81(a880),f333(f39(x84671),x84672)),f333(f39(x84671),x84673)),f333(f39(x84671),f333(f333(f115(f890(x84671,a874)),x84672),x84673)))+P4(f333(f333(f335(x84671),f870(x84673,x84672,x84671)),f333(f333(f106(f890(x84671,a874)),x84672),x84673))) % 191.49/191.42 [8829]~P124(x88292)+~E(x88291,f2(x88292))+~E(x88293,f2(x88292))+~P4(f333(f333(f251(x88292),f2(x88292)),f333(f333(f81(x88292),f333(f333(f82(x88292),x88293),x88293)),f333(f333(f82(x88292),x88291),x88291)))) % 191.49/191.42 [9363]~P40(x93631,x93633)+~P40(x93631,x93632)+P40(x93631,f333(f333(f115(f890(f889(x93631,x93631),a874)),x93632),x93633))+~P4(f333(f333(f250(f890(f889(x93631,x93631),a874)),f333(f333(f290(x93631,x93631,x93631),x93632),x93633)),x93632)) % 191.49/191.42 [9483]~P4(f333(x94831,x94833))+~P4(f333(f63(x94832),x94833))+P4(f333(x94831,f194(f890(x94832,a874))))+~P4(f333(x94831,f333(f333(f3(f890(x94832,a874)),f608(x94831,x94833,x94832)),f333(f333(f311(x94832),f605(x94831,x94833,x94832)),f194(f890(x94832,a874)))))) % 191.49/191.42 [9767]~P62(x97671)+~P62(x97672)+P14(x97671,f333(f333(f10(f890(x97672,x97671),a874,f881(x97671)),x97673),f333(f333(f10(f890(x97672,f884(x97671)),f890(x97672,x97671),f881(x97671)),f74(f884(x97671),x97671,x97672,f246(x97671))),f333(f333(f10(f881(f889(x97672,x97671)),f890(x97672,f884(x97671)),f881(x97671)),f178(x97672,x97671)),f333(f182(x97672,x97671),f57(x97672))))),f333(f195(f881(x97672)),f57(x97672)))+~P4(f333(f60(f890(x97672,x97671)),x97673)) % 191.49/191.42 [9768]~P62(x97681)+~P62(x97682)+P13(x97681,f333(f333(f10(f890(x97682,x97681),a874,f881(x97681)),x97683),f333(f333(f10(f890(x97682,f884(x97681)),f890(x97682,x97681),f881(x97681)),f74(f884(x97681),x97681,x97682,f246(x97681))),f333(f333(f10(f881(f889(x97682,x97681)),f890(x97682,f884(x97681)),f881(x97681)),f178(x97682,x97681)),f333(f182(x97682,x97681),f57(x97682))))),f333(f195(f881(x97682)),f57(x97682)))+~P4(f333(f59(f890(x97682,x97681)),x97683)) % 191.49/191.42 [9858]~P62(x98581)+~P62(x98582)+~P13(x98582,f333(f333(f10(f890(x98581,x98582),a874,f881(x98582)),x98583),f333(f333(f10(f890(x98581,f884(x98582)),f890(x98581,x98582),f881(x98582)),f74(f884(x98582),x98582,x98581,f246(x98582))),f333(f333(f10(f881(f889(x98581,x98582)),f890(x98581,f884(x98582)),f881(x98582)),f178(x98581,x98582)),f333(f182(x98581,x98582),f57(x98581))))),f333(f195(f881(x98581)),f57(x98581)))+P4(f333(f59(f890(x98581,x98582)),x98583)) % 191.49/191.42 [9859]~P62(x98591)+~P62(x98592)+~P14(x98592,f333(f333(f10(f890(x98591,x98592),a874,f881(x98592)),x98593),f333(f333(f10(f890(x98591,f884(x98592)),f890(x98591,x98592),f881(x98592)),f74(f884(x98592),x98592,x98591,f246(x98592))),f333(f333(f10(f881(f889(x98591,x98592)),f890(x98591,f884(x98592)),f881(x98592)),f178(x98591,x98592)),f333(f182(x98591,x98592),f57(x98591))))),f333(f195(f881(x98591)),f57(x98591)))+P4(f333(f60(f890(x98591,x98592)),x98593)) % 191.49/191.42 [8635]~P4(f333(f333(f251(a1),f2(a1)),x86353))+P4(f333(f333(f250(a1),f2(a1)),x86351))+~P4(f333(f333(f251(a1),x86352),x86353))+~P4(f333(f333(f250(a1),f2(a1)),f333(f333(f81(a1),f333(f333(f82(a1),x86353),x86351)),x86352))) % 191.49/191.42 [8650]~P6(x86501)+~P4(f333(f63(x86501),x86502))+E(f333(f333(f3(f890(x86501,a874)),x86502),f333(f333(f311(x86501),x86503),f194(f890(x86501,a874)))),f194(f890(x86501,a874)))+E(f333(f333(f115(x86501),x86503),f12(x86501,f333(f333(f3(f890(x86501,a874)),x86502),f333(f333(f311(x86501),x86503),f194(f890(x86501,a874)))))),f12(x86501,f333(f333(f311(x86501),x86503),x86502))) % 191.49/191.42 [8651]~P6(x86511)+~P4(f333(f63(x86511),x86512))+E(f333(f333(f3(f890(x86511,a874)),x86512),f333(f333(f311(x86511),x86513),f194(f890(x86511,a874)))),f194(f890(x86511,a874)))+E(f333(f333(f106(x86511),x86513),f13(x86511,f333(f333(f3(f890(x86511,a874)),x86512),f333(f333(f311(x86511),x86513),f194(f890(x86511,a874)))))),f13(x86511,f333(f333(f311(x86511),x86513),x86512))) % 191.49/191.42 [8652]~P109(x86521)+~P4(f333(f63(x86521),x86522))+E(f333(f333(f3(f890(x86521,a874)),x86522),f333(f333(f311(x86521),x86523),f194(f890(x86521,a874)))),f194(f890(x86521,a874)))+E(f333(f333(f248(x86521),x86523),f16(x86521,f333(f333(f3(f890(x86521,a874)),x86522),f333(f333(f311(x86521),x86523),f194(f890(x86521,a874)))))),f16(x86521,f333(f333(f311(x86521),x86523),x86522))) % 191.49/191.42 [8653]~P109(x86531)+~P4(f333(f63(x86531),x86532))+E(f333(f333(f3(f890(x86531,a874)),x86532),f333(f333(f311(x86531),x86533),f194(f890(x86531,a874)))),f194(f890(x86531,a874)))+E(f333(f333(f249(x86531),x86533),f17(x86531,f333(f333(f3(f890(x86531,a874)),x86532),f333(f333(f311(x86531),x86533),f194(f890(x86531,a874)))))),f17(x86531,f333(f333(f311(x86531),x86533),x86532))) % 191.49/191.42 [8715]~P109(x87151)+~P4(f333(f63(x87151),x87152))+E(f333(f333(f3(f890(x87151,a874)),x87152),f333(f333(f311(x87151),x87153),f194(f890(x87151,a874)))),f194(f890(x87151,a874)))+E(f333(f333(f248(x87151),x87153),f14(x87151,f248(x87151),f333(f333(f3(f890(x87151,a874)),x87152),f333(f333(f311(x87151),x87153),f194(f890(x87151,a874)))))),f14(x87151,f248(x87151),f333(f333(f311(x87151),x87153),x87152))) % 191.49/191.42 [8716]~P109(x87161)+~P4(f333(f63(x87161),x87162))+E(f333(f333(f3(f890(x87161,a874)),x87162),f333(f333(f311(x87161),x87163),f194(f890(x87161,a874)))),f194(f890(x87161,a874)))+E(f333(f333(f249(x87161),x87163),f15(x87161,f249(x87161),f333(f333(f3(f890(x87161,a874)),x87162),f333(f333(f311(x87161),x87163),f194(f890(x87161,a874)))))),f15(x87161,f249(x87161),f333(f333(f311(x87161),x87163),x87162))) % 191.49/191.42 [9299]E(x92991,x92992)+~E(f333(f143(f881(x92993),f881(x92993),f127(x92993),f118(x92993)),x92991),f333(f143(f881(x92993),f881(x92993),f127(x92993),f118(x92993)),x92992))+~E(f333(f195(f881(f881(x92993))),x92991),f333(f195(f881(f881(x92993))),x92992))+P4(f333(f333(f335(f889(f881(x92993),f881(x92993))),f659(x92992,x92991,x92993)),f333(f173(f889(f881(x92993),f881(x92993))),f333(f333(f182(f881(x92993),f881(x92993)),x92991),x92992)))) % 191.49/191.42 [9300]E(x93001,x93002)+~E(f333(f143(f881(x93003),f881(x93003),f127(x93003),f118(x93003)),x93001),f333(f143(f881(x93003),f881(x93003),f127(x93003),f118(x93003)),x93002))+~E(f333(f195(f881(f881(x93003))),x93001),f333(f195(f881(f881(x93003))),x93002))+P4(f333(f333(f335(f889(f881(x93003),f881(x93003))),f660(x93001,x93002,x93003)),f333(f173(f889(f881(x93003),f881(x93003))),f333(f333(f182(f881(x93003),f881(x93003)),x93002),x93001)))) % 191.49/191.42 [10164]~P99(x101642)+E(x101641,f194(f890(x101642,a874)))+~P4(f333(f63(x101642),x101641))+E(f13(x101642,f333(f255(x101642),f333(f333(f10(f890(x101642,a874),a874,x101642),f87(x101642)),f333(f333(f9(x101642,f890(x101642,a874),f890(x101642,a874)),f333(f333(f10(f890(x101642,f890(a874,a874)),f890(f890(x101642,a874),f890(x101642,a874)),x101642),f20(x101642,a874,a874)),f333(f333(f10(f890(x101642,a874),f890(x101642,f890(a874,a874)),x101642),f333(f10(a874,f890(a874,a874),x101642),a331)),f333(f333(f9(x101642,f890(x101642,x101642),f890(x101642,a874)),f333(f333(f10(f890(x101642,a874),f890(f890(x101642,x101642),f890(x101642,a874)),x101642),f10(x101642,a874,x101642)),a330)),f333(f115(x101642),x101643))))),f333(f333(f9(x101642,f890(x101642,a874),a874),f335(x101642)),x101641))))),f333(f333(f115(x101642),x101643),f13(x101642,x101641))) % 191.49/191.42 [10165]~P99(x101652)+E(x101651,f194(f890(x101652,a874)))+~P4(f333(f63(x101652),x101651))+E(f12(x101652,f333(f255(x101652),f333(f333(f10(f890(x101652,a874),a874,x101652),f87(x101652)),f333(f333(f9(x101652,f890(x101652,a874),f890(x101652,a874)),f333(f333(f10(f890(x101652,f890(a874,a874)),f890(f890(x101652,a874),f890(x101652,a874)),x101652),f20(x101652,a874,a874)),f333(f333(f10(f890(x101652,a874),f890(x101652,f890(a874,a874)),x101652),f333(f10(a874,f890(a874,a874),x101652),a331)),f333(f333(f9(x101652,f890(x101652,x101652),f890(x101652,a874)),f333(f333(f10(f890(x101652,a874),f890(f890(x101652,x101652),f890(x101652,a874)),x101652),f10(x101652,a874,x101652)),a330)),f333(f106(x101652),x101653))))),f333(f333(f9(x101652,f890(x101652,a874),a874),f335(x101652)),x101651))))),f333(f333(f106(x101652),x101653),f12(x101652,x101651))) % 191.49/191.42 [10166]~P78(x101662)+E(x101661,f194(f890(x101662,a874)))+~P4(f333(f63(x101662),x101661))+E(f16(x101662,f333(f255(x101662),f333(f333(f10(f890(x101662,a874),a874,x101662),f87(x101662)),f333(f333(f9(x101662,f890(x101662,a874),f890(x101662,a874)),f333(f333(f10(f890(x101662,f890(a874,a874)),f890(f890(x101662,a874),f890(x101662,a874)),x101662),f20(x101662,a874,a874)),f333(f333(f10(f890(x101662,a874),f890(x101662,f890(a874,a874)),x101662),f333(f10(a874,f890(a874,a874),x101662),a331)),f333(f333(f9(x101662,f890(x101662,x101662),f890(x101662,a874)),f333(f333(f10(f890(x101662,a874),f890(f890(x101662,x101662),f890(x101662,a874)),x101662),f10(x101662,a874,x101662)),a330)),f333(f81(x101662),x101663))))),f333(f333(f9(x101662,f890(x101662,a874),a874),f335(x101662)),x101661))))),f333(f333(f81(x101662),x101663),f16(x101662,x101661))) % 191.49/191.42 [10167]~P78(x101672)+E(x101671,f194(f890(x101672,a874)))+~P4(f333(f63(x101672),x101671))+E(f17(x101672,f333(f255(x101672),f333(f333(f10(f890(x101672,a874),a874,x101672),f87(x101672)),f333(f333(f9(x101672,f890(x101672,a874),f890(x101672,a874)),f333(f333(f10(f890(x101672,f890(a874,a874)),f890(f890(x101672,a874),f890(x101672,a874)),x101672),f20(x101672,a874,a874)),f333(f333(f10(f890(x101672,a874),f890(x101672,f890(a874,a874)),x101672),f333(f10(a874,f890(a874,a874),x101672),a331)),f333(f333(f9(x101672,f890(x101672,x101672),f890(x101672,a874)),f333(f333(f10(f890(x101672,a874),f890(f890(x101672,x101672),f890(x101672,a874)),x101672),f10(x101672,a874,x101672)),a330)),f333(f81(x101672),x101673))))),f333(f333(f9(x101672,f890(x101672,a874),a874),f335(x101672)),x101671))))),f333(f333(f81(x101672),x101673),f17(x101672,x101671))) % 191.49/191.42 [10168]~P109(x101682)+E(x101681,f194(f890(x101682,a874)))+~P4(f333(f63(x101682),x101681))+E(f15(x101682,f249(x101682),f333(f255(x101682),f333(f333(f10(f890(x101682,a874),a874,x101682),f87(x101682)),f333(f333(f9(x101682,f890(x101682,a874),f890(x101682,a874)),f333(f333(f10(f890(x101682,f890(a874,a874)),f890(f890(x101682,a874),f890(x101682,a874)),x101682),f20(x101682,a874,a874)),f333(f333(f10(f890(x101682,a874),f890(x101682,f890(a874,a874)),x101682),f333(f10(a874,f890(a874,a874),x101682),a331)),f333(f333(f9(x101682,f890(x101682,x101682),f890(x101682,a874)),f333(f333(f10(f890(x101682,a874),f890(f890(x101682,x101682),f890(x101682,a874)),x101682),f10(x101682,a874,x101682)),a330)),f333(f248(x101682),x101683))))),f333(f333(f9(x101682,f890(x101682,a874),a874),f335(x101682)),x101681))))),f333(f333(f248(x101682),x101683),f15(x101682,f249(x101682),x101681))) % 191.49/191.42 [10169]~P109(x101692)+E(x101691,f194(f890(x101692,a874)))+~P4(f333(f63(x101692),x101691))+E(f14(x101692,f248(x101692),f333(f255(x101692),f333(f333(f10(f890(x101692,a874),a874,x101692),f87(x101692)),f333(f333(f9(x101692,f890(x101692,a874),f890(x101692,a874)),f333(f333(f10(f890(x101692,f890(a874,a874)),f890(f890(x101692,a874),f890(x101692,a874)),x101692),f20(x101692,a874,a874)),f333(f333(f10(f890(x101692,a874),f890(x101692,f890(a874,a874)),x101692),f333(f10(a874,f890(a874,a874),x101692),a331)),f333(f333(f9(x101692,f890(x101692,x101692),f890(x101692,a874)),f333(f333(f10(f890(x101692,a874),f890(f890(x101692,x101692),f890(x101692,a874)),x101692),f10(x101692,a874,x101692)),a330)),f333(f249(x101692),x101693))))),f333(f333(f9(x101692,f890(x101692,a874),a874),f335(x101692)),x101691))))),f333(f333(f249(x101692),x101693),f14(x101692,f248(x101692),x101691))) % 191.49/191.42 [10109]~P120(x101091)+~E(x101093,f2(x101091))+~E(x101092,f2(x101091))+E(f333(f333(f81(x101091),f333(f333(f264(x101091),x101092),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101091),x101093),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f2(x101091)) % 191.49/191.42 [10173]~P123(x101731)+~P4(f333(f333(f250(x101731),f2(x101731)),x101733))+P4(f333(f333(f250(x101731),x101732),x101733))+~P4(f333(f333(f250(x101731),f333(f333(f264(x101731),x101732),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101731),x101733),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))))) % 191.49/191.42 [10196]~P120(x101962)+~E(x101961,f2(x101962))+~E(x101963,f2(x101962))+~P4(f333(f333(f251(x101962),f2(x101962)),f333(f333(f81(x101962),f333(f333(f264(x101962),x101963),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))),f333(f333(f264(x101962),x101961),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))))) % 191.49/191.42 [9258]E(x92581,x92582)+~E(f637(x92581,x92582,x92584,x92583),f641(x92581,x92582,x92584,x92583))+P4(f333(f333(f335(f889(f881(x92583),f881(x92583))),f333(f333(f263(f881(x92583),f881(x92583)),x92582),x92581)),f148(x92583,x92584)))+P4(f333(f333(f335(f889(f881(x92583),f881(x92583))),f333(f333(f263(f881(x92583),f881(x92583)),x92581),x92582)),f148(x92583,x92584))) % 191.49/191.42 [4875]~P63(x48752)+~E(x48754,f2(x48752))+~E(x48751,f2(x48752))+E(x48751,f333(f333(f291(x48752),x48753),x48754)) % 191.49/191.42 [4876]~P63(x48761)+~E(x48763,f2(x48761))+~E(x48764,f2(x48761))+E(f333(f333(f291(x48761),x48762),x48763),x48764) % 191.49/191.42 [4985]~P63(x49852)+E(x49851,f2(x49852))+~E(x49853,f2(x49852))+~E(x49851,f333(f333(f291(x49852),x49854),x49853)) % 191.49/191.42 [4986]~P63(x49862)+E(x49861,f2(x49862))+~E(x49863,f2(x49862))+~E(f333(f333(f291(x49862),x49864),x49863),x49861) % 191.49/191.42 [5160]~P118(x51602)+E(x51601,f2(x51602))+~E(f333(f333(f291(x51602),x51603),x51601),x51604)+E(x51603,f333(f333(f82(x51602),x51604),x51601)) % 191.49/191.42 [5162]~P118(x51622)+E(x51621,f2(x51622))+~E(f333(f333(f82(x51622),x51623),x51621),x51624)+E(x51623,f333(f333(f291(x51622),x51624),x51621)) % 191.49/191.42 [5163]~P63(x51632)+E(x51631,f2(x51632))+~E(f333(f333(f291(x51632),x51633),x51631),x51634)+E(x51633,f333(f333(f82(x51632),x51634),x51631)) % 191.49/191.42 [5164]~P63(x51642)+E(x51641,f2(x51642))+~E(f333(f333(f82(x51642),x51643),x51641),x51644)+E(x51643,f333(f333(f291(x51642),x51644),x51641)) % 191.49/191.42 [5165]~P118(x51652)+E(x51651,f2(x51652))+~E(x51653,f333(f333(f291(x51652),x51654),x51651))+E(f333(f333(f82(x51652),x51653),x51651),x51654) % 191.49/191.42 [5167]~P118(x51672)+E(x51671,f2(x51672))+~E(x51673,f333(f333(f82(x51672),x51674),x51671))+E(f333(f333(f291(x51672),x51673),x51671),x51674) % 191.49/191.42 [5168]~P63(x51682)+E(x51681,f2(x51682))+~E(x51683,f333(f333(f291(x51682),x51684),x51681))+E(f333(f333(f82(x51682),x51683),x51681),x51684) % 191.49/191.42 [5169]~P63(x51692)+E(x51691,f2(x51692))+~E(x51693,f333(f333(f82(x51692),x51694),x51691))+E(f333(f333(f291(x51692),x51693),x51691),x51694) % 191.49/191.42 [5202]~P63(x52022)+~E(x52021,f2(x52022))+~E(f333(f333(f82(x52022),x52021),x52024),x52023)+E(x52021,f333(f333(f291(x52022),x52023),x52024)) % 191.49/191.42 [5203]~P63(x52031)+~E(x52034,f2(x52031))+~E(x52032,f333(f333(f82(x52031),x52034),x52033))+E(f333(f333(f291(x52031),x52032),x52033),x52034) % 191.49/191.42 [5277]~E(x52773,x52774)+~E(x52772,x52773)+~P110(x52771)+E(f304(x52771,x52772,x52773),f333(f333(f311(x52771),x52774),f194(f890(x52771,a874)))) % 191.49/191.42 [5483]~E(f145(x54832,x54831),x54834)+~E(f119(x54832,x54831),x54833)+E(x54831,f118(x54832))+E(f333(f333(f127(x54832),x54833),f333(f333(f152(x54832),x54834),f118(x54832))),x54831) % 191.49/191.42 [6096]~P123(x60963)+E(x60961,x60962)+~E(f333(f333(f264(x60963),x60964),x60961),f333(f333(f264(x60963),x60964),x60962))+~P4(f333(f333(f251(x60963),f79(x60963)),x60964)) % 191.49/191.42 [6097]E(x60971,x60972)+~E(f333(f333(f311(x60973),x60974),x60971),f333(f333(f311(x60973),x60974),x60972))+P4(f333(f333(f335(x60973),x60974),x60972))+P4(f333(f333(f335(x60973),x60974),x60971)) % 191.49/191.42 [6135]E(f333(x61351,x61352),f79(a880))+~E(f333(f333(f11(x61353,a880),x61351),x61354),f79(a880))+~P4(f333(f63(x61353),x61354))+~P4(f333(f333(f335(x61353),x61352),x61354)) % 191.49/191.42 [6136]E(f333(x61361,x61362),f2(a880))+~E(f333(f333(f8(x61363,a880),x61361),x61364),f2(a880))+~P4(f333(f63(x61363),x61364))+~P4(f333(f333(f335(x61363),x61362),x61364)) % 191.49/191.42 [6350]~P110(x63501)+~P4(f333(f333(f251(x63501),x63504),x63503))+P4(f333(f333(f251(x63501),x63502),x63503))+~P4(f333(f333(f251(x63501),x63502),x63504)) % 191.49/191.42 [6351]~P110(x63511)+~P4(f333(f333(f250(x63511),x63514),x63513))+P4(f333(f333(f251(x63511),x63512),x63513))+~P4(f333(f333(f251(x63511),x63512),x63514)) % 191.49/191.42 [6352]~P110(x63521)+~P4(f333(f333(f250(x63521),x63522),x63524))+P4(f333(f333(f251(x63521),x63522),x63523))+~P4(f333(f333(f251(x63521),x63524),x63523)) % 191.49/191.42 [6353]~P108(x63531)+~P4(f333(f333(f251(x63531),x63532),x63534))+P4(f333(f333(f251(x63531),x63532),x63533))+~P4(f333(f333(f251(x63531),x63534),x63533)) % 191.49/191.42 [6354]~P108(x63541)+~P4(f333(f333(f250(x63541),x63542),x63544))+P4(f333(f333(f251(x63541),x63542),x63543))+~P4(f333(f333(f251(x63541),x63544),x63543)) % 191.49/191.42 [6355]~P108(x63551)+~P4(f333(f333(f250(x63551),x63554),x63553))+P4(f333(f333(f251(x63551),x63552),x63553))+~P4(f333(f333(f251(x63551),x63552),x63554)) % 191.49/191.42 [6356]~P110(x63561)+~P4(f333(f333(f250(x63561),x63564),x63563))+P4(f333(f333(f250(x63561),x63562),x63563))+~P4(f333(f333(f250(x63561),x63562),x63564)) % 191.49/191.42 [6357]~P108(x63571)+~P4(f333(f333(f250(x63571),x63572),x63574))+P4(f333(f333(f250(x63571),x63572),x63573))+~P4(f333(f333(f250(x63571),x63574),x63573)) % 191.49/191.42 [6440]~P38(x64404,x64403,x64402)+E(x64401,f812(x64402,x64403,x64404))+~P4(f333(x64403,x64401))+~P4(f333(f333(f335(x64404),x64401),f333(f173(x64404),x64402))) % 191.49/191.42 [6581]~P9(x65811)+~P4(f333(f333(f250(x65811),x65812),f42(x65811,x65814)))+P4(f333(f333(f250(x65811),x65812),x65813))+~P4(f333(f333(f335(x65811),x65813),x65814)) % 191.49/191.42 [6727]~P109(x67271)+~P17(x67271,f333(f333(f152(x67271),x67272),x67274))+~P4(f333(f333(f335(x67271),x67273),f333(f173(x67271),x67274)))+P4(f333(f333(f250(x67271),x67272),x67273)) % 191.49/191.42 [6810]~P9(x68101)+~P4(f333(f333(f250(x68101),f41(x68101,x68104)),x68103))+P4(f333(f333(f250(x68101),x68102),x68103))+~P4(f333(f333(f335(x68101),x68102),x68104)) % 191.49/191.42 [7212]~P109(x72121)+E(f333(f333(f115(f890(x72121,a874)),f333(f303(x72121,x72122),x72123)),f333(f303(x72121,x72123),x72124)),f333(f303(x72121,x72122),x72124))+~P4(f333(f333(f250(x72121),x72123),x72124))+~P4(f333(f333(f250(x72121),x72122),x72123)) % 191.49/191.42 [7251]P38(x72511,x72512,x72513)+~E(f816(x72513,x72512,x72511,x72514),x72514)+~P4(f333(x72512,x72514))+~P4(f333(f333(f335(x72511),x72514),f333(f173(x72511),x72513))) % 191.49/191.42 [7314]~P109(x73141)+E(f333(f333(f115(f890(x73141,a874)),f333(f303(x73141,x73142),x73143)),f304(x73141,x73143,x73144)),f304(x73141,x73142,x73144))+~P4(f333(f333(f250(x73141),x73143),x73144))+~P4(f333(f333(f250(x73141),x73142),x73143)) % 191.49/191.42 [7379]~P109(x73791)+E(f333(f333(f115(f890(x73791,a874)),f307(x73791,x73792,x73793)),f333(f303(x73791,x73793),x73794)),f307(x73791,x73792,x73794))+~P4(f333(f333(f251(x73791),x73792),x73793))+~P4(f333(f333(f250(x73791),x73793),x73794)) % 191.49/191.42 [7399]~P109(x73991)+E(f333(f333(f115(f890(x73991,a874)),f304(x73991,x73992,x73993)),f307(x73991,x73993,x73994)),f333(f303(x73991,x73992),x73994))+~P4(f333(f333(f251(x73991),x73993),x73994))+~P4(f333(f333(f250(x73991),x73992),x73993)) % 191.49/191.42 [7431]~P109(x74311)+E(f333(f333(f115(f890(x74311,a874)),f307(x74311,x74312,x74313)),f304(x74311,x74313,x74314)),f306(x74311,x74312,x74314))+~P4(f333(f333(f251(x74311),x74312),x74313))+~P4(f333(f333(f250(x74311),x74313),x74314)) % 191.49/191.42 [7432]~P109(x74321)+E(f333(f333(f115(f890(x74321,a874)),f306(x74321,x74322,x74323)),f307(x74321,x74323,x74324)),f307(x74321,x74322,x74324))+~P4(f333(f333(f251(x74321),x74323),x74324))+~P4(f333(f333(f250(x74321),x74322),x74323)) % 191.49/191.42 [7433]~P109(x74331)+E(f333(f333(f115(f890(x74331,a874)),f306(x74331,x74332,x74333)),f306(x74331,x74333,x74334)),f306(x74331,x74332,x74334))+~P4(f333(f333(f250(x74331),x74333),x74334))+~P4(f333(f333(f250(x74331),x74332),x74333)) % 191.49/191.42 [7434]~P109(x74341)+E(f333(f333(f115(f890(x74341,a874)),f304(x74341,x74342,x74343)),f306(x74341,x74343,x74344)),f304(x74341,x74342,x74344))+~P4(f333(f333(f250(x74341),x74343),x74344))+~P4(f333(f333(f250(x74341),x74342),x74343)) % 191.49/191.42 [8223]P28(x82231,x82232,f365(x82233,x82232,x82234,x82231),x82234)+~P4(f333(f63(x82232),x82233))+~P4(f333(f63(x82231),x82234))+~P4(f333(f333(f250(a880),f333(f39(x82231),x82234)),f333(f39(x82232),x82233))) % 191.49/191.42 [8244]P38(x82441,x82442,x82443)+~P4(f333(x82442,x82444))+P4(f333(x82442,f816(x82443,x82442,x82441,x82444)))+~P4(f333(f333(f335(x82441),x82444),f333(f173(x82441),x82443))) % 191.49/191.42 [8295]~P76(x82951)+~E(f333(x82953,f379(x82953,x82954,x82952,x82951)),f79(x82951))+E(f333(f333(f333(f67(x82951,x82952,f82(x82951)),x82953),f79(x82951)),x82954),f79(x82951))+~P4(f333(f63(x82952),x82954)) % 191.49/191.42 [8567]~P123(x85671)+~P4(f333(f333(f250(x85671),f2(x85671)),x85673))+P4(f333(f333(f250(x85671),x85672),x85673))+~P4(f333(f333(f250(x85671),f333(f333(f264(x85671),x85672),f333(a117,x85674))),f333(f333(f264(x85671),x85673),f333(a117,x85674)))) % 191.49/191.42 [8855]P38(x88551,x88552,x88553)+~P4(f333(x88552,x88554))+~P4(f333(f333(f335(x88551),x88554),f333(f173(x88551),x88553)))+P4(f333(f333(f335(x88551),f816(x88553,x88552,x88551,x88554)),f333(f173(x88551),x88553))) % 191.49/191.42 [8942]~P76(x89421)+E(f333(f333(f333(f67(x89421,x89422,f82(x89421)),x89423),f79(x89421)),x89424),f79(x89421))+~P4(f333(f63(x89422),x89424))+P4(f333(f333(f335(x89422),f379(x89423,x89424,x89422,x89421)),x89424)) % 191.49/191.42 [9423]~P4(f333(f333(f250(a1),x94234),f2(a1)))+P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f82(a1),x94231),f46(a1,x94232,x94233))),x94234)),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x94233))+~P4(f333(f333(f251(a1),x94231),x94234)) % 191.49/191.42 [9899]~P4(f333(f63(x98991),x98992))+~P4(f333(f333(f335(x98991),x98994),x98992))+~P4(f333(f333(f335(x98991),x98993),x98992))+P4(f333(f333(f251(a880),f333(f39(x98991),f333(f333(f3(f890(x98991,a874)),f333(f333(f3(f890(x98991,a874)),x98992),f333(f333(f311(x98991),x98993),f194(f890(x98991,a874))))),f333(f333(f311(x98991),x98994),f194(f890(x98991,a874)))))),f333(f39(x98991),x98992))) % 191.49/191.42 [6920]~P109(x69201)+~P4(f333(f333(f251(x69201),x69202),x69204))+~P4(f333(f333(f251(x69201),x69202),x69203))+P4(f333(f333(f251(x69201),x69202),f333(f333(f248(x69201),x69203),x69204))) % 191.49/191.42 [6923]~P102(x69231)+~P4(f333(f333(f250(x69231),x69232),x69234))+~P4(f333(f333(f250(x69231),x69232),x69233))+P4(f333(f333(f250(x69231),x69232),f333(f333(f106(x69231),x69233),x69234))) % 191.49/191.42 [6926]~P109(x69261)+~P4(f333(f333(f250(x69261),x69262),x69264))+~P4(f333(f333(f250(x69261),x69262),x69263))+P4(f333(f333(f250(x69261),x69262),f333(f333(f248(x69261),x69263),x69264))) % 191.49/191.42 [6945]~P64(x69452)+E(x69451,f2(x69452))+E(f333(f333(f291(x69452),f333(f333(f264(x69452),x69451),x69453)),f333(f333(f264(x69452),x69451),x69454)),f333(f333(f264(x69452),x69451),f333(f333(f3(a880),x69453),x69454)))+~P4(f333(f333(f250(a880),x69454),x69453)) % 191.49/191.42 [6991]~P109(x69911)+~P17(x69911,f333(f333(f152(x69911),x69913),x69914))+P17(x69911,f333(f333(f152(x69911),x69912),f333(f333(f152(x69911),x69913),x69914)))+~P4(f333(f333(f250(x69911),x69912),x69913)) % 191.49/191.42 [7032]~P123(x70321)+~P4(f333(f333(f251(x70321),f2(x70321)),x70323))+~P4(f333(f333(f251(x70321),x70322),x70324))+P4(f333(f333(f251(x70321),x70322),f333(f333(f81(x70321),x70323),x70324))) % 191.49/191.42 [7033]~P89(x70331)+~P4(f333(f333(f250(x70331),f2(x70331)),x70333))+~P4(f333(f333(f251(x70331),x70332),x70334))+P4(f333(f333(f251(x70331),x70332),f333(f333(f81(x70331),x70333),x70334))) % 191.49/191.42 [7034]~P89(x70341)+~P4(f333(f333(f250(x70341),x70342),x70344))+~P4(f333(f333(f251(x70341),f2(x70341)),x70343))+P4(f333(f333(f251(x70341),x70342),f333(f333(f81(x70341),x70343),x70344))) % 191.49/191.42 [7035]~P89(x70351)+~P4(f333(f333(f250(x70351),f2(x70351)),x70354))+~P4(f333(f333(f250(x70351),x70352),x70353))+P4(f333(f333(f250(x70351),x70352),f333(f333(f81(x70351),x70353),x70354))) % 191.49/191.42 [7036]~P89(x70361)+~P4(f333(f333(f250(x70361),f2(x70361)),x70363))+~P4(f333(f333(f250(x70361),x70362),x70364))+P4(f333(f333(f250(x70361),x70362),f333(f333(f81(x70361),x70363),x70364))) % 191.49/191.42 [7074]~P109(x70741)+P4(f333(f333(f251(x70741),x70742),x70743))+P4(f333(f333(f251(x70741),x70742),x70744))+~P4(f333(f333(f251(x70741),x70742),f333(f333(f249(x70741),x70744),x70743))) % 191.49/191.42 [7075]~P109(x70751)+P4(f333(f333(f250(x70751),x70752),x70753))+P4(f333(f333(f250(x70751),x70752),x70754))+~P4(f333(f333(f250(x70751),x70752),f333(f333(f249(x70751),x70754),x70753))) % 191.49/191.42 [7353]~P110(x73532)+~P62(x73531)+~P4(f333(f333(f251(f890(x73531,x73532)),x73533),x73534))+P4(f333(f333(f250(f890(x73531,x73532)),x73533),x73534)) % 191.49/191.42 [7714]~P66(x77141)+~P4(f333(f333(f251(x77141),x77144),f2(x77141)))+~P4(f333(f333(f251(x77141),x77143),f333(f333(f291(x77141),x77142),x77144)))+P4(f333(f333(f251(x77141),x77142),f333(f333(f82(x77141),x77143),x77144))) % 191.49/191.42 [7715]~P66(x77151)+~P4(f333(f333(f251(x77151),x77154),f2(x77151)))+~P4(f333(f333(f251(x77151),x77153),f333(f333(f82(x77151),x77152),x77154)))+P4(f333(f333(f251(x77151),x77152),f333(f333(f291(x77151),x77153),x77154))) % 191.49/191.42 [7716]~P66(x77161)+~P4(f333(f333(f251(x77161),x77164),f2(x77161)))+~P4(f333(f333(f250(x77161),x77163),f333(f333(f291(x77161),x77162),x77164)))+P4(f333(f333(f250(x77161),x77162),f333(f333(f82(x77161),x77163),x77164))) % 191.49/191.42 [7717]~P66(x77171)+~P4(f333(f333(f251(x77171),x77174),f2(x77171)))+~P4(f333(f333(f250(x77171),x77173),f333(f333(f82(x77171),x77172),x77174)))+P4(f333(f333(f250(x77171),x77172),f333(f333(f291(x77171),x77173),x77174))) % 191.49/191.42 [7830]~P124(x78301)+~P4(f333(f333(f251(x78301),x78303),f2(x78301)))+~P4(f333(f333(f251(x78301),x78304),x78302))+P4(f333(f333(f251(x78301),f333(f333(f82(x78301),x78302),x78303)),f333(f333(f82(x78301),x78304),x78303))) % 191.49/191.42 [7831]~P124(x78311)+~P4(f333(f333(f251(x78311),x78312),f2(x78311)))+~P4(f333(f333(f251(x78311),x78314),x78313))+P4(f333(f333(f251(x78311),f333(f333(f82(x78311),x78312),x78313)),f333(f333(f82(x78311),x78312),x78314))) % 191.49/191.42 [7832]~P66(x78321)+~P4(f333(f333(f251(x78321),x78323),f2(x78321)))+~P4(f333(f333(f251(x78321),x78324),x78322))+P4(f333(f333(f251(x78321),f333(f333(f291(x78321),x78322),x78323)),f333(f333(f291(x78321),x78324),x78323))) % 191.49/191.42 [7833]~P126(x78331)+~P4(f333(f333(f250(x78331),x78332),f2(x78331)))+~P4(f333(f333(f250(x78331),x78334),x78333))+P4(f333(f333(f250(x78331),f333(f333(f82(x78331),x78332),x78333)),f333(f333(f82(x78331),x78332),x78334))) % 191.49/191.42 [7834]~P124(x78341)+~P4(f333(f333(f251(x78341),x78342),f2(x78341)))+~P4(f333(f333(f250(x78341),x78344),x78343))+P4(f333(f333(f250(x78341),f333(f333(f82(x78341),x78342),x78343)),f333(f333(f82(x78341),x78342),x78344))) % 191.49/191.42 [7835]~P126(x78351)+~P4(f333(f333(f250(x78351),x78353),f2(x78351)))+~P4(f333(f333(f250(x78351),x78354),x78352))+P4(f333(f333(f250(x78351),f333(f333(f82(x78351),x78352),x78353)),f333(f333(f82(x78351),x78354),x78353))) % 191.49/191.42 [7836]~P65(x78361)+~P4(f333(f333(f250(x78361),x78363),f2(x78361)))+~P4(f333(f333(f250(x78361),x78364),x78362))+P4(f333(f333(f250(x78361),f333(f333(f291(x78361),x78362),x78363)),f333(f333(f291(x78361),x78364),x78363))) % 191.49/191.42 [7838]~P123(x78381)+~P4(f333(f333(f251(x78381),f79(x78381)),x78382))+~P4(f333(f333(f251(a880),x78383),x78384))+P4(f333(f333(f251(x78381),f333(f333(f264(x78381),x78382),x78383)),f333(f333(f264(x78381),x78382),x78384))) % 191.49/191.42 [7839]~P123(x78391)+~P4(f333(f333(f251(x78391),f79(x78391)),x78392))+~P4(f333(f333(f250(a880),x78393),x78394))+P4(f333(f333(f250(x78391),f333(f333(f264(x78391),x78392),x78393)),f333(f333(f264(x78391),x78392),x78394))) % 191.49/191.42 [7840]~P123(x78401)+~P4(f333(f333(f250(x78401),f79(x78401)),x78402))+~P4(f333(f333(f250(a880),x78403),x78404))+P4(f333(f333(f250(x78401),f333(f333(f264(x78401),x78402),x78403)),f333(f333(f264(x78401),x78402),x78404))) % 191.49/191.42 [7862]P4(f333(f333(f251(a880),f2(a880)),f333(x78621,x78622)))+~P4(f333(f63(x78623),x78624))+~P4(f333(f333(f335(x78623),x78622),x78624))+~P4(f333(f333(f251(a880),f2(a880)),f333(f333(f11(x78623,a880),x78621),x78624))) % 191.49/191.42 [7872]~P121(x78721)+~P4(f333(f333(f251(x78721),x78723),x78724))+~P4(f333(f333(f251(x78721),f2(x78721)),x78722))+P4(f333(f333(f251(x78721),f333(f333(f82(x78721),x78722),x78723)),f333(f333(f82(x78721),x78722),x78724))) % 191.49/191.42 [7873]~P129(x78731)+~P4(f333(f333(f251(x78731),x78733),x78734))+~P4(f333(f333(f251(x78731),f2(x78731)),x78732))+P4(f333(f333(f251(x78731),f333(f333(f82(x78731),x78732),x78733)),f333(f333(f82(x78731),x78732),x78734))) % 191.49/191.42 [7874]~P124(x78741)+~P4(f333(f333(f251(x78741),x78742),x78744))+~P4(f333(f333(f251(x78741),f2(x78741)),x78743))+P4(f333(f333(f251(x78741),f333(f333(f82(x78741),x78742),x78743)),f333(f333(f82(x78741),x78744),x78743))) % 191.49/191.42 [7875]~P129(x78751)+~P4(f333(f333(f251(x78751),x78752),x78754))+~P4(f333(f333(f251(x78751),f2(x78751)),x78753))+P4(f333(f333(f251(x78751),f333(f333(f82(x78751),x78752),x78753)),f333(f333(f82(x78751),x78754),x78753))) % 191.49/191.42 [7876]~P124(x78761)+~P4(f333(f333(f251(x78761),x78763),x78764))+~P4(f333(f333(f251(x78761),f2(x78761)),x78762))+P4(f333(f333(f251(x78761),f333(f333(f82(x78761),x78762),x78763)),f333(f333(f82(x78761),x78762),x78764))) % 191.49/191.42 [7877]~P66(x78771)+~P4(f333(f333(f251(x78771),x78772),x78774))+~P4(f333(f333(f251(x78771),f2(x78771)),x78773))+P4(f333(f333(f251(x78771),f333(f333(f291(x78771),x78772),x78773)),f333(f333(f291(x78771),x78774),x78773))) % 191.49/191.42 [7878]~P124(x78781)+~P4(f333(f333(f251(x78781),f2(x78781)),x78782))+~P4(f333(f333(f250(x78781),x78783),x78784))+P4(f333(f333(f250(x78781),f333(f333(f82(x78781),x78782),x78783)),f333(f333(f82(x78781),x78782),x78784))) % 191.49/191.42 [7879]~P135(x78791)+~P4(f333(f333(f250(x78791),x78793),x78794))+~P4(f333(f333(f250(x78791),f2(x78791)),x78792))+P4(f333(f333(f250(x78791),f333(f333(f82(x78791),x78792),x78793)),f333(f333(f82(x78791),x78792),x78794))) % 191.49/191.42 [7880]~P134(x78801)+~P4(f333(f333(f250(x78801),x78803),x78804))+~P4(f333(f333(f250(x78801),f2(x78801)),x78802))+P4(f333(f333(f250(x78801),f333(f333(f82(x78801),x78802),x78803)),f333(f333(f82(x78801),x78802),x78804))) % 191.49/191.42 [7881]~P135(x78811)+~P4(f333(f333(f250(x78811),x78812),x78814))+~P4(f333(f333(f250(x78811),f2(x78811)),x78813))+P4(f333(f333(f250(x78811),f333(f333(f82(x78811),x78812),x78813)),f333(f333(f82(x78811),x78814),x78813))) % 191.49/191.42 [7882]~P65(x78821)+~P4(f333(f333(f250(x78821),x78822),x78824))+~P4(f333(f333(f250(x78821),f2(x78821)),x78823))+P4(f333(f333(f250(x78821),f333(f333(f291(x78821),x78822),x78823)),f333(f333(f291(x78821),x78824),x78823))) % 191.49/191.42 [7883]~P123(x78831)+~P4(f333(f333(f250(x78831),x78832),x78834))+~P4(f333(f333(f250(x78831),f2(x78831)),x78832))+P4(f333(f333(f250(x78831),f333(f333(f264(x78831),x78832),x78833)),f333(f333(f264(x78831),x78834),x78833))) % 191.49/191.42 [7921]~P111(x79212)+P4(f333(f333(f250(f890(x79211,x79212)),x79214),x79213))+~P4(f333(f333(f250(f890(x79211,x79212)),x79213),x79214))+P4(f333(f333(f251(f890(x79211,x79212)),x79213),x79214)) % 191.49/191.42 [7962]P4(f333(f333(f335(x79621),x79622),x79623))+P4(f333(f333(f335(x79621),x79622),x79624))+~P4(f333(f333(f250(f890(x79621,a874)),x79624),x79623))+P4(f333(f333(f251(f890(x79621,a874)),x79624),f333(f333(f311(x79621),x79622),x79623))) % 191.49/191.42 [8130]P4(f333(f333(f335(x81301),x81302),x81303))+P4(f333(f333(f335(x81301),x81302),x81304))+~P4(f333(f333(f251(f890(x81301,a874)),x81304),f333(f333(f311(x81301),x81302),x81303)))+P4(f333(f333(f250(f890(x81301,a874)),x81304),x81303)) % 191.49/191.42 [8139]~P62(x81391)+P13(x81391,x81392,x81393)+~P4(f333(x81392,x81394))+~P4(f333(f333(f335(f881(x81391)),x81394),f333(f173(f881(x81391)),f56(x81391,x81393,f57(x81391))))) % 191.49/191.42 [8149]~P14(x81493,x81491,x81494)+~P62(x81493)+P4(f333(x81491,x81492))+~P4(f333(f333(f335(f881(x81493)),x81492),f333(f173(f881(x81493)),f56(x81493,x81494,f57(x81493))))) % 191.49/191.42 [8203]~P124(x82031)+P4(f333(f333(f251(x82031),x82033),x82032))+P4(f333(f333(f251(x82031),x82032),x82033))+~P4(f333(f333(f251(x82031),f333(f333(f82(x82031),x82034),x82032)),f333(f333(f82(x82031),x82034),x82033))) % 191.49/191.42 [8204]~P124(x82041)+P4(f333(f333(f251(x82041),x82043),x82042))+P4(f333(f333(f251(x82041),x82042),x82043))+~P4(f333(f333(f251(x82041),f333(f333(f82(x82041),x82042),x82044)),f333(f333(f82(x82041),x82043),x82044))) % 191.49/191.42 [8213]~P124(x82131)+P4(f333(f333(f251(x82131),x82134),f2(x82131)))+P4(f333(f333(f251(x82131),x82132),x82133))+~P4(f333(f333(f251(x82131),f333(f333(f82(x82131),x82132),x82134)),f333(f333(f82(x82131),x82133),x82134))) % 191.49/191.42 [8214]~P124(x82141)+P4(f333(f333(f251(x82141),x82144),f2(x82141)))+P4(f333(f333(f251(x82141),x82142),x82143))+~P4(f333(f333(f251(x82141),f333(f333(f82(x82141),x82144),x82142)),f333(f333(f82(x82141),x82144),x82143))) % 191.49/191.42 [8218]~P124(x82181)+P4(f333(f333(f251(x82181),x82182),x82183))+P4(f333(f333(f251(x82181),f2(x82181)),x82184))+~P4(f333(f333(f251(x82181),f333(f333(f82(x82181),x82184),x82183)),f333(f333(f82(x82181),x82184),x82182))) % 191.49/191.42 [8219]~P124(x82191)+P4(f333(f333(f251(x82191),x82192),x82193))+P4(f333(f333(f251(x82191),f2(x82191)),x82194))+~P4(f333(f333(f251(x82191),f333(f333(f82(x82191),x82193),x82194)),f333(f333(f82(x82191),x82192),x82194))) % 191.49/191.42 [8231]~P124(x82311)+P4(f333(f333(f251(x82311),x82312),f2(x82311)))+P4(f333(f333(f251(x82311),f2(x82311)),x82312))+~P4(f333(f333(f251(x82311),f333(f333(f82(x82311),x82313),x82312)),f333(f333(f82(x82311),x82314),x82312))) % 191.49/191.42 [8232]~P124(x82321)+P4(f333(f333(f251(x82321),x82322),f2(x82321)))+P4(f333(f333(f251(x82321),f2(x82321)),x82322))+~P4(f333(f333(f251(x82321),f333(f333(f82(x82321),x82322),x82323)),f333(f333(f82(x82321),x82322),x82324))) % 191.49/191.42 [8258]~P124(x82581)+~P4(f333(f333(f251(x82581),x82584),f2(x82581)))+P4(f333(f333(f251(x82581),x82582),x82583))+~P4(f333(f333(f251(x82581),f333(f333(f82(x82581),x82584),x82583)),f333(f333(f82(x82581),x82584),x82582))) % 191.49/191.42 [8259]~P124(x82591)+~P4(f333(f333(f251(x82591),x82594),f2(x82591)))+P4(f333(f333(f250(x82591),x82592),x82593))+~P4(f333(f333(f250(x82591),f333(f333(f82(x82591),x82594),x82593)),f333(f333(f82(x82591),x82594),x82592))) % 191.49/191.42 [8271]~P123(x82713)+~P4(f333(f333(f251(x82713),f79(x82713)),x82714))+P4(f333(f333(f251(a880),x82711),x82712))+~P4(f333(f333(f251(x82713),f333(f333(f264(x82713),x82714),x82711)),f333(f333(f264(x82713),x82714),x82712))) % 191.49/191.42 [8273]~P123(x82733)+~P4(f333(f333(f251(x82733),f79(x82733)),x82734))+P4(f333(f333(f250(a880),x82731),x82732))+~P4(f333(f333(f250(x82733),f333(f333(f264(x82733),x82734),x82731)),f333(f333(f264(x82733),x82734),x82732))) % 191.49/191.42 [8283]~P124(x82831)+P4(f333(f333(f251(x82831),x82832),x82833))+~P4(f333(f333(f251(x82831),f2(x82831)),x82834))+~P4(f333(f333(f251(x82831),f333(f333(f82(x82831),x82834),x82832)),f333(f333(f82(x82831),x82834),x82833))) % 191.49/191.42 [8284]~P129(x82841)+P4(f333(f333(f251(x82841),x82842),x82843))+~P4(f333(f333(f250(x82841),f2(x82841)),x82844))+~P4(f333(f333(f251(x82841),f333(f333(f82(x82841),x82844),x82842)),f333(f333(f82(x82841),x82844),x82843))) % 191.49/191.42 [8285]~P130(x82851)+P4(f333(f333(f251(x82851),x82852),x82853))+~P4(f333(f333(f250(x82851),f2(x82851)),x82854))+~P4(f333(f333(f251(x82851),f333(f333(f82(x82851),x82854),x82852)),f333(f333(f82(x82851),x82854),x82853))) % 191.49/191.42 [8286]~P123(x82861)+~P4(f333(f333(f250(x82861),f2(x82861)),x82863))+P4(f333(f333(f251(x82861),x82862),x82863))+~P4(f333(f333(f251(x82861),f333(f333(f264(x82861),x82862),x82864)),f333(f333(f264(x82861),x82863),x82864))) % 191.49/191.42 [8287]~P129(x82871)+P4(f333(f333(f251(x82871),x82872),x82873))+~P4(f333(f333(f250(x82871),f2(x82871)),x82874))+~P4(f333(f333(f251(x82871),f333(f333(f82(x82871),x82872),x82874)),f333(f333(f82(x82871),x82873),x82874))) % 191.49/191.42 [8288]~P130(x82881)+P4(f333(f333(f251(x82881),x82882),x82883))+~P4(f333(f333(f250(x82881),f2(x82881)),x82884))+~P4(f333(f333(f251(x82881),f333(f333(f82(x82881),x82882),x82884)),f333(f333(f82(x82881),x82883),x82884))) % 191.49/191.42 [8289]~P124(x82891)+P4(f333(f333(f250(x82891),x82892),x82893))+~P4(f333(f333(f251(x82891),f2(x82891)),x82894))+~P4(f333(f333(f250(x82891),f333(f333(f82(x82891),x82894),x82892)),f333(f333(f82(x82891),x82894),x82893))) % 191.49/191.42 [8290]~P129(x82901)+P4(f333(f333(f250(x82901),x82902),x82903))+~P4(f333(f333(f251(x82901),f2(x82901)),x82904))+~P4(f333(f333(f250(x82901),f333(f333(f82(x82901),x82904),x82902)),f333(f333(f82(x82901),x82904),x82903))) % 191.49/191.42 [8291]~P129(x82911)+P4(f333(f333(f250(x82911),x82912),x82913))+~P4(f333(f333(f251(x82911),f2(x82911)),x82914))+~P4(f333(f333(f250(x82911),f333(f333(f82(x82911),x82912),x82914)),f333(f333(f82(x82911),x82913),x82914))) % 191.49/191.42 [8331]P4(f333(f333(f335(x83311),x83312),x83313))+~P4(f333(f333(f250(f890(x83311,a874)),x83313),x83314))+~P4(f333(f333(f251(f890(x83311,a874)),x83313),x83314))+P4(f333(f333(f251(f890(x83311,a874)),x83313),f333(f333(f311(x83311),x83312),x83314))) % 191.49/191.42 [8590]~P62(x85901)+~P96(x85902)+~E(f333(x85903,f817(x85904,x85903,x85901,x85902)),f333(x85904,f817(x85904,x85903,x85901,x85902)))+P4(f333(f333(f92(f890(x85901,x85902)),x85903),x85904)) % 191.49/191.42 [8695]E(f333(f333(f3(a1),f441(x86951,x86952,x86953,x86954)),f442(x86951,x86952,x86953,x86954)),x86954)+~P4(f333(f333(f251(a1),f2(a1)),x86953))+~P4(f333(f333(f250(a1),x86951),x86954))+P4(f333(f333(f250(a1),x86951),f333(f333(f81(a1),x86954),x86953))) % 191.49/191.42 [8696]E(f333(f333(f3(a1),f448(x86961,x86962,x86963,x86964)),f449(x86961,x86962,x86963,x86964)),x86964)+~P4(f333(f333(f251(a1),f2(a1)),x86963))+~P4(f333(f333(f251(a1),x86961),x86964))+P4(f333(f333(f251(a1),x86961),f333(f333(f81(a1),x86964),x86963))) % 191.49/191.42 [8836]~E(f333(f333(f166(x88361),x88363),f643(x88364,x88363,x88361,x88362)),f333(f333(f166(x88361),x88364),f643(x88364,x88363,x88361,x88362)))+E(f333(f333(f174(x88361),x88362),x88363),f333(f333(f174(x88361),x88362),x88364))+~P4(f333(f333(f250(a880),x88362),f333(f195(f881(x88361)),x88363)))+~P4(f333(f333(f250(a880),x88362),f333(f195(f881(x88361)),x88364))) % 191.49/191.42 [8908]~P4(f333(f333(f251(a1),f2(a1)),x89083))+~P4(f333(f333(f250(a1),x89081),x89084))+P4(f333(f333(f335(a1),f441(x89081,x89082,x89083,x89084)),x89082))+P4(f333(f333(f250(a1),x89081),f333(f333(f81(a1),x89084),x89083))) % 191.49/191.42 [8909]~P4(f333(f333(f251(a1),f2(a1)),x89093))+~P4(f333(f333(f251(a1),x89091),x89094))+P4(f333(f333(f335(a1),f448(x89091,x89092,x89093,x89094)),x89092))+P4(f333(f333(f251(a1),x89091),f333(f333(f81(a1),x89094),x89093))) % 191.49/191.42 [8951]~P102(x89511)+~P4(f333(f63(x89511),x89513))+~P4(f333(f333(f335(x89511),x89514),x89513))+P4(f333(f333(f250(x89511),f333(f333(f66(x89511,x89511,f106(x89511)),x89512),x89513)),f333(f333(f106(x89511),x89514),x89512))) % 191.49/191.42 [8952]~P109(x89521)+~P4(f333(f63(x89521),x89523))+~P4(f333(f333(f335(x89521),x89524),x89523))+P4(f333(f333(f250(x89521),f333(f333(f66(x89521,x89521,f248(x89521)),x89522),x89523)),f333(f333(f248(x89521),x89524),x89522))) % 191.49/191.42 [8997]E(f333(f333(f174(x89971),x89972),x89973),f333(f333(f174(x89971),x89972),x89974))+P4(f333(f333(f251(a880),f643(x89973,x89974,x89971,x89972)),x89972))+~P4(f333(f333(f250(a880),x89972),f333(f195(f881(x89971)),x89973)))+~P4(f333(f333(f250(a880),x89972),f333(f195(f881(x89971)),x89974))) % 191.49/191.42 [9002]~P4(f333(f333(f251(a1),f2(a1)),x90023))+~P4(f333(f333(f251(a1),x90021),x90022))+P4(f333(f333(f335(a1),f449(x90021,x90024,x90023,x90022)),f304(a1,f79(a1),x90023)))+P4(f333(f333(f251(a1),x90021),f333(f333(f81(a1),x90022),x90023))) % 191.49/191.42 [9003]~P4(f333(f333(f251(a1),f2(a1)),x90033))+~P4(f333(f333(f250(a1),x90031),x90032))+P4(f333(f333(f335(a1),f442(x90031,x90034,x90033,x90032)),f304(a1,f79(a1),x90033)))+P4(f333(f333(f250(a1),x90031),f333(f333(f81(a1),x90032),x90033))) % 191.49/191.42 [9163]~E(f333(f178(x91631,x91632),x91633),f333(f178(x91631,x91632),x91634))+E(f333(f173(f889(x91631,x91632)),x91633),f333(f173(f889(x91631,x91632)),x91634))+~P4(f333(f138(x91631),f333(f333(f155(f889(x91631,x91632),x91631),f262(x91631,x91632)),x91634)))+~P4(f333(f138(x91631),f333(f333(f155(f889(x91631,x91632),x91631),f262(x91631,x91632)),x91633))) % 191.49/191.42 [9175]E(f333(f178(x91751,x91752),x91753),f333(f178(x91751,x91752),x91754))+~E(f333(f173(f889(x91751,x91752)),x91753),f333(f173(f889(x91751,x91752)),x91754))+~P4(f333(f138(x91751),f333(f333(f155(f889(x91751,x91752),x91751),f262(x91751,x91752)),x91754)))+~P4(f333(f138(x91751),f333(f333(f155(f889(x91751,x91752),x91751),f262(x91751,x91752)),x91753))) % 191.49/191.42 [9319]~P101(x93191)+~P4(f333(f63(x93191),x93194))+P4(f333(f333(f335(x93191),f383(x93192,x93193,x93194,x93191)),x93194))+P4(f333(f333(f250(x93191),f333(f333(f66(x93191,x93191,f115(x93191)),x93192),x93194)),f333(f333(f115(x93191),x93193),x93192))) % 191.49/191.42 [9320]~P109(x93201)+~P4(f333(f63(x93201),x93204))+P4(f333(f333(f335(x93201),f491(x93202,x93203,x93204,x93201)),x93204))+P4(f333(f333(f250(x93201),f333(f333(f66(x93201,x93201,f249(x93201)),x93202),x93204)),f333(f333(f249(x93201),x93203),x93202))) % 191.49/191.42 [9439]~P101(x94391)+~P4(f333(f63(x94391),x94393))+~P4(f333(f333(f250(x94391),f383(x94392,x94394,x94393,x94391)),x94394))+P4(f333(f333(f250(x94391),f333(f333(f66(x94391,x94391,f115(x94391)),x94392),x94393)),f333(f333(f115(x94391),x94394),x94392))) % 191.49/191.42 [9440]~P109(x94401)+~P4(f333(f63(x94401),x94403))+~P4(f333(f333(f250(x94401),f491(x94402,x94404,x94403,x94401)),x94404))+P4(f333(f333(f250(x94401),f333(f333(f66(x94401,x94401,f249(x94401)),x94402),x94403)),f333(f333(f249(x94401),x94404),x94402))) % 191.49/191.42 [9443]~P4(f333(f333(f251(a1),f2(a1)),x94433))+~P4(f333(f333(f250(a1),f2(a1)),x94434))+~P4(f333(f333(f251(a1),x94434),x94431))+P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f82(a1),x94431),f46(a1,x94432,x94433))),x94434)),f333(f333(f82(a1),x94431),x94433))) % 191.49/191.42 [9869]E(x98691,x98692)+P4(f333(f333(f335(f889(f881(x98693),f881(x98693))),f333(f333(f263(f881(x98693),f881(x98693)),x98692),x98691)),f148(x98693,x98694)))+P4(f333(f333(f335(f889(f881(x98693),f881(x98693))),f333(f333(f263(f881(x98693),f881(x98693)),x98691),x98692)),f148(x98693,x98694)))+~P4(f333(f333(f335(f889(x98693,x98693)),f333(f333(f263(x98693,x98693),f637(x98691,x98692,x98694,x98693)),f641(x98691,x98692,x98694,x98693))),x98694)) % 191.49/191.42 [9870]E(x98701,x98702)+P4(f333(f333(f335(f889(f881(x98703),f881(x98703))),f333(f333(f263(f881(x98703),f881(x98703)),x98702),x98701)),f148(x98703,x98704)))+P4(f333(f333(f335(f889(f881(x98703),f881(x98703))),f333(f333(f263(f881(x98703),f881(x98703)),x98701),x98702)),f148(x98703,x98704)))+~P4(f333(f333(f335(f889(x98703,x98703)),f333(f333(f263(x98703,x98703),f641(x98701,x98702,x98704,x98703)),f637(x98701,x98702,x98704,x98703))),x98704)) % 191.49/191.42 [7419]~P109(x74191)+~P4(f333(f333(f251(x74191),x74193),x74194))+~P4(f333(f333(f251(x74191),x74192),x74194))+P4(f333(f333(f251(x74191),f333(f333(f249(x74191),x74192),x74193)),x74194)) % 191.49/191.42 [7422]~P101(x74221)+~P4(f333(f333(f250(x74221),x74223),x74224))+~P4(f333(f333(f250(x74221),x74222),x74224))+P4(f333(f333(f250(x74221),f333(f333(f115(x74221),x74222),x74223)),x74224)) % 191.49/191.42 [7425]~P109(x74251)+~P4(f333(f333(f250(x74251),x74253),x74254))+~P4(f333(f333(f250(x74251),x74252),x74254))+P4(f333(f333(f250(x74251),f333(f333(f249(x74251),x74252),x74253)),x74254)) % 191.49/191.42 [7737]~E(x77371,x77373)+E(f140(a880,f333(f303(a880,x77371),x77372)),f333(f333(f152(a880),x77373),x77374))+~E(f140(a880,f333(f303(a880,f333(f333(f81(a880),x77371),f79(a880))),x77372)),x77374)+~P4(f333(f333(f251(a880),x77371),x77372)) % 191.49/191.42 [7749]~P109(x77491)+P4(f333(f333(f251(x77491),x77492),x77493))+P4(f333(f333(f251(x77491),x77494),x77493))+~P4(f333(f333(f251(x77491),f333(f333(f248(x77491),x77494),x77492)),x77493)) % 191.49/191.42 [7750]~P109(x77501)+P4(f333(f333(f250(x77501),x77502),x77503))+P4(f333(f333(f250(x77501),x77504),x77503))+~P4(f333(f333(f250(x77501),f333(f333(f248(x77501),x77504),x77502)),x77503)) % 191.49/191.42 [8023]~P65(x80231)+~P4(f333(f333(f251(x80231),f2(x80231)),x80233))+~P4(f333(f333(f251(x80231),x80232),f333(f333(f291(x80231),x80234),x80233)))+P4(f333(f333(f251(x80231),f333(f333(f82(x80231),x80232),x80233)),x80234)) % 191.49/191.42 [8024]~P66(x80241)+~P4(f333(f333(f251(x80241),f2(x80241)),x80243))+~P4(f333(f333(f251(x80241),x80242),f333(f333(f291(x80241),x80244),x80243)))+P4(f333(f333(f251(x80241),f333(f333(f82(x80241),x80242),x80243)),x80244)) % 191.49/191.42 [8026]~P65(x80261)+~P4(f333(f333(f251(x80261),f2(x80261)),x80263))+~P4(f333(f333(f251(x80261),x80262),f333(f333(f82(x80261),x80264),x80263)))+P4(f333(f333(f251(x80261),f333(f333(f291(x80261),x80262),x80263)),x80264)) % 191.49/191.42 [8027]~P66(x80271)+~P4(f333(f333(f251(x80271),f2(x80271)),x80273))+~P4(f333(f333(f251(x80271),x80272),f333(f333(f82(x80271),x80274),x80273)))+P4(f333(f333(f251(x80271),f333(f333(f291(x80271),x80272),x80273)),x80274)) % 191.49/191.42 [8028]~P65(x80281)+~P4(f333(f333(f251(x80281),f2(x80281)),x80283))+~P4(f333(f333(f250(x80281),x80282),f333(f333(f291(x80281),x80284),x80283)))+P4(f333(f333(f250(x80281),f333(f333(f82(x80281),x80282),x80283)),x80284)) % 191.49/191.42 [8029]~P66(x80291)+~P4(f333(f333(f251(x80291),f2(x80291)),x80293))+~P4(f333(f333(f250(x80291),x80292),f333(f333(f291(x80291),x80294),x80293)))+P4(f333(f333(f250(x80291),f333(f333(f82(x80291),x80292),x80293)),x80294)) % 191.49/191.42 [8031]~P65(x80311)+~P4(f333(f333(f251(x80311),f2(x80311)),x80313))+~P4(f333(f333(f250(x80311),x80312),f333(f333(f82(x80311),x80314),x80313)))+P4(f333(f333(f250(x80311),f333(f333(f291(x80311),x80312),x80313)),x80314)) % 191.49/191.42 [8032]~P66(x80321)+~P4(f333(f333(f251(x80321),f2(x80321)),x80323))+~P4(f333(f333(f250(x80321),x80322),f333(f333(f82(x80321),x80324),x80323)))+P4(f333(f333(f250(x80321),f333(f333(f291(x80321),x80322),x80323)),x80324)) % 191.49/191.42 [8171]~P65(x81711)+~P4(f333(f333(f251(x81711),f2(x81711)),x81714))+P4(f333(f333(f251(x81711),x81712),f333(f333(f82(x81711),x81713),x81714)))+~P4(f333(f333(f251(x81711),f333(f333(f291(x81711),x81712),x81714)),x81713)) % 191.49/191.42 [8173]~P65(x81731)+~P4(f333(f333(f251(x81731),f2(x81731)),x81734))+P4(f333(f333(f251(x81731),x81732),f333(f333(f291(x81731),x81733),x81734)))+~P4(f333(f333(f251(x81731),f333(f333(f82(x81731),x81732),x81734)),x81733)) % 191.49/191.42 [8174]~P66(x81741)+~P4(f333(f333(f251(x81741),f2(x81741)),x81744))+P4(f333(f333(f251(x81741),x81742),f333(f333(f82(x81741),x81743),x81744)))+~P4(f333(f333(f251(x81741),f333(f333(f291(x81741),x81742),x81744)),x81743)) % 191.49/191.42 [8175]~P66(x81751)+~P4(f333(f333(f251(x81751),f2(x81751)),x81754))+P4(f333(f333(f251(x81751),x81752),f333(f333(f291(x81751),x81753),x81754)))+~P4(f333(f333(f251(x81751),f333(f333(f82(x81751),x81752),x81754)),x81753)) % 191.49/191.42 [8176]~P65(x81761)+~P4(f333(f333(f251(x81761),f2(x81761)),x81764))+P4(f333(f333(f250(x81761),x81762),f333(f333(f82(x81761),x81763),x81764)))+~P4(f333(f333(f250(x81761),f333(f333(f291(x81761),x81762),x81764)),x81763)) % 191.49/191.42 [8178]~P65(x81781)+~P4(f333(f333(f251(x81781),f2(x81781)),x81784))+P4(f333(f333(f250(x81781),x81782),f333(f333(f291(x81781),x81783),x81784)))+~P4(f333(f333(f250(x81781),f333(f333(f82(x81781),x81782),x81784)),x81783)) % 191.49/191.42 [8179]~P66(x81791)+~P4(f333(f333(f251(x81791),f2(x81791)),x81794))+P4(f333(f333(f250(x81791),x81792),f333(f333(f82(x81791),x81793),x81794)))+~P4(f333(f333(f250(x81791),f333(f333(f291(x81791),x81792),x81794)),x81793)) % 191.49/191.42 [8180]~P66(x81801)+~P4(f333(f333(f251(x81801),f2(x81801)),x81804))+P4(f333(f333(f250(x81801),x81802),f333(f333(f291(x81801),x81803),x81804)))+~P4(f333(f333(f250(x81801),f333(f333(f82(x81801),x81802),x81804)),x81803)) % 191.49/191.42 [8335]~P66(x83351)+~P4(f333(f333(f251(x83351),x83353),f2(x83351)))+~P4(f333(f333(f251(x83351),f333(f333(f291(x83351),x83354),x83353)),x83352))+P4(f333(f333(f251(x83351),f333(f333(f82(x83351),x83352),x83353)),x83354)) % 191.49/191.42 [8336]~P66(x83361)+~P4(f333(f333(f251(x83361),x83363),f2(x83361)))+~P4(f333(f333(f251(x83361),f333(f333(f82(x83361),x83364),x83363)),x83362))+P4(f333(f333(f251(x83361),f333(f333(f291(x83361),x83362),x83363)),x83364)) % 191.49/191.42 [8337]~P66(x83371)+~P4(f333(f333(f251(x83371),x83373),f2(x83371)))+~P4(f333(f333(f250(x83371),f333(f333(f291(x83371),x83374),x83373)),x83372))+P4(f333(f333(f250(x83371),f333(f333(f82(x83371),x83372),x83373)),x83374)) % 191.49/191.42 [8338]~P66(x83381)+~P4(f333(f333(f251(x83381),x83383),f2(x83381)))+~P4(f333(f333(f250(x83381),f333(f333(f82(x83381),x83384),x83383)),x83382))+P4(f333(f333(f250(x83381),f333(f333(f291(x83381),x83382),x83383)),x83384)) % 191.49/191.42 [8348]~P4(f333(x83481,x83484))+~P4(f333(f333(f251(a880),x83482),f333(f333(f82(a880),x83483),f333(a117,x83484))))+P4(f333(x83481,f333(f333(f40(a880),x83482),x83483)))+~P4(f333(f333(f250(a880),f333(f333(f82(a880),x83483),x83484)),x83482)) % 191.49/191.42 [8564]~P101(x85641)+~P4(f333(f63(x85641),x85644))+~P4(f333(f333(f335(x85641),x85642),x85644))+P4(f333(f333(f250(x85641),f333(f333(f115(x85641),x85642),x85643)),f333(f333(f66(x85641,x85641,f115(x85641)),x85643),x85644))) % 191.49/191.42 [8565]~P109(x85651)+~P4(f333(f63(x85651),x85654))+~P4(f333(f333(f335(x85651),x85652),x85654))+P4(f333(f333(f250(x85651),f333(f333(f249(x85651),x85652),x85653)),f333(f333(f66(x85651,x85651,f249(x85651)),x85653),x85654))) % 191.49/191.42 [8697]~P4(f333(f63(x86971),x86972))+E(f333(f39(x86971),f333(f333(f3(f890(x86971,a874)),x86972),f333(f333(f311(x86971),x86973),x86974))),f333(f333(f3(a880),f333(f39(x86971),f333(f333(f3(f890(x86971,a874)),x86972),x86974))),f79(a880)))+P4(f333(f333(f335(x86971),x86973),x86974))+~P4(f333(f333(f335(x86971),x86973),x86972)) % 191.49/191.42 [8767]E(f333(f333(f81(a1),f443(x87671,x87672,x87673,x87674)),f444(x87671,x87672,x87673,x87674)),x87674)+~P4(f333(f333(f251(a1),f2(a1)),x87673))+~P4(f333(f333(f250(a1),x87674),x87671))+P4(f333(f333(f250(a1),f333(f333(f3(a1),x87674),x87673)),x87671)) % 191.49/191.42 [8768]E(f333(f333(f81(a1),f456(x87681,x87682,x87683,x87684)),f457(x87681,x87682,x87683,x87684)),x87684)+~P4(f333(f333(f251(a1),f2(a1)),x87683))+~P4(f333(f333(f251(a1),x87684),x87681))+P4(f333(f333(f251(a1),f333(f333(f3(a1),x87684),x87683)),x87681)) % 191.49/191.42 [8982]~P4(f333(f333(f251(a1),f2(a1)),x89823))+~P4(f333(f333(f250(a1),x89824),x89821))+P4(f333(f333(f335(a1),f443(x89821,x89822,x89823,x89824)),x89822))+P4(f333(f333(f250(a1),f333(f333(f3(a1),x89824),x89823)),x89821)) % 191.49/191.42 [8983]~P4(f333(f333(f251(a1),f2(a1)),x89833))+~P4(f333(f333(f251(a1),x89834),x89831))+P4(f333(f333(f335(a1),f456(x89831,x89832,x89833,x89834)),x89832))+P4(f333(f333(f251(a1),f333(f333(f3(a1),x89834),x89833)),x89831)) % 191.49/191.42 [9055]~P4(f333(f333(f251(a1),f2(a1)),x90552))+~P4(f333(f333(f251(a1),x90551),x90553))+P4(f333(f333(f335(a1),f457(x90553,x90554,x90552,x90551)),f304(a1,f79(a1),x90552)))+P4(f333(f333(f251(a1),f333(f333(f3(a1),x90551),x90552)),x90553)) % 191.49/191.42 [9056]~P4(f333(f333(f251(a1),f2(a1)),x90562))+~P4(f333(f333(f250(a1),x90561),x90563))+P4(f333(f333(f335(a1),f444(x90563,x90564,x90562,x90561)),f304(a1,f79(a1),x90562)))+P4(f333(f333(f250(a1),f333(f333(f3(a1),x90561),x90562)),x90563)) % 191.49/191.42 [9071]~P4(f333(f333(f251(a1),f2(a1)),x90713))+~P4(f333(f333(f250(a1),f2(a1)),x90714))+~P4(f333(f333(f251(a1),x90714),x90711))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f81(a1),f333(f333(f82(a1),x90711),f46(a1,x90712,x90713))),x90714))) % 191.49/191.42 [9146]~P102(x91461)+~P4(f333(f63(x91461),x91464))+~P4(f333(f333(f250(x91461),x91462),f381(x91463,x91462,x91464,x91461)))+P4(f333(f333(f250(x91461),f333(f333(f106(x91461),x91462),x91463)),f333(f333(f66(x91461,x91461,f106(x91461)),x91463),x91464))) % 191.49/191.42 [9147]~P109(x91471)+~P4(f333(f63(x91471),x91474))+~P4(f333(f333(f250(x91471),x91472),f478(x91473,x91472,x91474,x91471)))+P4(f333(f333(f250(x91471),f333(f333(f248(x91471),x91472),x91473)),f333(f333(f66(x91471,x91471,f248(x91471)),x91473),x91474))) % 191.49/191.42 [9162]~P4(f333(f333(f250(a1),x91624),f2(a1)))+~P4(f333(f333(f251(a1),f2(a1)),x91622))+~P4(f333(f333(f251(a1),x91621),x91624))+P4(f333(f333(f251(a1),f333(f333(f82(a1),x91621),x91622)),f333(f333(f81(a1),f333(f333(f82(a1),x91621),f46(a1,x91623,x91622))),x91624))) % 191.49/191.42 [9184]P4(f333(f63(x91841),x91842))+~P4(f333(f63(x91841),x91843))+~P4(f333(f333(f335(f890(x91841,a874)),x91842),f333(f333(f62(x91841),x91843),x91844)))+~P4(f333(f333(f250(f890(f889(x91841,x91841),a874)),x91844),f333(f333(f270(x91841,x91841),x91843),f333(f18(f890(x91841,a874),x91841),x91843)))) % 191.49/191.42 [9210]~P102(x92101)+~P4(f333(f63(x92101),x92104))+P4(f333(f333(f335(x92101),f381(x92102,x92103,x92104,x92101)),x92104))+P4(f333(f333(f250(x92101),f333(f333(f106(x92101),x92103),x92102)),f333(f333(f66(x92101,x92101,f106(x92101)),x92102),x92104))) % 191.49/191.42 [9211]~P109(x92111)+~P4(f333(f63(x92111),x92114))+P4(f333(f333(f335(x92111),f478(x92112,x92113,x92114,x92111)),x92114))+P4(f333(f333(f250(x92111),f333(f333(f248(x92111),x92113),x92112)),f333(f333(f66(x92111,x92111,f248(x92111)),x92112),x92114))) % 191.49/191.42 [9630]~P4(f333(f63(x96302),x96304))+~P4(f333(f63(x96301),x96303))+~P4(f333(f333(f250(a880),f333(f39(x96302),x96304)),f333(f39(x96301),x96303)))+P4(f333(f333(f250(f890(x96301,a874)),f333(f312(x96302,x96301,f365(x96303,x96301,x96304,x96302)),x96304)),x96303)) % 191.49/191.42 [9257]~P4(f333(f333(f335(x92571),x92572),x92574))+P4(f333(f333(f335(x92571),x92572),x92573))+~P4(f333(f333(f251(f890(x92571,a874)),x92574),f333(f333(f311(x92571),x92572),x92573)))+P4(f333(f333(f251(f890(x92571,a874)),f333(f333(f3(f890(x92571,a874)),x92574),f333(f333(f311(x92571),x92572),f194(f890(x92571,a874))))),x92573)) % 191.49/191.42 [9419]~P4(f333(f333(f335(x94191),x94192),x94194))+P4(f333(f333(f335(x94191),x94192),x94193))+P4(f333(f333(f251(f890(x94191,a874)),x94194),f333(f333(f311(x94191),x94192),x94193)))+~P4(f333(f333(f251(f890(x94191,a874)),f333(f333(f3(f890(x94191,a874)),x94194),f333(f333(f311(x94191),x94192),f194(f890(x94191,a874))))),x94193)) % 191.49/191.42 [9446]P4(f333(f333(f335(x94461),x94462),x94463))+~P4(f333(f333(f250(f890(x94461,a874)),x94464),x94463))+P4(f333(f333(f251(f890(x94461,a874)),x94464),f333(f333(f311(x94461),x94462),x94463)))+~P4(f333(f333(f251(f890(x94461,a874)),f333(f333(f3(f890(x94461,a874)),x94464),f333(f333(f311(x94461),x94462),f194(f890(x94461,a874))))),x94463)) % 191.49/191.42 [9451]~P4(f333(f333(f335(x94511),x94513),x94512))+~P4(f333(f333(f251(f890(x94511,a874)),x94512),x94514))+P4(f333(f333(f251(f890(x94511,a874)),x94512),f333(f333(f311(x94511),x94513),x94514)))+~P4(f333(f333(f251(f890(x94511,a874)),f333(f333(f3(f890(x94511,a874)),x94512),f333(f333(f311(x94511),x94513),f194(f890(x94511,a874))))),x94514)) % 191.49/191.42 [9464]~P4(f333(f333(f250(f890(x94641,a874)),x94642),x94644))+~P4(f333(f333(f251(f890(x94641,a874)),x94642),x94644))+P4(f333(f333(f251(f890(x94641,a874)),x94642),f333(f333(f311(x94641),x94643),x94644)))+~P4(f333(f333(f251(f890(x94641,a874)),f333(f333(f3(f890(x94641,a874)),x94642),f333(f333(f311(x94641),x94643),f194(f890(x94641,a874))))),x94644)) % 191.49/191.42 [9523]~P110(x95232)+~P62(x95231)+~P4(f333(f333(f250(f890(x95231,x95232)),x95233),x95234))+P4(f333(f60(x95231),f333(f333(f20(x95231,x95232,a874),f333(f333(f10(x95232,f890(x95232,a874),x95231),f250(x95232)),x95233)),x95234))) % 191.49/191.42 [9677]~P110(x96772)+~P62(x96771)+P4(f333(f333(f250(f890(x96771,x96772)),x96773),x96774))+~P4(f333(f60(x96771),f333(f333(f20(x96771,x96772,a874),f333(f333(f10(x96772,f890(x96772,a874),x96771),f250(x96772)),x96773)),x96774))) % 191.49/191.42 [9854]E(f333(f333(f166(x98541),f333(f333(f166(f881(x98541)),f180(x98541,x98542)),x98543)),x98544),f333(f333(f166(x98541),f333(f333(f166(f881(x98541)),x98542),x98544)),x98543))+~P4(f333(f333(f251(a880),x98543),f333(f195(f881(f881(x98541))),f180(x98541,x98542))))+~P17(a880,f333(f170(a880),f333(f333(f155(f881(x98541),a880),f195(f881(x98541))),x98542)))+~P4(f333(f333(f251(a880),x98544),f333(f195(f881(f881(x98541))),f333(f137(f881(x98541),f333(f333(f10(a880,a874,f881(x98541)),f333(f251(a880),x98543)),f195(f881(x98541)))),x98542)))) % 191.49/191.42 [9882]~P4(f333(f333(f335(f889(a880,a880)),x98824),x98821))+~P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),x98824),x98822)),a36))+~P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),x98821),x98823)),a37))+P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),x98821),f333(f333(f311(f889(a880,a880)),x98822),x98823))),a37)) % 191.49/191.42 [9883]~P4(f333(f333(f335(f889(a880,a880)),x98834),x98831))+~P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),x98834),x98832)),a71))+~P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),x98831),x98833)),a72))+P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),x98831),f333(f333(f311(f889(a880,a880)),x98832),x98833))),a72)) % 191.49/191.42 [9774]~P110(x97742)+~P62(x97741)+~P4(f333(f333(f251(f890(x97741,x97742)),x97743),x97744))+P4(f333(f59(x97741),f333(f333(f10(a874,a874,x97741),a328),f333(f333(f20(x97741,x97742,a874),f333(f333(f10(x97742,f890(x97742,a874),x97741),a330),x97743)),x97744)))) % 191.49/191.42 [9895]~P4(f333(f333(f335(f889(a880,a880)),x98954),x98953))+~P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),x98951),x98954)),a36))+~P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),x98952),x98953)),a38))+P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),f333(f333(f311(f889(a880,a880)),x98951),x98952)),x98953)),a38)) % 191.49/191.42 [9896]~P4(f333(f333(f335(f889(a880,a880)),x98964),x98963))+~P4(f333(f333(f335(f889(f889(a880,a880),f889(a880,a880))),f333(f333(f263(f889(a880,a880),f889(a880,a880)),x98961),x98964)),a71))+~P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),x98962),x98963)),a70))+P4(f333(f333(f335(f889(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874))),f333(f333(f263(f890(f889(a880,a880),a874),f890(f889(a880,a880),a874)),f333(f333(f311(f889(a880,a880)),x98961),x98962)),x98963)),a70)) % 191.49/191.42 [6045]~P11(x60454,x60451)+~P4(f333(f333(x60451,x60452),x60455))+P4(f333(f333(x60451,x60452),x60453))+~P4(f333(f333(x60451,x60455),x60453)) % 191.49/191.42 [5311]~P68(x53115)+E(x53111,x53112)+~E(x53113,x53114)+~E(f333(f333(f3(x53115),x53113),x53114),f333(f333(f3(x53115),x53111),x53112)) % 191.49/191.42 [6155]~P20(x61555,x61551,x61553)+E(f333(f333(x61551,x61552),f333(x61553,x61554)),f333(x61553,x61554))+~P4(f333(f63(x61555),x61554))+~P4(f333(f333(f335(x61555),x61552),x61554)) % 191.49/191.42 [6341]~P81(x63411)+~E(f333(f333(f3(x63411),x63414),x63415),f333(f333(f3(x63411),x63412),x63413))+~P4(f333(f333(f251(x63411),x63414),x63415))+P4(f333(f333(f251(x63411),x63412),x63413)) % 191.49/191.42 [6343]~P81(x63431)+~E(f333(f333(f3(x63431),x63434),x63435),f333(f333(f3(x63431),x63432),x63433))+~P4(f333(f333(f250(x63431),x63434),x63435))+P4(f333(f333(f250(x63431),x63432),x63433)) % 191.49/191.42 [7287]~E(x72872,f333(f333(f152(x72871),x72874),x72875))+P4(f333(f333(f335(f881(x72871)),x72872),f162(x72871,x72873)))+~P4(f333(f333(f335(f881(x72871)),x72875),f162(x72871,x72873)))+~P4(f333(f333(f335(x72871),x72874),x72873)) % 191.49/191.42 [7690]~E(f333(f195(f881(x76901)),x76903),f333(f195(f881(x76902)),x76904))+~E(f333(f333(f155(f889(x76901,x76902),x76902),f271(x76901,x76902)),x76905),x76904)+~E(f333(f333(f155(f889(x76901,x76902),x76901),f262(x76901,x76902)),x76905),x76903)+E(f333(f333(f182(x76901,x76902),x76903),x76904),x76905) % 191.49/191.42 [8020]~P110(x80201)+P4(f333(f333(f251(f890(x80201,a874)),f304(x80201,x80202,x80203)),f304(x80201,x80204,x80205)))+~P4(f333(f333(f250(x80201),x80204),x80205))+P4(f333(f333(f250(x80201),x80202),x80203)) % 191.49/191.42 [8122]~P110(x81221)+P4(f333(f333(f250(f890(x81221,a874)),f304(x81221,x81222,x81223)),f304(x81221,x81224,x81225)))+~P4(f333(f333(f250(x81221),x81223),x81225))+~P4(f333(f333(f250(x81221),x81224),x81222)) % 191.49/191.42 [8246]~P109(x82461)+P4(f333(f333(f250(x82461),x82462),x82463))+P4(f333(f333(f250(x82461),x82464),x82463))+~P4(f333(f333(f250(f890(x82461,a874)),f333(f303(x82461,x82463),x82462)),f333(f303(x82461,x82464),x82465))) % 191.49/191.42 [8247]~P109(x82471)+P4(f333(f333(f250(x82471),x82472),x82473))+P4(f333(f333(f250(x82471),x82472),x82474))+~P4(f333(f333(f250(f890(x82471,a874)),f333(f303(x82471,x82473),x82472)),f333(f303(x82471,x82475),x82474))) % 191.49/191.42 [8482]~P110(x84821)+~P4(f333(f333(f251(f890(x84821,a874)),f304(x84821,x84824,x84822)),f304(x84821,x84825,x84823)))+P4(f333(f333(f250(x84821),x84822),x84823))+~P4(f333(f333(f250(x84821),x84824),x84822)) % 191.49/191.42 [8483]~P110(x84831)+~P4(f333(f333(f250(f890(x84831,a874)),f304(x84831,x84834,x84832)),f304(x84831,x84835,x84833)))+P4(f333(f333(f250(x84831),x84832),x84833))+~P4(f333(f333(f250(x84831),x84834),x84832)) % 191.49/191.42 [8484]~P110(x84841)+~P4(f333(f333(f251(f890(x84841,a874)),f304(x84841,x84843,x84844)),f304(x84841,x84842,x84845)))+P4(f333(f333(f250(x84841),x84842),x84843))+~P4(f333(f333(f250(x84841),x84843),x84844)) % 191.49/191.42 [8485]~P110(x84851)+~P4(f333(f333(f250(f890(x84851,a874)),f304(x84851,x84853,x84854)),f304(x84851,x84852,x84855)))+P4(f333(f333(f250(x84851),x84852),x84853))+~P4(f333(f333(f250(x84851),x84853),x84854)) % 191.49/191.42 [6044]~P20(x60442,x60445,x60443)+E(x60441,f194(f890(x60442,a874)))+~P4(f333(f63(x60442),x60441))+E(f333(x60443,f333(f333(f311(x60442),x60444),x60441)),f333(f333(x60445,x60444),f333(x60443,x60441))) % 191.49/191.42 [6798]~E(x67981,x67982)+~E(f333(f333(f106(f890(x67983,a874)),x67984),x67985),f194(f890(x67983,a874)))+~P4(f333(f333(f335(x67983),x67982),x67985))+~P4(f333(f333(f335(x67983),x67981),x67984)) % 191.49/191.42 [6876]~P21(x68762,x68765,x68761)+~P4(f333(f63(x68762),x68764))+E(f333(x68761,f333(f333(f311(x68762),x68763),x68764)),f333(f333(f66(x68762,x68762,x68765),x68763),x68764))+P4(f333(f333(f335(x68762),x68763),x68764)) % 191.49/191.42 [6941]~P69(x69412)+~P4(f333(f63(x69411),x69415))+E(f333(f333(f8(x69411,x69412),x69413),f333(f333(f311(x69411),x69414),x69415)),f333(f333(f81(x69412),f333(x69413,x69414)),f333(f333(f8(x69411,x69412),x69413),x69415)))+P4(f333(f333(f335(x69411),x69414),x69415)) % 191.49/191.42 [6943]~P76(x69432)+~P4(f333(f63(x69431),x69435))+E(f333(f333(f11(x69431,x69432),x69433),f333(f333(f311(x69431),x69434),x69435)),f333(f333(f82(x69432),f333(x69433,x69434)),f333(f333(f11(x69431,x69432),x69433),x69435)))+P4(f333(f333(f335(x69431),x69434),x69435)) % 191.49/191.42 [7437]~P21(x74372,x74375,x74371)+~P4(f333(f63(x74372),x74374))+E(f333(x74371,f333(f333(f311(x74372),x74373),x74374)),x74373)+~E(f333(f333(f3(f890(x74372,a874)),x74374),f333(f333(f311(x74372),x74373),f194(f890(x74372,a874)))),f194(f890(x74372,a874))) % 191.49/191.42 [7742]~P4(f333(x77421,x77423))+~P4(f333(f333(f201(x77422),x77423),x77425))+~P4(f333(f333(f201(f33(x77421,x77422)),x77425),x77424))+P4(f333(f333(f201(f33(x77421,x77422)),x77423),x77424)) % 191.49/191.42 [7796]~P88(x77961)+~P4(f333(f333(f251(x77961),x77963),x77965))+~P4(f333(f333(f251(x77961),x77962),x77964))+P4(f333(f333(f251(x77961),f333(f333(f81(x77961),x77962),x77963)),f333(f333(f81(x77961),x77964),x77965))) % 191.49/191.42 [7797]~P88(x77971)+~P4(f333(f333(f250(x77971),x77972),x77974))+~P4(f333(f333(f251(x77971),x77973),x77975))+P4(f333(f333(f251(x77971),f333(f333(f81(x77971),x77972),x77973)),f333(f333(f81(x77971),x77974),x77975))) % 191.49/191.42 [7798]~P88(x77981)+~P4(f333(f333(f250(x77981),x77983),x77985))+~P4(f333(f333(f251(x77981),x77982),x77984))+P4(f333(f333(f251(x77981),f333(f333(f81(x77981),x77982),x77983)),f333(f333(f81(x77981),x77984),x77985))) % 191.49/191.42 [7799]~P101(x77991)+~P4(f333(f333(f250(x77991),x77993),x77995))+~P4(f333(f333(f250(x77991),x77992),x77994))+P4(f333(f333(f250(x77991),f333(f333(f115(x77991),x77992),x77993)),f333(f333(f115(x77991),x77994),x77995))) % 191.49/191.42 [7800]~P102(x78001)+~P4(f333(f333(f250(x78001),x78003),x78005))+~P4(f333(f333(f250(x78001),x78002),x78004))+P4(f333(f333(f250(x78001),f333(f333(f106(x78001),x78002),x78003)),f333(f333(f106(x78001),x78004),x78005))) % 191.49/191.42 [7801]~P86(x78011)+~P4(f333(f333(f250(x78011),x78013),x78015))+~P4(f333(f333(f250(x78011),x78012),x78014))+P4(f333(f333(f250(x78011),f333(f333(f81(x78011),x78012),x78013)),f333(f333(f81(x78011),x78014),x78015))) % 191.49/191.42 [7802]~P109(x78021)+~P4(f333(f333(f250(x78021),x78023),x78025))+~P4(f333(f333(f250(x78021),x78022),x78024))+P4(f333(f333(f250(x78021),f333(f333(f248(x78021),x78022),x78023)),f333(f333(f248(x78021),x78024),x78025))) % 191.49/191.42 [7803]~P109(x78031)+~P4(f333(f333(f250(x78031),x78033),x78035))+~P4(f333(f333(f250(x78031),x78032),x78034))+P4(f333(f333(f250(x78031),f333(f333(f249(x78031),x78032),x78033)),f333(f333(f249(x78031),x78034),x78035))) % 191.49/191.42 [7932]~P137(x79325)+E(x79321,x79322)+E(x79323,x79324)+~E(f333(f333(f81(x79325),f333(f333(f82(x79325),x79323),x79321)),f333(f333(f82(x79325),x79324),x79322)),f333(f333(f81(x79325),f333(f333(f82(x79325),x79323),x79322)),f333(f333(f82(x79325),x79324),x79321))) % 191.49/191.42 [8075]P30(x80751,x80752,x80753)+~P31(x80751,x80754,x80755)+~P30(x80751,x80752,f606(x80755,x80754,x80751,x80752))+~P4(f333(f333(f335(f879(x80751)),x80753),x80755)) % 191.49/191.42 [8146]~P109(x81464)+~P4(f333(f138(x81461),x81463))+P4(f333(f333(f335(x81461),x81462),f333(f173(x81461),x81463)))+P4(f333(f138(x81461),f333(f333(f149(x81461,x81464,x81465),x81462),x81463))) % 191.49/191.42 [8292]~P68(x82921)+E(f333(f333(f3(x82921),f333(f333(f8(a880,x82921),x82922),f333(f303(a880,x82923),x82924))),f333(f333(f8(a880,x82921),x82922),f333(f303(a880,x82923),x82925))),f333(f333(f8(a880,x82921),x82922),f333(f303(a880,x82925),x82924)))+~P4(f333(f333(f250(a880),x82925),x82924))+~P4(f333(f333(f250(a880),x82923),x82925)) % 191.49/191.42 [8293]~P69(x82931)+E(f333(f333(f81(x82931),f333(f333(f8(a880,x82931),x82932),f333(f303(a880,x82933),x82934))),f333(f333(f8(a880,x82931),x82932),f333(f303(a880,x82934),x82935))),f333(f333(f8(a880,x82931),x82932),f333(f303(a880,x82933),x82935)))+~P4(f333(f333(f250(a880),x82934),x82935))+~P4(f333(f333(f250(a880),x82933),x82934)) % 191.49/191.42 [8621]~P64(x86212)+E(x86211,f2(x86212))+E(x86213,f2(x86212))+E(f333(f333(f291(x86212),f333(f333(f3(x86212),f333(f333(f82(x86212),x86214),x86211)),f333(f333(f82(x86212),x86215),x86213))),f333(f333(f82(x86212),x86213),x86211)),f333(f333(f3(x86212),f333(f333(f291(x86212),x86214),x86213)),f333(f333(f291(x86212),x86215),x86211))) % 191.49/191.42 [8622]~P64(x86222)+E(x86221,f2(x86222))+E(x86223,f2(x86222))+E(f333(f333(f291(x86222),f333(f333(f81(x86222),f333(f333(f82(x86222),x86224),x86221)),f333(f333(f82(x86222),x86225),x86223))),f333(f333(f82(x86222),x86223),x86221)),f333(f333(f81(x86222),f333(f333(f291(x86222),x86224),x86223)),f333(f333(f291(x86222),x86225),x86221))) % 191.49/191.42 [8631]~E(x86312,f333(x86313,x86311))+E(x86311,f836(x86312,x86313,x86314,x86315))+~P28(x86315,x86314,x86313,f258(f890(x86315,a874)))+~P4(f333(f333(f335(x86314),x86312),f333(f312(x86315,x86314,x86313),f258(f890(x86315,a874))))) % 191.49/191.42 [8820]~P120(x88201)+~P4(f333(f333(f251(x88201),f333(f76(x88201),x88202)),x88204))+P4(f333(f333(f251(x88201),f333(f333(f82(x88201),f333(f76(x88201),x88202)),f333(f76(x88201),x88203))),f333(f333(f82(x88201),x88204),x88205)))+~P4(f333(f333(f251(x88201),f333(f76(x88201),x88203)),x88205)) % 191.49/191.42 [8838]~P31(x88381,x88385,x88384)+P30(x88381,x88382,x88383)+P4(f333(f333(f335(f879(x88381)),f606(x88384,x88385,x88381,x88382)),x88385))+~P4(f333(f333(f335(f879(x88381)),x88383),x88384)) % 191.49/191.42 [8943]~P28(x89431,x89433,x89435,x89432)+~P4(f333(f63(x89433),x89434))+P4(f333(f333(f250(a880),f333(f39(x89431),x89432)),f333(f39(x89433),x89434)))+~P4(f333(f333(f250(f890(x89433,a874)),f333(f312(x89431,x89433,x89435),x89432)),x89434)) % 191.49/191.42 [9011]~P69(x90112)+~P28(x90111,x90111,x90114,x90115)+~P4(f333(f63(x90111),x90115))+E(f333(f333(f8(x90111,x90112),f333(f74(x90111,x90112,x90111,x90113),x90114)),x90115),f333(f333(f8(x90111,x90112),x90113),f333(f312(x90111,x90111,x90114),x90115))) % 191.49/191.42 [9012]~P76(x90122)+~P28(x90121,x90121,x90124,x90125)+~P4(f333(f63(x90121),x90125))+E(f333(f333(f11(x90121,x90122),f333(f74(x90121,x90122,x90121,x90123),x90124)),x90125),f333(f333(f11(x90121,x90122),x90123),f333(f312(x90121,x90121,x90124),x90125))) % 191.49/191.42 [9114]~P40(x91141,x91142)+~P4(f333(f333(f335(x91141),x91143),x91144))+~P4(f333(f333(f335(x91141),x91145),x91144))+~P4(f333(f333(f335(f889(x91141,x91141)),f333(f333(f263(x91141,x91141),x91145),f786(x91142,x91141,x91144))),x91142)) % 191.49/191.42 [9161]~P28(x91612,x91613,x91615,x91611)+E(x91611,f194(f890(x91612,a874)))+E(f333(f312(x91613,x91612,f354(x91614,x91613,x91612,x91611)),x91614),x91611)+~P4(f333(f333(f250(f890(x91613,a874)),f333(f312(x91612,x91613,x91615),x91611)),x91614)) % 191.49/191.42 [9659]~P9(x96595)+~P109(x96595)+P4(f333(f333(f335(x96591),f540(x96592,x96593,x96591,x96594,x96595)),x96593))+~P4(f333(f333(f251(x96595),x96594),f333(f333(f44(x96591,x96595),x96593),x96592))) % 191.49/191.42 [9664]~P9(x96641)+~P109(x96641)+P4(f333(f333(f251(x96641),x96642),f333(x96643,f540(x96643,x96644,x96645,x96642,x96641))))+~P4(f333(f333(f251(x96641),x96642),f333(f333(f44(x96645,x96641),x96644),x96643))) % 191.49/191.42 [9747]~P73(x97471)+~P4(f333(f68(x97471,x97471,f82(x97471),x97472,x97473),x97475))+P4(f333(f333(f335(x97471),x97472),x97473))+P4(f333(f68(x97471,x97471,f82(x97471),x97474,f333(f333(f311(x97471),x97472),x97473)),f333(f333(f82(x97471),x97474),x97475))) % 191.49/191.42 [9951]~P69(x99512)+~P4(f333(f63(x99511),x99515))+E(f333(f333(f8(x99511,x99512),f333(f333(f9(x99511,x99512,x99512),f333(f333(f20(x99511,x99512,f890(x99512,x99512)),f333(f333(f10(a874,f890(x99512,f890(x99512,x99512)),x99511),f101(x99512)),f333(a330,x99513))),x99514)),f2(x99512))),x99515),f2(x99512))+P4(f333(f333(f335(x99511),x99513),x99515)) % 191.49/191.42 [9952]~P76(x99522)+~P4(f333(f63(x99521),x99525))+E(f333(f333(f11(x99521,x99522),f333(f333(f9(x99521,x99522,x99522),f333(f333(f20(x99521,x99522,f890(x99522,x99522)),f333(f333(f10(a874,f890(x99522,f890(x99522,x99522)),x99521),f101(x99522)),f333(a330,x99523))),x99524)),f79(x99522))),x99525),f79(x99522))+P4(f333(f333(f335(x99521),x99523),x99525)) % 191.49/191.42 [9953]~P69(x99532)+~P4(f333(f63(x99531),x99535))+E(f333(f333(f8(x99531,x99532),f333(f333(f9(x99531,x99532,x99532),f333(f333(f20(x99531,x99532,f890(x99532,x99532)),f333(f333(f10(a874,f890(x99532,f890(x99532,x99532)),x99531),f101(x99532)),f333(a330,x99533))),x99534)),f2(x99532))),x99535),f333(x99534,x99533))+~P4(f333(f333(f335(x99531),x99533),x99535)) % 191.49/191.42 [9954]~P76(x99542)+~P4(f333(f63(x99541),x99545))+E(f333(f333(f11(x99541,x99542),f333(f333(f9(x99541,x99542,x99542),f333(f333(f20(x99541,x99542,f890(x99542,x99542)),f333(f333(f10(a874,f890(x99542,f890(x99542,x99542)),x99541),f101(x99542)),f333(a330,x99543))),x99544)),f79(x99542))),x99545),f333(x99544,x99543))+~P4(f333(f333(f335(x99541),x99543),x99545)) % 191.49/191.42 [10007]~P69(x100072)+~P4(f333(f63(x100071),x100075))+E(f333(f333(f8(x100071,x100072),f333(f333(f9(x100071,x100072,x100072),f333(f333(f20(x100071,x100072,f890(x100072,x100072)),f333(f333(f10(a874,f890(x100072,f890(x100072,x100072)),x100071),f101(x100072)),f333(f333(f9(x100071,x100071,a874),a330),x100073))),x100074)),f2(x100072))),x100075),f2(x100072))+P4(f333(f333(f335(x100071),x100073),x100075)) % 191.49/191.42 [10008]~P76(x100082)+~P4(f333(f63(x100081),x100085))+E(f333(f333(f11(x100081,x100082),f333(f333(f9(x100081,x100082,x100082),f333(f333(f20(x100081,x100082,f890(x100082,x100082)),f333(f333(f10(a874,f890(x100082,f890(x100082,x100082)),x100081),f101(x100082)),f333(f333(f9(x100081,x100081,a874),a330),x100083))),x100084)),f79(x100082))),x100085),f79(x100082))+P4(f333(f333(f335(x100081),x100083),x100085)) % 191.49/191.42 [10010]~P69(x100102)+~P4(f333(f63(x100101),x100105))+E(f333(f333(f8(x100101,x100102),f333(f333(f9(x100101,x100102,x100102),f333(f333(f20(x100101,x100102,f890(x100102,x100102)),f333(f333(f10(a874,f890(x100102,f890(x100102,x100102)),x100101),f101(x100102)),f333(f333(f9(x100101,x100101,a874),a330),x100103))),x100104)),f2(x100102))),x100105),f333(x100104,x100103))+~P4(f333(f333(f335(x100101),x100103),x100105)) % 191.49/191.42 [10011]~P76(x100112)+~P4(f333(f63(x100111),x100115))+E(f333(f333(f11(x100111,x100112),f333(f333(f9(x100111,x100112,x100112),f333(f333(f20(x100111,x100112,f890(x100112,x100112)),f333(f333(f10(a874,f890(x100112,f890(x100112,x100112)),x100111),f101(x100112)),f333(f333(f9(x100111,x100111,a874),a330),x100113))),x100114)),f79(x100112))),x100115),f333(x100114,x100113))+~P4(f333(f333(f335(x100111),x100113),x100115)) % 191.49/191.42 [7795]~P68(x77952)+~P4(f333(f63(x77951),x77954))+E(f333(f333(f8(x77951,x77952),x77953),f333(f333(f3(f890(x77951,a874)),x77954),f333(f333(f311(x77951),x77955),f194(f890(x77951,a874))))),f333(f333(f8(x77951,x77952),x77953),x77954))+P4(f333(f333(f335(x77951),x77955),x77954)) % 191.49/191.42 [8298]~P106(x82982)+~P4(f333(f63(x82981),x82984))+E(f333(f333(f8(x82981,x82982),x82983),f333(f333(f3(f890(x82981,a874)),x82984),f333(f333(f311(x82981),x82985),f194(f890(x82981,a874))))),f333(f333(f3(x82982),f333(f333(f8(x82981,x82982),x82983),x82984)),f333(x82983,x82985)))+~P4(f333(f333(f335(x82981),x82985),x82984)) % 191.49/191.42 [8299]~P68(x82992)+~P4(f333(f63(x82991),x82994))+E(f333(f333(f8(x82991,x82992),x82993),f333(f333(f3(f890(x82991,a874)),x82994),f333(f333(f311(x82991),x82995),f194(f890(x82991,a874))))),f333(f333(f3(x82992),f333(f333(f8(x82991,x82992),x82993),x82994)),f333(x82993,x82995)))+~P4(f333(f333(f335(x82991),x82995),x82994)) % 191.49/191.42 [8327]~P68(x83271)+~P4(f333(f63(x83272),x83274))+E(f333(f333(f3(x83271),f333(f333(f8(x83272,x83271),x83273),x83274)),f333(f333(f8(x83272,x83271),x83273),x83275)),f333(f333(f8(x83272,x83271),x83273),f333(f333(f3(f890(x83272,a874)),x83274),x83275)))+~P4(f333(f333(f250(f890(x83272,a874)),x83275),x83274)) % 191.49/191.42 [8347]P4(f333(f63(x83471),f333(x83472,x83473)))+~P4(f333(f63(x83474),x83475))+~P4(f333(f333(f335(x83474),x83473),x83475))+~P4(f333(f63(x83471),f333(f333(f44(x83474,f890(x83471,a874)),x83475),x83472))) % 191.49/191.42 [8780]~P12(x87801,x87805,x87804)+~E(f333(f287(x87801,x87801,x87804),f333(f333(f311(x87801),x87802),f194(f890(x87801,a874)))),f333(f287(x87801,x87801,x87804),f333(f333(f311(x87801),x87803),f194(f890(x87801,a874)))))+~P4(f333(f333(f335(x87801),x87803),x87805))+P4(f333(f333(f335(f889(x87801,x87801)),f333(f333(f263(x87801,x87801),x87802),x87803)),x87804)) % 191.49/191.42 [9069]~P4(f333(x90691,x90695))+P4(f333(x90691,f422(x90691,x90692,x90693,x90694)))+P4(f333(x90691,f408(x90691,x90692,x90693,x90694)))+~P4(f333(f333(f335(x90694),x90695),f333(f333(f115(f890(x90694,a874)),x90693),x90692))) % 191.49/191.42 [9262]~P4(f333(x92621,x92625))+P4(f333(x92621,f408(x92621,x92622,x92623,x92624)))+P4(f333(f333(f335(x92624),f422(x92621,x92622,x92623,x92624)),x92622))+~P4(f333(f333(f335(x92624),x92625),f333(f333(f115(f890(x92624,a874)),x92623),x92622))) % 191.49/191.42 [9263]~P4(f333(x92631,x92635))+P4(f333(x92631,f422(x92631,x92632,x92633,x92634)))+P4(f333(f333(f335(x92634),f408(x92631,x92632,x92633,x92634)),x92633))+~P4(f333(f333(f335(x92634),x92635),f333(f333(f115(f890(x92634,a874)),x92633),x92632))) % 191.49/191.42 [9271]P4(f333(x92711,x92712))+~P4(f333(x92711,f463(x92711,x92713,x92714,x92715)))+~P4(f333(x92711,f450(x92711,x92713,x92714,x92715)))+~P4(f333(f333(f335(x92715),x92712),f333(f333(f115(f890(x92715,a874)),x92714),x92713))) % 191.49/191.42 [9314]E(x93141,x93142)+~P4(f333(f333(f335(f889(x93143,x93143)),f333(f333(f263(x93143,x93143),x93141),x93142)),f309(x93143,x93145)))+P4(f333(f333(f335(x93143),x93141),x93144))+~P4(f333(f333(f250(f890(f889(x93143,x93143),a874)),x93145),f333(f333(f270(x93143,x93143),x93144),f333(f18(f890(x93143,a874),x93143),x93144)))) % 191.49/191.42 [9333]P4(f333(x93331,x93332))+~P4(f333(x93331,f450(x93331,x93334,x93335,x93333)))+P4(f333(f333(f335(x93333),f463(x93331,x93334,x93335,x93333)),x93334))+~P4(f333(f333(f335(x93333),x93332),f333(f333(f115(f890(x93333,a874)),x93335),x93334))) % 191.49/191.42 [9334]P4(f333(x93341,x93342))+~P4(f333(x93341,f463(x93341,x93344,x93345,x93343)))+P4(f333(f333(f335(x93343),f450(x93341,x93344,x93345,x93343)),x93345))+~P4(f333(f333(f335(x93343),x93342),f333(f333(f115(f890(x93343,a874)),x93345),x93344))) % 191.49/191.42 [9394]P4(f333(x93941,x93942))+P4(f333(f333(f335(x93943),f463(x93941,x93944,x93945,x93943)),x93944))+P4(f333(f333(f335(x93943),f450(x93941,x93944,x93945,x93943)),x93945))+~P4(f333(f333(f335(x93943),x93942),f333(f333(f115(f890(x93943,a874)),x93945),x93944))) % 191.49/191.42 [9395]~P4(f333(x93952,x93955))+P4(f333(f333(f335(x93951),f422(x93952,x93953,x93954,x93951)),x93953))+P4(f333(f333(f335(x93951),f408(x93952,x93953,x93954,x93951)),x93954))+~P4(f333(f333(f335(x93951),x93955),f333(f333(f115(f890(x93951,a874)),x93954),x93953))) % 191.49/191.42 [9556]~P12(x95561,x95565,x95564)+~P4(f333(f333(f335(x95561),x95563),x95565))+P4(f333(f333(f335(f889(x95561,x95561)),f333(f333(f263(x95561,x95561),x95562),x95563)),x95564))+~P4(f333(f333(f250(f890(x95561,a874)),f333(f287(x95561,x95561,x95564),f333(f333(f311(x95561),x95563),f194(f890(x95561,a874))))),f333(f287(x95561,x95561,x95564),f333(f333(f311(x95561),x95562),f194(f890(x95561,a874)))))) % 191.49/191.42 [9690]~P9(x96905)+~P109(x96905)+P4(f333(f333(f335(x96901),f531(x96902,x96903,x96904,x96901,x96905)),x96904))+~P4(f333(f333(f251(x96905),f333(f333(f43(x96901,x96905),x96904),x96903)),x96902)) % 191.49/191.42 [9722]~P84(x97225)+~P86(x97225)+P4(f333(f333(f335(x97221),f640(x97222,x97223,x97224,x97221,x97225)),f333(f173(x97221),x97224)))+P4(f333(f333(f250(x97225),f333(f167(x97225),f333(f333(f155(x97221,x97225),x97223),x97224))),f333(f167(x97225),f333(f333(f155(x97221,x97225),x97222),x97224)))) % 191.49/191.42 [9852]~P9(x98521)+~P109(x98521)+P4(f333(f333(f251(x98521),f333(x98522,f531(x98523,x98522,x98524,x98525,x98521))),x98523))+~P4(f333(f333(f251(x98521),f333(f333(f43(x98525,x98521),x98524),x98522)),x98523)) % 191.49/191.42 [9968]~P84(x99681)+~P86(x99681)+~P4(f333(f333(f250(x99681),f333(x99683,f640(x99685,x99683,x99684,x99682,x99681))),f333(x99685,f640(x99685,x99683,x99684,x99682,x99681))))+P4(f333(f333(f250(x99681),f333(f167(x99681),f333(f333(f155(x99682,x99681),x99683),x99684))),f333(f167(x99681),f333(f333(f155(x99682,x99681),x99685),x99684)))) % 191.49/191.42 [8639]~P69(x86391)+~P4(f333(f63(x86394),x86395))+~P4(f333(f333(f335(x86394),x86393),x86395))+E(f333(f333(f81(x86391),f333(x86392,x86393)),f333(f333(f8(x86394,x86391),x86392),f333(f333(f3(f890(x86394,a874)),x86395),f333(f333(f311(x86394),x86393),f194(f890(x86394,a874)))))),f333(f333(f8(x86394,x86391),x86392),x86395)) % 191.49/191.42 [8640]~P76(x86401)+~P4(f333(f63(x86404),x86405))+~P4(f333(f333(f335(x86404),x86403),x86405))+E(f333(f333(f82(x86401),f333(x86402,x86403)),f333(f333(f11(x86404,x86401),x86402),f333(f333(f3(f890(x86404,a874)),x86405),f333(f333(f311(x86404),x86403),f194(f890(x86404,a874)))))),f333(f333(f11(x86404,x86401),x86402),x86405)) % 191.49/191.42 [8686]~P21(x86861,x86864,x86865)+~P4(f333(f63(x86861),x86862))+E(f333(f333(f3(f890(x86861,a874)),x86862),f333(f333(f311(x86861),x86863),f194(f890(x86861,a874)))),f194(f890(x86861,a874)))+E(f333(f333(x86864,x86863),f333(x86865,f333(f333(f3(f890(x86861,a874)),x86862),f333(f333(f311(x86861),x86863),f194(f890(x86861,a874)))))),f333(x86865,f333(f333(f311(x86861),x86863),x86862))) % 191.49/191.42 [9050]~P69(x90501)+~P4(f333(f63(x90502),x90505))+~P4(f333(f63(x90502),x90504))+E(f333(f333(f81(x90501),f333(f333(f8(x90502,x90501),x90503),f333(f333(f115(f890(x90502,a874)),x90504),x90505))),f333(f333(f8(x90502,x90501),x90503),f333(f333(f106(f890(x90502,a874)),x90504),x90505))),f333(f333(f81(x90501),f333(f333(f8(x90502,x90501),x90503),x90504)),f333(f333(f8(x90502,x90501),x90503),x90505))) % 191.49/191.42 [9052]~P76(x90521)+~P4(f333(f63(x90522),x90525))+~P4(f333(f63(x90522),x90524))+E(f333(f333(f82(x90521),f333(f333(f11(x90522,x90521),x90523),f333(f333(f115(f890(x90522,a874)),x90524),x90525))),f333(f333(f11(x90522,x90521),x90523),f333(f333(f106(f890(x90522,a874)),x90524),x90525))),f333(f333(f82(x90521),f333(f333(f11(x90522,x90521),x90523),x90524)),f333(f333(f11(x90522,x90521),x90523),x90525))) % 191.49/191.42 [9201]~P68(x92011)+~P4(f333(f63(x92012),x92015))+~P4(f333(f63(x92012),x92014))+E(f333(f333(f3(x92011),f333(f333(f81(x92011),f333(f333(f8(x92012,x92011),x92013),x92014)),f333(f333(f8(x92012,x92011),x92013),x92015))),f333(f333(f8(x92012,x92011),x92013),f333(f333(f106(f890(x92012,a874)),x92014),x92015))),f333(f333(f8(x92012,x92011),x92013),f333(f333(f115(f890(x92012,a874)),x92014),x92015))) % 191.49/191.42 [9404]~P28(x94041,x94042,x94043,x94045)+~P28(x94041,x94042,x94043,x94044)+P28(x94041,x94042,x94043,f333(f333(f115(f890(x94041,a874)),x94044),x94045))+~E(f333(f333(f106(f890(x94042,a874)),f333(f312(x94041,x94042,x94043),f333(f333(f3(f890(x94041,a874)),x94044),x94045))),f333(f312(x94041,x94042,x94043),f333(f333(f3(f890(x94041,a874)),x94045),x94044))),f194(f890(x94042,a874))) % 191.49/191.42 [9531]E(x95311,f2(a1))+~P4(f333(f333(f251(a1),f2(a1)),x95313))+~P4(f333(f50(x95312,x95311),f333(f333(f263(a1,a1),x95314),x95315)))+P4(f333(f50(x95312,f333(f333(f82(a1),x95311),x95313)),f333(f333(f263(a1,a1),f333(f333(f40(a1),x95314),x95313)),f333(f333(f81(a1),f333(f333(f82(a1),x95311),f46(a1,x95314,x95313))),x95315)))) % 191.49/191.42 [9539]~P4(f333(f333(f251(a880),f2(a880)),x95393))+~P4(f333(f333(f251(a880),f2(a880)),x95392))+~P4(f333(f49(x95391,x95392),f333(f333(f263(a880,a880),x95394),x95395)))+P4(f333(f49(x95391,f333(f333(f82(a880),x95392),x95393)),f333(f333(f263(a880,a880),f333(f333(f40(a880),x95394),x95393)),f333(f333(f81(a880),f333(f333(f82(a880),x95392),f46(a880,x95394,x95393))),x95395)))) % 191.49/191.42 [9594]~P76(x95941)+~P4(f333(f63(x95942),x95945))+~P4(f333(f63(x95942),x95944))+E(f333(f333(f82(x95941),f333(f333(f333(f67(x95941,x95942,f82(x95941)),x95943),f79(x95941)),f333(f333(f115(f890(x95942,a874)),x95944),x95945))),f333(f333(f333(f67(x95941,x95942,f82(x95941)),x95943),f79(x95941)),f333(f333(f106(f890(x95942,a874)),x95944),x95945))),f333(f333(f82(x95941),f333(f333(f333(f67(x95941,x95942,f82(x95941)),x95943),f79(x95941)),x95944)),f333(f333(f333(f67(x95941,x95942,f82(x95941)),x95943),f79(x95941)),x95945))) % 191.49/191.42 [9596]~E(f333(f333(f174(x95961),x95965),x95962),f333(f333(f174(x95961),x95965),x95963))+P4(f333(f333(f335(f889(f881(x95961),f881(x95961))),f333(f333(f263(f881(x95961),f881(x95961)),x95962),x95963)),f148(x95961,x95964)))+~P4(f333(f333(f251(a880),x95965),f333(f333(f248(a880),f333(f195(f881(x95961)),x95962)),f333(f195(f881(x95961)),x95963))))+~P4(f333(f333(f335(f889(x95961,x95961)),f333(f333(f263(x95961,x95961),f333(f333(f166(x95961),x95962),x95965)),f333(f333(f166(x95961),x95963),x95965))),x95964)) % 191.49/191.42 [9710]~P86(x97105)+~P143(x97105)+P4(f333(f333(f335(x97101),f395(x97102,x97103,x97104,x97101,x97105)),x97104))+P4(f333(f333(f250(x97105),f333(f333(f8(x97101,x97105),x97103),x97104)),f333(f333(f82(x97105),f333(f105(x97105),f333(f39(x97101),x97104))),x97102))) % 191.49/191.42 [9909]~P86(x99091)+~P143(x99091)+~P4(f333(f333(f250(x99091),f333(x99093,f395(x99095,x99093,x99094,x99092,x99091))),x99095))+P4(f333(f333(f250(x99091),f333(f333(f8(x99092,x99091),x99093),x99094)),f333(f333(f82(x99091),f333(f105(x99091),f333(f39(x99092),x99094))),x99095))) % 191.49/191.42 [8660]E(f333(f333(f127(x86601),x86602),x86603),f333(f333(f127(x86601),x86604),x86605))+~E(f333(f333(f174(x86601),f333(f195(f881(x86601)),x86602)),x86604),x86602)+~E(f333(f333(f127(x86601),f333(f333(f139(x86601),f333(f195(f881(x86601)),x86602)),x86604)),x86605),x86603)+P4(f333(f333(f250(a880),f333(f195(f881(x86601)),x86604)),f333(f195(f881(x86601)),x86602))) % 191.49/191.42 [8778]E(f333(f333(f127(x87781),x87782),x87783),f333(f333(f127(x87781),x87784),x87785))+~E(f333(f333(f174(x87781),f333(f195(f881(x87781)),x87782)),x87784),x87782)+~E(x87783,f333(f333(f127(x87781),f333(f333(f139(x87781),f333(f195(f881(x87781)),x87782)),x87784)),x87785))+~P4(f333(f333(f250(a880),f333(f195(f881(x87781)),x87782)),f333(f195(f881(x87781)),x87784))) % 191.49/191.42 [10031]~P4(f333(x100315,x100314))+~P4(f333(f63(x100312),f333(f255(x100312),x100315)))+P4(f333(f63(x100311),f333(f255(x100311),f333(f333(f9(x100311,x100312,a874),x100313),x100314))))+~P4(f333(f63(x100311),f333(f255(x100311),f333(f333(f10(f890(x100312,a874),a874,x100311),f87(x100312)),f333(f333(f10(f890(x100312,a874),f890(x100312,a874),x100311),f333(f20(x100312,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100312),a331),x100315))),x100313))))) % 191.49/191.42 [8462]~P22(x84625,x84621,x84626,x84622)+E(f333(f74(x84621,x84621,x84621,f333(x84622,x84623)),f333(x84622,x84624)),f333(f74(x84621,x84621,x84621,f333(x84622,x84624)),f333(x84622,x84623)))+~P4(f333(f63(x84625),x84624))+~P4(f333(f63(x84625),x84623)) % 191.49/191.42 [7852]~P28(x78521,x78522,x78524,x78523)+~E(f333(x78524,x78526),x78525)+E(f333(f78(x78521,x78522,x78523,x78524),x78525),x78526)+~P4(f333(f333(f335(x78521),x78526),x78523)) % 191.49/191.42 [8041]~P23(x80416,x80411,x80414,x80412)+E(f333(f74(x80411,x80411,x80411,f333(x80412,x80413)),f333(x80414,x80415)),f333(x80412,x80413))+~P4(f333(f63(x80416),x80413))+~P4(f333(f333(f335(x80416),x80415),x80413)) % 191.49/191.42 [9248]~P22(x92483,x92481,x92486,x92482)+E(f333(f74(x92481,x92481,x92481,f333(x92482,f333(f333(f3(f890(x92483,a874)),x92484),f333(f333(f311(x92483),x92485),f194(f890(x92483,a874)))))),f333(x92486,x92485)),f333(x92482,x92484))+~P4(f333(f63(x92483),x92484))+~P4(f333(f333(f335(x92483),x92485),x92484)) % 191.49/191.42 [6947]~P61(x69471)+~E(f46(x69471,x69473,x69474),f46(x69471,x69476,x69474))+~E(f46(x69471,x69472,x69474),f46(x69471,x69475,x69474))+E(f46(x69471,f333(f333(f3(x69471),x69472),x69473),x69474),f46(x69471,f333(f333(f3(x69471),x69475),x69476),x69474)) % 191.49/191.42 [6948]~P60(x69481)+~E(f46(x69481,x69483,x69484),f46(x69481,x69486,x69484))+~E(f46(x69481,x69482,x69484),f46(x69481,x69485,x69484))+E(f46(x69481,f333(f333(f81(x69481),x69482),x69483),x69484),f46(x69481,f333(f333(f81(x69481),x69485),x69486),x69484)) % 191.49/191.42 [6949]~P60(x69491)+~E(f46(x69491,x69493,x69494),f46(x69491,x69496,x69494))+~E(f46(x69491,x69492,x69494),f46(x69491,x69495,x69494))+E(f46(x69491,f333(f333(f82(x69491),x69492),x69493),x69494),f46(x69491,f333(f333(f82(x69491),x69495),x69496),x69494)) % 191.49/191.42 [7744]~P19(x77441,x77442,x77443)+~P4(f333(f63(x77441),x77446))+E(f333(f333(f66(x77441,x77442,x77443),x77444),f333(f333(f311(x77441),x77445),x77446)),f333(f333(f66(x77441,x77442,x77443),f333(f333(x77443,x77445),x77444)),x77446))+P4(f333(f333(f335(x77441),x77445),x77446)) % 191.49/191.42 [7809]~P9(x78091)+P4(f333(f333(f250(x78091),x78092),f333(x78093,x78094)))+~P4(f333(f333(f335(x78095),x78094),x78096))+~P4(f333(f333(f250(x78091),x78092),f333(f333(f43(x78095,x78091),x78096),x78093))) % 191.49/191.42 [7959]~P19(x79591,x79592,x79593)+~P4(f333(f63(x79591),x79596))+E(f333(f333(f66(x79591,x79592,x79593),x79594),f333(f333(f311(x79591),x79595),x79596)),f333(f333(x79593,x79595),f333(f333(f66(x79591,x79592,x79593),x79594),x79596)))+P4(f333(f333(f335(x79591),x79595),x79596)) % 191.49/191.42 [8060]~P109(x80603)+~P4(f333(x80602,x80605))+~P17(x80603,f333(f333(f155(x80601,x80603),x80604),x80606))+E(f333(f137(x80601,x80602),f333(f333(f149(x80601,x80603,x80604),x80605),x80606)),f333(f333(f149(x80601,x80603,x80604),x80605),f333(f137(x80601,x80602),x80606))) % 191.49/191.42 [8084]E(x80841,x80842)+E(x80843,f2(a1))+~P4(f333(f50(x80844,x80843),f333(f333(f263(a1,a1),x80845),x80842)))+~P4(f333(f50(x80844,x80843),f333(f333(f263(a1,a1),x80846),x80841))) % 191.49/191.42 [8085]E(x80851,x80852)+E(x80853,f2(a1))+~P4(f333(f50(x80854,x80853),f333(f333(f263(a1,a1),x80852),x80855)))+~P4(f333(f50(x80854,x80853),f333(f333(f263(a1,a1),x80851),x80856))) % 191.49/191.42 [8106]~P22(x81062,x81065,x81066,x81061)+~P4(f333(f63(x81062),x81064))+E(f333(x81061,f333(f333(f311(x81062),x81063),x81064)),f333(f74(x81065,x81065,x81065,f333(x81061,x81064)),f333(x81066,x81063)))+P4(f333(f333(f335(x81062),x81063),x81064)) % 191.49/191.42 [8330]~P23(x83305,x83301,x83306,x83302)+E(f333(f74(x83301,x83301,x83301,f333(x83302,x83303)),f333(x83302,x83304)),f333(x83302,x83303))+~P4(f333(f63(x83305),x83303))+~P4(f333(f333(f250(f890(x83305,a874)),x83304),x83303)) % 191.49/191.42 [9448]~P28(x94481,x94482,x94484,x94483)+~P4(f333(f333(f335(x94482),x94485),f333(f312(x94481,x94482,x94484),x94483)))+P4(f333(f333(f335(x94481),f333(f78(x94481,x94482,x94483,x94484),x94485)),x94486))+~P4(f333(f333(f250(f890(x94481,a874)),x94483),x94486)) % 191.49/191.42 [9856]~P69(x98562)+~E(f517(x98561,x98563,x98565,x98566,x98564,x98562),f518(x98561,x98563,x98565,x98566,x98564,x98562))+~P4(f333(f63(x98564),x98566))+E(f333(f333(f8(x98561,x98562),x98563),f333(f312(x98564,x98561,x98565),x98566)),f333(f333(f8(x98564,x98562),f333(f74(x98561,x98562,x98564,x98563),x98565)),x98566)) % 191.49/191.42 [9891]~P69(x98916)+E(f333(x98911,f517(x98912,x98913,x98911,x98914,x98915,x98916)),f333(x98911,f518(x98912,x98913,x98911,x98914,x98915,x98916)))+E(f333(f333(f8(x98912,x98916),x98913),f333(f312(x98915,x98912,x98911),x98914)),f333(f333(f8(x98915,x98916),f333(f74(x98912,x98916,x98915,x98913),x98911)),x98914))+~P4(f333(f63(x98915),x98914)) % 191.49/191.42 [9927]~P69(x99272)+~E(f333(x99273,f333(x99275,f518(x99271,x99273,x99275,x99276,x99274,x99272))),f2(x99272))+~P4(f333(f63(x99274),x99276))+E(f333(f333(f8(x99271,x99272),x99273),f333(f312(x99274,x99271,x99275),x99276)),f333(f333(f8(x99274,x99272),f333(f74(x99271,x99272,x99274,x99273),x99275)),x99276)) % 191.49/191.42 [9975]~P69(x99752)+~P4(f333(f63(x99754),x99756))+E(f333(f333(f8(x99751,x99752),x99753),f333(f312(x99754,x99751,x99755),x99756)),f333(f333(f8(x99754,x99752),f333(f74(x99751,x99752,x99754,x99753),x99755)),x99756))+P4(f333(f333(f335(x99754),f518(x99751,x99753,x99755,x99756,x99754,x99752)),x99756)) % 191.49/191.42 [9976]~P69(x99762)+~P4(f333(f63(x99764),x99766))+E(f333(f333(f8(x99761,x99762),x99763),f333(f312(x99764,x99761,x99765),x99766)),f333(f333(f8(x99764,x99762),f333(f74(x99761,x99762,x99764,x99763),x99765)),x99766))+P4(f333(f333(f335(x99764),f517(x99761,x99763,x99765,x99766,x99764,x99762)),x99766)) % 191.49/191.42 [10092]~P76(x100921)+~P4(f333(f63(x100922),x100926))+E(f333(f333(f333(f67(x100921,x100922,f82(x100921)),f333(f333(f20(x100922,f890(x100923,a874),x100921),f333(f333(f9(x100922,x100921,f890(f890(x100923,a874),x100921)),f333(f333(f10(f890(x100923,x100921),f890(x100921,f890(f890(x100923,a874),x100921)),x100922),f67(x100921,x100923,f82(x100921))),x100924)),f79(x100921))),x100925)),f79(x100921)),x100926),f333(f333(f333(f67(x100921,f889(x100922,x100923),f82(x100921)),f333(f272(x100922,x100923,x100921),x100924)),f79(x100921)),f333(f333(f270(x100922,x100923),x100926),x100925)))+P4(f333(f333(f335(x100922),f634(x100924,x100925,x100923,x100926,x100922,x100921)),x100926)) % 191.49/191.42 [10110]~P76(x101101)+~P4(f333(f63(x101102),x101106))+E(f333(f333(f333(f67(x101101,x101102,f82(x101101)),f333(f333(f20(x101102,f890(x101103,a874),x101101),f333(f333(f9(x101102,x101101,f890(f890(x101103,a874),x101101)),f333(f333(f10(f890(x101103,x101101),f890(x101101,f890(f890(x101103,a874),x101101)),x101102),f67(x101101,x101103,f82(x101101))),x101104)),f79(x101101))),x101105)),f79(x101101)),x101106),f333(f333(f333(f67(x101101,f889(x101102,x101103),f82(x101101)),f333(f272(x101102,x101103,x101101),x101104)),f79(x101101)),f333(f333(f270(x101102,x101103),x101106),x101105)))+~P4(f333(f63(x101103),f333(x101105,f634(x101104,x101105,x101103,x101106,x101102,x101101)))) % 191.49/191.42 [8245]~P23(x82452,x82455,x82456,x82451)+~P4(f333(f63(x82452),x82454))+~P4(f333(f63(x82452),x82453))+E(f333(x82451,f333(f333(f115(f890(x82452,a874)),x82453),x82454)),f333(f74(x82455,x82455,x82455,f333(x82451,x82453)),f333(x82451,x82454))) % 191.49/191.42 [8463]~P9(x84631)+P4(f333(f333(f250(x84631),f333(x84632,x84633)),x84634))+~P4(f333(f333(f335(x84635),x84633),x84636))+~P4(f333(f333(f250(x84631),f333(f333(f44(x84635,x84631),x84636),x84632)),x84634)) % 191.49/191.42 [8862]~P28(x88622,x88621,x88623,x88626)+E(f333(f333(f3(f890(x88621,a874)),f333(f312(x88622,x88621,x88623),x88624)),f333(f312(x88622,x88621,x88623),x88625)),f333(f312(x88622,x88621,x88623),f333(f333(f3(f890(x88622,a874)),x88624),x88625)))+~P4(f333(f333(f250(f890(x88622,a874)),x88625),x88626))+~P4(f333(f333(f250(f890(x88622,a874)),x88624),x88626)) % 191.49/191.42 [8863]~P28(x88632,x88631,x88633,x88636)+E(f333(f333(f106(f890(x88631,a874)),f333(f312(x88632,x88631,x88633),x88634)),f333(f312(x88632,x88631,x88633),x88635)),f333(f312(x88632,x88631,x88633),f333(f333(f106(f890(x88632,a874)),x88634),x88635)))+~P4(f333(f333(f250(f890(x88632,a874)),x88635),x88636))+~P4(f333(f333(f250(f890(x88632,a874)),x88634),x88636)) % 191.49/191.42 [8902]~P4(f333(x89021,x89023))+~P4(f333(f333(f333(f333(a203,x89022),x89023),x89024),x89026))+~P4(f333(f333(f333(f333(a203,f33(x89021,x89022)),x89026),x89024),x89025))+P4(f333(f333(f333(f333(a203,f33(x89021,x89022)),x89023),x89024),x89025)) % 191.49/191.42 [9116]E(x91161,x91162)+~P54(x91163,x91164,x91165)+~P4(f333(f333(f335(f889(x91163,x91164)),f333(f333(f263(x91163,x91164),x91166),x91162)),x91165))+~P4(f333(f333(f335(f889(x91163,x91164)),f333(f333(f263(x91163,x91164),x91166),x91161)),x91165)) % 191.49/191.42 [9923]~P73(x99231)+~E(f333(x99233,f382(x99234,x99236,x99233,x99235,x99232,x99231)),f333(x99236,f382(x99234,x99236,x99233,x99235,x99232,x99231)))+~P4(f333(f63(x99232),x99235))+E(f333(f333(f333(f67(x99231,x99232,f82(x99231)),x99233),x99234),x99235),f333(f333(f333(f67(x99231,x99232,f82(x99231)),x99236),x99234),x99235)) % 191.49/191.42 [9973]~P73(x99731)+~P4(f333(f63(x99732),x99735))+E(f333(f333(f333(f67(x99731,x99732,f82(x99731)),x99733),x99734),x99735),f333(f333(f333(f67(x99731,x99732,f82(x99731)),x99736),x99734),x99735))+P4(f333(f333(f335(x99732),f382(x99734,x99733,x99736,x99735,x99732,x99731)),x99735)) % 191.49/191.42 [8671]~P73(x86711)+~P4(f333(f63(x86712),x86716))+P4(f333(f333(f335(x86712),x86715),x86716))+E(f333(f333(f333(f67(x86711,x86712,f82(x86711)),x86713),x86714),f333(f333(f311(x86712),x86715),x86716)),f333(f333(f82(x86711),f333(x86713,x86715)),f333(f333(f333(f67(x86711,x86712,f82(x86711)),x86713),x86714),x86716))) % 191.49/191.42 [8717]~P12(x87171,x87176,x87173)+~P15(x87171,f890(x87172,a874),x87173,x87175)+~P4(f333(f333(f335(x87171),x87174),x87176))+E(f333(f333(f44(x87171,f890(x87172,a874)),f333(f287(x87171,x87171,x87173),f333(f333(f311(x87171),x87174),f194(f890(x87171,a874))))),x87175),f333(x87175,x87174)) % 191.49/191.42 [8839]~P19(x88393,x88394,x88391)+~P4(f333(f63(x88393),x88396))+~P4(f333(f333(f335(x88393),x88392),x88396))+E(f333(f333(x88391,x88392),f333(f333(f66(x88393,x88394,x88391),x88395),f333(f333(f3(f890(x88393,a874)),x88396),f333(f333(f311(x88393),x88392),f194(f890(x88393,a874)))))),f333(f333(f66(x88393,x88394,x88391),x88395),x88396)) % 191.49/191.42 [9136]~P22(x91363,x91361,x91366,x91362)+~P4(f333(f63(x91363),x91365))+~P4(f333(f63(x91363),x91364))+E(f333(f74(x91361,x91361,x91361,f333(x91362,f333(f333(f115(f890(x91363,a874)),x91364),x91365))),f333(x91362,f333(f333(f106(f890(x91363,a874)),x91364),x91365))),f333(f74(x91361,x91361,x91361,f333(x91362,x91364)),f333(x91362,x91365))) % 191.49/191.42 [9468]~E(x94683,f333(f333(f160(x94681,x94682),x94685),x94686))+P4(f333(f333(f335(f889(f881(x94681),f881(x94681))),f333(f333(f263(f881(x94681),f881(x94681)),x94682),x94683)),f158(x94681,x94684)))+~P4(f333(f333(f251(a880),x94685),f333(f195(f881(x94681)),x94682)))+~P4(f333(f333(f335(f889(x94681,x94681)),f333(f333(f263(x94681,x94681),f333(f333(f166(x94681),x94682),x94685)),x94686)),x94684)) % 191.49/191.42 [9985]~P69(x99852)+~P4(f333(f63(x99851),x99856))+P4(f333(f333(f335(x99851),f633(x99854,x99855,x99853,x99856,x99851,x99852)),x99856))+E(f333(f333(f8(x99851,x99852),f333(f333(f20(x99851,f890(x99853,a874),x99852),f333(f333(f10(f890(x99853,x99852),f890(f890(x99853,a874),x99852),x99851),f8(x99853,x99852)),x99854)),x99855)),x99856),f333(f333(f8(f889(x99851,x99853),x99852),f333(f272(x99851,x99853,x99852),x99854)),f333(f333(f270(x99851,x99853),x99856),x99855))) % 191.49/191.42 [9986]~P76(x99862)+~P4(f333(f63(x99861),x99866))+P4(f333(f333(f335(x99861),f631(x99864,x99865,x99863,x99866,x99861,x99862)),x99866))+E(f333(f333(f11(x99861,x99862),f333(f333(f20(x99861,f890(x99863,a874),x99862),f333(f333(f10(f890(x99863,x99862),f890(f890(x99863,a874),x99862),x99861),f11(x99863,x99862)),x99864)),x99865)),x99866),f333(f333(f11(f889(x99861,x99863),x99862),f333(f272(x99861,x99863,x99862),x99864)),f333(f333(f270(x99861,x99863),x99866),x99865))) % 191.49/191.42 [10028]~P69(x100282)+~P4(f333(f63(x100281),x100286))+~P4(f333(f63(x100283),f333(x100285,f633(x100284,x100285,x100283,x100286,x100281,x100282))))+E(f333(f333(f8(x100281,x100282),f333(f333(f20(x100281,f890(x100283,a874),x100282),f333(f333(f10(f890(x100283,x100282),f890(f890(x100283,a874),x100282),x100281),f8(x100283,x100282)),x100284)),x100285)),x100286),f333(f333(f8(f889(x100281,x100283),x100282),f333(f272(x100281,x100283,x100282),x100284)),f333(f333(f270(x100281,x100283),x100286),x100285))) % 191.49/191.42 [10029]~P76(x100292)+~P4(f333(f63(x100291),x100296))+~P4(f333(f63(x100293),f333(x100295,f631(x100294,x100295,x100293,x100296,x100291,x100292))))+E(f333(f333(f11(x100291,x100292),f333(f333(f20(x100291,f890(x100293,a874),x100292),f333(f333(f10(f890(x100293,x100292),f890(f890(x100293,a874),x100292),x100291),f11(x100293,x100292)),x100294)),x100295)),x100296),f333(f333(f11(f889(x100291,x100293),x100292),f333(f272(x100291,x100293,x100292),x100294)),f333(f333(f270(x100291,x100293),x100296),x100295))) % 191.49/191.42 [10009]~P76(x100092)+~P4(f333(f63(x100091),x100096))+P4(f333(f333(f335(x100091),x100093),x100096))+E(f333(f333(f11(x100091,x100092),f333(f333(f9(x100091,x100092,x100092),f333(f333(f20(x100091,x100092,f890(x100092,x100092)),f333(f333(f10(a874,f890(x100092,f890(x100092,x100092)),x100091),f101(x100092)),f333(f333(f9(x100091,x100091,a874),a330),x100093))),x100094)),x100095)),x100096),f333(f333(f264(x100092),x100095),f333(f39(x100091),x100096))) % 191.49/191.42 [10014]~P76(x100142)+~P4(f333(f63(x100141),x100146))+~P4(f333(f333(f335(x100141),x100143),x100146))+E(f333(f333(f11(x100141,x100142),f333(f333(f9(x100141,x100142,x100142),f333(f333(f20(x100141,x100142,f890(x100142,x100142)),f333(f333(f10(a874,f890(x100142,f890(x100142,x100142)),x100141),f101(x100142)),f333(f333(f9(x100141,x100141,a874),a330),x100143))),x100144)),x100145)),x100146),f333(f333(f82(x100142),f333(x100144,x100143)),f333(f333(f264(x100142),x100145),f333(f333(f3(a880),f333(f39(x100141),x100146)),f79(a880))))) % 191.49/191.42 [10085]~P4(f333(f63(x100851),x100855))+~P4(f333(f63(x100852),x100853))+P4(f333(f333(f335(x100852),f571(x100856,x100854,x100853,x100852,x100855,x100851)),x100853))+E(f333(f333(f8(x100851,a880),f333(f333(f10(f890(x100852,a874),a880,x100851),f39(x100852)),f333(f333(f10(f890(x100852,a874),f890(x100852,a874),x100851),f255(x100852)),f333(f333(f10(f890(x100852,a874),f890(x100852,a874),x100851),f333(f20(x100852,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100852),a331),f333(f333(f9(x100852,f890(x100852,a874),a874),f335(x100852)),x100853)))),x100854)))),x100855),f333(f333(f82(a880),x100856),f333(f39(x100852),x100853))) % 191.49/191.42 [10086]~P4(f333(f63(x100861),x100865))+~P4(f333(f63(x100862),x100863))+P4(f333(f333(f335(x100862),f572(x100866,x100864,x100863,x100862,x100865,x100861)),x100863))+E(f333(f333(f8(x100861,a880),f333(f333(f10(f890(x100862,a874),a880,x100861),f39(x100862)),f333(f333(f10(f890(x100862,a874),f890(x100862,a874),x100861),f255(x100862)),f333(f333(f10(f890(x100862,a874),f890(x100862,a874),x100861),f333(f20(x100862,a874,a874),f333(f333(f10(a874,f890(a874,a874),x100862),a331),f333(f333(f9(x100862,f890(x100862,a874),a874),f335(x100862)),x100863)))),x100864)))),x100865),f333(f333(f8(x100862,a880),x100866),x100863)) % 191.49/191.42 [10120]~P4(f333(f63(x101202),x101203))+~P4(f333(f63(x101201),x101205))+~E(f333(f39(x101201),f333(f255(x101201),f333(f333(f20(x101201,a874,a874),f333(f333(f10(a874,f890(a874,a874),x101201),a331),f333(f333(f9(x101201,f890(x101201,a874),a874),f335(x101201)),x101205))),f333(f333(f9(x101201,x101202,a874),x101204),f571(x101206,x101204,x101203,x101202,x101205,x101201))))),x101206)+E(f333(f333(f8(x101201,a880),f333(f333(f10(f890(x101202,a874),a880,x101201),f39(x101202)),f333(f333(f10(f890(x101202,a874),f890(x101202,a874),x101201),f255(x101202)),f333(f333(f10(f890(x101202,a874),f890(x101202,a874),x101201),f333(f20(x101202,a874,a874),f333(f333(f10(a874,f890(a874,a874),x101202),a331),f333(f333(f9(x101202,f890(x101202,a874),a874),f335(x101202)),x101203)))),x101204)))),x101205),f333(f333(f82(a880),x101206),f333(f39(x101202),x101203))) % 191.49/191.42 [10139]~P4(f333(f63(x101392),x101393))+~P4(f333(f63(x101391),x101395))+~E(f333(f39(x101391),f333(f255(x101391),f333(f333(f20(x101391,a874,a874),f333(f333(f10(a874,f890(a874,a874),x101391),a331),f333(f333(f9(x101391,f890(x101391,a874),a874),f335(x101391)),x101395))),f333(f333(f9(x101391,x101392,a874),x101394),f572(x101396,x101394,x101393,x101392,x101395,x101391))))),f333(x101396,f572(x101396,x101394,x101393,x101392,x101395,x101391)))+E(f333(f333(f8(x101391,a880),f333(f333(f10(f890(x101392,a874),a880,x101391),f39(x101392)),f333(f333(f10(f890(x101392,a874),f890(x101392,a874),x101391),f255(x101392)),f333(f333(f10(f890(x101392,a874),f890(x101392,a874),x101391),f333(f20(x101392,a874,a874),f333(f333(f10(a874,f890(a874,a874),x101392),a331),f333(f333(f9(x101392,f890(x101392,a874),a874),f335(x101392)),x101393)))),x101394)))),x101395),f333(f333(f8(x101392,a880),x101396),x101393)) % 191.49/191.42 [9792]E(x97921,x97922)+~P19(x97923,x97924,x97925)+~P4(f333(f68(x97923,x97924,x97925,x97926,x97927),x97922))+~P4(f333(f68(x97923,x97924,x97925,x97926,x97927),x97921)) % 191.49/191.42 [9559]P4(f333(x95591,x95592))+~P4(f333(f333(f335(x95597),x95592),f333(x95596,x95594)))+~P4(f333(x95591,f543(x95591,x95596,x95595,x95593,x95597)))+~P4(f333(f333(f335(x95593),x95594),x95595)) % 191.49/191.42 [10001]~P19(x100017,x100016,x100011)+E(f333(f333(x100011,x100012),f736(x100012,x100013,x100014,x100015,x100011,x100016,x100017)),x100013)+~P4(f333(f68(x100017,x100016,x100011,x100015,x100014),x100013))+~P4(f333(f333(f335(x100017),x100012),x100014)) % 191.49/191.42 [10060]~P19(x100601,x100602,x100603)+~P4(f333(f68(x100601,x100602,x100603,x100604,x100605),x100607))+P4(f333(f68(x100601,x100602,x100603,x100604,f333(f333(f3(f890(x100601,a874)),x100605),f333(f333(f311(x100601),x100606),f194(f890(x100601,a874))))),f736(x100606,x100607,x100605,x100604,x100603,x100602,x100601)))+~P4(f333(f333(f335(x100601),x100606),x100605)) % 191.49/191.42 [9444]~P73(x94441)+~P28(x94445,x94442,x94446,x94447)+~P4(f333(f63(x94445),x94447))+E(f333(f333(f333(f67(x94441,x94442,f82(x94441)),x94443),x94444),f333(f312(x94445,x94442,x94446),x94447)),f333(f333(f333(f67(x94441,x94445,f82(x94441)),f333(f74(x94442,x94441,x94445,x94443),x94446)),x94444),x94447)) % 191.49/191.42 [9581]~E(f333(f333(f311(x95811),x95815),x95816),f333(f333(f311(x95811),x95812),x95813))+~P4(f333(f68(x95811,x95811,x95814,x95812,x95813),x95817))+P4(f333(f333(f335(x95811),x95812),x95813))+P4(f333(f64(x95811,x95814,f333(f333(f311(x95811),x95815),x95816)),x95817)) % 191.49/191.42 [9676]P4(f333(x96761,x96762))+~P4(f333(f333(f335(x96763),x96762),f333(x96764,x96767)))+~P4(f333(f333(f335(x96766),x96767),x96765))+P4(f333(f333(f335(x96763),f543(x96761,x96764,x96765,x96766,x96763)),f333(f333(f44(x96766,f890(x96763,a874)),x96765),x96764))) % 191.49/191.42 [9691]~P28(x96912,x96911,x96915,x96914)+~P28(x96911,x96913,x96916,f333(f312(x96912,x96911,x96915),x96914))+E(f333(f333(f74(x96911,x96912,x96913,f78(x96912,x96911,x96914,x96915)),f78(x96911,x96913,f333(f312(x96912,x96911,x96915),x96914),x96916)),x96917),f333(f78(x96912,x96913,x96914,f333(f74(x96911,x96913,x96912,x96916),x96915)),x96917))+~P4(f333(f333(f335(x96913),x96917),f333(f312(x96911,x96913,x96916),f333(f312(x96912,x96911,x96915),x96914)))) % 191.49/191.42 [10002]~P19(x100027,x100026,x100021)+E(f333(f333(x100021,x100022),f830(x100023,x100024,x100022,x100025,x100021,x100026,x100027)),x100023)+P4(f333(f333(f335(x100027),x100022),x100024))+~P4(f333(f68(x100027,x100026,x100021,x100025,f333(f333(f311(x100027),x100022),x100024)),x100023)) % 191.49/191.42 [10059]~P19(x100591,x100594,x100595)+P4(f333(f68(x100591,x100594,x100595,x100596,x100593),f830(x100597,x100593,x100592,x100596,x100595,x100594,x100591)))+P4(f333(f333(f335(x100591),x100592),x100593))+~P4(f333(f68(x100591,x100594,x100595,x100596,f333(f333(f311(x100591),x100592),x100593)),x100597)) % 191.49/191.42 [9771]E(x97711,f2(a1))+~P4(f333(f50(x97713,x97711),f333(f333(f263(a1,a1),x97715),x97717)))+~P4(f333(f50(x97712,x97711),f333(f333(f263(a1,a1),x97714),x97716)))+P4(f333(f50(f333(f333(f81(a1),x97712),x97713),x97711),f333(f333(f263(a1,a1),f333(f333(f81(a1),f333(f333(f81(a1),x97714),x97715)),f333(f333(f40(a1),f333(f333(f81(a1),x97716),x97717)),x97711))),f46(a1,f333(f333(f81(a1),x97716),x97717),x97711)))) % 191.49/191.42 [9773]~P4(f333(f333(f251(a880),f2(a880)),x97733))+~P4(f333(f49(x97732,x97733),f333(f333(f263(a880,a880),x97735),x97737)))+~P4(f333(f49(x97731,x97733),f333(f333(f263(a880,a880),x97734),x97736)))+P4(f333(f49(f333(f333(f81(a880),x97731),x97732),x97733),f333(f333(f263(a880,a880),f333(f333(f81(a880),f333(f333(f81(a880),x97734),x97735)),f333(f333(f40(a880),f333(f333(f81(a880),x97736),x97737)),x97733))),f46(a880,f333(f333(f81(a880),x97736),x97737),x97733)))) % 191.49/191.42 [10119]~P69(x101192)+~P4(f333(f63(x101193),x101195))+~P4(f333(f63(x101191),x101197))+E(f333(f333(f8(x101191,x101192),f333(f333(f20(x101191,f890(x101193,a874),x101192),f333(f333(f10(f890(x101193,x101192),f890(f890(x101193,a874),x101192),x101191),f8(x101193,x101192)),x101194)),f333(f333(f10(f890(x101193,a874),f890(x101193,a874),x101191),f255(x101193)),f333(f333(f10(f890(x101193,a874),f890(x101193,a874),x101191),f333(f20(x101193,a874,a874),f333(f333(f10(a874,f890(a874,a874),x101193),a331),f333(f333(f9(x101193,f890(x101193,a874),a874),f335(x101193)),x101195)))),x101196)))),x101197),f333(f333(f8(x101193,x101192),f333(f333(f20(x101193,f890(x101191,a874),x101192),f333(f333(f10(f890(x101191,x101192),f890(f890(x101191,a874),x101192),x101193),f8(x101191,x101192)),f333(f9(x101191,x101193,x101192),x101194))),f333(f333(f10(f890(x101191,a874),f890(x101191,a874),x101193),f255(x101191)),f333(f333(f10(f890(x101191,a874),f890(x101191,a874),x101193),f333(f20(x101191,a874,a874),f333(f333(f10(a874,f890(a874,a874),x101191),a331),f333(f333(f9(x101191,f890(x101191,a874),a874),f335(x101191)),x101197)))),f333(f9(x101191,x101193,a874),x101196))))),x101195)) % 191.49/191.42 [9629]~P25(x96297,x96296,x96291,x96298,x96292,x96294)+E(f333(f333(x96291,f333(x96292,x96293)),f333(x96294,x96295)),f333(x96294,x96295))+~P4(f333(f63(x96296),x96295))+~P4(f333(f333(f335(x96296),x96293),x96295)) % 191.49/191.42 [9633]~P16(x96336,x96331,x96332,x96338,x96333,x96334)+~P12(x96336,x96337,x96338)+P15(x96331,x96332,x96333,f333(x96334,x96335))+~P4(f333(f333(f335(x96336),x96335),x96337)) % 191.49/191.42 [8061]~P30(x80618,x80617,f333(f333(f333(f93(x80618),x80614),x80616),x80611))+P4(f333(f333(x80611,x80612),x80613))+~P4(f333(f333(x80614,x80612),x80615))+~P4(f333(f333(f333(f333(a203,x80616),x80615),x80617),x80613)) % 191.49/191.42 [9230]~P22(x92307,x92301,x92308,x92303)+~P4(f333(f63(x92307),x92305))+~P4(f333(f63(x92307),x92304))+E(f333(f74(x92301,x92301,x92302,f333(x92303,x92304)),f333(f74(x92301,x92301,x92302,f333(x92303,x92305)),x92306)),f333(f74(x92301,x92301,x92302,f333(x92303,x92305)),f333(f74(x92301,x92301,x92302,f333(x92303,x92304)),x92306))) % 191.49/191.42 [9238]~P37(x92381,x92382,x92383,x92384,x92387)+P37(x92381,x92382,x92383,f333(f333(f160(x92381,x92384),x92385),x92386),f333(f333(f160(x92382,x92387),x92385),x92388))+~P4(f333(f333(x92383,x92386),x92388))+~P4(f333(f333(f251(a880),x92385),f333(f195(f881(x92381)),x92384))) % 191.49/191.42 [9239]~P37(x92391,x92392,x92393,x92394,x92397)+P37(x92391,x92392,x92393,f333(f333(f160(x92391,x92394),x92395),x92396),f333(f333(f160(x92392,x92397),x92395),x92398))+~P4(f333(f333(x92393,x92396),x92398))+~P4(f333(f333(f251(a880),x92395),f333(f195(f881(x92392)),x92397))) % 191.49/191.42 [9321]~P28(x93212,x93212,x93215,x93216)+~P24(x93213,x93212,x93217,x93218,x93211)+~P4(f333(f63(x93212),x93216))+E(f333(f333(x93211,f333(f74(x93212,x93213,x93212,x93214),x93215)),x93216),f333(f333(x93211,x93214),f333(f312(x93212,x93212,x93215),x93216))) % 191.49/191.42 [9631]~P26(x96317,x96312,x96315,x96318,x96316,x96311)+~P4(f333(f63(x96312),x96314))+E(f333(x96311,f333(f333(f311(x96312),x96313),x96314)),f333(f333(x96315,f333(x96316,x96313)),f333(x96311,x96314)))+P4(f333(f333(f335(x96312),x96313),x96314)) % 191.49/191.42 [9644]~P25(x96446,x96445,x96441,x96447,x96448,x96442)+E(f333(f333(x96441,f333(x96442,x96443)),f333(x96442,x96444)),f333(x96442,x96444))+~P4(f333(f63(x96445),x96444))+~P4(f333(f333(f250(f890(x96445,a874)),x96443),x96444)) % 191.49/191.42 [9216]P4(f333(f333(f335(f889(f881(x92161),f881(x92161))),f333(f333(f263(f881(x92161),f881(x92161)),x92162),x92163)),f158(x92161,x92164)))+~E(x92163,f333(f333(f127(x92161),x92165),f333(f333(f152(x92161),x92166),x92167)))+~E(x92162,f333(f333(f127(x92161),x92165),f333(f333(f152(x92161),x92168),x92167)))+~P4(f333(f333(f335(f889(x92161,x92161)),f333(f333(f263(x92161,x92161),x92168),x92166)),x92164)) % 191.49/191.42 [9640]~P25(x96406,x96402,x96405,x96407,x96408,x96401)+~P4(f333(f63(x96402),x96404))+~P4(f333(f63(x96402),x96403))+E(f333(x96401,f333(f333(f115(f890(x96402,a874)),x96403),x96404)),f333(f333(x96405,f333(x96401,x96403)),f333(x96401,x96404))) % 191.49/191.42 [10187]~P28(x101874,x101872,x101875,x101878)+E(f333(f333(f43(x101871,f890(x101872,a874)),x101873),f333(f333(f10(f890(x101874,a874),f890(x101872,a874),x101871),f312(x101874,x101872,x101875)),x101876)),f333(f312(x101874,x101872,x101875),f333(f333(f43(x101871,f890(x101874,a874)),x101873),x101876)))+~P4(f333(f333(f335(x101871),x101877),x101873))+P4(f333(f333(f335(x101871),f534(x101877,x101876,x101873,x101871,x101878,x101875,x101872,x101874)),x101873)) % 191.49/191.42 [10217]~P28(x102174,x102172,x102175,x102177)+E(f333(f333(f43(x102171,f890(x102172,a874)),x102173),f333(f333(f10(f890(x102174,a874),f890(x102172,a874),x102171),f312(x102174,x102172,x102175)),x102176)),f333(f312(x102174,x102172,x102175),f333(f333(f43(x102171,f890(x102174,a874)),x102173),x102176)))+~P4(f333(f333(f335(x102171),x102178),x102173))+~P4(f333(f333(f250(f890(x102174,a874)),f333(x102176,f534(x102178,x102176,x102173,x102171,x102177,x102175,x102172,x102174))),x102177)) % 191.49/191.42 [9700]~P26(x97007,x97005,x97001,x97008,x97002,x97004)+~P4(f333(f63(x97005),x97006))+~P4(f333(f333(f335(x97005),x97003),x97006))+E(f333(f333(x97001,f333(x97002,x97003)),f333(x97004,f333(f333(f3(f890(x97005,a874)),x97006),f333(f333(f311(x97005),x97003),f194(f890(x97005,a874)))))),f333(x97004,x97006)) % 191.49/191.42 [9708]~P26(x97086,x97083,x97081,x97087,x97088,x97082)+~P4(f333(f63(x97083),x97085))+~P4(f333(f63(x97083),x97084))+E(f333(f333(x97081,f333(x97082,f333(f333(f115(f890(x97083,a874)),x97084),x97085))),f333(x97082,f333(f333(f106(f890(x97083,a874)),x97084),x97085))),f333(f333(x97081,f333(x97082,x97084)),f333(x97082,x97085))) % 191.49/191.42 [9811]P44(x98111,x98112,x98113,x98114,x98115,f333(f333(x98113,x98116),x98117))+~P44(x98111,x98112,x98113,x98114,f333(f333(f3(f890(x98111,a874)),x98115),f333(f333(f311(x98111),x98118),f194(f890(x98111,a874)))),x98119)+~E(f333(f333(x98113,x98116),x98117),f333(f333(x98113,x98118),x98119))+~P4(f333(f333(f335(x98111),x98118),x98115)) % 191.49/191.42 [10232]P27(x102321,x102322,f333(f333(f311(f879(x102321)),f333(f333(f333(f93(x102321),f333(x102323,f515(x102324,x102325,x102326,x102327,x102323,x102322,x102321,x102328,x102329))),f333(x102327,f515(x102324,x102325,x102326,x102327,x102323,x102322,x102321,x102328,x102329))),f333(x102326,f515(x102324,x102325,x102326,x102327,x102323,x102322,x102321,x102328,x102329)))),f194(f890(f879(x102321),a874))))+~P4(f333(f63(x102329),x102328))+~P27(x102321,x102322,f333(f312(x102329,f879(x102321),f333(f333(f20(x102329,f890(x102321,f890(a875,a874)),f879(x102321)),f333(f333(f20(x102329,a876,f890(f890(x102321,f890(a875,a874)),f879(x102321))),f333(f333(f10(f890(x102321,f890(a875,a874)),f890(a876,f890(f890(x102321,f890(a875,a874)),f879(x102321))),x102329),f93(x102321)),x102323)),x102327)),x102326)),x102328))+P27(x102321,x102322,f333(f312(x102329,f879(x102321),f333(f333(f20(x102329,f890(x102321,f890(a875,a874)),f879(x102321)),f333(f333(f20(x102329,a876,f890(f890(x102321,f890(a875,a874)),f879(x102321))),f333(f333(f10(f890(x102321,f890(a875,a874)),f890(a876,f890(f890(x102321,f890(a875,a874)),f879(x102321))),x102329),f93(x102321)),x102325)),x102327)),x102324)),x102328)) % 191.49/191.42 [10233]~P27(x102331,x102332,f333(f333(f311(f879(x102331)),f333(f333(f333(f93(x102331),f333(x102334,f515(x102336,x102334,x102338,x102335,x102339,x102332,x102331,x102337,x102333))),f333(x102335,f515(x102336,x102334,x102338,x102335,x102339,x102332,x102331,x102337,x102333))),f333(x102336,f515(x102336,x102334,x102338,x102335,x102339,x102332,x102331,x102337,x102333)))),f194(f890(f879(x102331),a874))))+~P4(f333(f63(x102333),x102337))+~P27(x102331,x102332,f333(f312(x102333,f879(x102331),f333(f333(f20(x102333,f890(x102331,f890(a875,a874)),f879(x102331)),f333(f333(f20(x102333,a876,f890(f890(x102331,f890(a875,a874)),f879(x102331))),f333(f333(f10(f890(x102331,f890(a875,a874)),f890(a876,f890(f890(x102331,f890(a875,a874)),f879(x102331))),x102333),f93(x102331)),x102339)),x102335)),x102338)),x102337))+P27(x102331,x102332,f333(f312(x102333,f879(x102331),f333(f333(f20(x102333,f890(x102331,f890(a875,a874)),f879(x102331)),f333(f333(f20(x102333,a876,f890(f890(x102331,f890(a875,a874)),f879(x102331))),f333(f333(f10(f890(x102331,f890(a875,a874)),f890(a876,f890(f890(x102331,f890(a875,a874)),f879(x102331))),x102333),f93(x102331)),x102334)),x102335)),x102336)),x102337)) % 191.49/191.42 [9734]~P16(x97346,x97347,x97348,x97349,x973410,x97341)+E(f333(f333(x97341,x97342),x97343),f333(f333(x97341,x97344),x97345))+~P4(f333(f333(f335(f889(x97347,x97347)),f333(f333(f263(x97347,x97347),x97343),x97345)),x973410))+~P4(f333(f333(f335(f889(x97346,x97346)),f333(f333(f263(x97346,x97346),x97342),x97344)),x97349)) % 191.49/191.42 [9323]~P6(x93232)+E(x93231,f194(f890(x93232,a874)))+~P4(f333(f63(x93232),x93231))+P4(f333(f333(f335(x93232),f12(x93232,x93231)),x93231))+~P4(f333(f333(f335(x93232),f333(f333(f115(x93232),f537(x93231,x93232)),f542(x93231,x93232))),f333(f333(f311(x93232),f537(x93231,x93232)),f333(f333(f311(x93232),f542(x93231,x93232)),f194(f890(x93232,a874)))))) % 191.49/191.42 [9324]~P6(x93242)+E(x93241,f194(f890(x93242,a874)))+~P4(f333(f63(x93242),x93241))+P4(f333(f333(f335(x93242),f13(x93242,x93241)),x93241))+~P4(f333(f333(f335(x93242),f333(f333(f106(x93242),f630(x93241,x93242)),f638(x93241,x93242))),f333(f333(f311(x93242),f630(x93241,x93242)),f333(f333(f311(x93242),f638(x93241,x93242)),f194(f890(x93242,a874)))))) % 191.49/191.42 [9360]~P73(x93602)+E(x93601,f194(f890(x93602,a874)))+~P4(f333(f63(x93602),x93601))+P4(f333(f333(f335(x93602),f333(f65(x93602,f82(x93602)),x93601)),x93601))+~P4(f333(f333(f335(x93602),f333(f333(f82(x93602),f839(x93601,x93602)),f840(x93601,x93602))),f333(f333(f311(x93602),f839(x93601,x93602)),f333(f333(f311(x93602),f840(x93601,x93602)),f194(f890(x93602,a874)))))) % 191.49/191.42 [9366]~P109(x93662)+E(x93661,f194(f890(x93662,a874)))+~P4(f333(f63(x93662),x93661))+P4(f333(f333(f335(x93662),f14(x93662,f248(x93662),x93661)),x93661))+~P4(f333(f333(f335(x93662),f333(f333(f248(x93662),f469(x93661,x93662)),f470(x93661,x93662))),f333(f333(f311(x93662),f469(x93661,x93662)),f333(f333(f311(x93662),f470(x93661,x93662)),f194(f890(x93662,a874)))))) % 191.49/191.42 [9367]~P109(x93672)+E(x93671,f194(f890(x93672,a874)))+~P4(f333(f63(x93672),x93671))+P4(f333(f333(f335(x93672),f15(x93672,f249(x93672),x93671)),x93671))+~P4(f333(f333(f335(x93672),f333(f333(f249(x93672),f482(x93671,x93672)),f488(x93671,x93672))),f333(f333(f311(x93672),f482(x93671,x93672)),f333(f333(f311(x93672),f488(x93671,x93672)),f194(f890(x93672,a874)))))) % 191.49/191.42 [6524]~P89(x65242)+E(x65241,f2(x65242))+~E(f333(f333(f81(x65242),x65243),x65241),f2(x65242))+~P4(f333(f333(f250(x65242),f2(x65242)),x65243))+~P4(f333(f333(f250(x65242),f2(x65242)),x65241)) % 191.49/191.42 [6525]~P89(x65252)+E(x65251,f2(x65252))+~E(f333(f333(f81(x65252),x65251),x65253),f2(x65252))+~P4(f333(f333(f250(x65252),f2(x65252)),x65253))+~P4(f333(f333(f250(x65252),f2(x65252)),x65251)) % 191.49/191.42 [7049]~P109(x70492)+~P17(x70492,x70491)+E(x70491,f118(x70492))+~P4(f333(f333(f335(x70492),x70493),f333(f173(x70492),f645(x70491,x70492))))+P4(f333(f333(f250(x70492),f678(x70491,x70492)),x70493)) % 191.49/191.42 [7214]~P109(x72141)+E(f16(x72141,x72142),x72143)+~P4(f333(f63(x72141),x72142))+~P4(f333(f333(f250(x72141),x72143),f473(x72143,x72142,x72141)))+~P4(f333(f333(f335(x72141),x72143),x72142)) % 191.49/191.42 [7245]~P109(x72451)+~P17(x72451,x72452)+~P17(x72451,x72453)+P17(x72451,f333(f333(f127(x72451),x72452),x72453))+P4(f333(f333(f335(x72451),f651(x72453,x72452,x72451)),f333(f173(x72451),x72452))) % 191.49/191.42 [7246]~P109(x72461)+~P17(x72461,x72462)+~P17(x72461,x72463)+P17(x72461,f333(f333(f127(x72461),x72462),x72463))+P4(f333(f333(f335(x72461),f653(x72463,x72462,x72461)),f333(f173(x72461),x72463))) % 191.49/191.42 [7300]~P109(x73001)+E(f16(x73001,x73002),x73003)+~P4(f333(f63(x73001),x73002))+P4(f333(f333(f335(x73001),f473(x73003,x73002,x73001)),x73002))+~P4(f333(f333(f335(x73001),x73003),x73002)) % 191.49/191.42 [7301]~P109(x73011)+E(f17(x73011,x73012),x73013)+~P4(f333(f63(x73011),x73012))+P4(f333(f333(f335(x73011),f479(x73013,x73012,x73011)),x73012))+~P4(f333(f333(f335(x73011),x73013),x73012)) % 191.49/191.42 [7865]~P109(x78651)+E(f17(x78651,x78652),x78653)+~P4(f333(f63(x78651),x78652))+~P4(f333(f333(f335(x78651),x78653),x78652))+~P4(f333(f333(f250(x78651),f479(x78653,x78652,x78651)),x78653)) % 191.49/191.42 [8196]~P109(x81961)+~P17(x81961,x81962)+~P17(x81961,x81963)+P17(x81961,f333(f333(f127(x81961),x81962),x81963))+~P4(f333(f333(f250(x81961),f651(x81963,x81962,x81961)),f653(x81963,x81962,x81961))) % 191.49/191.42 [8967]~P6(x89672)+E(x89671,f194(f890(x89672,a874)))+~E(f333(f333(f115(x89672),f333(x89673,f797(x89671,x89673,x89672))),f333(x89673,f805(x89671,x89673,x89672))),f333(x89673,f333(f333(f115(x89672),f797(x89671,x89673,x89672)),f805(x89671,x89673,x89672))))+E(f12(x89672,f333(f312(x89672,x89672,x89673),x89671)),f333(x89673,f12(x89672,x89671)))+~P4(f333(f63(x89672),x89671)) % 191.49/191.42 [8968]~P6(x89682)+E(x89681,f194(f890(x89682,a874)))+~E(f333(f333(f106(x89682),f333(x89683,f772(x89681,x89683,x89682))),f333(x89683,f773(x89681,x89683,x89682))),f333(x89683,f333(f333(f106(x89682),f772(x89681,x89683,x89682)),f773(x89681,x89683,x89682))))+E(f13(x89682,f333(f312(x89682,x89682,x89683),x89681)),f333(x89683,f13(x89682,x89681)))+~P4(f333(f63(x89682),x89681)) % 191.49/191.42 [8969]~P109(x89692)+E(x89691,f194(f890(x89692,a874)))+~E(f333(f333(f248(x89692),f333(x89693,f474(x89691,x89693,x89692))),f333(x89693,f477(x89691,x89693,x89692))),f333(x89693,f333(f333(f248(x89692),f474(x89691,x89693,x89692)),f477(x89691,x89693,x89692))))+E(f16(x89692,f333(f312(x89692,x89692,x89693),x89691)),f333(x89693,f16(x89692,x89691)))+~P4(f333(f63(x89692),x89691)) % 191.49/191.42 [8970]~P109(x89702)+E(x89701,f194(f890(x89702,a874)))+~E(f333(f333(f249(x89702),f333(x89703,f486(x89701,x89703,x89702))),f333(x89703,f490(x89701,x89703,x89702))),f333(x89703,f333(f333(f249(x89702),f486(x89701,x89703,x89702)),f490(x89701,x89703,x89702))))+E(f17(x89702,f333(f312(x89702,x89702,x89703),x89701)),f333(x89703,f17(x89702,x89701)))+~P4(f333(f63(x89702),x89701)) % 191.49/191.42 [9034]~P109(x90342)+E(x90341,f194(f890(x90342,a874)))+~E(f333(f333(f248(x90342),f333(x90343,f475(x90341,x90343,x90342))),f333(x90343,f476(x90341,x90343,x90342))),f333(x90343,f333(f333(f248(x90342),f475(x90341,x90343,x90342)),f476(x90341,x90343,x90342))))+E(f14(x90342,f248(x90342),f333(f312(x90342,x90342,x90343),x90341)),f333(x90343,f14(x90342,f248(x90342),x90341)))+~P4(f333(f63(x90342),x90341)) % 191.49/191.42 [9035]~P109(x90352)+E(x90351,f194(f890(x90352,a874)))+~E(f333(f333(f249(x90352),f333(x90353,f487(x90351,x90353,x90352))),f333(x90353,f489(x90351,x90353,x90352))),f333(x90353,f333(f333(f249(x90352),f487(x90351,x90353,x90352)),f489(x90351,x90353,x90352))))+E(f15(x90352,f249(x90352),f333(f312(x90352,x90352,x90353),x90351)),f333(x90353,f15(x90352,f249(x90352),x90351)))+~P4(f333(f63(x90352),x90351)) % 191.49/191.42 [6542]~P73(x65422)+E(x65421,f194(f890(x65422,a874)))+~P4(f333(f63(x65422),x65421))+E(f333(f65(x65422,f82(x65422)),f333(f333(f311(x65422),x65423),x65421)),f333(f333(f82(x65422),x65423),f333(f65(x65422,f82(x65422)),x65421)))+P4(f333(f333(f335(x65422),x65423),x65421)) % 191.49/191.42 [7055]~P6(x70552)+E(f333(f333(f115(x70552),f12(x70552,x70551)),f12(x70552,x70553)),f12(x70552,x70553))+E(x70551,f194(f890(x70552,a874)))+~P4(f333(f63(x70552),x70553))+~P4(f333(f333(f250(f890(x70552,a874)),x70551),x70553)) % 191.49/191.42 [7056]~P6(x70562)+E(f333(f333(f106(x70562),f13(x70562,x70561)),f13(x70562,x70563)),f13(x70562,x70563))+E(x70561,f194(f890(x70562,a874)))+~P4(f333(f63(x70562),x70563))+~P4(f333(f333(f250(f890(x70562,a874)),x70561),x70563)) % 191.49/191.42 [7057]~P109(x70572)+E(f333(f333(f248(x70572),f16(x70572,x70571)),f16(x70572,x70573)),f16(x70572,x70573))+E(x70571,f194(f890(x70572,a874)))+~P4(f333(f63(x70572),x70573))+~P4(f333(f333(f250(f890(x70572,a874)),x70571),x70573)) % 191.49/191.42 [7058]~P109(x70582)+E(f333(f333(f249(x70582),f17(x70582,x70581)),f17(x70582,x70583)),f17(x70582,x70583))+E(x70581,f194(f890(x70582,a874)))+~P4(f333(f63(x70582),x70583))+~P4(f333(f333(f250(f890(x70582,a874)),x70581),x70583)) % 191.49/191.42 [7345]~P109(x73452)+E(x73451,f194(f890(x73452,a874)))+~P4(f333(f63(x73452),x73453))+P4(f333(f333(f250(x73452),f16(x73452,x73453)),f16(x73452,x73451)))+~P4(f333(f333(f250(f890(x73452,a874)),x73451),x73453)) % 191.49/191.42 [7346]~P109(x73462)+E(x73461,f194(f890(x73462,a874)))+~P4(f333(f63(x73462),x73463))+P4(f333(f333(f250(x73462),f17(x73462,x73461)),f17(x73462,x73463)))+~P4(f333(f333(f250(f890(x73462,a874)),x73461),x73463)) % 191.49/191.42 [7403]~P6(x74031)+E(f12(x74031,x74032),x74033)+~P4(f333(f63(x74031),x74032))+~E(f333(f333(f3(f890(x74031,a874)),x74032),f333(f333(f311(x74031),x74033),f194(f890(x74031,a874)))),f194(f890(x74031,a874)))+~P4(f333(f333(f335(x74031),x74033),x74032)) % 191.49/191.42 [7404]~P6(x74041)+E(f13(x74041,x74042),x74043)+~P4(f333(f63(x74041),x74042))+~E(f333(f333(f3(f890(x74041,a874)),x74042),f333(f333(f311(x74041),x74043),f194(f890(x74041,a874)))),f194(f890(x74041,a874)))+~P4(f333(f333(f335(x74041),x74043),x74042)) % 191.49/191.42 [7405]~P109(x74051)+E(f16(x74051,x74052),x74053)+~P4(f333(f63(x74051),x74052))+~E(f333(f333(f3(f890(x74051,a874)),x74052),f333(f333(f311(x74051),x74053),f194(f890(x74051,a874)))),f194(f890(x74051,a874)))+~P4(f333(f333(f335(x74051),x74053),x74052)) % 191.49/191.42 [7406]~P109(x74061)+E(f17(x74061,x74062),x74063)+~P4(f333(f63(x74061),x74062))+~E(f333(f333(f3(f890(x74061,a874)),x74062),f333(f333(f311(x74061),x74063),f194(f890(x74061,a874)))),f194(f890(x74061,a874)))+~P4(f333(f333(f335(x74061),x74063),x74062)) % 191.49/191.42 [7502]~P109(x75021)+E(f14(x75021,f248(x75021),x75022),x75023)+~P4(f333(f63(x75021),x75022))+~E(f333(f333(f3(f890(x75021,a874)),x75022),f333(f333(f311(x75021),x75023),f194(f890(x75021,a874)))),f194(f890(x75021,a874)))+~P4(f333(f333(f335(x75021),x75023),x75022)) % 191.49/191.42 [7503]~P109(x75031)+E(f15(x75031,f249(x75031),x75032),x75033)+~P4(f333(f63(x75031),x75032))+~E(f333(f333(f3(f890(x75031,a874)),x75032),f333(f333(f311(x75031),x75033),f194(f890(x75031,a874)))),f194(f890(x75031,a874)))+~P4(f333(f333(f335(x75031),x75033),x75032)) % 191.49/191.42 [7539]~P109(x75392)+E(x75391,f194(f890(x75392,a874)))+~P4(f333(f63(x75392),x75391))+~P4(f333(f333(f251(x75392),x75393),f464(x75393,x75391,x75392)))+P4(f333(f333(f251(x75392),x75393),f333(f65(x75392,f248(x75392)),x75391))) % 191.49/191.42 [7540]~P102(x75402)+E(x75401,f194(f890(x75402,a874)))+~P4(f333(f63(x75402),x75401))+~P4(f333(f333(f250(x75402),x75403),f352(x75403,x75401,x75402)))+P4(f333(f333(f250(x75402),x75403),f333(f65(x75402,f106(x75402)),x75401))) % 191.49/191.42 [7541]~P109(x75412)+E(x75411,f194(f890(x75412,a874)))+~P4(f333(f63(x75412),x75411))+~P4(f333(f333(f250(x75412),x75413),f465(x75413,x75411,x75412)))+P4(f333(f333(f250(x75412),x75413),f333(f65(x75412,f248(x75412)),x75411))) % 191.49/191.42 [7623]~P102(x76232)+E(x76231,f194(f890(x76232,a874)))+~P4(f333(f63(x76232),x76231))+P4(f333(f333(f335(x76232),f352(x76233,x76231,x76232)),x76231))+P4(f333(f333(f250(x76232),x76233),f333(f65(x76232,f106(x76232)),x76231))) % 191.49/191.42 [7624]~P109(x76242)+E(x76241,f194(f890(x76242,a874)))+~P4(f333(f63(x76242),x76241))+P4(f333(f333(f335(x76242),f465(x76243,x76241,x76242)),x76241))+P4(f333(f333(f250(x76242),x76243),f333(f65(x76242,f248(x76242)),x76241))) % 191.49/191.42 [7625]~P109(x76252)+E(x76251,f194(f890(x76252,a874)))+~P4(f333(f63(x76252),x76251))+P4(f333(f333(f335(x76252),f464(x76253,x76251,x76252)),x76251))+P4(f333(f333(f251(x76252),x76253),f333(f65(x76252,f248(x76252)),x76251))) % 191.49/191.42 [7746]~P109(x77462)+E(x77461,f194(f890(x77462,a874)))+E(f333(f333(f248(x77462),f14(x77462,f248(x77462),x77461)),f14(x77462,f248(x77462),x77463)),f14(x77462,f248(x77462),x77463))+~P4(f333(f63(x77462),x77463))+~P4(f333(f333(f250(f890(x77462,a874)),x77461),x77463)) % 191.49/191.42 [7747]~P109(x77472)+E(x77471,f194(f890(x77472,a874)))+E(f333(f333(f249(x77472),f15(x77472,f249(x77472),x77471)),f15(x77472,f249(x77472),x77473)),f15(x77472,f249(x77472),x77473))+~P4(f333(f63(x77472),x77473))+~P4(f333(f333(f250(f890(x77472,a874)),x77471),x77473)) % 191.49/191.42 [7940]~E(f376(x79401,x79403,x79402),f377(x79401,x79403,x79402))+~E(f333(f39(x79402),f378(x79401,x79403,x79402)),x79401)+E(f333(f333(f82(a880),x79401),f333(f39(f890(x79402,a874)),x79403)),f333(f39(x79402),f41(f890(x79402,a874),x79403)))+~P4(f333(f63(x79402),f41(f890(x79402,a874),x79403)))+~P4(f333(f63(f890(x79402,a874)),x79403)) % 191.49/191.42 [8128]~P109(x81282)+E(x81281,f194(f890(x81282,a874)))+~P4(f333(f63(x81282),x81283))+P4(f333(f333(f250(x81282),f333(f65(x81282,f248(x81282)),x81283)),f333(f65(x81282,f248(x81282)),x81281)))+~P4(f333(f333(f250(f890(x81282,a874)),x81281),x81283)) % 191.49/191.42 [8430]~E(f376(x84301,x84303,x84302),f377(x84301,x84303,x84302))+E(f333(f333(f82(a880),x84301),f333(f39(f890(x84302,a874)),x84303)),f333(f39(x84302),f41(f890(x84302,a874),x84303)))+P4(f333(f333(f335(f890(x84302,a874)),f378(x84301,x84303,x84302)),x84303))+~P4(f333(f63(x84302),f41(f890(x84302,a874),x84303)))+~P4(f333(f63(f890(x84302,a874)),x84303)) % 191.49/191.42 [8459]~E(f333(f39(x84592),f378(x84591,x84593,x84592)),x84591)+E(f333(f333(f82(a880),x84591),f333(f39(f890(x84592,a874)),x84593)),f333(f39(x84592),f41(f890(x84592,a874),x84593)))+P4(f333(f333(f335(f890(x84592,a874)),f377(x84591,x84593,x84592)),x84593))+~P4(f333(f63(x84592),f41(f890(x84592,a874),x84593)))+~P4(f333(f63(f890(x84592,a874)),x84593)) % 191.49/191.42 [8460]~E(f333(f39(x84602),f378(x84601,x84603,x84602)),x84601)+E(f333(f333(f82(a880),x84601),f333(f39(f890(x84602,a874)),x84603)),f333(f39(x84602),f41(f890(x84602,a874),x84603)))+P4(f333(f333(f335(f890(x84602,a874)),f376(x84601,x84603,x84602)),x84603))+~P4(f333(f63(x84602),f41(f890(x84602,a874),x84603)))+~P4(f333(f63(f890(x84602,a874)),x84603)) % 191.49/191.42 [8486]~E(f333(f39(x84862),f378(x84861,x84863,x84862)),x84861)+~E(f333(f333(f106(f890(x84862,a874)),f377(x84861,x84863,x84862)),f376(x84861,x84863,x84862)),f194(f890(x84862,a874)))+E(f333(f333(f82(a880),x84861),f333(f39(f890(x84862,a874)),x84863)),f333(f39(x84862),f41(f890(x84862,a874),x84863)))+~P4(f333(f63(f890(x84862,a874)),x84863))+~P4(f333(f63(x84862),f41(f890(x84862,a874),x84863))) % 191.49/191.42 [8724]E(f333(f333(f82(a880),x87241),f333(f39(f890(x87242,a874)),x87243)),f333(f39(x87242),f41(f890(x87242,a874),x87243)))+P4(f333(f333(f335(f890(x87242,a874)),f378(x87241,x87243,x87242)),x87243))+P4(f333(f333(f335(f890(x87242,a874)),f377(x87241,x87243,x87242)),x87243))+~P4(f333(f63(f890(x87242,a874)),x87243))+~P4(f333(f63(x87242),f41(f890(x87242,a874),x87243))) % 191.49/191.42 [8725]E(f333(f333(f82(a880),x87251),f333(f39(f890(x87252,a874)),x87253)),f333(f39(x87252),f41(f890(x87252,a874),x87253)))+P4(f333(f333(f335(f890(x87252,a874)),f378(x87251,x87253,x87252)),x87253))+P4(f333(f333(f335(f890(x87252,a874)),f376(x87251,x87253,x87252)),x87253))+~P4(f333(f63(f890(x87252,a874)),x87253))+~P4(f333(f63(x87252),f41(f890(x87252,a874),x87253))) % 191.49/191.42 [8750]~E(f333(f333(f106(f890(x87502,a874)),f377(x87501,x87503,x87502)),f376(x87501,x87503,x87502)),f194(f890(x87502,a874)))+E(f333(f333(f82(a880),x87501),f333(f39(f890(x87502,a874)),x87503)),f333(f39(x87502),f41(f890(x87502,a874),x87503)))+~P4(f333(f63(f890(x87502,a874)),x87503))+P4(f333(f333(f335(f890(x87502,a874)),f378(x87501,x87503,x87502)),x87503))+~P4(f333(f63(x87502),f41(f890(x87502,a874),x87503))) % 191.49/191.42 [9013]~P97(x90132)+E(x90131,f194(f890(x90132,a874)))+~E(f333(f333(f82(x90132),f333(x90133,f837(x90131,x90133,x90132))),f333(x90133,f841(x90131,x90133,x90132))),f333(x90133,f333(f333(f82(x90132),f837(x90131,x90133,x90132)),f841(x90131,x90133,x90132))))+~P4(f333(f63(x90132),x90131))+E(f333(f65(x90132,f82(x90132)),f333(f312(x90132,x90132,x90133),x90131)),f333(x90133,f333(f65(x90132,f82(x90132)),x90131))) % 191.49/191.42 [10136]P4(f333(f333(x101361,x101362),x101363))+P4(f333(f333(f251(a1),f507(x101361,x101363,x101362)),f508(x101361,x101363,x101362)))+P4(f333(f333(f250(a1),f508(x101361,x101363,x101362)),f2(a1)))+P4(f333(f333(x101361,f507(x101361,x101363,x101362)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f508(x101361,x101363,x101362))))+~P4(f333(f321(f889(a1,a1),a58),f333(f333(f263(a1,a1),x101362),x101363))) % 191.49/191.42 [10137]P4(f333(f333(x101371,x101372),x101373))+P4(f333(f333(f250(a1),f506(x101371,x101373,x101372)),f2(a1)))+P4(f333(f333(x101371,f505(x101371,x101373,x101372)),f333(f333(f82(a1),f333(f108(a1),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f506(x101371,x101373,x101372))))+P4(f333(f333(f250(a1),f2(a1)),f333(f333(f81(a1),f505(x101371,x101373,x101372)),f506(x101371,x101373,x101372))))+~P4(f333(f321(f889(a1,a1),a53),f333(f333(f263(a1,a1),x101372),x101373))) % 191.49/191.42 [7910]~P120(x79101)+~P4(f333(f333(f250(x79101),x79102),f79(x79101)))+~P4(f333(f333(f250(x79101),f2(x79101)),x79102))+~P4(f333(f333(f250(x79101),f2(x79101)),x79103))+P4(f333(f333(f250(x79101),f333(f333(f82(x79101),x79102),x79103)),x79103)) % 191.49/191.42 [7911]~P120(x79111)+~P4(f333(f333(f250(x79111),x79113),f79(x79111)))+~P4(f333(f333(f250(x79111),f2(x79111)),x79113))+~P4(f333(f333(f250(x79111),f2(x79111)),x79112))+P4(f333(f333(f250(x79111),f333(f333(f82(x79111),x79112),x79113)),x79112)) % 191.49/191.42 [8277]~P109(x82772)+E(x82771,f194(f890(x82772,a874)))+~P4(f333(f63(x82772),x82771))+P4(f333(f333(f335(x82772),f466(x82773,x82771,x82772)),x82771))+~P4(f333(f333(f250(x82772),f333(f65(x82772,f248(x82772)),x82771)),x82773)) % 191.49/191.42 [8278]~P109(x82782)+E(x82781,f194(f890(x82782,a874)))+~P4(f333(f63(x82782),x82781))+P4(f333(f333(f335(x82782),f467(x82783,x82781,x82782)),x82781))+~P4(f333(f333(f251(x82782),f333(f65(x82782,f248(x82782)),x82781)),x82783)) % 191.49/191.42 [8279]~P109(x82792)+E(x82791,f194(f890(x82792,a874)))+~P4(f333(f63(x82792),x82791))+P4(f333(f333(f251(x82792),f467(x82793,x82791,x82792)),x82793))+~P4(f333(f333(f251(x82792),f333(f65(x82792,f248(x82792)),x82791)),x82793)) % 191.49/191.42 [8280]~P109(x82802)+E(x82801,f194(f890(x82802,a874)))+~P4(f333(f63(x82802),x82801))+P4(f333(f333(f250(x82802),f466(x82803,x82801,x82802)),x82803))+~P4(f333(f333(f250(x82802),f333(f65(x82802,f248(x82802)),x82801)),x82803)) % 191.49/191.42 [8362]~P4(f333(x83621,x83623))+P4(f333(x83621,f445(x83621,x83622)))+P4(f333(x83621,f431(x83621,x83622)))+~P4(f333(f333(f251(a1),f2(a1)),x83622))+P4(f333(x83621,f333(f333(f3(a1),f431(x83621,x83622)),f333(f333(f82(a1),f446(x83621,x83622)),x83622)))) % 191.49/191.42 [8584]~P4(f333(x85841,x85843))+P4(f333(x85841,f431(x85841,x85842)))+~P4(f333(f333(f251(a1),f2(a1)),x85842))+P4(f333(f333(f335(a1),f445(x85841,x85842)),f304(a1,f79(a1),x85842)))+P4(f333(x85841,f333(f333(f3(a1),f431(x85841,x85842)),f333(f333(f82(a1),f446(x85841,x85842)),x85842)))) % 191.49/191.42 [8770]~P4(f333(x87701,x87703))+~P4(f333(x87701,f431(x87701,x87702)))+P4(f333(x87701,f445(x87701,x87702)))+~P4(f333(f333(f251(a1),f2(a1)),x87702))+~P4(f333(x87701,f333(f333(f3(a1),f431(x87701,x87702)),f333(f333(f82(a1),f446(x87701,x87702)),x87702)))) % 191.49/191.42 [8900]~P4(f333(x89001,x89003))+~P4(f333(x89001,f431(x89001,x89002)))+~P4(f333(f333(f251(a1),f2(a1)),x89002))+P4(f333(f333(f335(a1),f445(x89001,x89002)),f304(a1,f79(a1),x89002)))+~P4(f333(x89001,f333(f333(f3(a1),f431(x89001,x89002)),f333(f333(f82(a1),f446(x89001,x89002)),x89002)))) % 191.49/191.42 [8682]~P6(x86821)+~P4(f333(f63(x86821),x86822))+E(f333(f333(f3(f890(x86821,a874)),x86822),f333(f333(f311(x86821),x86823),f194(f890(x86821,a874)))),f194(f890(x86821,a874)))+~P4(f333(f333(f335(x86821),x86823),x86822))+E(f333(f333(f115(x86821),x86823),f12(x86821,f333(f333(f3(f890(x86821,a874)),x86822),f333(f333(f311(x86821),x86823),f194(f890(x86821,a874)))))),f12(x86821,x86822)) % 191.49/191.42 [8683]~P6(x86831)+~P4(f333(f63(x86831),x86832))+E(f333(f333(f3(f890(x86831,a874)),x86832),f333(f333(f311(x86831),x86833),f194(f890(x86831,a874)))),f194(f890(x86831,a874)))+~P4(f333(f333(f335(x86831),x86833),x86832))+E(f333(f333(f106(x86831),x86833),f13(x86831,f333(f333(f3(f890(x86831,a874)),x86832),f333(f333(f311(x86831),x86833),f194(f890(x86831,a874)))))),f13(x86831,x86832)) % 191.49/191.42 [8684]~P109(x86841)+~P4(f333(f63(x86841),x86842))+E(f333(f333(f3(f890(x86841,a874)),x86842),f333(f333(f311(x86841),x86843),f194(f890(x86841,a874)))),f194(f890(x86841,a874)))+~P4(f333(f333(f335(x86841),x86843),x86842))+E(f333(f333(f248(x86841),x86843),f16(x86841,f333(f333(f3(f890(x86841,a874)),x86842),f333(f333(f311(x86841),x86843),f194(f890(x86841,a874)))))),f16(x86841,x86842)) % 191.49/191.42 [8685]~P109(x86851)+~P4(f333(f63(x86851),x86852))+E(f333(f333(f3(f890(x86851,a874)),x86852),f333(f333(f311(x86851),x86853),f194(f890(x86851,a874)))),f194(f890(x86851,a874)))+~P4(f333(f333(f335(x86851),x86853),x86852))+E(f333(f333(f249(x86851),x86853),f17(x86851,f333(f333(f3(f890(x86851,a874)),x86852),f333(f333(f311(x86851),x86853),f194(f890(x86851,a874)))))),f17(x86851,x86852)) % 191.49/191.42 [8742]~P109(x87421)+~P4(f333(f63(x87421),x87422))+E(f333(f333(f3(f890(x87421,a874)),x87422),f333(f333(f311(x87421),x87423),f194(f890(x87421,a874)))),f194(f890(x87421,a874)))+~P4(f333(f333(f335(x87421),x87423),x87422))+E(f333(f333(f248(x87421),x87423),f14(x87421,f248(x87421),f333(f333(f3(f890(x87421,a874)),x87422),f333(f333(f311(x87421),x87423),f194(f890(x87421,a874)))))),f14(x87421,f248(x87421),x87422)) % 191.49/191.42 [8743]~P109(x87431)+~P4(f333(f63(x87431),x87432))+E(f333(f333(f3(f890(x87431,a874)),x87432),f333(f333(f311(x87431),x87433),f194(f890(x87431,a874)))),f194(f890(x87431,a874)))+~P4(f333(f333(f335(x87431),x87433),x87432))+E(f333(f333(f249(x87431),x87433),f15(x87431,f249(x87431),f333(f333(f3(f890(x87431,a874)),x87432),f333(f333(f311(x87431),x87433),f194(f890(x87431,a874)))))),f15(x87431,f249(x87431),x87432)) % 191.49/191.42 [8757]~P6(x87571)+~P4(f333(f63(x87571),x87573))+~P4(f333(f63(x87571),x87572))+E(f333(f333(f106(f890(x87571,a874)),x87572),x87573),f194(f890(x87571,a874)))+E(f333(f333(f115(x87571),f12(x87571,f333(f333(f115(f890(x87571,a874)),x87572),x87573))),f12(x87571,f333(f333(f106(f890(x87571,a874)),x87572),x87573))),f333(f333(f115(x87571),f12(x87571,x87572)),f12(x87571,x87573))) % 191.49/191.42 [8758]~P6(x87581)+~P4(f333(f63(x87581),x87583))+~P4(f333(f63(x87581),x87582))+E(f333(f333(f106(f890(x87581,a874)),x87582),x87583),f194(f890(x87581,a874)))+E(f333(f333(f106(x87581),f13(x87581,f333(f333(f115(f890(x87581,a874)),x87582),x87583))),f13(x87581,f333(f333(f106(f890(x87581,a874)),x87582),x87583))),f333(f333(f106(x87581),f13(x87581,x87582)),f13(x87581,x87583))) % 191.49/191.42 [8759]~P109(x87591)+~P4(f333(f63(x87591),x87593))+~P4(f333(f63(x87591),x87592))+E(f333(f333(f106(f890(x87591,a874)),x87592),x87593),f194(f890(x87591,a874)))+E(f333(f333(f248(x87591),f16(x87591,f333(f333(f115(f890(x87591,a874)),x87592),x87593))),f16(x87591,f333(f333(f106(f890(x87591,a874)),x87592),x87593))),f333(f333(f248(x87591),f16(x87591,x87592)),f16(x87591,x87593))) % 191.49/191.42 [8760]~P109(x87601)+~P4(f333(f63(x87601),x87603))+~P4(f333(f63(x87601),x87602))+E(f333(f333(f106(f890(x87601,a874)),x87602),x87603),f194(f890(x87601,a874)))+E(f333(f333(f249(x87601),f17(x87601,f333(f333(f115(f890(x87601,a874)),x87602),x87603))),f17(x87601,f333(f333(f106(f890(x87601,a874)),x87602),x87603))),f333(f333(f249(x87601),f17(x87601,x87602)),f17(x87601,x87603))) % 191.49/191.42 [8985]~P109(x89851)+~P4(f333(f63(x89851),x89853))+~P4(f333(f63(x89851),x89852))+E(f333(f333(f106(f890(x89851,a874)),x89852),x89853),f194(f890(x89851,a874)))+E(f333(f333(f248(x89851),f14(x89851,f248(x89851),f333(f333(f115(f890(x89851,a874)),x89852),x89853))),f14(x89851,f248(x89851),f333(f333(f106(f890(x89851,a874)),x89852),x89853))),f333(f333(f248(x89851),f14(x89851,f248(x89851),x89852)),f14(x89851,f248(x89851),x89853))) % 191.49/191.42 [8986]~P109(x89861)+~P4(f333(f63(x89861),x89863))+~P4(f333(f63(x89861),x89862))+E(f333(f333(f106(f890(x89861,a874)),x89862),x89863),f194(f890(x89861,a874)))+E(f333(f333(f249(x89861),f15(x89861,f249(x89861),f333(f333(f115(f890(x89861,a874)),x89862),x89863))),f15(x89861,f249(x89861),f333(f333(f106(f890(x89861,a874)),x89862),x89863))),f333(f333(f249(x89861),f15(x89861,f249(x89861),x89862)),f15(x89861,f249(x89861),x89863))) % 191.49/191.42 [10062]~P123(x100623)+E(x100621,x100622)+~P4(f333(f333(f250(x100623),f2(x100623)),x100622))+~P4(f333(f333(f250(x100623),f2(x100623)),x100621))+~E(f333(f333(f264(x100623),x100621),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102))),f333(f333(f264(x100623),x100622),f333(f108(a880),f333(f333(f81(a1),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),f333(f333(f81(a1),f333(f333(f81(a1),f79(a1)),a84)),a84))),a102)))) % 191.49/191.42 [6345]E(f859(x63451,x63452,x63453),x63454)+E(f333(x63451,x63454),f2(a880))+~E(f333(f333(f8(x63453,a880),x63451),x63452),f79(a880))+~P4(f333(f63(x63453),x63452))+~P4(f333(f333(f335(x63453),x63454),x63452)) % 191.49/191.42 [6409]E(f861(x64091,x64092,x64093),x64094)+E(f333(x64091,x64094),f2(a880))+~E(f333(f333(f8(x64093,a880),x64091),x64092),f333(a117,f2(a880)))+~P4(f333(f63(x64093),x64092))+~P4(f333(f333(f335(x64093),x64094),x64092)) % 191.49/191.42 [6514]~P9(x65141)+~P109(x65141)+P4(f333(f333(f251(x65141),x65142),f41(x65141,x65143)))+~P4(f333(f333(f251(x65141),x65142),x65144))+~P4(f333(f333(f335(x65141),x65144),x65143)) % 191.49/191.42 [6684]~P9(x66841)+~P109(x66841)+~P4(f333(f333(f251(x66841),x66844),x66843))+P4(f333(f333(f251(x66841),f42(x66841,x66842)),x66843))+~P4(f333(f333(f335(x66841),x66844),x66842)) % 191.49/191.42 [6932]~P123(x69323)+E(x69321,x69322)+~E(f333(f333(f264(x69323),x69321),f333(a117,x69324)),f333(f333(f264(x69323),x69322),f333(a117,x69324)))+~P4(f333(f333(f250(x69323),f2(x69323)),x69322))+~P4(f333(f333(f250(x69323),f2(x69323)),x69321)) % 191.49/191.42 [7143]~E(f867(x71432,x71433,x71431,x71434),x71434)+~E(f333(x71432,x71434),f79(a880))+E(f333(f333(f8(x71431,a880),x71432),x71433),f79(a880))+~P4(f333(f63(x71431),x71433))+~P4(f333(f333(f335(x71431),x71434),x71433)) % 191.49/191.42 [7150]~P115(x71504)+~P127(x71504)+E(f333(x71501,f851(x71501,x71502,x71503,x71504)),f2(x71504))+~E(f333(f333(f11(x71503,x71504),x71501),x71502),f2(x71504))+~P4(f333(f63(x71503),x71502)) % 191.49/191.42 [7236]~E(f864(x72362,x72363,x72361,x72364),x72364)+~E(f333(x72362,x72364),f333(a117,f2(a880)))+E(f333(f333(f8(x72361,a880),x72362),x72363),f333(a117,f2(a880)))+~P4(f333(f63(x72361),x72363))+~P4(f333(f333(f335(x72361),x72364),x72363)) % 191.49/191.42 [7950]~E(f333(x79502,x79504),f79(a880))+~E(f333(x79502,f867(x79502,x79503,x79501,x79504)),f2(a880))+E(f333(f333(f8(x79501,a880),x79502),x79503),f79(a880))+~P4(f333(f63(x79501),x79503))+~P4(f333(f333(f335(x79501),x79504),x79503)) % 191.49/191.42 [7993]~E(f333(x79932,x79934),f333(a117,f2(a880)))+~E(f333(x79932,f864(x79932,x79933,x79931,x79934)),f2(a880))+E(f333(f333(f8(x79931,a880),x79932),x79933),f333(a117,f2(a880)))+~P4(f333(f63(x79931),x79933))+~P4(f333(f333(f335(x79931),x79934),x79933)) % 191.49/191.42 [8555]~P109(x85551)+~P17(x85551,x85554)+P17(x85551,x85552)+~E(x85552,f333(f333(f152(x85551),x85553),x85554))+~P4(f333(f333(f250(x85551),x85553),f682(x85552,x85551,x85554,x85553))) % 191.49/191.42 [8588]E(x85881,x85882)+E(f333(f333(f3(a1),f433(x85883,x85882,x85884,x85881)),f434(x85883,x85882,x85884,x85881)),x85881)+~E(f333(f333(f81(a1),x85881),x85884),x85882)+~P4(f333(f333(f251(a1),f2(a1)),x85884))+~P4(f333(f333(f335(a1),x85882),x85883)) % 191.49/191.42 [8589]E(x85891,x85892)+E(f333(f333(f81(a1),f435(x85893,x85892,x85894,x85891)),f436(x85893,x85892,x85894,x85891)),x85891)+~E(f333(f333(f3(a1),x85891),x85894),x85892)+~P4(f333(f333(f251(a1),f2(a1)),x85894))+~P4(f333(f333(f335(a1),x85892),x85893)) % 191.49/191.42 [8755]E(f333(x87551,f460(x87552,x87551,x87553,x87554)),x87552)+P4(f333(f333(f250(a880),x87554),f461(x87552,x87551,x87553,x87554)))+~P4(f333(f333(f250(a1),x87552),f333(x87551,x87553)))+~P4(f333(f333(f251(a880),x87554),x87553))+~P4(f333(f333(f250(a1),f333(x87551,x87554)),x87552)) % 191.49/191.42 [8756]~P109(x87561)+~P17(x87561,x87563)+P17(x87561,x87562)+~E(x87562,f333(f333(f152(x87561),x87564),x87563))+P4(f333(f333(f335(x87561),f682(x87562,x87561,x87563,x87564)),f333(f173(x87561),x87563))) % 191.49/191.42 [8774]~P115(x87744)+~P127(x87744)+~E(f333(f333(f11(x87741,x87744),x87742),x87743),f2(x87744))+~P4(f333(f63(x87741),x87743))+P4(f333(f333(f335(x87741),f851(x87742,x87743,x87741,x87744)),x87743)) % 191.49/191.42 [8811]~E(f333(x88112,x88114),f79(a880))+E(f333(f333(f8(x88111,a880),x88112),x88113),f79(a880))+~P4(f333(f63(x88111),x88113))+~P4(f333(f333(f335(x88111),x88114),x88113))+P4(f333(f333(f335(x88111),f867(x88112,x88113,x88111,x88114)),x88113)) % 191.49/191.42 [8821]E(x88211,x88212)+~E(f333(f333(f3(a1),x88212),x88214),x88211)+~P4(f333(f333(f251(a1),f2(a1)),x88214))+~P4(f333(f333(f335(a1),x88211),x88213))+P4(f333(f333(f335(a1),f435(x88213,x88211,x88214,x88212)),x88213)) % 191.49/191.42 [8822]E(x88221,x88222)+~E(f333(f333(f81(a1),x88222),x88224),x88221)+~P4(f333(f333(f251(a1),f2(a1)),x88224))+~P4(f333(f333(f335(a1),x88221),x88223))+P4(f333(f333(f335(a1),f433(x88223,x88221,x88224,x88222)),x88223)) % 191.49/191.42 [8824]~E(f333(x88242,x88244),f333(a117,f2(a880)))+E(f333(f333(f8(x88241,a880),x88242),x88243),f333(a117,f2(a880)))+~P4(f333(f63(x88241),x88243))+~P4(f333(f333(f335(x88241),x88244),x88243))+P4(f333(f333(f335(x88241),f864(x88242,x88243,x88241,x88244)),x88243)) % 191.49/191.42 [8830]P58(x88302,x88303,x88304,x88301)+E(x88301,f194(f890(x88302,a874)))+~P4(f333(f63(x88302),x88304))+~P4(f333(f63(x88302),x88301))+P4(f333(f333(f335(x88302),f707(x88301,x88304,x88303,x88302)),x88304)) % 191.49/191.42 [8913]E(x89131,x89132)+~E(f333(f333(f3(a1),x89132),x89134),x89131)+~P4(f333(f333(f251(a1),f2(a1)),x89134))+~P4(f333(f333(f335(a1),x89131),x89133))+P4(f333(f333(f335(a1),f436(x89133,x89131,x89134,x89132)),f304(a1,f79(a1),x89134))) % 191.49/191.42 [8914]E(x89141,x89142)+~E(f333(f333(f81(a1),x89142),x89144),x89141)+~P4(f333(f333(f251(a1),f2(a1)),x89144))+~P4(f333(f333(f335(a1),x89141),x89143))+P4(f333(f333(f335(a1),f434(x89143,x89141,x89144,x89142)),f304(a1,f79(a1),x89144))) % 191.49/191.42 [8991]P4(f333(f333(f250(a880),x89911),f460(x89912,x89913,x89914,x89911)))+~P4(f333(f333(f250(a1),x89912),f333(x89913,x89914)))+P4(f333(f333(f250(a880),x89911),f461(x89912,x89913,x89914,x89911)))+~P4(f333(f333(f251(a880),x89911),x89914))+~P4(f333(f333(f250(a1),f333(x89913,x89911)),x89912)) % 191.49/191.42 [9092]E(f333(x90921,f460(x90922,x90921,x90923,x90924)),x90922)+~P4(f333(f333(f250(a1),x90922),f333(x90921,x90923)))+P4(f333(f333(f251(a880),f461(x90922,x90921,x90923,x90924)),x90923))+~P4(f333(f333(f251(a880),x90924),x90923))+~P4(f333(f333(f250(a1),f333(x90921,x90924)),x90922)) % 191.49/191.42 [9227]~P4(f333(f333(f250(a1),x92272),f333(x92273,x92274)))+P4(f333(f333(f250(a880),x92271),f461(x92272,x92273,x92274,x92271)))+P4(f333(f333(f250(a880),f460(x92272,x92273,x92274,x92271)),x92274))+~P4(f333(f333(f251(a880),x92271),x92274))+~P4(f333(f333(f250(a1),f333(x92273,x92271)),x92272)) % 191.49/191.42 [9228]~P4(f333(f333(f250(a1),x92282),f333(x92283,x92284)))+P4(f333(f333(f250(a880),x92281),f460(x92282,x92283,x92284,x92281)))+P4(f333(f333(f251(a880),f461(x92282,x92283,x92284,x92281)),x92284))+~P4(f333(f333(f251(a880),x92281),x92284))+~P4(f333(f333(f250(a1),f333(x92283,x92281)),x92282)) % 191.49/191.42 [9338]~P4(f333(f333(f250(a1),x93381),f333(x93382,x93383)))+P4(f333(f333(f250(a880),f460(x93381,x93382,x93383,x93384)),x93383))+~P4(f333(f333(f251(a880),x93384),x93383))+~P4(f333(f333(f250(a1),f333(x93382,x93384)),x93381))+P4(f333(f333(f251(a880),f461(x93381,x93382,x93383,x93384)),x93383)) % 191.49/191.42 [9412]E(x94121,f194(f890(x94122,a874)))+~P4(f333(f63(x94122),x94124))+~P4(f333(f63(x94122),x94121))+P4(f333(f333(f335(f889(f890(x94122,a874),f890(x94122,a874))),f333(f333(f263(f890(x94122,a874),f890(x94122,a874)),x94124),x94121)),f325(x94122,x94123)))+P4(f333(f333(f335(x94122),f709(x94123,x94121,x94124,x94122)),x94124)) % 191.49/191.42 [9413]E(x94131,f194(f890(x94132,a874)))+~P4(f333(f63(x94132),x94134))+~P4(f333(f63(x94132),x94131))+P4(f333(f333(f335(f889(f890(x94132,a874),f890(x94132,a874))),f333(f333(f263(f890(x94132,a874),f890(x94132,a874)),x94134),x94131)),f325(x94132,x94133)))+P4(f333(f333(f335(x94132),f758(x94133,x94131,x94134,x94132)),x94134)) % 191.49/191.42 [10093]E(f333(x100931,f460(x100932,x100931,x100933,x100934)),x100932)+~P4(f333(f333(f250(a1),x100932),f333(x100931,x100933)))+~P4(f333(f333(f250(a1),f333(f76(a1),f333(f333(f3(a1),f333(x100931,f333(f333(f81(a880),f461(x100932,x100931,x100933,x100934)),f79(a880)))),f333(x100931,f461(x100932,x100931,x100933,x100934))))),f79(a1)))+~P4(f333(f333(f251(a880),x100934),x100933))+~P4(f333(f333(f250(a1),f333(x100931,x100934)),x100932)) % 191.49/191.42 [10094]~P4(f333(f333(f250(a1),x100942),f333(x100943,x100944)))+P4(f333(f333(f250(a880),x100941),f460(x100942,x100943,x100944,x100941)))+~P4(f333(f333(f250(a1),f333(f76(a1),f333(f333(f3(a1),f333(x100943,f333(f333(f81(a880),f461(x100942,x100943,x100944,x100941)),f79(a880)))),f333(x100943,f461(x100942,x100943,x100944,x100941))))),f79(a1)))+~P4(f333(f333(f251(a880),x100941),x100944))+~P4(f333(f333(f250(a1),f333(x100943,x100941)),x100942)) % 191.49/191.42 [10095]~P4(f333(f333(f250(a1),x100951),f333(x100952,x100953)))+~P4(f333(f333(f250(a1),f333(f76(a1),f333(f333(f3(a1),f333(x100952,f333(f333(f81(a880),f461(x100951,x100952,x100953,x100954)),f79(a880)))),f333(x100952,f461(x100951,x100952,x100953,x100954))))),f79(a1)))+~P4(f333(f333(f251(a880),x100954),x100953))+~P4(f333(f333(f250(a1),f333(x100952,x100954)),x100951))+P4(f333(f333(f250(a880),f460(x100951,x100952,x100953,x100954)),x100953)) % 191.49/191.42 [7203]~P65(x72031)+P4(f333(f333(f251(x72031),x72032),f2(x72031)))+~P4(f333(f333(f251(x72031),x72033),f2(x72031)))+P4(f333(f333(f251(x72031),f2(x72031)),x72032))+P4(f333(f333(f251(x72031),x72033),f333(f333(f291(x72031),x72034),x72032))) % 191.49/191.42 [7204]~P65(x72041)+P4(f333(f333(f251(x72041),x72042),f2(x72041)))+~P4(f333(f333(f250(x72041),x72043),f2(x72041)))+P4(f333(f333(f251(x72041),f2(x72041)),x72042))+P4(f333(f333(f250(x72041),x72043),f333(f333(f291(x72041),x72044),x72042))) % 191.49/191.42 [7443]~P65(x74431)+P4(f333(f333(f251(x74431),x74432),f2(x74431)))+P4(f333(f333(f251(x74431),x74433),f2(x74431)))+P4(f333(f333(f251(x74431),f2(x74431)),x74433))+~P4(f333(f333(f251(x74431),x74432),f333(f333(f291(x74431),x74434),x74433))) % 191.49/191.42 [7444]~P65(x74441)+P4(f333(f333(f251(x74441),x74442),f2(x74441)))+P4(f333(f333(f250(x74441),x74443),f2(x74441)))+P4(f333(f333(f251(x74441),f2(x74441)),x74442))+~P4(f333(f333(f250(x74441),x74443),f333(f333(f291(x74441),x74444),x74442))) % 191.49/191.42 [7558]E(x75581,x75582)+~E(f333(f333(f166(x75583),x75584),x75581),f333(f333(f166(x75583),x75584),x75582))+~P4(f333(f138(x75583),x75584))+~P4(f333(f333(f251(a880),x75582),f333(f195(f881(x75583)),x75584)))+~P4(f333(f333(f251(a880),x75581),f333(f195(f881(x75583)),x75584))) % 191.49/191.42 [7912]~P65(x79121)+~P4(f333(f333(f251(x79121),x79123),f2(x79121)))+P4(f333(f333(f251(x79121),f2(x79121)),x79122))+~P4(f333(f333(f251(x79121),x79124),f333(f333(f82(x79121),x79123),x79122)))+P4(f333(f333(f251(x79121),x79123),f333(f333(f291(x79121),x79124),x79122))) % 191.49/191.42 [7913]~P65(x79131)+~P4(f333(f333(f250(x79131),x79133),f2(x79131)))+P4(f333(f333(f251(x79131),f2(x79131)),x79132))+~P4(f333(f333(f250(x79131),x79134),f333(f333(f82(x79131),x79133),x79132)))+P4(f333(f333(f250(x79131),x79133),f333(f333(f291(x79131),x79134),x79132))) % 191.49/191.42 [7914]~P65(x79141)+~P4(f333(f333(f251(x79141),x79142),f2(x79141)))+P4(f333(f333(f251(x79141),f2(x79141)),x79142))+~P4(f333(f333(f251(x79141),x79144),f333(f333(f82(x79141),x79143),x79142)))+P4(f333(f333(f251(x79141),x79143),f333(f333(f291(x79141),x79144),x79142))) % 191.49/191.42 [7915]~P65(x79151)+~P4(f333(f333(f251(x79151),x79152),f2(x79151)))+P4(f333(f333(f251(x79151),f2(x79151)),x79152))+~P4(f333(f333(f251(x79151),x79154),f333(f333(f291(x79151),x79153),x79152)))+P4(f333(f333(f251(x79151),x79153),f333(f333(f82(x79151),x79154),x79152))) % 191.49/191.42 [7916]~P65(x79161)+~P4(f333(f333(f251(x79161),x79162),f2(x79161)))+P4(f333(f333(f251(x79161),f2(x79161)),x79162))+~P4(f333(f333(f250(x79161),x79164),f333(f333(f82(x79161),x79163),x79162)))+P4(f333(f333(f250(x79161),x79163),f333(f333(f291(x79161),x79164),x79162))) % 191.49/191.42 [7917]~P65(x79171)+~P4(f333(f333(f251(x79171),x79172),f2(x79171)))+P4(f333(f333(f251(x79171),f2(x79171)),x79172))+~P4(f333(f333(f250(x79171),x79174),f333(f333(f291(x79171),x79173),x79172)))+P4(f333(f333(f250(x79171),x79173),f333(f333(f82(x79171),x79174),x79172))) % 191.49/191.42 [8065]~P109(x80651)+~P17(x80651,x80652)+~P4(f333(f333(f250(a880),x80653),x80654))+P4(f333(f333(f250(x80651),f333(f333(f166(x80651),x80652),x80653)),f333(f333(f166(x80651),x80652),x80654)))+~P4(f333(f333(f251(a880),x80654),f333(f195(f881(x80651)),x80652))) % 191.49/191.42 [8118]~P123(x81181)+~P4(f333(f333(f251(x81181),x81182),f79(x81181)))+~P4(f333(f333(f251(x81181),f2(x81181)),x81182))+~P4(f333(f333(f251(a880),x81184),x81183))+P4(f333(f333(f251(x81181),f333(f333(f264(x81181),x81182),x81183)),f333(f333(f264(x81181),x81182),x81184))) % 191.49/191.42 [8119]~P123(x81191)+~P4(f333(f333(f250(x81191),x81192),f79(x81191)))+~P4(f333(f333(f250(x81191),f2(x81191)),x81192))+~P4(f333(f333(f250(a880),x81194),x81193))+P4(f333(f333(f250(x81191),f333(f333(f264(x81191),x81192),x81193)),f333(f333(f264(x81191),x81192),x81194))) % 191.49/191.42 [8120]~P123(x81201)+~P4(f333(f333(f250(x81201),f2(x81201)),x81202))+~P4(f333(f333(f251(a880),f2(a880)),x81203))+~P4(f333(f333(f251(x81201),x81202),x81204))+P4(f333(f333(f251(x81201),f333(f333(f264(x81201),x81202),x81203)),f333(f333(f264(x81201),x81204),x81203))) % 191.49/191.42 [8141]~P109(x81411)+~P17(x81411,f333(f170(x81411),x81412))+~P4(f333(f333(f250(a880),x81414),x81413))+P4(f333(f333(f250(x81411),f333(f333(f166(x81411),x81412),x81413)),f333(f333(f166(x81411),x81412),x81414)))+~P4(f333(f333(f251(a880),x81413),f333(f195(f881(x81411)),x81412))) % 191.49/191.42 [8385]~P66(x83851)+~P4(f333(f333(f251(x83851),x83852),f2(x83851)))+~P4(f333(f333(f251(x83851),x83853),x83854))+~P4(f333(f333(f251(x83851),f2(x83851)),f333(f333(f82(x83851),x83853),x83854)))+P4(f333(f333(f251(x83851),f333(f333(f291(x83851),x83852),x83853)),f333(f333(f291(x83851),x83852),x83854))) % 191.49/191.42 [8386]~P65(x83861)+~P4(f333(f333(f250(x83861),x83862),f2(x83861)))+~P4(f333(f333(f250(x83861),x83863),x83864))+~P4(f333(f333(f251(x83861),f2(x83861)),f333(f333(f82(x83861),x83863),x83864)))+P4(f333(f333(f250(x83861),f333(f333(f291(x83861),x83862),x83863)),f333(f333(f291(x83861),x83862),x83864))) % 191.49/191.42 [8396]~P66(x83961)+~P4(f333(f333(f251(x83961),x83964),x83963))+~P4(f333(f333(f251(x83961),f2(x83961)),x83962))+~P4(f333(f333(f251(x83961),f2(x83961)),f333(f333(f82(x83961),x83963),x83964)))+P4(f333(f333(f251(x83961),f333(f333(f291(x83961),x83962),x83963)),f333(f333(f291(x83961),x83962),x83964))) % 191.49/191.42 [8397]~P66(x83971)+~P4(f333(f333(f250(x83971),x83974),x83973))+~P4(f333(f333(f250(x83971),f2(x83971)),x83972))+~P4(f333(f333(f251(x83971),f2(x83971)),f333(f333(f82(x83971),x83973),x83974)))+P4(f333(f333(f250(x83971),f333(f333(f291(x83971),x83972),x83973)),f333(f333(f291(x83971),x83972),x83974))) % 191.49/191.42 [8500]P4(f333(x85001,x85002))+~P4(f333(f63(x85004),x85002))+P4(f333(x85001,f366(x85001,x85003,x85002,x85004)))+~P4(f333(x85001,f194(f890(x85004,a874))))+~P4(f333(f333(f250(f890(x85004,a874)),x85002),x85003)) % 191.49/191.42 [8508]P4(f333(x85081,x85082))+P4(f333(f63(x85083),f366(x85081,x85084,x85082,x85083)))+~P4(f333(f63(x85083),x85082))+~P4(f333(x85081,f194(f890(x85083,a874))))+~P4(f333(f333(f250(f890(x85083,a874)),x85082),x85084)) % 191.49/191.42 [8751]E(f333(f333(f81(a1),f437(x87511,x87512,x87513,x87514)),f438(x87511,x87512,x87513,x87514)),x87514)+~P4(f333(f333(f251(a1),f2(a1)),x87513))+~P4(f333(f333(f251(a1),x87512),x87514))+~P4(f333(f333(f335(a1),x87512),x87511))+P4(f333(f333(f251(a1),x87512),f333(f333(f3(a1),x87514),x87513))) % 191.49/191.42 [8973]~P4(f333(f333(f251(a1),f2(a1)),x89733))+~P4(f333(f333(f251(a1),x89732),x89734))+~P4(f333(f333(f335(a1),x89732),x89731))+P4(f333(f333(f335(a1),f437(x89731,x89732,x89733,x89734)),x89731))+P4(f333(f333(f251(a1),x89732),f333(f333(f3(a1),x89734),x89733))) % 191.49/191.42 [8984]P4(f333(x89841,x89842))+~P4(f333(f63(x89843),x89842))+P4(f333(f333(f335(x89843),f367(x89841,x89844,x89842,x89843)),x89844))+~P4(f333(x89841,f194(f890(x89843,a874))))+~P4(f333(f333(f250(f890(x89843,a874)),x89842),x89844)) % 191.49/191.42 [9001]E(f333(f333(f81(a1),f418(x90011,x90012,x90013,x90014)),f419(x90011,x90012,x90013,x90014)),x90014)+~P4(f333(f333(f251(a1),f2(a1)),x90013))+~P4(f333(f333(f250(a1),x90012),x90014))+P4(f333(f333(f250(a1),x90012),f333(f333(f3(a1),x90014),x90013)))+~P4(f333(f333(f335(a1),f333(f333(f3(a1),x90012),f79(a1))),x90011)) % 191.49/191.42 [9046]~P4(f333(f333(f251(a1),f2(a1)),x90463))+~P4(f333(f333(f251(a1),x90461),x90462))+~P4(f333(f333(f335(a1),x90461),x90464))+P4(f333(f333(f335(a1),f438(x90464,x90461,x90463,x90462)),f304(a1,f79(a1),x90463)))+P4(f333(f333(f251(a1),x90461),f333(f333(f3(a1),x90462),x90463))) % 191.49/191.42 [9143]~P4(f333(f333(f251(a1),f2(a1)),x91433))+~P4(f333(f333(f250(a1),x91432),x91434))+P4(f333(f333(f335(a1),f418(x91431,x91432,x91433,x91434)),x91431))+P4(f333(f333(f250(a1),x91432),f333(f333(f3(a1),x91434),x91433)))+~P4(f333(f333(f335(a1),f333(f333(f3(a1),x91432),f79(a1))),x91431)) % 191.49/191.42 [9185]~P4(f333(f333(f251(a1),f2(a1)),x91853))+~P4(f333(f333(f250(a1),x91851),x91852))+P4(f333(f333(f335(a1),f419(x91854,x91851,x91853,x91852)),f304(a1,f79(a1),x91853)))+P4(f333(f333(f250(a1),x91851),f333(f333(f3(a1),x91852),x91853)))+~P4(f333(f333(f335(a1),f333(f333(f3(a1),x91851),f79(a1))),x91854)) % 191.49/191.42 [9416]P4(f333(x94161,x94162))+~P4(f333(f333(f335(x94163),f367(x94161,x94164,x94162,x94163)),f366(x94161,x94164,x94162,x94163)))+~P4(f333(f63(x94163),x94162))+~P4(f333(x94161,f194(f890(x94163,a874))))+~P4(f333(f333(f250(f890(x94163,a874)),x94162),x94164)) % 191.49/191.42 [9658]P4(f333(x96581,x96582))+~P4(f333(f63(x96583),x96582))+~P4(f333(x96581,f333(f333(f311(x96583),f367(x96581,x96584,x96582,x96583)),f366(x96581,x96584,x96582,x96583))))+~P4(f333(x96581,f194(f890(x96583,a874))))+~P4(f333(f333(f250(f890(x96583,a874)),x96582),x96584)) % 191.49/191.42 [7691]~P65(x76911)+P4(f333(f333(f251(x76911),x76912),f2(x76911)))+P4(f333(f333(f251(x76911),f2(x76911)),x76912))+~P4(f333(f333(f251(x76911),f2(x76911)),x76914))+P4(f333(f333(f251(x76911),f333(f333(f291(x76911),x76913),x76912)),x76914)) % 191.49/191.42 [7692]~P65(x76921)+P4(f333(f333(f251(x76921),x76922),f2(x76921)))+~P4(f333(f333(f250(x76921),f2(x76921)),x76924))+P4(f333(f333(f251(x76921),f2(x76921)),x76922))+P4(f333(f333(f250(x76921),f333(f333(f291(x76921),x76923),x76922)),x76924)) % 191.49/191.42 [7965]~P4(f333(f333(f250(a1),x79654),f2(a1)))+~E(x79652,f333(f333(f81(a1),f333(f333(f82(a1),x79651),x79653)),x79654))+P4(f333(f333(f251(a1),f2(a1)),x79651))+~P4(f333(f333(f251(a1),x79651),x79654))+P4(f333(f50(x79652,x79651),f333(f333(f263(a1,a1),x79653),x79654))) % 191.49/191.42 [8004]~P4(f333(x80041,x80044))+P4(f333(x80041,f394(x80042,x80041,x80043)))+~P4(f333(f333(f251(a1),f2(a1)),x80043))+~P4(f333(f333(f250(a1),f2(a1)),x80042))+P4(f333(x80041,f333(f333(f3(a1),x80044),f333(f333(f82(a1),x80042),x80043)))) % 191.49/191.42 [8005]~P4(f333(x80051,x80054))+P4(f333(x80051,f396(x80052,x80051,x80053)))+~P4(f333(f333(f251(a1),f2(a1)),x80053))+~P4(f333(f333(f250(a1),f2(a1)),x80052))+P4(f333(x80051,f333(f333(f81(a1),x80054),f333(f333(f82(a1),x80052),x80053)))) % 191.49/191.42 [8006]~P65(x80061)+P4(f333(f333(f251(x80061),x80062),f2(x80061)))+P4(f333(f333(f251(x80061),f2(x80061)),x80062))+P4(f333(f333(f251(x80061),f2(x80061)),x80063))+~P4(f333(f333(f251(x80061),f333(f333(f291(x80061),x80064),x80062)),x80063)) % 191.49/191.42 [8007]~P65(x80071)+P4(f333(f333(f251(x80071),x80072),f2(x80071)))+P4(f333(f333(f251(x80071),f2(x80071)),x80072))+P4(f333(f333(f250(x80071),f2(x80071)),x80073))+~P4(f333(f333(f250(x80071),f333(f333(f291(x80071),x80074),x80072)),x80073)) % 191.49/191.42 [8059]~E(x80591,f333(f333(f81(a1),f333(f333(f82(a1),x80592),x80593)),x80594))+~P4(f333(f333(f251(a1),f2(a1)),x80592))+~P4(f333(f333(f250(a1),f2(a1)),x80594))+~P4(f333(f333(f251(a1),x80594),x80592))+P4(f333(f50(x80591,x80592),f333(f333(f263(a1,a1),x80593),x80594))) % 191.49/191.42 [8185]~P65(x81851)+P4(f333(f333(f251(x81851),x81852),f2(x81851)))+~P4(f333(f333(f251(x81851),f2(x81851)),x81854))+~P4(f333(f333(f251(x81851),x81853),f333(f333(f82(x81851),x81854),x81852)))+P4(f333(f333(f251(x81851),f333(f333(f291(x81851),x81853),x81852)),x81854)) % 191.49/191.42 [8186]~P65(x81861)+P4(f333(f333(f251(x81861),x81862),f2(x81861)))+~P4(f333(f333(f250(x81861),f2(x81861)),x81864))+~P4(f333(f333(f250(x81861),x81863),f333(f333(f82(x81861),x81864),x81862)))+P4(f333(f333(f250(x81861),f333(f333(f291(x81861),x81863),x81862)),x81864)) % 191.49/191.42 [8265]~P65(x82651)+P4(f333(f333(f251(x82651),x82652),f2(x82651)))+~P4(f333(f333(f251(x82651),x82653),f2(x82651)))+P4(f333(f333(f251(x82651),x82653),f333(f333(f291(x82651),x82654),x82652)))+~P4(f333(f333(f251(x82651),f333(f333(f82(x82651),x82653),x82652)),x82654)) % 191.49/191.42 [8266]~P65(x82661)+P4(f333(f333(f251(x82661),x82662),f2(x82661)))+~P4(f333(f333(f250(x82661),x82663),f2(x82661)))+P4(f333(f333(f250(x82661),x82663),f333(f333(f291(x82661),x82664),x82662)))+~P4(f333(f333(f250(x82661),f333(f333(f82(x82661),x82663),x82662)),x82664)) % 191.49/191.42 [8419]~P65(x84191)+~P4(f333(f333(f251(x84191),x84192),f2(x84191)))+P4(f333(f333(f251(x84191),f2(x84191)),x84192))+~P4(f333(f333(f251(x84191),f333(f333(f291(x84191),x84194),x84192)),x84193))+P4(f333(f333(f251(x84191),f333(f333(f82(x84191),x84193),x84192)),x84194)) % 191.49/191.42 [8420]~P65(x84201)+~P4(f333(f333(f251(x84201),x84202),f2(x84201)))+P4(f333(f333(f251(x84201),f2(x84201)),x84202))+~P4(f333(f333(f251(x84201),f333(f333(f82(x84201),x84204),x84202)),x84203))+P4(f333(f333(f251(x84201),f333(f333(f291(x84201),x84203),x84202)),x84204)) % 191.49/191.42 [8421]~P65(x84211)+~P4(f333(f333(f251(x84211),x84212),f2(x84211)))+P4(f333(f333(f251(x84211),f2(x84211)),x84212))+~P4(f333(f333(f250(x84211),f333(f333(f291(x84211),x84214),x84212)),x84213))+P4(f333(f333(f250(x84211),f333(f333(f82(x84211),x84213),x84212)),x84214)) % 191.49/191.42 [8422]~P65(x84221)+~P4(f333(f333(f251(x84221),x84222),f2(x84221)))+P4(f333(f333(f251(x84221),f2(x84221)),x84222))+~P4(f333(f333(f250(x84221),f333(f333(f82(x84221),x84224),x84222)),x84223))+P4(f333(f333(f250(x84221),f333(f333(f291(x84221),x84223),x84222)),x84224)) % 191.49/191.42 [8446]~P65(x84461)+~P4(f333(f333(f251(x84461),f2(x84461)),x84464))+P4(f333(f333(f251(x84461),f2(x84461)),x84462))+~P4(f333(f333(f251(x84461),f333(f333(f82(x84461),x84464),x84462)),x84463))+P4(f333(f333(f251(x84461),f333(f333(f291(x84461),x84463),x84462)),x84464)) % 191.49/191.42 [8447]~P65(x84471)+~P4(f333(f333(f250(x84471),f2(x84471)),x84474))+P4(f333(f333(f251(x84471),f2(x84471)),x84472))+~P4(f333(f333(f250(x84471),f333(f333(f82(x84471),x84474),x84472)),x84473))+P4(f333(f333(f250(x84471),f333(f333(f291(x84471),x84473),x84472)),x84474)) % 191.49/191.42 [8521]~P65(x85211)+~P4(f333(f333(f251(x85211),x85214),f2(x85211)))+~P4(f333(f333(f251(x85211),x85213),f333(f333(f82(x85211),x85212),x85214)))+P4(f333(f333(f251(x85211),x85212),f333(f333(f291(x85211),x85213),x85214)))+~P4(f333(f333(f251(x85211),f333(f333(f82(x85211),x85212),x85214)),x85213)) % 191.49/191.42 [8522]~P65(x85221)+~P4(f333(f333(f251(x85221),x85222),f2(x85221)))+~P4(f333(f333(f251(x85221),x85223),f333(f333(f82(x85221),x85222),x85224)))+P4(f333(f333(f251(x85221),x85222),f333(f333(f291(x85221),x85223),x85224)))+~P4(f333(f333(f251(x85221),f333(f333(f82(x85221),x85222),x85224)),x85223)) % 191.49/191.42 [8523]~P65(x85231)+~P4(f333(f333(f251(x85231),x85234),f2(x85231)))+~P4(f333(f333(f250(x85231),x85233),f333(f333(f82(x85231),x85232),x85234)))+P4(f333(f333(f250(x85231),x85232),f333(f333(f291(x85231),x85233),x85234)))+~P4(f333(f333(f250(x85231),f333(f333(f82(x85231),x85232),x85234)),x85233)) % 191.49/191.42 [8524]~P65(x85241)+~P4(f333(f333(f250(x85241),x85242),f2(x85241)))+~P4(f333(f333(f250(x85241),x85243),f333(f333(f82(x85241),x85242),x85244)))+P4(f333(f333(f250(x85241),x85242),f333(f333(f291(x85241),x85243),x85244)))+~P4(f333(f333(f250(x85241),f333(f333(f82(x85241),x85242),x85244)),x85243)) % 191.49/191.42 [8636]~P65(x86361)+~P4(f333(f333(f251(x86361),x86363),f2(x86361)))+~P4(f333(f333(f251(x86361),x86362),f333(f333(f82(x86361),x86364),x86363)))+~P4(f333(f333(f251(x86361),f333(f333(f82(x86361),x86364),x86363)),x86362))+P4(f333(f333(f251(x86361),f333(f333(f291(x86361),x86362),x86363)),x86364)) % 191.49/191.42 [8637]~P65(x86371)+~P4(f333(f333(f251(x86371),x86373),f2(x86371)))+~P4(f333(f333(f250(x86371),x86372),f333(f333(f82(x86371),x86374),x86373)))+~P4(f333(f333(f250(x86371),f333(f333(f82(x86371),x86374),x86373)),x86372))+P4(f333(f333(f250(x86371),f333(f333(f291(x86371),x86372),x86373)),x86374)) % 191.49/191.42 [8646]~P65(x86461)+~P4(f333(f333(f251(x86461),f2(x86461)),x86464))+~P4(f333(f333(f251(x86461),x86462),f333(f333(f82(x86461),x86464),x86463)))+~P4(f333(f333(f251(x86461),f333(f333(f82(x86461),x86464),x86463)),x86462))+P4(f333(f333(f251(x86461),f333(f333(f291(x86461),x86462),x86463)),x86464)) % 191.49/191.42 [8647]~P65(x86471)+~P4(f333(f333(f250(x86471),f2(x86471)),x86474))+~P4(f333(f333(f250(x86471),x86472),f333(f333(f82(x86471),x86474),x86473)))+~P4(f333(f333(f250(x86471),f333(f333(f82(x86471),x86474),x86473)),x86472))+P4(f333(f333(f250(x86471),f333(f333(f291(x86471),x86472),x86473)),x86474)) % 191.49/191.42 [8814]E(f333(f333(f3(a1),f439(x88141,x88142,x88143,x88144)),f440(x88141,x88142,x88143,x88144)),x88144)+~P4(f333(f333(f251(a1),f2(a1)),x88143))+~P4(f333(f333(f335(a1),x88142),x88141))+~P4(f333(f333(f251(a1),x88144),x88142))+P4(f333(f333(f251(a1),f333(f333(f81(a1),x88144),x88143)),x88142)) % 191.49/191.42 [8896]~P4(f333(x88961,x88962))+~P4(f333(f333(f251(a1),f2(a1)),x88964))+~P4(f333(f333(f250(a1),f2(a1)),x88963))+~P4(f333(x88961,f333(f333(f3(a1),f394(x88963,x88961,x88964)),x88964)))+P4(f333(x88961,f333(f333(f3(a1),x88962),f333(f333(f82(a1),x88963),x88964)))) % 191.49/191.42 [8897]~P4(f333(x88971,x88972))+~P4(f333(f333(f251(a1),f2(a1)),x88974))+~P4(f333(f333(f250(a1),f2(a1)),x88973))+~P4(f333(x88971,f333(f333(f81(a1),f396(x88973,x88971,x88974)),x88974)))+P4(f333(x88971,f333(f333(f81(a1),x88972),f333(f333(f82(a1),x88973),x88974)))) % 191.49/191.42 [9040]~P4(f333(f333(f251(a1),f2(a1)),x90403))+~P4(f333(f333(f335(a1),x90402),x90401))+~P4(f333(f333(f251(a1),x90404),x90402))+P4(f333(f333(f335(a1),f439(x90401,x90402,x90403,x90404)),x90401))+P4(f333(f333(f251(a1),f333(f333(f81(a1),x90404),x90403)),x90402)) % 191.49/191.42 [9054]E(f333(f333(f3(a1),f420(x90541,x90542,x90543,x90544)),f421(x90541,x90542,x90543,x90544)),x90544)+~P4(f333(f333(f251(a1),f2(a1)),x90543))+~P4(f333(f333(f250(a1),x90544),x90542))+~P4(f333(f333(f335(a1),f333(f333(f81(a1),x90542),f79(a1))),x90541))+P4(f333(f333(f250(a1),f333(f333(f81(a1),x90544),x90543)),x90542)) % 191.49/191.42 [9079]~P4(f333(f333(f251(a1),f2(a1)),x90792))+~P4(f333(f333(f335(a1),x90793),x90794))+~P4(f333(f333(f251(a1),x90791),x90793))+P4(f333(f333(f335(a1),f440(x90794,x90793,x90792,x90791)),f304(a1,f79(a1),x90792)))+P4(f333(f333(f251(a1),f333(f333(f81(a1),x90791),x90792)),x90793)) % 191.49/191.42 [9180]~P4(f333(f333(f251(a1),f2(a1)),x91803))+~P4(f333(f333(f250(a1),x91804),x91802))+P4(f333(f333(f335(a1),f420(x91801,x91802,x91803,x91804)),x91801))+~P4(f333(f333(f335(a1),f333(f333(f81(a1),x91802),f79(a1))),x91801))+P4(f333(f333(f250(a1),f333(f333(f81(a1),x91804),x91803)),x91802)) % 191.49/191.42 [9223]~P4(f333(f333(f251(a1),f2(a1)),x92232))+~P4(f333(f333(f250(a1),x92231),x92233))+P4(f333(f333(f335(a1),f421(x92234,x92233,x92232,x92231)),f304(a1,f79(a1),x92232)))+~P4(f333(f333(f335(a1),f333(f333(f81(a1),x92233),f79(a1))),x92234))+P4(f333(f333(f250(a1),f333(f333(f81(a1),x92231),x92232)),x92233)) % 191.49/191.42 [9522]~P40(x95221,x95223)+~P29(x95221,x95224)+P40(x95221,f333(f333(f115(f890(f889(x95221,x95221),a874)),x95222),x95223))+~P4(f333(f333(f250(f890(f889(x95221,x95221),a874)),x95222),f333(f262(f890(f889(x95221,x95221),a874),f890(f889(x95221,x95221),a874)),x95224)))+~P4(f333(f333(f250(f890(f889(x95221,x95221),a874)),x95223),f333(f271(f890(f889(x95221,x95221),a874),f890(f889(x95221,x95221),a874)),x95224))) % 191.49/191.42 [9835]~E(f333(f523(x98351,x98354,x98353,x98352),f525(x98351,x98354,x98353,x98352)),f197(f881(a329)))+P4(f333(f333(f251(a1),f524(x98351,x98354,x98353,x98352)),f525(x98351,x98354,x98353,x98352)))+P4(f333(f333(f333(x98351,x98352),x98353),x98354))+P4(f333(f333(f333(x98351,f523(x98351,x98354,x98353,x98352)),f524(x98351,x98354,x98353,x98352)),f333(f333(f81(a1),f525(x98351,x98354,x98353,x98352)),f79(a1))))+~P4(f333(f321(f889(f890(a1,f884(f881(a329))),f889(a1,a1)),a319),f333(f333(f263(f890(a1,f884(f881(a329))),f889(a1,a1)),x98352),f333(f333(f263(a1,a1),x98353),x98354)))) % 191.49/191.42 [9926]~P21(x99262,x99264,x99263)+E(x99261,f194(f890(x99262,a874)))+~P4(f333(f63(x99262),x99261))+P4(f333(f333(f335(x99262),f333(x99263,x99261)),x99261))+~P4(f333(f333(f335(x99262),f333(f333(x99264,f560(x99261,x99263,x99264,x99262)),f573(x99261,x99263,x99264,x99262))),f333(f333(f311(x99262),f560(x99261,x99263,x99264,x99262)),f333(f333(f311(x99262),f573(x99261,x99263,x99264,x99262)),f194(f890(x99262,a874)))))) % 191.49/191.42 [9863]~P110(x98632)+~P62(x98631)+~P4(f333(f333(f250(f890(x98631,x98632)),x98633),x98634))+P4(f333(f333(f251(f890(x98631,x98632)),x98633),x98634))+~P4(f333(f59(x98631),f333(f333(f10(a874,a874,x98631),a328),f333(f333(f20(x98631,x98632,a874),f333(f333(f10(x98632,f890(x98632,a874),x98631),a330),x98633)),x98634)))) % 191.49/191.42 [9425]~P54(x94251,x94251,x94254)+P4(f333(f333(f335(f889(x94251,x94251)),f333(f333(f263(x94251,x94251),x94252),x94253)),f309(x94251,x94254)))+P4(f333(f333(f335(f889(x94251,x94251)),f333(f333(f263(x94251,x94251),x94253),x94252)),f309(x94251,x94254)))+~P4(f333(f333(f335(f889(x94251,x94251)),f333(f333(f263(x94251,x94251),x94255),x94252)),f309(x94251,x94254)))+~P4(f333(f333(f335(f889(x94251,x94251)),f333(f333(f263(x94251,x94251),x94255),x94253)),f309(x94251,x94254))) % 191.49/191.42 [5635]E(x56351,f2(a880))+~E(f333(f39(x56352),x56355),x56351)+E(f333(f39(x56352),x56353),f333(a117,x56351))+~E(x56353,f333(f333(f311(x56352),x56354),x56355))+P4(f333(f333(f335(x56352),x56354),x56355)) % 191.49/191.42 [5760]~P64(x57602)+E(x57601,f2(x57602))+E(x57603,f2(x57602))+~E(f333(f333(f291(x57602),x57604),x57603),f333(f333(f291(x57602),x57605),x57601))+E(f333(f333(f82(x57602),x57604),x57601),f333(f333(f82(x57602),x57605),x57603)) % 191.49/191.42 [5761]~P64(x57612)+E(x57611,f2(x57612))+E(x57613,f2(x57612))+~E(f333(f333(f82(x57612),x57614),x57613),f333(f333(f82(x57612),x57615),x57611))+E(f333(f333(f291(x57612),x57614),x57611),f333(f333(f291(x57612),x57615),x57613)) % 191.49/191.42 [5827]~E(f333(f39(x58271),x58275),x58273)+~E(x58275,f194(f890(x58271,a874)))+E(f333(f39(x58271),x58272),f333(a117,x58273))+~E(x58272,f333(f333(f311(x58271),x58274),x58275))+P4(f333(f333(f335(x58271),x58274),x58275)) % 191.49/191.42 [6054]~P115(x60542)+~E(f333(x60543,x60545),f2(x60542))+E(f333(f333(f11(x60541,x60542),x60543),x60544),f2(x60542))+~P4(f333(f63(x60541),x60544))+~P4(f333(f333(f335(x60541),x60545),x60544)) % 191.49/191.42 [6422]~P109(x64223)+E(x64221,x64222)+~E(f333(f303(x64223,x64224),x64221),f333(f303(x64223,x64225),x64222))+~P4(f333(f333(f251(x64223),x64225),x64222))+~P4(f333(f333(f251(x64223),x64224),x64221)) % 191.49/191.42 [6423]~P109(x64233)+E(x64231,x64232)+~E(f333(f303(x64233,x64231),x64234),f333(f303(x64233,x64232),x64235))+~P4(f333(f333(f251(x64233),x64232),x64235))+~P4(f333(f333(f251(x64233),x64231),x64234)) % 191.49/191.42 [7460]~P109(x74601)+~P17(x74601,f333(f333(f127(x74601),x74604),x74605))+~P4(f333(f333(f335(x74601),x74603),f333(f173(x74601),x74605)))+~P4(f333(f333(f335(x74601),x74602),f333(f173(x74601),x74604)))+P4(f333(f333(f250(x74601),x74602),x74603)) % 191.49/191.42 [8557]~P110(x85571)+~P4(f333(f333(f251(f890(x85571,a874)),f304(x85571,x85575,x85572)),f304(x85571,x85574,x85573)))+~P4(f333(f333(f250(x85571),x85575),x85572))+P4(f333(f333(f251(x85571),x85572),x85573))+P4(f333(f333(f251(x85571),x85574),x85575)) % 191.49/191.42 [9959]~P20(x99592,x99595,x99593)+E(x99591,f194(f890(x99592,a874)))+~E(f333(f333(x99595,f333(x99594,f828(x99591,x99594,x99593,x99595,x99592))),f333(x99594,f829(x99591,x99594,x99593,x99595,x99592))),f333(x99594,f333(f333(x99595,f828(x99591,x99594,x99593,x99595,x99592)),f829(x99591,x99594,x99593,x99595,x99592))))+E(f333(x99593,f333(f312(x99592,x99592,x99594),x99591)),f333(x99594,f333(x99593,x99591)))+~P4(f333(f63(x99592),x99591)) % 191.49/191.42 [6419]~P21(x64192,x64195,x64193)+E(x64191,f194(f890(x64192,a874)))+~P4(f333(f63(x64192),x64191))+E(f333(x64193,f333(f333(f311(x64192),x64194),x64191)),f333(f333(x64195,x64194),f333(x64193,x64191)))+P4(f333(f333(f335(x64192),x64194),x64191)) % 191.49/191.42 [7227]~P20(x72272,x72273,x72274)+E(f333(f333(x72273,f333(x72274,x72271)),f333(x72274,x72275)),f333(x72274,x72275))+E(x72271,f194(f890(x72272,a874)))+~P4(f333(f63(x72272),x72275))+~P4(f333(f333(f250(f890(x72272,a874)),x72271),x72275)) % 191.49/191.42 [7436]~P62(x74364)+~P96(x74365)+E(f333(x74361,x74362),f333(x74363,x74362))+~P4(f333(f333(f335(x74364),x74362),f333(f173(x74364),f57(x74364))))+~P4(f333(f333(f92(f890(x74364,x74365)),x74361),x74363)) % 191.49/191.42 [7589]~P21(x75894,x75895,x75891)+E(f333(x75891,x75892),x75893)+~P4(f333(f63(x75894),x75892))+~E(f333(f333(f3(f890(x75894,a874)),x75892),f333(f333(f311(x75894),x75893),f194(f890(x75894,a874)))),f194(f890(x75894,a874)))+~P4(f333(f333(f335(x75894),x75893),x75892)) % 191.49/191.42 [7674]E(x76741,x76742)+~E(f333(f195(f881(x76743)),x76742),f333(f195(f881(x76744)),x76745))+~E(f333(f195(f881(x76743)),x76741),f333(f195(f881(x76744)),x76745))+~E(f333(f178(x76744,x76743),f333(f333(f182(x76744,x76743),x76745),x76741)),f333(f178(x76744,x76743),f333(f333(f182(x76744,x76743),x76745),x76742)))+~P4(f333(f138(x76744),x76745)) % 191.49/191.42 [8528]E(x85281,x85282)+~P12(x85283,x85284,x85285)+E(f333(f333(f106(f890(x85283,a874)),x85281),x85282),f194(f890(x85283,a874)))+~P4(f333(f333(f335(f890(x85283,a874)),x85282),f333(f333(f62(x85283),x85284),x85285)))+~P4(f333(f333(f335(f890(x85283,a874)),x85281),f333(f333(f62(x85283),x85284),x85285))) % 191.49/191.42 [9308]~P69(x93082)+~E(f333(x93083,f355(x93083,x93084,x93085,x93081,x93082)),f2(x93082))+E(f333(f333(f8(x93081,x93082),x93083),x93084),f333(f333(f8(x93081,x93082),x93083),x93085))+~P4(f333(f63(x93081),x93085))+~P4(f333(f333(f250(f890(x93081,a874)),x93084),x93085)) % 191.49/191.42 [9309]~P69(x93092)+~E(f333(x93093,f361(x93093,x93094,x93095,x93091,x93092)),f2(x93092))+E(f333(f333(f8(x93091,x93092),x93093),x93094),f333(f333(f8(x93091,x93092),x93093),x93095))+~P4(f333(f63(x93091),x93095))+~P4(f333(f333(f250(f890(x93091,a874)),x93094),x93095)) % 191.49/191.42 [9310]~P76(x93102)+~E(f333(x93103,f356(x93103,x93104,x93105,x93101,x93102)),f79(x93102))+E(f333(f333(f11(x93101,x93102),x93103),x93104),f333(f333(f11(x93101,x93102),x93103),x93105))+~P4(f333(f63(x93101),x93105))+~P4(f333(f333(f250(f890(x93101,a874)),x93104),x93105)) % 191.49/191.42 [9311]~P76(x93112)+~E(f333(x93113,f360(x93113,x93114,x93115,x93111,x93112)),f79(x93112))+E(f333(f333(f11(x93111,x93112),x93113),x93114),f333(f333(f11(x93111,x93112),x93113),x93115))+~P4(f333(f63(x93111),x93115))+~P4(f333(f333(f250(f890(x93111,a874)),x93114),x93115)) % 191.49/191.42 [9816]~P89(x98161)+~P4(f333(f63(x98162),x98165))+~P4(f333(f333(f250(x98161),f2(x98161)),f333(x98163,f357(x98163,x98164,x98165,x98162,x98161))))+P4(f333(f333(f250(x98161),f333(f333(f8(x98162,x98161),x98163),x98164)),f333(f333(f8(x98162,x98161),x98163),x98165)))+~P4(f333(f333(f250(f890(x98162,a874)),x98164),x98165)) % 191.49/191.42 [7457]E(x74571,f2(a880))+P4(f333(x74572,x74573))+~E(x74574,f333(f333(f81(a880),f333(f333(f82(a880),x74571),x74573)),x74575))+~P4(f333(f333(f251(a880),x74575),x74571))+~P4(f333(x74572,f333(f333(f40(a880),x74574),x74571))) % 191.49/191.42 [7533]E(x75331,f2(a880))+P4(f333(x75332,x75333))+~P4(f333(x75332,f46(a880,x75334,x75331)))+~E(x75334,f333(f333(f81(a880),f333(f333(f82(a880),x75331),x75335)),x75333))+~P4(f333(f333(f251(a880),x75333),x75331)) % 191.49/191.42 [7823]~P64(x78233)+E(f333(x78231,x78232),f2(x78233))+~P4(f333(f63(x78234),x78235))+E(f333(f333(f11(x78234,x78233),x78231),f333(f333(f3(f890(x78234,a874)),x78235),f333(f333(f311(x78234),x78232),f194(f890(x78234,a874))))),f333(f333(f11(x78234,x78233),x78231),x78235))+P4(f333(f333(f335(x78234),x78232),x78235)) % 191.49/191.42 [8224]~P69(x82241)+~P4(f333(f63(x82242),x82245))+~P4(f333(f63(x82242),x82244))+~E(f333(f333(f106(f890(x82242,a874)),x82244),x82245),f194(f890(x82242,a874)))+E(f333(f333(f81(x82241),f333(f333(f8(x82242,x82241),x82243),x82244)),f333(f333(f8(x82242,x82241),x82243),x82245)),f333(f333(f8(x82242,x82241),x82243),f333(f333(f115(f890(x82242,a874)),x82244),x82245))) % 191.49/191.42 [8226]~P76(x82261)+~P4(f333(f63(x82262),x82265))+~P4(f333(f63(x82262),x82264))+~E(f333(f333(f106(f890(x82262,a874)),x82264),x82265),f194(f890(x82262,a874)))+E(f333(f333(f82(x82261),f333(f333(f11(x82262,x82261),x82263),x82264)),f333(f333(f11(x82262,x82261),x82263),x82265)),f333(f333(f11(x82262,x82261),x82263),f333(f333(f115(f890(x82262,a874)),x82264),x82265))) % 191.49/191.42 [8319]~P64(x83193)+E(f333(x83191,x83192),f2(x83193))+~P4(f333(f63(x83194),x83195))+E(f333(f333(f11(x83194,x83193),x83191),f333(f333(f3(f890(x83194,a874)),x83195),f333(f333(f311(x83194),x83192),f194(f890(x83194,a874))))),f333(f333(f291(x83193),f333(f333(f11(x83194,x83193),x83191),x83195)),f333(x83191,x83192)))+~P4(f333(f333(f335(x83194),x83192),x83195)) % 191.49/191.42 [9026]~P12(x90261,x90265,x90264)+~E(f333(f333(f62(x90261),f333(f333(f311(x90261),x90262),f194(f890(x90261,a874)))),x90264),f333(f333(f62(x90261),f333(f333(f311(x90261),x90263),f194(f890(x90261,a874)))),x90264))+~P4(f333(f333(f335(x90261),x90263),x90265))+~P4(f333(f333(f335(x90261),x90262),x90265))+P4(f333(f333(f335(f889(x90261,x90261)),f333(f333(f263(x90261,x90261),x90262),x90263)),x90264)) % 191.49/191.42 [9039]~P12(x90391,x90395,x90393)+E(f333(f333(f62(x90391),f333(f333(f311(x90391),x90392),f194(f890(x90391,a874)))),x90393),f333(f333(f62(x90391),f333(f333(f311(x90391),x90394),f194(f890(x90391,a874)))),x90393))+~P4(f333(f333(f335(x90391),x90394),x90395))+~P4(f333(f333(f335(x90391),x90392),x90395))+~P4(f333(f333(f335(f889(x90391,x90391)),f333(f333(f263(x90391,x90391),x90392),x90394)),x90393)) % 191.49/191.42 [9337]~P76(x93371)+~P4(f333(f63(x93372),x93375))+~P4(f333(f63(x93372),x93374))+~E(f333(f333(f106(f890(x93372,a874)),x93374),x93375),f194(f890(x93372,a874)))+E(f333(f333(f82(x93371),f333(f333(f333(f67(x93371,x93372,f82(x93371)),x93373),f79(x93371)),x93374)),f333(f333(f333(f67(x93371,x93372,f82(x93371)),x93373),f79(x93371)),x93375)),f333(f333(f333(f67(x93371,x93372,f82(x93371)),x93373),f79(x93371)),f333(f333(f115(f890(x93372,a874)),x93374),x93375))) % 191.49/191.42 [9346]~P69(x93461)+~E(f333(x93463,f871(x93463,x93465,x93464,x93462,x93461)),f2(x93461))+~P4(f333(f63(x93462),x93464))+~P4(f333(f63(x93462),x93465))+E(f333(f333(f81(x93461),f333(f333(f8(x93462,x93461),x93463),x93464)),f333(f333(f8(x93462,x93461),x93463),x93465)),f333(f333(f8(x93462,x93461),x93463),f333(f333(f115(f890(x93462,a874)),x93464),x93465))) % 191.49/191.42 [9347]~P69(x93471)+~E(f333(x93473,f872(x93473,x93475,x93474,x93472,x93471)),f2(x93471))+~P4(f333(f63(x93472),x93474))+~P4(f333(f63(x93472),x93475))+E(f333(f333(f81(x93471),f333(f333(f8(x93472,x93471),x93473),x93474)),f333(f333(f8(x93472,x93471),x93473),x93475)),f333(f333(f8(x93472,x93471),x93473),f333(f333(f115(f890(x93472,a874)),x93474),x93475))) % 191.49/191.42 [9348]~P76(x93481)+~E(f333(x93483,f848(x93483,x93485,x93484,x93482,x93481)),f79(x93481))+~P4(f333(f63(x93482),x93484))+~P4(f333(f63(x93482),x93485))+E(f333(f333(f82(x93481),f333(f333(f11(x93482,x93481),x93483),x93484)),f333(f333(f11(x93482,x93481),x93483),x93485)),f333(f333(f11(x93482,x93481),x93483),f333(f333(f115(f890(x93482,a874)),x93484),x93485))) % 191.49/191.42 [9349]~P76(x93491)+~E(f333(x93493,f849(x93493,x93495,x93494,x93492,x93491)),f79(x93491))+~P4(f333(f63(x93492),x93494))+~P4(f333(f63(x93492),x93495))+E(f333(f333(f82(x93491),f333(f333(f11(x93492,x93491),x93493),x93494)),f333(f333(f11(x93492,x93491),x93493),x93495)),f333(f333(f11(x93492,x93491),x93493),f333(f333(f115(f890(x93492,a874)),x93494),x93495))) % 191.49/191.42 [9564]~P76(x95641)+~E(f333(x95643,f854(x95643,x95645,x95644,x95642,x95641)),f79(x95641))+~P4(f333(f63(x95642),x95644))+~P4(f333(f63(x95642),x95645))+E(f333(f333(f82(x95641),f333(f333(f333(f67(x95641,x95642,f82(x95641)),x95643),f79(x95641)),x95644)),f333(f333(f333(f67(x95641,x95642,f82(x95641)),x95643),f79(x95641)),x95645)),f333(f333(f333(f67(x95641,x95642,f82(x95641)),x95643),f79(x95641)),f333(f333(f115(f890(x95642,a874)),x95644),x95645))) % 191.49/191.42 [9683]~P69(x96832)+E(f333(f333(f8(x96831,x96832),x96833),x96834),f333(f333(f8(x96831,x96832),x96833),x96835))+~P4(f333(f63(x96831),x96835))+~P4(f333(f333(f250(f890(x96831,a874)),x96834),x96835))+P4(f333(f333(f335(x96831),f355(x96833,x96834,x96835,x96831,x96832)),f333(f333(f3(f890(x96831,a874)),x96835),x96834))) % 191.49/191.42 [9684]~P69(x96842)+E(f333(f333(f8(x96841,x96842),x96843),x96844),f333(f333(f8(x96841,x96842),x96843),x96845))+~P4(f333(f63(x96841),x96845))+~P4(f333(f333(f250(f890(x96841,a874)),x96844),x96845))+P4(f333(f333(f335(x96841),f361(x96843,x96844,x96845,x96841,x96842)),f333(f333(f3(f890(x96841,a874)),x96845),x96844))) % 191.49/191.42 [9685]~P76(x96852)+E(f333(f333(f11(x96851,x96852),x96853),x96854),f333(f333(f11(x96851,x96852),x96853),x96855))+~P4(f333(f63(x96851),x96855))+~P4(f333(f333(f250(f890(x96851,a874)),x96854),x96855))+P4(f333(f333(f335(x96851),f356(x96853,x96854,x96855,x96851,x96852)),f333(f333(f3(f890(x96851,a874)),x96855),x96854))) % 191.49/191.42 [9686]~P76(x96862)+E(f333(f333(f11(x96861,x96862),x96863),x96864),f333(f333(f11(x96861,x96862),x96863),x96865))+~P4(f333(f63(x96861),x96865))+~P4(f333(f333(f250(f890(x96861,a874)),x96864),x96865))+P4(f333(f333(f335(x96861),f360(x96863,x96864,x96865,x96861,x96862)),f333(f333(f3(f890(x96861,a874)),x96865),x96864))) % 191.49/191.42 [9704]~P69(x97041)+~P4(f333(f63(x97042),x97044))+~P4(f333(f63(x97042),x97045))+E(f333(f333(f81(x97041),f333(f333(f8(x97042,x97041),x97043),x97044)),f333(f333(f8(x97042,x97041),x97043),x97045)),f333(f333(f8(x97042,x97041),x97043),f333(f333(f115(f890(x97042,a874)),x97044),x97045)))+P4(f333(f333(f335(x97042),f871(x97043,x97045,x97044,x97042,x97041)),f333(f333(f106(f890(x97042,a874)),x97044),x97045))) % 191.49/191.42 [9705]~P69(x97051)+~P4(f333(f63(x97052),x97054))+~P4(f333(f63(x97052),x97055))+E(f333(f333(f81(x97051),f333(f333(f8(x97052,x97051),x97053),x97054)),f333(f333(f8(x97052,x97051),x97053),x97055)),f333(f333(f8(x97052,x97051),x97053),f333(f333(f115(f890(x97052,a874)),x97054),x97055)))+P4(f333(f333(f335(x97052),f872(x97053,x97055,x97054,x97052,x97051)),f333(f333(f106(f890(x97052,a874)),x97054),x97055))) % 191.49/191.42 [9706]~P76(x97061)+~P4(f333(f63(x97062),x97064))+~P4(f333(f63(x97062),x97065))+E(f333(f333(f82(x97061),f333(f333(f11(x97062,x97061),x97063),x97064)),f333(f333(f11(x97062,x97061),x97063),x97065)),f333(f333(f11(x97062,x97061),x97063),f333(f333(f115(f890(x97062,a874)),x97064),x97065)))+P4(f333(f333(f335(x97062),f848(x97063,x97065,x97064,x97062,x97061)),f333(f333(f106(f890(x97062,a874)),x97064),x97065))) % 191.49/191.42 [9707]~P76(x97071)+~P4(f333(f63(x97072),x97074))+~P4(f333(f63(x97072),x97075))+E(f333(f333(f82(x97071),f333(f333(f11(x97072,x97071),x97073),x97074)),f333(f333(f11(x97072,x97071),x97073),x97075)),f333(f333(f11(x97072,x97071),x97073),f333(f333(f115(f890(x97072,a874)),x97074),x97075)))+P4(f333(f333(f335(x97072),f849(x97073,x97075,x97074,x97072,x97071)),f333(f333(f106(f890(x97072,a874)),x97074),x97075))) % 191.49/191.42 [9714]~P89(x97145)+~P4(f333(f63(x97141),x97144))+P4(f333(f333(f250(x97145),f333(f333(f8(x97141,x97145),x97142),x97143)),f333(f333(f8(x97141,x97145),x97142),x97144)))+~P4(f333(f333(f250(f890(x97141,a874)),x97143),x97144))+P4(f333(f333(f335(x97141),f357(x97142,x97143,x97144,x97141,x97145)),f333(f333(f3(f890(x97141,a874)),x97144),x97143))) % 191.49/191.42 [9779]~P76(x97791)+~P4(f333(f63(x97792),x97794))+~P4(f333(f63(x97792),x97795))+E(f333(f333(f82(x97791),f333(f333(f333(f67(x97791,x97792,f82(x97791)),x97793),f79(x97791)),x97794)),f333(f333(f333(f67(x97791,x97792,f82(x97791)),x97793),f79(x97791)),x97795)),f333(f333(f333(f67(x97791,x97792,f82(x97791)),x97793),f79(x97791)),f333(f333(f115(f890(x97792,a874)),x97794),x97795)))+P4(f333(f333(f335(x97792),f854(x97793,x97795,x97794,x97792,x97791)),f333(f333(f106(f890(x97792,a874)),x97794),x97795))) % 191.49/191.42 [8711]~P21(x87111,x87114,x87115)+~P4(f333(f63(x87111),x87112))+E(f333(f333(f3(f890(x87111,a874)),x87112),f333(f333(f311(x87111),x87113),f194(f890(x87111,a874)))),f194(f890(x87111,a874)))+~P4(f333(f333(f335(x87111),x87113),x87112))+E(f333(f333(x87114,x87113),f333(x87115,f333(f333(f3(f890(x87111,a874)),x87112),f333(f333(f311(x87111),x87113),f194(f890(x87111,a874)))))),f333(x87115,x87112)) % 191.49/191.42 [8785]~P21(x87851,x87854,x87855)+~P4(f333(f63(x87851),x87853))+~P4(f333(f63(x87851),x87852))+E(f333(f333(f106(f890(x87851,a874)),x87852),x87853),f194(f890(x87851,a874)))+E(f333(f333(x87854,f333(x87855,f333(f333(f115(f890(x87851,a874)),x87852),x87853))),f333(x87855,f333(f333(f106(f890(x87851,a874)),x87852),x87853))),f333(f333(x87854,f333(x87855,x87852)),f333(x87855,x87853))) % 191.49/191.42 [9351]~P4(f333(f333(f250(a1),x93514),f2(a1)))+~P4(f333(f333(f251(a1),x93513),x93515))+P4(f333(f333(f250(a1),x93511),x93512))+~P4(f333(f333(f251(a1),x93513),x93514))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f82(a1),x93513),x93512)),x93515)),f333(f333(f81(a1),f333(f333(f82(a1),x93513),x93511)),x93514))) % 191.49/191.42 [9358]~P4(f333(f333(f250(a1),f2(a1)),x93585))+P4(f333(f333(f250(a1),x93581),x93582))+~P4(f333(f333(f251(a1),x93583),x93584))+~P4(f333(f333(f251(a1),x93585),x93584))+~P4(f333(f333(f250(a1),f333(f333(f81(a1),f333(f333(f82(a1),x93584),x93581)),x93585)),f333(f333(f81(a1),f333(f333(f82(a1),x93584),x93582)),x93583))) % 191.49/191.42 [9460]~P64(x94605)+E(f333(x94601,f349(x94601,x94602,x94603,x94604,x94605)),f2(x94605))+~P4(f333(f63(x94604),x94603))+~P4(f333(f63(x94604),x94602))+E(f333(f333(f291(x94605),f333(f333(f82(x94605),f333(f333(f11(x94604,x94605),x94601),x94603)),f333(f333(f11(x94604,x94605),x94601),x94602))),f333(f333(f11(x94604,x94605),x94601),f333(f333(f106(f890(x94604,a874)),x94603),x94602))),f333(f333(f11(x94604,x94605),x94601),f333(f333(f115(f890(x94604,a874)),x94603),x94602))) % 191.49/191.42 [9772]~P64(x97721)+~P4(f333(f63(x97722),x97724))+~P4(f333(f63(x97722),x97725))+E(f333(f333(f291(x97721),f333(f333(f82(x97721),f333(f333(f11(x97722,x97721),x97723),x97724)),f333(f333(f11(x97722,x97721),x97723),x97725))),f333(f333(f11(x97722,x97721),x97723),f333(f333(f106(f890(x97722,a874)),x97724),x97725))),f333(f333(f11(x97722,x97721),x97723),f333(f333(f115(f890(x97722,a874)),x97724),x97725)))+P4(f333(f333(f335(x97722),f349(x97723,x97725,x97724,x97722,x97721)),f333(f333(f106(f890(x97722,a874)),x97724),x97725))) % 191.49/191.42 [9053]E(f333(f333(f127(x90531),x90532),x90533),f333(f333(f127(x90531),x90534),x90535))+~E(f333(f333(f174(x90531),f333(f195(f881(x90531)),x90534)),x90532),x90534)+~E(f333(f333(f174(x90531),f333(f195(f881(x90531)),x90532)),x90534),x90532)+~E(x90535,f333(f333(f127(x90531),f333(f333(f139(x90531),f333(f195(f881(x90531)),x90534)),x90532)),x90533))+~E(f333(f333(f127(x90531),f333(f333(f139(x90531),f333(f195(f881(x90531)),x90532)),x90534)),x90535),x90533) % 191.49/191.42 [9458]~P109(x94582)+E(f333(f333(f149(x94581,x94582,x94583),x94584),f171(x94581,x94584,x94585)),x94585)+~P17(x94582,f333(f333(f155(x94581,x94582),x94583),x94585))+~P4(f333(f333(f335(x94581),x94584),f333(f173(x94581),x94585)))+~E(f333(f142(x94581),f333(f137(x94581,f333(f333(f10(x94582,a874,x94581),f333(a330,f333(x94583,x94584))),x94583)),x94585)),x94584) % 191.49/191.42 [9832]~P73(x98321)+~P4(f333(f68(x98321,x98321,f82(x98321),x98322,x98323),x98325))+~P4(f333(f333(f335(x98321),x98324),x98323))+P4(f333(f333(f335(x98321),x98322),x98323))+P4(f333(f68(x98321,x98321,f82(x98321),x98324,f333(f333(f311(x98321),x98322),f333(f333(f3(f890(x98321,a874)),x98323),f333(f333(f311(x98321),x98324),f194(f890(x98321,a874)))))),x98325)) % 191.49/191.42 [7235]E(x72351,x72352)+~P28(x72354,x72355,x72353,x72356)+~E(f333(x72353,x72351),f333(x72353,x72352))+~P4(f333(f333(f335(x72354),x72352),x72356))+~P4(f333(f333(f335(x72354),x72351),x72356)) % 191.49/191.42 [6509]~P137(x65094)+E(x65091,x65092)+~E(x65095,x65096)+E(x65093,f2(x65094))+~E(f333(f333(f81(x65094),x65095),f333(f333(f82(x65094),x65093),x65091)),f333(f333(f81(x65094),x65096),f333(f333(f82(x65094),x65093),x65092))) % 191.49/191.42 [7514]~P9(x75141)+~P109(x75141)+~P4(f333(f333(f251(x75141),x75142),f333(x75145,x75146)))+~P4(f333(f333(f335(x75143),x75146),x75144))+P4(f333(f333(f251(x75141),x75142),f333(f333(f44(x75143,x75141),x75144),x75145))) % 191.49/191.42 [8197]~P9(x81971)+~P109(x81971)+~P4(f333(f333(f251(x81971),f333(x81974,x81976)),x81975))+~P4(f333(f333(f335(x81972),x81976),x81973))+P4(f333(f333(f251(x81971),f333(f333(f43(x81972,x81971),x81973),x81974)),x81975)) % 191.49/191.42 [8453]~P22(x84532,x84535,x84536,x84531)+~P4(f333(f63(x84532),x84534))+~P4(f333(f63(x84532),x84533))+~E(f333(f333(f106(f890(x84532,a874)),x84533),x84534),f194(f890(x84532,a874)))+E(f333(x84531,f333(f333(f115(f890(x84532,a874)),x84533),x84534)),f333(f74(x84535,x84535,x84535,f333(x84531,x84533)),f333(x84531,x84534))) % 191.49/191.42 [8754]E(x87541,x87542)+~P56(x87544,x87545,x87546,x87543,x87547)+~E(f333(x87543,x87541),f333(x87543,x87542))+~P4(f333(f333(f335(x87545),x87542),x87547))+~P4(f333(f333(f335(x87545),x87541),x87547)) % 191.49/191.42 [10054]~P4(f333(x100542,x100544))+~E(x100545,f333(f137(x100541,x100542),x100547))+E(f333(f137(x100541,x100542),x100543),f333(f333(f152(x100541),x100544),x100545))+~E(x100543,f333(f333(f127(x100541),x100546),f333(f333(f152(x100541),x100544),x100547)))+P4(f333(x100542,f752(x100545,x100544,x100543,x100542,x100541,x100546,x100547))) % 191.49/191.42 [10055]~P4(f333(x100554,x100552))+~E(x100553,f333(f137(x100551,x100554),x100557))+E(f333(f333(f152(x100551),x100552),x100553),f333(f137(x100551,x100554),x100555))+~E(x100555,f333(f333(f127(x100551),x100556),f333(f333(f152(x100551),x100552),x100557)))+P4(f333(x100554,f754(x100555,x100554,x100553,x100552,x100551,x100556,x100557))) % 191.49/191.42 [10096]~P4(f333(x100962,x100964))+~E(x100965,f333(f137(x100961,x100962),x100967))+E(f333(f137(x100961,x100962),x100963),f333(f333(f152(x100961),x100964),x100965))+~E(x100963,f333(f333(f127(x100961),x100966),f333(f333(f152(x100961),x100964),x100967)))+P4(f333(f333(f335(x100961),f752(x100965,x100964,x100963,x100962,x100961,x100966,x100967)),f333(f173(x100961),x100966))) % 191.49/191.42 [10097]~P4(f333(x100974,x100972))+~E(x100973,f333(f137(x100971,x100974),x100977))+E(f333(f333(f152(x100971),x100972),x100973),f333(f137(x100971,x100974),x100975))+~E(x100975,f333(f333(f127(x100971),x100976),f333(f333(f152(x100971),x100972),x100977)))+P4(f333(f333(f335(x100971),f754(x100975,x100974,x100973,x100972,x100971,x100976,x100977)),f333(f173(x100971),x100976))) % 191.49/191.42 [10101]~P12(x101011,x101017,x101016)+~P15(x101011,f890(x101015,a874),x101016,x101014)+P4(f333(f333(f335(x101011),f564(x101012,x101013,x101014,x101015,x101016,x101017,x101011)),x101017))+~P4(f333(f333(f335(f890(x101011,a874)),x101013),f333(f333(f62(x101011),x101017),x101016)))+P4(f333(f333(f335(f890(x101015,a874)),f333(f333(f44(x101011,f890(x101015,a874)),x101013),x101014)),x101012)) % 191.49/191.42 [10171]~P12(x101712,x101716,x101717)+~P15(x101712,f890(x101711,a874),x101717,x101714)+~P4(f333(f333(f335(f890(x101712,a874)),x101713),f333(f333(f62(x101712),x101716),x101717)))+~P4(f333(f333(f335(f890(x101711,a874)),f333(x101714,f564(x101715,x101713,x101714,x101711,x101717,x101716,x101712))),x101715))+P4(f333(f333(f335(f890(x101711,a874)),f333(f333(f44(x101712,f890(x101711,a874)),x101713),x101714)),x101715)) % 191.49/191.42 [8361]~P76(x83612)+~P28(x83611,x83615,x83618,x83614)+~E(x83613,f333(f74(x83615,x83612,x83611,x83616),x83618))+~E(x83617,f333(f312(x83611,x83615,x83618),x83614))+E(f333(f333(f11(x83611,x83612),x83613),x83614),f333(f333(f11(x83615,x83612),x83616),x83617)) % 191.49/191.42 [10179]~P76(x101792)+~P28(x101795,x101791,x101798,x101797)+~E(f333(x101796,f533(x101793,x101796,x101794,x101797,x101798,x101791,x101795,x101792)),f333(f333(f74(x101791,x101792,x101795,x101793),x101798),f533(x101793,x101796,x101794,x101797,x101798,x101791,x101795,x101792)))+~E(x101794,f333(f312(x101795,x101791,x101798),x101797))+E(f333(f333(f11(x101791,x101792),x101793),x101794),f333(f333(f11(x101795,x101792),x101796),x101797)) % 191.49/191.42 [10185]~P69(x101852)+~P28(x101851,x101855,x101858,x101854)+~E(x101857,f333(f312(x101851,x101855,x101858),x101854))+E(f333(f333(f8(x101851,x101852),x101853),x101854),f333(f333(f8(x101855,x101852),x101856),x101857))+P4(f333(f333(f335(x101851),f384(x101856,x101853,x101857,x101854,x101858,x101855,x101851,x101852)),x101854)) % 191.49/191.42 [10186]~P76(x101862)+~P28(x101861,x101865,x101868,x101864)+~E(x101867,f333(f312(x101861,x101865,x101868),x101864))+E(f333(f333(f11(x101861,x101862),x101863),x101864),f333(f333(f11(x101865,x101862),x101866),x101867))+P4(f333(f333(f335(x101861),f533(x101866,x101863,x101867,x101864,x101868,x101865,x101861,x101862)),x101864)) % 191.49/191.42 [10191]~P69(x101912)+~P28(x101915,x101911,x101918,x101917)+~E(x101914,f333(f312(x101915,x101911,x101918),x101917))+~E(f333(x101916,f384(x101913,x101916,x101914,x101917,x101918,x101911,x101915,x101912)),f333(x101913,f333(x101918,f384(x101913,x101916,x101914,x101917,x101918,x101911,x101915,x101912))))+E(f333(f333(f8(x101911,x101912),x101913),x101914),f333(f333(f8(x101915,x101912),x101916),x101917)) % 191.49/191.42 [9528]~E(f333(f195(f881(x95282)),x95285),f333(f195(f881(x95281)),x95283))+~E(f333(f195(f881(x95282)),x95284),f333(f195(f881(x95281)),x95283))+~E(f333(f333(f333(f73(x95281,f884(x95282)),f333(f178(x95281,x95282),f333(f333(f182(x95281,x95282),x95283),x95284))),x95286),f333(f242(x95282),x95287)),f333(f333(f333(f73(x95281,f884(x95282)),f333(f178(x95281,x95282),f333(f333(f182(x95281,x95282),x95283),x95285))),x95286),f333(f242(x95282),x95288)))+E(f333(f178(x95281,x95282),f333(f333(f182(x95281,x95282),x95283),x95284)),f333(f178(x95281,x95282),f333(f333(f182(x95281,x95282),x95283),x95285)))+P4(f333(f333(f335(x95281),x95286),f333(f173(x95281),x95283))) % 191.49/191.42 [9654]~P26(x96546,x96542,x96545,x96547,x96548,x96541)+~P4(f333(f63(x96542),x96544))+~P4(f333(f63(x96542),x96543))+~E(f333(f333(f106(f890(x96542,a874)),x96543),x96544),f194(f890(x96542,a874)))+E(f333(x96541,f333(f333(f115(f890(x96542,a874)),x96543),x96544)),f333(f333(x96545,f333(x96541,x96543)),f333(x96541,x96544))) % 191.49/191.42 [10043]~P26(x100438,x100432,x100435,x100437,x100436,x100431)+~E(f333(x100436,f661(x100434,x100433,x100431,x100436,x100437,x100435,x100432)),x100437)+~P4(f333(f63(x100432),x100433))+~P4(f333(f63(x100432),x100434))+E(f333(x100431,f333(f333(f115(f890(x100432,a874)),x100433),x100434)),f333(f333(x100435,f333(x100431,x100433)),f333(x100431,x100434))) % 191.49/191.42 [10106]~P26(x101068,x101062,x101065,x101067,x101066,x101061)+~P4(f333(f63(x101062),x101063))+~P4(f333(f63(x101062),x101064))+E(f333(x101061,f333(f333(f115(f890(x101062,a874)),x101063),x101064)),f333(f333(x101065,f333(x101061,x101063)),f333(x101061,x101064)))+P4(f333(f333(f335(x101062),f661(x101064,x101063,x101061,x101066,x101067,x101065,x101062)),f333(f333(f106(f890(x101062,a874)),x101063),x101064))) % 191.49/191.42 [9821]~P12(x98214,x98218,x98215)+~P12(x98211,x98219,x98213)+~P16(x98211,x98214,f890(x98212,a874),x98213,x98215,x98217)+P15(x98211,f890(x98212,a874),x98213,f333(f333(f10(f890(x98214,f890(x98212,a874)),f890(x98212,a874),x98211),f333(f44(x98214,f890(x98212,a874)),f333(f287(x98214,x98214,x98215),f333(f333(f311(x98214),x98216),f194(f890(x98214,a874)))))),x98217))+~P4(f333(f333(f335(x98214),x98216),x98218)) % 191.49/191.42 [5443]~P109(x54433)+~P17(x54433,x54431)+E(x54431,f723(x54432,x54433))+~E(f333(f173(x54433),x54431),x54432)+~P4(f333(f63(x54433),x54432))+~P4(f333(f138(x54433),x54431)) % 191.49/191.42 [5065]~P127(x50652)+~P128(x50652)+~P142(x50652)+~P113(x50652)+E(x50651,f2(x50652))+~E(f333(f333(f264(x50652),x50651),x50653),f2(x50652)) % 191.49/191.42 [5066]~P127(x50662)+~P128(x50662)+~P142(x50662)+~P113(x50662)+~E(x50661,f2(a880))+~E(f333(f333(f264(x50662),x50663),x50661),f2(x50662)) % 191.49/191.42 [6491]~P89(x64911)+~E(x64913,f2(x64911))+~E(x64912,f2(x64911))+E(f333(f333(f81(x64911),x64912),x64913),f2(x64911))+~P4(f333(f333(f250(x64911),f2(x64911)),x64913))+~P4(f333(f333(f250(x64911),f2(x64911)),x64912)) % 191.49/191.42 [8819]~E(f333(f262(a880,a880),x88193),f2(a880))+~E(x88191,f333(f333(f81(a880),f333(f333(f82(a880),f333(f262(a880,a880),x88193)),x88192)),f333(f271(a880,a880),x88193)))+P4(f333(f49(x88191,x88192),x88193))+~P4(f333(f333(f250(a880),f333(f271(a880,a880),x88193)),f2(a880)))+P4(f333(f333(f251(a880),f2(a880)),x88192))+~P4(f333(f333(f251(a880),x88192),f333(f271(a880,a880),x88193))) % 191.49/191.42 [8827]E(x88271,f2(a880))+~E(x88272,f333(f333(f81(a880),f333(f333(f82(a880),f333(f262(a880,a880),x88273)),x88271)),f333(f271(a880,a880),x88273)))+P4(f333(f49(x88272,x88271),x88273))+~P4(f333(f333(f251(a880),f2(a880)),x88271))+~P4(f333(f333(f250(a880),f2(a880)),f333(f271(a880,a880),x88273)))+~P4(f333(f333(f251(a880),f333(f271(a880,a880),x88273)),x88271)) % 191.49/191.42 [8845]~E(f333(f262(a880,a880),x88453),f2(a880))+~E(x88451,f333(f333(f81(a880),f333(f333(f82(a880),f333(f262(a880,a880),x88453)),x88452)),f333(f271(a880,a880),x88453)))+P4(f333(f49(x88451,x88452),x88453))+~P4(f333(f333(f251(a880),f2(a880)),x88452))+~P4(f333(f333(f250(a880),f2(a880)),f333(f271(a880,a880),x88453)))+~P4(f333(f333(f251(a880),f333(f271(a880,a880),x88453)),x88452)) % 191.49/191.42 [6860]~P6(x68602)+E(x68601,f194(f890(x68602,a874)))+E(x68603,f194(f890(x68602,a874)))+~P4(f333(f63(x68602),x68601))+~P4(f333(f63(x68602),x68603))+E(f12(x68602,f333(f333(f115(f890(x68602,a874)),x68603),x68601)),f333(f333(f115(x68602),f12(x68602,x68603)),f12(x68602,x68601))) % 191.49/191.42 [6861]~P6(x68612)+E(x68611,f194(f890(x68612,a874)))+E(x68613,f194(f890(x68612,a874)))+~P4(f333(f63(x68612),x68611))+~P4(f333(f63(x68612),x68613))+E(f13(x68612,f333(f333(f115(f890(x68612,a874)),x68613),x68611)),f333(f333(f106(x68612),f13(x68612,x68613)),f13(x68612,x68611))) % 191.49/191.42 [6862]~P109(x68622)+E(x68621,f194(f890(x68622,a874)))+E(x68623,f194(f890(x68622,a874)))+~P4(f333(f63(x68622),x68621))+~P4(f333(f63(x68622),x68623))+E(f16(x68622,f333(f333(f115(f890(x68622,a874)),x68623),x68621)),f333(f333(f248(x68622),f16(x68622,x68623)),f16(x68622,x68621))) % 191.49/191.42 [6863]~P109(x68632)+E(x68631,f194(f890(x68632,a874)))+E(x68633,f194(f890(x68632,a874)))+~P4(f333(f63(x68632),x68631))+~P4(f333(f63(x68632),x68633))+E(f17(x68632,f333(f333(f115(f890(x68632,a874)),x68633),x68631)),f333(f333(f249(x68632),f17(x68632,x68633)),f17(x68632,x68631))) % 191.49/191.42 [7489]~P97(x74892)+E(x74891,f194(f890(x74892,a874)))+E(x74893,f194(f890(x74892,a874)))+~P4(f333(f63(x74892),x74891))+~P4(f333(f63(x74892),x74893))+E(f333(f333(f82(x74892),f333(f65(x74892,f82(x74892)),x74893)),f333(f65(x74892,f82(x74892)),x74891)),f333(f65(x74892,f82(x74892)),f333(f333(f115(f890(x74892,a874)),x74893),x74891))) % 191.49/191.42 [7643]~P109(x76432)+E(x76431,f194(f890(x76432,a874)))+E(x76433,f194(f890(x76432,a874)))+~P4(f333(f63(x76432),x76431))+~P4(f333(f63(x76432),x76433))+E(f333(f333(f248(x76432),f14(x76432,f248(x76432),x76433)),f14(x76432,f248(x76432),x76431)),f14(x76432,f248(x76432),f333(f333(f115(f890(x76432,a874)),x76433),x76431))) % 191.49/191.42 [7644]~P109(x76442)+E(x76441,f194(f890(x76442,a874)))+E(x76443,f194(f890(x76442,a874)))+~P4(f333(f63(x76442),x76441))+~P4(f333(f63(x76442),x76443))+E(f333(f333(f249(x76442),f15(x76442,f249(x76442),x76443)),f15(x76442,f249(x76442),x76441)),f15(x76442,f249(x76442),f333(f333(f115(f890(x76442,a874)),x76443),x76441))) % 191.49/191.42 [8665]~P4(f333(x86651,x86653))+P4(f333(x86651,f447(x86651,x86652)))+P4(f333(x86651,f431(x86651,x86652)))+~P4(f333(f333(f251(a1),f2(a1)),x86652))+~P4(f333(f333(f335(a1),x86653),f304(a1,f79(a1),x86652)))+P4(f333(x86651,f333(f333(f3(a1),f431(x86651,x86652)),f333(f333(f82(a1),f446(x86651,x86652)),x86652)))) % 191.49/191.42 [8966]~P4(f333(x89661,x89663))+~P4(f333(x89661,f431(x89661,x89662)))+P4(f333(x89661,f447(x89661,x89662)))+~P4(f333(f333(f251(a1),f2(a1)),x89662))+~P4(f333(f333(f335(a1),x89663),f304(a1,f79(a1),x89662)))+~P4(f333(x89661,f333(f333(f3(a1),f431(x89661,x89662)),f333(f333(f82(a1),f446(x89661,x89662)),x89662)))) % 191.49/191.42 [10223]~P99(x102232)+E(x102231,f194(f890(x102232,a874)))+E(x102233,f194(f890(x102232,a874)))+~P4(f333(f63(x102232),x102231))+~P4(f333(f63(x102232),x102233))+E(f13(x102232,f333(f255(x102232),f333(f333(f10(f890(x102232,a874),a874,x102232),f87(x102232)),f333(f333(f10(f890(x102232,f890(x102232,a874)),f890(x102232,a874),x102232),f333(f10(f890(x102232,a874),a874,x102232),f87(x102232))),f333(f333(f9(x102232,f890(x102232,f890(x102232,a874)),f890(x102232,f890(x102232,a874))),f333(f333(f10(f890(x102232,f890(f890(x102232,a874),f890(x102232,a874))),f890(f890(x102232,f890(x102232,a874)),f890(x102232,f890(x102232,a874))),x102232),f20(x102232,f890(x102232,a874),f890(x102232,a874))),f333(f333(f10(f890(x102232,f890(x102232,f890(a874,a874))),f890(x102232,f890(f890(x102232,a874),f890(x102232,a874))),x102232),f333(f10(f890(x102232,f890(a874,a874)),f890(f890(x102232,a874),f890(x102232,a874)),x102232),f20(x102232,a874,a874))),f333(f333(f10(f890(x102232,f890(x102232,a874)),f890(x102232,f890(x102232,f890(a874,a874))),x102232),f333(f10(f890(x102232,a874),f890(x102232,f890(a874,a874)),x102232),f333(f10(a874,f890(a874,a874),x102232),a331))),f333(f333(f9(x102232,f890(x102232,f890(x102232,x102232)),f890(x102232,f890(x102232,a874))),f333(f333(f10(f890(f890(x102232,x102232),f890(x102232,a874)),f890(f890(x102232,f890(x102232,x102232)),f890(x102232,f890(x102232,a874))),x102232),f10(f890(x102232,x102232),f890(x102232,a874),x102232)),f333(f333(f10(f890(x102232,a874),f890(f890(x102232,x102232),f890(x102232,a874)),x102232),f10(x102232,a874,x102232)),a330))),f115(x102232)))))),f333(f333(f9(x102232,f890(x102232,a874),f890(x102232,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x102232,a874),f890(x102232,a874)),x102232),f10(a874,a874,x102232)),f333(f333(f10(a874,f890(a874,a874),x102232),a331),f333(f333(f9(x102232,f890(x102232,a874),a874),f335(x102232)),x102233)))),f333(f333(f9(x102232,f890(x102232,a874),a874),f335(x102232)),x102231))))))),f333(f333(f115(x102232),f13(x102232,x102233)),f13(x102232,x102231))) % 191.49/191.42 [10224]~P99(x102242)+E(x102241,f194(f890(x102242,a874)))+E(x102243,f194(f890(x102242,a874)))+~P4(f333(f63(x102242),x102241))+~P4(f333(f63(x102242),x102243))+E(f12(x102242,f333(f255(x102242),f333(f333(f10(f890(x102242,a874),a874,x102242),f87(x102242)),f333(f333(f10(f890(x102242,f890(x102242,a874)),f890(x102242,a874),x102242),f333(f10(f890(x102242,a874),a874,x102242),f87(x102242))),f333(f333(f9(x102242,f890(x102242,f890(x102242,a874)),f890(x102242,f890(x102242,a874))),f333(f333(f10(f890(x102242,f890(f890(x102242,a874),f890(x102242,a874))),f890(f890(x102242,f890(x102242,a874)),f890(x102242,f890(x102242,a874))),x102242),f20(x102242,f890(x102242,a874),f890(x102242,a874))),f333(f333(f10(f890(x102242,f890(x102242,f890(a874,a874))),f890(x102242,f890(f890(x102242,a874),f890(x102242,a874))),x102242),f333(f10(f890(x102242,f890(a874,a874)),f890(f890(x102242,a874),f890(x102242,a874)),x102242),f20(x102242,a874,a874))),f333(f333(f10(f890(x102242,f890(x102242,a874)),f890(x102242,f890(x102242,f890(a874,a874))),x102242),f333(f10(f890(x102242,a874),f890(x102242,f890(a874,a874)),x102242),f333(f10(a874,f890(a874,a874),x102242),a331))),f333(f333(f9(x102242,f890(x102242,f890(x102242,x102242)),f890(x102242,f890(x102242,a874))),f333(f333(f10(f890(f890(x102242,x102242),f890(x102242,a874)),f890(f890(x102242,f890(x102242,x102242)),f890(x102242,f890(x102242,a874))),x102242),f10(f890(x102242,x102242),f890(x102242,a874),x102242)),f333(f333(f10(f890(x102242,a874),f890(f890(x102242,x102242),f890(x102242,a874)),x102242),f10(x102242,a874,x102242)),a330))),f106(x102242)))))),f333(f333(f9(x102242,f890(x102242,a874),f890(x102242,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x102242,a874),f890(x102242,a874)),x102242),f10(a874,a874,x102242)),f333(f333(f10(a874,f890(a874,a874),x102242),a331),f333(f333(f9(x102242,f890(x102242,a874),a874),f335(x102242)),x102243)))),f333(f333(f9(x102242,f890(x102242,a874),a874),f335(x102242)),x102241))))))),f333(f333(f106(x102242),f12(x102242,x102243)),f12(x102242,x102241))) % 191.49/191.42 [10225]~P109(x102252)+E(x102251,f194(f890(x102252,a874)))+E(x102253,f194(f890(x102252,a874)))+~P4(f333(f63(x102252),x102251))+~P4(f333(f63(x102252),x102253))+E(f15(x102252,f249(x102252),f333(f255(x102252),f333(f333(f10(f890(x102252,a874),a874,x102252),f87(x102252)),f333(f333(f10(f890(x102252,f890(x102252,a874)),f890(x102252,a874),x102252),f333(f10(f890(x102252,a874),a874,x102252),f87(x102252))),f333(f333(f9(x102252,f890(x102252,f890(x102252,a874)),f890(x102252,f890(x102252,a874))),f333(f333(f10(f890(x102252,f890(f890(x102252,a874),f890(x102252,a874))),f890(f890(x102252,f890(x102252,a874)),f890(x102252,f890(x102252,a874))),x102252),f20(x102252,f890(x102252,a874),f890(x102252,a874))),f333(f333(f10(f890(x102252,f890(x102252,f890(a874,a874))),f890(x102252,f890(f890(x102252,a874),f890(x102252,a874))),x102252),f333(f10(f890(x102252,f890(a874,a874)),f890(f890(x102252,a874),f890(x102252,a874)),x102252),f20(x102252,a874,a874))),f333(f333(f10(f890(x102252,f890(x102252,a874)),f890(x102252,f890(x102252,f890(a874,a874))),x102252),f333(f10(f890(x102252,a874),f890(x102252,f890(a874,a874)),x102252),f333(f10(a874,f890(a874,a874),x102252),a331))),f333(f333(f9(x102252,f890(x102252,f890(x102252,x102252)),f890(x102252,f890(x102252,a874))),f333(f333(f10(f890(f890(x102252,x102252),f890(x102252,a874)),f890(f890(x102252,f890(x102252,x102252)),f890(x102252,f890(x102252,a874))),x102252),f10(f890(x102252,x102252),f890(x102252,a874),x102252)),f333(f333(f10(f890(x102252,a874),f890(f890(x102252,x102252),f890(x102252,a874)),x102252),f10(x102252,a874,x102252)),a330))),f248(x102252)))))),f333(f333(f9(x102252,f890(x102252,a874),f890(x102252,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x102252,a874),f890(x102252,a874)),x102252),f10(a874,a874,x102252)),f333(f333(f10(a874,f890(a874,a874),x102252),a331),f333(f333(f9(x102252,f890(x102252,a874),a874),f335(x102252)),x102253)))),f333(f333(f9(x102252,f890(x102252,a874),a874),f335(x102252)),x102251))))))),f333(f333(f248(x102252),f15(x102252,f249(x102252),x102253)),f15(x102252,f249(x102252),x102251))) % 191.49/191.42 [10226]~P109(x102262)+E(x102261,f194(f890(x102262,a874)))+E(x102263,f194(f890(x102262,a874)))+~P4(f333(f63(x102262),x102261))+~P4(f333(f63(x102262),x102263))+E(f14(x102262,f248(x102262),f333(f255(x102262),f333(f333(f10(f890(x102262,a874),a874,x102262),f87(x102262)),f333(f333(f10(f890(x102262,f890(x102262,a874)),f890(x102262,a874),x102262),f333(f10(f890(x102262,a874),a874,x102262),f87(x102262))),f333(f333(f9(x102262,f890(x102262,f890(x102262,a874)),f890(x102262,f890(x102262,a874))),f333(f333(f10(f890(x102262,f890(f890(x102262,a874),f890(x102262,a874))),f890(f890(x102262,f890(x102262,a874)),f890(x102262,f890(x102262,a874))),x102262),f20(x102262,f890(x102262,a874),f890(x102262,a874))),f333(f333(f10(f890(x102262,f890(x102262,f890(a874,a874))),f890(x102262,f890(f890(x102262,a874),f890(x102262,a874))),x102262),f333(f10(f890(x102262,f890(a874,a874)),f890(f890(x102262,a874),f890(x102262,a874)),x102262),f20(x102262,a874,a874))),f333(f333(f10(f890(x102262,f890(x102262,a874)),f890(x102262,f890(x102262,f890(a874,a874))),x102262),f333(f10(f890(x102262,a874),f890(x102262,f890(a874,a874)),x102262),f333(f10(a874,f890(a874,a874),x102262),a331))),f333(f333(f9(x102262,f890(x102262,f890(x102262,x102262)),f890(x102262,f890(x102262,a874))),f333(f333(f10(f890(f890(x102262,x102262),f890(x102262,a874)),f890(f890(x102262,f890(x102262,x102262)),f890(x102262,f890(x102262,a874))),x102262),f10(f890(x102262,x102262),f890(x102262,a874),x102262)),f333(f333(f10(f890(x102262,a874),f890(f890(x102262,x102262),f890(x102262,a874)),x102262),f10(x102262,a874,x102262)),a330))),f249(x102262)))))),f333(f333(f9(x102262,f890(x102262,a874),f890(x102262,a874)),f333(f333(f10(f890(a874,a874),f890(f890(x102262,a874),f890(x102262,a874)),x102262),f10(a874,a874,x102262)),f333(f333(f10(a874,f890(a874,a874),x102262),a331),f333(f333(f9(x102262,f890(x102262,a874),a874),f335(x102262)),x102263)))),f333(f333(f9(x102262,f890(x102262,a874),a874),f335(x102262)),x102261))))))),f333(f333(f249(x102262),f14(x102262,f248(x102262),x102263)),f14(x102262,f248(x102262),x102261))) % 191.49/191.42 [7186]~P123(x71863)+E(x71861,x71862)+~E(f333(f333(f264(x71863),x71861),x71864),f333(f333(f264(x71863),x71862),x71864))+~P4(f333(f333(f250(x71863),f2(x71863)),x71862))+~P4(f333(f333(f250(x71863),f2(x71863)),x71861))+~P4(f333(f333(f251(a880),f2(a880)),x71864)) % 191.49/191.42 [7449]~P109(x74492)+E(x74491,f194(f890(x74492,a874)))+~P4(f333(f63(x74492),x74491))+~P4(f333(f333(f335(x74492),x74494),x74491))+P4(f333(f333(f251(x74492),x74493),x74494))+~P4(f333(f333(f251(x74492),x74493),f333(f65(x74492,f248(x74492)),x74491))) % 191.49/191.42 [7450]~P102(x74502)+E(x74501,f194(f890(x74502,a874)))+~P4(f333(f63(x74502),x74501))+~P4(f333(f333(f335(x74502),x74504),x74501))+P4(f333(f333(f250(x74502),x74503),x74504))+~P4(f333(f333(f250(x74502),x74503),f333(f65(x74502,f106(x74502)),x74501))) % 191.49/191.42 [7451]~P109(x74512)+E(x74511,f194(f890(x74512,a874)))+~P4(f333(f63(x74512),x74511))+~P4(f333(f333(f335(x74512),x74514),x74511))+P4(f333(f333(f250(x74512),x74513),x74514))+~P4(f333(f333(f250(x74512),x74513),f333(f65(x74512,f248(x74512)),x74511))) % 191.49/191.42 [7351]E(x73511,f2(a1))+E(f333(f333(f40(a1),x73512),x73511),x73513)+~P4(f333(f333(f250(a1),x73514),f2(a1)))+~E(x73512,f333(f333(f81(a1),f333(f333(f82(a1),x73511),x73513)),x73514))+P4(f333(f333(f251(a1),f2(a1)),x73511))+~P4(f333(f333(f251(a1),x73511),x73514)) % 191.49/191.42 [7365]E(f46(a1,x73652,x73651),x73653)+E(x73651,f2(a1))+~P4(f333(f333(f250(a1),x73653),f2(a1)))+~E(x73652,f333(f333(f81(a1),f333(f333(f82(a1),x73651),x73654)),x73653))+P4(f333(f333(f251(a1),f2(a1)),x73651))+~P4(f333(f333(f251(a1),x73651),x73653)) % 191.49/191.42 [7488]E(x74881,f2(a1))+E(f333(f333(f40(a1),x74882),x74881),x74883)+~E(x74882,f333(f333(f81(a1),f333(f333(f82(a1),x74881),x74883)),x74884))+~P4(f333(f333(f251(a1),f2(a1)),x74881))+~P4(f333(f333(f250(a1),f2(a1)),x74884))+~P4(f333(f333(f251(a1),x74884),x74881)) % 191.49/191.42 [7510]E(f46(a1,x75102,x75101),x75103)+E(x75101,f2(a1))+~E(x75102,f333(f333(f81(a1),f333(f333(f82(a1),x75101),x75104)),x75103))+~P4(f333(f333(f251(a1),f2(a1)),x75101))+~P4(f333(f333(f250(a1),f2(a1)),x75103))+~P4(f333(f333(f251(a1),x75103),x75101)) % 191.49/191.42 [7647]~P109(x76472)+E(x76471,f194(f890(x76472,a874)))+~P4(f333(f63(x76472),x76471))+~P4(f333(f333(f251(x76472),x76474),x76473))+~P4(f333(f333(f335(x76472),x76474),x76471))+P4(f333(f333(f251(x76472),f333(f65(x76472,f248(x76472)),x76471)),x76473)) % 191.49/191.42 [7648]~P109(x76482)+E(x76481,f194(f890(x76482,a874)))+~P4(f333(f63(x76482),x76481))+~P4(f333(f333(f250(x76482),x76484),x76483))+~P4(f333(f333(f335(x76482),x76484),x76481))+P4(f333(f333(f250(x76482),f333(f65(x76482,f248(x76482)),x76481)),x76483)) % 191.49/191.42 [8220]~P4(f333(f333(f250(a1),x82204),f2(a1)))+~E(x82201,f333(f333(f81(a1),f333(f333(f82(a1),x82202),x82203)),x82204))+~P4(f333(f333(f250(a1),f2(a1)),x82204))+~P4(f333(f333(f251(a1),x82204),x82202))+~P4(f333(f333(f251(a1),x82202),x82204))+P4(f333(f50(x82201,x82202),f333(f333(f263(a1,a1),x82203),x82204))) % 191.49/191.42 [9155]~P62(x91553)+~P62(x91554)+E(x91551,x91552)+~E(f333(f195(f881(x91553)),x91552),f333(f195(f881(x91554)),f57(x91554)))+~E(f333(f195(f881(x91553)),x91551),f333(f195(f881(x91554)),f57(x91554)))+~E(f333(f74(f884(x91553),x91553,x91554,f246(x91553)),f333(f178(x91554,x91553),f333(f333(f182(x91554,x91553),f57(x91554)),x91551))),f333(f74(f884(x91553),x91553,x91554,f246(x91553)),f333(f178(x91554,x91553),f333(f333(f182(x91554,x91553),f57(x91554)),x91552)))) % 191.49/191.42 [8382]~P110(x83821)+P4(f333(f333(f251(f890(x83821,a874)),f304(x83821,x83822,x83823)),f304(x83821,x83824,x83825)))+~P4(f333(f333(f251(x83821),x83823),x83825))+~P4(f333(f333(f250(x83821),x83824),x83822))+~P4(f333(f333(f250(x83821),x83824),x83825))+~P4(f333(f333(f250(x83821),x83823),x83825)) % 191.49/191.42 [8383]~P110(x83831)+P4(f333(f333(f251(f890(x83831,a874)),f304(x83831,x83832,x83833)),f304(x83831,x83834,x83835)))+~P4(f333(f333(f251(x83831),x83834),x83832))+~P4(f333(f333(f250(x83831),x83833),x83835))+~P4(f333(f333(f250(x83831),x83834),x83835))+~P4(f333(f333(f250(x83831),x83834),x83832)) % 191.49/191.42 [9218]P58(x92182,x92183,x92184,x92181)+E(x92181,f194(f890(x92182,a874)))+~P4(f333(f63(x92182),x92184))+~P4(f333(f63(x92182),x92181))+~P4(f333(f333(x92183,f707(x92181,x92184,x92183,x92182)),x92185))+~P4(f333(f333(f335(x92182),x92185),x92181)) % 191.49/191.42 [9375]~E(x93753,x93755)+~P69(x93751)+~P76(x93751)+~P42(x93753)+E(f333(f333(f8(a1,x93751),x93752),x93753),f333(f333(f8(a1,x93751),x93754),x93755))+P4(f333(f333(f250(a1),f2(a1)),f698(x93752,x93754,x93753,x93755,x93751))) % 191.49/191.42 [9376]~E(x93763,x93765)+~P69(x93761)+~P76(x93761)+~P42(x93763)+E(f333(f333(f11(a1,x93761),x93762),x93763),f333(f333(f11(a1,x93761),x93764),x93765))+P4(f333(f333(f250(a1),f2(a1)),f691(x93762,x93764,x93763,x93765,x93761))) % 191.49/191.42 [9549]~E(x95495,x95493)+~P69(x95491)+~P76(x95491)+~P42(x95495)+~E(f333(x95492,f698(x95494,x95492,x95495,x95493,x95491)),f333(x95494,f698(x95494,x95492,x95495,x95493,x95491)))+E(f333(f333(f8(a1,x95491),x95492),x95493),f333(f333(f8(a1,x95491),x95494),x95495)) % 191.49/191.42 [9550]~E(x95505,x95503)+~P69(x95501)+~P76(x95501)+~P42(x95505)+~E(f333(x95502,f691(x95504,x95502,x95505,x95503,x95501)),f333(x95504,f691(x95504,x95502,x95505,x95503,x95501)))+E(f333(f333(f11(a1,x95501),x95502),x95503),f333(f333(f11(a1,x95501),x95504),x95505)) % 191.49/191.42 [9650]~P81(x96503)+E(f333(x96501,x96502),f2(x96503))+~E(f333(f333(f8(x96504,x96503),x96501),x96505),f2(x96503))+~P4(f333(f63(x96504),x96505))+P4(f333(f333(f335(x96504),f520(x96502,x96501,x96505,x96504,x96503)),x96505))+~P4(f333(f333(f335(x96504),x96502),x96505)) % 191.49/191.42 [9798]~P81(x97983)+E(f333(x97981,x97982),f2(x97983))+~E(f333(f333(f8(x97984,x97983),x97981),x97985),f2(x97983))+~P4(f333(f63(x97984),x97985))+~P4(f333(f333(f335(x97984),x97982),x97985))+~P4(f333(f333(f250(x97983),f2(x97983)),f333(x97981,f520(x97982,x97981,x97985,x97984,x97983)))) % 191.49/191.42 [8300]~P129(x83001)+~P4(f333(f333(f250(x83001),f2(x83001)),x83003))+~P4(f333(f333(f251(x83001),x83003),x83005))+~P4(f333(f333(f251(x83001),x83002),x83004))+~P4(f333(f333(f251(x83001),f2(x83001)),x83004))+P4(f333(f333(f251(x83001),f333(f333(f82(x83001),x83002),x83003)),f333(f333(f82(x83001),x83004),x83005))) % 191.49/191.42 [8301]~P129(x83011)+~P4(f333(f333(f250(x83011),f2(x83011)),x83013))+~P4(f333(f333(f250(x83011),f2(x83011)),x83012))+~P4(f333(f333(f251(x83011),x83013),x83015))+~P4(f333(f333(f251(x83011),x83012),x83014))+P4(f333(f333(f251(x83011),f333(f333(f82(x83011),x83012),x83013)),f333(f333(f82(x83011),x83014),x83015))) % 191.49/191.42 [8302]~P129(x83021)+~P4(f333(f333(f250(x83021),x83022),x83024))+~P4(f333(f333(f250(x83021),f2(x83021)),x83023))+~P4(f333(f333(f251(x83021),x83023),x83025))+~P4(f333(f333(f251(x83021),f2(x83021)),x83022))+P4(f333(f333(f251(x83021),f333(f333(f82(x83021),x83022),x83023)),f333(f333(f82(x83021),x83024),x83025))) % 191.49/191.42 [8303]~P129(x83031)+~P4(f333(f333(f250(x83031),x83033),x83035))+~P4(f333(f333(f250(x83031),f2(x83031)),x83032))+~P4(f333(f333(f251(x83031),x83032),x83034))+~P4(f333(f333(f251(x83031),f2(x83031)),x83033))+P4(f333(f333(f251(x83031),f333(f333(f82(x83031),x83032),x83033)),f333(f333(f82(x83031),x83034),x83035))) % 191.49/191.42 [8304]~P66(x83041)+~P4(f333(f333(f250(x83041),x83042),x83044))+~P4(f333(f333(f251(x83041),x83045),x83043))+~P4(f333(f333(f251(x83041),f2(x83041)),x83045))+~P4(f333(f333(f251(x83041),f2(x83041)),x83042))+P4(f333(f333(f251(x83041),f333(f333(f291(x83041),x83042),x83043)),f333(f333(f291(x83041),x83044),x83045))) % 191.49/191.42 [8305]~P66(x83051)+~P4(f333(f333(f250(x83051),x83055),x83053))+~P4(f333(f333(f250(x83051),f2(x83051)),x83052))+~P4(f333(f333(f251(x83051),x83052),x83054))+~P4(f333(f333(f251(x83051),f2(x83051)),x83055))+P4(f333(f333(f251(x83051),f333(f333(f291(x83051),x83052),x83053)),f333(f333(f291(x83051),x83054),x83055))) % 191.49/191.42 [8306]~P135(x83061)+~P4(f333(f333(f250(x83061),x83063),x83065))+~P4(f333(f333(f250(x83061),x83062),x83064))+~P4(f333(f333(f250(x83061),f2(x83061)),x83063))+~P4(f333(f333(f250(x83061),f2(x83061)),x83064))+P4(f333(f333(f250(x83061),f333(f333(f82(x83061),x83062),x83063)),f333(f333(f82(x83061),x83064),x83065))) % 191.49/191.42 [8307]~P135(x83071)+~P4(f333(f333(f250(x83071),x83073),x83075))+~P4(f333(f333(f250(x83071),x83072),x83074))+~P4(f333(f333(f250(x83071),f2(x83071)),x83073))+~P4(f333(f333(f250(x83071),f2(x83071)),x83072))+P4(f333(f333(f250(x83071),f333(f333(f82(x83071),x83072),x83073)),f333(f333(f82(x83071),x83074),x83075))) % 191.49/191.42 [8308]~P66(x83081)+~P4(f333(f333(f251(x83081),f2(x83081)),x83085))+~P4(f333(f333(f250(x83081),x83085),x83083))+~P4(f333(f333(f250(x83081),x83082),x83084))+~P4(f333(f333(f250(x83081),f2(x83081)),x83082))+P4(f333(f333(f250(x83081),f333(f333(f291(x83081),x83082),x83083)),f333(f333(f291(x83081),x83084),x83085))) % 191.49/191.42 [9688]~P69(x96885)+~P88(x96885)+E(x96881,f194(f890(x96882,a874)))+~P4(f333(f63(x96882),x96881))+P4(f333(f333(f335(x96882),f850(x96883,x96884,x96881,x96882,x96885)),x96881))+P4(f333(f333(f251(x96885),f333(f333(f8(x96882,x96885),x96884),x96881)),f333(f333(f8(x96882,x96885),x96883),x96881))) % 191.49/191.42 [9817]~P69(x98171)+~P86(x98171)+~P4(f333(f63(x98172),x98175))+~P4(f333(f333(f250(x98171),f2(x98171)),f333(x98173,f358(x98173,x98174,x98175,x98172,x98171))))+P4(f333(f333(f250(x98171),f333(f333(f8(x98172,x98171),x98173),x98174)),f333(f333(f8(x98172,x98171),x98173),x98175)))+~P4(f333(f333(f250(f890(x98172,a874)),x98174),x98175)) % 191.49/191.42 [9964]~P69(x99643)+~P88(x99643)+E(x99641,f194(f890(x99642,a874)))+~P4(f333(f63(x99642),x99641))+~P4(f333(f333(f251(x99643),f333(x99644,f850(x99645,x99644,x99641,x99642,x99643))),f333(x99645,f850(x99645,x99644,x99641,x99642,x99643))))+P4(f333(f333(f251(x99643),f333(f333(f8(x99642,x99643),x99644),x99641)),f333(f333(f8(x99642,x99643),x99645),x99641))) % 191.49/191.42 [7046]~P20(x70462,x70465,x70464)+E(x70461,f194(f890(x70462,a874)))+E(x70463,f194(f890(x70462,a874)))+~P4(f333(f63(x70462),x70461))+~P4(f333(f63(x70462),x70463))+E(f333(x70464,f333(f333(f115(f890(x70462,a874)),x70463),x70461)),f333(f333(x70465,f333(x70464,x70463)),f333(x70464,x70461))) % 191.49/191.42 [7613]~P147(x76131,x76134,x76133)+P4(f333(x76131,x76132))+~P4(f333(f333(f251(a1),x76134),f2(a1)))+~P4(f333(f333(f250(a1),x76135),f2(a1)))+~E(x76133,f333(f333(f81(a1),f333(f333(f82(a1),x76134),x76132)),x76135))+~P4(f333(f333(f251(a1),x76134),x76135)) % 191.49/191.42 [7614]~P146(x76141,x76144,x76143)+P4(f333(x76141,x76142))+~P4(f333(f333(f251(a1),x76144),f2(a1)))+~P4(f333(f333(f250(a1),x76142),f2(a1)))+~E(x76143,f333(f333(f81(a1),f333(f333(f82(a1),x76144),x76145)),x76142))+~P4(f333(f333(f251(a1),x76144),x76142)) % 191.49/191.42 [7656]~P147(x76561,x76564,x76563)+P4(f333(x76561,x76562))+~E(x76563,f333(f333(f81(a1),f333(f333(f82(a1),x76564),x76562)),x76565))+~P4(f333(f333(f251(a1),f2(a1)),x76564))+~P4(f333(f333(f250(a1),f2(a1)),x76565))+~P4(f333(f333(f251(a1),x76565),x76564)) % 191.49/191.42 [7657]~P146(x76571,x76574,x76573)+P4(f333(x76571,x76572))+~E(x76573,f333(f333(f81(a1),f333(f333(f82(a1),x76574),x76575)),x76572))+~P4(f333(f333(f251(a1),f2(a1)),x76574))+~P4(f333(f333(f250(a1),f2(a1)),x76572))+~P4(f333(f333(f251(a1),x76572),x76574)) % 191.49/191.42 [8594]P4(f333(f333(x85941,x85942),x85943))+~P4(f333(f333(x85941,f333(f333(f40(a1),x85944),x85945)),f46(a1,x85944,x85945)))+~P4(f333(f333(f251(a1),x85945),f2(a1)))+~P4(f333(f333(f250(a1),x85943),f2(a1)))+~E(x85944,f333(f333(f81(a1),f333(f333(f82(a1),x85945),x85942)),x85943))+~P4(f333(f333(f251(a1),x85945),x85943)) % 191.49/191.42 [8603]P4(f333(f333(x86031,x86032),x86033))+~P4(f333(f333(x86031,f333(f333(f40(a1),x86034),x86035)),f46(a1,x86034,x86035)))+~E(x86034,f333(f333(f81(a1),f333(f333(f82(a1),x86035),x86032)),x86033))+~P4(f333(f333(f251(a1),f2(a1)),x86035))+~P4(f333(f333(f250(a1),f2(a1)),x86033))+~P4(f333(f333(f251(a1),x86033),x86035)) % 191.49/191.42 [8834]E(x88341,x88342)+~P55(x88343,x88345,x88344)+~P4(f333(f333(f335(x88343),x88342),x88345))+~P4(f333(f333(f335(x88343),x88341),x88345))+P4(f333(f333(f335(f889(x88343,x88343)),f333(f333(f263(x88343,x88343),x88341),x88342)),x88344))+P4(f333(f333(f335(f889(x88343,x88343)),f333(f333(f263(x88343,x88343),x88342),x88341)),x88344)) % 191.49/191.42 [9715]~P69(x97155)+~P86(x97155)+~P4(f333(f63(x97151),x97154))+P4(f333(f333(f250(x97155),f333(f333(f8(x97151,x97155),x97152),x97153)),f333(f333(f8(x97151,x97155),x97152),x97154)))+~P4(f333(f333(f250(f890(x97151,a874)),x97153),x97154))+P4(f333(f333(f335(x97151),f358(x97152,x97153,x97154,x97151,x97155)),f333(f333(f3(f890(x97151,a874)),x97154),x97153))) % 191.49/191.42 [9824]E(x98241,f194(f890(x98242,a874)))+~P4(f333(f63(x98242),x98243))+~P4(f333(f63(x98242),x98241))+P4(f333(f333(f335(f889(f890(x98242,a874),f890(x98242,a874))),f333(f333(f263(f890(x98242,a874),f890(x98242,a874)),x98243),x98241)),f325(x98242,x98244)))+~P4(f333(f333(f335(x98242),x98245),x98241))+~P4(f333(f333(f335(f889(x98242,x98242)),f333(f333(f263(x98242,x98242),f709(x98244,x98241,x98243,x98242)),x98245)),x98244)) % 191.49/191.42 [9825]E(x98251,f194(f890(x98252,a874)))+~P4(f333(f63(x98252),x98253))+~P4(f333(f63(x98252),x98251))+P4(f333(f333(f335(f889(f890(x98252,a874),f890(x98252,a874))),f333(f333(f263(f890(x98252,a874),f890(x98252,a874)),x98253),x98251)),f325(x98252,x98254)))+~P4(f333(f333(f335(x98252),x98255),x98251))+~P4(f333(f333(f335(f889(x98252,x98252)),f333(f333(f263(x98252,x98252),f758(x98254,x98251,x98253,x98252)),x98255)),x98254)) % 191.49/191.42 [9969]~P81(x99691)+~E(f333(f333(f8(x99695,x99691),x99692),x99696),x99694)+~P4(f333(f63(x99695),x99696))+P4(f333(f333(f335(x99695),f521(x99693,x99694,x99692,x99696,x99695,x99691)),x99696))+P4(f333(f333(f250(x99691),f333(x99692,x99693)),x99694))+~P4(f333(f333(f335(x99695),x99693),x99696)) % 191.49/191.42 [10015]~P81(x100151)+~E(f333(f333(f8(x100155,x100151),x100152),x100156),x100154)+~P4(f333(f63(x100155),x100156))+~P4(f333(f333(f335(x100155),x100153),x100156))+~P4(f333(f333(f250(x100151),f2(x100151)),f333(x100152,f521(x100153,x100154,x100152,x100156,x100155,x100151))))+P4(f333(f333(f250(x100151),f333(x100152,x100153)),x100154)) % 191.49/191.42 [10155]~E(x101555,x101558)+~E(x101554,x101557)+~P69(x101552)+~P111(x101551)+E(f333(f333(f8(x101551,x101552),x101553),f333(f303(x101551,x101554),x101555)),f333(f333(f8(x101551,x101552),x101556),f333(f303(x101551,x101557),x101558)))+P4(f333(f333(f250(x101551),x101554),f462(x101553,x101556,x101555,x101558,x101554,x101557,x101551,x101552))) % 191.49/191.42 [10178]~E(x101787,x101784)+~E(x101788,x101785)+~P69(x101782)+~P111(x101781)+~E(f333(x101783,f462(x101786,x101783,x101788,x101785,x101787,x101784,x101781,x101782)),f333(x101786,f462(x101786,x101783,x101788,x101785,x101787,x101784,x101781,x101782)))+E(f333(f333(f8(x101781,x101782),x101783),f333(f303(x101781,x101784),x101785)),f333(f333(f8(x101781,x101782),x101786),f333(f303(x101781,x101787),x101788))) % 191.49/191.42 [10184]~E(x101844,x101847)+~E(x101845,x101848)+~P69(x101842)+~P111(x101841)+E(f333(f333(f8(x101841,x101842),x101843),f333(f303(x101841,x101844),x101845)),f333(f333(f8(x101841,x101842),x101846),f333(f303(x101841,x101847),x101848)))+P4(f333(f333(f251(x101841),f462(x101843,x101846,x101845,x101848,x101844,x101847,x101841,x101842)),x101845)) % 191.49/191.42 [9830]~P12(x98305,x98309,x98306)+~P12(x98301,x983010,x98303)+~P16(x98301,x98305,f890(x98302,a874),x98303,x98306,x98308)+~P4(f333(f333(f335(x98305),x98307),x98309))+~P4(f333(f333(f335(x98301),x98304),x983010))+E(f333(f333(f44(x98301,f890(x98302,a874)),f333(f287(x98301,x98301,x98303),f333(f333(f311(x98301),x98304),f194(f890(x98301,a874))))),f333(f333(f10(f890(x98305,f890(x98302,a874)),f890(x98302,a874),x98301),f333(f44(x98305,f890(x98302,a874)),f333(f287(x98305,x98305,x98306),f333(f333(f311(x98305),x98307),f194(f890(x98305,a874)))))),x98308)),f333(f333(x98308,x98304),x98307)) % 191.49/191.42 [5606]~P109(x56063)+~P17(x56063,x56062)+~P17(x56063,x56061)+E(x56061,x56062)+~E(f333(f173(x56063),x56061),f333(f173(x56063),x56062))+~P4(f333(f138(x56063),x56062))+~P4(f333(f138(x56063),x56061)) % 191.49/191.42 [4948]~P127(x49482)+~P128(x49482)+~P142(x49482)+~P113(x49482)+~E(x49483,f2(x49482))+E(x49481,f2(a880))+E(f333(f333(f264(x49482),x49483),x49481),f2(x49482)) % 191.49/191.42 [9085]E(x90851,f2(a880))+~E(x90852,f333(f333(f81(a880),f333(f333(f82(a880),f333(f262(a880,a880),x90853)),x90851)),f333(f271(a880,a880),x90853)))+P4(f333(f49(x90852,x90851),x90853))+~P4(f333(f333(f250(a880),f333(f271(a880,a880),x90853)),f2(a880)))+~P4(f333(f333(f250(a880),f2(a880)),f333(f271(a880,a880),x90853)))+~P4(f333(f333(f251(a880),x90851),f333(f271(a880,a880),x90853)))+~P4(f333(f333(f251(a880),f333(f271(a880,a880),x90853)),x90851)) % 191.49/191.42 [9100]~E(f333(f262(a880,a880),x91003),f2(a880))+~E(x91001,f333(f333(f81(a880),f333(f333(f82(a880),f333(f262(a880,a880),x91003)),x91002)),f333(f271(a880,a880),x91003)))+P4(f333(f49(x91001,x91002),x91003))+~P4(f333(f333(f250(a880),f333(f271(a880,a880),x91003)),f2(a880)))+~P4(f333(f333(f250(a880),f2(a880)),f333(f271(a880,a880),x91003)))+~P4(f333(f333(f251(a880),x91002),f333(f271(a880,a880),x91003)))+~P4(f333(f333(f251(a880),f333(f271(a880,a880),x91003)),x91002)) % 191.49/191.42 [7961]~P73(x79612)+E(x79611,f194(f890(x79612,a874)))+E(x79613,f194(f890(x79612,a874)))+~P4(f333(f63(x79612),x79611))+~P4(f333(f63(x79612),x79613))+~E(f333(f333(f106(f890(x79612,a874)),x79613),x79611),f194(f890(x79612,a874)))+E(f333(f333(f82(x79612),f333(f65(x79612,f82(x79612)),x79613)),f333(f65(x79612,f82(x79612)),x79611)),f333(f65(x79612,f82(x79612)),f333(f333(f115(f890(x79612,a874)),x79613),x79611))) % 191.49/191.42 [7752]E(x77521,f2(a1))+E(f333(f333(f40(a1),x77522),x77521),x77523)+~P4(f333(f333(f250(a1),x77524),f2(a1)))+~E(x77522,f333(f333(f81(a1),f333(f333(f82(a1),x77521),x77523)),x77524))+~P4(f333(f333(f250(a1),f2(a1)),x77524))+~P4(f333(f333(f251(a1),x77524),x77521))+~P4(f333(f333(f251(a1),x77521),x77524)) % 191.49/191.42 [7759]E(f46(a1,x77592,x77591),x77593)+E(x77591,f2(a1))+~P4(f333(f333(f250(a1),x77593),f2(a1)))+~E(x77592,f333(f333(f81(a1),f333(f333(f82(a1),x77591),x77594)),x77593))+~P4(f333(f333(f250(a1),f2(a1)),x77593))+~P4(f333(f333(f251(a1),x77593),x77591))+~P4(f333(f333(f251(a1),x77591),x77593)) % 191.49/191.42 [7664]~P21(x76642,x76645,x76644)+E(x76641,f194(f890(x76642,a874)))+E(x76643,f194(f890(x76642,a874)))+~P4(f333(f63(x76642),x76641))+~P4(f333(f63(x76642),x76643))+~E(f333(f333(f106(f890(x76642,a874)),x76643),x76641),f194(f890(x76642,a874)))+E(f333(x76644,f333(f333(f115(f890(x76642,a874)),x76643),x76641)),f333(f333(x76645,f333(x76644,x76643)),f333(x76644,x76641))) % 191.49/191.42 [9342]~P28(x93423,x93421,x93425,x93424)+~P28(x93421,x93423,x93426,x93422)+E(f333(f39(x93421),x93422),f333(f39(x93423),x93424))+~P4(f333(f63(x93423),x93424))+~P4(f333(f63(x93421),x93422))+~P4(f333(f333(f250(f890(x93423,a874)),f333(f312(x93421,x93423,x93426),x93422)),x93424))+~P4(f333(f333(f250(f890(x93421,a874)),f333(f312(x93423,x93421,x93425),x93424)),x93422)) % 191.49/191.42 [9291]~P4(f333(f333(f251(a1),f333(f333(f81(a1),f333(f333(f82(a1),x92915),x92911)),x92916)),f2(a1)))+~E(f333(f333(f81(a1),f333(f333(f82(a1),x92913),x92912)),x92914),f333(f333(f81(a1),f333(f333(f82(a1),x92915),x92911)),x92916))+~P4(f333(f333(f251(a1),f2(a1)),x92915))+~P4(f333(f333(f250(a1),f2(a1)),x92916))+~P4(f333(f333(f251(a1),x92914),x92913))+~P4(f333(f333(f250(a1),x92915),x92913))+P4(f333(f333(f250(a1),x92911),x92912)) % 191.49/191.42 [9045]~E(f333(f333(f81(a1),f333(f333(f82(a1),x90453),x90451)),x90454),f333(f333(f81(a1),f333(f333(f82(a1),x90455),x90452)),x90456))+~P4(f333(f333(f251(a1),f2(a1)),x90455))+~P4(f333(f333(f250(a1),f2(a1)),x90454))+~P4(f333(f333(f251(a1),x90456),x90455))+~P4(f333(f333(f250(a1),x90455),x90453))+P4(f333(f333(f250(a1),x90451),x90452))+~P4(f333(f333(f250(a1),f2(a1)),f333(f333(f81(a1),f333(f333(f82(a1),x90455),x90452)),x90456))) % 191.49/191.42 [9224]~P132(x92241)+~E(f333(f333(f81(x92241),x92242),x92244),f79(x92241))+~P4(f333(f333(f250(x92241),f2(x92241)),x92244))+~P4(f333(f333(f250(x92241),f2(x92241)),x92242))+~P4(f333(f333(f251(x92241),x92245),x92246))+~P4(f333(f333(f251(x92241),x92243),x92246))+P4(f333(f333(f251(x92241),f333(f333(f81(x92241),f333(f333(f82(x92241),x92242),x92243)),f333(f333(f82(x92241),x92244),x92245))),x92246)) % 191.49/191.42 [9225]~P131(x92251)+~E(f333(f333(f81(x92251),x92252),x92254),f79(x92251))+~P4(f333(f333(f250(x92251),x92255),x92256))+~P4(f333(f333(f250(x92251),x92253),x92256))+~P4(f333(f333(f250(x92251),f2(x92251)),x92254))+~P4(f333(f333(f250(x92251),f2(x92251)),x92252))+P4(f333(f333(f250(x92251),f333(f333(f81(x92251),f333(f333(f82(x92251),x92252),x92253)),f333(f333(f82(x92251),x92254),x92255))),x92256)) % 191.49/191.42 [10057]~P12(x100577,x100576,x100575)+E(x100571,x100572)+~P15(x100577,f890(x100574,a874),x100575,x100573)+E(f333(x100573,f561(x100571,x100572,x100573,x100574,x100575,x100576,x100577)),f333(x100573,f562(x100571,x100572,x100573,x100574,x100575,x100576,x100577)))+~E(f333(f333(f44(x100577,f890(x100574,a874)),x100571),x100573),f333(f333(f44(x100577,f890(x100574,a874)),x100572),x100573))+~P4(f333(f333(f335(f890(x100577,a874)),x100572),f333(f333(f62(x100577),x100576),x100575)))+~P4(f333(f333(f335(f890(x100577,a874)),x100571),f333(f333(f62(x100577),x100576),x100575))) % 191.49/191.42 [10099]~P12(x100993,x100997,x100996)+E(x100991,x100992)+~P15(x100993,f890(x100995,a874),x100996,x100994)+~E(f333(f333(f44(x100993,f890(x100995,a874)),x100991),x100994),f333(f333(f44(x100993,f890(x100995,a874)),x100992),x100994))+P4(f333(f333(f335(x100993),f562(x100991,x100992,x100994,x100995,x100996,x100997,x100993)),x100997))+~P4(f333(f333(f335(f890(x100993,a874)),x100992),f333(f333(f62(x100993),x100997),x100996)))+~P4(f333(f333(f335(f890(x100993,a874)),x100991),f333(f333(f62(x100993),x100997),x100996))) % 191.49/191.42 [10100]~P12(x101003,x101007,x101006)+E(x101001,x101002)+~P15(x101003,f890(x101005,a874),x101006,x101004)+~E(f333(f333(f44(x101003,f890(x101005,a874)),x101001),x101004),f333(f333(f44(x101003,f890(x101005,a874)),x101002),x101004))+P4(f333(f333(f335(x101003),f561(x101001,x101002,x101004,x101005,x101006,x101007,x101003)),x101007))+~P4(f333(f333(f335(f890(x101003,a874)),x101002),f333(f333(f62(x101003),x101007),x101006)))+~P4(f333(f333(f335(f890(x101003,a874)),x101001),f333(f333(f62(x101003),x101007),x101006))) % 191.49/191.42 [10204]E(x102041,x102042)+~P12(x102043,x102046,x102047)+~P15(x102043,f890(x102044,a874),x102047,x102045)+~E(f333(f333(f44(x102043,f890(x102044,a874)),x102041),x102045),f333(f333(f44(x102043,f890(x102044,a874)),x102042),x102045))+~P4(f333(f333(f335(f889(x102043,x102043)),f333(f333(f263(x102043,x102043),f562(x102041,x102042,x102045,x102044,x102047,x102046,x102043)),f561(x102041,x102042,x102045,x102044,x102047,x102046,x102043))),x102047))+~P4(f333(f333(f335(f890(x102043,a874)),x102042),f333(f333(f62(x102043),x102046),x102047)))+~P4(f333(f333(f335(f890(x102043,a874)),x102041),f333(f333(f62(x102043),x102046),x102047))) % 191.49/191.42 [9044]~P12(x90441,x90447,x90444)+~E(x90445,x90446)+~P4(f333(f333(f335(x90441),x90443),x90446))+~P4(f333(f333(f335(x90441),x90442),x90445))+~P4(f333(f333(f335(f890(x90441,a874)),x90446),f333(f333(f62(x90441),x90447),x90444)))+~P4(f333(f333(f335(f890(x90441,a874)),x90445),f333(f333(f62(x90441),x90447),x90444)))+P4(f333(f333(f335(f889(x90441,x90441)),f333(f333(f263(x90441,x90441),x90442),x90443)),x90444)) % 191.49/191.42 [9183]E(x91831,x91832)+~P12(x91833,x91834,x91835)+~P4(f333(f333(f335(x91833),x91836),x91832))+~P4(f333(f333(f335(x91833),x91837),x91831))+~P4(f333(f333(f335(f890(x91833,a874)),x91832),f333(f333(f62(x91833),x91834),x91835)))+~P4(f333(f333(f335(f890(x91833,a874)),x91831),f333(f333(f62(x91833),x91834),x91835)))+~P4(f333(f333(f335(f889(x91833,x91833)),f333(f333(f263(x91833,x91833),x91837),x91836)),x91835)) % 191.49/191.42 [10230]~P12(x102309,x102308,x102307)+~P12(x102301,x1023011,x1023010)+~P16(x102301,x102309,f890(x102306,a874),x1023010,x102307,x102305)+P4(f333(f333(f335(x102301),f565(x102302,x102303,x102304,x102305,x102306,x102307,x102308,x102309,x1023010,x1023011,x102301)),x1023011))+~P4(f333(f333(f335(f890(x102309,a874)),x102303),f333(f333(f62(x102309),x102308),x102307)))+~P4(f333(f333(f335(f890(x102301,a874)),x102304),f333(f333(f62(x102301),x1023011),x1023010)))+P4(f333(f333(f335(f890(x102306,a874)),f333(f333(f44(x102301,f890(x102306,a874)),x102304),f333(f333(f10(f890(x102309,f890(x102306,a874)),f890(x102306,a874),x102301),f333(f44(x102309,f890(x102306,a874)),x102303)),x102305))),x102302)) % 191.49/191.42 [10231]~P12(x1023111,x1023110,x102319)+~P12(x102311,x102318,x102317)+~P16(x1023111,x102311,f890(x102316,a874),x102319,x102317,x102315)+P4(f333(f333(f335(x102311),f566(x102312,x102313,x102314,x102315,x102316,x102317,x102318,x102311,x102319,x1023110,x1023111)),x102318))+~P4(f333(f333(f335(f890(x1023111,a874)),x102314),f333(f333(f62(x1023111),x1023110),x102319)))+~P4(f333(f333(f335(f890(x102311,a874)),x102313),f333(f333(f62(x102311),x102318),x102317)))+P4(f333(f333(f335(f890(x102316,a874)),f333(f333(f44(x1023111,f890(x102316,a874)),x102314),f333(f333(f10(f890(x102311,f890(x102316,a874)),f890(x102316,a874),x1023111),f333(f44(x102311,f890(x102316,a874)),x102313)),x102315))),x102312)) % 191.49/191.42 [10234]~P12(x102342,x102348,x102349)+~P12(x102344,x1023410,x1023411)+~P16(x102342,x102344,f890(x102341,a874),x102349,x1023411,x102346)+~P4(f333(f333(f335(f890(x102342,a874)),x102343),f333(f333(f62(x102342),x102348),x102349)))+~P4(f333(f333(f335(f890(x102344,a874)),x102345),f333(f333(f62(x102344),x1023410),x1023411)))+~P4(f333(f333(f335(f890(x102341,a874)),f333(f333(x102346,f565(x102347,x102345,x102343,x102346,x102341,x1023411,x1023410,x102344,x102349,x102348,x102342)),f566(x102347,x102345,x102343,x102346,x102341,x1023411,x1023410,x102344,x102349,x102348,x102342))),x102347))+P4(f333(f333(f335(f890(x102341,a874)),f333(f333(f44(x102342,f890(x102341,a874)),x102343),f333(f333(f10(f890(x102344,f890(x102341,a874)),f890(x102341,a874),x102342),f333(f44(x102344,f890(x102341,a874)),x102345)),x102346))),x102347)) % 191.49/191.42 [9072]E(x90721,x90722)+~P109(x90724)+~P28(x90723,x90724,x90725,f333(f333(f115(f890(x90723,a874)),f333(f173(x90723),x90721)),f333(f173(x90723),x90722)))+~E(f333(f173(x90723),x90721),f333(f173(x90723),x90722))+~P17(x90724,f333(f333(f155(x90723,x90724),x90725),x90722))+~P17(x90724,f333(f333(f155(x90723,x90724),x90725),x90721))+~P4(f333(f138(x90724),f333(f333(f155(x90723,x90724),x90725),x90722)))+~P4(f333(f138(x90724),f333(f333(f155(x90723,x90724),x90725),x90721))) % 191.49/191.42 %EqnAxiom % 191.49/191.42 [1]E(x11,x11) % 191.49/191.42 [2]E(x22,x21)+~E(x21,x22) % 191.49/191.42 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 191.49/191.42 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 191.49/191.42 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 191.49/191.42 [6]~E(x61,x62)+E(f105(x61),f105(x62)) % 191.49/191.42 [7]~E(x71,x72)+E(f194(x71),f194(x72)) % 191.49/191.42 [8]~E(x81,x82)+E(f333(x81,x83),f333(x82,x83)) % 191.49/191.42 [9]~E(x91,x92)+E(f333(x93,x91),f333(x93,x92)) % 191.49/191.42 [10]~E(x101,x102)+E(f32(x101),f32(x102)) % 191.49/191.42 [11]~E(x111,x112)+E(f46(x111,x113,x114),f46(x112,x113,x114)) % 191.49/191.42 [12]~E(x121,x122)+E(f46(x123,x121,x124),f46(x123,x122,x124)) % 191.49/191.42 [13]~E(x131,x132)+E(f46(x133,x134,x131),f46(x133,x134,x132)) % 191.49/191.42 [14]~E(x141,x142)+E(f85(x141),f85(x142)) % 191.49/191.42 [15]~E(x151,x152)+E(f79(x151),f79(x152)) % 191.49/191.42 [16]~E(x161,x162)+E(f10(x161,x163,x164),f10(x162,x163,x164)) % 191.49/191.42 [17]~E(x171,x172)+E(f10(x173,x171,x174),f10(x173,x172,x174)) % 191.49/191.42 [18]~E(x181,x182)+E(f10(x183,x184,x181),f10(x183,x184,x182)) % 191.49/191.42 [19]~E(x191,x192)+E(f566(x191,x193,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912),f566(x192,x193,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912)) % 191.49/191.42 [20]~E(x201,x202)+E(f566(x203,x201,x204,x205,x206,x207,x208,x209,x2010,x2011,x2012),f566(x203,x202,x204,x205,x206,x207,x208,x209,x2010,x2011,x2012)) % 191.49/191.42 [21]~E(x211,x212)+E(f566(x213,x214,x211,x215,x216,x217,x218,x219,x2110,x2111,x2112),f566(x213,x214,x212,x215,x216,x217,x218,x219,x2110,x2111,x2112)) % 191.49/191.42 [22]~E(x221,x222)+E(f566(x223,x224,x225,x221,x226,x227,x228,x229,x2210,x2211,x2212),f566(x223,x224,x225,x222,x226,x227,x228,x229,x2210,x2211,x2212)) % 191.49/191.42 [23]~E(x231,x232)+E(f566(x233,x234,x235,x236,x231,x237,x238,x239,x2310,x2311,x2312),f566(x233,x234,x235,x236,x232,x237,x238,x239,x2310,x2311,x2312)) % 191.49/191.42 [24]~E(x241,x242)+E(f566(x243,x244,x245,x246,x247,x241,x248,x249,x2410,x2411,x2412),f566(x243,x244,x245,x246,x247,x242,x248,x249,x2410,x2411,x2412)) % 191.49/191.42 [25]~E(x251,x252)+E(f566(x253,x254,x255,x256,x257,x258,x251,x259,x2510,x2511,x2512),f566(x253,x254,x255,x256,x257,x258,x252,x259,x2510,x2511,x2512)) % 191.49/191.42 [26]~E(x261,x262)+E(f566(x263,x264,x265,x266,x267,x268,x269,x261,x2610,x2611,x2612),f566(x263,x264,x265,x266,x267,x268,x269,x262,x2610,x2611,x2612)) % 191.49/191.42 [27]~E(x271,x272)+E(f566(x273,x274,x275,x276,x277,x278,x279,x2710,x271,x2711,x2712),f566(x273,x274,x275,x276,x277,x278,x279,x2710,x272,x2711,x2712)) % 191.49/191.42 [28]~E(x281,x282)+E(f566(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x281,x2812),f566(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x282,x2812)) % 191.49/191.42 [29]~E(x291,x292)+E(f566(x293,x294,x295,x296,x297,x298,x299,x2910,x2911,x2912,x291),f566(x293,x294,x295,x296,x297,x298,x299,x2910,x2911,x2912,x292)) % 191.49/191.42 [30]~E(x301,x302)+E(f106(x301),f106(x302)) % 191.49/191.42 [31]~E(x311,x312)+E(f248(x311),f248(x312)) % 191.49/191.42 [32]~E(x321,x322)+E(f115(x321),f115(x322)) % 191.49/191.42 [33]~E(x331,x332)+E(f249(x331),f249(x332)) % 191.49/191.42 [34]~E(x341,x342)+E(f107(x341),f107(x342)) % 191.49/191.42 [35]~E(x351,x352)+E(f35(x351),f35(x352)) % 191.49/191.42 [36]~E(x361,x362)+E(f335(x361),f335(x362)) % 191.49/191.42 [37]~E(x371,x372)+E(f81(x371),f81(x372)) % 191.49/191.42 [38]~E(x381,x382)+E(f565(x381,x383,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f565(x382,x383,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 191.49/191.42 [39]~E(x391,x392)+E(f565(x393,x391,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912),f565(x393,x392,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912)) % 191.49/191.42 [40]~E(x401,x402)+E(f565(x403,x404,x401,x405,x406,x407,x408,x409,x4010,x4011,x4012),f565(x403,x404,x402,x405,x406,x407,x408,x409,x4010,x4011,x4012)) % 191.49/191.42 [41]~E(x411,x412)+E(f565(x413,x414,x415,x411,x416,x417,x418,x419,x4110,x4111,x4112),f565(x413,x414,x415,x412,x416,x417,x418,x419,x4110,x4111,x4112)) % 191.49/191.42 [42]~E(x421,x422)+E(f565(x423,x424,x425,x426,x421,x427,x428,x429,x4210,x4211,x4212),f565(x423,x424,x425,x426,x422,x427,x428,x429,x4210,x4211,x4212)) % 191.49/191.42 [43]~E(x431,x432)+E(f565(x433,x434,x435,x436,x437,x431,x438,x439,x4310,x4311,x4312),f565(x433,x434,x435,x436,x437,x432,x438,x439,x4310,x4311,x4312)) % 191.49/191.42 [44]~E(x441,x442)+E(f565(x443,x444,x445,x446,x447,x448,x441,x449,x4410,x4411,x4412),f565(x443,x444,x445,x446,x447,x448,x442,x449,x4410,x4411,x4412)) % 191.49/191.42 [45]~E(x451,x452)+E(f565(x453,x454,x455,x456,x457,x458,x459,x451,x4510,x4511,x4512),f565(x453,x454,x455,x456,x457,x458,x459,x452,x4510,x4511,x4512)) % 191.49/191.42 [46]~E(x461,x462)+E(f565(x463,x464,x465,x466,x467,x468,x469,x4610,x461,x4611,x4612),f565(x463,x464,x465,x466,x467,x468,x469,x4610,x462,x4611,x4612)) % 191.49/191.42 [47]~E(x471,x472)+E(f565(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x471,x4712),f565(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x472,x4712)) % 191.49/191.42 [48]~E(x481,x482)+E(f565(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x4812,x481),f565(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x4812,x482)) % 191.49/191.42 [49]~E(x491,x492)+E(f116(x491),f116(x492)) % 191.49/191.42 [50]~E(x501,x502)+E(f250(x501),f250(x502)) % 191.49/191.42 [51]~E(x511,x512)+E(f890(x511,x513),f890(x512,x513)) % 191.49/191.42 [52]~E(x521,x522)+E(f890(x523,x521),f890(x523,x522)) % 191.49/191.42 [53]~E(x531,x532)+E(f6(x531),f6(x532)) % 191.49/191.42 [54]~E(x541,x542)+E(f251(x541),f251(x542)) % 191.49/191.42 [55]~E(x551,x552)+E(f879(x551),f879(x552)) % 191.49/191.42 [56]~E(x561,x562)+E(f884(x561),f884(x562)) % 191.49/191.42 [57]~E(x571,x572)+E(f881(x571),f881(x572)) % 191.49/191.42 [58]~E(x581,x582)+E(f882(x581),f882(x582)) % 191.49/191.42 [59]~E(x591,x592)+E(f108(x591),f108(x592)) % 191.49/191.42 [60]~E(x601,x602)+E(f702(x601,x603),f702(x602,x603)) % 191.49/191.42 [61]~E(x611,x612)+E(f702(x613,x611),f702(x613,x612)) % 191.49/191.42 [62]~E(x621,x622)+E(f325(x621,x623),f325(x622,x623)) % 191.49/191.42 [63]~E(x631,x632)+E(f325(x633,x631),f325(x633,x632)) % 191.49/191.42 [64]~E(x641,x642)+E(f138(x641),f138(x642)) % 191.49/191.42 [65]~E(x651,x652)+E(f80(x651),f80(x652)) % 191.49/191.42 [66]~E(x661,x662)+E(f82(x661),f82(x662)) % 191.49/191.42 [67]~E(x671,x672)+E(f195(x671),f195(x672)) % 191.49/191.42 [68]~E(x681,x682)+E(f16(x681,x683),f16(x682,x683)) % 191.49/191.42 [69]~E(x691,x692)+E(f16(x693,x691),f16(x693,x692)) % 191.49/191.42 [70]~E(x701,x702)+E(f127(x701),f127(x702)) % 191.49/191.42 [71]~E(x711,x712)+E(f291(x711),f291(x712)) % 191.49/191.42 [72]~E(x721,x722)+E(f821(x721,x723,x724),f821(x722,x723,x724)) % 191.49/191.42 [73]~E(x731,x732)+E(f821(x733,x731,x734),f821(x733,x732,x734)) % 191.49/191.42 [74]~E(x741,x742)+E(f821(x743,x744,x741),f821(x743,x744,x742)) % 191.49/191.42 [75]~E(x751,x752)+E(f92(x751),f92(x752)) % 191.49/191.42 [76]~E(x761,x762)+E(f87(x761),f87(x762)) % 191.49/191.42 [77]~E(x771,x772)+E(f889(x771,x773),f889(x772,x773)) % 191.49/191.42 [78]~E(x781,x782)+E(f889(x783,x781),f889(x783,x782)) % 191.49/191.42 [79]~E(x791,x792)+E(f173(x791),f173(x792)) % 191.49/191.42 [80]~E(x801,x802)+E(f311(x801),f311(x802)) % 191.49/191.42 [81]~E(x811,x812)+E(f888(x811,x813),f888(x812,x813)) % 191.49/191.42 [82]~E(x821,x822)+E(f888(x823,x821),f888(x823,x822)) % 191.49/191.42 [83]~E(x831,x832)+E(f47(x831,x833),f47(x832,x833)) % 191.49/191.42 [84]~E(x841,x842)+E(f47(x843,x841),f47(x843,x842)) % 191.49/191.42 [85]~E(x851,x852)+E(f788(x851,x853),f788(x852,x853)) % 191.49/191.42 [86]~E(x861,x862)+E(f788(x863,x861),f788(x863,x862)) % 191.49/191.42 [87]~E(x871,x872)+E(f148(x871,x873),f148(x872,x873)) % 191.49/191.42 [88]~E(x881,x882)+E(f148(x883,x881),f148(x883,x882)) % 191.49/191.42 [89]~E(x891,x892)+E(f310(x891),f310(x892)) % 191.49/191.42 [90]~E(x901,x902)+E(f62(x901),f62(x902)) % 191.49/191.42 [91]~E(x911,x912)+E(f114(x911),f114(x912)) % 191.49/191.42 [92]~E(x921,x922)+E(f162(x921,x923),f162(x922,x923)) % 191.49/191.42 [93]~E(x931,x932)+E(f162(x933,x931),f162(x933,x932)) % 191.49/191.42 [94]~E(x941,x942)+E(f272(x941,x943,x944),f272(x942,x943,x944)) % 191.49/191.42 [95]~E(x951,x952)+E(f272(x953,x951,x954),f272(x953,x952,x954)) % 191.49/191.42 [96]~E(x961,x962)+E(f272(x963,x964,x961),f272(x963,x964,x962)) % 191.49/191.42 [97]~E(x971,x972)+E(f614(x971,x973,x974,x975),f614(x972,x973,x974,x975)) % 191.49/191.42 [98]~E(x981,x982)+E(f614(x983,x981,x984,x985),f614(x983,x982,x984,x985)) % 191.49/191.42 [99]~E(x991,x992)+E(f614(x993,x994,x991,x995),f614(x993,x994,x992,x995)) % 191.49/191.42 [100]~E(x1001,x1002)+E(f614(x1003,x1004,x1005,x1001),f614(x1003,x1004,x1005,x1002)) % 191.49/191.42 [101]~E(x1011,x1012)+E(f202(x1011,x1013),f202(x1012,x1013)) % 191.49/191.42 [102]~E(x1021,x1022)+E(f202(x1023,x1021),f202(x1023,x1022)) % 191.49/191.42 [103]~E(x1031,x1032)+E(f33(x1031,x1033),f33(x1032,x1033)) % 191.49/191.42 [104]~E(x1041,x1042)+E(f33(x1043,x1041),f33(x1043,x1042)) % 191.49/191.42 [105]~E(x1051,x1052)+E(f91(x1051,x1053),f91(x1052,x1053)) % 191.49/191.42 [106]~E(x1061,x1062)+E(f91(x1063,x1061),f91(x1063,x1062)) % 191.49/191.42 [107]~E(x1071,x1072)+E(f178(x1071,x1073),f178(x1072,x1073)) % 191.49/191.42 [108]~E(x1081,x1082)+E(f178(x1083,x1081),f178(x1083,x1082)) % 191.49/191.42 [109]~E(x1091,x1092)+E(f8(x1091,x1093),f8(x1092,x1093)) % 191.49/191.42 [110]~E(x1101,x1102)+E(f8(x1103,x1101),f8(x1103,x1102)) % 191.49/191.42 [111]~E(x1111,x1112)+E(f66(x1111,x1113,x1114),f66(x1112,x1113,x1114)) % 191.49/191.42 [112]~E(x1121,x1122)+E(f66(x1123,x1121,x1124),f66(x1123,x1122,x1124)) % 191.49/191.42 [113]~E(x1131,x1132)+E(f66(x1133,x1134,x1131),f66(x1133,x1134,x1132)) % 191.49/191.42 [114]~E(x1141,x1142)+E(f175(x1141,x1143,x1144),f175(x1142,x1143,x1144)) % 191.49/191.42 [115]~E(x1151,x1152)+E(f175(x1153,x1151,x1154),f175(x1153,x1152,x1154)) % 191.49/191.42 [116]~E(x1161,x1162)+E(f175(x1163,x1164,x1161),f175(x1163,x1164,x1162)) % 191.49/191.42 [117]~E(x1171,x1172)+E(f39(x1171),f39(x1172)) % 191.49/191.42 [118]~E(x1181,x1182)+E(f242(x1181),f242(x1182)) % 191.49/191.42 [119]~E(x1191,x1192)+E(f152(x1191),f152(x1192)) % 191.49/191.42 [120]~E(x1201,x1202)+E(f14(x1201,x1203,x1204),f14(x1202,x1203,x1204)) % 191.49/191.42 [121]~E(x1211,x1212)+E(f14(x1213,x1211,x1214),f14(x1213,x1212,x1214)) % 191.49/191.42 [122]~E(x1221,x1222)+E(f14(x1223,x1224,x1221),f14(x1223,x1224,x1222)) % 191.49/191.42 [123]~E(x1231,x1232)+E(f155(x1231,x1233),f155(x1232,x1233)) % 191.49/191.42 [124]~E(x1241,x1242)+E(f155(x1243,x1241),f155(x1243,x1242)) % 191.49/191.42 [125]~E(x1251,x1252)+E(f17(x1251,x1253),f17(x1252,x1253)) % 191.49/191.42 [126]~E(x1261,x1262)+E(f17(x1263,x1261),f17(x1263,x1262)) % 191.49/191.42 [127]~E(x1271,x1272)+E(f255(x1271),f255(x1272)) % 191.49/191.42 [128]~E(x1281,x1282)+E(f819(x1281,x1283,x1284),f819(x1282,x1283,x1284)) % 191.49/191.42 [129]~E(x1291,x1292)+E(f819(x1293,x1291,x1294),f819(x1293,x1292,x1294)) % 191.49/191.42 [130]~E(x1301,x1302)+E(f819(x1303,x1304,x1301),f819(x1303,x1304,x1302)) % 191.49/191.42 [131]~E(x1311,x1312)+E(f312(x1311,x1313,x1314),f312(x1312,x1313,x1314)) % 191.49/191.42 [132]~E(x1321,x1322)+E(f312(x1323,x1321,x1324),f312(x1323,x1322,x1324)) % 191.49/191.42 [133]~E(x1331,x1332)+E(f312(x1333,x1334,x1331),f312(x1333,x1334,x1332)) % 191.49/191.42 [134]~E(x1341,x1342)+E(f40(x1341),f40(x1342)) % 191.49/191.42 [135]~E(x1351,x1352)+E(f74(x1351,x1353,x1354,x1355),f74(x1352,x1353,x1354,x1355)) % 191.49/191.42 [136]~E(x1361,x1362)+E(f74(x1363,x1361,x1364,x1365),f74(x1363,x1362,x1364,x1365)) % 191.49/191.42 [137]~E(x1371,x1372)+E(f74(x1373,x1374,x1371,x1375),f74(x1373,x1374,x1372,x1375)) % 191.49/191.42 [138]~E(x1381,x1382)+E(f74(x1383,x1384,x1385,x1381),f74(x1383,x1384,x1385,x1382)) % 191.49/191.42 [139]~E(x1391,x1392)+E(f51(x1391,x1393),f51(x1392,x1393)) % 191.49/191.42 [140]~E(x1401,x1402)+E(f51(x1403,x1401),f51(x1403,x1402)) % 191.49/191.42 [141]~E(x1411,x1412)+E(f264(x1411),f264(x1412)) % 191.49/191.42 [142]~E(x1421,x1422)+E(f12(x1421,x1423),f12(x1422,x1423)) % 191.49/191.42 [143]~E(x1431,x1432)+E(f12(x1433,x1431),f12(x1433,x1432)) % 191.49/191.42 [144]~E(x1441,x1442)+E(f321(x1441,x1443),f321(x1442,x1443)) % 191.49/191.42 [145]~E(x1451,x1452)+E(f321(x1453,x1451),f321(x1453,x1452)) % 191.49/191.42 [146]~E(x1461,x1462)+E(f815(x1461,x1463,x1464),f815(x1462,x1463,x1464)) % 191.49/191.42 [147]~E(x1471,x1472)+E(f815(x1473,x1471,x1474),f815(x1473,x1472,x1474)) % 191.49/191.42 [148]~E(x1481,x1482)+E(f815(x1483,x1484,x1481),f815(x1483,x1484,x1482)) % 191.49/191.42 [149]~E(x1491,x1492)+E(f110(x1491),f110(x1492)) % 191.49/191.42 [150]~E(x1501,x1502)+E(f112(x1501),f112(x1502)) % 191.49/191.42 [151]~E(x1511,x1512)+E(f334(x1511),f334(x1512)) % 191.49/191.42 [152]~E(x1521,x1522)+E(f170(x1521),f170(x1522)) % 191.49/191.42 [153]~E(x1531,x1532)+E(f197(x1531),f197(x1532)) % 191.49/191.42 [154]~E(x1541,x1542)+E(f698(x1541,x1543,x1544,x1545,x1546),f698(x1542,x1543,x1544,x1545,x1546)) % 191.49/191.42 [155]~E(x1551,x1552)+E(f698(x1553,x1551,x1554,x1555,x1556),f698(x1553,x1552,x1554,x1555,x1556)) % 191.49/191.42 [156]~E(x1561,x1562)+E(f698(x1563,x1564,x1561,x1565,x1566),f698(x1563,x1564,x1562,x1565,x1566)) % 191.49/191.42 [157]~E(x1571,x1572)+E(f698(x1573,x1574,x1575,x1571,x1576),f698(x1573,x1574,x1575,x1572,x1576)) % 191.49/191.42 [158]~E(x1581,x1582)+E(f698(x1583,x1584,x1585,x1586,x1581),f698(x1583,x1584,x1585,x1586,x1582)) % 191.49/191.42 [159]~E(x1591,x1592)+E(f263(x1591,x1593),f263(x1592,x1593)) % 191.49/191.42 [160]~E(x1601,x1602)+E(f263(x1603,x1601),f263(x1603,x1602)) % 191.49/191.42 [161]~E(x1611,x1612)+E(f820(x1611,x1613,x1614),f820(x1612,x1613,x1614)) % 191.49/191.42 [162]~E(x1621,x1622)+E(f820(x1623,x1621,x1624),f820(x1623,x1622,x1624)) % 191.49/191.42 [163]~E(x1631,x1632)+E(f820(x1633,x1634,x1631),f820(x1633,x1634,x1632)) % 191.49/191.42 [164]~E(x1641,x1642)+E(f7(x1641),f7(x1642)) % 191.49/191.42 [165]~E(x1651,x1652)+E(f93(x1651),f93(x1652)) % 191.49/191.42 [166]~E(x1661,x1662)+E(f9(x1661,x1663,x1664),f9(x1662,x1663,x1664)) % 191.49/191.42 [167]~E(x1671,x1672)+E(f9(x1673,x1671,x1674),f9(x1673,x1672,x1674)) % 191.49/191.42 [168]~E(x1681,x1682)+E(f9(x1683,x1684,x1681),f9(x1683,x1684,x1682)) % 191.49/191.42 [169]~E(x1691,x1692)+E(f42(x1691,x1693),f42(x1692,x1693)) % 191.49/191.42 [170]~E(x1701,x1702)+E(f42(x1703,x1701),f42(x1703,x1702)) % 191.49/191.42 [171]~E(x1711,x1712)+E(f167(x1711),f167(x1712)) % 191.49/191.42 [172]~E(x1721,x1722)+E(f246(x1721),f246(x1722)) % 191.49/191.42 [173]~E(x1731,x1732)+E(f169(x1731),f169(x1732)) % 191.49/191.42 [174]~E(x1741,x1742)+E(f118(x1741),f118(x1742)) % 191.49/191.42 [175]~E(x1751,x1752)+E(f63(x1751),f63(x1752)) % 191.49/191.42 [176]~E(x1761,x1762)+E(f50(x1761,x1763),f50(x1762,x1763)) % 191.49/191.42 [177]~E(x1771,x1772)+E(f50(x1773,x1771),f50(x1773,x1772)) % 191.49/191.42 [178]~E(x1781,x1782)+E(f395(x1781,x1783,x1784,x1785,x1786),f395(x1782,x1783,x1784,x1785,x1786)) % 191.49/191.42 [179]~E(x1791,x1792)+E(f395(x1793,x1791,x1794,x1795,x1796),f395(x1793,x1792,x1794,x1795,x1796)) % 191.49/191.42 [180]~E(x1801,x1802)+E(f395(x1803,x1804,x1801,x1805,x1806),f395(x1803,x1804,x1802,x1805,x1806)) % 191.49/191.42 [181]~E(x1811,x1812)+E(f395(x1813,x1814,x1815,x1811,x1816),f395(x1813,x1814,x1815,x1812,x1816)) % 191.49/191.42 [182]~E(x1821,x1822)+E(f395(x1823,x1824,x1825,x1826,x1821),f395(x1823,x1824,x1825,x1826,x1822)) % 191.49/191.42 [183]~E(x1831,x1832)+E(f44(x1831,x1833),f44(x1832,x1833)) % 191.49/191.42 [184]~E(x1841,x1842)+E(f44(x1843,x1841),f44(x1843,x1842)) % 191.49/191.42 [185]~E(x1851,x1852)+E(f20(x1851,x1853,x1854),f20(x1852,x1853,x1854)) % 191.49/191.42 [186]~E(x1861,x1862)+E(f20(x1863,x1861,x1864),f20(x1863,x1862,x1864)) % 191.49/191.42 [187]~E(x1871,x1872)+E(f20(x1873,x1874,x1871),f20(x1873,x1874,x1872)) % 191.49/191.42 [188]~E(x1881,x1882)+E(f258(x1881),f258(x1882)) % 191.49/191.42 [189]~E(x1891,x1892)+E(f262(x1891,x1893),f262(x1892,x1893)) % 191.49/191.42 [190]~E(x1901,x1902)+E(f262(x1903,x1901),f262(x1903,x1902)) % 191.49/191.42 [191]~E(x1911,x1912)+E(f259(x1911,x1913),f259(x1912,x1913)) % 191.49/191.42 [192]~E(x1921,x1922)+E(f259(x1923,x1921),f259(x1923,x1922)) % 191.49/191.42 [193]~E(x1931,x1932)+E(f496(x1931,x1933,x1934,x1935,x1936,x1937),f496(x1932,x1933,x1934,x1935,x1936,x1937)) % 191.49/191.42 [194]~E(x1941,x1942)+E(f496(x1943,x1941,x1944,x1945,x1946,x1947),f496(x1943,x1942,x1944,x1945,x1946,x1947)) % 191.49/191.42 [195]~E(x1951,x1952)+E(f496(x1953,x1954,x1951,x1955,x1956,x1957),f496(x1953,x1954,x1952,x1955,x1956,x1957)) % 191.49/191.42 [196]~E(x1961,x1962)+E(f496(x1963,x1964,x1965,x1961,x1966,x1967),f496(x1963,x1964,x1965,x1962,x1966,x1967)) % 191.49/191.42 [197]~E(x1971,x1972)+E(f496(x1973,x1974,x1975,x1976,x1971,x1977),f496(x1973,x1974,x1975,x1976,x1972,x1977)) % 191.49/191.42 [198]~E(x1981,x1982)+E(f496(x1983,x1984,x1985,x1986,x1987,x1981),f496(x1983,x1984,x1985,x1986,x1987,x1982)) % 191.49/191.42 [199]~E(x1991,x1992)+E(f320(x1991,x1993,x1994,x1995),f320(x1992,x1993,x1994,x1995)) % 191.49/191.42 [200]~E(x2001,x2002)+E(f320(x2003,x2001,x2004,x2005),f320(x2003,x2002,x2004,x2005)) % 191.49/191.42 [201]~E(x2011,x2012)+E(f320(x2013,x2014,x2011,x2015),f320(x2013,x2014,x2012,x2015)) % 191.49/191.42 [202]~E(x2021,x2022)+E(f320(x2023,x2024,x2025,x2021),f320(x2023,x2024,x2025,x2022)) % 191.49/191.42 [203]~E(x2031,x2032)+E(f187(x2031,x2033,x2034,x2035,x2036),f187(x2032,x2033,x2034,x2035,x2036)) % 191.49/191.42 [204]~E(x2041,x2042)+E(f187(x2043,x2041,x2044,x2045,x2046),f187(x2043,x2042,x2044,x2045,x2046)) % 191.49/191.42 [205]~E(x2051,x2052)+E(f187(x2053,x2054,x2051,x2055,x2056),f187(x2053,x2054,x2052,x2055,x2056)) % 191.49/191.42 [206]~E(x2061,x2062)+E(f187(x2063,x2064,x2065,x2061,x2066),f187(x2063,x2064,x2065,x2062,x2066)) % 191.49/191.42 [207]~E(x2071,x2072)+E(f187(x2073,x2074,x2075,x2076,x2071),f187(x2073,x2074,x2075,x2076,x2072)) % 191.49/191.42 [208]~E(x2081,x2082)+E(f166(x2081),f166(x2082)) % 191.49/191.42 [209]~E(x2091,x2092)+E(f201(x2091),f201(x2092)) % 191.49/191.42 [210]~E(x2101,x2102)+E(f257(x2101),f257(x2102)) % 191.49/191.42 [211]~E(x2111,x2112)+E(f41(x2111,x2113),f41(x2112,x2113)) % 191.49/191.42 [212]~E(x2121,x2122)+E(f41(x2123,x2121),f41(x2123,x2122)) % 191.49/191.42 [213]~E(x2131,x2132)+E(f290(x2131,x2133,x2134),f290(x2132,x2133,x2134)) % 191.49/191.42 [214]~E(x2141,x2142)+E(f290(x2143,x2141,x2144),f290(x2143,x2142,x2144)) % 191.49/191.42 [215]~E(x2151,x2152)+E(f290(x2153,x2154,x2151),f290(x2153,x2154,x2152)) % 191.49/191.42 [216]~E(x2161,x2162)+E(f287(x2161,x2163,x2164),f287(x2162,x2163,x2164)) % 191.49/191.42 [217]~E(x2171,x2172)+E(f287(x2173,x2171,x2174),f287(x2173,x2172,x2174)) % 191.49/191.42 [218]~E(x2181,x2182)+E(f287(x2183,x2184,x2181),f287(x2183,x2184,x2182)) % 191.49/191.42 [219]~E(x2191,x2192)+E(f410(x2191,x2193,x2194),f410(x2192,x2193,x2194)) % 191.49/191.42 [220]~E(x2201,x2202)+E(f410(x2203,x2201,x2204),f410(x2203,x2202,x2204)) % 191.49/191.42 [221]~E(x2211,x2212)+E(f410(x2213,x2214,x2211),f410(x2213,x2214,x2212)) % 191.49/191.42 [222]~E(x2221,x2222)+E(f309(x2221,x2223),f309(x2222,x2223)) % 191.49/191.42 [223]~E(x2231,x2232)+E(f309(x2233,x2231),f309(x2233,x2232)) % 191.49/191.42 [224]~E(x2241,x2242)+E(f153(x2241,x2243),f153(x2242,x2243)) % 191.49/191.42 [225]~E(x2251,x2252)+E(f153(x2253,x2251),f153(x2253,x2252)) % 191.49/191.42 [226]~E(x2261,x2262)+E(f454(x2261,x2263,x2264),f454(x2262,x2263,x2264)) % 191.49/191.42 [227]~E(x2271,x2272)+E(f454(x2273,x2271,x2274),f454(x2273,x2272,x2274)) % 191.49/191.42 [228]~E(x2281,x2282)+E(f454(x2283,x2284,x2281),f454(x2283,x2284,x2282)) % 191.49/191.42 [229]~E(x2291,x2292)+E(f67(x2291,x2293,x2294),f67(x2292,x2293,x2294)) % 191.49/191.42 [230]~E(x2301,x2302)+E(f67(x2303,x2301,x2304),f67(x2303,x2302,x2304)) % 191.49/191.42 [231]~E(x2311,x2312)+E(f67(x2313,x2314,x2311),f67(x2313,x2314,x2312)) % 191.49/191.42 [232]~E(x2321,x2322)+E(f288(x2321,x2323),f288(x2322,x2323)) % 191.49/191.42 [233]~E(x2331,x2332)+E(f288(x2333,x2331),f288(x2333,x2332)) % 191.49/191.42 [234]~E(x2341,x2342)+E(f192(x2341),f192(x2342)) % 191.49/191.42 [235]~E(x2351,x2352)+E(f18(x2351,x2353),f18(x2352,x2353)) % 191.49/191.42 [236]~E(x2361,x2362)+E(f18(x2363,x2361),f18(x2363,x2362)) % 191.49/191.42 [237]~E(x2371,x2372)+E(f207(x2371,x2373,x2374,x2375),f207(x2372,x2373,x2374,x2375)) % 191.49/191.42 [238]~E(x2381,x2382)+E(f207(x2383,x2381,x2384,x2385),f207(x2383,x2382,x2384,x2385)) % 191.49/191.42 [239]~E(x2391,x2392)+E(f207(x2393,x2394,x2391,x2395),f207(x2393,x2394,x2392,x2395)) % 191.49/191.42 [240]~E(x2401,x2402)+E(f207(x2403,x2404,x2405,x2401),f207(x2403,x2404,x2405,x2402)) % 191.49/191.42 [241]~E(x2411,x2412)+E(f154(x2411,x2413),f154(x2412,x2413)) % 191.49/191.42 [242]~E(x2421,x2422)+E(f154(x2423,x2421),f154(x2423,x2422)) % 191.49/191.42 [243]~E(x2431,x2432)+E(f303(x2431,x2433),f303(x2432,x2433)) % 191.49/191.42 [244]~E(x2441,x2442)+E(f303(x2443,x2441),f303(x2443,x2442)) % 191.49/191.42 [245]~E(x2451,x2452)+E(f86(x2451,x2453),f86(x2452,x2453)) % 191.49/191.42 [246]~E(x2461,x2462)+E(f86(x2463,x2461),f86(x2463,x2462)) % 191.49/191.42 [247]~E(x2471,x2472)+E(f119(x2471,x2473),f119(x2472,x2473)) % 191.49/191.42 [248]~E(x2481,x2482)+E(f119(x2483,x2481),f119(x2483,x2482)) % 191.49/191.42 [249]~E(x2491,x2492)+E(f76(x2491),f76(x2492)) % 191.49/191.42 [250]~E(x2501,x2502)+E(f73(x2501,x2503),f73(x2502,x2503)) % 191.49/191.42 [251]~E(x2511,x2512)+E(f73(x2513,x2511),f73(x2513,x2512)) % 191.49/191.42 [252]~E(x2521,x2522)+E(f189(x2521,x2523),f189(x2522,x2523)) % 191.49/191.42 [253]~E(x2531,x2532)+E(f189(x2533,x2531),f189(x2533,x2532)) % 191.49/191.42 [254]~E(x2541,x2542)+E(f273(x2541,x2543,x2544,x2545,x2546,x2547),f273(x2542,x2543,x2544,x2545,x2546,x2547)) % 191.49/191.42 [255]~E(x2551,x2552)+E(f273(x2553,x2551,x2554,x2555,x2556,x2557),f273(x2553,x2552,x2554,x2555,x2556,x2557)) % 191.49/191.42 [256]~E(x2561,x2562)+E(f273(x2563,x2564,x2561,x2565,x2566,x2567),f273(x2563,x2564,x2562,x2565,x2566,x2567)) % 191.49/191.42 [257]~E(x2571,x2572)+E(f273(x2573,x2574,x2575,x2571,x2576,x2577),f273(x2573,x2574,x2575,x2572,x2576,x2577)) % 191.49/191.42 [258]~E(x2581,x2582)+E(f273(x2583,x2584,x2585,x2586,x2581,x2587),f273(x2583,x2584,x2585,x2586,x2582,x2587)) % 191.49/191.42 [259]~E(x2591,x2592)+E(f273(x2593,x2594,x2595,x2596,x2597,x2591),f273(x2593,x2594,x2595,x2596,x2597,x2592)) % 191.49/191.42 [260]~E(x2601,x2602)+E(f198(x2601),f198(x2602)) % 191.49/191.42 [261]~E(x2611,x2612)+E(f143(x2611,x2613,x2614,x2615),f143(x2612,x2613,x2614,x2615)) % 191.49/191.42 [262]~E(x2621,x2622)+E(f143(x2623,x2621,x2624,x2625),f143(x2623,x2622,x2624,x2625)) % 191.49/191.42 [263]~E(x2631,x2632)+E(f143(x2633,x2634,x2631,x2635),f143(x2633,x2634,x2632,x2635)) % 191.49/191.42 [264]~E(x2641,x2642)+E(f143(x2643,x2644,x2645,x2641),f143(x2643,x2644,x2645,x2642)) % 191.49/191.42 [265]~E(x2651,x2652)+E(f120(x2651),f120(x2652)) % 191.49/191.42 [266]~E(x2661,x2662)+E(f313(x2661,x2663,x2664),f313(x2662,x2663,x2664)) % 191.49/191.42 [267]~E(x2671,x2672)+E(f313(x2673,x2671,x2674),f313(x2673,x2672,x2674)) % 191.49/191.42 [268]~E(x2681,x2682)+E(f313(x2683,x2684,x2681),f313(x2683,x2684,x2682)) % 191.49/191.42 [269]~E(x2691,x2692)+E(f222(x2691),f222(x2692)) % 191.49/191.42 [270]~E(x2701,x2702)+E(f863(x2701,x2703,x2704),f863(x2702,x2703,x2704)) % 191.49/191.42 [271]~E(x2711,x2712)+E(f863(x2713,x2711,x2714),f863(x2713,x2712,x2714)) % 191.49/191.42 [272]~E(x2721,x2722)+E(f863(x2723,x2724,x2721),f863(x2723,x2724,x2722)) % 191.49/191.42 [273]~E(x2731,x2732)+E(f612(x2731,x2733,x2734,x2735),f612(x2732,x2733,x2734,x2735)) % 191.49/191.42 [274]~E(x2741,x2742)+E(f612(x2743,x2741,x2744,x2745),f612(x2743,x2742,x2744,x2745)) % 191.49/191.42 [275]~E(x2751,x2752)+E(f612(x2753,x2754,x2751,x2755),f612(x2753,x2754,x2752,x2755)) % 191.49/191.42 [276]~E(x2761,x2762)+E(f612(x2763,x2764,x2765,x2761),f612(x2763,x2764,x2765,x2762)) % 191.49/191.42 [277]~E(x2771,x2772)+E(f135(x2771,x2773),f135(x2772,x2773)) % 191.49/191.42 [278]~E(x2781,x2782)+E(f135(x2783,x2781),f135(x2783,x2782)) % 191.49/191.42 [279]~E(x2791,x2792)+E(f11(x2791,x2793),f11(x2792,x2793)) % 191.49/191.42 [280]~E(x2801,x2802)+E(f11(x2803,x2801),f11(x2803,x2802)) % 191.49/191.42 [281]~E(x2811,x2812)+E(f685(x2811,x2813),f685(x2812,x2813)) % 191.49/191.42 [282]~E(x2821,x2822)+E(f685(x2823,x2821),f685(x2823,x2822)) % 191.49/191.42 [283]~E(x2831,x2832)+E(f364(x2831,x2833,x2834),f364(x2832,x2833,x2834)) % 191.49/191.42 [284]~E(x2841,x2842)+E(f364(x2843,x2841,x2844),f364(x2843,x2842,x2844)) % 191.49/191.42 [285]~E(x2851,x2852)+E(f364(x2853,x2854,x2851),f364(x2853,x2854,x2852)) % 191.49/191.42 [286]~E(x2861,x2862)+E(f885(x2861,x2863),f885(x2862,x2863)) % 191.49/191.42 [287]~E(x2871,x2872)+E(f885(x2873,x2871),f885(x2873,x2872)) % 191.49/191.42 [288]~E(x2881,x2882)+E(f182(x2881,x2883),f182(x2882,x2883)) % 191.49/191.42 [289]~E(x2891,x2892)+E(f182(x2893,x2891),f182(x2893,x2892)) % 191.49/191.42 [290]~E(x2901,x2902)+E(f121(x2901,x2903,x2904),f121(x2902,x2903,x2904)) % 191.49/191.42 [291]~E(x2911,x2912)+E(f121(x2913,x2911,x2914),f121(x2913,x2912,x2914)) % 191.49/191.42 [292]~E(x2921,x2922)+E(f121(x2923,x2924,x2921),f121(x2923,x2924,x2922)) % 191.49/191.42 [293]~E(x2931,x2932)+E(f158(x2931,x2933),f158(x2932,x2933)) % 191.49/191.42 [294]~E(x2941,x2942)+E(f158(x2943,x2941),f158(x2943,x2942)) % 191.49/191.42 [295]~E(x2951,x2952)+E(f721(x2951,x2953,x2954,x2955,x2956,x2957),f721(x2952,x2953,x2954,x2955,x2956,x2957)) % 191.49/191.42 [296]~E(x2961,x2962)+E(f721(x2963,x2961,x2964,x2965,x2966,x2967),f721(x2963,x2962,x2964,x2965,x2966,x2967)) % 191.49/191.42 [297]~E(x2971,x2972)+E(f721(x2973,x2974,x2971,x2975,x2976,x2977),f721(x2973,x2974,x2972,x2975,x2976,x2977)) % 191.49/191.42 [298]~E(x2981,x2982)+E(f721(x2983,x2984,x2985,x2981,x2986,x2987),f721(x2983,x2984,x2985,x2982,x2986,x2987)) % 191.49/191.42 [299]~E(x2991,x2992)+E(f721(x2993,x2994,x2995,x2996,x2991,x2997),f721(x2993,x2994,x2995,x2996,x2992,x2997)) % 191.49/191.42 [300]~E(x3001,x3002)+E(f721(x3003,x3004,x3005,x3006,x3007,x3001),f721(x3003,x3004,x3005,x3006,x3007,x3002)) % 191.49/191.42 [301]~E(x3011,x3012)+E(f476(x3011,x3013,x3014),f476(x3012,x3013,x3014)) % 191.49/191.42 [302]~E(x3021,x3022)+E(f476(x3023,x3021,x3024),f476(x3023,x3022,x3024)) % 191.49/191.42 [303]~E(x3031,x3032)+E(f476(x3033,x3034,x3031),f476(x3033,x3034,x3032)) % 191.49/191.42 [304]~E(x3041,x3042)+E(f30(x3041,x3043,x3044),f30(x3042,x3043,x3044)) % 191.49/191.42 [305]~E(x3051,x3052)+E(f30(x3053,x3051,x3054),f30(x3053,x3052,x3054)) % 191.49/191.42 [306]~E(x3061,x3062)+E(f30(x3063,x3064,x3061),f30(x3063,x3064,x3062)) % 191.49/191.42 [307]~E(x3071,x3072)+E(f185(x3071,x3073,x3074,x3075),f185(x3072,x3073,x3074,x3075)) % 191.49/191.42 [308]~E(x3081,x3082)+E(f185(x3083,x3081,x3084,x3085),f185(x3083,x3082,x3084,x3085)) % 191.49/191.42 [309]~E(x3091,x3092)+E(f185(x3093,x3094,x3091,x3095),f185(x3093,x3094,x3092,x3095)) % 191.49/191.42 [310]~E(x3101,x3102)+E(f185(x3103,x3104,x3105,x3101),f185(x3103,x3104,x3105,x3102)) % 191.49/191.42 [311]~E(x3111,x3112)+E(f172(x3111),f172(x3112)) % 191.49/191.42 [312]~E(x3121,x3122)+E(f160(x3121,x3123),f160(x3122,x3123)) % 191.49/191.42 [313]~E(x3131,x3132)+E(f160(x3133,x3131),f160(x3133,x3132)) % 191.49/191.42 [314]~E(x3141,x3142)+E(f427(x3141,x3143),f427(x3142,x3143)) % 191.49/191.42 [315]~E(x3151,x3152)+E(f427(x3153,x3151),f427(x3153,x3152)) % 191.49/191.42 [316]~E(x3161,x3162)+E(f49(x3161,x3163),f49(x3162,x3163)) % 191.49/191.42 [317]~E(x3171,x3172)+E(f49(x3173,x3171),f49(x3173,x3172)) % 191.49/191.42 [318]~E(x3181,x3182)+E(f399(x3181,x3183,x3184),f399(x3182,x3183,x3184)) % 191.49/191.42 [319]~E(x3191,x3192)+E(f399(x3193,x3191,x3194),f399(x3193,x3192,x3194)) % 191.49/191.42 [320]~E(x3201,x3202)+E(f399(x3203,x3204,x3201),f399(x3203,x3204,x3202)) % 191.49/191.42 [321]~E(x3211,x3212)+E(f326(x3211,x3213,x3214,x3215),f326(x3212,x3213,x3214,x3215)) % 191.49/191.42 [322]~E(x3221,x3222)+E(f326(x3223,x3221,x3224,x3225),f326(x3223,x3222,x3224,x3225)) % 191.49/191.42 [323]~E(x3231,x3232)+E(f326(x3233,x3234,x3231,x3235),f326(x3233,x3234,x3232,x3235)) % 191.49/191.42 [324]~E(x3241,x3242)+E(f326(x3243,x3244,x3245,x3241),f326(x3243,x3244,x3245,x3242)) % 191.49/191.42 [325]~E(x3251,x3252)+E(f774(x3251,x3253,x3254,x3255,x3256),f774(x3252,x3253,x3254,x3255,x3256)) % 191.49/191.42 [326]~E(x3261,x3262)+E(f774(x3263,x3261,x3264,x3265,x3266),f774(x3263,x3262,x3264,x3265,x3266)) % 191.49/191.42 [327]~E(x3271,x3272)+E(f774(x3273,x3274,x3271,x3275,x3276),f774(x3273,x3274,x3272,x3275,x3276)) % 191.49/191.42 [328]~E(x3281,x3282)+E(f774(x3283,x3284,x3285,x3281,x3286),f774(x3283,x3284,x3285,x3282,x3286)) % 191.49/191.42 [329]~E(x3291,x3292)+E(f774(x3293,x3294,x3295,x3296,x3291),f774(x3293,x3294,x3295,x3296,x3292)) % 191.49/191.42 [330]~E(x3301,x3302)+E(f137(x3301,x3303),f137(x3302,x3303)) % 191.49/191.42 [331]~E(x3311,x3312)+E(f137(x3313,x3311),f137(x3313,x3312)) % 191.49/191.42 [332]~E(x3321,x3322)+E(f15(x3321,x3323,x3324),f15(x3322,x3323,x3324)) % 191.49/191.42 [333]~E(x3331,x3332)+E(f15(x3333,x3331,x3334),f15(x3333,x3332,x3334)) % 191.49/191.42 [334]~E(x3341,x3342)+E(f15(x3343,x3344,x3341),f15(x3343,x3344,x3342)) % 191.49/191.42 [335]~E(x3351,x3352)+E(f244(x3351,x3353,x3354,x3355),f244(x3352,x3353,x3354,x3355)) % 191.49/191.42 [336]~E(x3361,x3362)+E(f244(x3363,x3361,x3364,x3365),f244(x3363,x3362,x3364,x3365)) % 191.49/191.42 [337]~E(x3371,x3372)+E(f244(x3373,x3374,x3371,x3375),f244(x3373,x3374,x3372,x3375)) % 191.49/191.42 [338]~E(x3381,x3382)+E(f244(x3383,x3384,x3385,x3381),f244(x3383,x3384,x3385,x3382)) % 191.49/191.42 [339]~E(x3391,x3392)+E(f803(x3391,x3393),f803(x3392,x3393)) % 191.49/191.42 [340]~E(x3401,x3402)+E(f803(x3403,x3401),f803(x3403,x3402)) % 191.49/191.42 [341]~E(x3411,x3412)+E(f101(x3411),f101(x3412)) % 191.49/191.42 [342]~E(x3421,x3422)+E(f814(x3421,x3423,x3424),f814(x3422,x3423,x3424)) % 191.49/191.42 [343]~E(x3431,x3432)+E(f814(x3433,x3431,x3434),f814(x3433,x3432,x3434)) % 191.49/191.42 [344]~E(x3441,x3442)+E(f814(x3443,x3444,x3441),f814(x3443,x3444,x3442)) % 191.49/191.42 [345]~E(x3451,x3452)+E(f78(x3451,x3453,x3454,x3455),f78(x3452,x3453,x3454,x3455)) % 191.49/191.42 [346]~E(x3461,x3462)+E(f78(x3463,x3461,x3464,x3465),f78(x3463,x3462,x3464,x3465)) % 191.49/191.42 [347]~E(x3471,x3472)+E(f78(x3473,x3474,x3471,x3475),f78(x3473,x3474,x3472,x3475)) % 191.49/191.42 [348]~E(x3481,x3482)+E(f78(x3483,x3484,x3485,x3481),f78(x3483,x3484,x3485,x3482)) % 191.49/191.42 [349]~E(x3491,x3492)+E(f489(x3491,x3493,x3494),f489(x3492,x3493,x3494)) % 191.49/191.42 [350]~E(x3501,x3502)+E(f489(x3503,x3501,x3504),f489(x3503,x3502,x3504)) % 191.49/191.42 [351]~E(x3511,x3512)+E(f489(x3513,x3514,x3511),f489(x3513,x3514,x3512)) % 191.49/191.42 [352]~E(x3521,x3522)+E(f324(x3521,x3523),f324(x3522,x3523)) % 191.49/191.42 [353]~E(x3531,x3532)+E(f324(x3533,x3531),f324(x3533,x3532)) % 191.49/191.42 [354]~E(x3541,x3542)+E(f271(x3541,x3543),f271(x3542,x3543)) % 191.49/191.42 [355]~E(x3551,x3552)+E(f271(x3553,x3551),f271(x3553,x3552)) % 191.49/191.42 [356]~E(x3561,x3562)+E(f68(x3561,x3563,x3564,x3565,x3566),f68(x3562,x3563,x3564,x3565,x3566)) % 191.49/191.42 [357]~E(x3571,x3572)+E(f68(x3573,x3571,x3574,x3575,x3576),f68(x3573,x3572,x3574,x3575,x3576)) % 191.49/191.42 [358]~E(x3581,x3582)+E(f68(x3583,x3584,x3581,x3585,x3586),f68(x3583,x3584,x3582,x3585,x3586)) % 191.49/191.42 [359]~E(x3591,x3592)+E(f68(x3593,x3594,x3595,x3591,x3596),f68(x3593,x3594,x3595,x3592,x3596)) % 191.49/191.42 [360]~E(x3601,x3602)+E(f68(x3603,x3604,x3605,x3606,x3601),f68(x3603,x3604,x3605,x3606,x3602)) % 191.49/191.42 [361]~E(x3611,x3612)+E(f294(x3611,x3613,x3614),f294(x3612,x3613,x3614)) % 191.49/191.42 [362]~E(x3621,x3622)+E(f294(x3623,x3621,x3624),f294(x3623,x3622,x3624)) % 191.49/191.42 [363]~E(x3631,x3632)+E(f294(x3633,x3634,x3631),f294(x3633,x3634,x3632)) % 191.49/191.42 [364]~E(x3641,x3642)+E(f174(x3641),f174(x3642)) % 191.49/191.42 [365]~E(x3651,x3652)+E(f64(x3651,x3653,x3654),f64(x3652,x3653,x3654)) % 191.49/191.42 [366]~E(x3661,x3662)+E(f64(x3663,x3661,x3664),f64(x3663,x3662,x3664)) % 191.49/191.42 [367]~E(x3671,x3672)+E(f64(x3673,x3674,x3671),f64(x3673,x3674,x3672)) % 191.49/191.42 [368]~E(x3681,x3682)+E(f539(x3681,x3683,x3684,x3685,x3686),f539(x3682,x3683,x3684,x3685,x3686)) % 191.49/191.42 [369]~E(x3691,x3692)+E(f539(x3693,x3691,x3694,x3695,x3696),f539(x3693,x3692,x3694,x3695,x3696)) % 191.49/191.42 [370]~E(x3701,x3702)+E(f539(x3703,x3704,x3701,x3705,x3706),f539(x3703,x3704,x3702,x3705,x3706)) % 191.49/191.42 [371]~E(x3711,x3712)+E(f539(x3713,x3714,x3715,x3711,x3716),f539(x3713,x3714,x3715,x3712,x3716)) % 191.49/191.42 [372]~E(x3721,x3722)+E(f539(x3723,x3724,x3725,x3726,x3721),f539(x3723,x3724,x3725,x3726,x3722)) % 191.49/191.42 [373]~E(x3731,x3732)+E(f516(x3731,x3733,x3734),f516(x3732,x3733,x3734)) % 191.49/191.42 [374]~E(x3741,x3742)+E(f516(x3743,x3741,x3744),f516(x3743,x3742,x3744)) % 191.49/191.42 [375]~E(x3751,x3752)+E(f516(x3753,x3754,x3751),f516(x3753,x3754,x3752)) % 191.49/191.42 [376]~E(x3761,x3762)+E(f289(x3761,x3763),f289(x3762,x3763)) % 191.49/191.42 [377]~E(x3771,x3772)+E(f289(x3773,x3771),f289(x3773,x3772)) % 191.49/191.42 [378]~E(x3781,x3782)+E(f371(x3781,x3783),f371(x3782,x3783)) % 191.49/191.42 [379]~E(x3791,x3792)+E(f371(x3793,x3791),f371(x3793,x3792)) % 191.49/191.42 [380]~E(x3801,x3802)+E(f139(x3801),f139(x3802)) % 191.49/191.42 [381]~E(x3811,x3812)+E(f855(x3811,x3813,x3814,x3815),f855(x3812,x3813,x3814,x3815)) % 191.49/191.42 [382]~E(x3821,x3822)+E(f855(x3823,x3821,x3824,x3825),f855(x3823,x3822,x3824,x3825)) % 191.49/191.42 [383]~E(x3831,x3832)+E(f855(x3833,x3834,x3831,x3835),f855(x3833,x3834,x3832,x3835)) % 191.49/191.42 [384]~E(x3841,x3842)+E(f855(x3843,x3844,x3845,x3841),f855(x3843,x3844,x3845,x3842)) % 191.49/191.42 [385]~E(x3851,x3852)+E(f140(x3851,x3853),f140(x3852,x3853)) % 191.49/191.42 [386]~E(x3861,x3862)+E(f140(x3863,x3861),f140(x3863,x3862)) % 191.49/191.42 [387]~E(x3871,x3872)+E(f483(x3871,x3873,x3874),f483(x3872,x3873,x3874)) % 191.49/191.42 [388]~E(x3881,x3882)+E(f483(x3883,x3881,x3884),f483(x3883,x3882,x3884)) % 191.49/191.42 [389]~E(x3891,x3892)+E(f483(x3893,x3894,x3891),f483(x3893,x3894,x3892)) % 191.49/191.42 [390]~E(x3901,x3902)+E(f184(x3901,x3903,x3904),f184(x3902,x3903,x3904)) % 191.49/191.42 [391]~E(x3911,x3912)+E(f184(x3913,x3911,x3914),f184(x3913,x3912,x3914)) % 191.49/191.42 [392]~E(x3921,x3922)+E(f184(x3923,x3924,x3921),f184(x3923,x3924,x3922)) % 191.49/191.42 [393]~E(x3931,x3932)+E(f615(x3931,x3933),f615(x3932,x3933)) % 191.49/191.42 [394]~E(x3941,x3942)+E(f615(x3943,x3941),f615(x3943,x3942)) % 191.49/191.42 [395]~E(x3951,x3952)+E(f277(x3951,x3953),f277(x3952,x3953)) % 191.49/191.42 [396]~E(x3961,x3962)+E(f277(x3963,x3961),f277(x3963,x3962)) % 191.49/191.42 [397]~E(x3971,x3972)+E(f665(x3971,x3973,x3974),f665(x3972,x3973,x3974)) % 191.49/191.42 [398]~E(x3981,x3982)+E(f665(x3983,x3981,x3984),f665(x3983,x3982,x3984)) % 191.49/191.42 [399]~E(x3991,x3992)+E(f665(x3993,x3994,x3991),f665(x3993,x3994,x3992)) % 191.49/191.42 [400]~E(x4001,x4002)+E(f485(x4001,x4003,x4004),f485(x4002,x4003,x4004)) % 191.49/191.42 [401]~E(x4011,x4012)+E(f485(x4013,x4011,x4014),f485(x4013,x4012,x4014)) % 191.49/191.42 [402]~E(x4021,x4022)+E(f485(x4023,x4024,x4021),f485(x4023,x4024,x4022)) % 191.49/191.42 [403]~E(x4031,x4032)+E(f482(x4031,x4033),f482(x4032,x4033)) % 191.49/191.42 [404]~E(x4041,x4042)+E(f482(x4043,x4041),f482(x4043,x4042)) % 191.49/191.42 [405]~E(x4051,x4052)+E(f270(x4051,x4053),f270(x4052,x4053)) % 191.49/191.42 [406]~E(x4061,x4062)+E(f270(x4063,x4061),f270(x4063,x4062)) % 191.49/191.42 [407]~E(x4071,x4072)+E(f208(x4071,x4073),f208(x4072,x4073)) % 191.49/191.42 [408]~E(x4081,x4082)+E(f208(x4083,x4081),f208(x4083,x4082)) % 191.49/191.42 [409]~E(x4091,x4092)+E(f179(x4091,x4093),f179(x4092,x4093)) % 191.49/191.42 [410]~E(x4101,x4102)+E(f179(x4103,x4101),f179(x4103,x4102)) % 191.49/191.42 [411]~E(x4111,x4112)+E(f159(x4111,x4113),f159(x4112,x4113)) % 191.49/191.42 [412]~E(x4121,x4122)+E(f159(x4123,x4121),f159(x4123,x4122)) % 191.49/191.42 [413]~E(x4131,x4132)+E(f89(x4131,x4133),f89(x4132,x4133)) % 191.49/191.42 [414]~E(x4141,x4142)+E(f89(x4143,x4141),f89(x4143,x4142)) % 191.49/191.42 [415]~E(x4151,x4152)+E(f304(x4151,x4153,x4154),f304(x4152,x4153,x4154)) % 191.49/191.42 [416]~E(x4161,x4162)+E(f304(x4163,x4161,x4164),f304(x4163,x4162,x4164)) % 191.49/191.42 [417]~E(x4171,x4172)+E(f304(x4173,x4174,x4171),f304(x4173,x4174,x4172)) % 191.49/191.42 [418]~E(x4181,x4182)+E(f83(x4181,x4183),f83(x4182,x4183)) % 191.49/191.42 [419]~E(x4191,x4192)+E(f83(x4193,x4191),f83(x4193,x4192)) % 191.49/191.42 [420]~E(x4201,x4202)+E(f156(x4201,x4203,x4204),f156(x4202,x4203,x4204)) % 191.49/191.42 [421]~E(x4211,x4212)+E(f156(x4213,x4211,x4214),f156(x4213,x4212,x4214)) % 191.49/191.42 [422]~E(x4221,x4222)+E(f156(x4223,x4224,x4221),f156(x4223,x4224,x4222)) % 191.49/191.42 [423]~E(x4231,x4232)+E(f239(x4231,x4233,x4234),f239(x4232,x4233,x4234)) % 191.49/191.42 [424]~E(x4241,x4242)+E(f239(x4243,x4241,x4244),f239(x4243,x4242,x4244)) % 191.49/191.42 [425]~E(x4251,x4252)+E(f239(x4253,x4254,x4251),f239(x4253,x4254,x4252)) % 191.49/191.42 [426]~E(x4261,x4262)+E(f149(x4261,x4263,x4264),f149(x4262,x4263,x4264)) % 191.49/191.42 [427]~E(x4271,x4272)+E(f149(x4273,x4271,x4274),f149(x4273,x4272,x4274)) % 191.49/191.42 [428]~E(x4281,x4282)+E(f149(x4283,x4284,x4281),f149(x4283,x4284,x4282)) % 191.49/191.42 [429]~E(x4291,x4292)+E(f43(x4291,x4293),f43(x4292,x4293)) % 191.49/191.42 [430]~E(x4301,x4302)+E(f43(x4303,x4301),f43(x4303,x4302)) % 191.49/191.42 [431]~E(x4311,x4312)+E(f274(x4311,x4313,x4314,x4315),f274(x4312,x4313,x4314,x4315)) % 191.49/191.42 [432]~E(x4321,x4322)+E(f274(x4323,x4321,x4324,x4325),f274(x4323,x4322,x4324,x4325)) % 191.49/191.42 [433]~E(x4331,x4332)+E(f274(x4333,x4334,x4331,x4335),f274(x4333,x4334,x4332,x4335)) % 191.49/191.42 [434]~E(x4341,x4342)+E(f274(x4343,x4344,x4345,x4341),f274(x4343,x4344,x4345,x4342)) % 191.49/191.42 [435]~E(x4351,x4352)+E(f480(x4351,x4353),f480(x4352,x4353)) % 191.49/191.42 [436]~E(x4361,x4362)+E(f480(x4363,x4361),f480(x4363,x4362)) % 191.49/191.42 [437]~E(x4371,x4372)+E(f445(x4371,x4373),f445(x4372,x4373)) % 191.49/191.42 [438]~E(x4381,x4382)+E(f445(x4383,x4381),f445(x4383,x4382)) % 191.49/191.42 [439]~E(x4391,x4392)+E(f378(x4391,x4393,x4394),f378(x4392,x4393,x4394)) % 191.49/191.42 [440]~E(x4401,x4402)+E(f378(x4403,x4401,x4404),f378(x4403,x4402,x4404)) % 191.49/191.42 [441]~E(x4411,x4412)+E(f378(x4413,x4414,x4411),f378(x4413,x4414,x4412)) % 191.49/191.42 [442]~E(x4421,x4422)+E(f97(x4421,x4423,x4424,x4425),f97(x4422,x4423,x4424,x4425)) % 191.49/191.42 [443]~E(x4431,x4432)+E(f97(x4433,x4431,x4434,x4435),f97(x4433,x4432,x4434,x4435)) % 191.49/191.42 [444]~E(x4441,x4442)+E(f97(x4443,x4444,x4441,x4445),f97(x4443,x4444,x4442,x4445)) % 191.49/191.42 [445]~E(x4451,x4452)+E(f97(x4453,x4454,x4455,x4451),f97(x4453,x4454,x4455,x4452)) % 191.49/191.42 [446]~E(x4461,x4462)+E(f743(x4461,x4463,x4464),f743(x4462,x4463,x4464)) % 191.49/191.42 [447]~E(x4471,x4472)+E(f743(x4473,x4471,x4474),f743(x4473,x4472,x4474)) % 191.49/191.42 [448]~E(x4481,x4482)+E(f743(x4483,x4484,x4481),f743(x4483,x4484,x4482)) % 191.49/191.42 [449]~E(x4491,x4492)+E(f307(x4491,x4493,x4494),f307(x4492,x4493,x4494)) % 191.49/191.42 [450]~E(x4501,x4502)+E(f307(x4503,x4501,x4504),f307(x4503,x4502,x4504)) % 191.49/191.42 [451]~E(x4511,x4512)+E(f307(x4513,x4514,x4511),f307(x4513,x4514,x4512)) % 191.49/191.42 [452]~E(x4521,x4522)+E(f54(x4521,x4523),f54(x4522,x4523)) % 191.49/191.42 [453]~E(x4531,x4532)+E(f54(x4533,x4531),f54(x4533,x4532)) % 191.49/191.42 [454]~E(x4541,x4542)+E(f122(x4541,x4543,x4544),f122(x4542,x4543,x4544)) % 191.49/191.42 [455]~E(x4551,x4552)+E(f122(x4553,x4551,x4554),f122(x4553,x4552,x4554)) % 191.49/191.42 [456]~E(x4561,x4562)+E(f122(x4563,x4564,x4561),f122(x4563,x4564,x4562)) % 191.49/191.42 [457]~E(x4571,x4572)+E(f583(x4571,x4573),f583(x4572,x4573)) % 191.49/191.42 [458]~E(x4581,x4582)+E(f583(x4583,x4581),f583(x4583,x4582)) % 191.49/191.42 [459]~E(x4591,x4592)+E(f571(x4591,x4593,x4594,x4595,x4596,x4597),f571(x4592,x4593,x4594,x4595,x4596,x4597)) % 191.49/191.42 [460]~E(x4601,x4602)+E(f571(x4603,x4601,x4604,x4605,x4606,x4607),f571(x4603,x4602,x4604,x4605,x4606,x4607)) % 191.49/191.42 [461]~E(x4611,x4612)+E(f571(x4613,x4614,x4611,x4615,x4616,x4617),f571(x4613,x4614,x4612,x4615,x4616,x4617)) % 191.49/191.42 [462]~E(x4621,x4622)+E(f571(x4623,x4624,x4625,x4621,x4626,x4627),f571(x4623,x4624,x4625,x4622,x4626,x4627)) % 191.49/191.42 [463]~E(x4631,x4632)+E(f571(x4633,x4634,x4635,x4636,x4631,x4637),f571(x4633,x4634,x4635,x4636,x4632,x4637)) % 191.49/191.42 [464]~E(x4641,x4642)+E(f571(x4643,x4644,x4645,x4646,x4647,x4641),f571(x4643,x4644,x4645,x4646,x4647,x4642)) % 191.49/191.42 [465]~E(x4651,x4652)+E(f180(x4651,x4653),f180(x4652,x4653)) % 191.49/191.42 [466]~E(x4661,x4662)+E(f180(x4663,x4661),f180(x4663,x4662)) % 191.49/191.42 [467]~E(x4671,x4672)+E(f171(x4671,x4673,x4674),f171(x4672,x4673,x4674)) % 191.49/191.42 [468]~E(x4681,x4682)+E(f171(x4683,x4681,x4684),f171(x4683,x4682,x4684)) % 191.49/191.42 [469]~E(x4691,x4692)+E(f171(x4693,x4694,x4691),f171(x4693,x4694,x4692)) % 191.49/191.42 [470]~E(x4701,x4702)+E(f57(x4701),f57(x4702)) % 191.49/191.42 [471]~E(x4711,x4712)+E(f828(x4711,x4713,x4714,x4715,x4716),f828(x4712,x4713,x4714,x4715,x4716)) % 191.49/191.42 [472]~E(x4721,x4722)+E(f828(x4723,x4721,x4724,x4725,x4726),f828(x4723,x4722,x4724,x4725,x4726)) % 191.49/191.42 [473]~E(x4731,x4732)+E(f828(x4733,x4734,x4731,x4735,x4736),f828(x4733,x4734,x4732,x4735,x4736)) % 191.49/191.42 [474]~E(x4741,x4742)+E(f828(x4743,x4744,x4745,x4741,x4746),f828(x4743,x4744,x4745,x4742,x4746)) % 191.49/191.42 [475]~E(x4751,x4752)+E(f828(x4753,x4754,x4755,x4756,x4751),f828(x4753,x4754,x4755,x4756,x4752)) % 191.49/191.42 [476]~E(x4761,x4762)+E(f136(x4761,x4763),f136(x4762,x4763)) % 191.49/191.42 [477]~E(x4771,x4772)+E(f136(x4773,x4771),f136(x4773,x4772)) % 191.49/191.42 [478]~E(x4781,x4782)+E(f96(x4781,x4783,x4784),f96(x4782,x4783,x4784)) % 191.49/191.42 [479]~E(x4791,x4792)+E(f96(x4793,x4791,x4794),f96(x4793,x4792,x4794)) % 191.49/191.42 [480]~E(x4801,x4802)+E(f96(x4803,x4804,x4801),f96(x4803,x4804,x4802)) % 191.49/191.42 [481]~E(x4811,x4812)+E(f644(x4811,x4813,x4814,x4815),f644(x4812,x4813,x4814,x4815)) % 191.49/191.42 [482]~E(x4821,x4822)+E(f644(x4823,x4821,x4824,x4825),f644(x4823,x4822,x4824,x4825)) % 191.49/191.42 [483]~E(x4831,x4832)+E(f644(x4833,x4834,x4831,x4835),f644(x4833,x4834,x4832,x4835)) % 191.49/191.42 [484]~E(x4841,x4842)+E(f644(x4843,x4844,x4845,x4841),f644(x4843,x4844,x4845,x4842)) % 191.49/191.42 [485]~E(x4851,x4852)+E(f177(x4851,x4853,x4854),f177(x4852,x4853,x4854)) % 191.49/191.42 [486]~E(x4861,x4862)+E(f177(x4863,x4861,x4864),f177(x4863,x4862,x4864)) % 191.49/191.42 [487]~E(x4871,x4872)+E(f177(x4873,x4874,x4871),f177(x4873,x4874,x4872)) % 191.49/191.42 [488]~E(x4881,x4882)+E(f308(x4881),f308(x4882)) % 191.49/191.42 [489]~E(x4891,x4892)+E(f461(x4891,x4893,x4894,x4895),f461(x4892,x4893,x4894,x4895)) % 191.49/191.42 [490]~E(x4901,x4902)+E(f461(x4903,x4901,x4904,x4905),f461(x4903,x4902,x4904,x4905)) % 191.49/191.42 [491]~E(x4911,x4912)+E(f461(x4913,x4914,x4911,x4915),f461(x4913,x4914,x4912,x4915)) % 191.49/191.42 [492]~E(x4921,x4922)+E(f461(x4923,x4924,x4925,x4921),f461(x4923,x4924,x4925,x4922)) % 191.49/191.42 [493]~E(x4931,x4932)+E(f513(x4931,x4933,x4934),f513(x4932,x4933,x4934)) % 191.49/191.42 [494]~E(x4941,x4942)+E(f513(x4943,x4941,x4944),f513(x4943,x4942,x4944)) % 191.49/191.42 [495]~E(x4951,x4952)+E(f513(x4953,x4954,x4951),f513(x4953,x4954,x4952)) % 191.49/191.42 [496]~E(x4961,x4962)+E(f282(x4961,x4963,x4964,x4965),f282(x4962,x4963,x4964,x4965)) % 191.49/191.42 [497]~E(x4971,x4972)+E(f282(x4973,x4971,x4974,x4975),f282(x4973,x4972,x4974,x4975)) % 191.49/191.42 [498]~E(x4981,x4982)+E(f282(x4983,x4984,x4981,x4985),f282(x4983,x4984,x4982,x4985)) % 191.49/191.42 [499]~E(x4991,x4992)+E(f282(x4993,x4994,x4995,x4991),f282(x4993,x4994,x4995,x4992)) % 191.49/191.42 [500]~E(x5001,x5002)+E(f689(x5001,x5003,x5004,x5005,x5006),f689(x5002,x5003,x5004,x5005,x5006)) % 191.49/191.42 [501]~E(x5011,x5012)+E(f689(x5013,x5011,x5014,x5015,x5016),f689(x5013,x5012,x5014,x5015,x5016)) % 191.49/191.42 [502]~E(x5021,x5022)+E(f689(x5023,x5024,x5021,x5025,x5026),f689(x5023,x5024,x5022,x5025,x5026)) % 191.49/191.42 [503]~E(x5031,x5032)+E(f689(x5033,x5034,x5035,x5031,x5036),f689(x5033,x5034,x5035,x5032,x5036)) % 191.49/191.42 [504]~E(x5041,x5042)+E(f689(x5043,x5044,x5045,x5046,x5041),f689(x5043,x5044,x5045,x5046,x5042)) % 191.49/191.42 [505]~E(x5051,x5052)+E(f146(x5051,x5053),f146(x5052,x5053)) % 191.49/191.42 [506]~E(x5061,x5062)+E(f146(x5063,x5061),f146(x5063,x5062)) % 191.49/191.42 [507]~E(x5071,x5072)+E(f365(x5071,x5073,x5074,x5075),f365(x5072,x5073,x5074,x5075)) % 191.49/191.42 [508]~E(x5081,x5082)+E(f365(x5083,x5081,x5084,x5085),f365(x5083,x5082,x5084,x5085)) % 191.49/191.42 [509]~E(x5091,x5092)+E(f365(x5093,x5094,x5091,x5095),f365(x5093,x5094,x5092,x5095)) % 191.49/191.42 [510]~E(x5101,x5102)+E(f365(x5103,x5104,x5105,x5101),f365(x5103,x5104,x5105,x5102)) % 191.49/191.42 [511]~E(x5111,x5112)+E(f256(x5111),f256(x5112)) % 191.49/191.42 [512]~E(x5121,x5122)+E(f34(x5121,x5123),f34(x5122,x5123)) % 191.49/191.42 [513]~E(x5131,x5132)+E(f34(x5133,x5131),f34(x5133,x5132)) % 191.49/191.42 [514]~E(x5141,x5142)+E(f452(x5141,x5143,x5144),f452(x5142,x5143,x5144)) % 191.49/191.42 [515]~E(x5151,x5152)+E(f452(x5153,x5151,x5154),f452(x5153,x5152,x5154)) % 191.49/191.42 [516]~E(x5161,x5162)+E(f452(x5163,x5164,x5161),f452(x5163,x5164,x5162)) % 191.49/191.42 [517]~E(x5171,x5172)+E(f150(x5171,x5173,x5174,x5175,x5176),f150(x5172,x5173,x5174,x5175,x5176)) % 191.49/191.42 [518]~E(x5181,x5182)+E(f150(x5183,x5181,x5184,x5185,x5186),f150(x5183,x5182,x5184,x5185,x5186)) % 191.49/191.42 [519]~E(x5191,x5192)+E(f150(x5193,x5194,x5191,x5195,x5196),f150(x5193,x5194,x5192,x5195,x5196)) % 191.49/191.42 [520]~E(x5201,x5202)+E(f150(x5203,x5204,x5205,x5201,x5206),f150(x5203,x5204,x5205,x5202,x5206)) % 191.49/191.42 [521]~E(x5211,x5212)+E(f150(x5213,x5214,x5215,x5216,x5211),f150(x5213,x5214,x5215,x5216,x5212)) % 191.49/191.42 [522]~E(x5221,x5222)+E(f283(x5221,x5223,x5224),f283(x5222,x5223,x5224)) % 191.49/191.42 [523]~E(x5231,x5232)+E(f283(x5233,x5231,x5234),f283(x5233,x5232,x5234)) % 191.49/191.42 [524]~E(x5241,x5242)+E(f283(x5243,x5244,x5241),f283(x5243,x5244,x5242)) % 191.49/191.42 [525]~E(x5251,x5252)+E(f631(x5251,x5253,x5254,x5255,x5256,x5257),f631(x5252,x5253,x5254,x5255,x5256,x5257)) % 191.49/191.42 [526]~E(x5261,x5262)+E(f631(x5263,x5261,x5264,x5265,x5266,x5267),f631(x5263,x5262,x5264,x5265,x5266,x5267)) % 191.49/191.42 [527]~E(x5271,x5272)+E(f631(x5273,x5274,x5271,x5275,x5276,x5277),f631(x5273,x5274,x5272,x5275,x5276,x5277)) % 191.49/191.42 [528]~E(x5281,x5282)+E(f631(x5283,x5284,x5285,x5281,x5286,x5287),f631(x5283,x5284,x5285,x5282,x5286,x5287)) % 191.49/191.42 [529]~E(x5291,x5292)+E(f631(x5293,x5294,x5295,x5296,x5291,x5297),f631(x5293,x5294,x5295,x5296,x5292,x5297)) % 191.49/191.42 [530]~E(x5301,x5302)+E(f631(x5303,x5304,x5305,x5306,x5307,x5301),f631(x5303,x5304,x5305,x5306,x5307,x5302)) % 191.49/191.42 [531]~E(x5311,x5312)+E(f772(x5311,x5313,x5314),f772(x5312,x5313,x5314)) % 191.49/191.42 [532]~E(x5321,x5322)+E(f772(x5323,x5321,x5324),f772(x5323,x5322,x5324)) % 191.49/191.42 [533]~E(x5331,x5332)+E(f772(x5333,x5334,x5331),f772(x5333,x5334,x5332)) % 191.49/191.42 [534]~E(x5341,x5342)+E(f59(x5341),f59(x5342)) % 191.49/191.42 [535]~E(x5351,x5352)+E(f833(x5351,x5353,x5354),f833(x5352,x5353,x5354)) % 191.49/191.42 [536]~E(x5361,x5362)+E(f833(x5363,x5361,x5364),f833(x5363,x5362,x5364)) % 191.49/191.42 [537]~E(x5371,x5372)+E(f833(x5373,x5374,x5371),f833(x5373,x5374,x5372)) % 191.49/191.42 [538]~E(x5381,x5382)+E(f777(x5381,x5383,x5384,x5385,x5386),f777(x5382,x5383,x5384,x5385,x5386)) % 191.49/191.42 [539]~E(x5391,x5392)+E(f777(x5393,x5391,x5394,x5395,x5396),f777(x5393,x5392,x5394,x5395,x5396)) % 191.49/191.42 [540]~E(x5401,x5402)+E(f777(x5403,x5404,x5401,x5405,x5406),f777(x5403,x5404,x5402,x5405,x5406)) % 191.49/191.42 [541]~E(x5411,x5412)+E(f777(x5413,x5414,x5415,x5411,x5416),f777(x5413,x5414,x5415,x5412,x5416)) % 191.49/191.42 [542]~E(x5421,x5422)+E(f777(x5423,x5424,x5425,x5426,x5421),f777(x5423,x5424,x5425,x5426,x5422)) % 191.49/191.42 [543]~E(x5431,x5432)+E(f775(x5431,x5433,x5434,x5435,x5436),f775(x5432,x5433,x5434,x5435,x5436)) % 191.49/191.42 [544]~E(x5441,x5442)+E(f775(x5443,x5441,x5444,x5445,x5446),f775(x5443,x5442,x5444,x5445,x5446)) % 191.49/191.42 [545]~E(x5451,x5452)+E(f775(x5453,x5454,x5451,x5455,x5456),f775(x5453,x5454,x5452,x5455,x5456)) % 191.49/191.42 [546]~E(x5461,x5462)+E(f775(x5463,x5464,x5465,x5461,x5466),f775(x5463,x5464,x5465,x5462,x5466)) % 191.49/191.42 [547]~E(x5471,x5472)+E(f775(x5473,x5474,x5475,x5476,x5471),f775(x5473,x5474,x5475,x5476,x5472)) % 191.49/191.42 [548]~E(x5481,x5482)+E(f641(x5481,x5483,x5484,x5485),f641(x5482,x5483,x5484,x5485)) % 191.49/191.42 [549]~E(x5491,x5492)+E(f641(x5493,x5491,x5494,x5495),f641(x5493,x5492,x5494,x5495)) % 191.49/191.42 [550]~E(x5501,x5502)+E(f641(x5503,x5504,x5501,x5505),f641(x5503,x5504,x5502,x5505)) % 191.49/191.42 [551]~E(x5511,x5512)+E(f641(x5513,x5514,x5515,x5511),f641(x5513,x5514,x5515,x5512)) % 191.49/191.42 [552]~E(x5521,x5522)+E(f151(x5521,x5523,x5524,x5525),f151(x5522,x5523,x5524,x5525)) % 191.49/191.42 [553]~E(x5531,x5532)+E(f151(x5533,x5531,x5534,x5535),f151(x5533,x5532,x5534,x5535)) % 191.49/191.42 [554]~E(x5541,x5542)+E(f151(x5543,x5544,x5541,x5545),f151(x5543,x5544,x5542,x5545)) % 191.49/191.42 [555]~E(x5551,x5552)+E(f151(x5553,x5554,x5555,x5551),f151(x5553,x5554,x5555,x5552)) % 191.49/191.42 [556]~E(x5561,x5562)+E(f144(x5561,x5563),f144(x5562,x5563)) % 191.49/191.42 [557]~E(x5571,x5572)+E(f144(x5573,x5571),f144(x5573,x5572)) % 191.49/191.42 [558]~E(x5581,x5582)+E(f165(x5581,x5583,x5584,x5585),f165(x5582,x5583,x5584,x5585)) % 191.49/191.42 [559]~E(x5591,x5592)+E(f165(x5593,x5591,x5594,x5595),f165(x5593,x5592,x5594,x5595)) % 191.49/191.42 [560]~E(x5601,x5602)+E(f165(x5603,x5604,x5601,x5605),f165(x5603,x5604,x5602,x5605)) % 191.49/191.42 [561]~E(x5611,x5612)+E(f165(x5613,x5614,x5615,x5611),f165(x5613,x5614,x5615,x5612)) % 191.49/191.42 [562]~E(x5621,x5622)+E(f548(x5621,x5623,x5624,x5625),f548(x5622,x5623,x5624,x5625)) % 191.49/191.42 [563]~E(x5631,x5632)+E(f548(x5633,x5631,x5634,x5635),f548(x5633,x5632,x5634,x5635)) % 191.49/191.42 [564]~E(x5641,x5642)+E(f548(x5643,x5644,x5641,x5645),f548(x5643,x5644,x5642,x5645)) % 191.49/191.42 [565]~E(x5651,x5652)+E(f548(x5653,x5654,x5655,x5651),f548(x5653,x5654,x5655,x5652)) % 191.49/191.42 [566]~E(x5661,x5662)+E(f211(x5661),f211(x5662)) % 191.49/191.42 [567]~E(x5671,x5672)+E(f157(x5671,x5673,x5674,x5675),f157(x5672,x5673,x5674,x5675)) % 191.49/191.42 [568]~E(x5681,x5682)+E(f157(x5683,x5681,x5684,x5685),f157(x5683,x5682,x5684,x5685)) % 191.49/191.42 [569]~E(x5691,x5692)+E(f157(x5693,x5694,x5691,x5695),f157(x5693,x5694,x5692,x5695)) % 191.49/191.42 [570]~E(x5701,x5702)+E(f157(x5703,x5704,x5705,x5701),f157(x5703,x5704,x5705,x5702)) % 191.49/191.42 [571]~E(x5711,x5712)+E(f164(x5711,x5713,x5714,x5715),f164(x5712,x5713,x5714,x5715)) % 191.49/191.42 [572]~E(x5721,x5722)+E(f164(x5723,x5721,x5724,x5725),f164(x5723,x5722,x5724,x5725)) % 191.49/191.42 [573]~E(x5731,x5732)+E(f164(x5733,x5734,x5731,x5735),f164(x5733,x5734,x5732,x5735)) % 191.49/191.42 [574]~E(x5741,x5742)+E(f164(x5743,x5744,x5745,x5741),f164(x5743,x5744,x5745,x5742)) % 191.49/191.42 [575]~E(x5751,x5752)+E(f132(x5751,x5753,x5754,x5755,x5756),f132(x5752,x5753,x5754,x5755,x5756)) % 191.49/191.42 [576]~E(x5761,x5762)+E(f132(x5763,x5761,x5764,x5765,x5766),f132(x5763,x5762,x5764,x5765,x5766)) % 191.49/191.42 [577]~E(x5771,x5772)+E(f132(x5773,x5774,x5771,x5775,x5776),f132(x5773,x5774,x5772,x5775,x5776)) % 191.49/191.42 [578]~E(x5781,x5782)+E(f132(x5783,x5784,x5785,x5781,x5786),f132(x5783,x5784,x5785,x5782,x5786)) % 191.49/191.42 [579]~E(x5791,x5792)+E(f132(x5793,x5794,x5795,x5796,x5791),f132(x5793,x5794,x5795,x5796,x5792)) % 191.49/191.42 [580]~E(x5801,x5802)+E(f241(x5801,x5803),f241(x5802,x5803)) % 191.49/191.42 [581]~E(x5811,x5812)+E(f241(x5813,x5811),f241(x5813,x5812)) % 191.49/191.42 [582]~E(x5821,x5822)+E(f873(x5821,x5823,x5824,x5825,x5826,x5827),f873(x5822,x5823,x5824,x5825,x5826,x5827)) % 191.49/191.42 [583]~E(x5831,x5832)+E(f873(x5833,x5831,x5834,x5835,x5836,x5837),f873(x5833,x5832,x5834,x5835,x5836,x5837)) % 191.49/191.42 [584]~E(x5841,x5842)+E(f873(x5843,x5844,x5841,x5845,x5846,x5847),f873(x5843,x5844,x5842,x5845,x5846,x5847)) % 191.49/191.42 [585]~E(x5851,x5852)+E(f873(x5853,x5854,x5855,x5851,x5856,x5857),f873(x5853,x5854,x5855,x5852,x5856,x5857)) % 191.49/191.42 [586]~E(x5861,x5862)+E(f873(x5863,x5864,x5865,x5866,x5861,x5867),f873(x5863,x5864,x5865,x5866,x5862,x5867)) % 191.49/191.42 [587]~E(x5871,x5872)+E(f873(x5873,x5874,x5875,x5876,x5877,x5871),f873(x5873,x5874,x5875,x5876,x5877,x5872)) % 191.49/191.42 [588]~E(x5881,x5882)+E(f474(x5881,x5883,x5884),f474(x5882,x5883,x5884)) % 191.49/191.42 [589]~E(x5891,x5892)+E(f474(x5893,x5891,x5894),f474(x5893,x5892,x5894)) % 191.49/191.42 [590]~E(x5901,x5902)+E(f474(x5903,x5904,x5901),f474(x5903,x5904,x5902)) % 191.49/191.42 [591]~E(x5911,x5912)+E(f318(x5911),f318(x5912)) % 191.49/191.42 [592]~E(x5921,x5922)+E(f190(x5921,x5923,x5924),f190(x5922,x5923,x5924)) % 191.49/191.42 [593]~E(x5931,x5932)+E(f190(x5933,x5931,x5934),f190(x5933,x5932,x5934)) % 191.49/191.42 [594]~E(x5941,x5942)+E(f190(x5943,x5944,x5941),f190(x5943,x5944,x5942)) % 191.49/191.42 [595]~E(x5951,x5952)+E(f219(x5951,x5953,x5954,x5955),f219(x5952,x5953,x5954,x5955)) % 191.49/191.42 [596]~E(x5961,x5962)+E(f219(x5963,x5961,x5964,x5965),f219(x5963,x5962,x5964,x5965)) % 191.49/191.42 [597]~E(x5971,x5972)+E(f219(x5973,x5974,x5971,x5975),f219(x5973,x5974,x5972,x5975)) % 191.49/191.42 [598]~E(x5981,x5982)+E(f219(x5983,x5984,x5985,x5981),f219(x5983,x5984,x5985,x5982)) % 191.49/191.42 [599]~E(x5991,x5992)+E(f31(x5991,x5993,x5994),f31(x5992,x5993,x5994)) % 191.49/191.42 [600]~E(x6001,x6002)+E(f31(x6003,x6001,x6004),f31(x6003,x6002,x6004)) % 191.49/191.42 [601]~E(x6011,x6012)+E(f31(x6013,x6014,x6011),f31(x6013,x6014,x6012)) % 191.49/191.42 [602]~E(x6021,x6022)+E(f598(x6021,x6023,x6024,x6025,x6026),f598(x6022,x6023,x6024,x6025,x6026)) % 191.49/191.42 [603]~E(x6031,x6032)+E(f598(x6033,x6031,x6034,x6035,x6036),f598(x6033,x6032,x6034,x6035,x6036)) % 191.49/191.42 [604]~E(x6041,x6042)+E(f598(x6043,x6044,x6041,x6045,x6046),f598(x6043,x6044,x6042,x6045,x6046)) % 191.49/191.42 [605]~E(x6051,x6052)+E(f598(x6053,x6054,x6055,x6051,x6056),f598(x6053,x6054,x6055,x6052,x6056)) % 191.49/191.42 [606]~E(x6061,x6062)+E(f598(x6063,x6064,x6065,x6066,x6061),f598(x6063,x6064,x6065,x6066,x6062)) % 191.49/191.42 [607]~E(x6071,x6072)+E(f792(x6071,x6073,x6074),f792(x6072,x6073,x6074)) % 191.49/191.42 [608]~E(x6081,x6082)+E(f792(x6083,x6081,x6084),f792(x6083,x6082,x6084)) % 191.49/191.42 [609]~E(x6091,x6092)+E(f792(x6093,x6094,x6091),f792(x6093,x6094,x6092)) % 191.49/191.42 [610]~E(x6101,x6102)+E(f832(x6101,x6103,x6104),f832(x6102,x6103,x6104)) % 191.49/191.42 [611]~E(x6111,x6112)+E(f832(x6113,x6111,x6114),f832(x6113,x6112,x6114)) % 191.49/191.42 [612]~E(x6121,x6122)+E(f832(x6123,x6124,x6121),f832(x6123,x6124,x6122)) % 191.49/191.42 [613]~E(x6131,x6132)+E(f455(x6131,x6133,x6134),f455(x6132,x6133,x6134)) % 191.49/191.42 [614]~E(x6141,x6142)+E(f455(x6143,x6141,x6144),f455(x6143,x6142,x6144)) % 191.49/191.42 [615]~E(x6151,x6152)+E(f455(x6153,x6154,x6151),f455(x6153,x6154,x6152)) % 191.49/191.42 [616]~E(x6161,x6162)+E(f416(x6161,x6163,x6164),f416(x6162,x6163,x6164)) % 191.49/191.42 [617]~E(x6171,x6172)+E(f416(x6173,x6171,x6174),f416(x6173,x6172,x6174)) % 191.49/191.42 [618]~E(x6181,x6182)+E(f416(x6183,x6184,x6181),f416(x6183,x6184,x6182)) % 191.49/191.42 [619]~E(x6191,x6192)+E(f94(x6191,x6193,x6194),f94(x6192,x6193,x6194)) % 191.49/191.42 [620]~E(x6201,x6202)+E(f94(x6203,x6201,x6204),f94(x6203,x6202,x6204)) % 191.49/191.42 [621]~E(x6211,x6212)+E(f94(x6213,x6214,x6211),f94(x6213,x6214,x6212)) % 191.49/191.42 [622]~E(x6221,x6222)+E(f161(x6221,x6223),f161(x6222,x6223)) % 191.49/191.42 [623]~E(x6231,x6232)+E(f161(x6233,x6231),f161(x6233,x6232)) % 191.49/191.42 [624]~E(x6241,x6242)+E(f363(x6241),f363(x6242)) % 191.49/191.42 [625]~E(x6251,x6252)+E(f29(x6251,x6253,x6254),f29(x6252,x6253,x6254)) % 191.49/191.42 [626]~E(x6261,x6262)+E(f29(x6263,x6261,x6264),f29(x6263,x6262,x6264)) % 191.49/191.42 [627]~E(x6271,x6272)+E(f29(x6273,x6274,x6271),f29(x6273,x6274,x6272)) % 191.49/191.42 [628]~E(x6281,x6282)+E(f269(x6281,x6283,x6284),f269(x6282,x6283,x6284)) % 191.49/191.42 [629]~E(x6291,x6292)+E(f269(x6293,x6291,x6294),f269(x6293,x6292,x6294)) % 191.49/191.42 [630]~E(x6301,x6302)+E(f269(x6303,x6304,x6301),f269(x6303,x6304,x6302)) % 191.49/191.42 [631]~E(x6311,x6312)+E(f372(x6311),f372(x6312)) % 191.49/191.42 [632]~E(x6321,x6322)+E(f611(x6321,x6323,x6324,x6325),f611(x6322,x6323,x6324,x6325)) % 191.49/191.42 [633]~E(x6331,x6332)+E(f611(x6333,x6331,x6334,x6335),f611(x6333,x6332,x6334,x6335)) % 191.49/191.42 [634]~E(x6341,x6342)+E(f611(x6343,x6344,x6341,x6345),f611(x6343,x6344,x6342,x6345)) % 191.49/191.42 [635]~E(x6351,x6352)+E(f611(x6353,x6354,x6355,x6351),f611(x6353,x6354,x6355,x6352)) % 191.49/191.42 [636]~E(x6361,x6362)+E(f823(x6361,x6363,x6364),f823(x6362,x6363,x6364)) % 191.49/191.42 [637]~E(x6371,x6372)+E(f823(x6373,x6371,x6374),f823(x6373,x6372,x6374)) % 191.49/191.42 [638]~E(x6381,x6382)+E(f823(x6383,x6384,x6381),f823(x6383,x6384,x6382)) % 191.49/191.42 [639]~E(x6391,x6392)+E(f230(x6391,x6393,x6394,x6395),f230(x6392,x6393,x6394,x6395)) % 191.49/191.42 [640]~E(x6401,x6402)+E(f230(x6403,x6401,x6404,x6405),f230(x6403,x6402,x6404,x6405)) % 191.49/191.42 [641]~E(x6411,x6412)+E(f230(x6413,x6414,x6411,x6415),f230(x6413,x6414,x6412,x6415)) % 191.49/191.42 [642]~E(x6421,x6422)+E(f230(x6423,x6424,x6425,x6421),f230(x6423,x6424,x6425,x6422)) % 191.49/191.42 [643]~E(x6431,x6432)+E(f232(x6431,x6433,x6434),f232(x6432,x6433,x6434)) % 191.49/191.42 [644]~E(x6441,x6442)+E(f232(x6443,x6441,x6444),f232(x6443,x6442,x6444)) % 191.49/191.42 [645]~E(x6451,x6452)+E(f232(x6453,x6454,x6451),f232(x6453,x6454,x6452)) % 191.49/191.42 [646]~E(x6461,x6462)+E(f55(x6461,x6463),f55(x6462,x6463)) % 191.49/191.42 [647]~E(x6471,x6472)+E(f55(x6473,x6471),f55(x6473,x6472)) % 191.49/191.42 [648]~E(x6481,x6482)+E(f266(x6481,x6483,x6484),f266(x6482,x6483,x6484)) % 191.49/191.42 [649]~E(x6491,x6492)+E(f266(x6493,x6491,x6494),f266(x6493,x6492,x6494)) % 191.49/191.42 [650]~E(x6501,x6502)+E(f266(x6503,x6504,x6501),f266(x6503,x6504,x6502)) % 191.49/191.42 [651]~E(x6511,x6512)+E(f450(x6511,x6513,x6514,x6515),f450(x6512,x6513,x6514,x6515)) % 191.49/191.42 [652]~E(x6521,x6522)+E(f450(x6523,x6521,x6524,x6525),f450(x6523,x6522,x6524,x6525)) % 191.49/191.42 [653]~E(x6531,x6532)+E(f450(x6533,x6534,x6531,x6535),f450(x6533,x6534,x6532,x6535)) % 191.49/191.42 [654]~E(x6541,x6542)+E(f450(x6543,x6544,x6545,x6541),f450(x6543,x6544,x6545,x6542)) % 191.49/191.42 [655]~E(x6551,x6552)+E(f56(x6551,x6553,x6554),f56(x6552,x6553,x6554)) % 191.49/191.42 [656]~E(x6561,x6562)+E(f56(x6563,x6561,x6564),f56(x6563,x6562,x6564)) % 191.49/191.42 [657]~E(x6571,x6572)+E(f56(x6573,x6574,x6571),f56(x6573,x6574,x6572)) % 191.49/191.42 [658]~E(x6581,x6582)+E(f810(x6581,x6583,x6584),f810(x6582,x6583,x6584)) % 191.49/191.42 [659]~E(x6591,x6592)+E(f810(x6593,x6591,x6594),f810(x6593,x6592,x6594)) % 191.49/191.42 [660]~E(x6601,x6602)+E(f810(x6603,x6604,x6601),f810(x6603,x6604,x6602)) % 191.49/191.42 [661]~E(x6611,x6612)+E(f314(x6611,x6613),f314(x6612,x6613)) % 191.49/191.42 [662]~E(x6621,x6622)+E(f314(x6623,x6621),f314(x6623,x6622)) % 191.49/191.42 [663]~E(x6631,x6632)+E(f686(x6631,x6633,x6634,x6635),f686(x6632,x6633,x6634,x6635)) % 191.49/191.42 [664]~E(x6641,x6642)+E(f686(x6643,x6641,x6644,x6645),f686(x6643,x6642,x6644,x6645)) % 191.49/191.42 [665]~E(x6651,x6652)+E(f686(x6653,x6654,x6651,x6655),f686(x6653,x6654,x6652,x6655)) % 191.49/191.42 [666]~E(x6661,x6662)+E(f686(x6663,x6664,x6665,x6661),f686(x6663,x6664,x6665,x6662)) % 191.49/191.42 [667]~E(x6671,x6672)+E(f65(x6671,x6673),f65(x6672,x6673)) % 191.49/191.42 [668]~E(x6681,x6682)+E(f65(x6683,x6681),f65(x6683,x6682)) % 191.49/191.42 [669]~E(x6691,x6692)+E(f88(x6691),f88(x6692)) % 191.49/191.42 [670]~E(x6701,x6702)+E(f60(x6701),f60(x6702)) % 191.49/191.42 [671]~E(x6711,x6712)+E(f431(x6711,x6713),f431(x6712,x6713)) % 191.49/191.42 [672]~E(x6721,x6722)+E(f431(x6723,x6721),f431(x6723,x6722)) % 191.49/191.42 [673]~E(x6731,x6732)+E(f447(x6731,x6733),f447(x6732,x6733)) % 191.49/191.42 [674]~E(x6741,x6742)+E(f447(x6743,x6741),f447(x6743,x6742)) % 191.49/191.42 [675]~E(x6751,x6752)+E(f525(x6751,x6753,x6754,x6755),f525(x6752,x6753,x6754,x6755)) % 191.49/191.42 [676]~E(x6761,x6762)+E(f525(x6763,x6761,x6764,x6765),f525(x6763,x6762,x6764,x6765)) % 191.49/191.42 [677]~E(x6771,x6772)+E(f525(x6773,x6774,x6771,x6775),f525(x6773,x6774,x6772,x6775)) % 191.49/191.42 [678]~E(x6781,x6782)+E(f525(x6783,x6784,x6785,x6781),f525(x6783,x6784,x6785,x6782)) % 191.49/191.42 [679]~E(x6791,x6792)+E(f707(x6791,x6793,x6794,x6795),f707(x6792,x6793,x6794,x6795)) % 191.49/191.42 [680]~E(x6801,x6802)+E(f707(x6803,x6801,x6804,x6805),f707(x6803,x6802,x6804,x6805)) % 191.49/191.42 [681]~E(x6811,x6812)+E(f707(x6813,x6814,x6811,x6815),f707(x6813,x6814,x6812,x6815)) % 191.49/191.42 [682]~E(x6821,x6822)+E(f707(x6823,x6824,x6825,x6821),f707(x6823,x6824,x6825,x6822)) % 191.49/191.42 [683]~E(x6831,x6832)+E(f796(x6831,x6833,x6834),f796(x6832,x6833,x6834)) % 191.49/191.42 [684]~E(x6841,x6842)+E(f796(x6843,x6841,x6844),f796(x6843,x6842,x6844)) % 191.49/191.42 [685]~E(x6851,x6852)+E(f796(x6853,x6854,x6851),f796(x6853,x6854,x6852)) % 191.49/191.42 [686]~E(x6861,x6862)+E(f549(x6861,x6863,x6864,x6865,x6866),f549(x6862,x6863,x6864,x6865,x6866)) % 191.49/191.42 [687]~E(x6871,x6872)+E(f549(x6873,x6871,x6874,x6875,x6876),f549(x6873,x6872,x6874,x6875,x6876)) % 191.49/191.42 [688]~E(x6881,x6882)+E(f549(x6883,x6884,x6881,x6885,x6886),f549(x6883,x6884,x6882,x6885,x6886)) % 191.49/191.42 [689]~E(x6891,x6892)+E(f549(x6893,x6894,x6895,x6891,x6896),f549(x6893,x6894,x6895,x6892,x6896)) % 191.49/191.42 [690]~E(x6901,x6902)+E(f549(x6903,x6904,x6905,x6906,x6901),f549(x6903,x6904,x6905,x6906,x6902)) % 191.49/191.42 [691]~E(x6911,x6912)+E(f225(x6911,x6913),f225(x6912,x6913)) % 191.49/191.42 [692]~E(x6921,x6922)+E(f225(x6923,x6921),f225(x6923,x6922)) % 191.49/191.42 [693]~E(x6931,x6932)+E(f479(x6931,x6933,x6934),f479(x6932,x6933,x6934)) % 191.49/191.42 [694]~E(x6941,x6942)+E(f479(x6943,x6941,x6944),f479(x6943,x6942,x6944)) % 191.49/191.42 [695]~E(x6951,x6952)+E(f479(x6953,x6954,x6951),f479(x6953,x6954,x6952)) % 191.49/191.42 [696]~E(x6961,x6962)+E(f518(x6961,x6963,x6964,x6965,x6966,x6967),f518(x6962,x6963,x6964,x6965,x6966,x6967)) % 191.49/191.42 [697]~E(x6971,x6972)+E(f518(x6973,x6971,x6974,x6975,x6976,x6977),f518(x6973,x6972,x6974,x6975,x6976,x6977)) % 191.49/191.42 [698]~E(x6981,x6982)+E(f518(x6983,x6984,x6981,x6985,x6986,x6987),f518(x6983,x6984,x6982,x6985,x6986,x6987)) % 191.49/191.42 [699]~E(x6991,x6992)+E(f518(x6993,x6994,x6995,x6991,x6996,x6997),f518(x6993,x6994,x6995,x6992,x6996,x6997)) % 191.49/191.42 [700]~E(x7001,x7002)+E(f518(x7003,x7004,x7005,x7006,x7001,x7007),f518(x7003,x7004,x7005,x7006,x7002,x7007)) % 191.49/191.42 [701]~E(x7011,x7012)+E(f518(x7013,x7014,x7015,x7016,x7017,x7011),f518(x7013,x7014,x7015,x7016,x7017,x7012)) % 191.49/191.42 [702]~E(x7021,x7022)+E(f100(x7021,x7023,x7024,x7025),f100(x7022,x7023,x7024,x7025)) % 191.49/191.42 [703]~E(x7031,x7032)+E(f100(x7033,x7031,x7034,x7035),f100(x7033,x7032,x7034,x7035)) % 191.49/191.42 [704]~E(x7041,x7042)+E(f100(x7043,x7044,x7041,x7045),f100(x7043,x7044,x7042,x7045)) % 191.49/191.42 [705]~E(x7051,x7052)+E(f100(x7053,x7054,x7055,x7051),f100(x7053,x7054,x7055,x7052)) % 191.49/191.42 [706]~E(x7061,x7062)+E(f306(x7061,x7063,x7064),f306(x7062,x7063,x7064)) % 191.49/191.42 [707]~E(x7071,x7072)+E(f306(x7073,x7071,x7074),f306(x7073,x7072,x7074)) % 191.49/191.42 [708]~E(x7081,x7082)+E(f306(x7083,x7084,x7081),f306(x7083,x7084,x7082)) % 191.49/191.42 [709]~E(x7091,x7092)+E(f176(x7091,x7093,x7094),f176(x7092,x7093,x7094)) % 191.49/191.42 [710]~E(x7101,x7102)+E(f176(x7103,x7101,x7104),f176(x7103,x7102,x7104)) % 191.49/191.42 [711]~E(x7111,x7112)+E(f176(x7113,x7114,x7111),f176(x7113,x7114,x7112)) % 191.49/191.42 [712]~E(x7121,x7122)+E(f546(x7121,x7123,x7124,x7125,x7126),f546(x7122,x7123,x7124,x7125,x7126)) % 191.49/191.42 [713]~E(x7131,x7132)+E(f546(x7133,x7131,x7134,x7135,x7136),f546(x7133,x7132,x7134,x7135,x7136)) % 191.49/191.42 [714]~E(x7141,x7142)+E(f546(x7143,x7144,x7141,x7145,x7146),f546(x7143,x7144,x7142,x7145,x7146)) % 191.49/191.42 [715]~E(x7151,x7152)+E(f546(x7153,x7154,x7155,x7151,x7156),f546(x7153,x7154,x7155,x7152,x7156)) % 191.49/191.42 [716]~E(x7161,x7162)+E(f546(x7163,x7164,x7165,x7166,x7161),f546(x7163,x7164,x7165,x7166,x7162)) % 191.49/191.42 [717]~E(x7171,x7172)+E(f657(x7171,x7173),f657(x7172,x7173)) % 191.49/191.42 [718]~E(x7181,x7182)+E(f657(x7183,x7181),f657(x7183,x7182)) % 191.49/191.42 [719]~E(x7191,x7192)+E(f798(x7191,x7193,x7194),f798(x7192,x7193,x7194)) % 191.49/191.42 [720]~E(x7201,x7202)+E(f798(x7203,x7201,x7204),f798(x7203,x7202,x7204)) % 191.49/191.42 [721]~E(x7211,x7212)+E(f798(x7213,x7214,x7211),f798(x7213,x7214,x7212)) % 191.49/191.42 [722]~E(x7221,x7222)+E(f463(x7221,x7223,x7224,x7225),f463(x7222,x7223,x7224,x7225)) % 191.49/191.42 [723]~E(x7231,x7232)+E(f463(x7233,x7231,x7234,x7235),f463(x7233,x7232,x7234,x7235)) % 191.49/191.42 [724]~E(x7241,x7242)+E(f463(x7243,x7244,x7241,x7245),f463(x7243,x7244,x7242,x7245)) % 191.49/191.42 [725]~E(x7251,x7252)+E(f463(x7253,x7254,x7255,x7251),f463(x7253,x7254,x7255,x7252)) % 191.49/191.42 [726]~E(x7261,x7262)+E(f658(x7261,x7263,x7264),f658(x7262,x7263,x7264)) % 191.49/191.42 [727]~E(x7271,x7272)+E(f658(x7273,x7271,x7274),f658(x7273,x7272,x7274)) % 191.49/191.42 [728]~E(x7281,x7282)+E(f658(x7283,x7284,x7281),f658(x7283,x7284,x7282)) % 191.49/191.42 [729]~E(x7291,x7292)+E(f13(x7291,x7293),f13(x7292,x7293)) % 191.49/191.42 [730]~E(x7301,x7302)+E(f13(x7303,x7301),f13(x7303,x7302)) % 191.49/191.42 [731]~E(x7311,x7312)+E(f98(x7311,x7313,x7314),f98(x7312,x7313,x7314)) % 191.49/191.42 [732]~E(x7321,x7322)+E(f98(x7323,x7321,x7324),f98(x7323,x7322,x7324)) % 191.49/191.42 [733]~E(x7331,x7332)+E(f98(x7333,x7334,x7331),f98(x7333,x7334,x7332)) % 191.49/191.42 [734]~E(x7341,x7342)+E(f446(x7341,x7343),f446(x7342,x7343)) % 191.49/191.42 [735]~E(x7351,x7352)+E(f446(x7353,x7351),f446(x7353,x7352)) % 191.49/191.42 [736]~E(x7361,x7362)+E(f723(x7361,x7363),f723(x7362,x7363)) % 191.49/191.42 [737]~E(x7371,x7372)+E(f723(x7373,x7371),f723(x7373,x7372)) % 191.49/191.42 [738]~E(x7381,x7382)+E(f260(x7381,x7383),f260(x7382,x7383)) % 191.49/191.42 [739]~E(x7391,x7392)+E(f260(x7393,x7391),f260(x7393,x7392)) % 191.49/191.42 [740]~E(x7401,x7402)+E(f352(x7401,x7403,x7404),f352(x7402,x7403,x7404)) % 191.49/191.42 [741]~E(x7411,x7412)+E(f352(x7413,x7411,x7414),f352(x7413,x7412,x7414)) % 191.49/191.42 [742]~E(x7421,x7422)+E(f352(x7423,x7424,x7421),f352(x7423,x7424,x7422)) % 191.49/191.42 [743]~E(x7431,x7432)+E(f581(x7431,x7433,x7434),f581(x7432,x7433,x7434)) % 191.49/191.42 [744]~E(x7441,x7442)+E(f581(x7443,x7441,x7444),f581(x7443,x7442,x7444)) % 191.49/191.42 [745]~E(x7451,x7452)+E(f581(x7453,x7454,x7451),f581(x7453,x7454,x7452)) % 191.49/191.42 [746]~E(x7461,x7462)+E(f512(x7461,x7463,x7464),f512(x7462,x7463,x7464)) % 191.49/191.42 [747]~E(x7471,x7472)+E(f512(x7473,x7471,x7474),f512(x7473,x7472,x7474)) % 191.49/191.42 [748]~E(x7481,x7482)+E(f512(x7483,x7484,x7481),f512(x7483,x7484,x7482)) % 191.49/191.42 [749]~E(x7491,x7492)+E(f61(x7491,x7493,x7494,x7495),f61(x7492,x7493,x7494,x7495)) % 191.49/191.42 [750]~E(x7501,x7502)+E(f61(x7503,x7501,x7504,x7505),f61(x7503,x7502,x7504,x7505)) % 191.49/191.42 [751]~E(x7511,x7512)+E(f61(x7513,x7514,x7511,x7515),f61(x7513,x7514,x7512,x7515)) % 191.49/191.42 [752]~E(x7521,x7522)+E(f61(x7523,x7524,x7525,x7521),f61(x7523,x7524,x7525,x7522)) % 191.49/191.42 [753]~E(x7531,x7532)+E(f453(x7531,x7533,x7534),f453(x7532,x7533,x7534)) % 191.49/191.42 [754]~E(x7541,x7542)+E(f453(x7543,x7541,x7544),f453(x7543,x7542,x7544)) % 191.49/191.42 [755]~E(x7551,x7552)+E(f453(x7553,x7554,x7551),f453(x7553,x7554,x7552)) % 191.49/191.42 [756]~E(x7561,x7562)+E(f322(x7561,x7563),f322(x7562,x7563)) % 191.49/191.42 [757]~E(x7571,x7572)+E(f322(x7573,x7571),f322(x7573,x7572)) % 191.49/191.42 [758]~E(x7581,x7582)+E(f428(x7581,x7583,x7584,x7585),f428(x7582,x7583,x7584,x7585)) % 191.49/191.42 [759]~E(x7591,x7592)+E(f428(x7593,x7591,x7594,x7595),f428(x7593,x7592,x7594,x7595)) % 191.49/191.42 [760]~E(x7601,x7602)+E(f428(x7603,x7604,x7601,x7605),f428(x7603,x7604,x7602,x7605)) % 191.49/191.42 [761]~E(x7611,x7612)+E(f428(x7613,x7614,x7615,x7611),f428(x7613,x7614,x7615,x7612)) % 191.49/191.42 [762]~E(x7621,x7622)+E(f860(x7621,x7623,x7624),f860(x7622,x7623,x7624)) % 191.49/191.42 [763]~E(x7631,x7632)+E(f860(x7633,x7631,x7634),f860(x7633,x7632,x7634)) % 191.49/191.42 [764]~E(x7641,x7642)+E(f860(x7643,x7644,x7641),f860(x7643,x7644,x7642)) % 191.49/191.42 [765]~E(x7651,x7652)+E(f649(x7651,x7653,x7654),f649(x7652,x7653,x7654)) % 191.49/191.42 [766]~E(x7661,x7662)+E(f649(x7663,x7661,x7664),f649(x7663,x7662,x7664)) % 191.49/191.42 [767]~E(x7671,x7672)+E(f649(x7673,x7674,x7671),f649(x7673,x7674,x7672)) % 191.49/191.42 [768]~E(x7681,x7682)+E(f813(x7681,x7683,x7684),f813(x7682,x7683,x7684)) % 191.49/191.42 [769]~E(x7691,x7692)+E(f813(x7693,x7691,x7694),f813(x7693,x7692,x7694)) % 191.49/191.42 [770]~E(x7701,x7702)+E(f813(x7703,x7704,x7701),f813(x7703,x7704,x7702)) % 191.49/191.42 [771]~E(x7711,x7712)+E(f367(x7711,x7713,x7714,x7715),f367(x7712,x7713,x7714,x7715)) % 191.49/191.42 [772]~E(x7721,x7722)+E(f367(x7723,x7721,x7724,x7725),f367(x7723,x7722,x7724,x7725)) % 191.49/191.42 [773]~E(x7731,x7732)+E(f367(x7733,x7734,x7731,x7735),f367(x7733,x7734,x7732,x7735)) % 191.49/191.42 [774]~E(x7741,x7742)+E(f367(x7743,x7744,x7745,x7741),f367(x7743,x7744,x7745,x7742)) % 191.49/191.42 [775]~E(x7751,x7752)+E(f400(x7751,x7753,x7754,x7755),f400(x7752,x7753,x7754,x7755)) % 191.49/191.42 [776]~E(x7761,x7762)+E(f400(x7763,x7761,x7764,x7765),f400(x7763,x7762,x7764,x7765)) % 191.49/191.42 [777]~E(x7771,x7772)+E(f400(x7773,x7774,x7771,x7775),f400(x7773,x7774,x7772,x7775)) % 191.49/191.42 [778]~E(x7781,x7782)+E(f400(x7783,x7784,x7785,x7781),f400(x7783,x7784,x7785,x7782)) % 191.49/191.42 [779]~E(x7791,x7792)+E(f794(x7791,x7793,x7794),f794(x7792,x7793,x7794)) % 191.49/191.42 [780]~E(x7801,x7802)+E(f794(x7803,x7801,x7804),f794(x7803,x7802,x7804)) % 191.49/191.42 [781]~E(x7811,x7812)+E(f794(x7813,x7814,x7811),f794(x7813,x7814,x7812)) % 191.49/191.42 [782]~E(x7821,x7822)+E(f421(x7821,x7823,x7824,x7825),f421(x7822,x7823,x7824,x7825)) % 191.49/191.42 [783]~E(x7831,x7832)+E(f421(x7833,x7831,x7834,x7835),f421(x7833,x7832,x7834,x7835)) % 191.49/191.42 [784]~E(x7841,x7842)+E(f421(x7843,x7844,x7841,x7845),f421(x7843,x7844,x7842,x7845)) % 191.49/191.42 [785]~E(x7851,x7852)+E(f421(x7853,x7854,x7855,x7851),f421(x7853,x7854,x7855,x7852)) % 191.49/191.42 [786]~E(x7861,x7862)+E(f827(x7861,x7863,x7864,x7865,x7866),f827(x7862,x7863,x7864,x7865,x7866)) % 191.49/191.42 [787]~E(x7871,x7872)+E(f827(x7873,x7871,x7874,x7875,x7876),f827(x7873,x7872,x7874,x7875,x7876)) % 191.49/191.42 [788]~E(x7881,x7882)+E(f827(x7883,x7884,x7881,x7885,x7886),f827(x7883,x7884,x7882,x7885,x7886)) % 191.49/191.42 [789]~E(x7891,x7892)+E(f827(x7893,x7894,x7895,x7891,x7896),f827(x7893,x7894,x7895,x7892,x7896)) % 191.49/191.42 [790]~E(x7901,x7902)+E(f827(x7903,x7904,x7905,x7906,x7901),f827(x7903,x7904,x7905,x7906,x7902)) % 191.49/191.42 [791]~E(x7911,x7912)+E(f188(x7911,x7913,x7914,x7915),f188(x7912,x7913,x7914,x7915)) % 191.49/191.42 [792]~E(x7921,x7922)+E(f188(x7923,x7921,x7924,x7925),f188(x7923,x7922,x7924,x7925)) % 191.49/191.42 [793]~E(x7931,x7932)+E(f188(x7933,x7934,x7931,x7935),f188(x7933,x7934,x7932,x7935)) % 191.49/191.42 [794]~E(x7941,x7942)+E(f188(x7943,x7944,x7945,x7941),f188(x7943,x7944,x7945,x7942)) % 191.49/191.42 [795]~E(x7951,x7952)+E(f585(x7951,x7953,x7954),f585(x7952,x7953,x7954)) % 191.49/191.42 [796]~E(x7961,x7962)+E(f585(x7963,x7961,x7964),f585(x7963,x7962,x7964)) % 191.49/191.42 [797]~E(x7971,x7972)+E(f585(x7973,x7974,x7971),f585(x7973,x7974,x7972)) % 191.49/191.42 [798]~E(x7981,x7982)+E(f261(x7981,x7983),f261(x7982,x7983)) % 191.49/191.42 [799]~E(x7991,x7992)+E(f261(x7993,x7991),f261(x7993,x7992)) % 191.49/191.42 [800]~E(x8001,x8002)+E(f437(x8001,x8003,x8004,x8005),f437(x8002,x8003,x8004,x8005)) % 191.49/191.42 [801]~E(x8011,x8012)+E(f437(x8013,x8011,x8014,x8015),f437(x8013,x8012,x8014,x8015)) % 191.49/191.42 [802]~E(x8021,x8022)+E(f437(x8023,x8024,x8021,x8025),f437(x8023,x8024,x8022,x8025)) % 191.49/191.42 [803]~E(x8031,x8032)+E(f437(x8033,x8034,x8035,x8031),f437(x8033,x8034,x8035,x8032)) % 191.49/191.42 [804]~E(x8041,x8042)+E(f710(x8041,x8043,x8044,x8045),f710(x8042,x8043,x8044,x8045)) % 191.49/191.42 [805]~E(x8051,x8052)+E(f710(x8053,x8051,x8054,x8055),f710(x8053,x8052,x8054,x8055)) % 191.49/191.42 [806]~E(x8061,x8062)+E(f710(x8063,x8064,x8061,x8065),f710(x8063,x8064,x8062,x8065)) % 191.49/191.42 [807]~E(x8071,x8072)+E(f710(x8073,x8074,x8075,x8071),f710(x8073,x8074,x8075,x8072)) % 191.49/191.42 [808]~E(x8081,x8082)+E(f817(x8081,x8083,x8084,x8085),f817(x8082,x8083,x8084,x8085)) % 191.49/191.42 [809]~E(x8091,x8092)+E(f817(x8093,x8091,x8094,x8095),f817(x8093,x8092,x8094,x8095)) % 191.49/191.42 [810]~E(x8101,x8102)+E(f817(x8103,x8104,x8101,x8105),f817(x8103,x8104,x8102,x8105)) % 191.49/191.42 [811]~E(x8111,x8112)+E(f817(x8113,x8114,x8115,x8111),f817(x8113,x8114,x8115,x8112)) % 191.49/191.42 [812]~E(x8121,x8122)+E(f553(x8121),f553(x8122)) % 191.49/191.42 [813]~E(x8131,x8132)+E(f735(x8131,x8133,x8134,x8135,x8136,x8137),f735(x8132,x8133,x8134,x8135,x8136,x8137)) % 191.49/191.42 [814]~E(x8141,x8142)+E(f735(x8143,x8141,x8144,x8145,x8146,x8147),f735(x8143,x8142,x8144,x8145,x8146,x8147)) % 191.49/191.42 [815]~E(x8151,x8152)+E(f735(x8153,x8154,x8151,x8155,x8156,x8157),f735(x8153,x8154,x8152,x8155,x8156,x8157)) % 191.49/191.42 [816]~E(x8161,x8162)+E(f735(x8163,x8164,x8165,x8161,x8166,x8167),f735(x8163,x8164,x8165,x8162,x8166,x8167)) % 191.49/191.42 [817]~E(x8171,x8172)+E(f735(x8173,x8174,x8175,x8176,x8171,x8177),f735(x8173,x8174,x8175,x8176,x8172,x8177)) % 191.49/191.42 [818]~E(x8181,x8182)+E(f735(x8183,x8184,x8185,x8186,x8187,x8181),f735(x8183,x8184,x8185,x8186,x8187,x8182)) % 191.49/191.42 [819]~E(x8191,x8192)+E(f499(x8191,x8193,x8194),f499(x8192,x8193,x8194)) % 191.49/191.42 [820]~E(x8201,x8202)+E(f499(x8203,x8201,x8204),f499(x8203,x8202,x8204)) % 191.49/191.42 [821]~E(x8211,x8212)+E(f499(x8213,x8214,x8211),f499(x8213,x8214,x8212)) % 191.49/191.42 [822]~E(x8221,x8222)+E(f656(x8221,x8223),f656(x8222,x8223)) % 191.49/191.42 [823]~E(x8231,x8232)+E(f656(x8233,x8231),f656(x8233,x8232)) % 191.49/191.42 [824]~E(x8241,x8242)+E(f588(x8241,x8243,x8244),f588(x8242,x8243,x8244)) % 191.49/191.42 [825]~E(x8251,x8252)+E(f588(x8253,x8251,x8254),f588(x8253,x8252,x8254)) % 191.49/191.42 [826]~E(x8261,x8262)+E(f588(x8263,x8264,x8261),f588(x8263,x8264,x8262)) % 191.49/191.42 [827]~E(x8271,x8272)+E(f268(x8271,x8273,x8274),f268(x8272,x8273,x8274)) % 191.49/191.42 [828]~E(x8281,x8282)+E(f268(x8283,x8281,x8284),f268(x8283,x8282,x8284)) % 191.49/191.42 [829]~E(x8291,x8292)+E(f268(x8293,x8294,x8291),f268(x8293,x8294,x8292)) % 191.49/191.42 [830]~E(x8301,x8302)+E(f639(x8301,x8303,x8304),f639(x8302,x8303,x8304)) % 191.49/191.42 [831]~E(x8311,x8312)+E(f639(x8313,x8311,x8314),f639(x8313,x8312,x8314)) % 191.49/191.42 [832]~E(x8321,x8322)+E(f639(x8323,x8324,x8321),f639(x8323,x8324,x8322)) % 191.49/191.42 [833]~E(x8331,x8332)+E(f340(x8331),f340(x8332)) % 191.49/191.42 [834]~E(x8341,x8342)+E(f458(x8341,x8343,x8344),f458(x8342,x8343,x8344)) % 191.49/191.42 [835]~E(x8351,x8352)+E(f458(x8353,x8351,x8354),f458(x8353,x8352,x8354)) % 191.49/191.42 [836]~E(x8361,x8362)+E(f458(x8363,x8364,x8361),f458(x8363,x8364,x8362)) % 191.49/191.42 [837]~E(x8371,x8372)+E(f867(x8371,x8373,x8374,x8375),f867(x8372,x8373,x8374,x8375)) % 191.49/191.42 [838]~E(x8381,x8382)+E(f867(x8383,x8381,x8384,x8385),f867(x8383,x8382,x8384,x8385)) % 191.49/191.42 [839]~E(x8391,x8392)+E(f867(x8393,x8394,x8391,x8395),f867(x8393,x8394,x8392,x8395)) % 191.49/191.42 [840]~E(x8401,x8402)+E(f867(x8403,x8404,x8405,x8401),f867(x8403,x8404,x8405,x8402)) % 191.49/191.42 [841]~E(x8411,x8412)+E(f145(x8411,x8413),f145(x8412,x8413)) % 191.49/191.42 [842]~E(x8421,x8422)+E(f145(x8423,x8421),f145(x8423,x8422)) % 191.49/191.42 [843]~E(x8431,x8432)+E(f659(x8431,x8433,x8434),f659(x8432,x8433,x8434)) % 191.49/191.42 [844]~E(x8441,x8442)+E(f659(x8443,x8441,x8444),f659(x8443,x8442,x8444)) % 191.49/191.42 [845]~E(x8451,x8452)+E(f659(x8453,x8454,x8451),f659(x8453,x8454,x8452)) % 191.49/191.42 [846]~E(x8461,x8462)+E(f286(x8461),f286(x8462)) % 191.49/191.42 [847]~E(x8471,x8472)+E(f369(x8471,x8473,x8474,x8475),f369(x8472,x8473,x8474,x8475)) % 191.49/191.42 [848]~E(x8481,x8482)+E(f369(x8483,x8481,x8484,x8485),f369(x8483,x8482,x8484,x8485)) % 191.49/191.42 [849]~E(x8491,x8492)+E(f369(x8493,x8494,x8491,x8495),f369(x8493,x8494,x8492,x8495)) % 191.49/191.42 [850]~E(x8501,x8502)+E(f369(x8503,x8504,x8505,x8501),f369(x8503,x8504,x8505,x8502)) % 191.49/191.42 [851]~E(x8511,x8512)+E(f392(x8511,x8513),f392(x8512,x8513)) % 191.49/191.42 [852]~E(x8521,x8522)+E(f392(x8523,x8521),f392(x8523,x8522)) % 191.49/191.42 [853]~E(x8531,x8532)+E(f605(x8531,x8533,x8534),f605(x8532,x8533,x8534)) % 191.49/191.42 [854]~E(x8541,x8542)+E(f605(x8543,x8541,x8544),f605(x8543,x8542,x8544)) % 191.49/191.42 [855]~E(x8551,x8552)+E(f605(x8553,x8554,x8551),f605(x8553,x8554,x8552)) % 191.49/191.42 [856]~E(x8561,x8562)+E(f305(x8561),f305(x8562)) % 191.49/191.42 [857]~E(x8571,x8572)+E(f297(x8571,x8573,x8574,x8575),f297(x8572,x8573,x8574,x8575)) % 191.49/191.42 [858]~E(x8581,x8582)+E(f297(x8583,x8581,x8584,x8585),f297(x8583,x8582,x8584,x8585)) % 191.49/191.42 [859]~E(x8591,x8592)+E(f297(x8593,x8594,x8591,x8595),f297(x8593,x8594,x8592,x8595)) % 191.49/191.42 [860]~E(x8601,x8602)+E(f297(x8603,x8604,x8605,x8601),f297(x8603,x8604,x8605,x8602)) % 191.49/191.42 [861]~E(x8611,x8612)+E(f302(x8611),f302(x8612)) % 191.49/191.42 [862]~E(x8621,x8622)+E(f168(x8621,x8623,x8624),f168(x8622,x8623,x8624)) % 191.49/191.42 [863]~E(x8631,x8632)+E(f168(x8633,x8631,x8634),f168(x8633,x8632,x8634)) % 191.49/191.42 [864]~E(x8641,x8642)+E(f168(x8643,x8644,x8641),f168(x8643,x8644,x8642)) % 191.49/191.42 [865]~E(x8651,x8652)+E(f640(x8651,x8653,x8654,x8655,x8656),f640(x8652,x8653,x8654,x8655,x8656)) % 191.49/191.42 [866]~E(x8661,x8662)+E(f640(x8663,x8661,x8664,x8665,x8666),f640(x8663,x8662,x8664,x8665,x8666)) % 191.49/191.42 [867]~E(x8671,x8672)+E(f640(x8673,x8674,x8671,x8675,x8676),f640(x8673,x8674,x8672,x8675,x8676)) % 191.49/191.42 [868]~E(x8681,x8682)+E(f640(x8683,x8684,x8685,x8681,x8686),f640(x8683,x8684,x8685,x8682,x8686)) % 191.49/191.42 [869]~E(x8691,x8692)+E(f640(x8693,x8694,x8695,x8696,x8691),f640(x8693,x8694,x8695,x8696,x8692)) % 191.49/191.42 [870]~E(x8701,x8702)+E(f199(x8701,x8703),f199(x8702,x8703)) % 191.49/191.42 [871]~E(x8711,x8712)+E(f199(x8713,x8711),f199(x8713,x8712)) % 191.49/191.42 [872]~E(x8721,x8722)+E(f801(x8721,x8723,x8724,x8725),f801(x8722,x8723,x8724,x8725)) % 191.49/191.42 [873]~E(x8731,x8732)+E(f801(x8733,x8731,x8734,x8735),f801(x8733,x8732,x8734,x8735)) % 191.49/191.42 [874]~E(x8741,x8742)+E(f801(x8743,x8744,x8741,x8745),f801(x8743,x8744,x8742,x8745)) % 191.49/191.42 [875]~E(x8751,x8752)+E(f801(x8753,x8754,x8755,x8751),f801(x8753,x8754,x8755,x8752)) % 191.49/191.42 [876]~E(x8761,x8762)+E(f124(x8761,x8763),f124(x8762,x8763)) % 191.49/191.42 [877]~E(x8771,x8772)+E(f124(x8773,x8771),f124(x8773,x8772)) % 191.49/191.42 [878]~E(x8781,x8782)+E(f376(x8781,x8783,x8784),f376(x8782,x8783,x8784)) % 191.49/191.42 [879]~E(x8791,x8792)+E(f376(x8793,x8791,x8794),f376(x8793,x8792,x8794)) % 191.49/191.42 [880]~E(x8801,x8802)+E(f376(x8803,x8804,x8801),f376(x8803,x8804,x8802)) % 191.49/191.42 [881]~E(x8811,x8812)+E(f444(x8811,x8813,x8814,x8815),f444(x8812,x8813,x8814,x8815)) % 191.49/191.42 [882]~E(x8821,x8822)+E(f444(x8823,x8821,x8824,x8825),f444(x8823,x8822,x8824,x8825)) % 191.49/191.42 [883]~E(x8831,x8832)+E(f444(x8833,x8834,x8831,x8835),f444(x8833,x8834,x8832,x8835)) % 191.49/191.42 [884]~E(x8841,x8842)+E(f444(x8843,x8844,x8845,x8841),f444(x8843,x8844,x8845,x8842)) % 191.49/191.42 [885]~E(x8851,x8852)+E(f756(x8851,x8853,x8854),f756(x8852,x8853,x8854)) % 191.49/191.42 [886]~E(x8861,x8862)+E(f756(x8863,x8861,x8864),f756(x8863,x8862,x8864)) % 191.49/191.42 [887]~E(x8871,x8872)+E(f756(x8873,x8874,x8871),f756(x8873,x8874,x8872)) % 191.49/191.42 [888]~E(x8881,x8882)+E(f654(x8881,x8883),f654(x8882,x8883)) % 191.49/191.42 [889]~E(x8891,x8892)+E(f654(x8893,x8891),f654(x8893,x8892)) % 191.49/191.42 [890]~E(x8901,x8902)+E(f690(x8901,x8903,x8904,x8905,x8906),f690(x8902,x8903,x8904,x8905,x8906)) % 191.49/191.42 [891]~E(x8911,x8912)+E(f690(x8913,x8911,x8914,x8915,x8916),f690(x8913,x8912,x8914,x8915,x8916)) % 191.49/191.42 [892]~E(x8921,x8922)+E(f690(x8923,x8924,x8921,x8925,x8926),f690(x8923,x8924,x8922,x8925,x8926)) % 191.49/191.42 [893]~E(x8931,x8932)+E(f690(x8933,x8934,x8935,x8931,x8936),f690(x8933,x8934,x8935,x8932,x8936)) % 191.49/191.42 [894]~E(x8941,x8942)+E(f690(x8943,x8944,x8945,x8946,x8941),f690(x8943,x8944,x8945,x8946,x8942)) % 191.49/191.42 [895]~E(x8951,x8952)+E(f413(x8951,x8953),f413(x8952,x8953)) % 191.49/191.42 [896]~E(x8961,x8962)+E(f413(x8963,x8961),f413(x8963,x8962)) % 191.49/191.42 [897]~E(x8971,x8972)+E(f457(x8971,x8973,x8974,x8975),f457(x8972,x8973,x8974,x8975)) % 191.49/191.42 [898]~E(x8981,x8982)+E(f457(x8983,x8981,x8984,x8985),f457(x8983,x8982,x8984,x8985)) % 191.49/191.42 [899]~E(x8991,x8992)+E(f457(x8993,x8994,x8991,x8995),f457(x8993,x8994,x8992,x8995)) % 191.49/191.42 [900]~E(x9001,x9002)+E(f457(x9003,x9004,x9005,x9001),f457(x9003,x9004,x9005,x9002)) % 191.49/191.42 [901]~E(x9011,x9012)+E(f506(x9011,x9013,x9014),f506(x9012,x9013,x9014)) % 191.49/191.42 [902]~E(x9021,x9022)+E(f506(x9023,x9021,x9024),f506(x9023,x9022,x9024)) % 191.49/191.42 [903]~E(x9031,x9032)+E(f506(x9033,x9034,x9031),f506(x9033,x9034,x9032)) % 191.49/191.42 [904]~E(x9041,x9042)+E(f676(x9041,x9043,x9044,x9045),f676(x9042,x9043,x9044,x9045)) % 191.49/191.42 [905]~E(x9051,x9052)+E(f676(x9053,x9051,x9054,x9055),f676(x9053,x9052,x9054,x9055)) % 191.49/191.42 [906]~E(x9061,x9062)+E(f676(x9063,x9064,x9061,x9065),f676(x9063,x9064,x9062,x9065)) % 191.49/191.42 [907]~E(x9071,x9072)+E(f676(x9073,x9074,x9075,x9071),f676(x9073,x9074,x9075,x9072)) % 191.49/191.42 [908]~E(x9081,x9082)+E(f672(x9081,x9083,x9084),f672(x9082,x9083,x9084)) % 191.49/191.42 [909]~E(x9091,x9092)+E(f672(x9093,x9091,x9094),f672(x9093,x9092,x9094)) % 191.49/191.42 [910]~E(x9101,x9102)+E(f672(x9103,x9104,x9101),f672(x9103,x9104,x9102)) % 191.49/191.42 [911]~E(x9111,x9112)+E(f570(x9111,x9113,x9114,x9115),f570(x9112,x9113,x9114,x9115)) % 191.49/191.42 [912]~E(x9121,x9122)+E(f570(x9123,x9121,x9124,x9125),f570(x9123,x9122,x9124,x9125)) % 191.49/191.42 [913]~E(x9131,x9132)+E(f570(x9133,x9134,x9131,x9135),f570(x9133,x9134,x9132,x9135)) % 191.49/191.42 [914]~E(x9141,x9142)+E(f570(x9143,x9144,x9145,x9141),f570(x9143,x9144,x9145,x9142)) % 191.49/191.42 [915]~E(x9151,x9152)+E(f564(x9151,x9153,x9154,x9155,x9156,x9157,x9158),f564(x9152,x9153,x9154,x9155,x9156,x9157,x9158)) % 191.49/191.42 [916]~E(x9161,x9162)+E(f564(x9163,x9161,x9164,x9165,x9166,x9167,x9168),f564(x9163,x9162,x9164,x9165,x9166,x9167,x9168)) % 191.49/191.42 [917]~E(x9171,x9172)+E(f564(x9173,x9174,x9171,x9175,x9176,x9177,x9178),f564(x9173,x9174,x9172,x9175,x9176,x9177,x9178)) % 191.49/191.42 [918]~E(x9181,x9182)+E(f564(x9183,x9184,x9185,x9181,x9186,x9187,x9188),f564(x9183,x9184,x9185,x9182,x9186,x9187,x9188)) % 191.49/191.42 [919]~E(x9191,x9192)+E(f564(x9193,x9194,x9195,x9196,x9191,x9197,x9198),f564(x9193,x9194,x9195,x9196,x9192,x9197,x9198)) % 191.49/191.42 [920]~E(x9201,x9202)+E(f564(x9203,x9204,x9205,x9206,x9207,x9201,x9208),f564(x9203,x9204,x9205,x9206,x9207,x9202,x9208)) % 191.49/191.42 [921]~E(x9211,x9212)+E(f564(x9213,x9214,x9215,x9216,x9217,x9218,x9211),f564(x9213,x9214,x9215,x9216,x9217,x9218,x9212)) % 191.49/191.42 [922]~E(x9221,x9222)+E(f590(x9221,x9223,x9224,x9225,x9226),f590(x9222,x9223,x9224,x9225,x9226)) % 191.49/191.42 [923]~E(x9231,x9232)+E(f590(x9233,x9231,x9234,x9235,x9236),f590(x9233,x9232,x9234,x9235,x9236)) % 191.49/191.42 [924]~E(x9241,x9242)+E(f590(x9243,x9244,x9241,x9245,x9246),f590(x9243,x9244,x9242,x9245,x9246)) % 191.49/191.42 [925]~E(x9251,x9252)+E(f590(x9253,x9254,x9255,x9251,x9256),f590(x9253,x9254,x9255,x9252,x9256)) % 191.49/191.42 [926]~E(x9261,x9262)+E(f590(x9263,x9264,x9265,x9266,x9261),f590(x9263,x9264,x9265,x9266,x9262)) % 191.49/191.42 [927]~E(x9271,x9272)+E(f773(x9271,x9273,x9274),f773(x9272,x9273,x9274)) % 191.49/191.42 [928]~E(x9281,x9282)+E(f773(x9283,x9281,x9284),f773(x9283,x9282,x9284)) % 191.49/191.42 [929]~E(x9291,x9292)+E(f773(x9293,x9294,x9291),f773(x9293,x9294,x9292)) % 191.49/191.42 [930]~E(x9301,x9302)+E(f163(x9301,x9303),f163(x9302,x9303)) % 191.49/191.42 [931]~E(x9311,x9312)+E(f163(x9313,x9311),f163(x9313,x9312)) % 191.49/191.42 [932]~E(x9321,x9322)+E(f712(x9321,x9323,x9324),f712(x9322,x9323,x9324)) % 191.49/191.42 [933]~E(x9331,x9332)+E(f712(x9333,x9331,x9334),f712(x9333,x9332,x9334)) % 191.49/191.42 [934]~E(x9341,x9342)+E(f712(x9343,x9344,x9341),f712(x9343,x9344,x9342)) % 191.49/191.42 [935]~E(x9351,x9352)+E(f398(x9351,x9353,x9354),f398(x9352,x9353,x9354)) % 191.49/191.42 [936]~E(x9361,x9362)+E(f398(x9363,x9361,x9364),f398(x9363,x9362,x9364)) % 191.49/191.42 [937]~E(x9371,x9372)+E(f398(x9373,x9374,x9371),f398(x9373,x9374,x9372)) % 191.49/191.42 [938]~E(x9381,x9382)+E(f353(x9381,x9383,x9384,x9385),f353(x9382,x9383,x9384,x9385)) % 191.49/191.42 [939]~E(x9391,x9392)+E(f353(x9393,x9391,x9394,x9395),f353(x9393,x9392,x9394,x9395)) % 191.49/191.42 [940]~E(x9401,x9402)+E(f353(x9403,x9404,x9401,x9405),f353(x9403,x9404,x9402,x9405)) % 191.49/191.42 [941]~E(x9411,x9412)+E(f353(x9413,x9414,x9415,x9411),f353(x9413,x9414,x9415,x9412)) % 191.49/191.42 [942]~E(x9421,x9422)+E(f592(x9421,x9423,x9424,x9425,x9426),f592(x9422,x9423,x9424,x9425,x9426)) % 191.49/191.42 [943]~E(x9431,x9432)+E(f592(x9433,x9431,x9434,x9435,x9436),f592(x9433,x9432,x9434,x9435,x9436)) % 191.49/191.42 [944]~E(x9441,x9442)+E(f592(x9443,x9444,x9441,x9445,x9446),f592(x9443,x9444,x9442,x9445,x9446)) % 191.49/191.42 [945]~E(x9451,x9452)+E(f592(x9453,x9454,x9455,x9451,x9456),f592(x9453,x9454,x9455,x9452,x9456)) % 191.49/191.42 [946]~E(x9461,x9462)+E(f592(x9463,x9464,x9465,x9466,x9461),f592(x9463,x9464,x9465,x9466,x9462)) % 191.49/191.42 [947]~E(x9471,x9472)+E(f530(x9471,x9473,x9474,x9475,x9476),f530(x9472,x9473,x9474,x9475,x9476)) % 191.49/191.42 [948]~E(x9481,x9482)+E(f530(x9483,x9481,x9484,x9485,x9486),f530(x9483,x9482,x9484,x9485,x9486)) % 191.49/191.42 [949]~E(x9491,x9492)+E(f530(x9493,x9494,x9491,x9495,x9496),f530(x9493,x9494,x9492,x9495,x9496)) % 191.49/191.42 [950]~E(x9501,x9502)+E(f530(x9503,x9504,x9505,x9501,x9506),f530(x9503,x9504,x9505,x9502,x9506)) % 191.49/191.42 [951]~E(x9511,x9512)+E(f530(x9513,x9514,x9515,x9516,x9511),f530(x9513,x9514,x9515,x9516,x9512)) % 191.49/191.42 [952]~E(x9521,x9522)+E(f809(x9521,x9523,x9524),f809(x9522,x9523,x9524)) % 191.49/191.42 [953]~E(x9531,x9532)+E(f809(x9533,x9531,x9534),f809(x9533,x9532,x9534)) % 191.49/191.42 [954]~E(x9541,x9542)+E(f809(x9543,x9544,x9541),f809(x9543,x9544,x9542)) % 191.49/191.42 [955]~E(x9551,x9552)+E(f708(x9551,x9553,x9554,x9555,x9556),f708(x9552,x9553,x9554,x9555,x9556)) % 191.49/191.42 [956]~E(x9561,x9562)+E(f708(x9563,x9561,x9564,x9565,x9566),f708(x9563,x9562,x9564,x9565,x9566)) % 191.49/191.42 [957]~E(x9571,x9572)+E(f708(x9573,x9574,x9571,x9575,x9576),f708(x9573,x9574,x9572,x9575,x9576)) % 191.49/191.42 [958]~E(x9581,x9582)+E(f708(x9583,x9584,x9585,x9581,x9586),f708(x9583,x9584,x9585,x9582,x9586)) % 191.49/191.42 [959]~E(x9591,x9592)+E(f708(x9593,x9594,x9595,x9596,x9591),f708(x9593,x9594,x9595,x9596,x9592)) % 191.49/191.42 [960]~E(x9601,x9602)+E(f683(x9601,x9603,x9604),f683(x9602,x9603,x9604)) % 191.49/191.42 [961]~E(x9611,x9612)+E(f683(x9613,x9611,x9614),f683(x9613,x9612,x9614)) % 191.49/191.42 [962]~E(x9621,x9622)+E(f683(x9623,x9624,x9621),f683(x9623,x9624,x9622)) % 191.49/191.42 [963]~E(x9631,x9632)+E(f620(x9631,x9633,x9634,x9635,x9636,x9637,x9638,x9639),f620(x9632,x9633,x9634,x9635,x9636,x9637,x9638,x9639)) % 191.49/191.42 [964]~E(x9641,x9642)+E(f620(x9643,x9641,x9644,x9645,x9646,x9647,x9648,x9649),f620(x9643,x9642,x9644,x9645,x9646,x9647,x9648,x9649)) % 191.49/191.42 [965]~E(x9651,x9652)+E(f620(x9653,x9654,x9651,x9655,x9656,x9657,x9658,x9659),f620(x9653,x9654,x9652,x9655,x9656,x9657,x9658,x9659)) % 191.49/191.42 [966]~E(x9661,x9662)+E(f620(x9663,x9664,x9665,x9661,x9666,x9667,x9668,x9669),f620(x9663,x9664,x9665,x9662,x9666,x9667,x9668,x9669)) % 191.49/191.42 [967]~E(x9671,x9672)+E(f620(x9673,x9674,x9675,x9676,x9671,x9677,x9678,x9679),f620(x9673,x9674,x9675,x9676,x9672,x9677,x9678,x9679)) % 191.49/191.42 [968]~E(x9681,x9682)+E(f620(x9683,x9684,x9685,x9686,x9687,x9681,x9688,x9689),f620(x9683,x9684,x9685,x9686,x9687,x9682,x9688,x9689)) % 191.49/191.42 [969]~E(x9691,x9692)+E(f620(x9693,x9694,x9695,x9696,x9697,x9698,x9691,x9699),f620(x9693,x9694,x9695,x9696,x9697,x9698,x9692,x9699)) % 191.49/191.42 [970]~E(x9701,x9702)+E(f620(x9703,x9704,x9705,x9706,x9707,x9708,x9709,x9701),f620(x9703,x9704,x9705,x9706,x9707,x9708,x9709,x9702)) % 191.49/191.42 [971]~E(x9711,x9712)+E(f77(x9711,x9713,x9714,x9715,x9716),f77(x9712,x9713,x9714,x9715,x9716)) % 191.49/191.42 [972]~E(x9721,x9722)+E(f77(x9723,x9721,x9724,x9725,x9726),f77(x9723,x9722,x9724,x9725,x9726)) % 191.49/191.42 [973]~E(x9731,x9732)+E(f77(x9733,x9734,x9731,x9735,x9736),f77(x9733,x9734,x9732,x9735,x9736)) % 191.49/191.42 [974]~E(x9741,x9742)+E(f77(x9743,x9744,x9745,x9741,x9746),f77(x9743,x9744,x9745,x9742,x9746)) % 191.49/191.42 [975]~E(x9751,x9752)+E(f77(x9753,x9754,x9755,x9756,x9751),f77(x9753,x9754,x9755,x9756,x9752)) % 191.49/191.42 [976]~E(x9761,x9762)+E(f346(x9761,x9763,x9764),f346(x9762,x9763,x9764)) % 191.49/191.42 [977]~E(x9771,x9772)+E(f346(x9773,x9771,x9774),f346(x9773,x9772,x9774)) % 191.49/191.42 [978]~E(x9781,x9782)+E(f346(x9783,x9784,x9781),f346(x9783,x9784,x9782)) % 191.49/191.42 [979]~E(x9791,x9792)+E(f533(x9791,x9793,x9794,x9795,x9796,x9797,x9798,x9799),f533(x9792,x9793,x9794,x9795,x9796,x9797,x9798,x9799)) % 191.49/191.42 [980]~E(x9801,x9802)+E(f533(x9803,x9801,x9804,x9805,x9806,x9807,x9808,x9809),f533(x9803,x9802,x9804,x9805,x9806,x9807,x9808,x9809)) % 191.49/191.42 [981]~E(x9811,x9812)+E(f533(x9813,x9814,x9811,x9815,x9816,x9817,x9818,x9819),f533(x9813,x9814,x9812,x9815,x9816,x9817,x9818,x9819)) % 191.49/191.42 [982]~E(x9821,x9822)+E(f533(x9823,x9824,x9825,x9821,x9826,x9827,x9828,x9829),f533(x9823,x9824,x9825,x9822,x9826,x9827,x9828,x9829)) % 191.49/191.42 [983]~E(x9831,x9832)+E(f533(x9833,x9834,x9835,x9836,x9831,x9837,x9838,x9839),f533(x9833,x9834,x9835,x9836,x9832,x9837,x9838,x9839)) % 191.49/191.42 [984]~E(x9841,x9842)+E(f533(x9843,x9844,x9845,x9846,x9847,x9841,x9848,x9849),f533(x9843,x9844,x9845,x9846,x9847,x9842,x9848,x9849)) % 191.49/191.42 [985]~E(x9851,x9852)+E(f533(x9853,x9854,x9855,x9856,x9857,x9858,x9851,x9859),f533(x9853,x9854,x9855,x9856,x9857,x9858,x9852,x9859)) % 191.49/191.42 [986]~E(x9861,x9862)+E(f533(x9863,x9864,x9865,x9866,x9867,x9868,x9869,x9861),f533(x9863,x9864,x9865,x9866,x9867,x9868,x9869,x9862)) % 191.49/191.42 [987]~E(x9871,x9872)+E(f864(x9871,x9873,x9874,x9875),f864(x9872,x9873,x9874,x9875)) % 191.49/191.42 [988]~E(x9881,x9882)+E(f864(x9883,x9881,x9884,x9885),f864(x9883,x9882,x9884,x9885)) % 191.49/191.42 [989]~E(x9891,x9892)+E(f864(x9893,x9894,x9891,x9895),f864(x9893,x9894,x9892,x9895)) % 191.49/191.42 [990]~E(x9901,x9902)+E(f864(x9903,x9904,x9905,x9901),f864(x9903,x9904,x9905,x9902)) % 191.49/191.42 [991]~E(x9911,x9912)+E(f48(x9911,x9913),f48(x9912,x9913)) % 191.49/191.42 [992]~E(x9921,x9922)+E(f48(x9923,x9921),f48(x9923,x9922)) % 191.49/191.42 [993]~E(x9931,x9932)+E(f843(x9931,x9933),f843(x9932,x9933)) % 191.49/191.42 [994]~E(x9941,x9942)+E(f843(x9943,x9941),f843(x9943,x9942)) % 191.49/191.42 [995]~E(x9951,x9952)+E(f619(x9951,x9953,x9954,x9955,x9956),f619(x9952,x9953,x9954,x9955,x9956)) % 191.49/191.42 [996]~E(x9961,x9962)+E(f619(x9963,x9961,x9964,x9965,x9966),f619(x9963,x9962,x9964,x9965,x9966)) % 191.49/191.42 [997]~E(x9971,x9972)+E(f619(x9973,x9974,x9971,x9975,x9976),f619(x9973,x9974,x9972,x9975,x9976)) % 191.49/191.42 [998]~E(x9981,x9982)+E(f619(x9983,x9984,x9985,x9981,x9986),f619(x9983,x9984,x9985,x9982,x9986)) % 191.49/191.42 [999]~E(x9991,x9992)+E(f619(x9993,x9994,x9995,x9996,x9991),f619(x9993,x9994,x9995,x9996,x9992)) % 191.49/191.42 [1000]~E(x10001,x10002)+E(f858(x10001,x10003,x10004,x10005,x10006),f858(x10002,x10003,x10004,x10005,x10006)) % 191.49/191.42 [1001]~E(x10011,x10012)+E(f858(x10013,x10011,x10014,x10015,x10016),f858(x10013,x10012,x10014,x10015,x10016)) % 191.49/191.42 [1002]~E(x10021,x10022)+E(f858(x10023,x10024,x10021,x10025,x10026),f858(x10023,x10024,x10022,x10025,x10026)) % 191.49/191.42 [1003]~E(x10031,x10032)+E(f858(x10033,x10034,x10035,x10031,x10036),f858(x10033,x10034,x10035,x10032,x10036)) % 191.49/191.42 [1004]~E(x10041,x10042)+E(f858(x10043,x10044,x10045,x10046,x10041),f858(x10043,x10044,x10045,x10046,x10042)) % 191.49/191.42 [1005]~E(x10051,x10052)+E(f700(x10051,x10053),f700(x10052,x10053)) % 191.49/191.42 [1006]~E(x10061,x10062)+E(f700(x10063,x10061),f700(x10063,x10062)) % 191.49/191.42 [1007]~E(x10071,x10072)+E(f196(x10071,x10073,x10074,x10075),f196(x10072,x10073,x10074,x10075)) % 191.49/191.42 [1008]~E(x10081,x10082)+E(f196(x10083,x10081,x10084,x10085),f196(x10083,x10082,x10084,x10085)) % 191.49/191.42 [1009]~E(x10091,x10092)+E(f196(x10093,x10094,x10091,x10095),f196(x10093,x10094,x10092,x10095)) % 191.49/191.42 [1010]~E(x10101,x10102)+E(f196(x10103,x10104,x10105,x10101),f196(x10103,x10104,x10105,x10102)) % 191.49/191.42 [1011]~E(x10111,x10112)+E(f522(x10111,x10113,x10114,x10115,x10116),f522(x10112,x10113,x10114,x10115,x10116)) % 191.49/191.42 [1012]~E(x10121,x10122)+E(f522(x10123,x10121,x10124,x10125,x10126),f522(x10123,x10122,x10124,x10125,x10126)) % 191.49/191.42 [1013]~E(x10131,x10132)+E(f522(x10133,x10134,x10131,x10135,x10136),f522(x10133,x10134,x10132,x10135,x10136)) % 191.49/191.42 [1014]~E(x10141,x10142)+E(f522(x10143,x10144,x10145,x10141,x10146),f522(x10143,x10144,x10145,x10142,x10146)) % 191.49/191.42 [1015]~E(x10151,x10152)+E(f522(x10153,x10154,x10155,x10156,x10151),f522(x10153,x10154,x10155,x10156,x10152)) % 191.49/191.42 [1016]~E(x10161,x10162)+E(f730(x10161,x10163,x10164,x10165),f730(x10162,x10163,x10164,x10165)) % 191.49/191.42 [1017]~E(x10171,x10172)+E(f730(x10173,x10171,x10174,x10175),f730(x10173,x10172,x10174,x10175)) % 191.49/191.42 [1018]~E(x10181,x10182)+E(f730(x10183,x10184,x10181,x10185),f730(x10183,x10184,x10182,x10185)) % 191.49/191.42 [1019]~E(x10191,x10192)+E(f730(x10193,x10194,x10195,x10191),f730(x10193,x10194,x10195,x10192)) % 191.49/191.42 [1020]~E(x10201,x10202)+E(f300(x10201,x10203,x10204,x10205),f300(x10202,x10203,x10204,x10205)) % 191.49/191.42 [1021]~E(x10211,x10212)+E(f300(x10213,x10211,x10214,x10215),f300(x10213,x10212,x10214,x10215)) % 191.49/191.42 [1022]~E(x10221,x10222)+E(f300(x10223,x10224,x10221,x10225),f300(x10223,x10224,x10222,x10225)) % 191.49/191.42 [1023]~E(x10231,x10232)+E(f300(x10233,x10234,x10235,x10231),f300(x10233,x10234,x10235,x10232)) % 191.49/191.42 [1024]~E(x10241,x10242)+E(f220(x10241,x10243,x10244,x10245),f220(x10242,x10243,x10244,x10245)) % 191.49/191.42 [1025]~E(x10251,x10252)+E(f220(x10253,x10251,x10254,x10255),f220(x10253,x10252,x10254,x10255)) % 191.49/191.42 [1026]~E(x10261,x10262)+E(f220(x10263,x10264,x10261,x10265),f220(x10263,x10264,x10262,x10265)) % 191.49/191.42 [1027]~E(x10271,x10272)+E(f220(x10273,x10274,x10275,x10271),f220(x10273,x10274,x10275,x10272)) % 191.49/191.42 [1028]~E(x10281,x10282)+E(f703(x10281,x10283,x10284),f703(x10282,x10283,x10284)) % 191.49/191.42 [1029]~E(x10291,x10292)+E(f703(x10293,x10291,x10294),f703(x10293,x10292,x10294)) % 191.49/191.42 [1030]~E(x10301,x10302)+E(f703(x10303,x10304,x10301),f703(x10303,x10304,x10302)) % 191.49/191.42 [1031]~E(x10311,x10312)+E(f569(x10311,x10313,x10314),f569(x10312,x10313,x10314)) % 191.49/191.42 [1032]~E(x10321,x10322)+E(f569(x10323,x10321,x10324),f569(x10323,x10322,x10324)) % 191.49/191.42 [1033]~E(x10331,x10332)+E(f569(x10333,x10334,x10331),f569(x10333,x10334,x10332)) % 191.49/191.42 [1034]~E(x10341,x10342)+E(f728(x10341,x10343,x10344),f728(x10342,x10343,x10344)) % 191.49/191.42 [1035]~E(x10351,x10352)+E(f728(x10353,x10351,x10354),f728(x10353,x10352,x10354)) % 191.49/191.42 [1036]~E(x10361,x10362)+E(f728(x10363,x10364,x10361),f728(x10363,x10364,x10362)) % 191.49/191.42 [1037]~E(x10371,x10372)+E(f281(x10371,x10373),f281(x10372,x10373)) % 191.49/191.42 [1038]~E(x10381,x10382)+E(f281(x10383,x10381),f281(x10383,x10382)) % 191.49/191.42 [1039]~E(x10391,x10392)+E(f724(x10391,x10393),f724(x10392,x10393)) % 191.49/191.42 [1040]~E(x10401,x10402)+E(f724(x10403,x10401),f724(x10403,x10402)) % 191.49/191.42 [1041]~E(x10411,x10412)+E(f850(x10411,x10413,x10414,x10415,x10416),f850(x10412,x10413,x10414,x10415,x10416)) % 191.49/191.42 [1042]~E(x10421,x10422)+E(f850(x10423,x10421,x10424,x10425,x10426),f850(x10423,x10422,x10424,x10425,x10426)) % 191.49/191.42 [1043]~E(x10431,x10432)+E(f850(x10433,x10434,x10431,x10435,x10436),f850(x10433,x10434,x10432,x10435,x10436)) % 191.49/191.42 [1044]~E(x10441,x10442)+E(f850(x10443,x10444,x10445,x10441,x10446),f850(x10443,x10444,x10445,x10442,x10446)) % 191.49/191.42 [1045]~E(x10451,x10452)+E(f850(x10453,x10454,x10455,x10456,x10451),f850(x10453,x10454,x10455,x10456,x10452)) % 191.49/191.42 [1046]~E(x10461,x10462)+E(f853(x10461,x10463,x10464,x10465),f853(x10462,x10463,x10464,x10465)) % 191.49/191.42 [1047]~E(x10471,x10472)+E(f853(x10473,x10471,x10474,x10475),f853(x10473,x10472,x10474,x10475)) % 191.49/191.42 [1048]~E(x10481,x10482)+E(f853(x10483,x10484,x10481,x10485),f853(x10483,x10484,x10482,x10485)) % 191.49/191.42 [1049]~E(x10491,x10492)+E(f853(x10493,x10494,x10495,x10491),f853(x10493,x10494,x10495,x10492)) % 191.49/191.42 [1050]~E(x10501,x10502)+E(f430(x10501,x10503,x10504),f430(x10502,x10503,x10504)) % 191.49/191.42 [1051]~E(x10511,x10512)+E(f430(x10513,x10511,x10514),f430(x10513,x10512,x10514)) % 191.49/191.42 [1052]~E(x10521,x10522)+E(f430(x10523,x10524,x10521),f430(x10523,x10524,x10522)) % 191.49/191.42 [1053]~E(x10531,x10532)+E(f422(x10531,x10533,x10534,x10535),f422(x10532,x10533,x10534,x10535)) % 191.49/191.42 [1054]~E(x10541,x10542)+E(f422(x10543,x10541,x10544,x10545),f422(x10543,x10542,x10544,x10545)) % 191.49/191.42 [1055]~E(x10551,x10552)+E(f422(x10553,x10554,x10551,x10555),f422(x10553,x10554,x10552,x10555)) % 191.49/191.42 [1056]~E(x10561,x10562)+E(f422(x10563,x10564,x10565,x10561),f422(x10563,x10564,x10565,x10562)) % 191.49/191.42 [1057]~E(x10571,x10572)+E(f186(x10571,x10573,x10574),f186(x10572,x10573,x10574)) % 191.49/191.42 [1058]~E(x10581,x10582)+E(f186(x10583,x10581,x10584),f186(x10583,x10582,x10584)) % 191.49/191.42 [1059]~E(x10591,x10592)+E(f186(x10593,x10594,x10591),f186(x10593,x10594,x10592)) % 191.49/191.42 [1060]~E(x10601,x10602)+E(f780(x10601,x10603,x10604,x10605,x10606),f780(x10602,x10603,x10604,x10605,x10606)) % 191.49/191.42 [1061]~E(x10611,x10612)+E(f780(x10613,x10611,x10614,x10615,x10616),f780(x10613,x10612,x10614,x10615,x10616)) % 191.49/191.42 [1062]~E(x10621,x10622)+E(f780(x10623,x10624,x10621,x10625,x10626),f780(x10623,x10624,x10622,x10625,x10626)) % 191.49/191.42 [1063]~E(x10631,x10632)+E(f780(x10633,x10634,x10635,x10631,x10636),f780(x10633,x10634,x10635,x10632,x10636)) % 191.49/191.42 [1064]~E(x10641,x10642)+E(f780(x10643,x10644,x10645,x10646,x10641),f780(x10643,x10644,x10645,x10646,x10642)) % 191.49/191.42 [1065]~E(x10651,x10652)+E(f691(x10651,x10653,x10654,x10655,x10656),f691(x10652,x10653,x10654,x10655,x10656)) % 191.49/191.42 [1066]~E(x10661,x10662)+E(f691(x10663,x10661,x10664,x10665,x10666),f691(x10663,x10662,x10664,x10665,x10666)) % 191.49/191.42 [1067]~E(x10671,x10672)+E(f691(x10673,x10674,x10671,x10675,x10676),f691(x10673,x10674,x10672,x10675,x10676)) % 191.49/191.42 [1068]~E(x10681,x10682)+E(f691(x10683,x10684,x10685,x10681,x10686),f691(x10683,x10684,x10685,x10682,x10686)) % 191.49/191.42 [1069]~E(x10691,x10692)+E(f691(x10693,x10694,x10695,x10696,x10691),f691(x10693,x10694,x10695,x10696,x10692)) % 191.49/191.42 [1070]~E(x10701,x10702)+E(f785(x10701,x10703),f785(x10702,x10703)) % 191.49/191.42 [1071]~E(x10711,x10712)+E(f785(x10713,x10711),f785(x10713,x10712)) % 191.49/191.42 [1072]~E(x10721,x10722)+E(f532(x10721,x10723,x10724,x10725,x10726,x10727,x10728),f532(x10722,x10723,x10724,x10725,x10726,x10727,x10728)) % 191.49/191.42 [1073]~E(x10731,x10732)+E(f532(x10733,x10731,x10734,x10735,x10736,x10737,x10738),f532(x10733,x10732,x10734,x10735,x10736,x10737,x10738)) % 191.49/191.42 [1074]~E(x10741,x10742)+E(f532(x10743,x10744,x10741,x10745,x10746,x10747,x10748),f532(x10743,x10744,x10742,x10745,x10746,x10747,x10748)) % 191.49/191.42 [1075]~E(x10751,x10752)+E(f532(x10753,x10754,x10755,x10751,x10756,x10757,x10758),f532(x10753,x10754,x10755,x10752,x10756,x10757,x10758)) % 191.49/191.42 [1076]~E(x10761,x10762)+E(f532(x10763,x10764,x10765,x10766,x10761,x10767,x10768),f532(x10763,x10764,x10765,x10766,x10762,x10767,x10768)) % 191.49/191.42 [1077]~E(x10771,x10772)+E(f532(x10773,x10774,x10775,x10776,x10777,x10771,x10778),f532(x10773,x10774,x10775,x10776,x10777,x10772,x10778)) % 191.49/191.42 [1078]~E(x10781,x10782)+E(f532(x10783,x10784,x10785,x10786,x10787,x10788,x10781),f532(x10783,x10784,x10785,x10786,x10787,x10788,x10782)) % 191.49/191.42 [1079]~E(x10791,x10792)+E(f645(x10791,x10793),f645(x10792,x10793)) % 191.49/191.42 [1080]~E(x10801,x10802)+E(f645(x10803,x10801),f645(x10803,x10802)) % 191.49/191.42 [1081]~E(x10811,x10812)+E(f327(x10811,x10813,x10814),f327(x10812,x10813,x10814)) % 191.49/191.42 [1082]~E(x10821,x10822)+E(f327(x10823,x10821,x10824),f327(x10823,x10822,x10824)) % 191.49/191.42 [1083]~E(x10831,x10832)+E(f327(x10833,x10834,x10831),f327(x10833,x10834,x10832)) % 191.49/191.42 [1084]~E(x10841,x10842)+E(f521(x10841,x10843,x10844,x10845,x10846,x10847),f521(x10842,x10843,x10844,x10845,x10846,x10847)) % 191.49/191.42 [1085]~E(x10851,x10852)+E(f521(x10853,x10851,x10854,x10855,x10856,x10857),f521(x10853,x10852,x10854,x10855,x10856,x10857)) % 191.49/191.42 [1086]~E(x10861,x10862)+E(f521(x10863,x10864,x10861,x10865,x10866,x10867),f521(x10863,x10864,x10862,x10865,x10866,x10867)) % 191.49/191.42 [1087]~E(x10871,x10872)+E(f521(x10873,x10874,x10875,x10871,x10876,x10877),f521(x10873,x10874,x10875,x10872,x10876,x10877)) % 191.49/191.42 [1088]~E(x10881,x10882)+E(f521(x10883,x10884,x10885,x10886,x10881,x10887),f521(x10883,x10884,x10885,x10886,x10882,x10887)) % 191.49/191.42 [1089]~E(x10891,x10892)+E(f521(x10893,x10894,x10895,x10896,x10897,x10891),f521(x10893,x10894,x10895,x10896,x10897,x10892)) % 191.49/191.42 [1090]~E(x10901,x10902)+E(f191(x10901,x10903,x10904,x10905),f191(x10902,x10903,x10904,x10905)) % 191.49/191.42 [1091]~E(x10911,x10912)+E(f191(x10913,x10911,x10914,x10915),f191(x10913,x10912,x10914,x10915)) % 191.49/191.42 [1092]~E(x10921,x10922)+E(f191(x10923,x10924,x10921,x10925),f191(x10923,x10924,x10922,x10925)) % 191.49/191.42 [1093]~E(x10931,x10932)+E(f191(x10933,x10934,x10935,x10931),f191(x10933,x10934,x10935,x10932)) % 191.49/191.42 [1094]~E(x10941,x10942)+E(f490(x10941,x10943,x10944),f490(x10942,x10943,x10944)) % 191.49/191.42 [1095]~E(x10951,x10952)+E(f490(x10953,x10951,x10954),f490(x10953,x10952,x10954)) % 191.49/191.42 [1096]~E(x10961,x10962)+E(f490(x10963,x10964,x10961),f490(x10963,x10964,x10962)) % 191.49/191.42 [1097]~E(x10971,x10972)+E(f344(x10971),f344(x10972)) % 191.49/191.42 [1098]~E(x10981,x10982)+E(f617(x10981,x10983,x10984),f617(x10982,x10983,x10984)) % 191.49/191.42 [1099]~E(x10991,x10992)+E(f617(x10993,x10991,x10994),f617(x10993,x10992,x10994)) % 191.49/191.42 [1100]~E(x11001,x11002)+E(f617(x11003,x11004,x11001),f617(x11003,x11004,x11002)) % 191.49/191.42 [1101]~E(x11011,x11012)+E(f629(x11011,x11013,x11014),f629(x11012,x11013,x11014)) % 191.49/191.42 [1102]~E(x11021,x11022)+E(f629(x11023,x11021,x11024),f629(x11023,x11022,x11024)) % 191.49/191.42 [1103]~E(x11031,x11032)+E(f629(x11033,x11034,x11031),f629(x11033,x11034,x11032)) % 191.49/191.42 [1104]~E(x11041,x11042)+E(f417(x11041,x11043,x11044),f417(x11042,x11043,x11044)) % 191.49/191.42 [1105]~E(x11051,x11052)+E(f417(x11053,x11051,x11054),f417(x11053,x11052,x11054)) % 191.49/191.42 [1106]~E(x11061,x11062)+E(f417(x11063,x11064,x11061),f417(x11063,x11064,x11062)) % 191.49/191.42 [1107]~E(x11071,x11072)+E(f425(x11071,x11073),f425(x11072,x11073)) % 191.49/191.42 [1108]~E(x11081,x11082)+E(f425(x11083,x11081),f425(x11083,x11082)) % 191.49/191.42 [1109]~E(x11091,x11092)+E(f503(x11091,x11093,x11094,x11095),f503(x11092,x11093,x11094,x11095)) % 191.49/191.42 [1110]~E(x11101,x11102)+E(f503(x11103,x11101,x11104,x11105),f503(x11103,x11102,x11104,x11105)) % 191.49/191.42 [1111]~E(x11111,x11112)+E(f503(x11113,x11114,x11111,x11115),f503(x11113,x11114,x11112,x11115)) % 191.49/191.42 [1112]~E(x11121,x11122)+E(f503(x11123,x11124,x11125,x11121),f503(x11123,x11124,x11125,x11122)) % 191.49/191.42 [1113]~E(x11131,x11132)+E(f545(x11131,x11133,x11134,x11135,x11136,x11137,x11138),f545(x11132,x11133,x11134,x11135,x11136,x11137,x11138)) % 191.49/191.42 [1114]~E(x11141,x11142)+E(f545(x11143,x11141,x11144,x11145,x11146,x11147,x11148),f545(x11143,x11142,x11144,x11145,x11146,x11147,x11148)) % 191.49/191.42 [1115]~E(x11151,x11152)+E(f545(x11153,x11154,x11151,x11155,x11156,x11157,x11158),f545(x11153,x11154,x11152,x11155,x11156,x11157,x11158)) % 191.49/191.42 [1116]~E(x11161,x11162)+E(f545(x11163,x11164,x11165,x11161,x11166,x11167,x11168),f545(x11163,x11164,x11165,x11162,x11166,x11167,x11168)) % 191.49/191.42 [1117]~E(x11171,x11172)+E(f545(x11173,x11174,x11175,x11176,x11171,x11177,x11178),f545(x11173,x11174,x11175,x11176,x11172,x11177,x11178)) % 191.49/191.42 [1118]~E(x11181,x11182)+E(f545(x11183,x11184,x11185,x11186,x11187,x11181,x11188),f545(x11183,x11184,x11185,x11186,x11187,x11182,x11188)) % 191.49/191.42 [1119]~E(x11191,x11192)+E(f545(x11193,x11194,x11195,x11196,x11197,x11198,x11191),f545(x11193,x11194,x11195,x11196,x11197,x11198,x11192)) % 191.49/191.42 [1120]~E(x11201,x11202)+E(f99(x11201,x11203,x11204,x11205),f99(x11202,x11203,x11204,x11205)) % 191.49/191.42 [1121]~E(x11211,x11212)+E(f99(x11213,x11211,x11214,x11215),f99(x11213,x11212,x11214,x11215)) % 191.49/191.42 [1122]~E(x11221,x11222)+E(f99(x11223,x11224,x11221,x11225),f99(x11223,x11224,x11222,x11225)) % 191.49/191.42 [1123]~E(x11231,x11232)+E(f99(x11233,x11234,x11235,x11231),f99(x11233,x11234,x11235,x11232)) % 191.49/191.42 [1124]~E(x11241,x11242)+E(f276(x11241,x11243,x11244,x11245,x11246),f276(x11242,x11243,x11244,x11245,x11246)) % 191.49/191.42 [1125]~E(x11251,x11252)+E(f276(x11253,x11251,x11254,x11255,x11256),f276(x11253,x11252,x11254,x11255,x11256)) % 191.49/191.42 [1126]~E(x11261,x11262)+E(f276(x11263,x11264,x11261,x11265,x11266),f276(x11263,x11264,x11262,x11265,x11266)) % 191.49/191.42 [1127]~E(x11271,x11272)+E(f276(x11273,x11274,x11275,x11271,x11276),f276(x11273,x11274,x11275,x11272,x11276)) % 191.49/191.42 [1128]~E(x11281,x11282)+E(f276(x11283,x11284,x11285,x11286,x11281),f276(x11283,x11284,x11285,x11286,x11282)) % 191.49/191.42 [1129]~E(x11291,x11292)+E(f315(x11291,x11293,x11294),f315(x11292,x11293,x11294)) % 191.49/191.42 [1130]~E(x11301,x11302)+E(f315(x11303,x11301,x11304),f315(x11303,x11302,x11304)) % 191.49/191.42 [1131]~E(x11311,x11312)+E(f315(x11313,x11314,x11311),f315(x11313,x11314,x11312)) % 191.49/191.42 [1132]~E(x11321,x11322)+E(f695(x11321,x11323),f695(x11322,x11323)) % 191.49/191.42 [1133]~E(x11331,x11332)+E(f695(x11333,x11331),f695(x11333,x11332)) % 191.49/191.42 [1134]~E(x11341,x11342)+E(f602(x11341,x11343,x11344),f602(x11342,x11343,x11344)) % 191.49/191.42 [1135]~E(x11351,x11352)+E(f602(x11353,x11351,x11354),f602(x11353,x11352,x11354)) % 191.49/191.42 [1136]~E(x11361,x11362)+E(f602(x11363,x11364,x11361),f602(x11363,x11364,x11362)) % 191.49/191.42 [1137]~E(x11371,x11372)+E(f141(x11371,x11373,x11374),f141(x11372,x11373,x11374)) % 191.49/191.42 [1138]~E(x11381,x11382)+E(f141(x11383,x11381,x11384),f141(x11383,x11382,x11384)) % 191.49/191.42 [1139]~E(x11391,x11392)+E(f141(x11393,x11394,x11391),f141(x11393,x11394,x11392)) % 191.49/191.42 [1140]~E(x11401,x11402)+E(f842(x11401),f842(x11402)) % 191.49/191.42 [1141]~E(x11411,x11412)+E(f755(x11411,x11413,x11414,x11415,x11416,x11417,x11418),f755(x11412,x11413,x11414,x11415,x11416,x11417,x11418)) % 191.49/191.42 [1142]~E(x11421,x11422)+E(f755(x11423,x11421,x11424,x11425,x11426,x11427,x11428),f755(x11423,x11422,x11424,x11425,x11426,x11427,x11428)) % 191.49/191.42 [1143]~E(x11431,x11432)+E(f755(x11433,x11434,x11431,x11435,x11436,x11437,x11438),f755(x11433,x11434,x11432,x11435,x11436,x11437,x11438)) % 191.49/191.42 [1144]~E(x11441,x11442)+E(f755(x11443,x11444,x11445,x11441,x11446,x11447,x11448),f755(x11443,x11444,x11445,x11442,x11446,x11447,x11448)) % 191.49/191.42 [1145]~E(x11451,x11452)+E(f755(x11453,x11454,x11455,x11456,x11451,x11457,x11458),f755(x11453,x11454,x11455,x11456,x11452,x11457,x11458)) % 191.49/191.42 [1146]~E(x11461,x11462)+E(f755(x11463,x11464,x11465,x11466,x11467,x11461,x11468),f755(x11463,x11464,x11465,x11466,x11467,x11462,x11468)) % 191.49/191.42 [1147]~E(x11471,x11472)+E(f755(x11473,x11474,x11475,x11476,x11477,x11478,x11471),f755(x11473,x11474,x11475,x11476,x11477,x11478,x11472)) % 191.49/191.42 [1148]~E(x11481,x11482)+E(f142(x11481),f142(x11482)) % 191.49/191.42 [1149]~E(x11491,x11492)+E(f782(x11491,x11493,x11494,x11495,x11496),f782(x11492,x11493,x11494,x11495,x11496)) % 191.49/191.42 [1150]~E(x11501,x11502)+E(f782(x11503,x11501,x11504,x11505,x11506),f782(x11503,x11502,x11504,x11505,x11506)) % 191.49/191.42 [1151]~E(x11511,x11512)+E(f782(x11513,x11514,x11511,x11515,x11516),f782(x11513,x11514,x11512,x11515,x11516)) % 191.49/191.42 [1152]~E(x11521,x11522)+E(f782(x11523,x11524,x11525,x11521,x11526),f782(x11523,x11524,x11525,x11522,x11526)) % 191.49/191.42 [1153]~E(x11531,x11532)+E(f782(x11533,x11534,x11535,x11536,x11531),f782(x11533,x11534,x11535,x11536,x11532)) % 191.49/191.42 [1154]~E(x11541,x11542)+E(f386(x11541),f386(x11542)) % 191.49/191.42 [1155]~E(x11551,x11552)+E(f209(x11551,x11553),f209(x11552,x11553)) % 191.49/191.42 [1156]~E(x11561,x11562)+E(f209(x11563,x11561),f209(x11563,x11562)) % 191.49/191.42 [1157]~E(x11571,x11572)+E(f212(x11571,x11573),f212(x11572,x11573)) % 191.49/191.42 [1158]~E(x11581,x11582)+E(f212(x11583,x11581),f212(x11583,x11582)) % 191.49/191.42 [1159]~E(x11591,x11592)+E(f811(x11591,x11593),f811(x11592,x11593)) % 191.49/191.42 [1160]~E(x11601,x11602)+E(f811(x11603,x11601),f811(x11603,x11602)) % 191.49/191.42 [1161]~E(x11611,x11612)+E(f481(x11611,x11613),f481(x11612,x11613)) % 191.49/191.42 [1162]~E(x11621,x11622)+E(f481(x11623,x11621),f481(x11623,x11622)) % 191.49/191.42 [1163]~E(x11631,x11632)+E(f552(x11631),f552(x11632)) % 191.49/191.42 [1164]~E(x11641,x11642)+E(f697(x11641,x11643),f697(x11642,x11643)) % 191.49/191.42 [1165]~E(x11651,x11652)+E(f697(x11653,x11651),f697(x11653,x11652)) % 191.49/191.42 [1166]~E(x11661,x11662)+E(f599(x11661),f599(x11662)) % 191.49/191.42 [1167]~E(x11671,x11672)+E(f650(x11671,x11673,x11674),f650(x11672,x11673,x11674)) % 191.49/191.42 [1168]~E(x11681,x11682)+E(f650(x11683,x11681,x11684),f650(x11683,x11682,x11684)) % 191.49/191.42 [1169]~E(x11691,x11692)+E(f650(x11693,x11694,x11691),f650(x11693,x11694,x11692)) % 191.49/191.42 [1170]~E(x11701,x11702)+E(f846(x11701,x11703,x11704),f846(x11702,x11703,x11704)) % 191.49/191.42 [1171]~E(x11711,x11712)+E(f846(x11713,x11711,x11714),f846(x11713,x11712,x11714)) % 191.49/191.42 [1172]~E(x11721,x11722)+E(f846(x11723,x11724,x11721),f846(x11723,x11724,x11722)) % 191.49/191.42 [1173]~E(x11731,x11732)+E(f834(x11731,x11733,x11734,x11735),f834(x11732,x11733,x11734,x11735)) % 191.49/191.42 [1174]~E(x11741,x11742)+E(f834(x11743,x11741,x11744,x11745),f834(x11743,x11742,x11744,x11745)) % 191.49/191.42 [1175]~E(x11751,x11752)+E(f834(x11753,x11754,x11751,x11755),f834(x11753,x11754,x11752,x11755)) % 191.49/191.42 [1176]~E(x11761,x11762)+E(f834(x11763,x11764,x11765,x11761),f834(x11763,x11764,x11765,x11762)) % 191.49/191.42 [1177]~E(x11771,x11772)+E(f770(x11771,x11773),f770(x11772,x11773)) % 191.49/191.42 [1178]~E(x11781,x11782)+E(f770(x11783,x11781),f770(x11783,x11782)) % 191.49/191.42 [1179]~E(x11791,x11792)+E(f285(x11791,x11793,x11794,x11795),f285(x11792,x11793,x11794,x11795)) % 191.49/191.42 [1180]~E(x11801,x11802)+E(f285(x11803,x11801,x11804,x11805),f285(x11803,x11802,x11804,x11805)) % 191.49/191.42 [1181]~E(x11811,x11812)+E(f285(x11813,x11814,x11811,x11815),f285(x11813,x11814,x11812,x11815)) % 191.49/191.42 [1182]~E(x11821,x11822)+E(f285(x11823,x11824,x11825,x11821),f285(x11823,x11824,x11825,x11822)) % 191.49/191.42 [1183]~E(x11831,x11832)+E(f647(x11831,x11833),f647(x11832,x11833)) % 191.49/191.42 [1184]~E(x11841,x11842)+E(f647(x11843,x11841),f647(x11843,x11842)) % 191.49/191.42 [1185]~E(x11851,x11852)+E(f382(x11851,x11853,x11854,x11855,x11856,x11857),f382(x11852,x11853,x11854,x11855,x11856,x11857)) % 191.49/191.42 [1186]~E(x11861,x11862)+E(f382(x11863,x11861,x11864,x11865,x11866,x11867),f382(x11863,x11862,x11864,x11865,x11866,x11867)) % 191.49/191.42 [1187]~E(x11871,x11872)+E(f382(x11873,x11874,x11871,x11875,x11876,x11877),f382(x11873,x11874,x11872,x11875,x11876,x11877)) % 191.49/191.42 [1188]~E(x11881,x11882)+E(f382(x11883,x11884,x11885,x11881,x11886,x11887),f382(x11883,x11884,x11885,x11882,x11886,x11887)) % 191.49/191.42 [1189]~E(x11891,x11892)+E(f382(x11893,x11894,x11895,x11896,x11891,x11897),f382(x11893,x11894,x11895,x11896,x11892,x11897)) % 191.49/191.42 [1190]~E(x11901,x11902)+E(f382(x11903,x11904,x11905,x11906,x11907,x11901),f382(x11903,x11904,x11905,x11906,x11907,x11902)) % 191.49/191.42 [1191]~E(x11911,x11912)+E(f128(x11911),f128(x11912)) % 191.49/191.42 [1192]~E(x11921,x11922)+E(f214(x11921),f214(x11922)) % 191.49/191.42 [1193]~E(x11931,x11932)+E(f472(x11931,x11933),f472(x11932,x11933)) % 191.49/191.42 [1194]~E(x11941,x11942)+E(f472(x11943,x11941),f472(x11943,x11942)) % 191.49/191.42 [1195]~E(x11951,x11952)+E(f206(x11951,x11953,x11954,x11955),f206(x11952,x11953,x11954,x11955)) % 191.49/191.42 [1196]~E(x11961,x11962)+E(f206(x11963,x11961,x11964,x11965),f206(x11963,x11962,x11964,x11965)) % 191.49/191.42 [1197]~E(x11971,x11972)+E(f206(x11973,x11974,x11971,x11975),f206(x11973,x11974,x11972,x11975)) % 191.49/191.42 [1198]~E(x11981,x11982)+E(f206(x11983,x11984,x11985,x11981),f206(x11983,x11984,x11985,x11982)) % 191.49/191.42 [1199]~E(x11991,x11992)+E(f383(x11991,x11993,x11994,x11995),f383(x11992,x11993,x11994,x11995)) % 191.49/191.42 [1200]~E(x12001,x12002)+E(f383(x12003,x12001,x12004,x12005),f383(x12003,x12002,x12004,x12005)) % 191.49/191.42 [1201]~E(x12011,x12012)+E(f383(x12013,x12014,x12011,x12015),f383(x12013,x12014,x12012,x12015)) % 191.49/191.42 [1202]~E(x12021,x12022)+E(f383(x12023,x12024,x12025,x12021),f383(x12023,x12024,x12025,x12022)) % 191.49/191.42 [1203]~E(x12031,x12032)+E(f507(x12031,x12033,x12034),f507(x12032,x12033,x12034)) % 191.49/191.42 [1204]~E(x12041,x12042)+E(f507(x12043,x12041,x12044),f507(x12043,x12042,x12044)) % 191.49/191.42 [1205]~E(x12051,x12052)+E(f507(x12053,x12054,x12051),f507(x12053,x12054,x12052)) % 191.49/191.42 [1206]~E(x12061,x12062)+E(f591(x12061,x12063,x12064,x12065,x12066),f591(x12062,x12063,x12064,x12065,x12066)) % 191.49/191.42 [1207]~E(x12071,x12072)+E(f591(x12073,x12071,x12074,x12075,x12076),f591(x12073,x12072,x12074,x12075,x12076)) % 191.49/191.42 [1208]~E(x12081,x12082)+E(f591(x12083,x12084,x12081,x12085,x12086),f591(x12083,x12084,x12082,x12085,x12086)) % 191.49/191.42 [1209]~E(x12091,x12092)+E(f591(x12093,x12094,x12095,x12091,x12096),f591(x12093,x12094,x12095,x12092,x12096)) % 191.49/191.42 [1210]~E(x12101,x12102)+E(f591(x12103,x12104,x12105,x12106,x12101),f591(x12103,x12104,x12105,x12106,x12102)) % 191.49/191.42 [1211]~E(x12111,x12112)+E(f486(x12111,x12113,x12114),f486(x12112,x12113,x12114)) % 191.49/191.42 [1212]~E(x12121,x12122)+E(f486(x12123,x12121,x12124),f486(x12123,x12122,x12124)) % 191.49/191.42 [1213]~E(x12131,x12132)+E(f486(x12133,x12134,x12131),f486(x12133,x12134,x12132)) % 191.49/191.42 [1214]~E(x12141,x12142)+E(f526(x12141,x12143,x12144,x12145,x12146),f526(x12142,x12143,x12144,x12145,x12146)) % 191.49/191.42 [1215]~E(x12151,x12152)+E(f526(x12153,x12151,x12154,x12155,x12156),f526(x12153,x12152,x12154,x12155,x12156)) % 191.49/191.42 [1216]~E(x12161,x12162)+E(f526(x12163,x12164,x12161,x12165,x12166),f526(x12163,x12164,x12162,x12165,x12166)) % 191.49/191.42 [1217]~E(x12171,x12172)+E(f526(x12173,x12174,x12175,x12171,x12176),f526(x12173,x12174,x12175,x12172,x12176)) % 191.49/191.42 [1218]~E(x12181,x12182)+E(f526(x12183,x12184,x12185,x12186,x12181),f526(x12183,x12184,x12185,x12186,x12182)) % 191.49/191.42 [1219]~E(x12191,x12192)+E(f732(x12191,x12193,x12194,x12195,x12196,x12197),f732(x12192,x12193,x12194,x12195,x12196,x12197)) % 191.49/191.42 [1220]~E(x12201,x12202)+E(f732(x12203,x12201,x12204,x12205,x12206,x12207),f732(x12203,x12202,x12204,x12205,x12206,x12207)) % 191.49/191.42 [1221]~E(x12211,x12212)+E(f732(x12213,x12214,x12211,x12215,x12216,x12217),f732(x12213,x12214,x12212,x12215,x12216,x12217)) % 191.49/191.42 [1222]~E(x12221,x12222)+E(f732(x12223,x12224,x12225,x12221,x12226,x12227),f732(x12223,x12224,x12225,x12222,x12226,x12227)) % 191.49/191.42 [1223]~E(x12231,x12232)+E(f732(x12233,x12234,x12235,x12236,x12231,x12237),f732(x12233,x12234,x12235,x12236,x12232,x12237)) % 191.49/191.42 [1224]~E(x12241,x12242)+E(f732(x12243,x12244,x12245,x12246,x12247,x12241),f732(x12243,x12244,x12245,x12246,x12247,x12242)) % 191.49/191.42 [1225]~E(x12251,x12252)+E(f236(x12251,x12253),f236(x12252,x12253)) % 191.49/191.42 [1226]~E(x12261,x12262)+E(f236(x12263,x12261),f236(x12263,x12262)) % 191.49/191.42 [1227]~E(x12271,x12272)+E(f668(x12271,x12273),f668(x12272,x12273)) % 191.49/191.42 [1228]~E(x12281,x12282)+E(f668(x12283,x12281),f668(x12283,x12282)) % 191.49/191.42 [1229]~E(x12291,x12292)+E(f469(x12291,x12293),f469(x12292,x12293)) % 191.49/191.42 [1230]~E(x12301,x12302)+E(f469(x12303,x12301),f469(x12303,x12302)) % 191.49/191.42 [1231]~E(x12311,x12312)+E(f123(x12311,x12313,x12314),f123(x12312,x12313,x12314)) % 191.49/191.42 [1232]~E(x12321,x12322)+E(f123(x12323,x12321,x12324),f123(x12323,x12322,x12324)) % 191.49/191.42 [1233]~E(x12331,x12332)+E(f123(x12333,x12334,x12331),f123(x12333,x12334,x12332)) % 191.49/191.42 [1234]~E(x12341,x12342)+E(f740(x12341),f740(x12342)) % 191.49/191.42 [1235]~E(x12351,x12352)+E(f497(x12351,x12353),f497(x12352,x12353)) % 191.49/191.42 [1236]~E(x12361,x12362)+E(f497(x12363,x12361),f497(x12363,x12362)) % 191.49/191.42 [1237]~E(x12371,x12372)+E(f510(x12371,x12373,x12374),f510(x12372,x12373,x12374)) % 191.49/191.42 [1238]~E(x12381,x12382)+E(f510(x12383,x12381,x12384),f510(x12383,x12382,x12384)) % 191.49/191.42 [1239]~E(x12391,x12392)+E(f510(x12393,x12394,x12391),f510(x12393,x12394,x12392)) % 191.49/191.42 [1240]~E(x12401,x12402)+E(f589(x12401,x12403,x12404,x12405,x12406),f589(x12402,x12403,x12404,x12405,x12406)) % 191.49/191.42 [1241]~E(x12411,x12412)+E(f589(x12413,x12411,x12414,x12415,x12416),f589(x12413,x12412,x12414,x12415,x12416)) % 191.49/191.42 [1242]~E(x12421,x12422)+E(f589(x12423,x12424,x12421,x12425,x12426),f589(x12423,x12424,x12422,x12425,x12426)) % 191.49/191.42 [1243]~E(x12431,x12432)+E(f589(x12433,x12434,x12435,x12431,x12436),f589(x12433,x12434,x12435,x12432,x12436)) % 191.49/191.42 [1244]~E(x12441,x12442)+E(f589(x12443,x12444,x12445,x12446,x12441),f589(x12443,x12444,x12445,x12446,x12442)) % 191.49/191.42 [1245]~E(x12451,x12452)+E(f403(x12451,x12453),f403(x12452,x12453)) % 191.49/191.42 [1246]~E(x12461,x12462)+E(f403(x12463,x12461),f403(x12463,x12462)) % 191.49/191.42 [1247]~E(x12471,x12472)+E(f393(x12471,x12473),f393(x12472,x12473)) % 191.49/191.42 [1248]~E(x12481,x12482)+E(f393(x12483,x12481),f393(x12483,x12482)) % 191.49/191.42 [1249]~E(x12491,x12492)+E(f760(x12491,x12493,x12494),f760(x12492,x12493,x12494)) % 191.49/191.42 [1250]~E(x12501,x12502)+E(f760(x12503,x12501,x12504),f760(x12503,x12502,x12504)) % 191.49/191.42 [1251]~E(x12511,x12512)+E(f760(x12513,x12514,x12511),f760(x12513,x12514,x12512)) % 191.49/191.42 [1252]~E(x12521,x12522)+E(f379(x12521,x12523,x12524,x12525),f379(x12522,x12523,x12524,x12525)) % 191.49/191.42 [1253]~E(x12531,x12532)+E(f379(x12533,x12531,x12534,x12535),f379(x12533,x12532,x12534,x12535)) % 191.49/191.42 [1254]~E(x12541,x12542)+E(f379(x12543,x12544,x12541,x12545),f379(x12543,x12544,x12542,x12545)) % 191.49/191.42 [1255]~E(x12551,x12552)+E(f379(x12553,x12554,x12555,x12551),f379(x12553,x12554,x12555,x12552)) % 191.49/191.42 [1256]~E(x12561,x12562)+E(f527(x12561,x12563,x12564,x12565),f527(x12562,x12563,x12564,x12565)) % 191.49/191.42 [1257]~E(x12571,x12572)+E(f527(x12573,x12571,x12574,x12575),f527(x12573,x12572,x12574,x12575)) % 191.49/191.42 [1258]~E(x12581,x12582)+E(f527(x12583,x12584,x12581,x12585),f527(x12583,x12584,x12582,x12585)) % 191.49/191.42 [1259]~E(x12591,x12592)+E(f527(x12593,x12594,x12595,x12591),f527(x12593,x12594,x12595,x12592)) % 191.49/191.42 [1260]~E(x12601,x12602)+E(f129(x12601,x12603,x12604),f129(x12602,x12603,x12604)) % 191.49/191.42 [1261]~E(x12611,x12612)+E(f129(x12613,x12611,x12614),f129(x12613,x12612,x12614)) % 191.49/191.42 [1262]~E(x12621,x12622)+E(f129(x12623,x12624,x12621),f129(x12623,x12624,x12622)) % 191.49/191.42 [1263]~E(x12631,x12632)+E(f517(x12631,x12633,x12634,x12635,x12636,x12637),f517(x12632,x12633,x12634,x12635,x12636,x12637)) % 191.49/191.42 [1264]~E(x12641,x12642)+E(f517(x12643,x12641,x12644,x12645,x12646,x12647),f517(x12643,x12642,x12644,x12645,x12646,x12647)) % 191.49/191.42 [1265]~E(x12651,x12652)+E(f517(x12653,x12654,x12651,x12655,x12656,x12657),f517(x12653,x12654,x12652,x12655,x12656,x12657)) % 191.49/191.42 [1266]~E(x12661,x12662)+E(f517(x12663,x12664,x12665,x12661,x12666,x12667),f517(x12663,x12664,x12665,x12662,x12666,x12667)) % 191.49/191.42 [1267]~E(x12671,x12672)+E(f517(x12673,x12674,x12675,x12676,x12671,x12677),f517(x12673,x12674,x12675,x12676,x12672,x12677)) % 191.49/191.42 [1268]~E(x12681,x12682)+E(f517(x12683,x12684,x12685,x12686,x12687,x12681),f517(x12683,x12684,x12685,x12686,x12687,x12682)) % 191.49/191.42 [1269]~E(x12691,x12692)+E(f872(x12691,x12693,x12694,x12695,x12696),f872(x12692,x12693,x12694,x12695,x12696)) % 191.49/191.42 [1270]~E(x12701,x12702)+E(f872(x12703,x12701,x12704,x12705,x12706),f872(x12703,x12702,x12704,x12705,x12706)) % 191.49/191.42 [1271]~E(x12711,x12712)+E(f872(x12713,x12714,x12711,x12715,x12716),f872(x12713,x12714,x12712,x12715,x12716)) % 191.49/191.42 [1272]~E(x12721,x12722)+E(f872(x12723,x12724,x12725,x12721,x12726),f872(x12723,x12724,x12725,x12722,x12726)) % 191.49/191.42 [1273]~E(x12731,x12732)+E(f872(x12733,x12734,x12735,x12736,x12731),f872(x12733,x12734,x12735,x12736,x12732)) % 191.49/191.42 [1274]~E(x12741,x12742)+E(f478(x12741,x12743,x12744,x12745),f478(x12742,x12743,x12744,x12745)) % 191.49/191.42 [1275]~E(x12751,x12752)+E(f478(x12753,x12751,x12754,x12755),f478(x12753,x12752,x12754,x12755)) % 191.49/191.42 [1276]~E(x12761,x12762)+E(f478(x12763,x12764,x12761,x12765),f478(x12763,x12764,x12762,x12765)) % 191.49/191.42 [1277]~E(x12771,x12772)+E(f478(x12773,x12774,x12775,x12771),f478(x12773,x12774,x12775,x12772)) % 191.49/191.42 [1278]~E(x12781,x12782)+E(f213(x12781,x12783,x12784),f213(x12782,x12783,x12784)) % 191.49/191.42 [1279]~E(x12791,x12792)+E(f213(x12793,x12791,x12794),f213(x12793,x12792,x12794)) % 191.49/191.42 [1280]~E(x12801,x12802)+E(f213(x12803,x12804,x12801),f213(x12803,x12804,x12802)) % 191.49/191.42 [1281]~E(x12811,x12812)+E(f409(x12811,x12813,x12814),f409(x12812,x12813,x12814)) % 191.49/191.42 [1282]~E(x12821,x12822)+E(f409(x12823,x12821,x12824),f409(x12823,x12822,x12824)) % 191.49/191.42 [1283]~E(x12831,x12832)+E(f409(x12833,x12834,x12831),f409(x12833,x12834,x12832)) % 191.49/191.42 [1284]~E(x12841,x12842)+E(f750(x12841,x12843,x12844,x12845,x12846),f750(x12842,x12843,x12844,x12845,x12846)) % 191.49/191.42 [1285]~E(x12851,x12852)+E(f750(x12853,x12851,x12854,x12855,x12856),f750(x12853,x12852,x12854,x12855,x12856)) % 191.49/191.42 [1286]~E(x12861,x12862)+E(f750(x12863,x12864,x12861,x12865,x12866),f750(x12863,x12864,x12862,x12865,x12866)) % 191.49/191.42 [1287]~E(x12871,x12872)+E(f750(x12873,x12874,x12875,x12871,x12876),f750(x12873,x12874,x12875,x12872,x12876)) % 191.49/191.42 [1288]~E(x12881,x12882)+E(f750(x12883,x12884,x12885,x12886,x12881),f750(x12883,x12884,x12885,x12886,x12882)) % 191.49/191.42 [1289]~E(x12891,x12892)+E(f682(x12891,x12893,x12894,x12895),f682(x12892,x12893,x12894,x12895)) % 191.49/191.42 [1290]~E(x12901,x12902)+E(f682(x12903,x12901,x12904,x12905),f682(x12903,x12902,x12904,x12905)) % 191.49/191.42 [1291]~E(x12911,x12912)+E(f682(x12913,x12914,x12911,x12915),f682(x12913,x12914,x12912,x12915)) % 191.49/191.42 [1292]~E(x12921,x12922)+E(f682(x12923,x12924,x12925,x12921),f682(x12923,x12924,x12925,x12922)) % 191.49/191.42 [1293]~E(x12931,x12932)+E(f492(x12931,x12933,x12934,x12935),f492(x12932,x12933,x12934,x12935)) % 191.49/191.42 [1294]~E(x12941,x12942)+E(f492(x12943,x12941,x12944,x12945),f492(x12943,x12942,x12944,x12945)) % 191.49/191.42 [1295]~E(x12951,x12952)+E(f492(x12953,x12954,x12951,x12955),f492(x12953,x12954,x12952,x12955)) % 191.49/191.42 [1296]~E(x12961,x12962)+E(f492(x12963,x12964,x12965,x12961),f492(x12963,x12964,x12965,x12962)) % 191.49/191.42 [1297]~E(x12971,x12972)+E(f284(x12971,x12973),f284(x12972,x12973)) % 191.49/191.42 [1298]~E(x12981,x12982)+E(f284(x12983,x12981),f284(x12983,x12982)) % 191.49/191.42 [1299]~E(x12991,x12992)+E(f449(x12991,x12993,x12994,x12995),f449(x12992,x12993,x12994,x12995)) % 191.49/191.42 [1300]~E(x13001,x13002)+E(f449(x13003,x13001,x13004,x13005),f449(x13003,x13002,x13004,x13005)) % 191.49/191.42 [1301]~E(x13011,x13012)+E(f449(x13013,x13014,x13011,x13015),f449(x13013,x13014,x13012,x13015)) % 191.49/191.42 [1302]~E(x13021,x13022)+E(f449(x13023,x13024,x13025,x13021),f449(x13023,x13024,x13025,x13022)) % 191.49/191.42 [1303]~E(x13031,x13032)+E(f696(x13031,x13033),f696(x13032,x13033)) % 191.49/191.42 [1304]~E(x13041,x13042)+E(f696(x13043,x13041),f696(x13043,x13042)) % 191.49/191.42 [1305]~E(x13051,x13052)+E(f677(x13051,x13053,x13054,x13055,x13056),f677(x13052,x13053,x13054,x13055,x13056)) % 191.49/191.42 [1306]~E(x13061,x13062)+E(f677(x13063,x13061,x13064,x13065,x13066),f677(x13063,x13062,x13064,x13065,x13066)) % 191.49/191.42 [1307]~E(x13071,x13072)+E(f677(x13073,x13074,x13071,x13075,x13076),f677(x13073,x13074,x13072,x13075,x13076)) % 191.49/191.42 [1308]~E(x13081,x13082)+E(f677(x13083,x13084,x13085,x13081,x13086),f677(x13083,x13084,x13085,x13082,x13086)) % 191.49/191.42 [1309]~E(x13091,x13092)+E(f677(x13093,x13094,x13095,x13096,x13091),f677(x13093,x13094,x13095,x13096,x13092)) % 191.49/191.42 [1310]~E(x13101,x13102)+E(f709(x13101,x13103,x13104,x13105),f709(x13102,x13103,x13104,x13105)) % 191.49/191.42 [1311]~E(x13111,x13112)+E(f709(x13113,x13111,x13114,x13115),f709(x13113,x13112,x13114,x13115)) % 191.49/191.42 [1312]~E(x13121,x13122)+E(f709(x13123,x13124,x13121,x13125),f709(x13123,x13124,x13122,x13125)) % 191.49/191.42 [1313]~E(x13131,x13132)+E(f709(x13133,x13134,x13135,x13131),f709(x13133,x13134,x13135,x13132)) % 191.49/191.42 [1314]~E(x13141,x13142)+E(f675(x13141,x13143,x13144,x13145),f675(x13142,x13143,x13144,x13145)) % 191.49/191.42 [1315]~E(x13151,x13152)+E(f675(x13153,x13151,x13154,x13155),f675(x13153,x13152,x13154,x13155)) % 191.49/191.42 [1316]~E(x13161,x13162)+E(f675(x13163,x13164,x13161,x13165),f675(x13163,x13164,x13162,x13165)) % 191.49/191.42 [1317]~E(x13171,x13172)+E(f675(x13173,x13174,x13175,x13171),f675(x13173,x13174,x13175,x13172)) % 191.49/191.42 [1318]~E(x13181,x13182)+E(f578(x13181,x13183,x13184),f578(x13182,x13183,x13184)) % 191.49/191.42 [1319]~E(x13191,x13192)+E(f578(x13193,x13191,x13194),f578(x13193,x13192,x13194)) % 191.49/191.42 [1320]~E(x13201,x13202)+E(f578(x13203,x13204,x13201),f578(x13203,x13204,x13202)) % 191.49/191.42 [1321]~E(x13211,x13212)+E(f126(x13211),f126(x13212)) % 191.49/191.42 [1322]~E(x13221,x13222)+E(f415(x13221,x13223),f415(x13222,x13223)) % 191.49/191.42 [1323]~E(x13231,x13232)+E(f415(x13233,x13231),f415(x13233,x13232)) % 191.49/191.42 [1324]~E(x13241,x13242)+E(f292(x13241,x13243),f292(x13242,x13243)) % 191.49/191.42 [1325]~E(x13251,x13252)+E(f292(x13253,x13251),f292(x13253,x13252)) % 191.49/191.42 [1326]~E(x13261,x13262)+E(f607(x13261,x13263,x13264),f607(x13262,x13263,x13264)) % 191.49/191.42 [1327]~E(x13271,x13272)+E(f607(x13273,x13271,x13274),f607(x13273,x13272,x13274)) % 191.49/191.42 [1328]~E(x13281,x13282)+E(f607(x13283,x13284,x13281),f607(x13283,x13284,x13282)) % 191.49/191.42 [1329]~E(x13291,x13292)+E(f432(x13291,x13293,x13294,x13295),f432(x13292,x13293,x13294,x13295)) % 191.49/191.42 [1330]~E(x13301,x13302)+E(f432(x13303,x13301,x13304,x13305),f432(x13303,x13302,x13304,x13305)) % 191.49/191.42 [1331]~E(x13311,x13312)+E(f432(x13313,x13314,x13311,x13315),f432(x13313,x13314,x13312,x13315)) % 191.49/191.42 [1332]~E(x13321,x13322)+E(f432(x13323,x13324,x13325,x13321),f432(x13323,x13324,x13325,x13322)) % 191.49/191.42 [1333]~E(x13331,x13332)+E(f861(x13331,x13333,x13334),f861(x13332,x13333,x13334)) % 191.49/191.42 [1334]~E(x13341,x13342)+E(f861(x13343,x13341,x13344),f861(x13343,x13342,x13344)) % 191.49/191.42 [1335]~E(x13351,x13352)+E(f861(x13353,x13354,x13351),f861(x13353,x13354,x13352)) % 191.49/191.42 [1336]~E(x13361,x13362)+E(f390(x13361),f390(x13362)) % 191.49/191.42 [1337]~E(x13371,x13372)+E(f439(x13371,x13373,x13374,x13375),f439(x13372,x13373,x13374,x13375)) % 191.49/191.42 [1338]~E(x13381,x13382)+E(f439(x13383,x13381,x13384,x13385),f439(x13383,x13382,x13384,x13385)) % 191.49/191.42 [1339]~E(x13391,x13392)+E(f439(x13393,x13394,x13391,x13395),f439(x13393,x13394,x13392,x13395)) % 191.49/191.42 [1340]~E(x13401,x13402)+E(f439(x13403,x13404,x13405,x13401),f439(x13403,x13404,x13405,x13402)) % 191.49/191.42 [1341]~E(x13411,x13412)+E(f402(x13411,x13413,x13414),f402(x13412,x13413,x13414)) % 191.49/191.42 [1342]~E(x13421,x13422)+E(f402(x13423,x13421,x13424),f402(x13423,x13422,x13424)) % 191.49/191.42 [1343]~E(x13431,x13432)+E(f402(x13433,x13434,x13431),f402(x13433,x13434,x13432)) % 191.49/191.42 [1344]~E(x13441,x13442)+E(f133(x13441,x13443,x13444,x13445),f133(x13442,x13443,x13444,x13445)) % 191.49/191.42 [1345]~E(x13451,x13452)+E(f133(x13453,x13451,x13454,x13455),f133(x13453,x13452,x13454,x13455)) % 191.49/191.42 [1346]~E(x13461,x13462)+E(f133(x13463,x13464,x13461,x13465),f133(x13463,x13464,x13462,x13465)) % 191.49/191.42 [1347]~E(x13471,x13472)+E(f133(x13473,x13474,x13475,x13471),f133(x13473,x13474,x13475,x13472)) % 191.49/191.42 [1348]~E(x13481,x13482)+E(f868(x13481,x13483,x13484),f868(x13482,x13483,x13484)) % 191.49/191.42 [1349]~E(x13491,x13492)+E(f868(x13493,x13491,x13494),f868(x13493,x13492,x13494)) % 191.49/191.42 [1350]~E(x13501,x13502)+E(f868(x13503,x13504,x13501),f868(x13503,x13504,x13502)) % 191.49/191.42 [1351]~E(x13511,x13512)+E(f859(x13511,x13513,x13514),f859(x13512,x13513,x13514)) % 191.49/191.42 [1352]~E(x13521,x13522)+E(f859(x13523,x13521,x13524),f859(x13523,x13522,x13524)) % 191.49/191.42 [1353]~E(x13531,x13532)+E(f859(x13533,x13534,x13531),f859(x13533,x13534,x13532)) % 191.49/191.42 [1354]~E(x13541,x13542)+E(f356(x13541,x13543,x13544,x13545,x13546),f356(x13542,x13543,x13544,x13545,x13546)) % 191.49/191.42 [1355]~E(x13551,x13552)+E(f356(x13553,x13551,x13554,x13555,x13556),f356(x13553,x13552,x13554,x13555,x13556)) % 191.49/191.42 [1356]~E(x13561,x13562)+E(f356(x13563,x13564,x13561,x13565,x13566),f356(x13563,x13564,x13562,x13565,x13566)) % 191.49/191.42 [1357]~E(x13571,x13572)+E(f356(x13573,x13574,x13575,x13571,x13576),f356(x13573,x13574,x13575,x13572,x13576)) % 191.49/191.42 [1358]~E(x13581,x13582)+E(f356(x13583,x13584,x13585,x13586,x13581),f356(x13583,x13584,x13585,x13586,x13582)) % 191.49/191.42 [1359]~E(x13591,x13592)+E(f736(x13591,x13593,x13594,x13595,x13596,x13597,x13598),f736(x13592,x13593,x13594,x13595,x13596,x13597,x13598)) % 191.49/191.42 [1360]~E(x13601,x13602)+E(f736(x13603,x13601,x13604,x13605,x13606,x13607,x13608),f736(x13603,x13602,x13604,x13605,x13606,x13607,x13608)) % 191.49/191.42 [1361]~E(x13611,x13612)+E(f736(x13613,x13614,x13611,x13615,x13616,x13617,x13618),f736(x13613,x13614,x13612,x13615,x13616,x13617,x13618)) % 191.49/191.42 [1362]~E(x13621,x13622)+E(f736(x13623,x13624,x13625,x13621,x13626,x13627,x13628),f736(x13623,x13624,x13625,x13622,x13626,x13627,x13628)) % 191.49/191.42 [1363]~E(x13631,x13632)+E(f736(x13633,x13634,x13635,x13636,x13631,x13637,x13638),f736(x13633,x13634,x13635,x13636,x13632,x13637,x13638)) % 191.49/191.42 [1364]~E(x13641,x13642)+E(f736(x13643,x13644,x13645,x13646,x13647,x13641,x13648),f736(x13643,x13644,x13645,x13646,x13647,x13642,x13648)) % 191.49/191.42 [1365]~E(x13651,x13652)+E(f736(x13653,x13654,x13655,x13656,x13657,x13658,x13651),f736(x13653,x13654,x13655,x13656,x13657,x13658,x13652)) % 191.49/191.42 [1366]~E(x13661,x13662)+E(f538(x13661,x13663,x13664,x13665,x13666),f538(x13662,x13663,x13664,x13665,x13666)) % 191.49/191.42 [1367]~E(x13671,x13672)+E(f538(x13673,x13671,x13674,x13675,x13676),f538(x13673,x13672,x13674,x13675,x13676)) % 191.49/191.42 [1368]~E(x13681,x13682)+E(f538(x13683,x13684,x13681,x13685,x13686),f538(x13683,x13684,x13682,x13685,x13686)) % 191.49/191.42 [1369]~E(x13691,x13692)+E(f538(x13693,x13694,x13695,x13691,x13696),f538(x13693,x13694,x13695,x13692,x13696)) % 191.49/191.42 [1370]~E(x13701,x13702)+E(f538(x13703,x13704,x13705,x13706,x13701),f538(x13703,x13704,x13705,x13706,x13702)) % 191.49/191.42 [1371]~E(x13711,x13712)+E(f243(x13711,x13713,x13714),f243(x13712,x13713,x13714)) % 191.49/191.42 [1372]~E(x13721,x13722)+E(f243(x13723,x13721,x13724),f243(x13723,x13722,x13724)) % 191.49/191.42 [1373]~E(x13731,x13732)+E(f243(x13733,x13734,x13731),f243(x13733,x13734,x13732)) % 191.49/191.42 [1374]~E(x13741,x13742)+E(f671(x13741,x13743,x13744),f671(x13742,x13743,x13744)) % 191.49/191.42 [1375]~E(x13751,x13752)+E(f671(x13753,x13751,x13754),f671(x13753,x13752,x13754)) % 191.49/191.42 [1376]~E(x13761,x13762)+E(f671(x13763,x13764,x13761),f671(x13763,x13764,x13762)) % 191.49/191.42 [1377]~E(x13771,x13772)+E(f805(x13771,x13773,x13774),f805(x13772,x13773,x13774)) % 191.49/191.42 [1378]~E(x13781,x13782)+E(f805(x13783,x13781,x13784),f805(x13783,x13782,x13784)) % 191.49/191.42 [1379]~E(x13791,x13792)+E(f805(x13793,x13794,x13791),f805(x13793,x13794,x13792)) % 191.49/191.42 [1380]~E(x13801,x13802)+E(f204(x13801,x13803,x13804,x13805),f204(x13802,x13803,x13804,x13805)) % 191.49/191.42 [1381]~E(x13811,x13812)+E(f204(x13813,x13811,x13814,x13815),f204(x13813,x13812,x13814,x13815)) % 191.49/191.42 [1382]~E(x13821,x13822)+E(f204(x13823,x13824,x13821,x13825),f204(x13823,x13824,x13822,x13825)) % 191.49/191.42 [1383]~E(x13831,x13832)+E(f204(x13833,x13834,x13835,x13831),f204(x13833,x13834,x13835,x13832)) % 191.49/191.42 [1384]~E(x13841,x13842)+E(f831(x13841),f831(x13842)) % 191.49/191.42 [1385]~E(x13851,x13852)+E(f613(x13851,x13853,x13854,x13855),f613(x13852,x13853,x13854,x13855)) % 191.49/191.42 [1386]~E(x13861,x13862)+E(f613(x13863,x13861,x13864,x13865),f613(x13863,x13862,x13864,x13865)) % 191.49/191.42 [1387]~E(x13871,x13872)+E(f613(x13873,x13874,x13871,x13875),f613(x13873,x13874,x13872,x13875)) % 191.49/191.42 [1388]~E(x13881,x13882)+E(f613(x13883,x13884,x13885,x13881),f613(x13883,x13884,x13885,x13882)) % 191.49/191.42 [1389]~E(x13891,x13892)+E(f515(x13891,x13893,x13894,x13895,x13896,x13897,x13898,x13899,x138910),f515(x13892,x13893,x13894,x13895,x13896,x13897,x13898,x13899,x138910)) % 191.49/191.42 [1390]~E(x13901,x13902)+E(f515(x13903,x13901,x13904,x13905,x13906,x13907,x13908,x13909,x139010),f515(x13903,x13902,x13904,x13905,x13906,x13907,x13908,x13909,x139010)) % 191.49/191.42 [1391]~E(x13911,x13912)+E(f515(x13913,x13914,x13911,x13915,x13916,x13917,x13918,x13919,x139110),f515(x13913,x13914,x13912,x13915,x13916,x13917,x13918,x13919,x139110)) % 191.49/191.42 [1392]~E(x13921,x13922)+E(f515(x13923,x13924,x13925,x13921,x13926,x13927,x13928,x13929,x139210),f515(x13923,x13924,x13925,x13922,x13926,x13927,x13928,x13929,x139210)) % 191.49/191.42 [1393]~E(x13931,x13932)+E(f515(x13933,x13934,x13935,x13936,x13931,x13937,x13938,x13939,x139310),f515(x13933,x13934,x13935,x13936,x13932,x13937,x13938,x13939,x139310)) % 191.49/191.42 [1394]~E(x13941,x13942)+E(f515(x13943,x13944,x13945,x13946,x13947,x13941,x13948,x13949,x139410),f515(x13943,x13944,x13945,x13946,x13947,x13942,x13948,x13949,x139410)) % 191.49/191.42 [1395]~E(x13951,x13952)+E(f515(x13953,x13954,x13955,x13956,x13957,x13958,x13951,x13959,x139510),f515(x13953,x13954,x13955,x13956,x13957,x13958,x13952,x13959,x139510)) % 191.49/191.42 [1396]~E(x13961,x13962)+E(f515(x13963,x13964,x13965,x13966,x13967,x13968,x13969,x13961,x139610),f515(x13963,x13964,x13965,x13966,x13967,x13968,x13969,x13962,x139610)) % 191.49/191.42 [1397]~E(x13971,x13972)+E(f515(x13973,x13974,x13975,x13976,x13977,x13978,x13979,x139710,x13971),f515(x13973,x13974,x13975,x13976,x13977,x13978,x13979,x139710,x13972)) % 191.49/191.42 [1398]~E(x13981,x13982)+E(f514(x13981,x13983,x13984),f514(x13982,x13983,x13984)) % 191.49/191.42 [1399]~E(x13991,x13992)+E(f514(x13993,x13991,x13994),f514(x13993,x13992,x13994)) % 191.49/191.42 [1400]~E(x14001,x14002)+E(f514(x14003,x14004,x14001),f514(x14003,x14004,x14002)) % 191.49/191.42 [1401]~E(x14011,x14012)+E(f267(x14011,x14013),f267(x14012,x14013)) % 191.49/191.42 [1402]~E(x14021,x14022)+E(f267(x14023,x14021),f267(x14023,x14022)) % 191.49/191.42 [1403]~E(x14031,x14032)+E(f568(x14031),f568(x14032)) % 191.49/191.42 [1404]~E(x14041,x14042)+E(f822(x14041,x14043,x14044),f822(x14042,x14043,x14044)) % 191.49/191.42 [1405]~E(x14051,x14052)+E(f822(x14053,x14051,x14054),f822(x14053,x14052,x14054)) % 191.49/191.42 [1406]~E(x14061,x14062)+E(f822(x14063,x14064,x14061),f822(x14063,x14064,x14062)) % 191.49/191.42 [1407]~E(x14071,x14072)+E(f349(x14071,x14073,x14074,x14075,x14076),f349(x14072,x14073,x14074,x14075,x14076)) % 191.49/191.42 [1408]~E(x14081,x14082)+E(f349(x14083,x14081,x14084,x14085,x14086),f349(x14083,x14082,x14084,x14085,x14086)) % 191.49/191.42 [1409]~E(x14091,x14092)+E(f349(x14093,x14094,x14091,x14095,x14096),f349(x14093,x14094,x14092,x14095,x14096)) % 191.49/191.42 [1410]~E(x14101,x14102)+E(f349(x14103,x14104,x14105,x14101,x14106),f349(x14103,x14104,x14105,x14102,x14106)) % 191.49/191.42 [1411]~E(x14111,x14112)+E(f349(x14113,x14114,x14115,x14116,x14111),f349(x14113,x14114,x14115,x14116,x14112)) % 191.49/191.42 [1412]~E(x14121,x14122)+E(f854(x14121,x14123,x14124,x14125,x14126),f854(x14122,x14123,x14124,x14125,x14126)) % 191.49/191.42 [1413]~E(x14131,x14132)+E(f854(x14133,x14131,x14134,x14135,x14136),f854(x14133,x14132,x14134,x14135,x14136)) % 191.49/191.42 [1414]~E(x14141,x14142)+E(f854(x14143,x14144,x14141,x14145,x14146),f854(x14143,x14144,x14142,x14145,x14146)) % 191.49/191.42 [1415]~E(x14151,x14152)+E(f854(x14153,x14154,x14155,x14151,x14156),f854(x14153,x14154,x14155,x14152,x14156)) % 191.49/191.42 [1416]~E(x14161,x14162)+E(f854(x14163,x14164,x14165,x14166,x14161),f854(x14163,x14164,x14165,x14166,x14162)) % 191.49/191.42 [1417]~E(x14171,x14172)+E(f625(x14171,x14173,x14174),f625(x14172,x14173,x14174)) % 191.49/191.42 [1418]~E(x14181,x14182)+E(f625(x14183,x14181,x14184),f625(x14183,x14182,x14184)) % 191.49/191.42 [1419]~E(x14191,x14192)+E(f625(x14193,x14194,x14191),f625(x14193,x14194,x14192)) % 191.49/191.42 [1420]~E(x14201,x14202)+E(f69(x14201,x14203,x14204),f69(x14202,x14203,x14204)) % 191.49/191.42 [1421]~E(x14211,x14212)+E(f69(x14213,x14211,x14214),f69(x14213,x14212,x14214)) % 191.49/191.42 [1422]~E(x14221,x14222)+E(f69(x14223,x14224,x14221),f69(x14223,x14224,x14222)) % 191.49/191.42 [1423]~E(x14231,x14232)+E(f401(x14231,x14233,x14234),f401(x14232,x14233,x14234)) % 191.49/191.42 [1424]~E(x14241,x14242)+E(f401(x14243,x14241,x14244),f401(x14243,x14242,x14244)) % 191.49/191.42 [1425]~E(x14251,x14252)+E(f401(x14253,x14254,x14251),f401(x14253,x14254,x14252)) % 191.49/191.42 [1426]~E(x14261,x14262)+E(f235(x14261,x14263,x14264,x14265,x14266),f235(x14262,x14263,x14264,x14265,x14266)) % 191.49/191.42 [1427]~E(x14271,x14272)+E(f235(x14273,x14271,x14274,x14275,x14276),f235(x14273,x14272,x14274,x14275,x14276)) % 191.49/191.42 [1428]~E(x14281,x14282)+E(f235(x14283,x14284,x14281,x14285,x14286),f235(x14283,x14284,x14282,x14285,x14286)) % 191.49/191.42 [1429]~E(x14291,x14292)+E(f235(x14293,x14294,x14295,x14291,x14296),f235(x14293,x14294,x14295,x14292,x14296)) % 191.49/191.42 [1430]~E(x14301,x14302)+E(f235(x14303,x14304,x14305,x14306,x14301),f235(x14303,x14304,x14305,x14306,x14302)) % 191.49/191.42 [1431]~E(x14311,x14312)+E(f519(x14311,x14313,x14314),f519(x14312,x14313,x14314)) % 191.49/191.42 [1432]~E(x14321,x14322)+E(f519(x14323,x14321,x14324),f519(x14323,x14322,x14324)) % 191.49/191.42 [1433]~E(x14331,x14332)+E(f519(x14333,x14334,x14331),f519(x14333,x14334,x14332)) % 191.49/191.42 [1434]~E(x14341,x14342)+E(f226(x14341,x14343),f226(x14342,x14343)) % 191.49/191.42 [1435]~E(x14351,x14352)+E(f226(x14353,x14351),f226(x14353,x14352)) % 191.49/191.42 [1436]~E(x14361,x14362)+E(f666(x14361,x14363,x14364),f666(x14362,x14363,x14364)) % 191.49/191.42 [1437]~E(x14371,x14372)+E(f666(x14373,x14371,x14374),f666(x14373,x14372,x14374)) % 191.49/191.42 [1438]~E(x14381,x14382)+E(f666(x14383,x14384,x14381),f666(x14383,x14384,x14382)) % 191.49/191.42 [1439]~E(x14391,x14392)+E(f442(x14391,x14393,x14394,x14395),f442(x14392,x14393,x14394,x14395)) % 191.49/191.42 [1440]~E(x14401,x14402)+E(f442(x14403,x14401,x14404,x14405),f442(x14403,x14402,x14404,x14405)) % 191.49/191.42 [1441]~E(x14411,x14412)+E(f442(x14413,x14414,x14411,x14415),f442(x14413,x14414,x14412,x14415)) % 191.49/191.42 [1442]~E(x14421,x14422)+E(f442(x14423,x14424,x14425,x14421),f442(x14423,x14424,x14425,x14422)) % 191.49/191.42 [1443]~E(x14431,x14432)+E(f509(x14431,x14433,x14434,x14435,x14436,x14437,x14438),f509(x14432,x14433,x14434,x14435,x14436,x14437,x14438)) % 191.49/191.42 [1444]~E(x14441,x14442)+E(f509(x14443,x14441,x14444,x14445,x14446,x14447,x14448),f509(x14443,x14442,x14444,x14445,x14446,x14447,x14448)) % 191.49/191.42 [1445]~E(x14451,x14452)+E(f509(x14453,x14454,x14451,x14455,x14456,x14457,x14458),f509(x14453,x14454,x14452,x14455,x14456,x14457,x14458)) % 191.49/191.42 [1446]~E(x14461,x14462)+E(f509(x14463,x14464,x14465,x14461,x14466,x14467,x14468),f509(x14463,x14464,x14465,x14462,x14466,x14467,x14468)) % 191.49/191.42 [1447]~E(x14471,x14472)+E(f509(x14473,x14474,x14475,x14476,x14471,x14477,x14478),f509(x14473,x14474,x14475,x14476,x14472,x14477,x14478)) % 191.49/191.42 [1448]~E(x14481,x14482)+E(f509(x14483,x14484,x14485,x14486,x14487,x14481,x14488),f509(x14483,x14484,x14485,x14486,x14487,x14482,x14488)) % 191.49/191.42 [1449]~E(x14491,x14492)+E(f509(x14493,x14494,x14495,x14496,x14497,x14498,x14491),f509(x14493,x14494,x14495,x14496,x14497,x14498,x14492)) % 191.49/191.42 [1450]~E(x14501,x14502)+E(f429(x14501,x14503,x14504),f429(x14502,x14503,x14504)) % 191.49/191.42 [1451]~E(x14511,x14512)+E(f429(x14513,x14511,x14514),f429(x14513,x14512,x14514)) % 191.49/191.42 [1452]~E(x14521,x14522)+E(f429(x14523,x14524,x14521),f429(x14523,x14524,x14522)) % 191.49/191.42 [1453]~E(x14531,x14532)+E(f423(x14531,x14533),f423(x14532,x14533)) % 191.49/191.42 [1454]~E(x14541,x14542)+E(f423(x14543,x14541),f423(x14543,x14542)) % 191.49/191.42 [1455]~E(x14551,x14552)+E(f836(x14551,x14553,x14554,x14555),f836(x14552,x14553,x14554,x14555)) % 191.49/191.42 [1456]~E(x14561,x14562)+E(f836(x14563,x14561,x14564,x14565),f836(x14563,x14562,x14564,x14565)) % 191.49/191.42 [1457]~E(x14571,x14572)+E(f836(x14573,x14574,x14571,x14575),f836(x14573,x14574,x14572,x14575)) % 191.49/191.42 [1458]~E(x14581,x14582)+E(f836(x14583,x14584,x14585,x14581),f836(x14583,x14584,x14585,x14582)) % 191.49/191.42 [1459]~E(x14591,x14592)+E(f603(x14591,x14593,x14594,x14595),f603(x14592,x14593,x14594,x14595)) % 191.49/191.42 [1460]~E(x14601,x14602)+E(f603(x14603,x14601,x14604,x14605),f603(x14603,x14602,x14604,x14605)) % 191.49/191.42 [1461]~E(x14611,x14612)+E(f603(x14613,x14614,x14611,x14615),f603(x14613,x14614,x14612,x14615)) % 191.49/191.42 [1462]~E(x14621,x14622)+E(f603(x14623,x14624,x14625,x14621),f603(x14623,x14624,x14625,x14622)) % 191.49/191.42 [1463]~E(x14631,x14632)+E(f224(x14631,x14633),f224(x14632,x14633)) % 191.49/191.42 [1464]~E(x14641,x14642)+E(f224(x14643,x14641),f224(x14643,x14642)) % 191.49/191.42 [1465]~E(x14651,x14652)+E(f812(x14651,x14653,x14654),f812(x14652,x14653,x14654)) % 191.49/191.42 [1466]~E(x14661,x14662)+E(f812(x14663,x14661,x14664),f812(x14663,x14662,x14664)) % 191.49/191.42 [1467]~E(x14671,x14672)+E(f812(x14673,x14674,x14671),f812(x14673,x14674,x14672)) % 191.49/191.42 [1468]~E(x14681,x14682)+E(f586(x14681,x14683,x14684),f586(x14682,x14683,x14684)) % 191.49/191.42 [1469]~E(x14691,x14692)+E(f586(x14693,x14691,x14694),f586(x14693,x14692,x14694)) % 191.49/191.42 [1470]~E(x14701,x14702)+E(f586(x14703,x14704,x14701),f586(x14703,x14704,x14702)) % 191.49/191.42 [1471]~E(x14711,x14712)+E(f460(x14711,x14713,x14714,x14715),f460(x14712,x14713,x14714,x14715)) % 191.49/191.42 [1472]~E(x14721,x14722)+E(f460(x14723,x14721,x14724,x14725),f460(x14723,x14722,x14724,x14725)) % 191.49/191.42 [1473]~E(x14731,x14732)+E(f460(x14733,x14734,x14731,x14735),f460(x14733,x14734,x14732,x14735)) % 191.49/191.42 [1474]~E(x14741,x14742)+E(f460(x14743,x14744,x14745,x14741),f460(x14743,x14744,x14745,x14742)) % 191.49/191.42 [1475]~E(x14751,x14752)+E(f734(x14751,x14753,x14754,x14755,x14756,x14757),f734(x14752,x14753,x14754,x14755,x14756,x14757)) % 191.49/191.42 [1476]~E(x14761,x14762)+E(f734(x14763,x14761,x14764,x14765,x14766,x14767),f734(x14763,x14762,x14764,x14765,x14766,x14767)) % 191.49/191.42 [1477]~E(x14771,x14772)+E(f734(x14773,x14774,x14771,x14775,x14776,x14777),f734(x14773,x14774,x14772,x14775,x14776,x14777)) % 191.49/191.42 [1478]~E(x14781,x14782)+E(f734(x14783,x14784,x14785,x14781,x14786,x14787),f734(x14783,x14784,x14785,x14782,x14786,x14787)) % 191.49/191.42 [1479]~E(x14791,x14792)+E(f734(x14793,x14794,x14795,x14796,x14791,x14797),f734(x14793,x14794,x14795,x14796,x14792,x14797)) % 191.49/191.42 [1480]~E(x14801,x14802)+E(f734(x14803,x14804,x14805,x14806,x14807,x14801),f734(x14803,x14804,x14805,x14806,x14807,x14802)) % 191.49/191.42 [1481]~E(x14811,x14812)+E(f562(x14811,x14813,x14814,x14815,x14816,x14817,x14818),f562(x14812,x14813,x14814,x14815,x14816,x14817,x14818)) % 191.49/191.42 [1482]~E(x14821,x14822)+E(f562(x14823,x14821,x14824,x14825,x14826,x14827,x14828),f562(x14823,x14822,x14824,x14825,x14826,x14827,x14828)) % 191.49/191.42 [1483]~E(x14831,x14832)+E(f562(x14833,x14834,x14831,x14835,x14836,x14837,x14838),f562(x14833,x14834,x14832,x14835,x14836,x14837,x14838)) % 191.49/191.42 [1484]~E(x14841,x14842)+E(f562(x14843,x14844,x14845,x14841,x14846,x14847,x14848),f562(x14843,x14844,x14845,x14842,x14846,x14847,x14848)) % 191.49/191.42 [1485]~E(x14851,x14852)+E(f562(x14853,x14854,x14855,x14856,x14851,x14857,x14858),f562(x14853,x14854,x14855,x14856,x14852,x14857,x14858)) % 191.49/191.42 [1486]~E(x14861,x14862)+E(f562(x14863,x14864,x14865,x14866,x14867,x14861,x14868),f562(x14863,x14864,x14865,x14866,x14867,x14862,x14868)) % 191.49/191.42 [1487]~E(x14871,x14872)+E(f562(x14873,x14874,x14875,x14876,x14877,x14878,x14871),f562(x14873,x14874,x14875,x14876,x14877,x14878,x14872)) % 191.49/191.42 [1488]~E(x14881,x14882)+E(f561(x14881,x14883,x14884,x14885,x14886,x14887,x14888),f561(x14882,x14883,x14884,x14885,x14886,x14887,x14888)) % 191.49/191.42 [1489]~E(x14891,x14892)+E(f561(x14893,x14891,x14894,x14895,x14896,x14897,x14898),f561(x14893,x14892,x14894,x14895,x14896,x14897,x14898)) % 191.49/191.42 [1490]~E(x14901,x14902)+E(f561(x14903,x14904,x14901,x14905,x14906,x14907,x14908),f561(x14903,x14904,x14902,x14905,x14906,x14907,x14908)) % 191.49/191.42 [1491]~E(x14911,x14912)+E(f561(x14913,x14914,x14915,x14911,x14916,x14917,x14918),f561(x14913,x14914,x14915,x14912,x14916,x14917,x14918)) % 191.49/191.42 [1492]~E(x14921,x14922)+E(f561(x14923,x14924,x14925,x14926,x14921,x14927,x14928),f561(x14923,x14924,x14925,x14926,x14922,x14927,x14928)) % 191.49/191.42 [1493]~E(x14931,x14932)+E(f561(x14933,x14934,x14935,x14936,x14937,x14931,x14938),f561(x14933,x14934,x14935,x14936,x14937,x14932,x14938)) % 191.49/191.42 [1494]~E(x14941,x14942)+E(f561(x14943,x14944,x14945,x14946,x14947,x14948,x14941),f561(x14943,x14944,x14945,x14946,x14947,x14948,x14942)) % 191.49/191.42 [1495]~E(x14951,x14952)+E(f228(x14951,x14953),f228(x14952,x14953)) % 191.49/191.42 [1496]~E(x14961,x14962)+E(f228(x14963,x14961),f228(x14963,x14962)) % 191.49/191.42 [1497]~E(x14971,x14972)+E(f800(x14971,x14973,x14974),f800(x14972,x14973,x14974)) % 191.49/191.42 [1498]~E(x14981,x14982)+E(f800(x14983,x14981,x14984),f800(x14983,x14982,x14984)) % 191.49/191.42 [1499]~E(x14991,x14992)+E(f800(x14993,x14994,x14991),f800(x14993,x14994,x14992)) % 191.49/191.42 [1500]~E(x15001,x15002)+E(f600(x15001,x15003,x15004),f600(x15002,x15003,x15004)) % 191.49/191.42 [1501]~E(x15011,x15012)+E(f600(x15013,x15011,x15014),f600(x15013,x15012,x15014)) % 191.49/191.42 [1502]~E(x15021,x15022)+E(f600(x15023,x15024,x15021),f600(x15023,x15024,x15022)) % 191.49/191.42 [1503]~E(x15031,x15032)+E(f181(x15031),f181(x15032)) % 191.49/191.42 [1504]~E(x15041,x15042)+E(f609(x15041,x15043,x15044,x15045),f609(x15042,x15043,x15044,x15045)) % 191.49/191.42 [1505]~E(x15051,x15052)+E(f609(x15053,x15051,x15054,x15055),f609(x15053,x15052,x15054,x15055)) % 191.49/191.42 [1506]~E(x15061,x15062)+E(f609(x15063,x15064,x15061,x15065),f609(x15063,x15064,x15062,x15065)) % 191.49/191.42 [1507]~E(x15071,x15072)+E(f609(x15073,x15074,x15075,x15071),f609(x15073,x15074,x15075,x15072)) % 191.49/191.42 [1508]~E(x15081,x15082)+E(f488(x15081,x15083),f488(x15082,x15083)) % 191.49/191.42 [1509]~E(x15091,x15092)+E(f488(x15093,x15091),f488(x15093,x15092)) % 191.49/191.42 [1510]~E(x15101,x15102)+E(f618(x15101,x15103,x15104,x15105),f618(x15102,x15103,x15104,x15105)) % 191.49/191.42 [1511]~E(x15111,x15112)+E(f618(x15113,x15111,x15114,x15115),f618(x15113,x15112,x15114,x15115)) % 191.49/191.42 [1512]~E(x15121,x15122)+E(f618(x15123,x15124,x15121,x15125),f618(x15123,x15124,x15122,x15125)) % 191.49/191.42 [1513]~E(x15131,x15132)+E(f618(x15133,x15134,x15135,x15131),f618(x15133,x15134,x15135,x15132)) % 191.49/191.42 [1514]~E(x15141,x15142)+E(f789(x15141,x15143,x15144,x15145),f789(x15142,x15143,x15144,x15145)) % 191.49/191.42 [1515]~E(x15151,x15152)+E(f789(x15153,x15151,x15154,x15155),f789(x15153,x15152,x15154,x15155)) % 191.49/191.42 [1516]~E(x15161,x15162)+E(f789(x15163,x15164,x15161,x15165),f789(x15163,x15164,x15162,x15165)) % 191.49/191.42 [1517]~E(x15171,x15172)+E(f789(x15173,x15174,x15175,x15171),f789(x15173,x15174,x15175,x15172)) % 191.49/191.42 [1518]~E(x15181,x15182)+E(f758(x15181,x15183,x15184,x15185),f758(x15182,x15183,x15184,x15185)) % 191.49/191.42 [1519]~E(x15191,x15192)+E(f758(x15193,x15191,x15194,x15195),f758(x15193,x15192,x15194,x15195)) % 191.49/191.42 [1520]~E(x15201,x15202)+E(f758(x15203,x15204,x15201,x15205),f758(x15203,x15204,x15202,x15205)) % 191.49/191.42 [1521]~E(x15211,x15212)+E(f758(x15213,x15214,x15215,x15211),f758(x15213,x15214,x15215,x15212)) % 191.49/191.42 [1522]~E(x15221,x15222)+E(f856(x15221,x15223,x15224,x15225),f856(x15222,x15223,x15224,x15225)) % 191.49/191.42 [1523]~E(x15231,x15232)+E(f856(x15233,x15231,x15234,x15235),f856(x15233,x15232,x15234,x15235)) % 191.49/191.42 [1524]~E(x15241,x15242)+E(f856(x15243,x15244,x15241,x15245),f856(x15243,x15244,x15242,x15245)) % 191.49/191.42 [1525]~E(x15251,x15252)+E(f856(x15253,x15254,x15255,x15251),f856(x15253,x15254,x15255,x15252)) % 191.49/191.42 [1526]~E(x15261,x15262)+E(f793(x15261,x15263,x15264),f793(x15262,x15263,x15264)) % 191.49/191.42 [1527]~E(x15271,x15272)+E(f793(x15273,x15271,x15274),f793(x15273,x15272,x15274)) % 191.49/191.42 [1528]~E(x15281,x15282)+E(f793(x15283,x15284,x15281),f793(x15283,x15284,x15282)) % 191.49/191.42 [1529]~E(x15291,x15292)+E(f759(x15291,x15293,x15294,x15295,x15296),f759(x15292,x15293,x15294,x15295,x15296)) % 191.49/191.42 [1530]~E(x15301,x15302)+E(f759(x15303,x15301,x15304,x15305,x15306),f759(x15303,x15302,x15304,x15305,x15306)) % 191.49/191.42 [1531]~E(x15311,x15312)+E(f759(x15313,x15314,x15311,x15315,x15316),f759(x15313,x15314,x15312,x15315,x15316)) % 191.49/191.42 [1532]~E(x15321,x15322)+E(f759(x15323,x15324,x15325,x15321,x15326),f759(x15323,x15324,x15325,x15322,x15326)) % 191.49/191.42 [1533]~E(x15331,x15332)+E(f759(x15333,x15334,x15335,x15336,x15331),f759(x15333,x15334,x15335,x15336,x15332)) % 191.49/191.42 [1534]~E(x15341,x15342)+E(f473(x15341,x15343,x15344),f473(x15342,x15343,x15344)) % 191.49/191.42 [1535]~E(x15351,x15352)+E(f473(x15353,x15351,x15354),f473(x15353,x15352,x15354)) % 191.49/191.42 [1536]~E(x15361,x15362)+E(f473(x15363,x15364,x15361),f473(x15363,x15364,x15362)) % 191.49/191.42 [1537]~E(x15371,x15372)+E(f766(x15371,x15373,x15374),f766(x15372,x15373,x15374)) % 191.49/191.42 [1538]~E(x15381,x15382)+E(f766(x15383,x15381,x15384),f766(x15383,x15382,x15384)) % 191.49/191.42 [1539]~E(x15391,x15392)+E(f766(x15393,x15394,x15391),f766(x15393,x15394,x15392)) % 191.49/191.42 [1540]~E(x15401,x15402)+E(f459(x15401,x15403,x15404),f459(x15402,x15403,x15404)) % 191.49/191.42 [1541]~E(x15411,x15412)+E(f459(x15413,x15411,x15414),f459(x15413,x15412,x15414)) % 191.49/191.42 [1542]~E(x15421,x15422)+E(f459(x15423,x15424,x15421),f459(x15423,x15424,x15422)) % 191.49/191.42 [1543]~E(x15431,x15432)+E(f45(x15431),f45(x15432)) % 191.49/191.42 [1544]~E(x15441,x15442)+E(f508(x15441,x15443,x15444),f508(x15442,x15443,x15444)) % 191.49/191.42 [1545]~E(x15451,x15452)+E(f508(x15453,x15451,x15454),f508(x15453,x15452,x15454)) % 191.49/191.42 [1546]~E(x15461,x15462)+E(f508(x15463,x15464,x15461),f508(x15463,x15464,x15462)) % 191.49/191.42 [1547]~E(x15471,x15472)+E(f131(x15471,x15473),f131(x15472,x15473)) % 191.49/191.42 [1548]~E(x15481,x15482)+E(f131(x15483,x15481),f131(x15483,x15482)) % 191.49/191.42 [1549]~E(x15491,x15492)+E(f377(x15491,x15493,x15494),f377(x15492,x15493,x15494)) % 191.49/191.42 [1550]~E(x15501,x15502)+E(f377(x15503,x15501,x15504),f377(x15503,x15502,x15504)) % 191.49/191.42 [1551]~E(x15511,x15512)+E(f377(x15513,x15514,x15511),f377(x15513,x15514,x15512)) % 191.49/191.42 [1552]~E(x15521,x15522)+E(f701(x15521,x15523,x15524),f701(x15522,x15523,x15524)) % 191.49/191.42 [1553]~E(x15531,x15532)+E(f701(x15533,x15531,x15534),f701(x15533,x15532,x15534)) % 191.49/191.42 [1554]~E(x15541,x15542)+E(f701(x15543,x15544,x15541),f701(x15543,x15544,x15542)) % 191.49/191.42 [1555]~E(x15551,x15552)+E(f748(x15551,x15553,x15554,x15555,x15556),f748(x15552,x15553,x15554,x15555,x15556)) % 191.49/191.42 [1556]~E(x15561,x15562)+E(f748(x15563,x15561,x15564,x15565,x15566),f748(x15563,x15562,x15564,x15565,x15566)) % 191.49/191.42 [1557]~E(x15571,x15572)+E(f748(x15573,x15574,x15571,x15575,x15576),f748(x15573,x15574,x15572,x15575,x15576)) % 191.49/191.42 [1558]~E(x15581,x15582)+E(f748(x15583,x15584,x15585,x15581,x15586),f748(x15583,x15584,x15585,x15582,x15586)) % 191.49/191.42 [1559]~E(x15591,x15592)+E(f748(x15593,x15594,x15595,x15596,x15591),f748(x15593,x15594,x15595,x15596,x15592)) % 191.49/191.42 [1560]~E(x15601,x15602)+E(f456(x15601,x15603,x15604,x15605),f456(x15602,x15603,x15604,x15605)) % 191.49/191.42 [1561]~E(x15611,x15612)+E(f456(x15613,x15611,x15614,x15615),f456(x15613,x15612,x15614,x15615)) % 191.49/191.42 [1562]~E(x15621,x15622)+E(f456(x15623,x15624,x15621,x15625),f456(x15623,x15624,x15622,x15625)) % 191.49/191.42 [1563]~E(x15631,x15632)+E(f456(x15633,x15634,x15635,x15631),f456(x15633,x15634,x15635,x15632)) % 191.49/191.42 [1564]~E(x15641,x15642)+E(f130(x15641),f130(x15642)) % 191.49/191.42 [1565]~E(x15651,x15652)+E(f652(x15651,x15653,x15654,x15655,x15656),f652(x15652,x15653,x15654,x15655,x15656)) % 191.49/191.42 [1566]~E(x15661,x15662)+E(f652(x15663,x15661,x15664,x15665,x15666),f652(x15663,x15662,x15664,x15665,x15666)) % 191.49/191.42 [1567]~E(x15671,x15672)+E(f652(x15673,x15674,x15671,x15675,x15676),f652(x15673,x15674,x15672,x15675,x15676)) % 191.49/191.42 [1568]~E(x15681,x15682)+E(f652(x15683,x15684,x15685,x15681,x15686),f652(x15683,x15684,x15685,x15682,x15686)) % 191.49/191.42 [1569]~E(x15691,x15692)+E(f652(x15693,x15694,x15695,x15696,x15691),f652(x15693,x15694,x15695,x15696,x15692)) % 191.49/191.42 [1570]~E(x15701,x15702)+E(f673(x15701,x15703,x15704,x15705),f673(x15702,x15703,x15704,x15705)) % 191.49/191.42 [1571]~E(x15711,x15712)+E(f673(x15713,x15711,x15714,x15715),f673(x15713,x15712,x15714,x15715)) % 191.49/191.42 [1572]~E(x15721,x15722)+E(f673(x15723,x15724,x15721,x15725),f673(x15723,x15724,x15722,x15725)) % 191.49/191.42 [1573]~E(x15731,x15732)+E(f673(x15733,x15734,x15735,x15731),f673(x15733,x15734,x15735,x15732)) % 191.49/191.42 [1574]~E(x15741,x15742)+E(f839(x15741,x15743),f839(x15742,x15743)) % 191.49/191.42 [1575]~E(x15751,x15752)+E(f839(x15753,x15751),f839(x15753,x15752)) % 191.49/191.42 [1576]~E(x15761,x15762)+E(f265(x15761,x15763,x15764),f265(x15762,x15763,x15764)) % 191.49/191.42 [1577]~E(x15771,x15772)+E(f265(x15773,x15771,x15774),f265(x15773,x15772,x15774)) % 191.49/191.42 [1578]~E(x15781,x15782)+E(f265(x15783,x15784,x15781),f265(x15783,x15784,x15782)) % 191.49/191.42 [1579]~E(x15791,x15792)+E(f357(x15791,x15793,x15794,x15795,x15796),f357(x15792,x15793,x15794,x15795,x15796)) % 191.49/191.42 [1580]~E(x15801,x15802)+E(f357(x15803,x15801,x15804,x15805,x15806),f357(x15803,x15802,x15804,x15805,x15806)) % 191.49/191.42 [1581]~E(x15811,x15812)+E(f357(x15813,x15814,x15811,x15815,x15816),f357(x15813,x15814,x15812,x15815,x15816)) % 191.49/191.42 [1582]~E(x15821,x15822)+E(f357(x15823,x15824,x15825,x15821,x15826),f357(x15823,x15824,x15825,x15822,x15826)) % 191.49/191.42 [1583]~E(x15831,x15832)+E(f357(x15833,x15834,x15835,x15836,x15831),f357(x15833,x15834,x15835,x15836,x15832)) % 191.49/191.42 [1584]~E(x15841,x15842)+E(f524(x15841,x15843,x15844,x15845),f524(x15842,x15843,x15844,x15845)) % 191.49/191.42 [1585]~E(x15851,x15852)+E(f524(x15853,x15851,x15854,x15855),f524(x15853,x15852,x15854,x15855)) % 191.49/191.42 [1586]~E(x15861,x15862)+E(f524(x15863,x15864,x15861,x15865),f524(x15863,x15864,x15862,x15865)) % 191.49/191.42 [1587]~E(x15871,x15872)+E(f524(x15873,x15874,x15875,x15871),f524(x15873,x15874,x15875,x15872)) % 191.49/191.42 [1588]~E(x15881,x15882)+E(f587(x15881,x15883,x15884,x15885),f587(x15882,x15883,x15884,x15885)) % 191.49/191.42 [1589]~E(x15891,x15892)+E(f587(x15893,x15891,x15894,x15895),f587(x15893,x15892,x15894,x15895)) % 191.49/191.42 [1590]~E(x15901,x15902)+E(f587(x15903,x15904,x15901,x15905),f587(x15903,x15904,x15902,x15905)) % 191.49/191.42 [1591]~E(x15911,x15912)+E(f587(x15913,x15914,x15915,x15911),f587(x15913,x15914,x15915,x15912)) % 191.49/191.42 [1592]~E(x15921,x15922)+E(f626(x15921,x15923,x15924),f626(x15922,x15923,x15924)) % 191.49/191.42 [1593]~E(x15931,x15932)+E(f626(x15933,x15931,x15934),f626(x15933,x15932,x15934)) % 191.49/191.42 [1594]~E(x15941,x15942)+E(f626(x15943,x15944,x15941),f626(x15943,x15944,x15942)) % 191.49/191.42 [1595]~E(x15951,x15952)+E(f385(x15951,x15953,x15954,x15955),f385(x15952,x15953,x15954,x15955)) % 191.49/191.42 [1596]~E(x15961,x15962)+E(f385(x15963,x15961,x15964,x15965),f385(x15963,x15962,x15964,x15965)) % 191.49/191.42 [1597]~E(x15971,x15972)+E(f385(x15973,x15974,x15971,x15975),f385(x15973,x15974,x15972,x15975)) % 191.49/191.42 [1598]~E(x15981,x15982)+E(f385(x15983,x15984,x15985,x15981),f385(x15983,x15984,x15985,x15982)) % 191.49/191.42 [1599]~E(x15991,x15992)+E(f869(x15991,x15993,x15994,x15995),f869(x15992,x15993,x15994,x15995)) % 191.49/191.42 [1600]~E(x16001,x16002)+E(f869(x16003,x16001,x16004,x16005),f869(x16003,x16002,x16004,x16005)) % 191.49/191.42 [1601]~E(x16011,x16012)+E(f869(x16013,x16014,x16011,x16015),f869(x16013,x16014,x16012,x16015)) % 191.49/191.42 [1602]~E(x16021,x16022)+E(f869(x16023,x16024,x16025,x16021),f869(x16023,x16024,x16025,x16022)) % 191.49/191.42 [1603]~E(x16031,x16032)+E(f388(x16031),f388(x16032)) % 191.49/191.42 [1604]~E(x16041,x16042)+E(f621(x16041,x16043,x16044,x16045,x16046,x16047,x16048,x16049),f621(x16042,x16043,x16044,x16045,x16046,x16047,x16048,x16049)) % 191.49/191.42 [1605]~E(x16051,x16052)+E(f621(x16053,x16051,x16054,x16055,x16056,x16057,x16058,x16059),f621(x16053,x16052,x16054,x16055,x16056,x16057,x16058,x16059)) % 191.49/191.42 [1606]~E(x16061,x16062)+E(f621(x16063,x16064,x16061,x16065,x16066,x16067,x16068,x16069),f621(x16063,x16064,x16062,x16065,x16066,x16067,x16068,x16069)) % 191.49/191.42 [1607]~E(x16071,x16072)+E(f621(x16073,x16074,x16075,x16071,x16076,x16077,x16078,x16079),f621(x16073,x16074,x16075,x16072,x16076,x16077,x16078,x16079)) % 191.49/191.42 [1608]~E(x16081,x16082)+E(f621(x16083,x16084,x16085,x16086,x16081,x16087,x16088,x16089),f621(x16083,x16084,x16085,x16086,x16082,x16087,x16088,x16089)) % 191.49/191.42 [1609]~E(x16091,x16092)+E(f621(x16093,x16094,x16095,x16096,x16097,x16091,x16098,x16099),f621(x16093,x16094,x16095,x16096,x16097,x16092,x16098,x16099)) % 191.49/191.42 [1610]~E(x16101,x16102)+E(f621(x16103,x16104,x16105,x16106,x16107,x16108,x16101,x16109),f621(x16103,x16104,x16105,x16106,x16107,x16108,x16102,x16109)) % 191.49/191.42 [1611]~E(x16111,x16112)+E(f621(x16113,x16114,x16115,x16116,x16117,x16118,x16119,x16111),f621(x16113,x16114,x16115,x16116,x16117,x16118,x16119,x16112)) % 191.49/191.42 [1612]~E(x16121,x16122)+E(f684(x16121,x16123),f684(x16122,x16123)) % 191.49/191.42 [1613]~E(x16131,x16132)+E(f684(x16133,x16131),f684(x16133,x16132)) % 191.49/191.42 [1614]~E(x16141,x16142)+E(f407(x16141,x16143,x16144),f407(x16142,x16143,x16144)) % 191.49/191.42 [1615]~E(x16151,x16152)+E(f407(x16153,x16151,x16154),f407(x16153,x16152,x16154)) % 191.49/191.42 [1616]~E(x16161,x16162)+E(f407(x16163,x16164,x16161),f407(x16163,x16164,x16162)) % 191.49/191.42 [1617]~E(x16171,x16172)+E(f837(x16171,x16173,x16174),f837(x16172,x16173,x16174)) % 191.49/191.42 [1618]~E(x16181,x16182)+E(f837(x16183,x16181,x16184),f837(x16183,x16182,x16184)) % 191.49/191.42 [1619]~E(x16191,x16192)+E(f837(x16193,x16194,x16191),f837(x16193,x16194,x16192)) % 191.49/191.42 [1620]~E(x16201,x16202)+E(f747(x16201,x16203,x16204),f747(x16202,x16203,x16204)) % 191.49/191.42 [1621]~E(x16211,x16212)+E(f747(x16213,x16211,x16214),f747(x16213,x16212,x16214)) % 191.49/191.42 [1622]~E(x16221,x16222)+E(f747(x16223,x16224,x16221),f747(x16223,x16224,x16222)) % 191.49/191.42 [1623]~E(x16231,x16232)+E(f420(x16231,x16233,x16234,x16235),f420(x16232,x16233,x16234,x16235)) % 191.49/191.42 [1624]~E(x16241,x16242)+E(f420(x16243,x16241,x16244,x16245),f420(x16243,x16242,x16244,x16245)) % 191.49/191.42 [1625]~E(x16251,x16252)+E(f420(x16253,x16254,x16251,x16255),f420(x16253,x16254,x16252,x16255)) % 191.49/191.42 [1626]~E(x16261,x16262)+E(f420(x16263,x16264,x16265,x16261),f420(x16263,x16264,x16265,x16262)) % 191.49/191.42 [1627]~E(x16271,x16272)+E(f411(x16271,x16273,x16274),f411(x16272,x16273,x16274)) % 191.49/191.42 [1628]~E(x16281,x16282)+E(f411(x16283,x16281,x16284),f411(x16283,x16282,x16284)) % 191.49/191.42 [1629]~E(x16291,x16292)+E(f411(x16293,x16294,x16291),f411(x16293,x16294,x16292)) % 191.49/191.42 [1630]~E(x16301,x16302)+E(f799(x16301,x16303,x16304),f799(x16302,x16303,x16304)) % 191.49/191.42 [1631]~E(x16311,x16312)+E(f799(x16313,x16311,x16314),f799(x16313,x16312,x16314)) % 191.49/191.42 [1632]~E(x16321,x16322)+E(f799(x16323,x16324,x16321),f799(x16323,x16324,x16322)) % 191.49/191.42 [1633]~E(x16331,x16332)+E(f761(x16331,x16333,x16334),f761(x16332,x16333,x16334)) % 191.49/191.42 [1634]~E(x16341,x16342)+E(f761(x16343,x16341,x16344),f761(x16343,x16342,x16344)) % 191.49/191.42 [1635]~E(x16351,x16352)+E(f761(x16353,x16354,x16351),f761(x16353,x16354,x16352)) % 191.49/191.42 [1636]~E(x16361,x16362)+E(f234(x16361,x16363,x16364,x16365,x16366),f234(x16362,x16363,x16364,x16365,x16366)) % 191.49/191.42 [1637]~E(x16371,x16372)+E(f234(x16373,x16371,x16374,x16375,x16376),f234(x16373,x16372,x16374,x16375,x16376)) % 191.49/191.42 [1638]~E(x16381,x16382)+E(f234(x16383,x16384,x16381,x16385,x16386),f234(x16383,x16384,x16382,x16385,x16386)) % 191.49/191.42 [1639]~E(x16391,x16392)+E(f234(x16393,x16394,x16395,x16391,x16396),f234(x16393,x16394,x16395,x16392,x16396)) % 191.49/191.42 [1640]~E(x16401,x16402)+E(f234(x16403,x16404,x16405,x16406,x16401),f234(x16403,x16404,x16405,x16406,x16402)) % 191.49/191.42 [1641]~E(x16411,x16412)+E(f501(x16411,x16413,x16414),f501(x16412,x16413,x16414)) % 191.49/191.42 [1642]~E(x16421,x16422)+E(f501(x16423,x16421,x16424),f501(x16423,x16422,x16424)) % 191.49/191.42 [1643]~E(x16431,x16432)+E(f501(x16433,x16434,x16431),f501(x16433,x16434,x16432)) % 191.49/191.42 [1644]~E(x16441,x16442)+E(f616(x16441,x16443,x16444),f616(x16442,x16443,x16444)) % 191.49/191.42 [1645]~E(x16451,x16452)+E(f616(x16453,x16451,x16454),f616(x16453,x16452,x16454)) % 191.49/191.42 [1646]~E(x16461,x16462)+E(f616(x16463,x16464,x16461),f616(x16463,x16464,x16462)) % 191.49/191.42 [1647]~E(x16471,x16472)+E(f218(x16471,x16473,x16474,x16475,x16476,x16477,x16478),f218(x16472,x16473,x16474,x16475,x16476,x16477,x16478)) % 191.49/191.42 [1648]~E(x16481,x16482)+E(f218(x16483,x16481,x16484,x16485,x16486,x16487,x16488),f218(x16483,x16482,x16484,x16485,x16486,x16487,x16488)) % 191.49/191.42 [1649]~E(x16491,x16492)+E(f218(x16493,x16494,x16491,x16495,x16496,x16497,x16498),f218(x16493,x16494,x16492,x16495,x16496,x16497,x16498)) % 191.49/191.42 [1650]~E(x16501,x16502)+E(f218(x16503,x16504,x16505,x16501,x16506,x16507,x16508),f218(x16503,x16504,x16505,x16502,x16506,x16507,x16508)) % 191.49/191.42 [1651]~E(x16511,x16512)+E(f218(x16513,x16514,x16515,x16516,x16511,x16517,x16518),f218(x16513,x16514,x16515,x16516,x16512,x16517,x16518)) % 191.49/191.42 [1652]~E(x16521,x16522)+E(f218(x16523,x16524,x16525,x16526,x16527,x16521,x16528),f218(x16523,x16524,x16525,x16526,x16527,x16522,x16528)) % 191.49/191.42 [1653]~E(x16531,x16532)+E(f218(x16533,x16534,x16535,x16536,x16537,x16538,x16531),f218(x16533,x16534,x16535,x16536,x16537,x16538,x16532)) % 191.49/191.42 [1654]~E(x16541,x16542)+E(f412(x16541,x16543),f412(x16542,x16543)) % 191.49/191.42 [1655]~E(x16551,x16552)+E(f412(x16553,x16551),f412(x16553,x16552)) % 191.49/191.42 [1656]~E(x16561,x16562)+E(f559(x16561,x16563,x16564,x16565,x16566),f559(x16562,x16563,x16564,x16565,x16566)) % 191.49/191.42 [1657]~E(x16571,x16572)+E(f559(x16573,x16571,x16574,x16575,x16576),f559(x16573,x16572,x16574,x16575,x16576)) % 191.49/191.42 [1658]~E(x16581,x16582)+E(f559(x16583,x16584,x16581,x16585,x16586),f559(x16583,x16584,x16582,x16585,x16586)) % 191.49/191.42 [1659]~E(x16591,x16592)+E(f559(x16593,x16594,x16595,x16591,x16596),f559(x16593,x16594,x16595,x16592,x16596)) % 191.49/191.42 [1660]~E(x16601,x16602)+E(f559(x16603,x16604,x16605,x16606,x16601),f559(x16603,x16604,x16605,x16606,x16602)) % 191.49/191.42 [1661]~E(x16611,x16612)+E(f660(x16611,x16613,x16614),f660(x16612,x16613,x16614)) % 191.49/191.42 [1662]~E(x16621,x16622)+E(f660(x16623,x16621,x16624),f660(x16623,x16622,x16624)) % 191.49/191.42 [1663]~E(x16631,x16632)+E(f660(x16633,x16634,x16631),f660(x16633,x16634,x16632)) % 191.49/191.42 [1664]~E(x16641,x16642)+E(f23(x16641,x16643),f23(x16642,x16643)) % 191.49/191.42 [1665]~E(x16651,x16652)+E(f23(x16653,x16651),f23(x16653,x16652)) % 191.49/191.42 [1666]~E(x16661,x16662)+E(f341(x16661),f341(x16662)) % 191.49/191.42 [1667]~E(x16671,x16672)+E(f558(x16671,x16673,x16674,x16675),f558(x16672,x16673,x16674,x16675)) % 191.49/191.42 [1668]~E(x16681,x16682)+E(f558(x16683,x16681,x16684,x16685),f558(x16683,x16682,x16684,x16685)) % 191.49/191.42 [1669]~E(x16691,x16692)+E(f558(x16693,x16694,x16691,x16695),f558(x16693,x16694,x16692,x16695)) % 191.49/191.42 [1670]~E(x16701,x16702)+E(f558(x16703,x16704,x16705,x16701),f558(x16703,x16704,x16705,x16702)) % 191.49/191.42 [1671]~E(x16711,x16712)+E(f711(x16711,x16713,x16714,x16715),f711(x16712,x16713,x16714,x16715)) % 191.49/191.42 [1672]~E(x16721,x16722)+E(f711(x16723,x16721,x16724,x16725),f711(x16723,x16722,x16724,x16725)) % 191.49/191.42 [1673]~E(x16731,x16732)+E(f711(x16733,x16734,x16731,x16735),f711(x16733,x16734,x16732,x16735)) % 191.49/191.42 [1674]~E(x16741,x16742)+E(f711(x16743,x16744,x16745,x16741),f711(x16743,x16744,x16745,x16742)) % 191.49/191.42 [1675]~E(x16751,x16752)+E(f462(x16751,x16753,x16754,x16755,x16756,x16757,x16758,x16759),f462(x16752,x16753,x16754,x16755,x16756,x16757,x16758,x16759)) % 191.49/191.42 [1676]~E(x16761,x16762)+E(f462(x16763,x16761,x16764,x16765,x16766,x16767,x16768,x16769),f462(x16763,x16762,x16764,x16765,x16766,x16767,x16768,x16769)) % 191.49/191.42 [1677]~E(x16771,x16772)+E(f462(x16773,x16774,x16771,x16775,x16776,x16777,x16778,x16779),f462(x16773,x16774,x16772,x16775,x16776,x16777,x16778,x16779)) % 191.49/191.42 [1678]~E(x16781,x16782)+E(f462(x16783,x16784,x16785,x16781,x16786,x16787,x16788,x16789),f462(x16783,x16784,x16785,x16782,x16786,x16787,x16788,x16789)) % 191.49/191.42 [1679]~E(x16791,x16792)+E(f462(x16793,x16794,x16795,x16796,x16791,x16797,x16798,x16799),f462(x16793,x16794,x16795,x16796,x16792,x16797,x16798,x16799)) % 191.49/191.42 [1680]~E(x16801,x16802)+E(f462(x16803,x16804,x16805,x16806,x16807,x16801,x16808,x16809),f462(x16803,x16804,x16805,x16806,x16807,x16802,x16808,x16809)) % 191.49/191.42 [1681]~E(x16811,x16812)+E(f462(x16813,x16814,x16815,x16816,x16817,x16818,x16811,x16819),f462(x16813,x16814,x16815,x16816,x16817,x16818,x16812,x16819)) % 191.49/191.42 [1682]~E(x16821,x16822)+E(f462(x16823,x16824,x16825,x16826,x16827,x16828,x16829,x16821),f462(x16823,x16824,x16825,x16826,x16827,x16828,x16829,x16822)) % 191.49/191.42 [1683]~E(x16831,x16832)+E(f762(x16831,x16833),f762(x16832,x16833)) % 191.49/191.42 [1684]~E(x16841,x16842)+E(f762(x16843,x16841),f762(x16843,x16842)) % 191.49/191.42 [1685]~E(x16851,x16852)+E(f542(x16851,x16853),f542(x16852,x16853)) % 191.49/191.42 [1686]~E(x16861,x16862)+E(f542(x16863,x16861),f542(x16863,x16862)) % 191.49/191.42 [1687]~E(x16871,x16872)+E(f737(x16871,x16873,x16874,x16875),f737(x16872,x16873,x16874,x16875)) % 191.49/191.42 [1688]~E(x16881,x16882)+E(f737(x16883,x16881,x16884,x16885),f737(x16883,x16882,x16884,x16885)) % 191.49/191.42 [1689]~E(x16891,x16892)+E(f737(x16893,x16894,x16891,x16895),f737(x16893,x16894,x16892,x16895)) % 191.49/191.42 [1690]~E(x16901,x16902)+E(f737(x16903,x16904,x16905,x16901),f737(x16903,x16904,x16905,x16902)) % 191.49/191.42 [1691]~E(x16911,x16912)+E(f342(x16911),f342(x16912)) % 191.49/191.42 [1692]~E(x16921,x16922)+E(f418(x16921,x16923,x16924,x16925),f418(x16922,x16923,x16924,x16925)) % 191.49/191.42 [1693]~E(x16931,x16932)+E(f418(x16933,x16931,x16934,x16935),f418(x16933,x16932,x16934,x16935)) % 191.49/191.42 [1694]~E(x16941,x16942)+E(f418(x16943,x16944,x16941,x16945),f418(x16943,x16944,x16942,x16945)) % 191.49/191.42 [1695]~E(x16951,x16952)+E(f418(x16953,x16954,x16955,x16951),f418(x16953,x16954,x16955,x16952)) % 191.49/191.42 [1696]~E(x16961,x16962)+E(f375(x16961,x16963,x16964),f375(x16962,x16963,x16964)) % 191.49/191.42 [1697]~E(x16971,x16972)+E(f375(x16973,x16971,x16974),f375(x16973,x16972,x16974)) % 191.49/191.42 [1698]~E(x16981,x16982)+E(f375(x16983,x16984,x16981),f375(x16983,x16984,x16982)) % 191.49/191.42 [1699]~E(x16991,x16992)+E(f355(x16991,x16993,x16994,x16995,x16996),f355(x16992,x16993,x16994,x16995,x16996)) % 191.49/191.42 [1700]~E(x17001,x17002)+E(f355(x17003,x17001,x17004,x17005,x17006),f355(x17003,x17002,x17004,x17005,x17006)) % 191.49/191.42 [1701]~E(x17011,x17012)+E(f355(x17013,x17014,x17011,x17015,x17016),f355(x17013,x17014,x17012,x17015,x17016)) % 191.49/191.42 [1702]~E(x17021,x17022)+E(f355(x17023,x17024,x17025,x17021,x17026),f355(x17023,x17024,x17025,x17022,x17026)) % 191.49/191.42 [1703]~E(x17031,x17032)+E(f355(x17033,x17034,x17035,x17036,x17031),f355(x17033,x17034,x17035,x17036,x17032)) % 191.49/191.42 [1704]~E(x17041,x17042)+E(f577(x17041,x17043,x17044,x17045,x17046),f577(x17042,x17043,x17044,x17045,x17046)) % 191.49/191.42 [1705]~E(x17051,x17052)+E(f577(x17053,x17051,x17054,x17055,x17056),f577(x17053,x17052,x17054,x17055,x17056)) % 191.49/191.42 [1706]~E(x17061,x17062)+E(f577(x17063,x17064,x17061,x17065,x17066),f577(x17063,x17064,x17062,x17065,x17066)) % 191.49/191.42 [1707]~E(x17071,x17072)+E(f577(x17073,x17074,x17075,x17071,x17076),f577(x17073,x17074,x17075,x17072,x17076)) % 191.49/191.42 [1708]~E(x17081,x17082)+E(f577(x17083,x17084,x17085,x17086,x17081),f577(x17083,x17084,x17085,x17086,x17082)) % 191.49/191.42 [1709]~E(x17091,x17092)+E(f435(x17091,x17093,x17094,x17095),f435(x17092,x17093,x17094,x17095)) % 191.49/191.42 [1710]~E(x17101,x17102)+E(f435(x17103,x17101,x17104,x17105),f435(x17103,x17102,x17104,x17105)) % 191.49/191.42 [1711]~E(x17111,x17112)+E(f435(x17113,x17114,x17111,x17115),f435(x17113,x17114,x17112,x17115)) % 191.49/191.42 [1712]~E(x17121,x17122)+E(f435(x17123,x17124,x17125,x17121),f435(x17123,x17124,x17125,x17122)) % 191.49/191.42 [1713]~E(x17131,x17132)+E(f742(x17131,x17133,x17134),f742(x17132,x17133,x17134)) % 191.49/191.42 [1714]~E(x17141,x17142)+E(f742(x17143,x17141,x17144),f742(x17143,x17142,x17144)) % 191.49/191.42 [1715]~E(x17151,x17152)+E(f742(x17153,x17154,x17151),f742(x17153,x17154,x17152)) % 191.49/191.42 [1716]~E(x17161,x17162)+E(f134(x17161),f134(x17162)) % 191.49/191.42 [1717]~E(x17171,x17172)+E(f414(x17171,x17173),f414(x17172,x17173)) % 191.49/191.42 [1718]~E(x17181,x17182)+E(f414(x17183,x17181),f414(x17183,x17182)) % 191.49/191.42 [1719]~E(x17191,x17192)+E(f787(x17191,x17193,x17194),f787(x17192,x17193,x17194)) % 191.49/191.42 [1720]~E(x17201,x17202)+E(f787(x17203,x17201,x17204),f787(x17203,x17202,x17204)) % 191.49/191.42 [1721]~E(x17211,x17212)+E(f787(x17213,x17214,x17211),f787(x17213,x17214,x17212)) % 191.49/191.42 [1722]~E(x17221,x17222)+E(f634(x17221,x17223,x17224,x17225,x17226,x17227),f634(x17222,x17223,x17224,x17225,x17226,x17227)) % 191.49/191.42 [1723]~E(x17231,x17232)+E(f634(x17233,x17231,x17234,x17235,x17236,x17237),f634(x17233,x17232,x17234,x17235,x17236,x17237)) % 191.49/191.42 [1724]~E(x17241,x17242)+E(f634(x17243,x17244,x17241,x17245,x17246,x17247),f634(x17243,x17244,x17242,x17245,x17246,x17247)) % 191.49/191.42 [1725]~E(x17251,x17252)+E(f634(x17253,x17254,x17255,x17251,x17256,x17257),f634(x17253,x17254,x17255,x17252,x17256,x17257)) % 191.49/191.42 [1726]~E(x17261,x17262)+E(f634(x17263,x17264,x17265,x17266,x17261,x17267),f634(x17263,x17264,x17265,x17266,x17262,x17267)) % 191.49/191.42 [1727]~E(x17271,x17272)+E(f634(x17273,x17274,x17275,x17276,x17277,x17271),f634(x17273,x17274,x17275,x17276,x17277,x17272)) % 191.49/191.42 [1728]~E(x17281,x17282)+E(f720(x17281,x17283,x17284,x17285),f720(x17282,x17283,x17284,x17285)) % 191.49/191.42 [1729]~E(x17291,x17292)+E(f720(x17293,x17291,x17294,x17295),f720(x17293,x17292,x17294,x17295)) % 191.49/191.42 [1730]~E(x17301,x17302)+E(f720(x17303,x17304,x17301,x17305),f720(x17303,x17304,x17302,x17305)) % 191.49/191.42 [1731]~E(x17311,x17312)+E(f720(x17313,x17314,x17315,x17311),f720(x17313,x17314,x17315,x17312)) % 191.49/191.42 [1732]~E(x17321,x17322)+E(f746(x17321,x17323,x17324),f746(x17322,x17323,x17324)) % 191.49/191.42 [1733]~E(x17331,x17332)+E(f746(x17333,x17331,x17334),f746(x17333,x17332,x17334)) % 191.49/191.42 [1734]~E(x17341,x17342)+E(f746(x17343,x17344,x17341),f746(x17343,x17344,x17342)) % 191.49/191.42 [1735]~E(x17351,x17352)+E(f125(x17351,x17353,x17354,x17355),f125(x17352,x17353,x17354,x17355)) % 191.49/191.42 [1736]~E(x17361,x17362)+E(f125(x17363,x17361,x17364,x17365),f125(x17363,x17362,x17364,x17365)) % 191.49/191.42 [1737]~E(x17371,x17372)+E(f125(x17373,x17374,x17371,x17375),f125(x17373,x17374,x17372,x17375)) % 191.49/191.42 [1738]~E(x17381,x17382)+E(f125(x17383,x17384,x17385,x17381),f125(x17383,x17384,x17385,x17382)) % 191.49/191.42 [1739]~E(x17391,x17392)+E(f741(x17391,x17393),f741(x17392,x17393)) % 191.49/191.42 [1740]~E(x17401,x17402)+E(f741(x17403,x17401),f741(x17403,x17402)) % 191.49/191.42 [1741]~E(x17411,x17412)+E(f825(x17411,x17413,x17414,x17415,x17416),f825(x17412,x17413,x17414,x17415,x17416)) % 191.49/191.42 [1742]~E(x17421,x17422)+E(f825(x17423,x17421,x17424,x17425,x17426),f825(x17423,x17422,x17424,x17425,x17426)) % 191.49/191.42 [1743]~E(x17431,x17432)+E(f825(x17433,x17434,x17431,x17435,x17436),f825(x17433,x17434,x17432,x17435,x17436)) % 191.49/191.42 [1744]~E(x17441,x17442)+E(f825(x17443,x17444,x17445,x17441,x17446),f825(x17443,x17444,x17445,x17442,x17446)) % 191.49/191.42 [1745]~E(x17451,x17452)+E(f825(x17453,x17454,x17455,x17456,x17451),f825(x17453,x17454,x17455,x17456,x17452)) % 191.49/191.42 [1746]~E(x17461,x17462)+E(f426(x17461,x17463),f426(x17462,x17463)) % 191.49/191.42 [1747]~E(x17471,x17472)+E(f426(x17473,x17471),f426(x17473,x17472)) % 191.49/191.42 [1748]~E(x17481,x17482)+E(f216(x17481,x17483,x17484,x17485),f216(x17482,x17483,x17484,x17485)) % 191.49/191.42 [1749]~E(x17491,x17492)+E(f216(x17493,x17491,x17494,x17495),f216(x17493,x17492,x17494,x17495)) % 191.49/191.42 [1750]~E(x17501,x17502)+E(f216(x17503,x17504,x17501,x17505),f216(x17503,x17504,x17502,x17505)) % 191.49/191.42 [1751]~E(x17511,x17512)+E(f216(x17513,x17514,x17515,x17511),f216(x17513,x17514,x17515,x17512)) % 191.49/191.42 [1752]~E(x17521,x17522)+E(f397(x17521),f397(x17522)) % 191.49/191.42 [1753]~E(x17531,x17532)+E(f536(x17531,x17533,x17534,x17535),f536(x17532,x17533,x17534,x17535)) % 191.49/191.42 [1754]~E(x17541,x17542)+E(f536(x17543,x17541,x17544,x17545),f536(x17543,x17542,x17544,x17545)) % 191.49/191.42 [1755]~E(x17551,x17552)+E(f536(x17553,x17554,x17551,x17555),f536(x17553,x17554,x17552,x17555)) % 191.49/191.42 [1756]~E(x17561,x17562)+E(f536(x17563,x17564,x17565,x17561),f536(x17563,x17564,x17565,x17562)) % 191.49/191.42 [1757]~E(x17571,x17572)+E(f722(x17571,x17573),f722(x17572,x17573)) % 191.49/191.42 [1758]~E(x17581,x17582)+E(f722(x17583,x17581),f722(x17583,x17582)) % 191.49/191.42 [1759]~E(x17591,x17592)+E(f405(x17591,x17593),f405(x17592,x17593)) % 191.49/191.42 [1760]~E(x17601,x17602)+E(f405(x17603,x17601),f405(x17603,x17602)) % 191.49/191.42 [1761]~E(x17611,x17612)+E(f757(x17611,x17613,x17614,x17615),f757(x17612,x17613,x17614,x17615)) % 191.49/191.42 [1762]~E(x17621,x17622)+E(f757(x17623,x17621,x17624,x17625),f757(x17623,x17622,x17624,x17625)) % 191.49/191.42 [1763]~E(x17631,x17632)+E(f757(x17633,x17634,x17631,x17635),f757(x17633,x17634,x17632,x17635)) % 191.49/191.42 [1764]~E(x17641,x17642)+E(f757(x17643,x17644,x17645,x17641),f757(x17643,x17644,x17645,x17642)) % 191.49/191.42 [1765]~E(x17651,x17652)+E(f688(x17651,x17653,x17654,x17655,x17656),f688(x17652,x17653,x17654,x17655,x17656)) % 191.49/191.42 [1766]~E(x17661,x17662)+E(f688(x17663,x17661,x17664,x17665,x17666),f688(x17663,x17662,x17664,x17665,x17666)) % 191.49/191.42 [1767]~E(x17671,x17672)+E(f688(x17673,x17674,x17671,x17675,x17676),f688(x17673,x17674,x17672,x17675,x17676)) % 191.49/191.42 [1768]~E(x17681,x17682)+E(f688(x17683,x17684,x17685,x17681,x17686),f688(x17683,x17684,x17685,x17682,x17686)) % 191.49/191.42 [1769]~E(x17691,x17692)+E(f688(x17693,x17694,x17695,x17696,x17691),f688(x17693,x17694,x17695,x17696,x17692)) % 191.49/191.42 [1770]~E(x17701,x17702)+E(f804(x17701,x17703,x17704,x17705,x17706),f804(x17702,x17703,x17704,x17705,x17706)) % 191.49/191.42 [1771]~E(x17711,x17712)+E(f804(x17713,x17711,x17714,x17715,x17716),f804(x17713,x17712,x17714,x17715,x17716)) % 191.49/191.42 [1772]~E(x17721,x17722)+E(f804(x17723,x17724,x17721,x17725,x17726),f804(x17723,x17724,x17722,x17725,x17726)) % 191.49/191.42 [1773]~E(x17731,x17732)+E(f804(x17733,x17734,x17735,x17731,x17736),f804(x17733,x17734,x17735,x17732,x17736)) % 191.49/191.42 [1774]~E(x17741,x17742)+E(f804(x17743,x17744,x17745,x17746,x17741),f804(x17743,x17744,x17745,x17746,x17742)) % 191.49/191.42 [1775]~E(x17751,x17752)+E(f763(x17751,x17753,x17754,x17755,x17756,x17757,x17758),f763(x17752,x17753,x17754,x17755,x17756,x17757,x17758)) % 191.49/191.42 [1776]~E(x17761,x17762)+E(f763(x17763,x17761,x17764,x17765,x17766,x17767,x17768),f763(x17763,x17762,x17764,x17765,x17766,x17767,x17768)) % 191.49/191.42 [1777]~E(x17771,x17772)+E(f763(x17773,x17774,x17771,x17775,x17776,x17777,x17778),f763(x17773,x17774,x17772,x17775,x17776,x17777,x17778)) % 191.49/191.42 [1778]~E(x17781,x17782)+E(f763(x17783,x17784,x17785,x17781,x17786,x17787,x17788),f763(x17783,x17784,x17785,x17782,x17786,x17787,x17788)) % 191.49/191.42 [1779]~E(x17791,x17792)+E(f763(x17793,x17794,x17795,x17796,x17791,x17797,x17798),f763(x17793,x17794,x17795,x17796,x17792,x17797,x17798)) % 191.49/191.42 [1780]~E(x17801,x17802)+E(f763(x17803,x17804,x17805,x17806,x17807,x17801,x17808),f763(x17803,x17804,x17805,x17806,x17807,x17802,x17808)) % 191.49/191.42 [1781]~E(x17811,x17812)+E(f763(x17813,x17814,x17815,x17816,x17817,x17818,x17811),f763(x17813,x17814,x17815,x17816,x17817,x17818,x17812)) % 191.49/191.42 [1782]~E(x17821,x17822)+E(f725(x17821,x17823,x17824,x17825),f725(x17822,x17823,x17824,x17825)) % 191.49/191.42 [1783]~E(x17831,x17832)+E(f725(x17833,x17831,x17834,x17835),f725(x17833,x17832,x17834,x17835)) % 191.49/191.42 [1784]~E(x17841,x17842)+E(f725(x17843,x17844,x17841,x17845),f725(x17843,x17844,x17842,x17845)) % 191.49/191.42 [1785]~E(x17851,x17852)+E(f725(x17853,x17854,x17855,x17851),f725(x17853,x17854,x17855,x17852)) % 191.49/191.42 [1786]~E(x17861,x17862)+E(f824(x17861,x17863,x17864),f824(x17862,x17863,x17864)) % 191.49/191.42 [1787]~E(x17871,x17872)+E(f824(x17873,x17871,x17874),f824(x17873,x17872,x17874)) % 191.49/191.42 [1788]~E(x17881,x17882)+E(f824(x17883,x17884,x17881),f824(x17883,x17884,x17882)) % 191.49/191.42 [1789]~E(x17891,x17892)+E(f348(x17891,x17893,x17894),f348(x17892,x17893,x17894)) % 191.49/191.42 [1790]~E(x17901,x17902)+E(f348(x17903,x17901,x17904),f348(x17903,x17902,x17904)) % 191.49/191.42 [1791]~E(x17911,x17912)+E(f348(x17913,x17914,x17911),f348(x17913,x17914,x17912)) % 191.49/191.42 [1792]~E(x17921,x17922)+E(f717(x17921,x17923),f717(x17922,x17923)) % 191.49/191.42 [1793]~E(x17931,x17932)+E(f717(x17933,x17931),f717(x17933,x17932)) % 191.49/191.42 [1794]~E(x17941,x17942)+E(f465(x17941,x17943,x17944),f465(x17942,x17943,x17944)) % 191.49/191.42 [1795]~E(x17951,x17952)+E(f465(x17953,x17951,x17954),f465(x17953,x17952,x17954)) % 191.49/191.42 [1796]~E(x17961,x17962)+E(f465(x17963,x17964,x17961),f465(x17963,x17964,x17962)) % 191.49/191.42 [1797]~E(x17971,x17972)+E(f404(x17971),f404(x17972)) % 191.49/191.42 [1798]~E(x17981,x17982)+E(f781(x17981,x17983,x17984,x17985,x17986),f781(x17982,x17983,x17984,x17985,x17986)) % 191.49/191.42 [1799]~E(x17991,x17992)+E(f781(x17993,x17991,x17994,x17995,x17996),f781(x17993,x17992,x17994,x17995,x17996)) % 191.49/191.42 [1800]~E(x18001,x18002)+E(f781(x18003,x18004,x18001,x18005,x18006),f781(x18003,x18004,x18002,x18005,x18006)) % 191.49/191.42 [1801]~E(x18011,x18012)+E(f781(x18013,x18014,x18015,x18011,x18016),f781(x18013,x18014,x18015,x18012,x18016)) % 191.49/191.42 [1802]~E(x18021,x18022)+E(f781(x18023,x18024,x18025,x18026,x18021),f781(x18023,x18024,x18025,x18026,x18022)) % 191.49/191.42 [1803]~E(x18031,x18032)+E(f373(x18031,x18033),f373(x18032,x18033)) % 191.49/191.42 [1804]~E(x18041,x18042)+E(f373(x18043,x18041),f373(x18043,x18042)) % 191.49/191.42 [1805]~E(x18051,x18052)+E(f537(x18051,x18053),f537(x18052,x18053)) % 191.49/191.42 [1806]~E(x18061,x18062)+E(f537(x18063,x18061),f537(x18063,x18062)) % 191.49/191.42 [1807]~E(x18071,x18072)+E(f584(x18071,x18073),f584(x18072,x18073)) % 191.49/191.42 [1808]~E(x18081,x18082)+E(f584(x18083,x18081),f584(x18083,x18082)) % 191.49/191.42 [1809]~E(x18091,x18092)+E(f608(x18091,x18093,x18094),f608(x18092,x18093,x18094)) % 191.49/191.42 [1810]~E(x18101,x18102)+E(f608(x18103,x18101,x18104),f608(x18103,x18102,x18104)) % 191.49/191.42 [1811]~E(x18111,x18112)+E(f608(x18113,x18114,x18111),f608(x18113,x18114,x18112)) % 191.49/191.42 [1812]~E(x18121,x18122)+E(f726(x18121,x18123,x18124,x18125),f726(x18122,x18123,x18124,x18125)) % 191.49/191.42 [1813]~E(x18131,x18132)+E(f726(x18133,x18131,x18134,x18135),f726(x18133,x18132,x18134,x18135)) % 191.49/191.42 [1814]~E(x18141,x18142)+E(f726(x18143,x18144,x18141,x18145),f726(x18143,x18144,x18142,x18145)) % 191.49/191.42 [1815]~E(x18151,x18152)+E(f726(x18153,x18154,x18155,x18151),f726(x18153,x18154,x18155,x18152)) % 191.49/191.42 [1816]~E(x18161,x18162)+E(f719(x18161,x18163,x18164,x18165),f719(x18162,x18163,x18164,x18165)) % 191.49/191.42 [1817]~E(x18171,x18172)+E(f719(x18173,x18171,x18174,x18175),f719(x18173,x18172,x18174,x18175)) % 191.49/191.42 [1818]~E(x18181,x18182)+E(f719(x18183,x18184,x18181,x18185),f719(x18183,x18184,x18182,x18185)) % 191.49/191.42 [1819]~E(x18191,x18192)+E(f719(x18193,x18194,x18195,x18191),f719(x18193,x18194,x18195,x18192)) % 191.49/191.42 [1820]~E(x18201,x18202)+E(f580(x18201,x18203),f580(x18202,x18203)) % 191.49/191.42 [1821]~E(x18211,x18212)+E(f580(x18213,x18211),f580(x18213,x18212)) % 191.49/191.42 [1822]~E(x18221,x18222)+E(f438(x18221,x18223,x18224,x18225),f438(x18222,x18223,x18224,x18225)) % 191.49/191.42 [1823]~E(x18231,x18232)+E(f438(x18233,x18231,x18234,x18235),f438(x18233,x18232,x18234,x18235)) % 191.49/191.42 [1824]~E(x18241,x18242)+E(f438(x18243,x18244,x18241,x18245),f438(x18243,x18244,x18242,x18245)) % 191.49/191.42 [1825]~E(x18251,x18252)+E(f438(x18253,x18254,x18255,x18251),f438(x18253,x18254,x18255,x18252)) % 191.49/191.42 [1826]~E(x18261,x18262)+E(f301(x18261,x18263,x18264,x18265,x18266),f301(x18262,x18263,x18264,x18265,x18266)) % 191.49/191.42 [1827]~E(x18271,x18272)+E(f301(x18273,x18271,x18274,x18275,x18276),f301(x18273,x18272,x18274,x18275,x18276)) % 191.49/191.42 [1828]~E(x18281,x18282)+E(f301(x18283,x18284,x18281,x18285,x18286),f301(x18283,x18284,x18282,x18285,x18286)) % 191.49/191.42 [1829]~E(x18291,x18292)+E(f301(x18293,x18294,x18295,x18291,x18296),f301(x18293,x18294,x18295,x18292,x18296)) % 191.49/191.42 [1830]~E(x18301,x18302)+E(f301(x18303,x18304,x18305,x18306,x18301),f301(x18303,x18304,x18305,x18306,x18302)) % 191.49/191.42 [1831]~E(x18311,x18312)+E(f554(x18311,x18313),f554(x18312,x18313)) % 191.49/191.42 [1832]~E(x18321,x18322)+E(f554(x18323,x18321),f554(x18323,x18322)) % 191.49/191.42 [1833]~E(x18331,x18332)+E(f279(x18331,x18333),f279(x18332,x18333)) % 191.49/191.42 [1834]~E(x18341,x18342)+E(f279(x18343,x18341),f279(x18343,x18342)) % 191.49/191.42 [1835]~E(x18351,x18352)+E(f627(x18351,x18353,x18354),f627(x18352,x18353,x18354)) % 191.49/191.42 [1836]~E(x18361,x18362)+E(f627(x18363,x18361,x18364),f627(x18363,x18362,x18364)) % 191.49/191.42 [1837]~E(x18371,x18372)+E(f627(x18373,x18374,x18371),f627(x18373,x18374,x18372)) % 191.49/191.42 [1838]~E(x18381,x18382)+E(f687(x18381,x18383,x18384,x18385,x18386),f687(x18382,x18383,x18384,x18385,x18386)) % 191.49/191.42 [1839]~E(x18391,x18392)+E(f687(x18393,x18391,x18394,x18395,x18396),f687(x18393,x18392,x18394,x18395,x18396)) % 191.49/191.42 [1840]~E(x18401,x18402)+E(f687(x18403,x18404,x18401,x18405,x18406),f687(x18403,x18404,x18402,x18405,x18406)) % 191.49/191.42 [1841]~E(x18411,x18412)+E(f687(x18413,x18414,x18415,x18411,x18416),f687(x18413,x18414,x18415,x18412,x18416)) % 191.49/191.42 [1842]~E(x18421,x18422)+E(f687(x18423,x18424,x18425,x18426,x18421),f687(x18423,x18424,x18425,x18426,x18422)) % 191.49/191.42 [1843]~E(x18431,x18432)+E(f637(x18431,x18433,x18434,x18435),f637(x18432,x18433,x18434,x18435)) % 191.49/191.42 [1844]~E(x18441,x18442)+E(f637(x18443,x18441,x18444,x18445),f637(x18443,x18442,x18444,x18445)) % 191.49/191.42 [1845]~E(x18451,x18452)+E(f637(x18453,x18454,x18451,x18455),f637(x18453,x18454,x18452,x18455)) % 191.49/191.42 [1846]~E(x18461,x18462)+E(f637(x18463,x18464,x18465,x18461),f637(x18463,x18464,x18465,x18462)) % 191.49/191.42 [1847]~E(x18471,x18472)+E(f529(x18471,x18473,x18474,x18475,x18476),f529(x18472,x18473,x18474,x18475,x18476)) % 191.49/191.42 [1848]~E(x18481,x18482)+E(f529(x18483,x18481,x18484,x18485,x18486),f529(x18483,x18482,x18484,x18485,x18486)) % 191.49/191.42 [1849]~E(x18491,x18492)+E(f529(x18493,x18494,x18491,x18495,x18496),f529(x18493,x18494,x18492,x18495,x18496)) % 191.49/191.42 [1850]~E(x18501,x18502)+E(f529(x18503,x18504,x18505,x18501,x18506),f529(x18503,x18504,x18505,x18502,x18506)) % 191.49/191.42 [1851]~E(x18511,x18512)+E(f529(x18513,x18514,x18515,x18516,x18511),f529(x18513,x18514,x18515,x18516,x18512)) % 191.49/191.42 [1852]~E(x18521,x18522)+E(f381(x18521,x18523,x18524,x18525),f381(x18522,x18523,x18524,x18525)) % 191.49/191.42 [1853]~E(x18531,x18532)+E(f381(x18533,x18531,x18534,x18535),f381(x18533,x18532,x18534,x18535)) % 191.49/191.42 [1854]~E(x18541,x18542)+E(f381(x18543,x18544,x18541,x18545),f381(x18543,x18544,x18542,x18545)) % 191.49/191.42 [1855]~E(x18551,x18552)+E(f381(x18553,x18554,x18555,x18551),f381(x18553,x18554,x18555,x18552)) % 191.49/191.42 [1856]~E(x18561,x18562)+E(f495(x18561,x18563,x18564,x18565,x18566),f495(x18562,x18563,x18564,x18565,x18566)) % 191.49/191.42 [1857]~E(x18571,x18572)+E(f495(x18573,x18571,x18574,x18575,x18576),f495(x18573,x18572,x18574,x18575,x18576)) % 191.49/191.42 [1858]~E(x18581,x18582)+E(f495(x18583,x18584,x18581,x18585,x18586),f495(x18583,x18584,x18582,x18585,x18586)) % 191.49/191.42 [1859]~E(x18591,x18592)+E(f495(x18593,x18594,x18595,x18591,x18596),f495(x18593,x18594,x18595,x18592,x18596)) % 191.49/191.42 [1860]~E(x18601,x18602)+E(f495(x18603,x18604,x18605,x18606,x18601),f495(x18603,x18604,x18605,x18606,x18602)) % 191.49/191.42 [1861]~E(x18611,x18612)+E(f622(x18611,x18613,x18614),f622(x18612,x18613,x18614)) % 191.49/191.42 [1862]~E(x18621,x18622)+E(f622(x18623,x18621,x18624),f622(x18623,x18622,x18624)) % 191.49/191.42 [1863]~E(x18631,x18632)+E(f622(x18633,x18634,x18631),f622(x18633,x18634,x18632)) % 191.49/191.42 [1864]~E(x18641,x18642)+E(f646(x18641,x18643),f646(x18642,x18643)) % 191.49/191.42 [1865]~E(x18651,x18652)+E(f646(x18653,x18651),f646(x18653,x18652)) % 191.49/191.42 [1866]~E(x18661,x18662)+E(f556(x18661,x18663),f556(x18662,x18663)) % 191.49/191.42 [1867]~E(x18671,x18672)+E(f556(x18673,x18671),f556(x18673,x18672)) % 191.49/191.42 [1868]~E(x18681,x18682)+E(f572(x18681,x18683,x18684,x18685,x18686,x18687),f572(x18682,x18683,x18684,x18685,x18686,x18687)) % 191.49/191.42 [1869]~E(x18691,x18692)+E(f572(x18693,x18691,x18694,x18695,x18696,x18697),f572(x18693,x18692,x18694,x18695,x18696,x18697)) % 191.49/191.42 [1870]~E(x18701,x18702)+E(f572(x18703,x18704,x18701,x18705,x18706,x18707),f572(x18703,x18704,x18702,x18705,x18706,x18707)) % 191.49/191.42 [1871]~E(x18711,x18712)+E(f572(x18713,x18714,x18715,x18711,x18716,x18717),f572(x18713,x18714,x18715,x18712,x18716,x18717)) % 191.49/191.42 [1872]~E(x18721,x18722)+E(f572(x18723,x18724,x18725,x18726,x18721,x18727),f572(x18723,x18724,x18725,x18726,x18722,x18727)) % 191.49/191.42 [1873]~E(x18731,x18732)+E(f572(x18733,x18734,x18735,x18736,x18737,x18731),f572(x18733,x18734,x18735,x18736,x18737,x18732)) % 191.49/191.42 [1874]~E(x18741,x18742)+E(f852(x18741,x18743,x18744),f852(x18742,x18743,x18744)) % 191.49/191.42 [1875]~E(x18751,x18752)+E(f852(x18753,x18751,x18754),f852(x18753,x18752,x18754)) % 191.49/191.42 [1876]~E(x18761,x18762)+E(f852(x18763,x18764,x18761),f852(x18763,x18764,x18762)) % 191.49/191.42 [1877]~E(x18771,x18772)+E(f791(x18771,x18773,x18774,x18775),f791(x18772,x18773,x18774,x18775)) % 191.49/191.42 [1878]~E(x18781,x18782)+E(f791(x18783,x18781,x18784,x18785),f791(x18783,x18782,x18784,x18785)) % 191.49/191.42 [1879]~E(x18791,x18792)+E(f791(x18793,x18794,x18791,x18795),f791(x18793,x18794,x18792,x18795)) % 191.49/191.42 [1880]~E(x18801,x18802)+E(f791(x18803,x18804,x18805,x18801),f791(x18803,x18804,x18805,x18802)) % 191.49/191.42 [1881]~E(x18811,x18812)+E(f468(x18811,x18813),f468(x18812,x18813)) % 191.49/191.42 [1882]~E(x18821,x18822)+E(f468(x18823,x18821),f468(x18823,x18822)) % 191.49/191.42 [1883]~E(x18831,x18832)+E(f384(x18831,x18833,x18834,x18835,x18836,x18837,x18838,x18839),f384(x18832,x18833,x18834,x18835,x18836,x18837,x18838,x18839)) % 191.49/191.42 [1884]~E(x18841,x18842)+E(f384(x18843,x18841,x18844,x18845,x18846,x18847,x18848,x18849),f384(x18843,x18842,x18844,x18845,x18846,x18847,x18848,x18849)) % 191.49/191.42 [1885]~E(x18851,x18852)+E(f384(x18853,x18854,x18851,x18855,x18856,x18857,x18858,x18859),f384(x18853,x18854,x18852,x18855,x18856,x18857,x18858,x18859)) % 191.49/191.42 [1886]~E(x18861,x18862)+E(f384(x18863,x18864,x18865,x18861,x18866,x18867,x18868,x18869),f384(x18863,x18864,x18865,x18862,x18866,x18867,x18868,x18869)) % 191.49/191.42 [1887]~E(x18871,x18872)+E(f384(x18873,x18874,x18875,x18876,x18871,x18877,x18878,x18879),f384(x18873,x18874,x18875,x18876,x18872,x18877,x18878,x18879)) % 191.49/191.42 [1888]~E(x18881,x18882)+E(f384(x18883,x18884,x18885,x18886,x18887,x18881,x18888,x18889),f384(x18883,x18884,x18885,x18886,x18887,x18882,x18888,x18889)) % 191.49/191.42 [1889]~E(x18891,x18892)+E(f384(x18893,x18894,x18895,x18896,x18897,x18898,x18891,x18899),f384(x18893,x18894,x18895,x18896,x18897,x18898,x18892,x18899)) % 191.49/191.42 [1890]~E(x18901,x18902)+E(f384(x18903,x18904,x18905,x18906,x18907,x18908,x18909,x18901),f384(x18903,x18904,x18905,x18906,x18907,x18908,x18909,x18902)) % 191.49/191.42 [1891]~E(x18911,x18912)+E(f764(x18911,x18913,x18914),f764(x18912,x18913,x18914)) % 191.49/191.42 [1892]~E(x18921,x18922)+E(f764(x18923,x18921,x18924),f764(x18923,x18922,x18924)) % 191.49/191.42 [1893]~E(x18931,x18932)+E(f764(x18933,x18934,x18931),f764(x18933,x18934,x18932)) % 191.49/191.42 [1894]~E(x18941,x18942)+E(f802(x18941,x18943,x18944,x18945),f802(x18942,x18943,x18944,x18945)) % 191.49/191.42 [1895]~E(x18951,x18952)+E(f802(x18953,x18951,x18954,x18955),f802(x18953,x18952,x18954,x18955)) % 191.49/191.42 [1896]~E(x18961,x18962)+E(f802(x18963,x18964,x18961,x18965),f802(x18963,x18964,x18962,x18965)) % 191.49/191.42 [1897]~E(x18971,x18972)+E(f802(x18973,x18974,x18975,x18971),f802(x18973,x18974,x18975,x18972)) % 191.49/191.42 [1898]~E(x18981,x18982)+E(f147(x18981,x18983),f147(x18982,x18983)) % 191.49/191.42 [1899]~E(x18991,x18992)+E(f147(x18993,x18991),f147(x18993,x18992)) % 191.49/191.42 [1900]~E(x19001,x19002)+E(f706(x19001,x19003,x19004,x19005),f706(x19002,x19003,x19004,x19005)) % 191.49/191.42 [1901]~E(x19011,x19012)+E(f706(x19013,x19011,x19014,x19015),f706(x19013,x19012,x19014,x19015)) % 191.49/191.42 [1902]~E(x19021,x19022)+E(f706(x19023,x19024,x19021,x19025),f706(x19023,x19024,x19022,x19025)) % 191.49/191.42 [1903]~E(x19031,x19032)+E(f706(x19033,x19034,x19035,x19031),f706(x19033,x19034,x19035,x19032)) % 191.49/191.42 [1904]~E(x19041,x19042)+E(f245(x19041,x19043,x19044,x19045,x19046),f245(x19042,x19043,x19044,x19045,x19046)) % 191.49/191.42 [1905]~E(x19051,x19052)+E(f245(x19053,x19051,x19054,x19055,x19056),f245(x19053,x19052,x19054,x19055,x19056)) % 191.49/191.42 [1906]~E(x19061,x19062)+E(f245(x19063,x19064,x19061,x19065,x19066),f245(x19063,x19064,x19062,x19065,x19066)) % 191.49/191.42 [1907]~E(x19071,x19072)+E(f245(x19073,x19074,x19075,x19071,x19076),f245(x19073,x19074,x19075,x19072,x19076)) % 191.49/191.42 [1908]~E(x19081,x19082)+E(f245(x19083,x19084,x19085,x19086,x19081),f245(x19083,x19084,x19085,x19086,x19082)) % 191.49/191.42 [1909]~E(x19091,x19092)+E(f779(x19091,x19093,x19094,x19095,x19096),f779(x19092,x19093,x19094,x19095,x19096)) % 191.49/191.42 [1910]~E(x19101,x19102)+E(f779(x19103,x19101,x19104,x19105,x19106),f779(x19103,x19102,x19104,x19105,x19106)) % 191.49/191.42 [1911]~E(x19111,x19112)+E(f779(x19113,x19114,x19111,x19115,x19116),f779(x19113,x19114,x19112,x19115,x19116)) % 191.49/191.42 [1912]~E(x19121,x19122)+E(f779(x19123,x19124,x19125,x19121,x19126),f779(x19123,x19124,x19125,x19122,x19126)) % 191.49/191.42 [1913]~E(x19131,x19132)+E(f779(x19133,x19134,x19135,x19136,x19131),f779(x19133,x19134,x19135,x19136,x19132)) % 191.49/191.42 [1914]~E(x19141,x19142)+E(f574(x19141),f574(x19142)) % 191.49/191.42 [1915]~E(x19151,x19152)+E(f849(x19151,x19153,x19154,x19155,x19156),f849(x19152,x19153,x19154,x19155,x19156)) % 191.49/191.42 [1916]~E(x19161,x19162)+E(f849(x19163,x19161,x19164,x19165,x19166),f849(x19163,x19162,x19164,x19165,x19166)) % 191.49/191.42 [1917]~E(x19171,x19172)+E(f849(x19173,x19174,x19171,x19175,x19176),f849(x19173,x19174,x19172,x19175,x19176)) % 191.49/191.42 [1918]~E(x19181,x19182)+E(f849(x19183,x19184,x19185,x19181,x19186),f849(x19183,x19184,x19185,x19182,x19186)) % 191.49/191.42 [1919]~E(x19191,x19192)+E(f849(x19193,x19194,x19195,x19196,x19191),f849(x19193,x19194,x19195,x19196,x19192)) % 191.49/191.42 [1920]~E(x19201,x19202)+E(f380(x19201,x19203,x19204,x19205),f380(x19202,x19203,x19204,x19205)) % 191.49/191.42 [1921]~E(x19211,x19212)+E(f380(x19213,x19211,x19214,x19215),f380(x19213,x19212,x19214,x19215)) % 191.49/191.42 [1922]~E(x19221,x19222)+E(f380(x19223,x19224,x19221,x19225),f380(x19223,x19224,x19222,x19225)) % 191.49/191.42 [1923]~E(x19231,x19232)+E(f380(x19233,x19234,x19235,x19231),f380(x19233,x19234,x19235,x19232)) % 191.49/191.42 [1924]~E(x19241,x19242)+E(f807(x19241,x19243,x19244,x19245,x19246,x19247),f807(x19242,x19243,x19244,x19245,x19246,x19247)) % 191.49/191.42 [1925]~E(x19251,x19252)+E(f807(x19253,x19251,x19254,x19255,x19256,x19257),f807(x19253,x19252,x19254,x19255,x19256,x19257)) % 191.49/191.42 [1926]~E(x19261,x19262)+E(f807(x19263,x19264,x19261,x19265,x19266,x19267),f807(x19263,x19264,x19262,x19265,x19266,x19267)) % 191.49/191.42 [1927]~E(x19271,x19272)+E(f807(x19273,x19274,x19275,x19271,x19276,x19277),f807(x19273,x19274,x19275,x19272,x19276,x19277)) % 191.49/191.42 [1928]~E(x19281,x19282)+E(f807(x19283,x19284,x19285,x19286,x19281,x19287),f807(x19283,x19284,x19285,x19286,x19282,x19287)) % 191.49/191.42 [1929]~E(x19291,x19292)+E(f807(x19293,x19294,x19295,x19296,x19297,x19291),f807(x19293,x19294,x19295,x19296,x19297,x19292)) % 191.49/191.42 [1930]~E(x19301,x19302)+E(f679(x19301,x19303),f679(x19302,x19303)) % 191.49/191.42 [1931]~E(x19311,x19312)+E(f679(x19313,x19311),f679(x19313,x19312)) % 191.49/191.42 [1932]~E(x19321,x19322)+E(f783(x19321,x19323,x19324,x19325,x19326),f783(x19322,x19323,x19324,x19325,x19326)) % 191.49/191.42 [1933]~E(x19331,x19332)+E(f783(x19333,x19331,x19334,x19335,x19336),f783(x19333,x19332,x19334,x19335,x19336)) % 191.49/191.42 [1934]~E(x19341,x19342)+E(f783(x19343,x19344,x19341,x19345,x19346),f783(x19343,x19344,x19342,x19345,x19346)) % 191.49/191.42 [1935]~E(x19351,x19352)+E(f783(x19353,x19354,x19355,x19351,x19356),f783(x19353,x19354,x19355,x19352,x19356)) % 191.49/191.42 [1936]~E(x19361,x19362)+E(f783(x19363,x19364,x19365,x19366,x19361),f783(x19363,x19364,x19365,x19366,x19362)) % 191.49/191.42 [1937]~E(x19371,x19372)+E(f797(x19371,x19373,x19374),f797(x19372,x19373,x19374)) % 191.49/191.42 [1938]~E(x19381,x19382)+E(f797(x19383,x19381,x19384),f797(x19383,x19382,x19384)) % 191.49/191.42 [1939]~E(x19391,x19392)+E(f797(x19393,x19394,x19391),f797(x19393,x19394,x19392)) % 191.49/191.42 [1940]~E(x19401,x19402)+E(f498(x19401,x19403,x19404),f498(x19402,x19403,x19404)) % 191.49/191.42 [1941]~E(x19411,x19412)+E(f498(x19413,x19411,x19414),f498(x19413,x19412,x19414)) % 191.49/191.42 [1942]~E(x19421,x19422)+E(f498(x19423,x19424,x19421),f498(x19423,x19424,x19422)) % 191.49/191.42 [1943]~E(x19431,x19432)+E(f594(x19431,x19433,x19434),f594(x19432,x19433,x19434)) % 191.49/191.42 [1944]~E(x19441,x19442)+E(f594(x19443,x19441,x19444),f594(x19443,x19442,x19444)) % 191.49/191.42 [1945]~E(x19451,x19452)+E(f594(x19453,x19454,x19451),f594(x19453,x19454,x19452)) % 191.49/191.42 [1946]~E(x19461,x19462)+E(f504(x19461,x19463,x19464),f504(x19462,x19463,x19464)) % 191.49/191.42 [1947]~E(x19471,x19472)+E(f504(x19473,x19471,x19474),f504(x19473,x19472,x19474)) % 191.49/191.42 [1948]~E(x19481,x19482)+E(f504(x19483,x19484,x19481),f504(x19483,x19484,x19482)) % 191.49/191.42 [1949]~E(x19491,x19492)+E(f694(x19491,x19493,x19494),f694(x19492,x19493,x19494)) % 191.49/191.42 [1950]~E(x19501,x19502)+E(f694(x19503,x19501,x19504),f694(x19503,x19502,x19504)) % 191.49/191.42 [1951]~E(x19511,x19512)+E(f694(x19513,x19514,x19511),f694(x19513,x19514,x19512)) % 191.49/191.42 [1952]~E(x19521,x19522)+E(f217(x19521,x19523,x19524,x19525),f217(x19522,x19523,x19524,x19525)) % 191.49/191.42 [1953]~E(x19531,x19532)+E(f217(x19533,x19531,x19534,x19535),f217(x19533,x19532,x19534,x19535)) % 191.49/191.42 [1954]~E(x19541,x19542)+E(f217(x19543,x19544,x19541,x19545),f217(x19543,x19544,x19542,x19545)) % 191.49/191.42 [1955]~E(x19551,x19552)+E(f217(x19553,x19554,x19555,x19551),f217(x19553,x19554,x19555,x19552)) % 191.49/191.42 [1956]~E(x19561,x19562)+E(f745(x19561,x19563,x19564),f745(x19562,x19563,x19564)) % 191.49/191.42 [1957]~E(x19571,x19572)+E(f745(x19573,x19571,x19574),f745(x19573,x19572,x19574)) % 191.49/191.42 [1958]~E(x19581,x19582)+E(f745(x19583,x19584,x19581),f745(x19583,x19584,x19582)) % 191.49/191.42 [1959]~E(x19591,x19592)+E(f630(x19591,x19593),f630(x19592,x19593)) % 191.49/191.42 [1960]~E(x19601,x19602)+E(f630(x19603,x19601),f630(x19603,x19602)) % 191.49/191.42 [1961]~E(x19611,x19612)+E(f298(x19611,x19613,x19614,x19615,x19616),f298(x19612,x19613,x19614,x19615,x19616)) % 191.49/191.42 [1962]~E(x19621,x19622)+E(f298(x19623,x19621,x19624,x19625,x19626),f298(x19623,x19622,x19624,x19625,x19626)) % 191.49/191.42 [1963]~E(x19631,x19632)+E(f298(x19633,x19634,x19631,x19635,x19636),f298(x19633,x19634,x19632,x19635,x19636)) % 191.49/191.42 [1964]~E(x19641,x19642)+E(f298(x19643,x19644,x19645,x19641,x19646),f298(x19643,x19644,x19645,x19642,x19646)) % 191.49/191.42 [1965]~E(x19651,x19652)+E(f298(x19653,x19654,x19655,x19656,x19651),f298(x19653,x19654,x19655,x19656,x19652)) % 191.49/191.42 [1966]~E(x19661,x19662)+E(f551(x19661,x19663,x19664,x19665),f551(x19662,x19663,x19664,x19665)) % 191.49/191.42 [1967]~E(x19671,x19672)+E(f551(x19673,x19671,x19674,x19675),f551(x19673,x19672,x19674,x19675)) % 191.49/191.42 [1968]~E(x19681,x19682)+E(f551(x19683,x19684,x19681,x19685),f551(x19683,x19684,x19682,x19685)) % 191.49/191.42 [1969]~E(x19691,x19692)+E(f551(x19693,x19694,x19695,x19691),f551(x19693,x19694,x19695,x19692)) % 191.49/191.42 [1970]~E(x19701,x19702)+E(f278(x19701),f278(x19702)) % 191.49/191.42 [1971]~E(x19711,x19712)+E(f795(x19711,x19713,x19714),f795(x19712,x19713,x19714)) % 191.49/191.42 [1972]~E(x19721,x19722)+E(f795(x19723,x19721,x19724),f795(x19723,x19722,x19724)) % 191.49/191.42 [1973]~E(x19731,x19732)+E(f795(x19733,x19734,x19731),f795(x19733,x19734,x19732)) % 191.49/191.42 [1974]~E(x19741,x19742)+E(f733(x19741,x19743,x19744,x19745,x19746,x19747),f733(x19742,x19743,x19744,x19745,x19746,x19747)) % 191.49/191.42 [1975]~E(x19751,x19752)+E(f733(x19753,x19751,x19754,x19755,x19756,x19757),f733(x19753,x19752,x19754,x19755,x19756,x19757)) % 191.49/191.42 [1976]~E(x19761,x19762)+E(f733(x19763,x19764,x19761,x19765,x19766,x19767),f733(x19763,x19764,x19762,x19765,x19766,x19767)) % 191.49/191.42 [1977]~E(x19771,x19772)+E(f733(x19773,x19774,x19775,x19771,x19776,x19777),f733(x19773,x19774,x19775,x19772,x19776,x19777)) % 191.49/191.42 [1978]~E(x19781,x19782)+E(f733(x19783,x19784,x19785,x19786,x19781,x19787),f733(x19783,x19784,x19785,x19786,x19782,x19787)) % 191.49/191.42 [1979]~E(x19791,x19792)+E(f733(x19793,x19794,x19795,x19796,x19797,x19791),f733(x19793,x19794,x19795,x19796,x19797,x19792)) % 191.49/191.42 [1980]~E(x19801,x19802)+E(f560(x19801,x19803,x19804,x19805),f560(x19802,x19803,x19804,x19805)) % 191.49/191.42 [1981]~E(x19811,x19812)+E(f560(x19813,x19811,x19814,x19815),f560(x19813,x19812,x19814,x19815)) % 191.49/191.42 [1982]~E(x19821,x19822)+E(f560(x19823,x19824,x19821,x19825),f560(x19823,x19824,x19822,x19825)) % 191.49/191.42 [1983]~E(x19831,x19832)+E(f560(x19833,x19834,x19835,x19831),f560(x19833,x19834,x19835,x19832)) % 191.49/191.42 [1984]~E(x19841,x19842)+E(f451(x19841,x19843,x19844),f451(x19842,x19843,x19844)) % 191.49/191.42 [1985]~E(x19851,x19852)+E(f451(x19853,x19851,x19854),f451(x19853,x19852,x19854)) % 191.49/191.42 [1986]~E(x19861,x19862)+E(f451(x19863,x19864,x19861),f451(x19863,x19864,x19862)) % 191.49/191.42 [1987]~E(x19871,x19872)+E(f738(x19871,x19873,x19874,x19875,x19876),f738(x19872,x19873,x19874,x19875,x19876)) % 191.49/191.42 [1988]~E(x19881,x19882)+E(f738(x19883,x19881,x19884,x19885,x19886),f738(x19883,x19882,x19884,x19885,x19886)) % 191.49/191.42 [1989]~E(x19891,x19892)+E(f738(x19893,x19894,x19891,x19895,x19896),f738(x19893,x19894,x19892,x19895,x19896)) % 191.49/191.42 [1990]~E(x19901,x19902)+E(f738(x19903,x19904,x19905,x19901,x19906),f738(x19903,x19904,x19905,x19902,x19906)) % 191.49/191.42 [1991]~E(x19911,x19912)+E(f738(x19913,x19914,x19915,x19916,x19911),f738(x19913,x19914,x19915,x19916,x19912)) % 191.49/191.42 [1992]~E(x19921,x19922)+E(f434(x19921,x19923,x19924,x19925),f434(x19922,x19923,x19924,x19925)) % 191.49/191.42 [1993]~E(x19931,x19932)+E(f434(x19933,x19931,x19934,x19935),f434(x19933,x19932,x19934,x19935)) % 191.49/191.42 [1994]~E(x19941,x19942)+E(f434(x19943,x19944,x19941,x19945),f434(x19943,x19944,x19942,x19945)) % 191.49/191.42 [1995]~E(x19951,x19952)+E(f434(x19953,x19954,x19955,x19951),f434(x19953,x19954,x19955,x19952)) % 191.49/191.42 [1996]~E(x19961,x19962)+E(f643(x19961,x19963,x19964,x19965),f643(x19962,x19963,x19964,x19965)) % 191.49/191.42 [1997]~E(x19971,x19972)+E(f643(x19973,x19971,x19974,x19975),f643(x19973,x19972,x19974,x19975)) % 191.49/191.42 [1998]~E(x19981,x19982)+E(f643(x19983,x19984,x19981,x19985),f643(x19983,x19984,x19982,x19985)) % 191.49/191.42 [1999]~E(x19991,x19992)+E(f643(x19993,x19994,x19995,x19991),f643(x19993,x19994,x19995,x19992)) % 191.49/191.42 [2000]~E(x20001,x20002)+E(f778(x20001,x20003,x20004,x20005,x20006),f778(x20002,x20003,x20004,x20005,x20006)) % 191.49/191.42 [2001]~E(x20011,x20012)+E(f778(x20013,x20011,x20014,x20015,x20016),f778(x20013,x20012,x20014,x20015,x20016)) % 191.49/191.42 [2002]~E(x20021,x20022)+E(f778(x20023,x20024,x20021,x20025,x20026),f778(x20023,x20024,x20022,x20025,x20026)) % 191.49/191.42 [2003]~E(x20031,x20032)+E(f778(x20033,x20034,x20035,x20031,x20036),f778(x20033,x20034,x20035,x20032,x20036)) % 191.49/191.42 [2004]~E(x20041,x20042)+E(f778(x20043,x20044,x20045,x20046,x20041),f778(x20043,x20044,x20045,x20046,x20042)) % 191.49/191.42 [2005]~E(x20051,x20052)+E(f361(x20051,x20053,x20054,x20055,x20056),f361(x20052,x20053,x20054,x20055,x20056)) % 191.49/191.42 [2006]~E(x20061,x20062)+E(f361(x20063,x20061,x20064,x20065,x20066),f361(x20063,x20062,x20064,x20065,x20066)) % 191.49/191.42 [2007]~E(x20071,x20072)+E(f361(x20073,x20074,x20071,x20075,x20076),f361(x20073,x20074,x20072,x20075,x20076)) % 191.49/191.42 [2008]~E(x20081,x20082)+E(f361(x20083,x20084,x20085,x20081,x20086),f361(x20083,x20084,x20085,x20082,x20086)) % 191.49/191.42 [2009]~E(x20091,x20092)+E(f361(x20093,x20094,x20095,x20096,x20091),f361(x20093,x20094,x20095,x20096,x20092)) % 191.49/191.42 [2010]~E(x20101,x20102)+E(f623(x20101,x20103),f623(x20102,x20103)) % 191.49/191.42 [2011]~E(x20111,x20112)+E(f623(x20113,x20111),f623(x20113,x20112)) % 191.49/191.42 [2012]~E(x20121,x20122)+E(f389(x20121,x20123,x20124,x20125),f389(x20122,x20123,x20124,x20125)) % 191.49/191.42 [2013]~E(x20131,x20132)+E(f389(x20133,x20131,x20134,x20135),f389(x20133,x20132,x20134,x20135)) % 191.49/191.42 [2014]~E(x20141,x20142)+E(f389(x20143,x20144,x20141,x20145),f389(x20143,x20144,x20142,x20145)) % 191.49/191.42 [2015]~E(x20151,x20152)+E(f389(x20153,x20154,x20155,x20151),f389(x20153,x20154,x20155,x20152)) % 191.49/191.42 [2016]~E(x20161,x20162)+E(f642(x20161,x20163,x20164),f642(x20162,x20163,x20164)) % 191.49/191.42 [2017]~E(x20171,x20172)+E(f642(x20173,x20171,x20174),f642(x20173,x20172,x20174)) % 191.49/191.42 [2018]~E(x20181,x20182)+E(f642(x20183,x20184,x20181),f642(x20183,x20184,x20182)) % 191.49/191.42 [2019]~E(x20191,x20192)+E(f808(x20191,x20193,x20194,x20195,x20196,x20197),f808(x20192,x20193,x20194,x20195,x20196,x20197)) % 191.49/191.42 [2020]~E(x20201,x20202)+E(f808(x20203,x20201,x20204,x20205,x20206,x20207),f808(x20203,x20202,x20204,x20205,x20206,x20207)) % 191.49/191.42 [2021]~E(x20211,x20212)+E(f808(x20213,x20214,x20211,x20215,x20216,x20217),f808(x20213,x20214,x20212,x20215,x20216,x20217)) % 191.49/191.42 [2022]~E(x20221,x20222)+E(f808(x20223,x20224,x20225,x20221,x20226,x20227),f808(x20223,x20224,x20225,x20222,x20226,x20227)) % 191.49/191.42 [2023]~E(x20231,x20232)+E(f808(x20233,x20234,x20235,x20236,x20231,x20237),f808(x20233,x20234,x20235,x20236,x20232,x20237)) % 191.49/191.42 [2024]~E(x20241,x20242)+E(f808(x20243,x20244,x20245,x20246,x20247,x20241),f808(x20243,x20244,x20245,x20246,x20247,x20242)) % 191.49/191.42 [2025]~E(x20251,x20252)+E(f816(x20251,x20253,x20254,x20255),f816(x20252,x20253,x20254,x20255)) % 191.49/191.42 [2026]~E(x20261,x20262)+E(f816(x20263,x20261,x20264,x20265),f816(x20263,x20262,x20264,x20265)) % 191.49/191.42 [2027]~E(x20271,x20272)+E(f816(x20273,x20274,x20271,x20275),f816(x20273,x20274,x20272,x20275)) % 191.49/191.42 [2028]~E(x20281,x20282)+E(f816(x20283,x20284,x20285,x20281),f816(x20283,x20284,x20285,x20282)) % 191.49/191.42 [2029]~E(x20291,x20292)+E(f563(x20291,x20293,x20294,x20295,x20296),f563(x20292,x20293,x20294,x20295,x20296)) % 191.49/191.42 [2030]~E(x20301,x20302)+E(f563(x20303,x20301,x20304,x20305,x20306),f563(x20303,x20302,x20304,x20305,x20306)) % 191.49/191.42 [2031]~E(x20311,x20312)+E(f563(x20313,x20314,x20311,x20315,x20316),f563(x20313,x20314,x20312,x20315,x20316)) % 191.49/191.42 [2032]~E(x20321,x20322)+E(f563(x20323,x20324,x20325,x20321,x20326),f563(x20323,x20324,x20325,x20322,x20326)) % 191.49/191.42 [2033]~E(x20331,x20332)+E(f563(x20333,x20334,x20335,x20336,x20331),f563(x20333,x20334,x20335,x20336,x20332)) % 191.49/191.42 [2034]~E(x20341,x20342)+E(f406(x20341,x20343,x20344),f406(x20342,x20343,x20344)) % 191.49/191.42 [2035]~E(x20351,x20352)+E(f406(x20353,x20351,x20354),f406(x20353,x20352,x20354)) % 191.49/191.42 [2036]~E(x20361,x20362)+E(f406(x20363,x20364,x20361),f406(x20363,x20364,x20362)) % 191.49/191.42 [2037]~E(x20371,x20372)+E(f359(x20371,x20373,x20374,x20375,x20376,x20377),f359(x20372,x20373,x20374,x20375,x20376,x20377)) % 191.49/191.42 [2038]~E(x20381,x20382)+E(f359(x20383,x20381,x20384,x20385,x20386,x20387),f359(x20383,x20382,x20384,x20385,x20386,x20387)) % 191.49/191.42 [2039]~E(x20391,x20392)+E(f359(x20393,x20394,x20391,x20395,x20396,x20397),f359(x20393,x20394,x20392,x20395,x20396,x20397)) % 191.49/191.42 [2040]~E(x20401,x20402)+E(f359(x20403,x20404,x20405,x20401,x20406,x20407),f359(x20403,x20404,x20405,x20402,x20406,x20407)) % 191.49/191.42 [2041]~E(x20411,x20412)+E(f359(x20413,x20414,x20415,x20416,x20411,x20417),f359(x20413,x20414,x20415,x20416,x20412,x20417)) % 191.49/191.42 [2042]~E(x20421,x20422)+E(f359(x20423,x20424,x20425,x20426,x20427,x20421),f359(x20423,x20424,x20425,x20426,x20427,x20422)) % 191.49/191.42 [2043]~E(x20431,x20432)+E(f75(x20431,x20433),f75(x20432,x20433)) % 191.49/191.42 [2044]~E(x20441,x20442)+E(f75(x20443,x20441),f75(x20443,x20442)) % 191.49/191.42 [2045]~E(x20451,x20452)+E(f238(x20451,x20453,x20454,x20455),f238(x20452,x20453,x20454,x20455)) % 191.49/191.42 [2046]~E(x20461,x20462)+E(f238(x20463,x20461,x20464,x20465),f238(x20463,x20462,x20464,x20465)) % 191.49/191.42 [2047]~E(x20471,x20472)+E(f238(x20473,x20474,x20471,x20475),f238(x20473,x20474,x20472,x20475)) % 191.49/191.42 [2048]~E(x20481,x20482)+E(f238(x20483,x20484,x20485,x20481),f238(x20483,x20484,x20485,x20482)) % 191.49/191.42 [2049]~E(x20491,x20492)+E(f575(x20491,x20493,x20494),f575(x20492,x20493,x20494)) % 191.49/191.42 [2050]~E(x20501,x20502)+E(f575(x20503,x20501,x20504),f575(x20503,x20502,x20504)) % 191.49/191.42 [2051]~E(x20511,x20512)+E(f575(x20513,x20514,x20511),f575(x20513,x20514,x20512)) % 191.49/191.42 [2052]~E(x20521,x20522)+E(f544(x20521,x20523,x20524,x20525,x20526),f544(x20522,x20523,x20524,x20525,x20526)) % 191.49/191.42 [2053]~E(x20531,x20532)+E(f544(x20533,x20531,x20534,x20535,x20536),f544(x20533,x20532,x20534,x20535,x20536)) % 191.49/191.42 [2054]~E(x20541,x20542)+E(f544(x20543,x20544,x20541,x20545,x20546),f544(x20543,x20544,x20542,x20545,x20546)) % 191.49/191.42 [2055]~E(x20551,x20552)+E(f544(x20553,x20554,x20555,x20551,x20556),f544(x20553,x20554,x20555,x20552,x20556)) % 191.49/191.42 [2056]~E(x20561,x20562)+E(f544(x20563,x20564,x20565,x20566,x20561),f544(x20563,x20564,x20565,x20566,x20562)) % 191.49/191.42 [2057]~E(x20571,x20572)+E(f252(x20571,x20573),f252(x20572,x20573)) % 191.49/191.42 [2058]~E(x20581,x20582)+E(f252(x20583,x20581),f252(x20583,x20582)) % 191.49/191.42 [2059]~E(x20591,x20592)+E(f293(x20591,x20593),f293(x20592,x20593)) % 191.49/191.42 [2060]~E(x20601,x20602)+E(f293(x20603,x20601),f293(x20603,x20602)) % 191.49/191.42 [2061]~E(x20611,x20612)+E(f739(x20611,x20613,x20614),f739(x20612,x20613,x20614)) % 191.49/191.42 [2062]~E(x20621,x20622)+E(f739(x20623,x20621,x20624),f739(x20623,x20622,x20624)) % 191.49/191.42 [2063]~E(x20631,x20632)+E(f739(x20633,x20634,x20631),f739(x20633,x20634,x20632)) % 191.49/191.42 [2064]~E(x20641,x20642)+E(f494(x20641,x20643,x20644,x20645),f494(x20642,x20643,x20644,x20645)) % 191.49/191.42 [2065]~E(x20651,x20652)+E(f494(x20653,x20651,x20654,x20655),f494(x20653,x20652,x20654,x20655)) % 191.49/191.42 [2066]~E(x20661,x20662)+E(f494(x20663,x20664,x20661,x20665),f494(x20663,x20664,x20662,x20665)) % 191.49/191.42 [2067]~E(x20671,x20672)+E(f494(x20673,x20674,x20675,x20671),f494(x20673,x20674,x20675,x20672)) % 191.49/191.42 [2068]~E(x20681,x20682)+E(f19(x20681,x20683,x20684,x20685),f19(x20682,x20683,x20684,x20685)) % 191.49/191.42 [2069]~E(x20691,x20692)+E(f19(x20693,x20691,x20694,x20695),f19(x20693,x20692,x20694,x20695)) % 191.49/191.42 [2070]~E(x20701,x20702)+E(f19(x20703,x20704,x20701,x20705),f19(x20703,x20704,x20702,x20705)) % 191.49/191.42 [2071]~E(x20711,x20712)+E(f19(x20713,x20714,x20715,x20711),f19(x20713,x20714,x20715,x20712)) % 191.49/191.42 [2072]~E(x20721,x20722)+E(f751(x20721,x20723,x20724,x20725,x20726),f751(x20722,x20723,x20724,x20725,x20726)) % 191.49/191.42 [2073]~E(x20731,x20732)+E(f751(x20733,x20731,x20734,x20735,x20736),f751(x20733,x20732,x20734,x20735,x20736)) % 191.49/191.42 [2074]~E(x20741,x20742)+E(f751(x20743,x20744,x20741,x20745,x20746),f751(x20743,x20744,x20742,x20745,x20746)) % 191.49/191.42 [2075]~E(x20751,x20752)+E(f751(x20753,x20754,x20755,x20751,x20756),f751(x20753,x20754,x20755,x20752,x20756)) % 191.49/191.42 [2076]~E(x20761,x20762)+E(f751(x20763,x20764,x20765,x20766,x20761),f751(x20763,x20764,x20765,x20766,x20762)) % 191.49/191.42 [2077]~E(x20771,x20772)+E(f387(x20771),f387(x20772)) % 191.49/191.42 [2078]~E(x20781,x20782)+E(f441(x20781,x20783,x20784,x20785),f441(x20782,x20783,x20784,x20785)) % 191.49/191.42 [2079]~E(x20791,x20792)+E(f441(x20793,x20791,x20794,x20795),f441(x20793,x20792,x20794,x20795)) % 191.49/191.42 [2080]~E(x20801,x20802)+E(f441(x20803,x20804,x20801,x20805),f441(x20803,x20804,x20802,x20805)) % 191.49/191.42 [2081]~E(x20811,x20812)+E(f441(x20813,x20814,x20815,x20811),f441(x20813,x20814,x20815,x20812)) % 191.49/191.42 [2082]~E(x20821,x20822)+E(f693(x20821,x20823,x20824,x20825,x20826),f693(x20822,x20823,x20824,x20825,x20826)) % 191.49/191.42 [2083]~E(x20831,x20832)+E(f693(x20833,x20831,x20834,x20835,x20836),f693(x20833,x20832,x20834,x20835,x20836)) % 191.49/191.42 [2084]~E(x20841,x20842)+E(f693(x20843,x20844,x20841,x20845,x20846),f693(x20843,x20844,x20842,x20845,x20846)) % 191.49/191.42 [2085]~E(x20851,x20852)+E(f693(x20853,x20854,x20855,x20851,x20856),f693(x20853,x20854,x20855,x20852,x20856)) % 191.49/191.42 [2086]~E(x20861,x20862)+E(f693(x20863,x20864,x20865,x20866,x20861),f693(x20863,x20864,x20865,x20866,x20862)) % 191.49/191.42 [2087]~E(x20871,x20872)+E(f368(x20871,x20873,x20874),f368(x20872,x20873,x20874)) % 191.49/191.42 [2088]~E(x20881,x20882)+E(f368(x20883,x20881,x20884),f368(x20883,x20882,x20884)) % 191.49/191.42 [2089]~E(x20891,x20892)+E(f368(x20893,x20894,x20891),f368(x20893,x20894,x20892)) % 191.49/191.42 [2090]~E(x20901,x20902)+E(f749(x20901,x20903,x20904,x20905,x20906),f749(x20902,x20903,x20904,x20905,x20906)) % 191.49/191.42 [2091]~E(x20911,x20912)+E(f749(x20913,x20911,x20914,x20915,x20916),f749(x20913,x20912,x20914,x20915,x20916)) % 191.49/191.42 [2092]~E(x20921,x20922)+E(f749(x20923,x20924,x20921,x20925,x20926),f749(x20923,x20924,x20922,x20925,x20926)) % 191.49/191.42 [2093]~E(x20931,x20932)+E(f749(x20933,x20934,x20935,x20931,x20936),f749(x20933,x20934,x20935,x20932,x20936)) % 191.49/191.42 [2094]~E(x20941,x20942)+E(f749(x20943,x20944,x20945,x20946,x20941),f749(x20943,x20944,x20945,x20946,x20942)) % 191.49/191.42 [2095]~E(x20951,x20952)+E(f424(x20951,x20953),f424(x20952,x20953)) % 191.49/191.42 [2096]~E(x20961,x20962)+E(f424(x20963,x20961),f424(x20963,x20962)) % 191.49/191.42 [2097]~E(x20971,x20972)+E(f299(x20971,x20973,x20974),f299(x20972,x20973,x20974)) % 191.49/191.42 [2098]~E(x20981,x20982)+E(f299(x20983,x20981,x20984),f299(x20983,x20982,x20984)) % 191.49/191.42 [2099]~E(x20991,x20992)+E(f299(x20993,x20994,x20991),f299(x20993,x20994,x20992)) % 191.49/191.42 [2100]~E(x21001,x21002)+E(f448(x21001,x21003,x21004,x21005),f448(x21002,x21003,x21004,x21005)) % 191.49/191.42 [2101]~E(x21011,x21012)+E(f448(x21013,x21011,x21014,x21015),f448(x21013,x21012,x21014,x21015)) % 191.49/191.42 [2102]~E(x21021,x21022)+E(f448(x21023,x21024,x21021,x21025),f448(x21023,x21024,x21022,x21025)) % 191.49/191.42 [2103]~E(x21031,x21032)+E(f448(x21033,x21034,x21035,x21031),f448(x21033,x21034,x21035,x21032)) % 191.49/191.42 [2104]~E(x21041,x21042)+E(f754(x21041,x21043,x21044,x21045,x21046,x21047,x21048),f754(x21042,x21043,x21044,x21045,x21046,x21047,x21048)) % 191.49/191.42 [2105]~E(x21051,x21052)+E(f754(x21053,x21051,x21054,x21055,x21056,x21057,x21058),f754(x21053,x21052,x21054,x21055,x21056,x21057,x21058)) % 191.49/191.42 [2106]~E(x21061,x21062)+E(f754(x21063,x21064,x21061,x21065,x21066,x21067,x21068),f754(x21063,x21064,x21062,x21065,x21066,x21067,x21068)) % 191.49/191.42 [2107]~E(x21071,x21072)+E(f754(x21073,x21074,x21075,x21071,x21076,x21077,x21078),f754(x21073,x21074,x21075,x21072,x21076,x21077,x21078)) % 191.49/191.42 [2108]~E(x21081,x21082)+E(f754(x21083,x21084,x21085,x21086,x21081,x21087,x21088),f754(x21083,x21084,x21085,x21086,x21082,x21087,x21088)) % 191.49/191.42 [2109]~E(x21091,x21092)+E(f754(x21093,x21094,x21095,x21096,x21097,x21091,x21098),f754(x21093,x21094,x21095,x21096,x21097,x21092,x21098)) % 191.49/191.42 [2110]~E(x21101,x21102)+E(f754(x21103,x21104,x21105,x21106,x21107,x21108,x21101),f754(x21103,x21104,x21105,x21106,x21107,x21108,x21102)) % 191.49/191.42 [2111]~E(x21111,x21112)+E(f628(x21111,x21113,x21114,x21115),f628(x21112,x21113,x21114,x21115)) % 191.49/191.42 [2112]~E(x21121,x21122)+E(f628(x21123,x21121,x21124,x21125),f628(x21123,x21122,x21124,x21125)) % 191.49/191.42 [2113]~E(x21131,x21132)+E(f628(x21133,x21134,x21131,x21135),f628(x21133,x21134,x21132,x21135)) % 191.49/191.42 [2114]~E(x21141,x21142)+E(f628(x21143,x21144,x21145,x21141),f628(x21143,x21144,x21145,x21142)) % 191.49/191.42 [2115]~E(x21151,x21152)+E(f776(x21151,x21153,x21154,x21155,x21156),f776(x21152,x21153,x21154,x21155,x21156)) % 191.49/191.42 [2116]~E(x21161,x21162)+E(f776(x21163,x21161,x21164,x21165,x21166),f776(x21163,x21162,x21164,x21165,x21166)) % 191.49/191.42 [2117]~E(x21171,x21172)+E(f776(x21173,x21174,x21171,x21175,x21176),f776(x21173,x21174,x21172,x21175,x21176)) % 191.49/191.42 [2118]~E(x21181,x21182)+E(f776(x21183,x21184,x21185,x21181,x21186),f776(x21183,x21184,x21185,x21182,x21186)) % 191.49/191.42 [2119]~E(x21191,x21192)+E(f776(x21193,x21194,x21195,x21196,x21191),f776(x21193,x21194,x21195,x21196,x21192)) % 191.49/191.42 [2120]~E(x21201,x21202)+E(f771(x21201,x21203,x21204),f771(x21202,x21203,x21204)) % 191.49/191.42 [2121]~E(x21211,x21212)+E(f771(x21213,x21211,x21214),f771(x21213,x21212,x21214)) % 191.49/191.42 [2122]~E(x21221,x21222)+E(f771(x21223,x21224,x21221),f771(x21223,x21224,x21222)) % 191.49/191.42 [2123]~E(x21231,x21232)+E(f464(x21231,x21233,x21234),f464(x21232,x21233,x21234)) % 191.49/191.42 [2124]~E(x21241,x21242)+E(f464(x21243,x21241,x21244),f464(x21243,x21242,x21244)) % 191.49/191.42 [2125]~E(x21251,x21252)+E(f464(x21253,x21254,x21251),f464(x21253,x21254,x21252)) % 191.49/191.42 [2126]~E(x21261,x21262)+E(f865(x21261,x21263,x21264,x21265,x21266,x21267),f865(x21262,x21263,x21264,x21265,x21266,x21267)) % 191.49/191.42 [2127]~E(x21271,x21272)+E(f865(x21273,x21271,x21274,x21275,x21276,x21277),f865(x21273,x21272,x21274,x21275,x21276,x21277)) % 191.49/191.42 [2128]~E(x21281,x21282)+E(f865(x21283,x21284,x21281,x21285,x21286,x21287),f865(x21283,x21284,x21282,x21285,x21286,x21287)) % 191.49/191.42 [2129]~E(x21291,x21292)+E(f865(x21293,x21294,x21295,x21291,x21296,x21297),f865(x21293,x21294,x21295,x21292,x21296,x21297)) % 191.49/191.42 [2130]~E(x21301,x21302)+E(f865(x21303,x21304,x21305,x21306,x21301,x21307),f865(x21303,x21304,x21305,x21306,x21302,x21307)) % 191.49/191.42 [2131]~E(x21311,x21312)+E(f865(x21313,x21314,x21315,x21316,x21317,x21311),f865(x21313,x21314,x21315,x21316,x21317,x21312)) % 191.49/191.42 [2132]~E(x21321,x21322)+E(f632(x21321,x21323,x21324,x21325),f632(x21322,x21323,x21324,x21325)) % 191.49/191.42 [2133]~E(x21331,x21332)+E(f632(x21333,x21331,x21334,x21335),f632(x21333,x21332,x21334,x21335)) % 191.49/191.42 [2134]~E(x21341,x21342)+E(f632(x21343,x21344,x21341,x21345),f632(x21343,x21344,x21342,x21345)) % 191.49/191.42 [2135]~E(x21351,x21352)+E(f632(x21353,x21354,x21355,x21351),f632(x21353,x21354,x21355,x21352)) % 191.49/191.42 [2136]~E(x21361,x21362)+E(f337(x21361,x21363,x21364,x21365),f337(x21362,x21363,x21364,x21365)) % 191.49/191.42 [2137]~E(x21371,x21372)+E(f337(x21373,x21371,x21374,x21375),f337(x21373,x21372,x21374,x21375)) % 191.49/191.42 [2138]~E(x21381,x21382)+E(f337(x21383,x21384,x21381,x21385),f337(x21383,x21384,x21382,x21385)) % 191.49/191.42 [2139]~E(x21391,x21392)+E(f337(x21393,x21394,x21395,x21391),f337(x21393,x21394,x21395,x21392)) % 191.49/191.42 [2140]~E(x21401,x21402)+E(f769(x21401,x21403,x21404),f769(x21402,x21403,x21404)) % 191.49/191.42 [2141]~E(x21411,x21412)+E(f769(x21413,x21411,x21414),f769(x21413,x21412,x21414)) % 191.49/191.42 [2142]~E(x21421,x21422)+E(f769(x21423,x21424,x21421),f769(x21423,x21424,x21422)) % 191.49/191.42 [2143]~E(x21431,x21432)+E(f705(x21431,x21433,x21434,x21435),f705(x21432,x21433,x21434,x21435)) % 191.49/191.42 [2144]~E(x21441,x21442)+E(f705(x21443,x21441,x21444,x21445),f705(x21443,x21442,x21444,x21445)) % 191.49/191.42 [2145]~E(x21451,x21452)+E(f705(x21453,x21454,x21451,x21455),f705(x21453,x21454,x21452,x21455)) % 191.49/191.42 [2146]~E(x21461,x21462)+E(f705(x21463,x21464,x21465,x21461),f705(x21463,x21464,x21465,x21462)) % 191.49/191.42 [2147]~E(x21471,x21472)+E(f664(x21471,x21473),f664(x21472,x21473)) % 191.49/191.42 [2148]~E(x21481,x21482)+E(f664(x21483,x21481),f664(x21483,x21482)) % 191.49/191.42 [2149]~E(x21491,x21492)+E(f520(x21491,x21493,x21494,x21495,x21496),f520(x21492,x21493,x21494,x21495,x21496)) % 191.49/191.42 [2150]~E(x21501,x21502)+E(f520(x21503,x21501,x21504,x21505,x21506),f520(x21503,x21502,x21504,x21505,x21506)) % 191.49/191.42 [2151]~E(x21511,x21512)+E(f520(x21513,x21514,x21511,x21515,x21516),f520(x21513,x21514,x21512,x21515,x21516)) % 191.49/191.42 [2152]~E(x21521,x21522)+E(f520(x21523,x21524,x21525,x21521,x21526),f520(x21523,x21524,x21525,x21522,x21526)) % 191.49/191.42 [2153]~E(x21531,x21532)+E(f520(x21533,x21534,x21535,x21536,x21531),f520(x21533,x21534,x21535,x21536,x21532)) % 191.49/191.42 [2154]~E(x21541,x21542)+E(f845(x21541,x21543,x21544),f845(x21542,x21543,x21544)) % 191.49/191.42 [2155]~E(x21551,x21552)+E(f845(x21553,x21551,x21554),f845(x21553,x21552,x21554)) % 191.49/191.42 [2156]~E(x21561,x21562)+E(f845(x21563,x21564,x21561),f845(x21563,x21564,x21562)) % 191.49/191.42 [2157]~E(x21571,x21572)+E(f215(x21571),f215(x21572)) % 191.49/191.42 [2158]~E(x21581,x21582)+E(f838(x21581,x21583,x21584,x21585,x21586),f838(x21582,x21583,x21584,x21585,x21586)) % 191.49/191.42 [2159]~E(x21591,x21592)+E(f838(x21593,x21591,x21594,x21595,x21596),f838(x21593,x21592,x21594,x21595,x21596)) % 191.49/191.42 [2160]~E(x21601,x21602)+E(f838(x21603,x21604,x21601,x21605,x21606),f838(x21603,x21604,x21602,x21605,x21606)) % 191.49/191.42 [2161]~E(x21611,x21612)+E(f838(x21613,x21614,x21615,x21611,x21616),f838(x21613,x21614,x21615,x21612,x21616)) % 191.49/191.42 [2162]~E(x21621,x21622)+E(f838(x21623,x21624,x21625,x21626,x21621),f838(x21623,x21624,x21625,x21626,x21622)) % 191.49/191.42 [2163]~E(x21631,x21632)+E(f579(x21631,x21633,x21634),f579(x21632,x21633,x21634)) % 191.49/191.42 [2164]~E(x21641,x21642)+E(f579(x21643,x21641,x21644),f579(x21643,x21642,x21644)) % 191.49/191.42 [2165]~E(x21651,x21652)+E(f579(x21653,x21654,x21651),f579(x21653,x21654,x21652)) % 191.49/191.42 [2166]~E(x21661,x21662)+E(f543(x21661,x21663,x21664,x21665,x21666),f543(x21662,x21663,x21664,x21665,x21666)) % 191.49/191.42 [2167]~E(x21671,x21672)+E(f543(x21673,x21671,x21674,x21675,x21676),f543(x21673,x21672,x21674,x21675,x21676)) % 191.49/191.42 [2168]~E(x21681,x21682)+E(f543(x21683,x21684,x21681,x21685,x21686),f543(x21683,x21684,x21682,x21685,x21686)) % 191.49/191.42 [2169]~E(x21691,x21692)+E(f543(x21693,x21694,x21695,x21691,x21696),f543(x21693,x21694,x21695,x21692,x21696)) % 191.49/191.42 [2170]~E(x21701,x21702)+E(f543(x21703,x21704,x21705,x21706,x21701),f543(x21703,x21704,x21705,x21706,x21702)) % 191.49/191.42 [2171]~E(x21711,x21712)+E(f366(x21711,x21713,x21714,x21715),f366(x21712,x21713,x21714,x21715)) % 191.49/191.42 [2172]~E(x21721,x21722)+E(f366(x21723,x21721,x21724,x21725),f366(x21723,x21722,x21724,x21725)) % 191.49/191.42 [2173]~E(x21731,x21732)+E(f366(x21733,x21734,x21731,x21735),f366(x21733,x21734,x21732,x21735)) % 191.49/191.42 [2174]~E(x21741,x21742)+E(f366(x21743,x21744,x21745,x21741),f366(x21743,x21744,x21745,x21742)) % 191.49/191.42 [2175]~E(x21751,x21752)+E(f648(x21751,x21753),f648(x21752,x21753)) % 191.49/191.42 [2176]~E(x21761,x21762)+E(f648(x21763,x21761),f648(x21763,x21762)) % 191.49/191.42 [2177]~E(x21771,x21772)+E(f338(x21771),f338(x21772)) % 191.49/191.42 [2178]~E(x21781,x21782)+E(f704(x21781,x21783,x21784,x21785),f704(x21782,x21783,x21784,x21785)) % 191.49/191.42 [2179]~E(x21791,x21792)+E(f704(x21793,x21791,x21794,x21795),f704(x21793,x21792,x21794,x21795)) % 191.49/191.42 [2180]~E(x21801,x21802)+E(f704(x21803,x21804,x21801,x21805),f704(x21803,x21804,x21802,x21805)) % 191.49/191.42 [2181]~E(x21811,x21812)+E(f704(x21813,x21814,x21815,x21811),f704(x21813,x21814,x21815,x21812)) % 191.49/191.42 [2182]~E(x21821,x21822)+E(f362(x21821,x21823),f362(x21822,x21823)) % 191.49/191.42 [2183]~E(x21831,x21832)+E(f362(x21833,x21831),f362(x21833,x21832)) % 191.49/191.42 [2184]~E(x21841,x21842)+E(f767(x21841,x21843,x21844),f767(x21842,x21843,x21844)) % 191.49/191.42 [2185]~E(x21851,x21852)+E(f767(x21853,x21851,x21854),f767(x21853,x21852,x21854)) % 191.49/191.42 [2186]~E(x21861,x21862)+E(f767(x21863,x21864,x21861),f767(x21863,x21864,x21862)) % 191.49/191.42 [2187]~E(x21871,x21872)+E(f350(x21871,x21873,x21874,x21875,x21876),f350(x21872,x21873,x21874,x21875,x21876)) % 191.49/191.42 [2188]~E(x21881,x21882)+E(f350(x21883,x21881,x21884,x21885,x21886),f350(x21883,x21882,x21884,x21885,x21886)) % 191.49/191.42 [2189]~E(x21891,x21892)+E(f350(x21893,x21894,x21891,x21895,x21896),f350(x21893,x21894,x21892,x21895,x21896)) % 191.49/191.42 [2190]~E(x21901,x21902)+E(f350(x21903,x21904,x21905,x21901,x21906),f350(x21903,x21904,x21905,x21902,x21906)) % 191.49/191.42 [2191]~E(x21911,x21912)+E(f350(x21913,x21914,x21915,x21916,x21911),f350(x21913,x21914,x21915,x21916,x21912)) % 191.49/191.42 [2192]~E(x21921,x21922)+E(f744(x21921,x21923,x21924),f744(x21922,x21923,x21924)) % 191.49/191.42 [2193]~E(x21931,x21932)+E(f744(x21933,x21931,x21934),f744(x21933,x21932,x21934)) % 191.49/191.42 [2194]~E(x21941,x21942)+E(f744(x21943,x21944,x21941),f744(x21943,x21944,x21942)) % 191.49/191.42 [2195]~E(x21951,x21952)+E(f870(x21951,x21953,x21954),f870(x21952,x21953,x21954)) % 191.49/191.42 [2196]~E(x21961,x21962)+E(f870(x21963,x21961,x21964),f870(x21963,x21962,x21964)) % 191.49/191.42 [2197]~E(x21971,x21972)+E(f870(x21973,x21974,x21971),f870(x21973,x21974,x21972)) % 191.49/191.42 [2198]~E(x21981,x21982)+E(f857(x21981,x21983,x21984,x21985,x21986,x21987),f857(x21982,x21983,x21984,x21985,x21986,x21987)) % 191.49/191.42 [2199]~E(x21991,x21992)+E(f857(x21993,x21991,x21994,x21995,x21996,x21997),f857(x21993,x21992,x21994,x21995,x21996,x21997)) % 191.49/191.42 [2200]~E(x22001,x22002)+E(f857(x22003,x22004,x22001,x22005,x22006,x22007),f857(x22003,x22004,x22002,x22005,x22006,x22007)) % 191.49/191.42 [2201]~E(x22011,x22012)+E(f857(x22013,x22014,x22015,x22011,x22016,x22017),f857(x22013,x22014,x22015,x22012,x22016,x22017)) % 191.49/191.42 [2202]~E(x22021,x22022)+E(f857(x22023,x22024,x22025,x22026,x22021,x22027),f857(x22023,x22024,x22025,x22026,x22022,x22027)) % 191.49/191.42 [2203]~E(x22031,x22032)+E(f857(x22033,x22034,x22035,x22036,x22037,x22031),f857(x22033,x22034,x22035,x22036,x22037,x22032)) % 191.49/191.42 [2204]~E(x22041,x22042)+E(f240(x22041,x22043,x22044,x22045),f240(x22042,x22043,x22044,x22045)) % 191.49/191.42 [2205]~E(x22051,x22052)+E(f240(x22053,x22051,x22054,x22055),f240(x22053,x22052,x22054,x22055)) % 191.49/191.42 [2206]~E(x22061,x22062)+E(f240(x22063,x22064,x22061,x22065),f240(x22063,x22064,x22062,x22065)) % 191.49/191.42 [2207]~E(x22071,x22072)+E(f240(x22073,x22074,x22075,x22071),f240(x22073,x22074,x22075,x22072)) % 191.49/191.42 [2208]~E(x22081,x22082)+E(f655(x22081,x22083,x22084),f655(x22082,x22083,x22084)) % 191.49/191.42 [2209]~E(x22091,x22092)+E(f655(x22093,x22091,x22094),f655(x22093,x22092,x22094)) % 191.49/191.42 [2210]~E(x22101,x22102)+E(f655(x22103,x22104,x22101),f655(x22103,x22104,x22102)) % 191.49/191.42 [2211]~E(x22111,x22112)+E(f534(x22111,x22113,x22114,x22115,x22116,x22117,x22118,x22119),f534(x22112,x22113,x22114,x22115,x22116,x22117,x22118,x22119)) % 191.49/191.42 [2212]~E(x22121,x22122)+E(f534(x22123,x22121,x22124,x22125,x22126,x22127,x22128,x22129),f534(x22123,x22122,x22124,x22125,x22126,x22127,x22128,x22129)) % 191.49/191.42 [2213]~E(x22131,x22132)+E(f534(x22133,x22134,x22131,x22135,x22136,x22137,x22138,x22139),f534(x22133,x22134,x22132,x22135,x22136,x22137,x22138,x22139)) % 191.49/191.42 [2214]~E(x22141,x22142)+E(f534(x22143,x22144,x22145,x22141,x22146,x22147,x22148,x22149),f534(x22143,x22144,x22145,x22142,x22146,x22147,x22148,x22149)) % 191.49/191.42 [2215]~E(x22151,x22152)+E(f534(x22153,x22154,x22155,x22156,x22151,x22157,x22158,x22159),f534(x22153,x22154,x22155,x22156,x22152,x22157,x22158,x22159)) % 191.49/191.42 [2216]~E(x22161,x22162)+E(f534(x22163,x22164,x22165,x22166,x22167,x22161,x22168,x22169),f534(x22163,x22164,x22165,x22166,x22167,x22162,x22168,x22169)) % 191.49/191.42 [2217]~E(x22171,x22172)+E(f534(x22173,x22174,x22175,x22176,x22177,x22178,x22171,x22179),f534(x22173,x22174,x22175,x22176,x22177,x22178,x22172,x22179)) % 191.49/191.42 [2218]~E(x22181,x22182)+E(f534(x22183,x22184,x22185,x22186,x22187,x22188,x22189,x22181),f534(x22183,x22184,x22185,x22186,x22187,x22188,x22189,x22182)) % 191.49/191.42 [2219]~E(x22191,x22192)+E(f535(x22191,x22193),f535(x22192,x22193)) % 191.49/191.42 [2220]~E(x22201,x22202)+E(f535(x22203,x22201),f535(x22203,x22202)) % 191.49/191.42 [2221]~E(x22211,x22212)+E(f436(x22211,x22213,x22214,x22215),f436(x22212,x22213,x22214,x22215)) % 191.49/191.42 [2222]~E(x22221,x22222)+E(f436(x22223,x22221,x22224,x22225),f436(x22223,x22222,x22224,x22225)) % 191.49/191.42 [2223]~E(x22231,x22232)+E(f436(x22233,x22234,x22231,x22235),f436(x22233,x22234,x22232,x22235)) % 191.49/191.42 [2224]~E(x22241,x22242)+E(f436(x22243,x22244,x22245,x22241),f436(x22243,x22244,x22245,x22242)) % 191.49/191.42 [2225]~E(x22251,x22252)+E(f606(x22251,x22253,x22254,x22255),f606(x22252,x22253,x22254,x22255)) % 191.49/191.42 [2226]~E(x22261,x22262)+E(f606(x22263,x22261,x22264,x22265),f606(x22263,x22262,x22264,x22265)) % 191.49/191.42 [2227]~E(x22271,x22272)+E(f606(x22273,x22274,x22271,x22275),f606(x22273,x22274,x22272,x22275)) % 191.49/191.42 [2228]~E(x22281,x22282)+E(f606(x22283,x22284,x22285,x22281),f606(x22283,x22284,x22285,x22282)) % 191.49/191.42 [2229]~E(x22291,x22292)+E(f360(x22291,x22293,x22294,x22295,x22296),f360(x22292,x22293,x22294,x22295,x22296)) % 191.49/191.42 [2230]~E(x22301,x22302)+E(f360(x22303,x22301,x22304,x22305,x22306),f360(x22303,x22302,x22304,x22305,x22306)) % 191.49/191.42 [2231]~E(x22311,x22312)+E(f360(x22313,x22314,x22311,x22315,x22316),f360(x22313,x22314,x22312,x22315,x22316)) % 191.49/191.42 [2232]~E(x22321,x22322)+E(f360(x22323,x22324,x22325,x22321,x22326),f360(x22323,x22324,x22325,x22322,x22326)) % 191.49/191.42 [2233]~E(x22331,x22332)+E(f360(x22333,x22334,x22335,x22336,x22331),f360(x22333,x22334,x22335,x22336,x22332)) % 191.49/191.42 [2234]~E(x22341,x22342)+E(f540(x22341,x22343,x22344,x22345,x22346),f540(x22342,x22343,x22344,x22345,x22346)) % 191.49/191.42 [2235]~E(x22351,x22352)+E(f540(x22353,x22351,x22354,x22355,x22356),f540(x22353,x22352,x22354,x22355,x22356)) % 191.49/191.42 [2236]~E(x22361,x22362)+E(f540(x22363,x22364,x22361,x22365,x22366),f540(x22363,x22364,x22362,x22365,x22366)) % 191.49/191.42 [2237]~E(x22371,x22372)+E(f540(x22373,x22374,x22375,x22371,x22376),f540(x22373,x22374,x22375,x22372,x22376)) % 191.49/191.42 [2238]~E(x22381,x22382)+E(f540(x22383,x22384,x22385,x22386,x22381),f540(x22383,x22384,x22385,x22386,x22382)) % 191.49/191.42 [2239]~E(x22391,x22392)+E(f847(x22391,x22393,x22394,x22395),f847(x22392,x22393,x22394,x22395)) % 191.49/191.42 [2240]~E(x22401,x22402)+E(f847(x22403,x22401,x22404,x22405),f847(x22403,x22402,x22404,x22405)) % 191.49/191.42 [2241]~E(x22411,x22412)+E(f847(x22413,x22414,x22411,x22415),f847(x22413,x22414,x22412,x22415)) % 191.49/191.42 [2242]~E(x22421,x22422)+E(f847(x22423,x22424,x22425,x22421),f847(x22423,x22424,x22425,x22422)) % 191.49/191.42 [2243]~E(x22431,x22432)+E(f835(x22431,x22433,x22434,x22435),f835(x22432,x22433,x22434,x22435)) % 191.49/191.42 [2244]~E(x22441,x22442)+E(f835(x22443,x22441,x22444,x22445),f835(x22443,x22442,x22444,x22445)) % 191.49/191.42 [2245]~E(x22451,x22452)+E(f835(x22453,x22454,x22451,x22455),f835(x22453,x22454,x22452,x22455)) % 191.49/191.42 [2246]~E(x22461,x22462)+E(f835(x22463,x22464,x22465,x22461),f835(x22463,x22464,x22465,x22462)) % 191.49/191.42 [2247]~E(x22471,x22472)+E(f713(x22471,x22473,x22474,x22475),f713(x22472,x22473,x22474,x22475)) % 191.49/191.42 [2248]~E(x22481,x22482)+E(f713(x22483,x22481,x22484,x22485),f713(x22483,x22482,x22484,x22485)) % 191.49/191.42 [2249]~E(x22491,x22492)+E(f713(x22493,x22494,x22491,x22495),f713(x22493,x22494,x22492,x22495)) % 191.49/191.42 [2250]~E(x22501,x22502)+E(f713(x22503,x22504,x22505,x22501),f713(x22503,x22504,x22505,x22502)) % 191.49/191.42 [2251]~E(x22511,x22512)+E(f818(x22511,x22513,x22514,x22515,x22516),f818(x22512,x22513,x22514,x22515,x22516)) % 191.49/191.42 [2252]~E(x22521,x22522)+E(f818(x22523,x22521,x22524,x22525,x22526),f818(x22523,x22522,x22524,x22525,x22526)) % 191.49/191.42 [2253]~E(x22531,x22532)+E(f818(x22533,x22534,x22531,x22535,x22536),f818(x22533,x22534,x22532,x22535,x22536)) % 191.49/191.42 [2254]~E(x22541,x22542)+E(f818(x22543,x22544,x22545,x22541,x22546),f818(x22543,x22544,x22545,x22542,x22546)) % 191.49/191.42 [2255]~E(x22551,x22552)+E(f818(x22553,x22554,x22555,x22556,x22551),f818(x22553,x22554,x22555,x22556,x22552)) % 191.49/191.42 [2256]~E(x22561,x22562)+E(f523(x22561,x22563,x22564,x22565),f523(x22562,x22563,x22564,x22565)) % 191.49/191.42 [2257]~E(x22571,x22572)+E(f523(x22573,x22571,x22574,x22575),f523(x22573,x22572,x22574,x22575)) % 191.49/191.42 [2258]~E(x22581,x22582)+E(f523(x22583,x22584,x22581,x22585),f523(x22583,x22584,x22582,x22585)) % 191.49/191.42 [2259]~E(x22591,x22592)+E(f523(x22593,x22594,x22595,x22591),f523(x22593,x22594,x22595,x22592)) % 191.49/191.42 [2260]~E(x22601,x22602)+E(f370(x22601,x22603,x22604,x22605),f370(x22602,x22603,x22604,x22605)) % 191.49/191.42 [2261]~E(x22611,x22612)+E(f370(x22613,x22611,x22614,x22615),f370(x22613,x22612,x22614,x22615)) % 191.49/191.42 [2262]~E(x22621,x22622)+E(f370(x22623,x22624,x22621,x22625),f370(x22623,x22624,x22622,x22625)) % 191.49/191.42 [2263]~E(x22631,x22632)+E(f370(x22633,x22634,x22635,x22631),f370(x22633,x22634,x22635,x22632)) % 191.49/191.42 [2264]~E(x22641,x22642)+E(f295(x22641,x22643,x22644),f295(x22642,x22643,x22644)) % 191.49/191.42 [2265]~E(x22651,x22652)+E(f295(x22653,x22651,x22654),f295(x22653,x22652,x22654)) % 191.49/191.42 [2266]~E(x22661,x22662)+E(f295(x22663,x22664,x22661),f295(x22663,x22664,x22662)) % 191.49/191.42 [2267]~E(x22671,x22672)+E(f470(x22671,x22673),f470(x22672,x22673)) % 191.49/191.42 [2268]~E(x22681,x22682)+E(f470(x22683,x22681),f470(x22683,x22682)) % 191.49/191.42 [2269]~E(x22691,x22692)+E(f408(x22691,x22693,x22694,x22695),f408(x22692,x22693,x22694,x22695)) % 191.49/191.42 [2270]~E(x22701,x22702)+E(f408(x22703,x22701,x22704,x22705),f408(x22703,x22702,x22704,x22705)) % 191.49/191.42 [2271]~E(x22711,x22712)+E(f408(x22713,x22714,x22711,x22715),f408(x22713,x22714,x22712,x22715)) % 191.49/191.42 [2272]~E(x22721,x22722)+E(f408(x22723,x22724,x22725,x22721),f408(x22723,x22724,x22725,x22722)) % 191.49/191.42 [2273]~E(x22731,x22732)+E(f345(x22731,x22733),f345(x22732,x22733)) % 191.49/191.42 [2274]~E(x22741,x22742)+E(f345(x22743,x22741),f345(x22743,x22742)) % 191.49/191.42 [2275]~E(x22751,x22752)+E(f752(x22751,x22753,x22754,x22755,x22756,x22757,x22758),f752(x22752,x22753,x22754,x22755,x22756,x22757,x22758)) % 191.49/191.42 [2276]~E(x22761,x22762)+E(f752(x22763,x22761,x22764,x22765,x22766,x22767,x22768),f752(x22763,x22762,x22764,x22765,x22766,x22767,x22768)) % 191.49/191.42 [2277]~E(x22771,x22772)+E(f752(x22773,x22774,x22771,x22775,x22776,x22777,x22778),f752(x22773,x22774,x22772,x22775,x22776,x22777,x22778)) % 191.49/191.42 [2278]~E(x22781,x22782)+E(f752(x22783,x22784,x22785,x22781,x22786,x22787,x22788),f752(x22783,x22784,x22785,x22782,x22786,x22787,x22788)) % 191.49/191.42 [2279]~E(x22791,x22792)+E(f752(x22793,x22794,x22795,x22796,x22791,x22797,x22798),f752(x22793,x22794,x22795,x22796,x22792,x22797,x22798)) % 191.49/191.42 [2280]~E(x22801,x22802)+E(f752(x22803,x22804,x22805,x22806,x22807,x22801,x22808),f752(x22803,x22804,x22805,x22806,x22807,x22802,x22808)) % 191.49/191.42 [2281]~E(x22811,x22812)+E(f752(x22813,x22814,x22815,x22816,x22817,x22818,x22811),f752(x22813,x22814,x22815,x22816,x22817,x22818,x22812)) % 191.49/191.42 [2282]~E(x22821,x22822)+E(f557(x22821,x22823,x22824,x22825,x22826),f557(x22822,x22823,x22824,x22825,x22826)) % 191.49/191.42 [2283]~E(x22831,x22832)+E(f557(x22833,x22831,x22834,x22835,x22836),f557(x22833,x22832,x22834,x22835,x22836)) % 191.49/191.42 [2284]~E(x22841,x22842)+E(f557(x22843,x22844,x22841,x22845,x22846),f557(x22843,x22844,x22842,x22845,x22846)) % 191.49/191.42 [2285]~E(x22851,x22852)+E(f557(x22853,x22854,x22855,x22851,x22856),f557(x22853,x22854,x22855,x22852,x22856)) % 191.49/191.42 [2286]~E(x22861,x22862)+E(f557(x22863,x22864,x22865,x22866,x22861),f557(x22863,x22864,x22865,x22866,x22862)) % 191.49/191.42 [2287]~E(x22871,x22872)+E(f528(x22871,x22873,x22874,x22875),f528(x22872,x22873,x22874,x22875)) % 191.49/191.42 [2288]~E(x22881,x22882)+E(f528(x22883,x22881,x22884,x22885),f528(x22883,x22882,x22884,x22885)) % 191.49/191.42 [2289]~E(x22891,x22892)+E(f528(x22893,x22894,x22891,x22895),f528(x22893,x22894,x22892,x22895)) % 191.49/191.42 [2290]~E(x22901,x22902)+E(f528(x22903,x22904,x22905,x22901),f528(x22903,x22904,x22905,x22902)) % 191.49/191.42 [2291]~E(x22911,x22912)+E(f467(x22911,x22913,x22914),f467(x22912,x22913,x22914)) % 191.49/191.42 [2292]~E(x22921,x22922)+E(f467(x22923,x22921,x22924),f467(x22923,x22922,x22924)) % 191.49/191.42 [2293]~E(x22931,x22932)+E(f467(x22933,x22934,x22931),f467(x22933,x22934,x22932)) % 191.49/191.42 [2294]~E(x22941,x22942)+E(f347(x22941,x22943,x22944),f347(x22942,x22943,x22944)) % 191.49/191.42 [2295]~E(x22951,x22952)+E(f347(x22953,x22951,x22954),f347(x22953,x22952,x22954)) % 191.49/191.42 [2296]~E(x22961,x22962)+E(f347(x22963,x22964,x22961),f347(x22963,x22964,x22962)) % 191.49/191.42 [2297]~E(x22971,x22972)+E(f662(x22971,x22973,x22974),f662(x22972,x22973,x22974)) % 191.49/191.42 [2298]~E(x22981,x22982)+E(f662(x22983,x22981,x22984),f662(x22983,x22982,x22984)) % 191.49/191.42 [2299]~E(x22991,x22992)+E(f662(x22993,x22994,x22991),f662(x22993,x22994,x22992)) % 191.49/191.42 [2300]~E(x23001,x23002)+E(f597(x23001,x23003,x23004,x23005,x23006),f597(x23002,x23003,x23004,x23005,x23006)) % 191.49/191.42 [2301]~E(x23011,x23012)+E(f597(x23013,x23011,x23014,x23015,x23016),f597(x23013,x23012,x23014,x23015,x23016)) % 191.49/191.42 [2302]~E(x23021,x23022)+E(f597(x23023,x23024,x23021,x23025,x23026),f597(x23023,x23024,x23022,x23025,x23026)) % 191.49/191.42 [2303]~E(x23031,x23032)+E(f597(x23033,x23034,x23035,x23031,x23036),f597(x23033,x23034,x23035,x23032,x23036)) % 191.49/191.42 [2304]~E(x23041,x23042)+E(f597(x23043,x23044,x23045,x23046,x23041),f597(x23043,x23044,x23045,x23046,x23042)) % 191.49/191.42 [2305]~E(x23051,x23052)+E(f374(x23051,x23053),f374(x23052,x23053)) % 191.49/191.42 [2306]~E(x23061,x23062)+E(f374(x23063,x23061),f374(x23063,x23062)) % 191.49/191.42 [2307]~E(x23071,x23072)+E(f871(x23071,x23073,x23074,x23075,x23076),f871(x23072,x23073,x23074,x23075,x23076)) % 191.49/191.42 [2308]~E(x23081,x23082)+E(f871(x23083,x23081,x23084,x23085,x23086),f871(x23083,x23082,x23084,x23085,x23086)) % 191.49/191.42 [2309]~E(x23091,x23092)+E(f871(x23093,x23094,x23091,x23095,x23096),f871(x23093,x23094,x23092,x23095,x23096)) % 191.49/191.42 [2310]~E(x23101,x23102)+E(f871(x23103,x23104,x23105,x23101,x23106),f871(x23103,x23104,x23105,x23102,x23106)) % 191.49/191.42 [2311]~E(x23111,x23112)+E(f871(x23113,x23114,x23115,x23116,x23111),f871(x23113,x23114,x23115,x23116,x23112)) % 191.49/191.42 [2312]~E(x23121,x23122)+E(f531(x23121,x23123,x23124,x23125,x23126),f531(x23122,x23123,x23124,x23125,x23126)) % 191.49/191.42 [2313]~E(x23131,x23132)+E(f531(x23133,x23131,x23134,x23135,x23136),f531(x23133,x23132,x23134,x23135,x23136)) % 191.49/191.42 [2314]~E(x23141,x23142)+E(f531(x23143,x23144,x23141,x23145,x23146),f531(x23143,x23144,x23142,x23145,x23146)) % 191.49/191.42 [2315]~E(x23151,x23152)+E(f531(x23153,x23154,x23155,x23151,x23156),f531(x23153,x23154,x23155,x23152,x23156)) % 191.49/191.42 [2316]~E(x23161,x23162)+E(f531(x23163,x23164,x23165,x23166,x23161),f531(x23163,x23164,x23165,x23166,x23162)) % 191.49/191.42 [2317]~E(x23171,x23172)+E(f663(x23171,x23173,x23174,x23175,x23176),f663(x23172,x23173,x23174,x23175,x23176)) % 191.49/191.42 [2318]~E(x23181,x23182)+E(f663(x23183,x23181,x23184,x23185,x23186),f663(x23183,x23182,x23184,x23185,x23186)) % 191.49/191.42 [2319]~E(x23191,x23192)+E(f663(x23193,x23194,x23191,x23195,x23196),f663(x23193,x23194,x23192,x23195,x23196)) % 191.49/191.42 [2320]~E(x23201,x23202)+E(f663(x23203,x23204,x23205,x23201,x23206),f663(x23203,x23204,x23205,x23202,x23206)) % 191.49/191.42 [2321]~E(x23211,x23212)+E(f663(x23213,x23214,x23215,x23216,x23211),f663(x23213,x23214,x23215,x23216,x23212)) % 191.49/191.42 [2322]~E(x23221,x23222)+E(f205(x23221,x23223,x23224,x23225),f205(x23222,x23223,x23224,x23225)) % 191.49/191.42 [2323]~E(x23231,x23232)+E(f205(x23233,x23231,x23234,x23235),f205(x23233,x23232,x23234,x23235)) % 191.49/191.42 [2324]~E(x23241,x23242)+E(f205(x23243,x23244,x23241,x23245),f205(x23243,x23244,x23242,x23245)) % 191.49/191.42 [2325]~E(x23251,x23252)+E(f205(x23253,x23254,x23255,x23251),f205(x23253,x23254,x23255,x23252)) % 191.49/191.42 [2326]~E(x23261,x23262)+E(f681(x23261,x23263),f681(x23262,x23263)) % 191.49/191.42 [2327]~E(x23271,x23272)+E(f681(x23273,x23271),f681(x23273,x23272)) % 191.49/191.42 [2328]~E(x23281,x23282)+E(f596(x23281,x23283,x23284,x23285,x23286),f596(x23282,x23283,x23284,x23285,x23286)) % 191.49/191.42 [2329]~E(x23291,x23292)+E(f596(x23293,x23291,x23294,x23295,x23296),f596(x23293,x23292,x23294,x23295,x23296)) % 191.49/191.42 [2330]~E(x23301,x23302)+E(f596(x23303,x23304,x23301,x23305,x23306),f596(x23303,x23304,x23302,x23305,x23306)) % 191.49/191.42 [2331]~E(x23311,x23312)+E(f596(x23313,x23314,x23315,x23311,x23316),f596(x23313,x23314,x23315,x23312,x23316)) % 191.49/191.42 [2332]~E(x23321,x23322)+E(f596(x23323,x23324,x23325,x23326,x23321),f596(x23323,x23324,x23325,x23326,x23322)) % 191.49/191.42 [2333]~E(x23331,x23332)+E(f280(x23331,x23333),f280(x23332,x23333)) % 191.49/191.42 [2334]~E(x23341,x23342)+E(f280(x23343,x23341),f280(x23343,x23342)) % 191.49/191.42 [2335]~E(x23351,x23352)+E(f765(x23351,x23353,x23354,x23355,x23356),f765(x23352,x23353,x23354,x23355,x23356)) % 191.49/191.42 [2336]~E(x23361,x23362)+E(f765(x23363,x23361,x23364,x23365,x23366),f765(x23363,x23362,x23364,x23365,x23366)) % 191.49/191.42 [2337]~E(x23371,x23372)+E(f765(x23373,x23374,x23371,x23375,x23376),f765(x23373,x23374,x23372,x23375,x23376)) % 191.49/191.42 [2338]~E(x23381,x23382)+E(f765(x23383,x23384,x23385,x23381,x23386),f765(x23383,x23384,x23385,x23382,x23386)) % 191.49/191.42 [2339]~E(x23391,x23392)+E(f765(x23393,x23394,x23395,x23396,x23391),f765(x23393,x23394,x23395,x23396,x23392)) % 191.49/191.42 [2340]~E(x23401,x23402)+E(f862(x23401,x23403,x23404),f862(x23402,x23403,x23404)) % 191.49/191.42 [2341]~E(x23411,x23412)+E(f862(x23413,x23411,x23414),f862(x23413,x23412,x23414)) % 191.49/191.42 [2342]~E(x23421,x23422)+E(f862(x23423,x23424,x23421),f862(x23423,x23424,x23422)) % 191.49/191.42 [2343]~E(x23431,x23432)+E(f866(x23431,x23433,x23434),f866(x23432,x23433,x23434)) % 191.49/191.42 [2344]~E(x23441,x23442)+E(f866(x23443,x23441,x23444),f866(x23443,x23442,x23444)) % 191.49/191.42 [2345]~E(x23451,x23452)+E(f866(x23453,x23454,x23451),f866(x23453,x23454,x23452)) % 191.49/191.42 [2346]~E(x23461,x23462)+E(f547(x23461,x23463,x23464,x23465,x23466),f547(x23462,x23463,x23464,x23465,x23466)) % 191.49/191.42 [2347]~E(x23471,x23472)+E(f547(x23473,x23471,x23474,x23475,x23476),f547(x23473,x23472,x23474,x23475,x23476)) % 191.49/191.42 [2348]~E(x23481,x23482)+E(f547(x23483,x23484,x23481,x23485,x23486),f547(x23483,x23484,x23482,x23485,x23486)) % 191.49/191.42 [2349]~E(x23491,x23492)+E(f547(x23493,x23494,x23495,x23491,x23496),f547(x23493,x23494,x23495,x23492,x23496)) % 191.49/191.42 [2350]~E(x23501,x23502)+E(f547(x23503,x23504,x23505,x23506,x23501),f547(x23503,x23504,x23505,x23506,x23502)) % 191.49/191.42 [2351]~E(x23511,x23512)+E(f275(x23511,x23513,x23514,x23515,x23516),f275(x23512,x23513,x23514,x23515,x23516)) % 191.49/191.42 [2352]~E(x23521,x23522)+E(f275(x23523,x23521,x23524,x23525,x23526),f275(x23523,x23522,x23524,x23525,x23526)) % 191.49/191.42 [2353]~E(x23531,x23532)+E(f275(x23533,x23534,x23531,x23535,x23536),f275(x23533,x23534,x23532,x23535,x23536)) % 191.49/191.42 [2354]~E(x23541,x23542)+E(f275(x23543,x23544,x23545,x23541,x23546),f275(x23543,x23544,x23545,x23542,x23546)) % 191.49/191.42 [2355]~E(x23551,x23552)+E(f275(x23553,x23554,x23555,x23556,x23551),f275(x23553,x23554,x23555,x23556,x23552)) % 191.49/191.42 [2356]~E(x23561,x23562)+E(f582(x23561,x23563,x23564),f582(x23562,x23563,x23564)) % 191.49/191.42 [2357]~E(x23571,x23572)+E(f582(x23573,x23571,x23574),f582(x23573,x23572,x23574)) % 191.49/191.42 [2358]~E(x23581,x23582)+E(f582(x23583,x23584,x23581),f582(x23583,x23584,x23582)) % 191.49/191.42 [2359]~E(x23591,x23592)+E(f477(x23591,x23593,x23594),f477(x23592,x23593,x23594)) % 191.49/191.42 [2360]~E(x23601,x23602)+E(f477(x23603,x23601,x23604),f477(x23603,x23602,x23604)) % 191.49/191.42 [2361]~E(x23611,x23612)+E(f477(x23613,x23614,x23611),f477(x23613,x23614,x23612)) % 191.49/191.42 [2362]~E(x23621,x23622)+E(f680(x23621,x23623),f680(x23622,x23623)) % 191.49/191.42 [2363]~E(x23631,x23632)+E(f680(x23633,x23631),f680(x23633,x23632)) % 191.49/191.42 [2364]~E(x23641,x23642)+E(f714(x23641,x23643,x23644,x23645,x23646,x23647,x23648,x23649),f714(x23642,x23643,x23644,x23645,x23646,x23647,x23648,x23649)) % 191.49/191.42 [2365]~E(x23651,x23652)+E(f714(x23653,x23651,x23654,x23655,x23656,x23657,x23658,x23659),f714(x23653,x23652,x23654,x23655,x23656,x23657,x23658,x23659)) % 191.49/191.42 [2366]~E(x23661,x23662)+E(f714(x23663,x23664,x23661,x23665,x23666,x23667,x23668,x23669),f714(x23663,x23664,x23662,x23665,x23666,x23667,x23668,x23669)) % 191.49/191.42 [2367]~E(x23671,x23672)+E(f714(x23673,x23674,x23675,x23671,x23676,x23677,x23678,x23679),f714(x23673,x23674,x23675,x23672,x23676,x23677,x23678,x23679)) % 191.49/191.42 [2368]~E(x23681,x23682)+E(f714(x23683,x23684,x23685,x23686,x23681,x23687,x23688,x23689),f714(x23683,x23684,x23685,x23686,x23682,x23687,x23688,x23689)) % 191.49/191.42 [2369]~E(x23691,x23692)+E(f714(x23693,x23694,x23695,x23696,x23697,x23691,x23698,x23699),f714(x23693,x23694,x23695,x23696,x23697,x23692,x23698,x23699)) % 191.49/191.42 [2370]~E(x23701,x23702)+E(f714(x23703,x23704,x23705,x23706,x23707,x23708,x23701,x23709),f714(x23703,x23704,x23705,x23706,x23707,x23708,x23702,x23709)) % 191.49/191.42 [2371]~E(x23711,x23712)+E(f714(x23713,x23714,x23715,x23716,x23717,x23718,x23719,x23711),f714(x23713,x23714,x23715,x23716,x23717,x23718,x23719,x23712)) % 191.49/191.42 [2372]~E(x23721,x23722)+E(f296(x23721,x23723,x23724),f296(x23722,x23723,x23724)) % 191.49/191.42 [2373]~E(x23731,x23732)+E(f296(x23733,x23731,x23734),f296(x23733,x23732,x23734)) % 191.49/191.42 [2374]~E(x23741,x23742)+E(f296(x23743,x23744,x23741),f296(x23743,x23744,x23742)) % 191.49/191.42 [2375]~E(x23751,x23752)+E(f595(x23751,x23753,x23754,x23755),f595(x23752,x23753,x23754,x23755)) % 191.49/191.42 [2376]~E(x23761,x23762)+E(f595(x23763,x23761,x23764,x23765),f595(x23763,x23762,x23764,x23765)) % 191.49/191.42 [2377]~E(x23771,x23772)+E(f595(x23773,x23774,x23771,x23775),f595(x23773,x23774,x23772,x23775)) % 191.49/191.42 [2378]~E(x23781,x23782)+E(f595(x23783,x23784,x23785,x23781),f595(x23783,x23784,x23785,x23782)) % 191.49/191.42 [2379]~E(x23791,x23792)+E(f844(x23791,x23793),f844(x23792,x23793)) % 191.49/191.42 [2380]~E(x23801,x23802)+E(f844(x23803,x23801),f844(x23803,x23802)) % 191.49/191.42 [2381]~E(x23811,x23812)+E(f487(x23811,x23813,x23814),f487(x23812,x23813,x23814)) % 191.49/191.42 [2382]~E(x23821,x23822)+E(f487(x23823,x23821,x23824),f487(x23823,x23822,x23824)) % 191.49/191.42 [2383]~E(x23831,x23832)+E(f487(x23833,x23834,x23831),f487(x23833,x23834,x23832)) % 191.49/191.42 [2384]~E(x23841,x23842)+E(f840(x23841,x23843),f840(x23842,x23843)) % 191.49/191.42 [2385]~E(x23851,x23852)+E(f840(x23853,x23851),f840(x23853,x23852)) % 191.49/191.42 [2386]~E(x23861,x23862)+E(f500(x23861,x23863,x23864),f500(x23862,x23863,x23864)) % 191.49/191.42 [2387]~E(x23871,x23872)+E(f500(x23873,x23871,x23874),f500(x23873,x23872,x23874)) % 191.49/191.42 [2388]~E(x23881,x23882)+E(f500(x23883,x23884,x23881),f500(x23883,x23884,x23882)) % 191.49/191.42 [2389]~E(x23891,x23892)+E(f692(x23891,x23893,x23894,x23895,x23896),f692(x23892,x23893,x23894,x23895,x23896)) % 191.49/191.42 [2390]~E(x23901,x23902)+E(f692(x23903,x23901,x23904,x23905,x23906),f692(x23903,x23902,x23904,x23905,x23906)) % 191.49/191.42 [2391]~E(x23911,x23912)+E(f692(x23913,x23914,x23911,x23915,x23916),f692(x23913,x23914,x23912,x23915,x23916)) % 191.49/191.42 [2392]~E(x23921,x23922)+E(f692(x23923,x23924,x23925,x23921,x23926),f692(x23923,x23924,x23925,x23922,x23926)) % 191.49/191.42 [2393]~E(x23931,x23932)+E(f692(x23933,x23934,x23935,x23936,x23931),f692(x23933,x23934,x23935,x23936,x23932)) % 191.49/191.42 [2394]~E(x23941,x23942)+E(f635(x23941,x23943,x23944),f635(x23942,x23943,x23944)) % 191.49/191.42 [2395]~E(x23951,x23952)+E(f635(x23953,x23951,x23954),f635(x23953,x23952,x23954)) % 191.49/191.42 [2396]~E(x23961,x23962)+E(f635(x23963,x23964,x23961),f635(x23963,x23964,x23962)) % 191.49/191.42 [2397]~E(x23971,x23972)+E(f653(x23971,x23973,x23974),f653(x23972,x23973,x23974)) % 191.49/191.42 [2398]~E(x23981,x23982)+E(f653(x23983,x23981,x23984),f653(x23983,x23982,x23984)) % 191.49/191.42 [2399]~E(x23991,x23992)+E(f653(x23993,x23994,x23991),f653(x23993,x23994,x23992)) % 191.49/191.42 [2400]~E(x24001,x24002)+E(f674(x24001,x24003,x24004),f674(x24002,x24003,x24004)) % 191.49/191.42 [2401]~E(x24011,x24012)+E(f674(x24013,x24011,x24014),f674(x24013,x24012,x24014)) % 191.49/191.42 [2402]~E(x24021,x24022)+E(f674(x24023,x24024,x24021),f674(x24023,x24024,x24022)) % 191.49/191.42 [2403]~E(x24031,x24032)+E(f830(x24031,x24033,x24034,x24035,x24036,x24037,x24038),f830(x24032,x24033,x24034,x24035,x24036,x24037,x24038)) % 191.49/191.42 [2404]~E(x24041,x24042)+E(f830(x24043,x24041,x24044,x24045,x24046,x24047,x24048),f830(x24043,x24042,x24044,x24045,x24046,x24047,x24048)) % 191.49/191.42 [2405]~E(x24051,x24052)+E(f830(x24053,x24054,x24051,x24055,x24056,x24057,x24058),f830(x24053,x24054,x24052,x24055,x24056,x24057,x24058)) % 191.49/191.42 [2406]~E(x24061,x24062)+E(f830(x24063,x24064,x24065,x24061,x24066,x24067,x24068),f830(x24063,x24064,x24065,x24062,x24066,x24067,x24068)) % 191.49/191.42 [2407]~E(x24071,x24072)+E(f830(x24073,x24074,x24075,x24076,x24071,x24077,x24078),f830(x24073,x24074,x24075,x24076,x24072,x24077,x24078)) % 191.49/191.42 [2408]~E(x24081,x24082)+E(f830(x24083,x24084,x24085,x24086,x24087,x24081,x24088),f830(x24083,x24084,x24085,x24086,x24087,x24082,x24088)) % 191.49/191.42 [2409]~E(x24091,x24092)+E(f830(x24093,x24094,x24095,x24096,x24097,x24098,x24091),f830(x24093,x24094,x24095,x24096,x24097,x24098,x24092)) % 191.49/191.42 [2410]~E(x24101,x24102)+E(f253(x24101,x24103),f253(x24102,x24103)) % 191.49/191.42 [2411]~E(x24111,x24112)+E(f253(x24113,x24111),f253(x24113,x24112)) % 191.49/191.42 [2412]~E(x24121,x24122)+E(f343(x24121,x24123),f343(x24122,x24123)) % 191.49/191.42 [2413]~E(x24131,x24132)+E(f343(x24133,x24131),f343(x24133,x24132)) % 191.49/191.42 [2414]~E(x24141,x24142)+E(f95(x24141),f95(x24142)) % 191.49/191.42 [2415]~E(x24151,x24152)+E(f731(x24151,x24153,x24154,x24155,x24156),f731(x24152,x24153,x24154,x24155,x24156)) % 191.49/191.42 [2416]~E(x24161,x24162)+E(f731(x24163,x24161,x24164,x24165,x24166),f731(x24163,x24162,x24164,x24165,x24166)) % 191.49/191.42 [2417]~E(x24171,x24172)+E(f731(x24173,x24174,x24171,x24175,x24176),f731(x24173,x24174,x24172,x24175,x24176)) % 191.49/191.42 [2418]~E(x24181,x24182)+E(f731(x24183,x24184,x24185,x24181,x24186),f731(x24183,x24184,x24185,x24182,x24186)) % 191.49/191.42 [2419]~E(x24191,x24192)+E(f731(x24193,x24194,x24195,x24196,x24191),f731(x24193,x24194,x24195,x24196,x24192)) % 191.49/191.42 [2420]~E(x24201,x24202)+E(f440(x24201,x24203,x24204,x24205),f440(x24202,x24203,x24204,x24205)) % 191.49/191.42 [2421]~E(x24211,x24212)+E(f440(x24213,x24211,x24214,x24215),f440(x24213,x24212,x24214,x24215)) % 191.49/191.42 [2422]~E(x24221,x24222)+E(f440(x24223,x24224,x24221,x24225),f440(x24223,x24224,x24222,x24225)) % 191.49/191.42 [2423]~E(x24231,x24232)+E(f440(x24233,x24234,x24235,x24231),f440(x24233,x24234,x24235,x24232)) % 191.49/191.42 [2424]~E(x24241,x24242)+E(f667(x24241,x24243),f667(x24242,x24243)) % 191.49/191.42 [2425]~E(x24251,x24252)+E(f667(x24253,x24251),f667(x24253,x24252)) % 191.49/191.42 [2426]~E(x24261,x24262)+E(f661(x24261,x24263,x24264,x24265,x24266,x24267,x24268),f661(x24262,x24263,x24264,x24265,x24266,x24267,x24268)) % 191.49/191.42 [2427]~E(x24271,x24272)+E(f661(x24273,x24271,x24274,x24275,x24276,x24277,x24278),f661(x24273,x24272,x24274,x24275,x24276,x24277,x24278)) % 191.49/191.42 [2428]~E(x24281,x24282)+E(f661(x24283,x24284,x24281,x24285,x24286,x24287,x24288),f661(x24283,x24284,x24282,x24285,x24286,x24287,x24288)) % 191.49/191.42 [2429]~E(x24291,x24292)+E(f661(x24293,x24294,x24295,x24291,x24296,x24297,x24298),f661(x24293,x24294,x24295,x24292,x24296,x24297,x24298)) % 191.49/191.42 [2430]~E(x24301,x24302)+E(f661(x24303,x24304,x24305,x24306,x24301,x24307,x24308),f661(x24303,x24304,x24305,x24306,x24302,x24307,x24308)) % 191.49/191.42 [2431]~E(x24311,x24312)+E(f661(x24313,x24314,x24315,x24316,x24317,x24311,x24318),f661(x24313,x24314,x24315,x24316,x24317,x24312,x24318)) % 191.49/191.42 [2432]~E(x24321,x24322)+E(f661(x24323,x24324,x24325,x24326,x24327,x24328,x24321),f661(x24323,x24324,x24325,x24326,x24327,x24328,x24322)) % 191.49/191.42 [2433]~E(x24331,x24332)+E(f471(x24331,x24333),f471(x24332,x24333)) % 191.49/191.42 [2434]~E(x24341,x24342)+E(f471(x24343,x24341),f471(x24343,x24342)) % 191.49/191.42 [2435]~E(x24351,x24352)+E(f729(x24351,x24353,x24354),f729(x24352,x24353,x24354)) % 191.49/191.42 [2436]~E(x24361,x24362)+E(f729(x24363,x24361,x24364),f729(x24363,x24362,x24364)) % 191.49/191.42 [2437]~E(x24371,x24372)+E(f729(x24373,x24374,x24371),f729(x24373,x24374,x24372)) % 191.49/191.42 [2438]~E(x24381,x24382)+E(f466(x24381,x24383,x24384),f466(x24382,x24383,x24384)) % 191.49/191.42 [2439]~E(x24391,x24392)+E(f466(x24393,x24391,x24394),f466(x24393,x24392,x24394)) % 191.49/191.42 [2440]~E(x24401,x24402)+E(f466(x24403,x24404,x24401),f466(x24403,x24404,x24402)) % 191.49/191.42 [2441]~E(x24411,x24412)+E(f848(x24411,x24413,x24414,x24415,x24416),f848(x24412,x24413,x24414,x24415,x24416)) % 191.49/191.42 [2442]~E(x24421,x24422)+E(f848(x24423,x24421,x24424,x24425,x24426),f848(x24423,x24422,x24424,x24425,x24426)) % 191.49/191.42 [2443]~E(x24431,x24432)+E(f848(x24433,x24434,x24431,x24435,x24436),f848(x24433,x24434,x24432,x24435,x24436)) % 191.49/191.42 [2444]~E(x24441,x24442)+E(f848(x24443,x24444,x24445,x24441,x24446),f848(x24443,x24444,x24445,x24442,x24446)) % 191.49/191.42 [2445]~E(x24451,x24452)+E(f848(x24453,x24454,x24455,x24456,x24451),f848(x24453,x24454,x24455,x24456,x24452)) % 191.49/191.42 [2446]~E(x24461,x24462)+E(f358(x24461,x24463,x24464,x24465,x24466),f358(x24462,x24463,x24464,x24465,x24466)) % 191.49/191.42 [2447]~E(x24471,x24472)+E(f358(x24473,x24471,x24474,x24475,x24476),f358(x24473,x24472,x24474,x24475,x24476)) % 191.49/191.42 [2448]~E(x24481,x24482)+E(f358(x24483,x24484,x24481,x24485,x24486),f358(x24483,x24484,x24482,x24485,x24486)) % 191.49/191.42 [2449]~E(x24491,x24492)+E(f358(x24493,x24494,x24495,x24491,x24496),f358(x24493,x24494,x24495,x24492,x24496)) % 191.49/191.42 [2450]~E(x24501,x24502)+E(f358(x24503,x24504,x24505,x24506,x24501),f358(x24503,x24504,x24505,x24506,x24502)) % 191.49/191.42 [2451]~E(x24511,x24512)+E(f851(x24511,x24513,x24514,x24515),f851(x24512,x24513,x24514,x24515)) % 191.49/191.42 [2452]~E(x24521,x24522)+E(f851(x24523,x24521,x24524,x24525),f851(x24523,x24522,x24524,x24525)) % 191.49/191.42 [2453]~E(x24531,x24532)+E(f851(x24533,x24534,x24531,x24535),f851(x24533,x24534,x24532,x24535)) % 191.49/191.42 [2454]~E(x24541,x24542)+E(f851(x24543,x24544,x24545,x24541),f851(x24543,x24544,x24545,x24542)) % 191.49/191.42 [2455]~E(x24551,x24552)+E(f484(x24551,x24553,x24554),f484(x24552,x24553,x24554)) % 191.49/191.42 [2456]~E(x24561,x24562)+E(f484(x24563,x24561,x24564),f484(x24563,x24562,x24564)) % 191.49/191.42 [2457]~E(x24571,x24572)+E(f484(x24573,x24574,x24571),f484(x24573,x24574,x24572)) % 191.49/191.42 [2458]~E(x24581,x24582)+E(f678(x24581,x24583),f678(x24582,x24583)) % 191.49/191.42 [2459]~E(x24591,x24592)+E(f678(x24593,x24591),f678(x24593,x24592)) % 191.49/191.42 [2460]~E(x24601,x24602)+E(f727(x24601,x24603,x24604),f727(x24602,x24603,x24604)) % 191.49/191.42 [2461]~E(x24611,x24612)+E(f727(x24613,x24611,x24614),f727(x24613,x24612,x24614)) % 191.49/191.42 [2462]~E(x24621,x24622)+E(f727(x24623,x24624,x24621),f727(x24623,x24624,x24622)) % 191.49/191.42 [2463]~E(x24631,x24632)+E(f829(x24631,x24633,x24634,x24635,x24636),f829(x24632,x24633,x24634,x24635,x24636)) % 191.49/191.42 [2464]~E(x24641,x24642)+E(f829(x24643,x24641,x24644,x24645,x24646),f829(x24643,x24642,x24644,x24645,x24646)) % 191.49/191.42 [2465]~E(x24651,x24652)+E(f829(x24653,x24654,x24651,x24655,x24656),f829(x24653,x24654,x24652,x24655,x24656)) % 191.49/191.42 [2466]~E(x24661,x24662)+E(f829(x24663,x24664,x24665,x24661,x24666),f829(x24663,x24664,x24665,x24662,x24666)) % 191.49/191.42 [2467]~E(x24671,x24672)+E(f829(x24673,x24674,x24675,x24676,x24671),f829(x24673,x24674,x24675,x24676,x24672)) % 191.49/191.42 [2468]~E(x24681,x24682)+E(f316(x24681,x24683,x24684),f316(x24682,x24683,x24684)) % 191.49/191.42 [2469]~E(x24691,x24692)+E(f316(x24693,x24691,x24694),f316(x24693,x24692,x24694)) % 191.49/191.42 [2470]~E(x24701,x24702)+E(f316(x24703,x24704,x24701),f316(x24703,x24704,x24702)) % 191.49/191.42 [2471]~E(x24711,x24712)+E(f624(x24711,x24713,x24714),f624(x24712,x24713,x24714)) % 191.49/191.42 [2472]~E(x24721,x24722)+E(f624(x24723,x24721,x24724),f624(x24723,x24722,x24724)) % 191.49/191.42 [2473]~E(x24731,x24732)+E(f624(x24733,x24734,x24731),f624(x24733,x24734,x24732)) % 191.49/191.42 [2474]~E(x24741,x24742)+E(f491(x24741,x24743,x24744,x24745),f491(x24742,x24743,x24744,x24745)) % 191.49/191.42 [2475]~E(x24751,x24752)+E(f491(x24753,x24751,x24754,x24755),f491(x24753,x24752,x24754,x24755)) % 191.49/191.42 [2476]~E(x24761,x24762)+E(f491(x24763,x24764,x24761,x24765),f491(x24763,x24764,x24762,x24765)) % 191.49/191.42 [2477]~E(x24771,x24772)+E(f491(x24773,x24774,x24775,x24771),f491(x24773,x24774,x24775,x24772)) % 191.49/191.42 [2478]~E(x24781,x24782)+E(f351(x24781,x24783,x24784,x24785),f351(x24782,x24783,x24784,x24785)) % 191.49/191.42 [2479]~E(x24791,x24792)+E(f351(x24793,x24791,x24794,x24795),f351(x24793,x24792,x24794,x24795)) % 191.49/191.42 [2480]~E(x24801,x24802)+E(f351(x24803,x24804,x24801,x24805),f351(x24803,x24804,x24802,x24805)) % 191.49/191.42 [2481]~E(x24811,x24812)+E(f351(x24813,x24814,x24815,x24811),f351(x24813,x24814,x24815,x24812)) % 191.49/191.42 [2482]~E(x24821,x24822)+E(f567(x24821),f567(x24822)) % 191.49/191.42 [2483]~E(x24831,x24832)+E(f394(x24831,x24833,x24834),f394(x24832,x24833,x24834)) % 191.49/191.42 [2484]~E(x24841,x24842)+E(f394(x24843,x24841,x24844),f394(x24843,x24842,x24844)) % 191.49/191.42 [2485]~E(x24851,x24852)+E(f394(x24853,x24854,x24851),f394(x24853,x24854,x24852)) % 191.49/191.42 [2486]~E(x24861,x24862)+E(f237(x24861,x24863,x24864),f237(x24862,x24863,x24864)) % 191.49/191.42 [2487]~E(x24871,x24872)+E(f237(x24873,x24871,x24874),f237(x24873,x24872,x24874)) % 191.49/191.42 [2488]~E(x24881,x24882)+E(f237(x24883,x24884,x24881),f237(x24883,x24884,x24882)) % 191.49/191.42 [2489]~E(x24891,x24892)+E(f670(x24891,x24893),f670(x24892,x24893)) % 191.49/191.42 [2490]~E(x24901,x24902)+E(f670(x24903,x24901),f670(x24903,x24902)) % 191.49/191.42 [2491]~E(x24911,x24912)+E(f573(x24911,x24913,x24914,x24915),f573(x24912,x24913,x24914,x24915)) % 191.49/191.42 [2492]~E(x24921,x24922)+E(f573(x24923,x24921,x24924,x24925),f573(x24923,x24922,x24924,x24925)) % 191.49/191.42 [2493]~E(x24931,x24932)+E(f573(x24933,x24934,x24931,x24935),f573(x24933,x24934,x24932,x24935)) % 191.49/191.42 [2494]~E(x24941,x24942)+E(f573(x24943,x24944,x24945,x24941),f573(x24943,x24944,x24945,x24942)) % 191.49/191.42 [2495]~E(x24951,x24952)+E(f604(x24951,x24953,x24954),f604(x24952,x24953,x24954)) % 191.49/191.42 [2496]~E(x24961,x24962)+E(f604(x24963,x24961,x24964),f604(x24963,x24962,x24964)) % 191.49/191.42 [2497]~E(x24971,x24972)+E(f604(x24973,x24974,x24971),f604(x24973,x24974,x24972)) % 191.49/191.42 [2498]~E(x24981,x24982)+E(f443(x24981,x24983,x24984,x24985),f443(x24982,x24983,x24984,x24985)) % 191.49/191.42 [2499]~E(x24991,x24992)+E(f443(x24993,x24991,x24994,x24995),f443(x24993,x24992,x24994,x24995)) % 191.49/191.42 [2500]~E(x25001,x25002)+E(f443(x25003,x25004,x25001,x25005),f443(x25003,x25004,x25002,x25005)) % 191.49/191.42 [2501]~E(x25011,x25012)+E(f443(x25013,x25014,x25015,x25011),f443(x25013,x25014,x25015,x25012)) % 191.49/191.42 [2502]~E(x25021,x25022)+E(f638(x25021,x25023),f638(x25022,x25023)) % 191.49/191.42 [2503]~E(x25031,x25032)+E(f638(x25033,x25031),f638(x25033,x25032)) % 191.49/191.42 [2504]~E(x25041,x25042)+E(f633(x25041,x25043,x25044,x25045,x25046,x25047),f633(x25042,x25043,x25044,x25045,x25046,x25047)) % 191.49/191.42 [2505]~E(x25051,x25052)+E(f633(x25053,x25051,x25054,x25055,x25056,x25057),f633(x25053,x25052,x25054,x25055,x25056,x25057)) % 191.49/191.42 [2506]~E(x25061,x25062)+E(f633(x25063,x25064,x25061,x25065,x25066,x25067),f633(x25063,x25064,x25062,x25065,x25066,x25067)) % 191.49/191.42 [2507]~E(x25071,x25072)+E(f633(x25073,x25074,x25075,x25071,x25076,x25077),f633(x25073,x25074,x25075,x25072,x25076,x25077)) % 191.49/191.42 [2508]~E(x25081,x25082)+E(f633(x25083,x25084,x25085,x25086,x25081,x25087),f633(x25083,x25084,x25085,x25086,x25082,x25087)) % 191.49/191.42 [2509]~E(x25091,x25092)+E(f633(x25093,x25094,x25095,x25096,x25097,x25091),f633(x25093,x25094,x25095,x25096,x25097,x25092)) % 191.49/191.42 [2510]~E(x25101,x25102)+E(f502(x25101,x25103,x25104,x25105),f502(x25102,x25103,x25104,x25105)) % 191.49/191.42 [2511]~E(x25111,x25112)+E(f502(x25113,x25111,x25114,x25115),f502(x25113,x25112,x25114,x25115)) % 191.49/191.42 [2512]~E(x25121,x25122)+E(f502(x25123,x25124,x25121,x25125),f502(x25123,x25124,x25122,x25125)) % 191.49/191.42 [2513]~E(x25131,x25132)+E(f502(x25133,x25134,x25135,x25131),f502(x25133,x25134,x25135,x25132)) % 191.49/191.42 [2514]~E(x25141,x25142)+E(f826(x25141,x25143,x25144,x25145,x25146),f826(x25142,x25143,x25144,x25145,x25146)) % 191.49/191.42 [2515]~E(x25151,x25152)+E(f826(x25153,x25151,x25154,x25155,x25156),f826(x25153,x25152,x25154,x25155,x25156)) % 191.49/191.42 [2516]~E(x25161,x25162)+E(f826(x25163,x25164,x25161,x25165,x25166),f826(x25163,x25164,x25162,x25165,x25166)) % 191.49/191.42 [2517]~E(x25171,x25172)+E(f826(x25173,x25174,x25175,x25171,x25176),f826(x25173,x25174,x25175,x25172,x25176)) % 191.49/191.42 [2518]~E(x25181,x25182)+E(f826(x25183,x25184,x25185,x25186,x25181),f826(x25183,x25184,x25185,x25186,x25182)) % 191.49/191.42 [2519]~E(x25191,x25192)+E(f753(x25191,x25193,x25194,x25195,x25196,x25197),f753(x25192,x25193,x25194,x25195,x25196,x25197)) % 191.49/191.42 [2520]~E(x25201,x25202)+E(f753(x25203,x25201,x25204,x25205,x25206,x25207),f753(x25203,x25202,x25204,x25205,x25206,x25207)) % 191.49/191.42 [2521]~E(x25211,x25212)+E(f753(x25213,x25214,x25211,x25215,x25216,x25217),f753(x25213,x25214,x25212,x25215,x25216,x25217)) % 191.49/191.42 [2522]~E(x25221,x25222)+E(f753(x25223,x25224,x25225,x25221,x25226,x25227),f753(x25223,x25224,x25225,x25222,x25226,x25227)) % 191.49/191.42 [2523]~E(x25231,x25232)+E(f753(x25233,x25234,x25235,x25236,x25231,x25237),f753(x25233,x25234,x25235,x25236,x25232,x25237)) % 191.49/191.42 [2524]~E(x25241,x25242)+E(f753(x25243,x25244,x25245,x25246,x25247,x25241),f753(x25243,x25244,x25245,x25246,x25247,x25242)) % 191.49/191.42 [2525]~E(x25251,x25252)+E(f669(x25251,x25253),f669(x25252,x25253)) % 191.49/191.42 [2526]~E(x25261,x25262)+E(f669(x25263,x25261),f669(x25263,x25262)) % 191.49/191.42 [2527]~E(x25271,x25272)+E(f221(x25271,x25273,x25274,x25275,x25276,x25277,x25278),f221(x25272,x25273,x25274,x25275,x25276,x25277,x25278)) % 191.49/191.42 [2528]~E(x25281,x25282)+E(f221(x25283,x25281,x25284,x25285,x25286,x25287,x25288),f221(x25283,x25282,x25284,x25285,x25286,x25287,x25288)) % 191.49/191.42 [2529]~E(x25291,x25292)+E(f221(x25293,x25294,x25291,x25295,x25296,x25297,x25298),f221(x25293,x25294,x25292,x25295,x25296,x25297,x25298)) % 191.49/191.42 [2530]~E(x25301,x25302)+E(f221(x25303,x25304,x25305,x25301,x25306,x25307,x25308),f221(x25303,x25304,x25305,x25302,x25306,x25307,x25308)) % 191.49/191.42 [2531]~E(x25311,x25312)+E(f221(x25313,x25314,x25315,x25316,x25311,x25317,x25318),f221(x25313,x25314,x25315,x25316,x25312,x25317,x25318)) % 191.49/191.42 [2532]~E(x25321,x25322)+E(f221(x25323,x25324,x25325,x25326,x25327,x25321,x25328),f221(x25323,x25324,x25325,x25326,x25327,x25322,x25328)) % 191.49/191.42 [2533]~E(x25331,x25332)+E(f221(x25333,x25334,x25335,x25336,x25337,x25338,x25331),f221(x25333,x25334,x25335,x25336,x25337,x25338,x25332)) % 191.49/191.42 [2534]~E(x25341,x25342)+E(f493(x25341,x25343,x25344,x25345),f493(x25342,x25343,x25344,x25345)) % 191.49/191.42 [2535]~E(x25351,x25352)+E(f493(x25353,x25351,x25354,x25355),f493(x25353,x25352,x25354,x25355)) % 191.49/191.42 [2536]~E(x25361,x25362)+E(f493(x25363,x25364,x25361,x25365),f493(x25363,x25364,x25362,x25365)) % 191.49/191.42 [2537]~E(x25371,x25372)+E(f493(x25373,x25374,x25375,x25371),f493(x25373,x25374,x25375,x25372)) % 191.49/191.42 [2538]~E(x25381,x25382)+E(f505(x25381,x25383,x25384),f505(x25382,x25383,x25384)) % 191.49/191.42 [2539]~E(x25391,x25392)+E(f505(x25393,x25391,x25394),f505(x25393,x25392,x25394)) % 191.49/191.42 [2540]~E(x25401,x25402)+E(f505(x25403,x25404,x25401),f505(x25403,x25404,x25402)) % 191.49/191.42 [2541]~E(x25411,x25412)+E(f593(x25411,x25413,x25414,x25415,x25416),f593(x25412,x25413,x25414,x25415,x25416)) % 191.49/191.42 [2542]~E(x25421,x25422)+E(f593(x25423,x25421,x25424,x25425,x25426),f593(x25423,x25422,x25424,x25425,x25426)) % 191.49/191.42 [2543]~E(x25431,x25432)+E(f593(x25433,x25434,x25431,x25435,x25436),f593(x25433,x25434,x25432,x25435,x25436)) % 191.49/191.42 [2544]~E(x25441,x25442)+E(f593(x25443,x25444,x25445,x25441,x25446),f593(x25443,x25444,x25445,x25442,x25446)) % 191.49/191.42 [2545]~E(x25451,x25452)+E(f593(x25453,x25454,x25455,x25456,x25451),f593(x25453,x25454,x25455,x25456,x25452)) % 191.49/191.42 [2546]~E(x25461,x25462)+E(f784(x25461,x25463),f784(x25462,x25463)) % 191.49/191.42 [2547]~E(x25471,x25472)+E(f784(x25473,x25471),f784(x25473,x25472)) % 191.49/191.42 [2548]~E(x25481,x25482)+E(f610(x25481,x25483,x25484,x25485),f610(x25482,x25483,x25484,x25485)) % 191.49/191.42 [2549]~E(x25491,x25492)+E(f610(x25493,x25491,x25494,x25495),f610(x25493,x25492,x25494,x25495)) % 191.49/191.42 [2550]~E(x25501,x25502)+E(f610(x25503,x25504,x25501,x25505),f610(x25503,x25504,x25502,x25505)) % 191.49/191.42 [2551]~E(x25511,x25512)+E(f610(x25513,x25514,x25515,x25511),f610(x25513,x25514,x25515,x25512)) % 191.49/191.42 [2552]~E(x25521,x25522)+E(f790(x25521,x25523,x25524,x25525,x25526),f790(x25522,x25523,x25524,x25525,x25526)) % 191.49/191.42 [2553]~E(x25531,x25532)+E(f790(x25533,x25531,x25534,x25535,x25536),f790(x25533,x25532,x25534,x25535,x25536)) % 191.49/191.42 [2554]~E(x25541,x25542)+E(f790(x25543,x25544,x25541,x25545,x25546),f790(x25543,x25544,x25542,x25545,x25546)) % 191.49/191.42 [2555]~E(x25551,x25552)+E(f790(x25553,x25554,x25555,x25551,x25556),f790(x25553,x25554,x25555,x25552,x25556)) % 191.49/191.42 [2556]~E(x25561,x25562)+E(f790(x25563,x25564,x25565,x25566,x25561),f790(x25563,x25564,x25565,x25566,x25562)) % 191.49/191.42 [2557]~E(x25571,x25572)+E(f391(x25571),f391(x25572)) % 191.49/191.42 [2558]~E(x25581,x25582)+E(f806(x25581,x25583,x25584,x25585,x25586,x25587),f806(x25582,x25583,x25584,x25585,x25586,x25587)) % 191.49/191.42 [2559]~E(x25591,x25592)+E(f806(x25593,x25591,x25594,x25595,x25596,x25597),f806(x25593,x25592,x25594,x25595,x25596,x25597)) % 191.49/191.42 [2560]~E(x25601,x25602)+E(f806(x25603,x25604,x25601,x25605,x25606,x25607),f806(x25603,x25604,x25602,x25605,x25606,x25607)) % 191.49/191.42 [2561]~E(x25611,x25612)+E(f806(x25613,x25614,x25615,x25611,x25616,x25617),f806(x25613,x25614,x25615,x25612,x25616,x25617)) % 191.49/191.42 [2562]~E(x25621,x25622)+E(f806(x25623,x25624,x25625,x25626,x25621,x25627),f806(x25623,x25624,x25625,x25626,x25622,x25627)) % 191.49/191.42 [2563]~E(x25631,x25632)+E(f806(x25633,x25634,x25635,x25636,x25637,x25631),f806(x25633,x25634,x25635,x25636,x25637,x25632)) % 191.49/191.42 [2564]~E(x25641,x25642)+E(f511(x25641,x25643,x25644),f511(x25642,x25643,x25644)) % 191.49/191.42 [2565]~E(x25651,x25652)+E(f511(x25653,x25651,x25654),f511(x25653,x25652,x25654)) % 191.49/191.42 [2566]~E(x25661,x25662)+E(f511(x25663,x25664,x25661),f511(x25663,x25664,x25662)) % 191.49/191.42 [2567]~E(x25671,x25672)+E(f210(x25671),f210(x25672)) % 191.49/191.42 [2568]~E(x25681,x25682)+E(f396(x25681,x25683,x25684),f396(x25682,x25683,x25684)) % 191.49/191.42 [2569]~E(x25691,x25692)+E(f396(x25693,x25691,x25694),f396(x25693,x25692,x25694)) % 191.49/191.42 [2570]~E(x25701,x25702)+E(f396(x25703,x25704,x25701),f396(x25703,x25704,x25702)) % 191.49/191.42 [2571]~E(x25711,x25712)+E(f786(x25711,x25713,x25714),f786(x25712,x25713,x25714)) % 191.49/191.42 [2572]~E(x25721,x25722)+E(f786(x25723,x25721,x25724),f786(x25723,x25722,x25724)) % 191.49/191.42 [2573]~E(x25731,x25732)+E(f786(x25733,x25734,x25731),f786(x25733,x25734,x25732)) % 191.49/191.42 [2574]~E(x25741,x25742)+E(f541(x25741,x25743,x25744,x25745,x25746),f541(x25742,x25743,x25744,x25745,x25746)) % 191.49/191.42 [2575]~E(x25751,x25752)+E(f541(x25753,x25751,x25754,x25755,x25756),f541(x25753,x25752,x25754,x25755,x25756)) % 191.49/191.42 [2576]~E(x25761,x25762)+E(f541(x25763,x25764,x25761,x25765,x25766),f541(x25763,x25764,x25762,x25765,x25766)) % 191.49/191.42 [2577]~E(x25771,x25772)+E(f541(x25773,x25774,x25775,x25771,x25776),f541(x25773,x25774,x25775,x25772,x25776)) % 191.49/191.42 [2578]~E(x25781,x25782)+E(f541(x25783,x25784,x25785,x25786,x25781),f541(x25783,x25784,x25785,x25786,x25782)) % 191.49/191.42 [2579]~E(x25791,x25792)+E(f354(x25791,x25793,x25794,x25795),f354(x25792,x25793,x25794,x25795)) % 191.49/191.42 [2580]~E(x25801,x25802)+E(f354(x25803,x25801,x25804,x25805),f354(x25803,x25802,x25804,x25805)) % 191.49/191.42 [2581]~E(x25811,x25812)+E(f354(x25813,x25814,x25811,x25815),f354(x25813,x25814,x25812,x25815)) % 191.49/191.42 [2582]~E(x25821,x25822)+E(f354(x25823,x25824,x25825,x25821),f354(x25823,x25824,x25825,x25822)) % 191.49/191.42 [2583]~E(x25831,x25832)+E(f841(x25831,x25833,x25834),f841(x25832,x25833,x25834)) % 191.49/191.42 [2584]~E(x25841,x25842)+E(f841(x25843,x25841,x25844),f841(x25843,x25842,x25844)) % 191.49/191.42 [2585]~E(x25851,x25852)+E(f841(x25853,x25854,x25851),f841(x25853,x25854,x25852)) % 191.49/191.42 [2586]~E(x25861,x25862)+E(f555(x25861),f555(x25862)) % 191.49/191.42 [2587]~E(x25871,x25872)+E(f576(x25871,x25873,x25874,x25875,x25876),f576(x25872,x25873,x25874,x25875,x25876)) % 191.49/191.42 [2588]~E(x25881,x25882)+E(f576(x25883,x25881,x25884,x25885,x25886),f576(x25883,x25882,x25884,x25885,x25886)) % 191.49/191.42 [2589]~E(x25891,x25892)+E(f576(x25893,x25894,x25891,x25895,x25896),f576(x25893,x25894,x25892,x25895,x25896)) % 191.49/191.42 [2590]~E(x25901,x25902)+E(f576(x25903,x25904,x25905,x25901,x25906),f576(x25903,x25904,x25905,x25902,x25906)) % 191.49/191.42 [2591]~E(x25911,x25912)+E(f576(x25913,x25914,x25915,x25916,x25911),f576(x25913,x25914,x25915,x25916,x25912)) % 191.49/191.42 [2592]~E(x25921,x25922)+E(f718(x25921),f718(x25922)) % 191.49/191.42 [2593]~E(x25931,x25932)+E(f636(x25931,x25933,x25934),f636(x25932,x25933,x25934)) % 191.49/191.42 [2594]~E(x25941,x25942)+E(f636(x25943,x25941,x25944),f636(x25943,x25942,x25944)) % 191.49/191.42 [2595]~E(x25951,x25952)+E(f636(x25953,x25954,x25951),f636(x25953,x25954,x25952)) % 191.49/191.42 [2596]~E(x25961,x25962)+E(f339(x25961,x25963),f339(x25962,x25963)) % 191.49/191.42 [2597]~E(x25971,x25972)+E(f339(x25973,x25971),f339(x25973,x25972)) % 191.49/191.42 [2598]~E(x25981,x25982)+E(f651(x25981,x25983,x25984),f651(x25982,x25983,x25984)) % 191.49/191.42 [2599]~E(x25991,x25992)+E(f651(x25993,x25991,x25994),f651(x25993,x25992,x25994)) % 191.49/191.42 [2600]~E(x26001,x26002)+E(f651(x26003,x26004,x26001),f651(x26003,x26004,x26002)) % 191.49/191.42 [2601]~E(x26011,x26012)+E(f419(x26011,x26013,x26014,x26015),f419(x26012,x26013,x26014,x26015)) % 191.49/191.42 [2602]~E(x26021,x26022)+E(f419(x26023,x26021,x26024,x26025),f419(x26023,x26022,x26024,x26025)) % 191.49/191.42 [2603]~E(x26031,x26032)+E(f419(x26033,x26034,x26031,x26035),f419(x26033,x26034,x26032,x26035)) % 191.49/191.42 [2604]~E(x26041,x26042)+E(f419(x26043,x26044,x26045,x26041),f419(x26043,x26044,x26045,x26042)) % 191.49/191.42 [2605]~E(x26051,x26052)+E(f475(x26051,x26053,x26054),f475(x26052,x26053,x26054)) % 191.49/191.42 [2606]~E(x26061,x26062)+E(f475(x26063,x26061,x26064),f475(x26063,x26062,x26064)) % 191.49/191.42 [2607]~E(x26071,x26072)+E(f475(x26073,x26074,x26071),f475(x26073,x26074,x26072)) % 191.49/191.42 [2608]~E(x26081,x26082)+E(f233(x26081,x26083,x26084,x26085,x26086),f233(x26082,x26083,x26084,x26085,x26086)) % 191.49/191.42 [2609]~E(x26091,x26092)+E(f233(x26093,x26091,x26094,x26095,x26096),f233(x26093,x26092,x26094,x26095,x26096)) % 191.49/191.42 [2610]~E(x26101,x26102)+E(f233(x26103,x26104,x26101,x26105,x26106),f233(x26103,x26104,x26102,x26105,x26106)) % 191.49/191.42 [2611]~E(x26111,x26112)+E(f233(x26113,x26114,x26115,x26111,x26116),f233(x26113,x26114,x26115,x26112,x26116)) % 191.49/191.42 [2612]~E(x26121,x26122)+E(f233(x26123,x26124,x26125,x26126,x26121),f233(x26123,x26124,x26125,x26126,x26122)) % 191.49/191.42 [2613]~E(x26131,x26132)+E(f433(x26131,x26133,x26134,x26135),f433(x26132,x26133,x26134,x26135)) % 191.49/191.42 [2614]~E(x26141,x26142)+E(f433(x26143,x26141,x26144,x26145),f433(x26143,x26142,x26144,x26145)) % 191.49/191.42 [2615]~E(x26151,x26152)+E(f433(x26153,x26154,x26151,x26155),f433(x26153,x26154,x26152,x26155)) % 191.49/191.42 [2616]~E(x26161,x26162)+E(f433(x26163,x26164,x26165,x26161),f433(x26163,x26164,x26165,x26162)) % 191.49/191.42 [2617]~E(x26171,x26172)+E(f716(x26171,x26173),f716(x26172,x26173)) % 191.49/191.42 [2618]~E(x26181,x26182)+E(f716(x26183,x26181),f716(x26183,x26182)) % 191.49/191.42 [2619]~E(x26191,x26192)+E(f550(x26191,x26193,x26194),f550(x26192,x26193,x26194)) % 191.49/191.42 [2620]~E(x26201,x26202)+E(f550(x26203,x26201,x26204),f550(x26203,x26202,x26204)) % 191.49/191.42 [2621]~E(x26211,x26212)+E(f550(x26213,x26214,x26211),f550(x26213,x26214,x26212)) % 191.49/191.42 [2622]~E(x26221,x26222)+E(f317(x26221,x26223,x26224),f317(x26222,x26223,x26224)) % 191.49/191.42 [2623]~E(x26231,x26232)+E(f317(x26233,x26231,x26234),f317(x26233,x26232,x26234)) % 191.49/191.42 [2624]~E(x26241,x26242)+E(f317(x26243,x26244,x26241),f317(x26243,x26244,x26242)) % 191.49/191.42 [2625]~E(x26251,x26252)+E(f715(x26251,x26253,x26254,x26255),f715(x26252,x26253,x26254,x26255)) % 191.49/191.42 [2626]~E(x26261,x26262)+E(f715(x26263,x26261,x26264,x26265),f715(x26263,x26262,x26264,x26265)) % 191.49/191.42 [2627]~E(x26271,x26272)+E(f715(x26273,x26274,x26271,x26275),f715(x26273,x26274,x26272,x26275)) % 191.49/191.42 [2628]~E(x26281,x26282)+E(f715(x26283,x26284,x26285,x26281),f715(x26283,x26284,x26285,x26282)) % 191.49/191.42 [2629]~E(x26291,x26292)+E(f768(x26291,x26293),f768(x26292,x26293)) % 191.49/191.42 [2630]~E(x26301,x26302)+E(f768(x26303,x26301),f768(x26303,x26302)) % 191.49/191.42 [2631]~E(x26311,x26312)+E(f699(x26311,x26313),f699(x26312,x26313)) % 191.49/191.42 [2632]~E(x26321,x26322)+E(f699(x26323,x26321),f699(x26323,x26322)) % 191.49/191.42 [2633]~P1(x26331)+P1(x26332)+~E(x26331,x26332) % 191.49/191.42 [2634]~P4(x26341)+P4(x26342)+~E(x26341,x26342) % 191.49/191.42 [2635]~P5(x26351)+P5(x26352)+~E(x26351,x26352) % 191.49/191.42 [2636]P147(x26362,x26363,x26364)+~E(x26361,x26362)+~P147(x26361,x26363,x26364) % 191.49/191.42 [2637]P147(x26373,x26372,x26374)+~E(x26371,x26372)+~P147(x26373,x26371,x26374) % 191.49/191.42 [2638]P147(x26383,x26384,x26382)+~E(x26381,x26382)+~P147(x26383,x26384,x26381) % 191.49/191.42 [2639]~P6(x26391)+P6(x26392)+~E(x26391,x26392) % 191.49/191.42 [2640]~P9(x26401)+P9(x26402)+~E(x26401,x26402) % 191.49/191.42 [2641]~P109(x26411)+P109(x26412)+~E(x26411,x26412) % 191.49/191.42 [2642]~P7(x26421)+P7(x26422)+~E(x26421,x26422) % 191.49/191.42 [2643]~P8(x26431)+P8(x26432)+~E(x26431,x26432) % 191.49/191.42 [2644]P17(x26442,x26443)+~E(x26441,x26442)+~P17(x26441,x26443) % 191.49/191.42 [2645]P17(x26453,x26452)+~E(x26451,x26452)+~P17(x26453,x26451) % 191.49/191.42 [2646]~P101(x26461)+P101(x26462)+~E(x26461,x26462) % 191.49/191.42 [2647]P28(x26472,x26473,x26474,x26475)+~E(x26471,x26472)+~P28(x26471,x26473,x26474,x26475) % 191.49/191.42 [2648]P28(x26483,x26482,x26484,x26485)+~E(x26481,x26482)+~P28(x26483,x26481,x26484,x26485) % 191.49/191.42 [2649]P28(x26493,x26494,x26492,x26495)+~E(x26491,x26492)+~P28(x26493,x26494,x26491,x26495) % 191.49/191.42 [2650]P28(x26503,x26504,x26505,x26502)+~E(x26501,x26502)+~P28(x26503,x26504,x26505,x26501) % 191.49/191.42 [2651]~P67(x26511)+P67(x26512)+~E(x26511,x26512) % 191.49/191.42 [2652]~P69(x26521)+P69(x26522)+~E(x26521,x26522) % 191.49/191.42 [2653]P146(x26532,x26533,x26534)+~E(x26531,x26532)+~P146(x26531,x26533,x26534) % 191.49/191.42 [2654]P146(x26543,x26542,x26544)+~E(x26541,x26542)+~P146(x26543,x26541,x26544) % 191.49/191.42 [2655]P146(x26553,x26554,x26552)+~E(x26551,x26552)+~P146(x26553,x26554,x26551) % 191.49/191.42 [2656]~P87(x26561)+P87(x26562)+~E(x26561,x26562) % 191.49/191.42 [2657]P59(x26572,x26573)+~E(x26571,x26572)+~P59(x26571,x26573) % 191.49/191.42 [2658]P59(x26583,x26582)+~E(x26581,x26582)+~P59(x26583,x26581) % 191.49/191.42 [2659]~P102(x26591)+P102(x26592)+~E(x26591,x26592) % 191.49/191.42 [2660]~P81(x26601)+P81(x26602)+~E(x26601,x26602) % 191.49/191.42 [2661]~P65(x26611)+P65(x26612)+~E(x26611,x26612) % 191.49/191.42 [2662]~P99(x26621)+P99(x26622)+~E(x26621,x26622) % 191.49/191.42 [2663]~P110(x26631)+P110(x26632)+~E(x26631,x26632) % 191.49/191.42 [2664]~P124(x26641)+P124(x26642)+~E(x26641,x26642) % 191.49/191.42 [2665]P40(x26652,x26653)+~E(x26651,x26652)+~P40(x26651,x26653) % 191.49/191.42 [2666]P40(x26663,x26662)+~E(x26661,x26662)+~P40(x26663,x26661) % 191.49/191.42 [2667]~P68(x26671)+P68(x26672)+~E(x26671,x26672) % 191.49/191.42 [2668]~P106(x26681)+P106(x26682)+~E(x26681,x26682) % 191.49/191.42 [2669]~P79(x26691)+P79(x26692)+~E(x26691,x26692) % 191.49/191.42 [2670]~P80(x26701)+P80(x26702)+~E(x26701,x26702) % 191.49/191.42 [2671]~P143(x26711)+P143(x26712)+~E(x26711,x26712) % 191.49/191.42 [2672]P19(x26722,x26723,x26724)+~E(x26721,x26722)+~P19(x26721,x26723,x26724) % 191.49/191.42 [2673]P19(x26733,x26732,x26734)+~E(x26731,x26732)+~P19(x26733,x26731,x26734) % 191.49/191.42 [2674]P19(x26743,x26744,x26742)+~E(x26741,x26742)+~P19(x26743,x26744,x26741) % 191.49/191.42 [2675]~P140(x26751)+P140(x26752)+~E(x26751,x26752) % 191.49/191.42 [2676]~P91(x26761)+P91(x26762)+~E(x26761,x26762) % 191.49/191.42 [2677]~P70(x26771)+P70(x26772)+~E(x26771,x26772) % 191.49/191.42 [2678]P34(x26782,x26783,x26784)+~E(x26781,x26782)+~P34(x26781,x26783,x26784) % 191.49/191.42 [2679]P34(x26793,x26792,x26794)+~E(x26791,x26792)+~P34(x26793,x26791,x26794) % 191.49/191.42 [2680]P34(x26803,x26804,x26802)+~E(x26801,x26802)+~P34(x26803,x26804,x26801) % 191.49/191.42 [2681]~P66(x26811)+P66(x26812)+~E(x26811,x26812) % 191.49/191.42 [2682]~P71(x26821)+P71(x26822)+~E(x26821,x26822) % 191.49/191.42 [2683]P15(x26832,x26833,x26834,x26835)+~E(x26831,x26832)+~P15(x26831,x26833,x26834,x26835) % 191.49/191.42 [2684]P15(x26843,x26842,x26844,x26845)+~E(x26841,x26842)+~P15(x26843,x26841,x26844,x26845) % 191.49/191.42 [2685]P15(x26853,x26854,x26852,x26855)+~E(x26851,x26852)+~P15(x26853,x26854,x26851,x26855) % 191.49/191.42 [2686]P15(x26863,x26864,x26865,x26862)+~E(x26861,x26862)+~P15(x26863,x26864,x26865,x26861) % 191.49/191.42 [2687]~P93(x26871)+P93(x26872)+~E(x26871,x26872) % 191.49/191.42 [2688]~P72(x26881)+P72(x26882)+~E(x26881,x26882) % 191.49/191.42 [2689]~P94(x26891)+P94(x26892)+~E(x26891,x26892) % 191.49/191.42 [2690]P37(x26902,x26903,x26904,x26905,x26906)+~E(x26901,x26902)+~P37(x26901,x26903,x26904,x26905,x26906) % 191.49/191.42 [2691]P37(x26913,x26912,x26914,x26915,x26916)+~E(x26911,x26912)+~P37(x26913,x26911,x26914,x26915,x26916) % 191.49/191.42 [2692]P37(x26923,x26924,x26922,x26925,x26926)+~E(x26921,x26922)+~P37(x26923,x26924,x26921,x26925,x26926) % 191.49/191.42 [2693]P37(x26933,x26934,x26935,x26932,x26936)+~E(x26931,x26932)+~P37(x26933,x26934,x26935,x26931,x26936) % 191.49/191.42 [2694]P37(x26943,x26944,x26945,x26946,x26942)+~E(x26941,x26942)+~P37(x26943,x26944,x26945,x26946,x26941) % 191.49/191.43 [2695]~P107(x26951)+P107(x26952)+~E(x26951,x26952) % 191.49/191.43 [2696]~P75(x26961)+P75(x26962)+~E(x26961,x26962) % 191.49/191.43 [2697]~P100(x26971)+P100(x26972)+~E(x26971,x26972) % 191.49/191.43 [2698]~P112(x26981)+P112(x26982)+~E(x26981,x26982) % 191.49/191.43 [2699]~P115(x26991)+P115(x26992)+~E(x26991,x26992) % 191.49/191.43 [2700]~P120(x27001)+P120(x27002)+~E(x27001,x27002) % 191.49/191.43 [2701]~P95(x27011)+P95(x27012)+~E(x27011,x27012) % 191.49/191.43 [2702]~P73(x27021)+P73(x27022)+~E(x27021,x27022) % 191.49/191.43 [2703]~P97(x27031)+P97(x27032)+~E(x27031,x27032) % 191.49/191.43 [2704]~P62(x27041)+P62(x27042)+~E(x27041,x27042) % 191.49/191.43 [2705]~P137(x27051)+P137(x27052)+~E(x27051,x27052) % 191.49/191.43 [2706]~P117(x27061)+P117(x27062)+~E(x27061,x27062) % 191.49/191.43 [2707]~P108(x27071)+P108(x27072)+~E(x27071,x27072) % 191.49/191.43 [2708]~P116(x27081)+P116(x27082)+~E(x27081,x27082) % 191.49/191.43 [2709]P50(x27092,x27093,x27094)+~E(x27091,x27092)+~P50(x27091,x27093,x27094) % 191.49/191.43 [2710]P50(x27103,x27102,x27104)+~E(x27101,x27102)+~P50(x27103,x27101,x27104) % 191.49/191.43 [2711]P50(x27113,x27114,x27112)+~E(x27111,x27112)+~P50(x27113,x27114,x27111) % 191.49/191.43 [2712]~P64(x27121)+P64(x27122)+~E(x27121,x27122) % 191.49/191.43 [2713]~P138(x27131)+P138(x27132)+~E(x27131,x27132) % 191.49/191.43 [2714]P25(x27142,x27143,x27144,x27145,x27146,x27147)+~E(x27141,x27142)+~P25(x27141,x27143,x27144,x27145,x27146,x27147) % 191.49/191.43 [2715]P25(x27153,x27152,x27154,x27155,x27156,x27157)+~E(x27151,x27152)+~P25(x27153,x27151,x27154,x27155,x27156,x27157) % 191.49/191.43 [2716]P25(x27163,x27164,x27162,x27165,x27166,x27167)+~E(x27161,x27162)+~P25(x27163,x27164,x27161,x27165,x27166,x27167) % 191.49/191.43 [2717]P25(x27173,x27174,x27175,x27172,x27176,x27177)+~E(x27171,x27172)+~P25(x27173,x27174,x27175,x27171,x27176,x27177) % 191.49/191.43 [2718]P25(x27183,x27184,x27185,x27186,x27182,x27187)+~E(x27181,x27182)+~P25(x27183,x27184,x27185,x27186,x27181,x27187) % 191.49/191.43 [2719]P25(x27193,x27194,x27195,x27196,x27197,x27192)+~E(x27191,x27192)+~P25(x27193,x27194,x27195,x27196,x27197,x27191) % 191.49/191.43 [2720]P54(x27202,x27203,x27204)+~E(x27201,x27202)+~P54(x27201,x27203,x27204) % 191.49/191.43 [2721]P54(x27213,x27212,x27214)+~E(x27211,x27212)+~P54(x27213,x27211,x27214) % 191.49/191.43 [2722]P54(x27223,x27224,x27222)+~E(x27221,x27222)+~P54(x27223,x27224,x27221) % 191.49/191.43 [2723]~P76(x27231)+P76(x27232)+~E(x27231,x27232) % 191.49/191.43 [2724]~P60(x27241)+P60(x27242)+~E(x27241,x27242) % 191.49/191.43 [2725]~P123(x27251)+P123(x27252)+~E(x27251,x27252) % 191.49/191.43 [2726]P55(x27262,x27263,x27264)+~E(x27261,x27262)+~P55(x27261,x27263,x27264) % 191.49/191.43 [2727]P55(x27273,x27272,x27274)+~E(x27271,x27272)+~P55(x27273,x27271,x27274) % 191.49/191.43 [2728]P55(x27283,x27284,x27282)+~E(x27281,x27282)+~P55(x27283,x27284,x27281) % 191.49/191.43 [2729]P33(x27292,x27293)+~E(x27291,x27292)+~P33(x27291,x27293) % 191.49/191.43 [2730]P33(x27303,x27302)+~E(x27301,x27302)+~P33(x27303,x27301) % 191.49/191.43 [2731]~P88(x27311)+P88(x27312)+~E(x27311,x27312) % 191.49/191.43 [2732]P38(x27322,x27323,x27324)+~E(x27321,x27322)+~P38(x27321,x27323,x27324) % 191.49/191.43 [2733]P38(x27333,x27332,x27334)+~E(x27331,x27332)+~P38(x27333,x27331,x27334) % 191.49/191.43 [2734]P38(x27343,x27344,x27342)+~E(x27341,x27342)+~P38(x27343,x27344,x27341) % 191.49/191.43 [2735]~P144(x27351)+P144(x27352)+~E(x27351,x27352) % 191.49/191.43 [2736]~P63(x27361)+P63(x27362)+~E(x27361,x27362) % 191.49/191.43 [2737]~P77(x27371)+P77(x27372)+~E(x27371,x27372) % 191.49/191.43 [2738]~P136(x27381)+P136(x27382)+~E(x27381,x27382) % 191.49/191.43 [2739]P26(x27392,x27393,x27394,x27395,x27396,x27397)+~E(x27391,x27392)+~P26(x27391,x27393,x27394,x27395,x27396,x27397) % 191.49/191.43 [2740]P26(x27403,x27402,x27404,x27405,x27406,x27407)+~E(x27401,x27402)+~P26(x27403,x27401,x27404,x27405,x27406,x27407) % 191.49/191.43 [2741]P26(x27413,x27414,x27412,x27415,x27416,x27417)+~E(x27411,x27412)+~P26(x27413,x27414,x27411,x27415,x27416,x27417) % 191.49/191.43 [2742]P26(x27423,x27424,x27425,x27422,x27426,x27427)+~E(x27421,x27422)+~P26(x27423,x27424,x27425,x27421,x27426,x27427) % 191.49/191.43 [2743]P26(x27433,x27434,x27435,x27436,x27432,x27437)+~E(x27431,x27432)+~P26(x27433,x27434,x27435,x27436,x27431,x27437) % 191.49/191.43 [2744]P26(x27443,x27444,x27445,x27446,x27447,x27442)+~E(x27441,x27442)+~P26(x27443,x27444,x27445,x27446,x27447,x27441) % 191.49/191.43 [2745]~P42(x27451)+P42(x27452)+~E(x27451,x27452) % 191.49/191.43 [2746]P44(x27462,x27463,x27464,x27465,x27466,x27467)+~E(x27461,x27462)+~P44(x27461,x27463,x27464,x27465,x27466,x27467) % 191.49/191.43 [2747]P44(x27473,x27472,x27474,x27475,x27476,x27477)+~E(x27471,x27472)+~P44(x27473,x27471,x27474,x27475,x27476,x27477) % 191.49/191.43 [2748]P44(x27483,x27484,x27482,x27485,x27486,x27487)+~E(x27481,x27482)+~P44(x27483,x27484,x27481,x27485,x27486,x27487) % 191.49/191.43 [2749]P44(x27493,x27494,x27495,x27492,x27496,x27497)+~E(x27491,x27492)+~P44(x27493,x27494,x27495,x27491,x27496,x27497) % 191.49/191.43 [2750]P44(x27503,x27504,x27505,x27506,x27502,x27507)+~E(x27501,x27502)+~P44(x27503,x27504,x27505,x27506,x27501,x27507) % 191.49/191.43 [2751]P44(x27513,x27514,x27515,x27516,x27517,x27512)+~E(x27511,x27512)+~P44(x27513,x27514,x27515,x27516,x27517,x27511) % 191.49/191.43 [2752]P36(x27522,x27523,x27524)+~E(x27521,x27522)+~P36(x27521,x27523,x27524) % 191.49/191.43 [2753]P36(x27533,x27532,x27534)+~E(x27531,x27532)+~P36(x27533,x27531,x27534) % 191.49/191.43 [2754]P36(x27543,x27544,x27542)+~E(x27541,x27542)+~P36(x27543,x27544,x27541) % 191.49/191.43 [2755]~P111(x27551)+P111(x27552)+~E(x27551,x27552) % 191.49/191.43 [2756]P12(x27562,x27563,x27564)+~E(x27561,x27562)+~P12(x27561,x27563,x27564) % 191.49/191.43 [2757]P12(x27573,x27572,x27574)+~E(x27571,x27572)+~P12(x27573,x27571,x27574) % 191.49/191.43 [2758]P12(x27583,x27584,x27582)+~E(x27581,x27582)+~P12(x27583,x27584,x27581) % 191.49/191.43 [2759]~P139(x27591)+P139(x27592)+~E(x27591,x27592) % 191.49/191.43 [2760]~P89(x27601)+P89(x27602)+~E(x27601,x27602) % 191.49/191.43 [2761]~P82(x27611)+P82(x27612)+~E(x27611,x27612) % 191.49/191.43 [2762]P45(x27622,x27623)+~E(x27621,x27622)+~P45(x27621,x27623) % 191.49/191.43 [2763]P45(x27633,x27632)+~E(x27631,x27632)+~P45(x27633,x27631) % 191.49/191.43 [2764]~P141(x27641)+P141(x27642)+~E(x27641,x27642) % 191.49/191.43 [2765]~P133(x27651)+P133(x27652)+~E(x27651,x27652) % 191.49/191.43 [2766]~P126(x27661)+P126(x27662)+~E(x27661,x27662) % 191.49/191.43 [2767]~P127(x27671)+P127(x27672)+~E(x27671,x27672) % 191.49/191.43 [2768]P22(x27682,x27683,x27684,x27685)+~E(x27681,x27682)+~P22(x27681,x27683,x27684,x27685) % 191.49/191.43 [2769]P22(x27693,x27692,x27694,x27695)+~E(x27691,x27692)+~P22(x27693,x27691,x27694,x27695) % 191.49/191.43 [2770]P22(x27703,x27704,x27702,x27705)+~E(x27701,x27702)+~P22(x27703,x27704,x27701,x27705) % 191.49/191.43 [2771]P22(x27713,x27714,x27715,x27712)+~E(x27711,x27712)+~P22(x27713,x27714,x27715,x27711) % 191.49/191.43 [2772]~P83(x27721)+P83(x27722)+~E(x27721,x27722) % 191.49/191.43 [2773]P27(x27732,x27733,x27734)+~E(x27731,x27732)+~P27(x27731,x27733,x27734) % 191.49/191.43 [2774]P27(x27743,x27742,x27744)+~E(x27741,x27742)+~P27(x27743,x27741,x27744) % 191.49/191.43 [2775]P27(x27753,x27754,x27752)+~E(x27751,x27752)+~P27(x27753,x27754,x27751) % 191.49/191.43 [2776]P49(x27762,x27763,x27764)+~E(x27761,x27762)+~P49(x27761,x27763,x27764) % 191.49/191.43 [2777]P49(x27773,x27772,x27774)+~E(x27771,x27772)+~P49(x27773,x27771,x27774) % 191.49/191.43 [2778]P49(x27783,x27784,x27782)+~E(x27781,x27782)+~P49(x27783,x27784,x27781) % 191.49/191.43 [2779]~P85(x27791)+P85(x27792)+~E(x27791,x27792) % 191.49/191.43 [2780]P30(x27802,x27803,x27804)+~E(x27801,x27802)+~P30(x27801,x27803,x27804) % 191.49/191.43 [2781]P30(x27813,x27812,x27814)+~E(x27811,x27812)+~P30(x27813,x27811,x27814) % 191.49/191.43 [2782]P30(x27823,x27824,x27822)+~E(x27821,x27822)+~P30(x27823,x27824,x27821) % 191.49/191.43 [2783]P23(x27832,x27833,x27834,x27835)+~E(x27831,x27832)+~P23(x27831,x27833,x27834,x27835) % 191.49/191.43 [2784]P23(x27843,x27842,x27844,x27845)+~E(x27841,x27842)+~P23(x27843,x27841,x27844,x27845) % 191.49/191.43 [2785]P23(x27853,x27854,x27852,x27855)+~E(x27851,x27852)+~P23(x27853,x27854,x27851,x27855) % 191.49/191.43 [2786]P23(x27863,x27864,x27865,x27862)+~E(x27861,x27862)+~P23(x27863,x27864,x27865,x27861) % 191.49/191.43 [2787]~P96(x27871)+P96(x27872)+~E(x27871,x27872) % 191.49/191.43 [2788]~P10(x27881)+P10(x27882)+~E(x27881,x27882) % 191.49/191.43 [2789]~P104(x27891)+P104(x27892)+~E(x27891,x27892) % 191.49/191.43 [2790]P20(x27902,x27903,x27904)+~E(x27901,x27902)+~P20(x27901,x27903,x27904) % 191.49/191.43 [2791]P20(x27913,x27912,x27914)+~E(x27911,x27912)+~P20(x27913,x27911,x27914) % 191.49/191.43 [2792]P20(x27923,x27924,x27922)+~E(x27921,x27922)+~P20(x27923,x27924,x27921) % 191.49/191.43 [2793]~P61(x27931)+P61(x27932)+~E(x27931,x27932) % 191.49/191.43 [2794]~P92(x27941)+P92(x27942)+~E(x27941,x27942) % 191.49/191.43 [2795]~P128(x27951)+P128(x27952)+~E(x27951,x27952) % 191.49/191.43 [2796]~P118(x27961)+P118(x27962)+~E(x27961,x27962) % 191.49/191.43 [2797]~P84(x27971)+P84(x27972)+~E(x27971,x27972) % 191.49/191.43 [2798]~P119(x27981)+P119(x27982)+~E(x27981,x27982) % 191.49/191.43 [2799]~P125(x27991)+P125(x27992)+~E(x27991,x27992) % 191.49/191.43 [2800]P57(x28002,x28003)+~E(x28001,x28002)+~P57(x28001,x28003) % 191.49/191.43 [2801]P57(x28013,x28012)+~E(x28011,x28012)+~P57(x28013,x28011) % 191.49/191.43 [2802]P56(x28022,x28023,x28024,x28025,x28026)+~E(x28021,x28022)+~P56(x28021,x28023,x28024,x28025,x28026) % 191.49/191.43 [2803]P56(x28033,x28032,x28034,x28035,x28036)+~E(x28031,x28032)+~P56(x28033,x28031,x28034,x28035,x28036) % 191.49/191.43 [2804]P56(x28043,x28044,x28042,x28045,x28046)+~E(x28041,x28042)+~P56(x28043,x28044,x28041,x28045,x28046) % 191.49/191.43 [2805]P56(x28053,x28054,x28055,x28052,x28056)+~E(x28051,x28052)+~P56(x28053,x28054,x28055,x28051,x28056) % 191.49/191.43 [2806]P56(x28063,x28064,x28065,x28066,x28062)+~E(x28061,x28062)+~P56(x28063,x28064,x28065,x28066,x28061) % 191.49/191.43 [2807]P18(x28072,x28073,x28074)+~E(x28071,x28072)+~P18(x28071,x28073,x28074) % 191.49/191.43 [2808]P18(x28083,x28082,x28084)+~E(x28081,x28082)+~P18(x28083,x28081,x28084) % 191.49/191.43 [2809]P18(x28093,x28094,x28092)+~E(x28091,x28092)+~P18(x28093,x28094,x28091) % 191.49/191.43 [2810]~P90(x28101)+P90(x28102)+~E(x28101,x28102) % 191.49/191.43 [2811]~P142(x28111)+P142(x28112)+~E(x28111,x28112) % 191.49/191.43 [2812]P13(x28122,x28123,x28124)+~E(x28121,x28122)+~P13(x28121,x28123,x28124) % 191.49/191.43 [2813]P13(x28133,x28132,x28134)+~E(x28131,x28132)+~P13(x28133,x28131,x28134) % 191.49/191.43 [2814]P13(x28143,x28144,x28142)+~E(x28141,x28142)+~P13(x28143,x28144,x28141) % 191.49/191.43 [2815]P52(x28152,x28153)+~E(x28151,x28152)+~P52(x28151,x28153) % 191.49/191.43 [2816]P52(x28163,x28162)+~E(x28161,x28162)+~P52(x28163,x28161) % 191.49/191.43 [2817]P11(x28172,x28173)+~E(x28171,x28172)+~P11(x28171,x28173) % 191.49/191.43 [2818]P11(x28183,x28182)+~E(x28181,x28182)+~P11(x28183,x28181) % 191.49/191.43 [2819]~P113(x28191)+P113(x28192)+~E(x28191,x28192) % 191.49/191.43 [2820]P29(x28202,x28203)+~E(x28201,x28202)+~P29(x28201,x28203) % 191.49/191.43 [2821]P29(x28213,x28212)+~E(x28211,x28212)+~P29(x28213,x28211) % 191.49/191.43 [2822]~P129(x28221)+P129(x28222)+~E(x28221,x28222) % 191.49/191.43 [2823]~P98(x28231)+P98(x28232)+~E(x28231,x28232) % 191.49/191.43 [2824]P21(x28242,x28243,x28244)+~E(x28241,x28242)+~P21(x28241,x28243,x28244) % 191.49/191.43 [2825]P21(x28253,x28252,x28254)+~E(x28251,x28252)+~P21(x28253,x28251,x28254) % 191.49/191.43 [2826]P21(x28263,x28264,x28262)+~E(x28261,x28262)+~P21(x28263,x28264,x28261) % 191.49/191.43 [2827]P35(x28272,x28273,x28274,x28275)+~E(x28271,x28272)+~P35(x28271,x28273,x28274,x28275) % 191.49/191.43 [2828]P35(x28283,x28282,x28284,x28285)+~E(x28281,x28282)+~P35(x28283,x28281,x28284,x28285) % 191.49/191.43 [2829]P35(x28293,x28294,x28292,x28295)+~E(x28291,x28292)+~P35(x28293,x28294,x28291,x28295) % 191.49/191.43 [2830]P35(x28303,x28304,x28305,x28302)+~E(x28301,x28302)+~P35(x28303,x28304,x28305,x28301) % 191.49/191.43 [2831]~P135(x28311)+P135(x28312)+~E(x28311,x28312) % 191.49/191.43 [2832]P31(x28322,x28323,x28324)+~E(x28321,x28322)+~P31(x28321,x28323,x28324) % 191.49/191.43 [2833]P31(x28333,x28332,x28334)+~E(x28331,x28332)+~P31(x28333,x28331,x28334) % 191.49/191.43 [2834]P31(x28343,x28344,x28342)+~E(x28341,x28342)+~P31(x28343,x28344,x28341) % 191.49/191.43 [2835]~P121(x28351)+P121(x28352)+~E(x28351,x28352) % 191.49/191.43 [2836]P16(x28362,x28363,x28364,x28365,x28366,x28367)+~E(x28361,x28362)+~P16(x28361,x28363,x28364,x28365,x28366,x28367) % 191.49/191.43 [2837]P16(x28373,x28372,x28374,x28375,x28376,x28377)+~E(x28371,x28372)+~P16(x28373,x28371,x28374,x28375,x28376,x28377) % 191.49/191.43 [2838]P16(x28383,x28384,x28382,x28385,x28386,x28387)+~E(x28381,x28382)+~P16(x28383,x28384,x28381,x28385,x28386,x28387) % 191.49/191.43 [2839]P16(x28393,x28394,x28395,x28392,x28396,x28397)+~E(x28391,x28392)+~P16(x28393,x28394,x28395,x28391,x28396,x28397) % 191.49/191.43 [2840]P16(x28403,x28404,x28405,x28406,x28402,x28407)+~E(x28401,x28402)+~P16(x28403,x28404,x28405,x28406,x28401,x28407) % 191.49/191.43 [2841]P16(x28413,x28414,x28415,x28416,x28417,x28412)+~E(x28411,x28412)+~P16(x28413,x28414,x28415,x28416,x28417,x28411) % 191.49/191.43 [2842]~P131(x28421)+P131(x28422)+~E(x28421,x28422) % 191.49/191.43 [2843]P14(x28432,x28433,x28434)+~E(x28431,x28432)+~P14(x28431,x28433,x28434) % 191.49/191.43 [2844]P14(x28443,x28442,x28444)+~E(x28441,x28442)+~P14(x28443,x28441,x28444) % 191.49/191.43 [2845]P14(x28453,x28454,x28452)+~E(x28451,x28452)+~P14(x28453,x28454,x28451) % 191.49/191.43 [2846]~P86(x28461)+P86(x28462)+~E(x28461,x28462) % 191.49/191.43 [2847]~P145(x28471)+P145(x28472)+~E(x28471,x28472) % 191.49/191.43 [2848]~P78(x28481)+P78(x28482)+~E(x28481,x28482) % 191.49/191.43 [2849]~P32(x28491)+P32(x28492)+~E(x28491,x28492) % 191.49/191.43 [2850]P41(x28502,x28503)+~E(x28501,x28502)+~P41(x28501,x28503) % 191.49/191.43 [2851]P41(x28513,x28512)+~E(x28511,x28512)+~P41(x28513,x28511) % 191.49/191.43 [2852]P3(x28522,x28523,x28524,x28525,x28526)+~E(x28521,x28522)+~P3(x28521,x28523,x28524,x28525,x28526) % 191.49/191.43 [2853]P3(x28533,x28532,x28534,x28535,x28536)+~E(x28531,x28532)+~P3(x28533,x28531,x28534,x28535,x28536) % 191.49/191.43 [2854]P3(x28543,x28544,x28542,x28545,x28546)+~E(x28541,x28542)+~P3(x28543,x28544,x28541,x28545,x28546) % 191.49/191.43 [2855]P3(x28553,x28554,x28555,x28552,x28556)+~E(x28551,x28552)+~P3(x28553,x28554,x28555,x28551,x28556) % 191.49/191.43 [2856]P3(x28563,x28564,x28565,x28566,x28562)+~E(x28561,x28562)+~P3(x28563,x28564,x28565,x28566,x28561) % 191.49/191.43 [2857]~P105(x28571)+P105(x28572)+~E(x28571,x28572) % 191.49/191.43 [2858]~P148(x28581)+P148(x28582)+~E(x28581,x28582) % 191.49/191.43 [2859]P43(x28592,x28593,x28594,x28595)+~E(x28591,x28592)+~P43(x28591,x28593,x28594,x28595) % 191.49/191.43 [2860]P43(x28603,x28602,x28604,x28605)+~E(x28601,x28602)+~P43(x28603,x28601,x28604,x28605) % 191.49/191.43 [2861]P43(x28613,x28614,x28612,x28615)+~E(x28611,x28612)+~P43(x28613,x28614,x28611,x28615) % 191.49/191.43 [2862]P43(x28623,x28624,x28625,x28622)+~E(x28621,x28622)+~P43(x28623,x28624,x28625,x28621) % 191.49/191.43 [2863]P24(x28632,x28633,x28634,x28635,x28636)+~E(x28631,x28632)+~P24(x28631,x28633,x28634,x28635,x28636) % 191.49/191.43 [2864]P24(x28643,x28642,x28644,x28645,x28646)+~E(x28641,x28642)+~P24(x28643,x28641,x28644,x28645,x28646) % 191.49/191.43 [2865]P24(x28653,x28654,x28652,x28655,x28656)+~E(x28651,x28652)+~P24(x28653,x28654,x28651,x28655,x28656) % 191.49/191.43 [2866]P24(x28663,x28664,x28665,x28662,x28666)+~E(x28661,x28662)+~P24(x28663,x28664,x28665,x28661,x28666) % 191.49/191.43 [2867]P24(x28673,x28674,x28675,x28676,x28672)+~E(x28671,x28672)+~P24(x28673,x28674,x28675,x28676,x28671) % 191.49/191.43 [2868]~P46(x28681)+P46(x28682)+~E(x28681,x28682) % 191.49/191.43 [2869]P47(x28692,x28693)+~E(x28691,x28692)+~P47(x28691,x28693) % 191.49/191.43 [2870]P47(x28703,x28702)+~E(x28701,x28702)+~P47(x28703,x28701) % 191.49/191.43 [2871]P58(x28712,x28713,x28714,x28715)+~E(x28711,x28712)+~P58(x28711,x28713,x28714,x28715) % 191.49/191.43 [2872]P58(x28723,x28722,x28724,x28725)+~E(x28721,x28722)+~P58(x28723,x28721,x28724,x28725) % 191.49/191.43 [2873]P58(x28733,x28734,x28732,x28735)+~E(x28731,x28732)+~P58(x28733,x28734,x28731,x28735) % 191.49/191.43 [2874]P58(x28743,x28744,x28745,x28742)+~E(x28741,x28742)+~P58(x28743,x28744,x28745,x28741) % 191.49/191.43 [2875]P51(x28752,x28753)+~E(x28751,x28752)+~P51(x28751,x28753) % 191.49/191.43 [2876]P51(x28763,x28762)+~E(x28761,x28762)+~P51(x28763,x28761) % 191.49/191.43 [2877]~P134(x28771)+P134(x28772)+~E(x28771,x28772) % 191.49/191.43 [2878]P53(x28782,x28783,x28784,x28785,x28786,x28787,x28788)+~E(x28781,x28782)+~P53(x28781,x28783,x28784,x28785,x28786,x28787,x28788) % 191.49/191.43 [2879]P53(x28793,x28792,x28794,x28795,x28796,x28797,x28798)+~E(x28791,x28792)+~P53(x28793,x28791,x28794,x28795,x28796,x28797,x28798) % 191.49/191.43 [2880]P53(x28803,x28804,x28802,x28805,x28806,x28807,x28808)+~E(x28801,x28802)+~P53(x28803,x28804,x28801,x28805,x28806,x28807,x28808) % 191.49/191.43 [2881]P53(x28813,x28814,x28815,x28812,x28816,x28817,x28818)+~E(x28811,x28812)+~P53(x28813,x28814,x28815,x28811,x28816,x28817,x28818) % 191.49/191.43 [2882]P53(x28823,x28824,x28825,x28826,x28822,x28827,x28828)+~E(x28821,x28822)+~P53(x28823,x28824,x28825,x28826,x28821,x28827,x28828) % 191.49/191.43 [2883]P53(x28833,x28834,x28835,x28836,x28837,x28832,x28838)+~E(x28831,x28832)+~P53(x28833,x28834,x28835,x28836,x28837,x28831,x28838) % 191.49/191.43 [2884]P53(x28843,x28844,x28845,x28846,x28847,x28848,x28842)+~E(x28841,x28842)+~P53(x28843,x28844,x28845,x28846,x28847,x28848,x28841) % 191.49/191.43 [2885]~P74(x28851)+P74(x28852)+~E(x28851,x28852) % 191.49/191.43 [2886]~P130(x28861)+P130(x28862)+~E(x28861,x28862) % 191.49/191.43 [2887]P48(x28872,x28873,x28874)+~E(x28871,x28872)+~P48(x28871,x28873,x28874) % 191.49/191.43 [2888]P48(x28883,x28882,x28884)+~E(x28881,x28882)+~P48(x28883,x28881,x28884) % 191.49/191.43 [2889]P48(x28893,x28894,x28892)+~E(x28891,x28892)+~P48(x28893,x28894,x28891) % 191.49/191.43 [2890]P2(x28902,x28903,x28904)+~E(x28901,x28902)+~P2(x28901,x28903,x28904) % 191.49/191.43 [2891]P2(x28913,x28912,x28914)+~E(x28911,x28912)+~P2(x28913,x28911,x28914) % 191.49/191.43 [2892]P2(x28923,x28924,x28922)+~E(x28921,x28922)+~P2(x28923,x28924,x28921) % 191.49/191.43 [2893]~P114(x28931)+P114(x28932)+~E(x28931,x28932) % 191.49/191.43 [2894]~P132(x28941)+P132(x28942)+~E(x28941,x28942) % 191.49/191.43 [2895]~P122(x28951)+P122(x28952)+~E(x28951,x28952) % 191.49/191.43 [2896]~P103(x28961)+P103(x28962)+~E(x28961,x28962) % 191.49/191.43 [2897]~P39(x28971)+P39(x28972)+~E(x28971,x28972) % 191.49/191.43 % 191.49/191.43 %------------------------------------------- % 191.49/191.45 cnf(10238,plain, % 191.49/191.45 (E(f333(f259(x102381,x102381),f260(x102381,x102382)),x102382)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(10241,plain, % 191.49/191.45 (~E(f333(a117,x102411),x102411)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10244,plain, % 191.49/191.45 (~E(f333(a117,x102441),x102441)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10247,plain, % 191.49/191.45 (E(f333(f259(x102471,x102471),f260(x102471,x102472)),x102472)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(10254,plain, % 191.49/191.45 (~E(f333(a117,x102541),x102541)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10265,plain, % 191.49/191.45 (~E(f333(a117,x102651),x102651)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10270,plain, % 191.49/191.45 (~P4(f333(f64(x102701,x102702,f194(f890(x102701,a874))),x102703))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(10273,plain, % 191.49/191.45 (~P4(f333(f64(x102731,x102732,f194(f890(x102731,a874))),x102733))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(10276,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x102761),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(10279,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x102791),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(10292,plain, % 191.49/191.45 (~P4(f333(f194(f890(x102921,a874)),x102922))), % 191.49/191.45 inference(scs_inference,[],[4487,10241,10244,10254,3101,3269,10238,3145,3210,3153,3295,4560,10276,4557,4508,4567,3286,4550,4581,10270,4584,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057])). % 191.49/191.45 cnf(10296,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x102961)),x102961))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(10299,plain, % 191.49/191.45 (~E(f333(f333(f152(x102991),x102992),x102993),x102993)), % 191.49/191.45 inference(rename_variables,[],[4512])). % 191.49/191.45 cnf(10305,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x103051),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(10307,plain, % 191.49/191.45 (E(f46(a880,f333(f259(x103071,x103071),f260(x103071,f333(f333(f82(a880),x103072),x103073))),x103072),f2(a880))), % 191.49/191.45 inference(scs_inference,[],[4487,10241,10244,10254,3101,3269,10238,10247,3145,3210,3176,3153,4512,3295,4560,10276,10279,4557,4508,4569,4567,3286,4550,4581,10270,4584,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084])). % 191.49/191.45 cnf(10308,plain, % 191.49/191.45 (E(f333(f259(x103081,x103081),f260(x103081,x103082)),x103082)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(10311,plain, % 191.49/191.45 (E(f333(f259(x103111,x103111),f260(x103111,x103112)),x103112)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(10318,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x103181),x103182)),x103182))), % 191.49/191.45 inference(rename_variables,[],[4582])). % 191.49/191.45 cnf(10321,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x103211),x103212)),x103212))), % 191.49/191.45 inference(rename_variables,[],[4582])). % 191.49/191.45 cnf(10325,plain, % 191.49/191.45 (~E(x103251,f333(a117,x103251))), % 191.49/191.45 inference(scs_inference,[],[4487,10241,10244,10254,3101,3269,10238,10247,10308,3145,3210,3176,3153,4512,3383,3295,4560,10276,10279,4557,4508,4569,4567,3286,4550,4581,10270,4584,4582,10318,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197])). % 191.49/191.45 cnf(10339,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x103391),x103391))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(10342,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f46(a880,x103421,x103422)),x103421))), % 191.49/191.45 inference(rename_variables,[],[3765])). % 191.49/191.45 cnf(10365,plain, % 191.49/191.45 (E(f333(f39(a880),f333(f256(a880),x103651)),x103651)), % 191.49/191.45 inference(rename_variables,[],[3206])). % 191.49/191.45 cnf(10373,plain, % 191.49/191.45 (~E(f333(a117,x103731),x103731)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10376,plain, % 191.49/191.45 (~E(f333(a117,x103761),x103761)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10379,plain, % 191.49/191.45 (~E(f333(a117,x103791),x103791)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10384,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x103841),f333(a117,x103841)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(10393,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x103931),x103931))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(10400,plain, % 191.49/191.45 (E(f333(f259(x104001,x104001),f260(x104001,x104002)),x104002)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(10403,plain, % 191.49/191.45 (E(f333(f259(x104031,x104031),f260(x104031,x104032)),x104032)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(10422,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x104221),x104221))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(10431,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x104311),x104311))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(10436,plain, % 191.49/191.45 (~E(f333(f333(f333(f73(x104361,f884(x104362)),x104363),x104364),f333(f242(x104362),x104365)),f333(f18(f884(x104362),x104361),f197(x104362)))), % 191.49/191.45 inference(rename_variables,[],[4578])). % 191.49/191.45 cnf(10463,plain, % 191.49/191.45 (~E(f333(f333(f152(x104631),x104632),x104633),x104633)), % 191.49/191.45 inference(rename_variables,[],[4512])). % 191.49/191.45 cnf(10466,plain, % 191.49/191.45 (~E(f333(a26,x104661),f34(x104662,x104663))), % 191.49/191.45 inference(rename_variables,[],[4503])). % 191.49/191.45 cnf(10477,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x104771),x104771))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(10482,plain, % 191.49/191.45 (~E(f333(a117,x104821),x104821)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10489,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x104891),x104891))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(10502,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x105021),f333(a117,x105021)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(10507,plain, % 191.49/191.45 (E(f333(f333(f127(x105071),f118(x105071)),x105072),x105072)), % 191.49/191.45 inference(rename_variables,[],[3264])). % 191.49/191.45 cnf(10525,plain, % 191.49/191.45 (~P4(f333(f64(x105251,x105252,f194(f890(x105251,a874))),x105253))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(10544,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x105441),x105441))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(10559,plain, % 191.49/191.45 (~E(f333(a26,x105591),f34(x105592,x105593))), % 191.49/191.45 inference(rename_variables,[],[4503])). % 191.49/191.45 cnf(10568,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x105681),x105681))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(10573,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x105731),f333(a117,x105731)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(10576,plain, % 191.49/191.45 (~P4(f333(f64(x105761,x105762,f194(f890(x105761,a874))),x105763))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(10579,plain, % 191.49/191.45 (~P4(f333(f64(x105791,x105792,f194(f890(x105791,a874))),x105793))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(10584,plain, % 191.49/191.45 (~P4(f333(f64(x105841,x105842,f194(f890(x105841,a874))),x105843))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(10594,plain, % 191.49/191.45 (~E(f333(f170(x105941),f333(a117,f333(f333(f127(x105941),f333(f170(x105941),x105942)),f333(f333(f152(x105941),x105943),f118(x105941))))),f333(f333(f152(x105941),x105943),x105942))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,4503,10466,3101,3269,10238,10247,10308,10311,10400,3145,3210,3176,3153,3242,3264,10507,4578,4512,10299,3206,4081,4592,3225,3675,3383,10384,10502,10573,3295,4560,10276,10279,10305,4574,3743,3888,3341,3342,3316,4557,4508,4034,3312,10393,3313,3314,10422,3315,4556,10339,10431,10544,3408,3827,3765,10342,4569,10296,4567,4546,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4584,3786,4582,10318,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021])). % 191.49/191.45 cnf(10595,plain, % 191.49/191.45 (~E(f333(a117,x105951),x105951)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10609,plain, % 191.49/191.45 (P4(f333(f333(f251(a104),f333(a5,x106091)),f333(a5,f333(a117,x106091))))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,4503,10466,3101,3269,10238,10247,10308,10311,10400,3145,3210,3176,3153,3242,3264,10507,4578,4512,10299,3206,4081,4592,3225,3675,3383,10384,10502,10573,3756,3295,4560,10276,10279,10305,4574,3743,3888,3341,3342,3316,4557,4508,4034,3312,10393,3313,3314,10422,3315,4556,10339,10431,10544,3408,3827,3765,10342,4569,10296,4567,4546,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4584,3786,4582,10318,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101])). % 191.49/191.45 cnf(10620,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x106201),x106201))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(10623,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x106231),f333(a117,f333(f333(f81(a880),x106232),x106231))))), % 191.49/191.45 inference(rename_variables,[],[3754])). % 191.49/191.45 cnf(10625,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x106251),f333(f333(f82(a880),f333(a117,x106251)),f333(a117,x106251))))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,4503,10466,3101,3269,10238,10247,10308,10311,10400,3145,3210,3176,3153,3242,3264,10507,4578,4512,10299,3206,4081,4592,3225,3675,3383,10384,10502,10573,3756,3295,4560,10276,10279,10305,4574,3743,3888,3341,3342,3316,4557,4508,4034,3312,10393,10489,3313,3314,10422,3315,4556,10339,10431,10544,3408,3827,3765,10342,4569,10296,4567,4546,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,3580,4584,3786,4582,10318,3754,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126])). % 191.49/191.45 cnf(10626,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x106261),f333(f333(f82(a880),x106261),x106261)))), % 191.49/191.45 inference(rename_variables,[],[3580])). % 191.49/191.45 cnf(10629,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x106291),f333(f333(f82(a880),x106291),x106291)))), % 191.49/191.45 inference(rename_variables,[],[3580])). % 191.49/191.45 cnf(10634,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x106341),f333(a117,x106341)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(10637,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x106371),f333(a117,x106371)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(10640,plain, % 191.49/191.45 (P4(f333(f333(f335(x106401),x106402),f258(f890(x106401,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(10657,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x106571),x106572)),x106572))), % 191.49/191.45 inference(rename_variables,[],[4582])). % 191.49/191.45 cnf(10660,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x106601),x106602)),x106602))), % 191.49/191.45 inference(rename_variables,[],[4582])). % 191.49/191.45 cnf(10663,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x106631)),x106631))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(10666,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x106661)),x106661))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(10669,plain, % 191.49/191.45 (P4(f333(f258(f890(x106691,a874)),x106692))), % 191.49/191.45 inference(rename_variables,[],[3377])). % 191.49/191.45 cnf(10672,plain, % 191.49/191.45 (E(f333(f39(a880),f333(f256(a880),x106721)),x106721)), % 191.49/191.45 inference(rename_variables,[],[3206])). % 191.49/191.45 cnf(10675,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x106751),f333(a117,x106751)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(10682,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x106821),x106821))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(10687,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x106871),x106871))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(10696,plain, % 191.49/191.45 (E(f333(f259(x106961,x106961),f260(x106961,x106962)),x106962)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(10699,plain, % 191.49/191.45 (P4(f333(f258(f890(x106991,a874)),x106992))), % 191.49/191.45 inference(rename_variables,[],[3377])). % 191.49/191.45 cnf(10702,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f2(a880)),x107021))), % 191.49/191.45 inference(rename_variables,[],[3335])). % 191.49/191.45 cnf(10705,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x107051,a874)),f194(f890(x107051,a874))),x107052))), % 191.49/191.45 inference(rename_variables,[],[3752])). % 191.49/191.45 cnf(10708,plain, % 191.49/191.45 (P4(f333(f258(f890(x107081,a874)),x107082))), % 191.49/191.45 inference(rename_variables,[],[3377])). % 191.49/191.45 cnf(10711,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x107111),f333(f333(f82(a880),x107111),x107111)))), % 191.49/191.45 inference(rename_variables,[],[3580])). % 191.49/191.45 cnf(10728,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,f333(a117,f333(f333(f81(a880),x107281),x107282)))),f333(a117,x107282)))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,4503,10466,3101,3269,10238,10247,10308,10311,10400,10403,3145,3965,3210,3176,3153,3242,3264,10507,4578,4512,10299,3206,10365,4081,4592,3225,3675,3615,3383,10384,10502,10573,10634,10637,10675,3756,3295,4560,10276,10279,10305,4574,3743,3523,3888,3341,3342,3316,4557,4508,4034,3312,10393,10489,10620,3313,3314,10422,10477,3315,4556,10339,10431,10544,3470,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,3335,4567,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4591,3752,3580,10626,10629,4584,3786,4582,10318,10321,10657,3754,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382])). % 191.49/191.45 cnf(10751,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x107511),x107511))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(10762,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x107621,f890(x107622,a874))),x107623),x107624))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(10769,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x107691),f333(a117,x107691)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(10771,plain, % 191.49/191.45 (P4(f333(f333(f251(a1),f333(f333(f3(a1),x107711),f79(a1))),x107711))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,4503,10466,3101,3269,10238,10247,10308,10311,10400,10403,3145,3965,3210,3176,3153,3242,3264,10507,4578,4512,10299,3206,10365,4081,3941,4592,3225,3675,3615,3383,10384,10502,10573,10634,10637,10675,3756,3295,4560,10276,10279,10305,4574,3743,3523,3888,3341,3342,3316,4557,4508,4034,3312,10393,10489,10620,3313,10751,3314,10422,10477,10687,3315,4556,10339,10431,10544,3470,4572,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,3335,4567,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4591,3752,3580,10626,10629,4584,4585,3786,4582,10318,10321,10657,3754,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633])). % 191.49/191.45 cnf(10772,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x107721),x107721))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(10777,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x107771),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(10790,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x107901),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(10793,plain, % 191.49/191.45 (~P4(f333(f333(f251(f890(x107931,a874)),x107932),f194(f890(x107931,a874))))), % 191.49/191.45 inference(rename_variables,[],[4579])). % 191.49/191.45 cnf(10796,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x107961),x107961))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(10799,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x107991),x107991))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(10814,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x108141),x108141))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(10823,plain, % 191.49/191.45 (~P4(f333(f333(f335(x108231),x108232),f194(f890(x108231,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(10832,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x108321),x108321))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(10835,plain, % 191.49/191.45 (~P4(f333(f333(f335(x108351),x108352),f194(f890(x108351,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(10838,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x108381,a874)),f333(f312(x108382,x108381,x108383),f333(f313(x108382,x108381,x108383),x108384))),x108384))), % 191.49/191.45 inference(rename_variables,[],[4180])). % 191.49/191.45 cnf(10845,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x108451,a874)),f333(f173(x108451),f333(f137(x108451,x108452),x108453))),f333(f173(x108451),x108453)))), % 191.49/191.45 inference(rename_variables,[],[3950])). % 191.49/191.45 cnf(10848,plain, % 191.49/191.45 (E(f333(f312(x108481,x108481,f7(x108481)),x108482),x108482)), % 191.49/191.45 inference(rename_variables,[],[3375])). % 191.49/191.45 cnf(10853,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f2(a880)),x108531))), % 191.49/191.45 inference(rename_variables,[],[3335])). % 191.49/191.45 cnf(10856,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x108561),x108561))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(10859,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x108591),x108591))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(10862,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x108621,f890(x108622,a874))),x108623),x108624))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(10869,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x108691),x108691))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(10880,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x108801),f333(a117,f333(f333(f81(a880),x108802),x108801))))), % 191.49/191.45 inference(rename_variables,[],[3754])). % 191.49/191.45 cnf(10883,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x108831),f333(f333(f82(a880),x108831),x108831)))), % 191.49/191.45 inference(rename_variables,[],[3580])). % 191.49/191.45 cnf(10893,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x108931),x108931))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(10896,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x108961),x108961))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(10899,plain, % 191.49/191.45 (~E(f333(a117,x108991),x108991)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(10904,plain, % 191.49/191.45 (P4(f333(f333(f335(x109041),x109042),f258(f890(x109041,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(10909,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x109091),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(10911,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x109111,a874)),x109112),f41(f890(x109111,a874),f333(f310(x109111),x109112))))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,4503,10466,3101,3269,10238,10247,10308,10311,10400,10403,3145,3965,3210,3176,3153,3375,3242,3264,10507,4578,4512,10299,3206,10365,4081,3941,4592,3225,3514,3675,3615,3383,10384,10502,10573,10634,10637,10675,10769,3756,3295,4560,10276,10279,10305,10777,10790,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,3676,4034,4579,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,4572,10823,10835,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,3335,10702,4567,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4591,3752,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483])). % 191.49/191.45 cnf(10924,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f2(a880)),x109241))), % 191.49/191.45 inference(rename_variables,[],[3335])). % 191.49/191.45 cnf(10931,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x109311),x109311))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(10940,plain, % 191.49/191.45 (~P4(f333(f333(f335(x109401),x109402),f194(f890(x109401,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(10942,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x109421,a874)),f42(f890(x109421,a874),f333(f310(x109421),x109422))),x109422))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,4503,10466,3101,3269,10238,10247,10308,10311,10400,10403,3145,3965,3210,3176,3153,3375,3242,3264,10507,4578,4512,10299,3206,10365,4081,3941,4592,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,3756,3295,4560,10276,10279,10305,10777,10790,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,3676,4034,4579,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,4572,10823,10835,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4591,3752,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754])). % 191.49/191.45 cnf(10947,plain, % 191.49/191.45 (P4(f333(f333(f335(f881(x109471)),x109472),f162(x109471,f258(f890(x109471,a874)))))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,4503,10466,3101,3269,10238,10247,10308,10311,10400,10403,3145,3965,3210,3176,3153,3375,3242,3264,10507,4578,4512,10299,3206,10365,4081,3941,4592,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,3756,3295,4560,10276,10279,10305,10777,10790,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,3676,4034,4579,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,4572,10823,10835,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4591,3752,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766])). % 191.49/191.45 cnf(10948,plain, % 191.49/191.45 (P4(f333(f333(f335(x109481),x109482),f258(f890(x109481,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(10951,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x109511),f881(x109511))),f333(f333(f263(f881(x109511),f881(x109511)),x109512),f118(x109511))),f146(x109511,x109513)))), % 191.49/191.45 inference(rename_variables,[],[4592])). % 191.49/191.45 cnf(10957,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(x109571,x109571)),x109572),f260(x109571,f194(f890(x109571,a874)))))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,4503,10466,3101,3269,10238,10247,10308,10311,10400,10403,3145,3965,3210,3176,3153,3375,3242,3264,10507,4578,4512,10299,3206,10365,4081,3941,4592,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,3756,3295,4560,10276,10279,10305,10777,10790,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,3676,4034,4579,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,4572,10823,10835,10940,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4591,3752,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894])). % 191.49/191.45 cnf(10958,plain, % 191.49/191.45 (~P4(f333(f333(f335(x109581),x109582),f194(f890(x109581,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(10960,plain, % 191.49/191.45 (~P4(f333(f333(f335(x109601),x109602),f333(f313(x109601,x109603,x109604),f194(f890(x109603,a874)))))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,4503,10466,3101,3269,10238,10247,10308,10311,10400,10403,3145,3965,3210,3176,3153,3375,3242,3264,10507,4578,4512,10299,3206,10365,4081,3941,4592,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,3756,3295,4560,10276,10279,10305,10777,10790,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,3676,4034,4579,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,4572,10823,10835,10940,10958,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,4591,3752,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924])). % 191.49/191.45 cnf(10961,plain, % 191.49/191.45 (~P4(f333(f333(f335(x109611),x109612),f194(f890(x109611,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(10964,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x109641,a874)),x109642),f333(f333(f311(x109641),x109643),x109642)))), % 191.49/191.45 inference(rename_variables,[],[3750])). % 191.49/191.45 cnf(10967,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x109671),x109671))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(10970,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x109701,a874)),x109702),f333(f333(f311(x109701),x109703),x109702)))), % 191.49/191.45 inference(rename_variables,[],[3750])). % 191.49/191.45 cnf(10985,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x109851,a874)),x109852),f333(f333(f311(x109851),x109853),x109852)))), % 191.49/191.45 inference(rename_variables,[],[3750])). % 191.49/191.45 cnf(10990,plain, % 191.49/191.45 (~P4(f333(f64(x109901,x109902,f194(f890(x109901,a874))),x109903))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(10994,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(a880,a880)),f333(f333(f263(a880,a880),f333(a117,x109941)),x109941)),f309(a880,a323)))), % 191.49/191.45 inference(scs_inference,[],[4500,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,4503,10466,3101,3155,3269,10238,10247,10308,10311,10400,10403,3145,3965,3210,3176,3153,3375,3242,3264,10507,4578,4512,10299,3206,10365,4081,3941,4592,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,3756,3295,4560,10276,10279,10305,10777,10790,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,3676,4034,4579,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3752,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357])). % 191.49/191.45 cnf(11003,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x110031),f333(a117,x110031)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(11010,plain, % 191.49/191.45 (E(f333(f74(x110101,x110102,x110101,x110103),f35(x110101)),x110103)), % 191.49/191.45 inference(rename_variables,[],[3768])). % 191.49/191.45 cnf(11013,plain, % 191.49/191.45 (~E(f333(f312(x110131,f890(x110131,a874),x110132),x110133),f333(f310(x110131),x110133))), % 191.49/191.45 inference(rename_variables,[],[4570])). % 191.49/191.45 cnf(11016,plain, % 191.49/191.45 (~P4(f333(f333(f335(x110161),x110162),f194(f890(x110161,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11019,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x110191,x110191)),f333(f333(f263(x110191,x110191),x110192),x110192)),f309(x110191,x110193)))), % 191.49/191.45 inference(rename_variables,[],[3941])). % 191.49/191.45 cnf(11022,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x110221,a874)),x110222),f258(f890(x110221,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(11025,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x110251,a874)),f333(f173(x110251),f171(x110251,x110252,x110253))),f333(f173(x110251),x110253)))), % 191.49/191.45 inference(rename_variables,[],[4000])). % 191.49/191.45 cnf(11041,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x110411,a874)),f194(f890(x110411,a874))),x110412))), % 191.49/191.45 inference(rename_variables,[],[3752])). % 191.49/191.45 cnf(11052,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x110521),f881(x110521))),f333(f333(f263(f881(x110521),f881(x110521)),x110522),f118(x110521))),f148(x110521,x110523)))), % 191.49/191.45 inference(rename_variables,[],[4593])). % 191.49/191.45 cnf(11063,plain, % 191.49/191.45 (~E(f333(a117,x110631),x110631)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11066,plain, % 191.49/191.45 (~E(f333(a117,x110661),x110661)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11078,plain, % 191.49/191.45 (P28(x110781,x110781,f7(x110781),x110782)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(11083,plain, % 191.49/191.45 (~E(f333(f312(x110831,f890(x110831,a874),x110832),x110833),f333(f310(x110831),x110833))), % 191.49/191.45 inference(rename_variables,[],[4570])). % 191.49/191.45 cnf(11088,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x110881,a874)),x110882),f258(f890(x110881,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(11102,plain, % 191.49/191.45 (~P4(f333(f333(f335(x111021),x111022),f194(f890(x111021,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11105,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x111051)),x111051))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11110,plain, % 191.49/191.45 (~P4(f333(f333(f335(x111101),x111102),f194(f890(x111101,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11122,plain, % 191.49/191.45 (~P4(f333(f333(f335(a880),f333(a117,f333(f143(a880,a880,f81(a880),f2(a880)),x111221))),f333(f173(a880),x111221)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,4592,10951,4593,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,4579,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3752,10705,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802])). % 191.49/191.45 cnf(11123,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x111231)),x111231))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11126,plain, % 191.49/191.45 (~P4(f333(f333(f335(x111261),x111262),f194(f890(x111261,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11136,plain, % 191.49/191.45 (E(f333(x111361,f557(f333(x111361,x111362),f333(f242(x111363),x111362),x111361,x111364,x111363)),f333(x111361,x111362))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,4592,10951,4593,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,4579,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3752,10705,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880])). % 191.49/191.45 cnf(11145,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x111451,x111451)),f333(f333(f263(x111451,x111451),x111452),x111452)),f309(x111451,x111453)))), % 191.49/191.45 inference(rename_variables,[],[3941])). % 191.49/191.45 cnf(11150,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x111501),f881(x111501))),f333(f333(f263(f881(x111501),f881(x111501)),x111502),f118(x111501))),f146(x111501,x111503)))), % 191.49/191.45 inference(rename_variables,[],[4592])). % 191.49/191.45 cnf(11153,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x111531),f881(x111531))),f333(f333(f263(f881(x111531),f881(x111531)),x111532),f118(x111531))),f148(x111531,x111533)))), % 191.49/191.45 inference(rename_variables,[],[4593])). % 191.49/191.45 cnf(11156,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x111561),f881(x111561))),f333(f333(f263(f881(x111561),f881(x111561)),x111562),f118(x111561))),f158(x111561,x111563)))), % 191.49/191.45 inference(rename_variables,[],[4594])). % 191.49/191.45 cnf(11161,plain, % 191.49/191.45 (~P4(f333(f333(f251(f890(x111611,a874)),x111612),f194(f890(x111611,a874))))), % 191.49/191.45 inference(rename_variables,[],[4579])). % 191.49/191.45 cnf(11163,plain, % 191.49/191.45 (~P4(f333(f333(f335(x111631),x111632),f333(f312(x111633,x111631,x111634),f194(f890(x111633,a874)))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,4592,10951,11150,4593,11052,4594,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,4579,10793,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3752,10705,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041])). % 191.49/191.45 cnf(11164,plain, % 191.49/191.45 (~P4(f333(f333(f335(x111641),x111642),f194(f890(x111641,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11168,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x111681,a874)),x111682),f333(f333(f115(f890(x111681,a874)),x111683),f258(f890(x111681,a874)))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,4592,10951,11150,4593,11052,4594,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,11088,4579,10793,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3752,10705,3580,10626,10629,10711,10883,4584,4585,10762,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063])). % 191.49/191.45 cnf(11169,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x111691,a874)),x111692),f258(f890(x111691,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(11172,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x111721,f890(x111722,a874))),x111723),x111724))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(11181,plain, % 191.49/191.45 (~P4(f333(f333(f335(x111811),x111812),f194(f890(x111811,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11184,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(x111841,x111841)),f333(f333(f263(x111841,x111841),x111842),x111843)),f154(x111841,f118(f890(x111841,a880)))))), % 191.49/191.45 inference(rename_variables,[],[4591])). % 191.49/191.45 cnf(11187,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x111871,a874)),x111872),x111872))), % 191.49/191.45 inference(rename_variables,[],[3611])). % 191.49/191.45 cnf(11190,plain, % 191.49/191.45 (~P4(f333(f333(f335(x111901),x111902),f194(f890(x111901,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11192,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x111921,a874)),f333(f287(x111922,x111921,f194(f890(f889(x111922,x111921),a874))),x111923)),x111924))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,4592,10951,11150,4593,11052,4594,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,11088,4579,10793,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3611,3752,10705,11041,3580,10626,10629,10711,10883,4584,4585,10762,10862,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243])). % 191.49/191.45 cnf(11193,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x111931,a874)),f194(f890(x111931,a874))),x111932))), % 191.49/191.45 inference(rename_variables,[],[3752])). % 191.49/191.45 cnf(11196,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x111961,x111961)),f333(f333(f263(x111961,x111961),x111962),x111962)),f309(x111961,x111963)))), % 191.49/191.45 inference(rename_variables,[],[3941])). % 191.49/191.45 cnf(11198,plain, % 191.49/191.45 (~P37(x111981,x111982,x111983,f333(f333(f155(x111984,x111981),x111985),f333(a117,f118(x111984))),f118(x111982))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,11145,4592,10951,11150,4593,11052,4594,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,11088,4579,10793,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3611,3752,10705,11041,3580,10626,10629,10711,10883,4584,4585,10762,10862,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252])). % 191.49/191.45 cnf(11200,plain, % 191.49/191.45 (~E(f333(f333(f106(f890(f889(f881(x112001),f881(x112001)),a874)),f333(f288(f881(x112001),f881(x112001)),f159(x112001,x112002))),f309(f881(x112001),f159(x112001,x112002))),f194(f890(f889(f881(x112001),f881(x112001)),a874)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,11145,4592,10951,11150,4593,11052,4594,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,11088,4579,10793,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3611,3752,10705,11041,3580,10626,10629,10711,10883,4584,4585,10762,10862,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277])). % 191.49/191.45 cnf(11202,plain, % 191.49/191.45 (P37(x112021,x112022,x112023,f333(f333(f155(x112024,x112021),x112025),f119(x112024,f118(x112024))),f118(x112022))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,11145,4592,10951,11150,4593,11052,4594,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,11088,4579,10793,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3611,3752,10705,11041,3580,10626,10629,10711,10883,4584,4585,10762,10862,4180,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278])). % 191.49/191.45 cnf(11207,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x112071),f881(x112071))),f333(f333(f263(f881(x112071),f881(x112071)),x112072),f118(x112071))),f158(x112071,x112073)))), % 191.49/191.45 inference(rename_variables,[],[4594])). % 191.49/191.45 cnf(11210,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x112101),f881(x112101))),f333(f333(f263(f881(x112101),f881(x112101)),f118(x112101)),x112102)),f146(x112101,x112103)))), % 191.49/191.45 inference(rename_variables,[],[4595])). % 191.49/191.45 cnf(11218,plain, % 191.49/191.45 (P4(f333(f333(f335(x112181),x112182),f258(f890(x112181,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(11223,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x112231,a874)),f194(f890(x112231,a874))),x112232))), % 191.49/191.45 inference(rename_variables,[],[3752])). % 191.49/191.45 cnf(11226,plain, % 191.49/191.45 (~P4(f333(f333(f335(x112261),x112262),f194(f890(x112261,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11229,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x112291,a874)),x112292),f258(f890(x112291,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(11233,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x112331,a874)),f333(f287(x112332,x112331,x112333),f194(f890(x112332,a874)))),x112334))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,4570,11013,3419,3206,10365,4081,3941,11019,11145,4592,10951,11150,4593,11052,4594,11156,4595,4596,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,3377,10669,10699,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,4585,10762,10862,4180,4087,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521])). % 191.49/191.45 cnf(11234,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x112341,a874)),f194(f890(x112341,a874))),x112342))), % 191.49/191.45 inference(rename_variables,[],[3752])). % 191.49/191.45 cnf(11247,plain, % 191.49/191.45 (P4(f333(f258(f890(x112471,a874)),x112472))), % 191.49/191.45 inference(rename_variables,[],[3377])). % 191.49/191.45 cnf(11255,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x112551),f881(x112551))),f333(f333(f263(f881(x112551),f881(x112551)),x112552),f118(x112551))),f146(x112551,x112553)))), % 191.49/191.45 inference(rename_variables,[],[4592])). % 191.49/191.45 cnf(11258,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x112581),f881(x112581))),f333(f333(f263(f881(x112581),f881(x112581)),x112582),f118(x112581))),f148(x112581,x112583)))), % 191.49/191.45 inference(rename_variables,[],[4593])). % 191.49/191.45 cnf(11261,plain, % 191.49/191.45 (~E(f333(f333(f152(x112611),x112612),x112613),x112613)), % 191.49/191.45 inference(rename_variables,[],[4512])). % 191.49/191.45 cnf(11264,plain, % 191.49/191.45 (~E(f333(a117,x112641),x112641)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11267,plain, % 191.49/191.45 (~P4(f333(f333(f335(x112671),x112672),f194(f890(x112671,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11272,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(f881(x112721),f881(x112721))),f333(f333(f263(f881(x112721),f881(x112721)),x112722),x112722)),f159(x112721,f309(x112721,x112723))))), % 191.49/191.45 inference(rename_variables,[],[4075])). % 191.49/191.45 cnf(11277,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x112771),f881(x112771))),f333(f333(f263(f881(x112771),f881(x112771)),x112772),f118(x112771))),f146(x112771,x112773)))), % 191.49/191.45 inference(rename_variables,[],[4592])). % 191.49/191.45 cnf(11286,plain, % 191.49/191.45 (~P4(f333(f333(f335(x112861),x112862),f186(x112863,x112861,f188(x112863,x112861,x112864,f194(f890(x112863,a874))))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,4570,11013,3419,3206,10365,4081,3941,11019,11145,4592,10951,11150,11255,4593,11052,11153,4594,11156,4595,11210,4596,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4075,11272,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,3377,10669,10699,10708,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,3905,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,4585,10762,10862,4180,4087,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752])). % 191.49/191.45 cnf(11287,plain, % 191.49/191.45 (~P4(f333(f333(f335(x112871),x112872),f194(f890(x112871,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11290,plain, % 191.49/191.45 (~P4(f333(f333(f335(x112901),x112902),f194(f890(x112901,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11293,plain, % 191.49/191.45 (~P4(f333(f333(f335(x112931),x112932),f194(f890(x112931,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11296,plain, % 191.49/191.45 (P4(f333(f333(f335(x112961),x112962),f258(f890(x112961,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(11301,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(x113011,x113011)),f333(f333(f263(x113011,x113011),x113012),x113013)),f154(x113011,f118(f890(x113011,a880)))))), % 191.49/191.45 inference(rename_variables,[],[4591])). % 191.49/191.45 cnf(11304,plain, % 191.49/191.45 (~E(f333(f312(x113041,f890(x113041,a874),x113042),x113043),f333(f310(x113041),x113043))), % 191.49/191.45 inference(rename_variables,[],[4570])). % 191.49/191.45 cnf(11307,plain, % 191.49/191.45 (~E(f333(f312(x113071,f890(x113071,a874),x113072),x113073),f333(f310(x113071),x113073))), % 191.49/191.45 inference(rename_variables,[],[4570])). % 191.49/191.45 cnf(11309,plain, % 191.49/191.45 (E(f333(f333(f263(a880,a880),f806(f309(a880,a323),a323,a880,f333(f333(f263(a880,a880),x113091),f333(a117,x113091)),a880,a880)),f808(f309(a880,a323),a323,a880,f333(f333(f263(a880,a880),x113091),f333(a117,x113091)),a880,a880)),f333(f333(f263(a880,a880),x113091),f333(a117,x113091)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,4570,11013,11083,11304,3419,3206,10365,4081,3941,11019,11145,4592,10951,11150,11255,4593,11052,11153,4594,11156,4595,11210,4596,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4075,11272,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,11218,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,3377,10669,10699,10708,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,11184,3905,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,4585,10762,10862,4180,4087,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919])). % 191.49/191.45 cnf(11312,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x113121),f881(x113121))),f333(f333(f263(f881(x113121),f881(x113121)),x113122),f118(x113121))),f146(x113121,x113123)))), % 191.49/191.45 inference(rename_variables,[],[4592])). % 191.49/191.45 cnf(11318,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x113181),f881(x113181))),f333(f333(f263(f881(x113181),f881(x113181)),x113182),f118(x113181))),f146(x113181,x113183)))), % 191.49/191.45 inference(rename_variables,[],[4592])). % 191.49/191.45 cnf(11321,plain, % 191.49/191.45 (~P4(f333(f333(f335(x113211),x113212),f194(f890(x113211,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11324,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x113241,f890(x113242,a874))),x113243),x113244))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(11327,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x113271),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(11331,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x113311,x113312)),f333(f333(f263(x113311,x113312),f333(x113313,x113314)),f333(x113315,x113314))),f333(f312(f889(x113316,x113316),f889(x113311,x113312),f273(x113316,x113311,x113316,x113312,x113313,x113315)),f309(x113316,x113317))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,4503,10466,10559,3101,3155,3269,10238,10247,10308,10311,10400,10403,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,4570,11013,11083,11304,3419,3206,10365,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4075,11272,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,11218,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,3377,10669,10699,10708,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4581,10270,10273,10525,10576,10579,10584,4591,11184,3905,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,4585,10762,10862,11172,4180,4087,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036])). % 191.49/191.45 cnf(11334,plain, % 191.49/191.45 (~P4(f333(f333(f335(x113341),x113342),f194(f890(x113341,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11337,plain, % 191.49/191.45 (~P4(f333(f333(f335(x113371),x113372),f194(f890(x113371,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11340,plain, % 191.49/191.45 (P4(f333(f333(f335(x113401),f333(x113402,x113403)),f333(f312(x113404,x113401,x113402),f258(f890(x113404,a874)))))), % 191.49/191.45 inference(rename_variables,[],[3905])). % 191.49/191.45 cnf(11343,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(x113431,x113431)),f333(f333(f263(x113431,x113431),x113432),x113433)),f154(x113431,f118(f890(x113431,a880)))))), % 191.49/191.45 inference(rename_variables,[],[4591])). % 191.49/191.45 cnf(11351,plain, % 191.49/191.45 (E(f119(x113511,f118(x113511)),f118(x113511))), % 191.49/191.45 inference(rename_variables,[],[3155])). % 191.49/191.45 cnf(11354,plain, % 191.49/191.45 (~E(f333(a117,x113541),x113541)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11361,plain, % 191.49/191.45 (~E(f333(a117,x113611),x113611)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11366,plain, % 191.49/191.45 (E(f333(f259(x113661,x113661),f260(x113661,x113662)),x113662)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(11369,plain, % 191.49/191.45 (E(f333(f259(x113691,x113691),f260(x113691,x113692)),x113692)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(11375,plain, % 191.49/191.45 (~E(f333(a117,x113751),x113751)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11386,plain, % 191.49/191.45 (~E(f333(a28,x113861),f333(f242(a876),a886))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,4503,10466,10559,3230,2898,2925,2927,2943,2953,2969,2983,3004,3053,3054,3101,3155,3269,10238,10247,10308,10311,10400,10403,10696,11366,3768,3145,3965,3210,3176,3153,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,4570,11013,11083,11304,11307,3419,3205,3206,10365,3123,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,4574,3743,3523,3888,3341,3342,3316,4557,4508,4075,11272,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,11218,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,3377,10669,10699,10708,3408,3827,3765,10342,4569,10296,10663,10666,11105,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4590,4581,10270,10273,10525,10576,10579,10584,4591,11184,11301,3905,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,4585,10762,10862,11172,4180,4087,3786,4582,10318,10321,10657,3754,10623,4019,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860])). % 191.49/191.45 cnf(11393,plain, % 191.49/191.45 (E(f333(f333(f3(a880),f2(a880)),x113931),f2(a880))), % 191.49/191.45 inference(rename_variables,[],[3226])). % 191.49/191.45 cnf(11402,plain, % 191.49/191.45 (E(f333(f333(f81(a1),f333(f333(f82(a1),x114021),f333(f333(f40(a1),x114022),x114021))),f46(a1,x114022,x114021)),x114022)), % 191.49/191.45 inference(rename_variables,[],[3856])). % 191.49/191.45 cnf(11426,plain, % 191.49/191.45 (~E(f333(a117,x114261),x114261)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11429,plain, % 191.49/191.45 (~E(f333(a117,x114291),x114291)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11455,plain, % 191.49/191.45 (~P4(f333(f64(x114551,x114552,f194(f890(x114551,a874))),x114553))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(11458,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x114581,f890(x114582,a874))),x114583),x114584))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(11461,plain, % 191.49/191.45 (P4(f333(f333(f335(x114611),x114612),f258(f890(x114611,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(11473,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x114731),x114731))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(11480,plain, % 191.49/191.45 (P4(f333(f68(x114801,x114802,x114803,x114804,f194(f890(x114801,a874))),x114804))), % 191.49/191.45 inference(rename_variables,[],[4226])). % 191.49/191.45 cnf(11481,plain, % 191.49/191.45 (E(f333(f259(x114811,x114811),f260(x114811,x114812)),x114812)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(11486,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x114861,f890(x114862,a874))),x114863),x114864))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(11497,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x114971),x114972)),x114972))), % 191.49/191.45 inference(rename_variables,[],[4582])). % 191.49/191.45 cnf(11500,plain, % 191.49/191.45 (~P4(f333(f333(f251(a1),f333(f105(a1),x115001)),f2(a1)))), % 191.49/191.45 inference(rename_variables,[],[4574])). % 191.49/191.45 cnf(11516,plain, % 191.49/191.45 (~E(f333(f333(f106(a880),f333(a117,x115161)),x115161),f333(a117,x115161))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,4503,10466,10559,3230,2898,2906,2912,2919,2925,2927,2930,2933,2943,2952,2953,2961,2967,2969,2973,2974,2983,3004,3027,3053,3054,3058,3077,3084,3101,4483,3155,11351,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,3768,3145,3965,3856,11402,3210,3176,3153,3159,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,11327,4574,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,10682,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,3315,4556,10339,10431,10544,10568,10814,10859,3470,10640,10904,10948,11218,11296,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,3377,10669,10699,10708,3408,3827,3765,10342,4569,10296,10663,10666,11105,11123,3335,10702,10853,4567,3834,4546,4548,3286,3287,4547,4550,4551,4590,4226,4581,10270,10273,10525,10576,10579,10584,10990,4591,11184,11301,3905,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,4585,10762,10862,11172,11324,11458,4180,4087,3786,4582,10318,10321,10657,10660,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388])). % 191.49/191.45 cnf(11523,plain, % 191.49/191.45 (E(f333(f259(x115231,x115231),f260(x115231,x115232)),x115232)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(11528,plain, % 191.49/191.45 (E(f333(f259(x115281,x115281),f260(x115281,x115282)),x115282)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(11531,plain, % 191.49/191.45 (~P4(f333(f333(f251(a1),f333(f105(a1),x115311)),f2(a1)))), % 191.49/191.45 inference(rename_variables,[],[4574])). % 191.49/191.45 cnf(11536,plain, % 191.49/191.45 (~E(f333(a117,x115361),x115361)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11545,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x115451),x115451))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11566,plain, % 191.49/191.45 (~P4(f333(f333(f251(a1),f333(f105(a1),x115661)),f2(a1)))), % 191.49/191.45 inference(rename_variables,[],[4574])). % 191.49/191.45 cnf(11579,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x115791),x115791))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11582,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x115821)),x115821))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11583,plain, % 191.49/191.45 (~E(f333(a117,x115831),x115831)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11593,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x115931),x115932)),x115931))), % 191.49/191.45 inference(rename_variables,[],[4583])). % 191.49/191.45 cnf(11596,plain, % 191.49/191.45 (~P4(f333(f333(f251(a1),f333(f105(a1),x115961)),f2(a1)))), % 191.49/191.45 inference(rename_variables,[],[4574])). % 191.49/191.45 cnf(11599,plain, % 191.49/191.45 (~E(f333(a117,x115991),x115991)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11612,plain, % 191.49/191.45 (P4(f333(f333(f335(x116121),x116122),f333(f333(f311(x116121),x116122),x116123)))), % 191.49/191.45 inference(rename_variables,[],[3624])). % 191.49/191.45 cnf(11613,plain, % 191.49/191.45 (~P4(f333(f333(f250(a1),f2(a1)),f333(f80(a1),f333(f105(a1),f333(a117,x116131)))))), % 191.49/191.45 inference(rename_variables,[],[4584])). % 191.49/191.45 cnf(11616,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),f333(f333(f3(a880),x116161),x116162)),f333(a117,x116161)))), % 191.49/191.45 inference(rename_variables,[],[3756])). % 191.49/191.45 cnf(11619,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f46(a880,x116191,x116192)),x116191))), % 191.49/191.45 inference(rename_variables,[],[3765])). % 191.49/191.45 cnf(11625,plain, % 191.49/191.45 (E(f333(f333(f127(x116251),x116252),f118(x116251)),x116252)), % 191.49/191.45 inference(rename_variables,[],[3243])). % 191.49/191.45 cnf(11628,plain, % 191.49/191.45 (E(f333(f259(x116281,x116281),f260(x116281,x116282)),x116282)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(11631,plain, % 191.49/191.45 (E(f333(f74(x116311,x116312,x116311,x116313),f35(x116311)),x116313)), % 191.49/191.45 inference(rename_variables,[],[3768])). % 191.49/191.45 cnf(11637,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x116371)),x116371))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11646,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x116461),x116461))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11649,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f46(a880,x116491,x116492)),x116491))), % 191.49/191.45 inference(rename_variables,[],[3765])). % 191.49/191.45 cnf(11650,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f2(a880)),x116501))), % 191.49/191.45 inference(rename_variables,[],[3335])). % 191.49/191.45 cnf(11652,plain, % 191.49/191.45 (~P4(f333(f333(f250(a1),f79(a1)),f2(a1)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,4503,10466,10559,3230,2898,2906,2912,2913,2919,2920,2925,2927,2930,2933,2943,2952,2953,2961,2966,2967,2969,2970,2973,2974,2983,3004,3027,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,3243,11625,3768,11010,11631,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,3295,4560,10276,10279,10305,10777,10790,10909,11327,4574,11500,11531,11566,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,10682,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,10896,3315,4556,10339,10431,10544,10568,10814,10859,10869,11545,3470,10640,10904,10948,11218,11296,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,3377,10669,10699,10708,3414,3408,3827,3765,10342,11619,4569,10296,10663,10666,11105,11123,11582,3335,10702,10853,10924,4567,3834,4546,4548,3286,3287,4547,4550,4551,4590,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,4591,11184,11301,3905,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,4585,10762,10862,11172,11324,11458,4180,4087,3786,4582,10318,10321,10657,10660,4583,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824])). % 191.49/191.45 cnf(11667,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x116671),x116671))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11670,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x116701),x116701))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11673,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x116731),x116731))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11676,plain, % 191.49/191.45 (P4(f333(f333(f335(x116761),f333(x116762,x116763)),f333(f312(x116764,x116761,x116762),f258(f890(x116764,a874)))))), % 191.49/191.45 inference(rename_variables,[],[3905])). % 191.49/191.45 cnf(11677,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x116771),x116772)),x116772))), % 191.49/191.45 inference(rename_variables,[],[4582])). % 191.49/191.45 cnf(11680,plain, % 191.49/191.45 (P4(f333(f333(f335(x116801),f333(x116802,x116803)),f333(f312(x116804,x116801,x116802),f258(f890(x116804,a874)))))), % 191.49/191.45 inference(rename_variables,[],[3905])). % 191.49/191.45 cnf(11681,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x116811)),x116811))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11686,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x116861),x116862)),x116861))), % 191.49/191.45 inference(rename_variables,[],[4583])). % 191.49/191.45 cnf(11689,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x116891),x116891))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11692,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x116921),x116921))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(11698,plain, % 191.49/191.45 (~P38(x116981,x116982,f118(x116981))), % 191.49/191.45 inference(rename_variables,[],[4523])). % 191.49/191.45 cnf(11701,plain, % 191.49/191.45 (P4(f333(f333(f335(x117011),x117012),f258(f890(x117011,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(11702,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x117021)),x117021))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11705,plain, % 191.49/191.45 (~P4(f333(f64(x117051,x117052,f194(f890(x117051,a874))),x117053))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(11718,plain, % 191.49/191.45 (~P4(f333(f333(f335(x117181),x117182),f194(f890(x117181,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11721,plain, % 191.49/191.45 (E(f333(f333(f18(x117211,x117212),x117213),x117214),x117213)), % 191.49/191.45 inference(rename_variables,[],[3302])). % 191.49/191.45 cnf(11724,plain, % 191.49/191.45 (E(f333(f333(f18(x117241,x117242),x117243),x117244),x117243)), % 191.49/191.45 inference(rename_variables,[],[3302])). % 191.49/191.45 cnf(11736,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),f2(a880)),f333(a117,x117361)))), % 191.49/191.45 inference(rename_variables,[],[3395])). % 191.49/191.45 cnf(11739,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x117391),x117391))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(11742,plain, % 191.49/191.45 (P4(f333(f333(f335(x117421),f333(x117422,x117423)),f333(f312(x117424,x117421,x117422),f258(f890(x117424,a874)))))), % 191.49/191.45 inference(rename_variables,[],[3905])). % 191.49/191.45 cnf(11745,plain, % 191.49/191.45 (P4(f333(f63(x117451),f333(f173(x117451),x117452)))), % 191.49/191.45 inference(rename_variables,[],[3355])). % 191.49/191.45 cnf(11748,plain, % 191.49/191.45 (P4(f333(f63(x117481),f333(f173(x117481),x117482)))), % 191.49/191.45 inference(rename_variables,[],[3355])). % 191.49/191.45 cnf(11751,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),f333(f80(a1),f333(f105(a1),x117511))),f333(f105(a1),x117512)))), % 191.49/191.45 inference(rename_variables,[],[3787])). % 191.49/191.45 cnf(11754,plain, % 191.49/191.45 (~P4(f333(f333(f335(x117541),x117542),f194(f890(x117541,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(11766,plain, % 191.49/191.45 (~P4(f333(f333(f335(a880),x117661),f333(f256(a880),f2(a880))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4522,4523,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,4503,10466,10559,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2966,2967,2969,2970,2973,2974,2977,2983,3004,3027,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,3243,11625,3768,11010,11631,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,11616,3295,3395,4560,10276,10279,10305,10777,10790,10909,11327,4574,11500,11531,11566,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,10896,3315,3391,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,3470,10640,10904,10948,11218,11296,11461,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,3377,10669,10699,10708,3414,3408,3827,3765,10342,11619,4569,10296,10663,10666,11105,11123,11582,11637,11681,3335,10702,10853,10924,3787,4567,3834,4546,4548,3286,3287,4547,4550,4551,4590,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,4180,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158])). % 191.49/191.45 cnf(11773,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x117731),x117731))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(11776,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x117761),x117761))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11785,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x117851),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(11788,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x117881),x117881))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11793,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x117931),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(11800,plain, % 191.49/191.45 (P4(f333(f258(f890(x118001,a874)),x118002))), % 191.49/191.45 inference(rename_variables,[],[3377])). % 191.49/191.45 cnf(11805,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f2(a880)),x118051))), % 191.49/191.45 inference(rename_variables,[],[3335])). % 191.49/191.45 cnf(11806,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x118061)),x118061))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11809,plain, % 191.49/191.45 (~P4(f333(f64(x118091,x118092,f194(f890(x118091,a874))),x118093))), % 191.49/191.45 inference(rename_variables,[],[4581])). % 191.49/191.45 cnf(11826,plain, % 191.49/191.45 (P4(f333(f333(f251(a1),f333(f80(a1),f79(a1))),f2(a1)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4522,4523,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,4503,10466,10559,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2973,2974,2977,2983,2984,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,3243,11625,3768,11010,11631,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,11616,3295,3395,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,4045,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,10896,11579,11776,3315,3391,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,3470,10640,10904,10948,11218,11296,11461,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,3335,10702,10853,10924,11650,3787,4567,3834,4546,4548,3286,3287,4547,4550,4551,4590,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,4180,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460])). % 191.49/191.45 cnf(11831,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x118311),x118311))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11834,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x118341),x118341))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11837,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x118371),x118371))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11840,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x118401),x118401))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11843,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x118431)),x118431))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11846,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x118461)),x118461))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11849,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x118491)),x118491))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11852,plain, % 191.49/191.45 (~P4(f333(f333(f250(a880),f333(a117,x118521)),x118521))), % 191.49/191.45 inference(rename_variables,[],[4569])). % 191.49/191.45 cnf(11869,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x118691),x118691))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(11875,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x118751),x118751))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11886,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x118861),x118861))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11889,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(f889(f881(x118891),f881(x118891)),a874)),f159(x118891,x118892)),f309(f881(x118891),f158(x118891,x118892))))), % 191.49/191.45 inference(rename_variables,[],[4005])). % 191.49/191.45 cnf(11896,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x118961),f333(a117,x118961)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(11899,plain, % 191.49/191.45 (P4(f333(f333(f335(f890(x118991,a874)),x118992),f333(f310(x118991),x118992)))), % 191.49/191.45 inference(rename_variables,[],[3676])). % 191.49/191.45 cnf(11900,plain, % 191.49/191.45 (~E(f333(a117,x119001),x119001)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11907,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x119071),x119071))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11912,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x119121),x119121))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11918,plain, % 191.49/191.45 (~P4(f333(f333(f251(a1),f333(f80(a1),a102)),f2(a1)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4522,4523,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,4503,10466,10559,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2973,2974,2977,2983,2984,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,3243,11625,3768,11010,11631,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,3756,11616,3295,3395,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,4045,4005,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,3313,10751,10796,10799,10832,10856,10893,10931,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,3315,3391,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,3470,10640,10904,10948,11218,11296,11461,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,3335,10702,10853,10924,11650,3787,4567,3834,4546,4548,3286,3287,4547,4550,4551,4590,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,4180,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690])). % 191.49/191.45 cnf(11921,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x119211,a874)),x119212),f333(f333(f311(x119211),x119213),x119212)))), % 191.49/191.45 inference(rename_variables,[],[3750])). % 191.49/191.45 cnf(11924,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x119241),x119241))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(11925,plain, % 191.49/191.45 (~E(f333(a117,x119251),x119251)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11936,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x119361),x119361))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11937,plain, % 191.49/191.45 (~E(f333(a117,x119371),x119371)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11940,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x119401),x119401))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(11943,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x119431),x119431))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(11946,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x119461),x119461))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(11949,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x119491),x119491))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(11951,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),f333(a109,f2(a1))),f333(a117,x119511)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4522,4523,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,4503,10466,10559,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2973,2974,2977,2983,2984,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,3243,11625,3768,11010,11631,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,3756,11616,3295,3395,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,4045,4005,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,3315,3391,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,3470,10640,10904,10948,11218,11296,11461,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,3335,10702,10853,10924,11650,3787,4567,3834,4546,4548,3286,3287,4547,4550,4551,4590,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,10985,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,4180,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791])). % 191.49/191.45 cnf(11952,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x119521),x119521))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11955,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x119551),x119551))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11958,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x119581),x119581))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11959,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x119591),f333(a117,x119591)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(11968,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x119681),x119681))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(11969,plain, % 191.49/191.45 (~E(f333(a117,x119691),x119691)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(11974,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x119741),x119741))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11989,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),x119891),x119891))), % 191.49/191.45 inference(rename_variables,[],[3314])). % 191.49/191.45 cnf(11994,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f2(a880)),x119941))), % 191.49/191.45 inference(rename_variables,[],[3335])). % 191.49/191.45 cnf(12011,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x120111),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12014,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x120141),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12017,plain, % 191.49/191.45 (~P4(f333(f333(f335(x120171),x120172),f194(f890(x120171,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12020,plain, % 191.49/191.45 (~P4(f333(f333(f335(x120201),x120202),f194(f890(x120201,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12023,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x120231),x120231))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12025,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x120251),f333(f333(f106(a880),x120251),x120252)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4522,4523,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,4503,10466,10559,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2973,2974,2977,2983,2984,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,3243,11625,3254,3768,11010,11631,4068,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,3756,11616,3295,3395,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,4045,4005,3950,10845,4000,3676,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,3470,10640,10904,10948,11218,11296,11461,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,3787,4567,3798,3834,4546,4548,3286,3287,4547,4550,4551,4590,3806,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,10985,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,4180,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021])). % 191.49/191.45 cnf(12026,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x120261),x120261))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12029,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x120291),x120291))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12032,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x120321),x120321))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12035,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x120351),f333(a117,x120351)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(12042,plain, % 191.49/191.45 (P4(f333(f333(f335(f890(x120421,a874)),x120422),f333(f310(x120421),x120422)))), % 191.49/191.45 inference(rename_variables,[],[3676])). % 191.49/191.45 cnf(12046,plain, % 191.49/191.45 (~P4(f333(f333(f335(a880),f333(a117,f333(f143(a880,a880,f81(a880),f2(a880)),x120461))),f333(f173(a880),f333(f137(a880,x120462),x120461))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,4522,4523,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,4503,10466,10559,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2973,2974,2977,2983,2984,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,3243,11625,3254,3768,11010,11631,4068,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,3756,11616,3295,3395,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,4045,4005,3950,10845,4000,3676,11899,4034,3693,11022,11088,11169,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,3470,10640,10904,10948,11218,11296,11461,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,3787,4567,3798,3834,4546,4548,3286,3287,4547,4550,4551,4590,3806,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,10985,3611,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,4180,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120])). % 191.49/191.45 cnf(12047,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x120471,a874)),f333(f173(x120471),f333(f137(x120471,x120472),x120473))),f333(f173(x120471),x120473)))), % 191.49/191.45 inference(rename_variables,[],[3950])). % 191.49/191.45 cnf(12054,plain, % 191.49/191.45 (~P4(f333(f333(f335(x120541),x120542),f194(f890(x120541,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12059,plain, % 191.49/191.45 (E(f333(f195(f881(x120591)),f333(f169(x120591),x120592)),f333(f195(f881(x120591)),x120592))), % 191.49/191.45 inference(rename_variables,[],[3326])). % 191.49/191.45 cnf(12066,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x120661,a874)),x120662),f258(f890(x120661,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(12067,plain, % 191.49/191.45 (~E(f333(a117,x120671),x120671)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(12070,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x120701,a874)),f333(f173(x120701),f333(f137(x120701,x120702),x120703))),f333(f173(x120701),x120703)))), % 191.49/191.45 inference(rename_variables,[],[3950])). % 191.49/191.45 cnf(12076,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x120761),f333(a117,x120761)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(12085,plain, % 191.49/191.45 (E(f333(f259(x120851,x120851),f260(x120851,x120852)),x120852)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12096,plain, % 191.49/191.45 (P4(f333(f63(x120961),f194(f890(x120961,a874))))), % 191.49/191.45 inference(rename_variables,[],[3391])). % 191.49/191.45 cnf(12097,plain, % 191.49/191.45 (~P4(f333(f333(f335(x120971),x120972),f194(f890(x120971,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12102,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x121021),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12103,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x121031),x121031))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12108,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x121081,a874)),f333(f173(x121081),f171(x121081,x121082,x121083))),f333(f173(x121081),x121083)))), % 191.49/191.45 inference(rename_variables,[],[4000])). % 191.49/191.45 cnf(12111,plain, % 191.49/191.45 (P28(x121111,x121111,f7(x121111),x121112)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12116,plain, % 191.49/191.45 (P4(f333(f333(f335(f890(x121161,a874)),x121162),f333(f310(x121161),x121162)))), % 191.49/191.45 inference(rename_variables,[],[3676])). % 191.49/191.45 cnf(12123,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x121231),x121231))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(12126,plain, % 191.49/191.45 (~P4(f333(f333(f335(x121261),x121262),f194(f890(x121261,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12129,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x121291,a874)),x121292),f333(f333(f311(x121291),x121293),x121292)))), % 191.49/191.45 inference(rename_variables,[],[3750])). % 191.49/191.45 cnf(12130,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x121301,a874)),x121302),f258(f890(x121301,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(12137,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x121371),f333(a117,x121371)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(12140,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x121401),f333(a117,x121401)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(12143,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x121431),x121431))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(12146,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x121461),x121461))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(12149,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x121491),x121491))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(12152,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x121521),x121521))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(12155,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x121551,a874)),x121552),x121552))), % 191.49/191.45 inference(rename_variables,[],[3611])). % 191.49/191.45 cnf(12159,plain, % 191.49/191.45 (~P4(f333(f333(f250(a1),f333(f333(f3(a1),a84),a102)),f2(a1)))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,11078,4522,4523,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,4503,10466,10559,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,3243,11625,3254,3768,11010,11631,4068,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3326,3375,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,3756,11616,3295,3395,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,11748,4045,4005,3950,10845,12047,4000,11025,3676,11899,12042,4034,3693,11022,11088,11169,11229,12066,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,12096,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,3470,10640,10904,10948,11218,11296,11461,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,3787,4567,3798,3834,4546,4548,3286,3287,4547,4550,4551,4590,3806,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,10985,11921,3611,11187,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,4180,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618])). % 191.49/191.45 cnf(12162,plain, % 191.49/191.45 (P4(f333(f333(f335(f890(x121621,a874)),x121622),f333(f310(x121621),x121622)))), % 191.49/191.45 inference(rename_variables,[],[3676])). % 191.49/191.45 cnf(12171,plain, % 191.49/191.45 (~E(f333(a117,x121711),x121711)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(12172,plain, % 191.49/191.45 (E(f333(f312(x121721,x121721,f7(x121721)),x121722),x121722)), % 191.49/191.45 inference(rename_variables,[],[3375])). % 191.49/191.45 cnf(12175,plain, % 191.49/191.45 (P35(x121751,x121752,f118(x121751),f118(x121751))), % 191.49/191.45 inference(rename_variables,[],[3561])). % 191.49/191.45 cnf(12178,plain, % 191.49/191.45 (~E(f333(a117,x121781),x121781)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(12181,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x121811,a874)),f333(f173(x121811),f171(x121811,x121812,x121813))),f333(f173(x121811),x121813)))), % 191.49/191.45 inference(rename_variables,[],[4000])). % 191.49/191.45 cnf(12182,plain, % 191.49/191.45 (P4(f333(f63(x121821),f333(f173(x121821),x121822)))), % 191.49/191.45 inference(rename_variables,[],[3355])). % 191.49/191.45 cnf(12193,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x121931),x121931))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12196,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x121961),x121961))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12201,plain, % 191.49/191.45 (E(f333(f195(f881(x122011)),f333(f169(x122011),x122012)),f333(f195(f881(x122011)),x122012))), % 191.49/191.45 inference(rename_variables,[],[3326])). % 191.49/191.45 cnf(12208,plain, % 191.49/191.45 (P17(a880,f333(f170(a880),f333(f333(f155(f881(x122081),a880),f195(f881(x122081))),f180(x122081,x122082))))), % 191.49/191.45 inference(rename_variables,[],[3866])). % 191.49/191.45 cnf(12211,plain, % 191.49/191.45 (P28(x122111,x122111,f7(x122111),x122112)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12214,plain, % 191.49/191.45 (P4(f333(f333(f335(f881(x122141)),f118(x122141)),f162(x122141,x122142)))), % 191.49/191.45 inference(rename_variables,[],[3514])). % 191.49/191.45 cnf(12217,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x122171,f890(x122172,a874))),x122173),x122174))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(12222,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x122221),x122221))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(12223,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),f2(a880)),x122231))), % 191.49/191.45 inference(rename_variables,[],[3335])). % 191.49/191.45 cnf(12225,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),f2(a1)),f401(x122251,f194(f890(x122252,f890(x122253,a874))),f79(a1))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,11078,12111,3561,4522,4523,4506,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,4503,10466,10559,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,3243,11625,3254,3768,11010,11631,4068,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3190,3326,12059,3375,10848,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,11318,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,3675,4369,4370,3615,3823,3866,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,3756,11616,3295,3395,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,11748,4045,4005,3950,10845,12047,4000,11025,12108,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,12096,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,3470,10640,10904,10948,11218,11296,11461,11701,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,3787,4567,3798,3834,4546,4548,3286,3287,4547,4550,4551,4590,3806,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,10985,11921,3611,11187,3752,10705,11041,11193,11223,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,11486,12217,4180,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927])). % 191.49/191.45 cnf(12226,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x122261,f890(x122262,a874))),x122263),x122264))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(12229,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(f889(f881(x122291),f881(x122291)),a874)),f159(x122291,x122292)),f309(f881(x122291),f158(x122291,x122292))))), % 191.49/191.45 inference(rename_variables,[],[4005])). % 191.49/191.45 cnf(12235,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122351,a874)),f194(f890(x122351,a874))),x122352))), % 191.49/191.45 inference(rename_variables,[],[3752])). % 191.49/191.45 cnf(12238,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122381,a874)),f333(f312(x122382,x122381,x122383),f333(f313(x122382,x122381,x122383),x122384))),x122384))), % 191.49/191.45 inference(rename_variables,[],[4180])). % 191.49/191.45 cnf(12241,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122411,a874)),f333(f173(x122411),f171(x122411,x122412,x122413))),f333(f173(x122411),x122413)))), % 191.49/191.45 inference(rename_variables,[],[4000])). % 191.49/191.45 cnf(12242,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122421,a874)),f333(f173(x122421),f333(f137(x122421,x122422),x122423))),f333(f173(x122421),x122423)))), % 191.49/191.45 inference(rename_variables,[],[3950])). % 191.49/191.45 cnf(12245,plain, % 191.49/191.45 (P28(x122451,f884(x122451),f242(x122451),x122452)), % 191.49/191.45 inference(rename_variables,[],[3562])). % 191.49/191.45 cnf(12250,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122501,a874)),f333(f312(x122502,x122501,x122503),f333(f313(x122502,x122501,x122503),x122504))),x122504))), % 191.49/191.45 inference(rename_variables,[],[4180])). % 191.49/191.45 cnf(12253,plain, % 191.49/191.45 (P4(f333(f63(f884(x122531)),f333(f312(x122532,f884(x122531),f333(f178(x122532,x122531),x122533)),f258(f890(x122532,a874)))))), % 191.49/191.45 inference(rename_variables,[],[4012])). % 191.49/191.45 cnf(12258,plain, % 191.49/191.45 (P4(f333(f333(f335(f881(x122581)),f118(x122581)),f162(x122581,x122582)))), % 191.49/191.45 inference(rename_variables,[],[3514])). % 191.49/191.45 cnf(12261,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x122611),f881(x122611))),f333(f333(f263(f881(x122611),f881(x122611)),x122612),f118(x122611))),f146(x122611,x122613)))), % 191.49/191.45 inference(rename_variables,[],[4592])). % 191.49/191.45 cnf(12264,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x122641),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12266,plain, % 191.49/191.45 (~P4(f333(f63(x122661),f258(f890(x122661,a874))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,11078,12111,3561,3562,3280,4522,4523,3185,4506,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,4503,10466,10559,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,3243,11625,3254,3768,11010,11631,4068,3145,3965,3856,11402,3210,3176,3171,3153,3154,3159,3190,3326,12059,3375,10848,3242,3264,10507,3418,4578,3938,4512,10299,10463,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,3941,11019,11145,11196,4592,10951,11150,11255,11277,11312,11318,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,3675,4369,4370,3615,3823,3866,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,3756,11616,3295,3395,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3506,4577,4075,11272,3634,3355,11745,11748,4045,4005,11889,12229,3950,10845,12047,12070,4000,11025,12108,12181,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,12096,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,3470,10640,10904,10948,11218,11296,11461,11701,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,3787,4567,3798,3834,4546,4548,3286,3287,4547,4550,4551,4590,3806,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,4012,3905,11340,11676,11680,3750,10964,10970,10985,11921,3611,11187,12155,3752,10705,11041,11193,11223,11234,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,11486,12217,4180,10838,12238,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151])). % 191.49/191.45 cnf(12267,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122671,a874)),x122672),x122672))), % 191.49/191.45 inference(rename_variables,[],[3611])). % 191.49/191.45 cnf(12270,plain, % 191.49/191.45 (~P4(f333(f333(f335(x122701),x122702),f194(f890(x122701,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12273,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x122731,f890(x122732,a874))),x122733),x122734))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(12276,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122761,a874)),f333(f312(x122762,x122761,x122763),f333(f313(x122762,x122761,x122763),x122764))),x122764))), % 191.49/191.45 inference(rename_variables,[],[4180])). % 191.49/191.45 cnf(12277,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122771,a874)),x122772),x122772))), % 191.49/191.45 inference(rename_variables,[],[3611])). % 191.49/191.45 cnf(12282,plain, % 191.49/191.45 (E(f333(f259(x122821,x122821),f260(x122821,x122822)),x122822)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12285,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x122851,a874)),f333(f173(x122851),f171(x122851,x122852,x122853))),f333(f173(x122851),x122853)))), % 191.49/191.45 inference(rename_variables,[],[4000])). % 191.49/191.45 cnf(12286,plain, % 191.49/191.45 (P4(f333(f63(x122861),f333(f173(x122861),x122862)))), % 191.49/191.45 inference(rename_variables,[],[3355])). % 191.49/191.45 cnf(12289,plain, % 191.49/191.45 (P4(f333(f333(f201(a24),x122891),x122891))), % 191.49/191.45 inference(rename_variables,[],[3312])). % 191.49/191.45 cnf(12292,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x122921),x122921))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12295,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x122951),x122951))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12306,plain, % 191.49/191.45 (P28(x123061,x123061,f7(x123061),x123062)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12313,plain, % 191.49/191.45 (~P4(f333(f333(f335(x123131),x123132),f194(f890(x123131,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12316,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x123161,x123161)),f333(f333(f263(x123161,x123161),x123162),x123162)),f309(x123161,x123163)))), % 191.49/191.45 inference(rename_variables,[],[3941])). % 191.49/191.45 cnf(12319,plain, % 191.49/191.45 (~P4(f333(f333(f335(x123191),x123192),f194(f890(x123191,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12322,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x123221,x123221)),f333(f333(f263(x123221,x123221),x123222),x123222)),f309(x123221,x123223)))), % 191.49/191.45 inference(rename_variables,[],[3941])). % 191.49/191.45 cnf(12329,plain, % 191.49/191.45 (~E(f333(f333(f152(x123291),x123292),x123293),x123293)), % 191.49/191.45 inference(rename_variables,[],[4512])). % 191.49/191.45 cnf(12332,plain, % 191.49/191.45 (P4(f333(f333(f335(x123321),x123322),f258(f890(x123321,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(12333,plain, % 191.49/191.45 (~E(f333(a117,x123331),x123331)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(12336,plain, % 191.49/191.45 (P4(f333(f333(f335(f881(x123361)),f118(x123361)),f162(x123361,x123362)))), % 191.49/191.45 inference(rename_variables,[],[3514])). % 191.49/191.45 cnf(12337,plain, % 191.49/191.45 (~E(f333(f333(f152(x123371),x123372),x123373),f118(x123371))), % 191.49/191.45 inference(rename_variables,[],[4521])). % 191.49/191.45 cnf(12340,plain, % 191.49/191.45 (P4(f333(f333(f335(x123401),f333(x123402,x123403)),f333(f312(x123404,x123401,x123402),f258(f890(x123404,a874)))))), % 191.49/191.45 inference(rename_variables,[],[3905])). % 191.49/191.45 cnf(12341,plain, % 191.49/191.45 (P28(x123411,x123411,f7(x123411),x123412)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12344,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x123441,a874)),f194(f890(x123441,a874))),x123442))), % 191.49/191.45 inference(rename_variables,[],[3752])). % 191.49/191.45 cnf(12345,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x123451,a874)),x123452),x123452))), % 191.49/191.45 inference(rename_variables,[],[3611])). % 191.49/191.45 cnf(12348,plain, % 191.49/191.45 (P4(f333(f333(f335(x123481),f333(x123482,x123483)),f333(f312(x123484,x123481,x123482),f258(f890(x123484,a874)))))), % 191.49/191.45 inference(rename_variables,[],[3905])). % 191.49/191.45 cnf(12349,plain, % 191.49/191.45 (P28(x123491,x123491,f7(x123491),x123492)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12352,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(f881(x123521),f881(x123521))),f333(f333(f263(f881(x123521),f881(x123521)),f118(x123521)),f118(x123521))),f159(x123521,x123522)))), % 191.49/191.45 inference(rename_variables,[],[4081])). % 191.49/191.45 cnf(12355,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x123551),x123551))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12356,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x123561),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12362,plain, % 191.49/191.45 (P28(x123621,x123621,f7(x123621),x123622)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12365,plain, % 191.49/191.45 (E(f333(f333(f127(x123651),x123652),f118(x123651)),x123652)), % 191.49/191.45 inference(rename_variables,[],[3243])). % 191.49/191.45 cnf(12366,plain, % 191.49/191.45 (~E(f333(f333(f152(x123661),x123662),x123663),x123663)), % 191.49/191.45 inference(rename_variables,[],[4512])). % 191.49/191.45 cnf(12369,plain, % 191.49/191.45 (E(f333(f333(f127(x123691),x123692),f118(x123691)),x123692)), % 191.49/191.45 inference(rename_variables,[],[3243])). % 191.49/191.45 cnf(12370,plain, % 191.49/191.45 (~E(f333(f333(f152(x123701),x123702),x123703),x123703)), % 191.49/191.45 inference(rename_variables,[],[4512])). % 191.49/191.45 cnf(12373,plain, % 191.49/191.45 (E(f333(f333(f127(x123731),x123732),f118(x123731)),x123732)), % 191.49/191.45 inference(rename_variables,[],[3243])). % 191.49/191.45 cnf(12382,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x123821,a874)),x123822),f258(f890(x123821,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(12386,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x123861),x123861))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12387,plain, % 191.49/191.45 (~E(f333(a117,x123871),x123871)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(12390,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x123901,a874)),f194(f890(x123901,a874))),x123902))), % 191.49/191.45 inference(rename_variables,[],[3752])). % 191.49/191.45 cnf(12393,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x123931),x123931))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(12396,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x123961,a874)),x123962),x123962))), % 191.49/191.45 inference(rename_variables,[],[3611])). % 191.49/191.45 cnf(12401,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x124011,a874)),x124012),f333(f333(f311(x124011),x124013),x124012)))), % 191.49/191.45 inference(rename_variables,[],[3750])). % 191.49/191.45 cnf(12404,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x124041,a874)),x124042),x124042))), % 191.49/191.45 inference(rename_variables,[],[3611])). % 191.49/191.45 cnf(12405,plain, % 191.49/191.45 (~P4(f333(f333(f335(x124051),x124052),f194(f890(x124051,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12408,plain, % 191.49/191.45 (~P4(f333(f333(f335(x124081),x124082),f194(f890(x124081,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12416,plain, % 191.49/191.45 (~P4(f333(f333(f250(f890(f889(x124161,x124161),a874)),f333(f312(f889(x124161,x124161),f889(x124161,x124161),f7(f889(x124161,x124161))),f258(f890(f889(x124161,x124161),a874)))),f333(f312(f889(x124161,x124161),f889(x124161,x124161),f7(f889(x124161,x124161))),f333(a117,f258(f890(f889(x124161,x124161),a874))))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,3561,3562,3280,4522,4523,3185,4506,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,4503,10466,10559,3372,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,3243,11625,12365,12369,3254,3768,11010,11631,4068,3145,3965,4499,3856,11402,3210,3176,3171,3153,3154,3159,3190,3326,12059,3375,10848,12172,3241,3242,3264,10507,3418,4578,3938,4512,10299,10463,11261,12329,12366,4521,12337,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,12352,3941,11019,11145,11196,12316,12322,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3823,3866,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,3756,11616,3295,3395,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3702,3506,4577,4075,11272,3634,3355,11745,11748,12182,4045,4005,11889,12229,3950,10845,12047,12070,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,12096,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,3470,10640,10904,10948,11218,11296,11461,11701,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,3377,10669,10699,10708,11247,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,3787,4567,3798,3834,4546,4548,3286,3287,4547,4550,4551,4590,3806,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,3905,11340,11676,11680,11742,12340,3750,10964,10970,10985,11921,12129,3611,11187,12155,12267,12277,12345,12396,3752,10705,11041,11193,11223,11234,12235,12344,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,11486,12217,12226,4180,10838,12238,12250,4087,3786,3731,4582,10318,10321,10657,10660,11497,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,889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% 191.49/191.45 cnf(12417,plain, % 191.49/191.45 (P28(x124171,x124171,f7(x124171),x124172)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12420,plain, % 191.49/191.45 (E(f333(f195(f881(x124201)),f333(f169(x124201),x124202)),f333(f195(f881(x124201)),x124202))), % 191.49/191.45 inference(rename_variables,[],[3326])). % 191.49/191.45 cnf(12423,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x124231),x124231))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12424,plain, % 191.49/191.45 (P4(f333(f258(f890(x124241,a874)),x124242))), % 191.49/191.45 inference(rename_variables,[],[3377])). % 191.49/191.45 cnf(12427,plain, % 191.49/191.45 (~P4(f333(f333(f335(x124271),x124272),f194(f890(x124271,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12430,plain, % 191.49/191.45 (P4(f333(f333(f335(x124301),f333(x124302,x124303)),f333(f312(x124304,x124301,x124302),f258(f890(x124304,a874)))))), % 191.49/191.45 inference(rename_variables,[],[3905])). % 191.49/191.45 cnf(12431,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x124311,x124311)),f333(f333(f263(x124311,x124311),x124312),x124312)),f309(x124311,x124313)))), % 191.49/191.45 inference(rename_variables,[],[3941])). % 191.49/191.45 cnf(12434,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x124341,x124341)),f333(f333(f263(x124341,x124341),x124342),x124342)),f309(x124341,x124343)))), % 191.49/191.45 inference(rename_variables,[],[3941])). % 191.49/191.45 cnf(12437,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x124371),x124371))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(12438,plain, % 191.49/191.45 (P4(f333(f258(f890(x124381,a874)),x124382))), % 191.49/191.45 inference(rename_variables,[],[3377])). % 191.49/191.45 cnf(12441,plain, % 191.49/191.45 (P4(f333(f63(x124411),f333(f173(x124411),x124412)))), % 191.49/191.45 inference(rename_variables,[],[3355])). % 191.49/191.45 cnf(12451,plain, % 191.49/191.45 (~P4(f333(f333(f194(f890(x124511,f890(x124512,a874))),x124513),x124514))), % 191.49/191.45 inference(rename_variables,[],[4585])). % 191.49/191.45 cnf(12454,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x124541,a874)),x124542),f258(f890(x124541,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(12457,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(x124571,x124571)),f333(f333(f263(x124571,x124571),x124572),x124572)),f309(x124571,x124573)))), % 191.49/191.45 inference(rename_variables,[],[3941])). % 191.49/191.45 cnf(12460,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x124601),x124602)),x124602))), % 191.49/191.45 inference(rename_variables,[],[4582])). % 191.49/191.45 cnf(12461,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x124611),f333(a117,x124611)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(12464,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x124641,a874)),f333(f173(x124641),f333(f137(x124641,x124642),x124643))),f333(f173(x124641),x124643)))), % 191.49/191.45 inference(rename_variables,[],[3950])). % 191.49/191.45 cnf(12467,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x124671,a874)),x124672),f258(f890(x124671,a874))))), % 191.49/191.45 inference(rename_variables,[],[3693])). % 191.49/191.45 cnf(12470,plain, % 191.49/191.45 (E(f333(f259(x124701,x124701),f260(x124701,x124702)),x124702)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12481,plain, % 191.49/191.45 (~P4(f333(f333(f335(x124811),x124812),f194(f890(x124811,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12482,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(f881(x124821),f881(x124821))),f333(f333(f263(f881(x124821),f881(x124821)),f118(x124821)),f118(x124821))),f159(x124821,x124822)))), % 191.49/191.45 inference(rename_variables,[],[4081])). % 191.49/191.45 cnf(12484,plain, % 191.49/191.45 (P4(f333(f333(f335(f889(a880,a880)),f333(f333(f263(a880,a880),f333(a117,x124841)),f333(a117,f333(a117,x124841)))),f333(f333(f290(a880,a880,a880),f309(a880,a323)),f309(a880,f309(a880,a323)))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,3561,3562,3280,4522,4523,3185,4506,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,4503,10466,10559,3372,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3650,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3145,3965,4499,3856,11402,3210,3176,3171,3153,3154,3159,3190,3326,12059,12201,3375,10848,12172,3241,3242,3264,10507,3418,4578,3938,4512,10299,10463,11261,12329,12366,4521,12337,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,12352,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3823,3866,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,3756,11616,3295,3395,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3702,4218,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,4045,4005,11889,12229,3950,10845,12047,12070,12242,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,12096,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,3470,10640,10904,10948,11218,11296,11461,11701,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,3377,10669,10699,10708,11247,11800,12424,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,3787,4567,3798,3834,4546,4548,3286,3287,4547,4550,4551,4590,3806,3624,4226,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,3905,11340,11676,11680,11742,12340,12348,3750,10964,10970,10985,11921,12129,3611,11187,12155,12267,12277,12345,12396,4079,3752,10705,11041,11193,11223,11234,12235,12344,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,4180,10838,12238,12250,4087,3786,3731,4582,10318,10321,10657,10660,11497,11677,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519])). % 191.49/191.45 cnf(12487,plain, % 191.49/191.45 (~P4(f333(f333(f335(x124871),x124872),f194(f890(x124871,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12490,plain, % 191.49/191.45 (P34(x124901,x124902,f118(x124901))), % 191.49/191.45 inference(rename_variables,[],[3248])). % 191.49/191.45 cnf(12493,plain, % 191.49/191.45 (E(f333(f195(f881(x124931)),f333(f169(x124931),x124932)),f333(f195(f881(x124931)),x124932))), % 191.49/191.45 inference(rename_variables,[],[3326])). % 191.49/191.45 cnf(12496,plain, % 191.49/191.45 (~P4(f333(f333(f335(x124961),x124962),f194(f890(x124961,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12503,plain, % 191.49/191.45 (~P4(f333(f333(f335(f889(f881(x125031),f881(x125031))),f333(f333(f263(f881(x125031),f881(x125031)),x125032),x125032)),f148(x125031,f154(x125031,f118(f890(x125031,a880))))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,3561,3562,3280,3248,4522,4523,3185,4506,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,4503,10466,10559,3372,3521,3230,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,3004,3027,3046,3053,3054,3056,3058,3077,3084,3101,4483,3650,3155,11351,3356,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3145,3965,4499,3856,11402,3210,3176,3171,3153,3154,3159,3190,3326,12059,12201,12420,3375,10848,12172,3241,3242,3264,10507,3418,4578,3938,4512,10299,10463,11261,12329,12366,4521,12337,3302,11721,4570,11013,11083,11304,11307,3419,3205,3206,10365,10672,3475,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3823,3866,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,3756,11616,3295,3395,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,4574,11500,11531,11566,11596,3743,3523,3888,3341,3342,3316,4557,4508,3702,4218,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,4045,4005,11889,12229,3950,10845,12047,12070,12242,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,12096,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,3470,10640,10904,10948,11218,11296,11461,11701,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,3377,10669,10699,10708,11247,11800,12424,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,3787,4567,3798,3834,4546,4548,3286,3287,4547,4550,4551,4590,3806,3624,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,3905,11340,11676,11680,11742,12340,12348,3750,10964,10970,10985,11921,12129,3611,11187,12155,12267,12277,12345,12396,4079,3752,10705,11041,11193,11223,11234,12235,12344,3580,10626,10629,10711,10883,4584,11613,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,4180,10838,12238,12250,4087,3786,3731,4582,10318,10321,10657,10660,11497,11677,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906])). % 191.49/191.45 cnf(12505,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x125051),x125051))), % 191.49/191.45 inference(rename_variables,[],[4556])). % 191.49/191.45 cnf(12508,plain, % 191.49/191.45 (P4(f333(f333(f335(x125081),x125082),f258(f890(x125081,a874))))), % 191.49/191.45 inference(rename_variables,[],[3470])). % 191.49/191.45 cnf(12512,plain, % 191.49/191.45 (P27(x125121,x125122,f333(f333(f311(f879(x125121)),f333(f333(f333(f93(x125121),f333(f333(f9(x125121,f890(a875,a874),f890(a875,a874)),f333(f333(f10(f890(a875,f890(a874,a874)),f890(f890(a875,a874),f890(a875,a874)),x125121),f20(a875,a874,a874)),f333(f333(f10(f890(a875,a874),f890(a875,f890(a874,a874)),x125121),f333(f10(a874,f890(a874,a874),a875),a331)),x125123))),f333(f333(f10(a874,a874,a875),a328),x125124))),f33(x125124,x125125)),x125123)),f194(f890(f879(x125121),a874))))), % 191.49/191.45 inference(rename_variables,[],[4466])). % 191.49/191.45 cnf(12515,plain, % 191.49/191.45 (P4(f333(f333(f250(f890(x125151,a874)),x125152),x125152))), % 191.49/191.45 inference(rename_variables,[],[3611])). % 191.49/191.45 cnf(12518,plain, % 191.49/191.45 (~P4(f333(f333(f335(x125181),x125182),f194(f890(x125181,a874))))), % 191.49/191.45 inference(rename_variables,[],[4572])). % 191.49/191.45 cnf(12521,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),f2(a1)),f333(f333(f264(a1),f333(f76(a1),x125211)),x125212)))), % 191.49/191.45 inference(rename_variables,[],[3786])). % 191.49/191.45 cnf(12524,plain, % 191.49/191.45 (~E(f333(a117,x125241),x125241)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(12526,plain, % 191.49/191.45 (E(f333(f259(x125261,x125261),f260(x125261,x125262)),x125262)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12531,plain, % 191.49/191.45 (E(f333(f259(x125311,x125311),f260(x125311,x125312)),x125312)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12533,plain, % 191.49/191.45 (E(f333(f259(x125331,x125331),f260(x125331,x125332)),x125332)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12537,plain, % 191.49/191.45 (P28(x125371,x125371,f7(x125371),x125372)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12539,plain, % 191.49/191.45 (P28(x125391,x125391,f7(x125391),x125392)), % 191.49/191.45 inference(rename_variables,[],[3551])). % 191.49/191.45 cnf(12550,plain, % 191.49/191.45 (E(f333(f259(x125501,x125501),f260(x125501,x125502)),x125502)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12552,plain, % 191.49/191.45 (P40(x125521,f154(x125521,x125522))), % 191.49/191.45 inference(rename_variables,[],[3185])). % 191.49/191.45 cnf(12556,plain, % 191.49/191.45 (E(f333(f259(x125561,x125561),f260(x125561,x125562)),x125562)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12568,plain, % 191.49/191.45 (E(f333(f259(x125681,x125681),f260(x125681,x125682)),x125682)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12570,plain, % 191.49/191.45 (E(f333(f259(x125701,x125701),f260(x125701,x125702)),x125702)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12572,plain, % 191.49/191.45 (E(f333(f259(x125721,x125721),f260(x125721,x125722)),x125722)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12574,plain, % 191.49/191.45 (P50(x125741,x125742,f260(x125741,x125742))), % 191.49/191.45 inference(rename_variables,[],[3279])). % 191.49/191.45 cnf(12576,plain, % 191.49/191.45 (P50(x125761,x125762,f260(x125761,x125762))), % 191.49/191.45 inference(rename_variables,[],[3279])). % 191.49/191.45 cnf(12580,plain, % 191.49/191.45 (P54(x125801,x125801,f260(x125801,x125802))), % 191.49/191.45 inference(rename_variables,[],[3280])). % 191.49/191.45 cnf(12586,plain, % 191.49/191.45 (P55(x125861,f194(f890(x125861,a874)),x125862)), % 191.49/191.45 inference(rename_variables,[],[3333])). % 191.49/191.45 cnf(12595,plain, % 191.49/191.45 (E(f333(f259(x125951,x125951),f260(x125951,x125952)),x125952)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12597,plain, % 191.49/191.45 (P44(x125971,x125972,x125973,x125974,f194(f890(x125971,a874)),x125974)), % 191.49/191.45 inference(rename_variables,[],[4248])). % 191.49/191.45 cnf(12600,plain, % 191.49/191.45 (P44(x126001,x126002,x126003,x126004,f194(f890(x126001,a874)),x126004)), % 191.49/191.45 inference(rename_variables,[],[4248])). % 191.49/191.45 cnf(12614,plain, % 191.49/191.45 (P30(x126141,f2(a880),f333(f333(f333(f93(x126141),x126142),f333(a26,x126143)),x126144))), % 191.49/191.45 inference(rename_variables,[],[3686])). % 191.49/191.45 cnf(12620,plain, % 191.49/191.45 (E(f333(f259(x126201,x126201),f260(x126201,x126202)),x126202)), % 191.49/191.45 inference(rename_variables,[],[3269])). % 191.49/191.45 cnf(12624,plain, % 191.49/191.45 (P18(x126241,f890(x126241,a874),f311(x126241))), % 191.49/191.45 inference(rename_variables,[],[3283])). % 191.49/191.45 cnf(12630,plain, % 191.49/191.45 (P35(x126301,x126302,f118(x126301),f118(x126301))), % 191.49/191.45 inference(rename_variables,[],[3561])). % 191.49/191.45 cnf(12632,plain, % 191.49/191.45 (P35(x126321,x126322,f118(x126321),f118(x126321))), % 191.49/191.45 inference(rename_variables,[],[3561])). % 191.49/191.45 cnf(12637,plain, % 191.49/191.45 (P41(x126371,f197(x126371))), % 191.49/191.45 inference(rename_variables,[],[3142])). % 191.49/191.45 cnf(12646,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),f2(a880)),f333(a117,x126461)))), % 191.49/191.45 inference(rename_variables,[],[3395])). % 191.49/191.45 cnf(12647,plain, % 191.49/191.45 (~E(f333(a117,x126471),x126471)), % 191.49/191.45 inference(rename_variables,[],[4487])). % 191.49/191.45 cnf(12653,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x126531),f333(a117,x126531)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(12658,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x126581),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12661,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x126611),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12668,plain, % 191.49/191.45 (~P4(f333(f333(f251(a1),f333(f105(a1),x126681)),f333(f80(a1),f333(f105(a1),x126682))))), % 191.49/191.45 inference(rename_variables,[],[4580])). % 191.49/191.45 cnf(12678,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x126781),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12681,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x126811),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12684,plain, % 191.49/191.45 (P4(f333(f63(a880),f306(a880,x126841,x126842)))), % 191.49/191.45 inference(rename_variables,[],[3524])). % 191.49/191.45 cnf(12687,plain, % 191.49/191.45 (P4(f333(f63(a880),f306(a880,x126871,x126872)))), % 191.49/191.45 inference(rename_variables,[],[3524])). % 191.49/191.45 cnf(12690,plain, % 191.49/191.45 (P4(f333(f63(a880),f306(a880,x126901,x126902)))), % 191.49/191.45 inference(rename_variables,[],[3524])). % 191.49/191.45 cnf(12693,plain, % 191.49/191.45 (P4(f333(f63(a880),f306(a880,x126931,x126932)))), % 191.49/191.45 inference(rename_variables,[],[3524])). % 191.49/191.45 cnf(12700,plain, % 191.49/191.45 (P4(f333(f333(f250(a1),f333(f80(a1),f333(f105(a1),x127001))),f333(f105(a1),x127002)))), % 191.49/191.45 inference(rename_variables,[],[3787])). % 191.49/191.45 cnf(12703,plain, % 191.49/191.45 (~P4(f333(f333(f251(a880),x127031),f2(a880)))), % 191.49/191.45 inference(rename_variables,[],[4560])). % 191.49/191.45 cnf(12704,plain, % 191.49/191.45 (P4(f333(f333(f250(a880),x127041),x127041))), % 191.49/191.45 inference(rename_variables,[],[3313])). % 191.49/191.45 cnf(12711,plain, % 191.49/191.45 (P4(f333(f333(f251(a880),x127111),f333(a117,x127111)))), % 191.49/191.45 inference(rename_variables,[],[3383])). % 191.49/191.45 cnf(12714,plain, % 191.49/191.45 (P4(f333(f333(f335(x127141),f333(x127142,x127143)),f333(f312(x127144,x127141,x127142),f258(f890(x127144,a874)))))), % 191.49/191.45 inference(rename_variables,[],[3905])). % 191.49/191.45 cnf(12715,plain, % 191.49/191.45 (~E(f333(a117,x127151),f2(a880))), % 191.49/191.45 inference(rename_variables,[],[4497])). % 191.49/191.45 cnf(12717,plain, % 191.49/191.45 (~P4(f333(f333(f251(a1),f2(a1)),f333(f108(a1),f2(a1))))), % 191.49/191.45 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,4503,10466,10559,3372,3333,12586,3521,3230,4497,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,3004,3026,3027,3046,3053,3054,3056,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,4521,12337,3302,11721,4570,11013,11083,11304,11307,3396,3711,3419,3635,3386,3205,3206,10365,10672,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3653,3823,3866,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,3756,11616,3295,3395,11736,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,4574,11500,11531,11566,11596,3743,3523,3524,12684,12687,12690,3888,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,4045,4005,11889,12229,3950,10845,12047,12070,12242,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,3315,3391,12096,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,3470,10640,10904,10948,11218,11296,11461,11701,12332,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,3377,10669,10699,10708,11247,11800,12424,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,3787,11751,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,3806,3624,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,3750,10964,10970,10985,11921,12129,3611,11187,12155,12267,12277,12345,12396,12404,4079,3752,10705,11041,11193,11223,11234,12235,12344,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,4087,3786,3731,3732,4582,10318,10321,10657,10660,11497,11677,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279])). % 191.49/191.46 cnf(12719,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),f333(f108(a1),a84)),f2(a1)))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,4503,10466,10559,3372,3333,12586,3521,3230,4497,2898,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,3004,3026,3027,3046,3053,3054,3056,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,4521,12337,3302,11721,4570,11013,11083,11304,11307,3396,3711,3419,3635,3386,3205,3206,10365,10672,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3653,3823,3866,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,3756,11616,3295,3395,11736,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,4574,11500,11531,11566,11596,3743,3523,3524,12684,12687,12690,3888,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,4045,4005,11889,12229,3950,10845,12047,12070,12242,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,3315,3391,12096,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,3470,10640,10904,10948,11218,11296,11461,11701,12332,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,3377,10669,10699,10708,11247,11800,12424,3414,3408,3827,3765,10342,11619,11649,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,3787,11751,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,3806,3624,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,3750,10964,10970,10985,11921,12129,3611,11187,12155,12267,12277,12345,12396,12404,4079,3752,10705,11041,11193,11223,11234,12235,12344,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,4087,3786,3731,3732,4582,10318,10321,10657,10660,11497,11677,4583,11593,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,68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% 191.49/191.46 cnf(12720,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),x127201),x127201))), % 191.49/191.46 inference(rename_variables,[],[3314])). % 191.49/191.46 cnf(12723,plain, % 191.49/191.46 (P4(f333(f63(a880),f306(a880,x127231,x127232)))), % 191.49/191.46 inference(rename_variables,[],[3524])). % 191.49/191.46 cnf(12726,plain, % 191.49/191.46 (P4(f333(f63(a880),f306(a880,x127261,x127262)))), % 191.49/191.46 inference(rename_variables,[],[3524])). % 191.49/191.46 cnf(12729,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x127291),x127291))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12742,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x127421),f333(a117,x127421)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(12747,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),f46(a880,x127471,x127472)),x127471))), % 191.49/191.46 inference(rename_variables,[],[3765])). % 191.49/191.46 cnf(12754,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x127541),f333(a117,x127541)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(12755,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),x127551),f2(a880)))), % 191.49/191.46 inference(rename_variables,[],[4560])). % 191.49/191.46 cnf(12764,plain, % 191.49/191.46 (~P4(f333(f333(f251(a1),f333(f105(a1),x127641)),f2(a1)))), % 191.49/191.46 inference(rename_variables,[],[4574])). % 191.49/191.46 cnf(12765,plain, % 191.49/191.46 (P4(f333(f258(f890(x127651,a874)),x127652))), % 191.49/191.46 inference(rename_variables,[],[3377])). % 191.49/191.46 cnf(12768,plain, % 191.49/191.46 (~P4(f333(f333(f251(a1),f333(f105(a1),x127681)),f2(a1)))), % 191.49/191.46 inference(rename_variables,[],[4574])). % 191.49/191.46 cnf(12769,plain, % 191.49/191.46 (P4(f333(f258(f890(x127691,a874)),x127692))), % 191.49/191.46 inference(rename_variables,[],[3377])). % 191.49/191.46 cnf(12772,plain, % 191.49/191.46 (P4(f333(f258(f890(x127721,a874)),x127722))), % 191.49/191.46 inference(rename_variables,[],[3377])). % 191.49/191.46 cnf(12783,plain, % 191.49/191.46 (~P4(f333(f333(f335(x127831),x127832),f194(f890(x127831,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(12784,plain, % 191.49/191.46 (P4(f333(f63(x127841),f194(f890(x127841,a874))))), % 191.49/191.46 inference(rename_variables,[],[3391])). % 191.49/191.46 cnf(12793,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),f2(a880)),x127931))), % 191.49/191.46 inference(rename_variables,[],[3335])). % 191.49/191.46 cnf(12796,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x127961),f333(a117,x127961)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(12797,plain, % 191.49/191.46 (~E(f333(a117,x127971),x127971)), % 191.49/191.46 inference(rename_variables,[],[4487])). % 191.49/191.46 cnf(12800,plain, % 191.49/191.46 (~P4(f333(f333(f335(x128001),x128002),f194(f890(x128001,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(12803,plain, % 191.49/191.46 (~P4(f333(f333(f335(x128031),x128032),f194(f890(x128031,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(12806,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128061),x128061))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12813,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128131),x128131))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12817,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x128171),f333(a117,x128171)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(12820,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128201),x128201))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12825,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128251),x128251))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12828,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128281),x128281))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12831,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128311),x128311))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12834,plain, % 191.49/191.46 (E(f333(f333(f3(f890(x128341,a874)),f194(f890(x128341,a874))),x128342),f194(f890(x128341,a874)))), % 191.49/191.46 inference(rename_variables,[],[3583])). % 191.49/191.46 cnf(12835,plain, % 191.49/191.46 (P4(f333(f63(x128351),f194(f890(x128351,a874))))), % 191.49/191.46 inference(rename_variables,[],[3391])). % 191.49/191.46 cnf(12838,plain, % 191.49/191.46 (E(f333(f333(f3(f890(x128381,a874)),f194(f890(x128381,a874))),x128382),f194(f890(x128381,a874)))), % 191.49/191.46 inference(rename_variables,[],[3583])). % 191.49/191.46 cnf(12839,plain, % 191.49/191.46 (P4(f333(f63(x128391),f194(f890(x128391,a874))))), % 191.49/191.46 inference(rename_variables,[],[3391])). % 191.49/191.46 cnf(12842,plain, % 191.49/191.46 (E(f333(f333(f3(f890(x128421,a874)),f194(f890(x128421,a874))),x128422),f194(f890(x128421,a874)))), % 191.49/191.46 inference(rename_variables,[],[3583])). % 191.49/191.46 cnf(12843,plain, % 191.49/191.46 (P4(f333(f63(x128431),f194(f890(x128431,a874))))), % 191.49/191.46 inference(rename_variables,[],[3391])). % 191.49/191.46 cnf(12846,plain, % 191.49/191.46 (E(f333(f333(f3(f890(x128461,a874)),f194(f890(x128461,a874))),x128462),f194(f890(x128461,a874)))), % 191.49/191.46 inference(rename_variables,[],[3583])). % 191.49/191.46 cnf(12847,plain, % 191.49/191.46 (P4(f333(f63(x128471),f194(f890(x128471,a874))))), % 191.49/191.46 inference(rename_variables,[],[3391])). % 191.49/191.46 cnf(12851,plain, % 191.49/191.46 (E(f333(f259(x128511,x128511),f260(x128511,x128512)),x128512)), % 191.49/191.46 inference(rename_variables,[],[3269])). % 191.49/191.46 cnf(12856,plain, % 191.49/191.46 (E(f333(f333(f3(f890(x128561,a874)),f194(f890(x128561,a874))),x128562),f194(f890(x128561,a874)))), % 191.49/191.46 inference(rename_variables,[],[3583])). % 191.49/191.46 cnf(12857,plain, % 191.49/191.46 (P4(f333(f63(x128571),f194(f890(x128571,a874))))), % 191.49/191.46 inference(rename_variables,[],[3391])). % 191.49/191.46 cnf(12861,plain, % 191.49/191.46 (P4(f333(f63(x128611),f194(f890(x128611,a874))))), % 191.49/191.46 inference(rename_variables,[],[3391])). % 191.49/191.46 cnf(12864,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128641),x128641))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12870,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),x128701),x128701))), % 191.49/191.46 inference(rename_variables,[],[3314])). % 191.49/191.46 cnf(12873,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x128731),f333(a117,x128731)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(12876,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128761),x128761))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12879,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x128791),f333(a117,x128791)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(12894,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x128941),x128941))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12897,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),x128971),x128971))), % 191.49/191.46 inference(rename_variables,[],[3314])). % 191.49/191.46 cnf(12900,plain, % 191.49/191.46 (~P4(f333(f333(f335(x129001),x129002),f194(f890(x129001,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(12911,plain, % 191.49/191.46 (P4(f333(f333(f335(x129111),x129112),f258(f890(x129111,a874))))), % 191.49/191.46 inference(rename_variables,[],[3470])). % 191.49/191.46 cnf(12917,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x129171,a874)),f333(f173(x129171),f333(f137(x129171,x129172),x129173))),f333(f173(x129171),x129173)))), % 191.49/191.46 inference(rename_variables,[],[3950])). % 191.49/191.46 cnf(12923,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),x129231),f2(a880)))), % 191.49/191.46 inference(rename_variables,[],[4560])). % 191.49/191.46 cnf(12924,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),x129241),x129241))), % 191.49/191.46 inference(rename_variables,[],[3314])). % 191.49/191.46 cnf(12928,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),x129281),f2(a880)))), % 191.49/191.46 inference(rename_variables,[],[4560])). % 191.49/191.46 cnf(12929,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),x129291),x129291))), % 191.49/191.46 inference(rename_variables,[],[3314])). % 191.49/191.46 cnf(12938,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x129381),x129381))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12945,plain, % 191.49/191.46 (E(f333(f333(f18(x129451,x129452),x129453),x129454),x129453)), % 191.49/191.46 inference(rename_variables,[],[3302])). % 191.49/191.46 cnf(12948,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x129481,a874)),f333(f173(x129481),f171(x129481,x129482,x129483))),f333(f173(x129481),x129483)))), % 191.49/191.46 inference(rename_variables,[],[4000])). % 191.49/191.46 cnf(12952,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),x129521),f2(a880)))), % 191.49/191.46 inference(rename_variables,[],[4560])). % 191.49/191.46 cnf(12953,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),x129531),x129531))), % 191.49/191.46 inference(rename_variables,[],[3314])). % 191.49/191.46 cnf(12957,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),x129571),f2(a880)))), % 191.49/191.46 inference(rename_variables,[],[4560])). % 191.49/191.46 cnf(12962,plain, % 191.49/191.46 (~P4(f333(f333(f251(f890(a880,a874)),f304(a880,f333(a117,x129621),f333(a117,x129621))),f304(a880,x129622,x129621)))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,4503,10466,10559,3372,3333,12586,3521,3230,4497,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3015,3017,3024,3026,3027,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,4521,12337,3302,11721,11724,4570,11013,11083,11304,11307,3396,3711,3419,3635,3386,3205,3206,10365,10672,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,3756,11616,3295,3395,11736,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,3888,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,12223,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,3806,3624,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,3750,10964,10970,10985,11921,12129,3611,11187,12155,12267,12277,12345,12396,12404,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482])). % 191.49/191.46 cnf(12963,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x129631),x129631))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12965,plain, % 191.49/191.46 (~P4(f333(f333(f250(f890(a880,a874)),f304(a880,f333(a117,x129651),f333(a117,x129651))),f304(a880,x129652,x129651)))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,4503,10466,10559,3372,3333,12586,3521,3230,4497,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3015,3017,3024,3026,3027,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,4521,12337,3302,11721,11724,4570,11013,11083,11304,11307,3396,3711,3419,3635,3386,3205,3206,10365,10672,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,3756,11616,3295,3395,11736,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,3888,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,3335,10702,10853,10924,11650,11805,11994,12223,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,3806,3624,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,3750,10964,10970,10985,11921,12129,3611,11187,12155,12267,12277,12345,12396,12404,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483])). % 191.49/191.46 cnf(12966,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x129661),x129661))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(12969,plain, % 191.49/191.46 (~P4(f333(f333(f250(a880),f333(a117,x129691)),x129691))), % 191.49/191.46 inference(rename_variables,[],[4569])). % 191.49/191.46 cnf(12974,plain, % 191.49/191.46 (E(x129741,f836(f333(f7(x129742),f333(f7(x129742),x129741)),f7(x129742),x129742,x129742))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,12539,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,4503,10466,10559,3372,3333,12586,3521,3230,4497,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3015,3017,3024,3026,3027,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3144,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,4521,12337,3302,11721,11724,4570,11013,11083,11304,11307,3396,3711,3419,3635,3386,3205,3206,10365,10672,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,3756,11616,3295,3395,11736,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,3888,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,4579,10793,11161,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,12966,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,12969,3335,10702,10853,10924,11650,11805,11994,12223,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,3806,3624,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,12714,3750,10964,10970,10985,11921,12129,3611,11187,12155,12267,12277,12345,12396,12404,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483,8484,8485,8631])). % 191.49/191.46 cnf(12975,plain, % 191.49/191.46 (P4(f333(f333(f335(x129751),f333(x129752,x129753)),f333(f312(x129754,x129751,x129752),f258(f890(x129754,a874)))))), % 191.49/191.46 inference(rename_variables,[],[3905])). % 191.49/191.46 cnf(12976,plain, % 191.49/191.46 (P28(x129761,x129761,f7(x129761),x129762)), % 191.49/191.46 inference(rename_variables,[],[3551])). % 191.49/191.46 cnf(12980,plain, % 191.49/191.46 (P4(f333(f333(f335(x129801),x129802),f258(f890(x129801,a874))))), % 191.49/191.46 inference(rename_variables,[],[3470])). % 191.49/191.46 cnf(12981,plain, % 191.49/191.46 (~P4(f333(f333(f335(x129811),x129812),f194(f890(x129811,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(12985,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x129851,a874)),x129852),f258(f890(x129851,a874))))), % 191.49/191.46 inference(rename_variables,[],[3693])). % 191.49/191.46 cnf(12986,plain, % 191.49/191.46 (P28(x129861,x129861,f7(x129861),x129862)), % 191.49/191.46 inference(rename_variables,[],[3551])). % 191.49/191.46 cnf(12990,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x129901,a874)),x129902),f258(f890(x129901,a874))))), % 191.49/191.46 inference(rename_variables,[],[3693])). % 191.49/191.46 cnf(12991,plain, % 191.49/191.46 (P28(x129911,x129911,f7(x129911),x129912)), % 191.49/191.46 inference(rename_variables,[],[3551])). % 191.49/191.46 cnf(12995,plain, % 191.49/191.46 (P28(x129951,x129951,f7(x129951),x129952)), % 191.49/191.46 inference(rename_variables,[],[3551])). % 191.49/191.46 cnf(12998,plain, % 191.49/191.46 (~P4(f333(f333(f251(f890(x129981,a874)),x129982),f194(f890(x129981,a874))))), % 191.49/191.46 inference(rename_variables,[],[4579])). % 191.49/191.46 cnf(13001,plain, % 191.49/191.46 (P28(x130011,x130011,f7(x130011),x130012)), % 191.49/191.46 inference(rename_variables,[],[3551])). % 191.49/191.46 cnf(13004,plain, % 191.49/191.46 (P28(x130041,x130041,f7(x130041),x130042)), % 191.49/191.46 inference(rename_variables,[],[3551])). % 191.49/191.46 cnf(13015,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x130151,a874)),f194(f890(x130151,a874))),x130152))), % 191.49/191.46 inference(rename_variables,[],[3752])). % 191.49/191.46 cnf(13019,plain, % 191.49/191.46 (E(f333(f259(x130191,x130191),f260(x130191,x130192)),x130192)), % 191.49/191.46 inference(rename_variables,[],[3269])). % 191.49/191.46 cnf(13023,plain, % 191.49/191.46 (~P4(f333(f333(f335(x130231),x130232),f194(f890(x130231,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13027,plain, % 191.49/191.46 (P4(f333(f333(f335(x130271),f333(x130272,x130273)),f333(f312(x130274,x130271,x130272),f258(f890(x130274,a874)))))), % 191.49/191.46 inference(rename_variables,[],[3905])). % 191.49/191.46 cnf(13028,plain, % 191.49/191.46 (P28(x130281,x130281,f7(x130281),x130282)), % 191.49/191.46 inference(rename_variables,[],[3551])). % 191.49/191.46 cnf(13031,plain, % 191.49/191.46 (P4(f333(f333(f335(x130311),x130312),f258(f890(x130311,a874))))), % 191.49/191.46 inference(rename_variables,[],[3470])). % 191.49/191.46 cnf(13038,plain, % 191.49/191.46 (~P4(f333(f333(f335(x130381),x130382),f194(f890(x130381,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13041,plain, % 191.49/191.46 (~P4(f333(f333(f335(x130411),x130412),f194(f890(x130411,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13045,plain, % 191.49/191.46 (E(f333(f333(f18(x130451,x130452),x130453),x130454),x130453)), % 191.49/191.46 inference(rename_variables,[],[3302])). % 191.49/191.46 cnf(13048,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x130481),f333(a117,x130481)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(13049,plain, % 191.49/191.46 (~E(f333(a117,x130491),x130491)), % 191.49/191.46 inference(rename_variables,[],[4487])). % 191.49/191.46 cnf(13052,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x130521),f333(a117,f333(f333(f81(a880),x130522),x130521))))), % 191.49/191.46 inference(rename_variables,[],[3754])). % 191.49/191.46 cnf(13053,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x130531),f333(a117,x130531)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(13055,plain, % 191.49/191.46 (~E(f333(f333(f82(a880),f333(a117,f2(a880))),f34(x130551,x130552)),f333(f333(f82(a880),f333(a117,f2(a880))),f33(x130553,x130554)))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,12539,12976,12986,12991,12995,13001,13004,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,12797,13049,4503,10466,10559,3372,3333,12586,3521,3230,4497,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2946,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3015,3017,3024,3026,3027,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,12851,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3144,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3191,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,12370,4521,12337,3302,11721,11724,12945,4570,11013,11083,11304,11307,3396,3711,3297,3419,3635,3386,3205,3206,10365,10672,4554,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,11207,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,13048,3756,11616,3295,3395,11736,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,3888,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,4000,11025,12108,12181,12241,12285,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,12985,12990,4579,10793,11161,12998,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,12966,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,12911,12980,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,12900,12981,13023,13038,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,12969,3335,10702,10853,10924,11650,11805,11994,12223,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,3806,3624,11612,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,12714,12975,13027,3750,10964,10970,10985,11921,12129,12401,3611,11187,12155,12267,12277,12345,12396,12404,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,12390,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,12276,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,10880,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483,8484,8485,8631,8838,8862,8863,8943,8957,9011,9012,9116,9161,9184,9216,9257,9448,9734,9927,9973,9975,6054,6422,6423,6509])). % 191.49/191.46 cnf(13062,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),f2(a1)),f333(f105(a1),x130621)))), % 191.49/191.46 inference(rename_variables,[],[3414])). % 191.49/191.46 cnf(13065,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),f2(a880)),x130651))), % 191.49/191.46 inference(rename_variables,[],[3335])). % 191.49/191.46 cnf(13066,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x130661),x130661))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(13069,plain, % 191.49/191.46 (~E(f333(a117,x130691),f2(a880))), % 191.49/191.46 inference(rename_variables,[],[4497])). % 191.49/191.46 cnf(13078,plain, % 191.49/191.46 (~P4(f333(f333(f335(x130781),x130782),f194(f890(x130781,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13081,plain, % 191.49/191.46 (P4(f333(f63(a880),f306(a880,x130811,x130812)))), % 191.49/191.46 inference(rename_variables,[],[3524])). % 191.49/191.46 cnf(13082,plain, % 191.49/191.46 (E(f333(f333(f248(a880),f333(a117,x130821)),f333(a117,x130822)),f333(a117,f333(f333(f248(a880),x130821),x130822)))), % 191.49/191.46 inference(rename_variables,[],[3486])). % 191.49/191.46 cnf(13085,plain, % 191.49/191.46 (P4(f333(f63(a880),f306(a880,x130851,x130852)))), % 191.49/191.46 inference(rename_variables,[],[3524])). % 191.49/191.46 cnf(13086,plain, % 191.49/191.46 (E(f333(f333(f249(a880),f333(a117,x130861)),f333(a117,x130862)),f333(a117,f333(f333(f249(a880),x130861),x130862)))), % 191.49/191.46 inference(rename_variables,[],[3487])). % 191.49/191.46 cnf(13089,plain, % 191.49/191.46 (P4(f333(f63(a880),f306(a880,x130891,x130892)))), % 191.49/191.46 inference(rename_variables,[],[3524])). % 191.49/191.46 cnf(13097,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x130971,a874)),f333(f173(x130971),f333(f137(x130971,x130972),x130973))),f333(f173(x130971),x130973)))), % 191.49/191.46 inference(rename_variables,[],[3950])). % 191.49/191.46 cnf(13098,plain, % 191.49/191.46 (E(f333(f333(f18(x130981,x130982),x130983),x130984),x130983)), % 191.49/191.46 inference(rename_variables,[],[3302])). % 191.49/191.46 cnf(13101,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x131011,a874)),f333(f173(x131011),f333(f333(f174(x131011),x131012),x131013))),f333(f173(x131011),x131013)))), % 191.49/191.46 inference(rename_variables,[],[3995])). % 191.49/191.46 cnf(13102,plain, % 191.49/191.46 (E(f333(f333(f18(x131021,x131022),x131023),x131024),x131023)), % 191.49/191.46 inference(rename_variables,[],[3302])). % 191.49/191.46 cnf(13106,plain, % 191.49/191.46 (E(f333(f333(f18(x131061,x131062),x131063),x131064),x131063)), % 191.49/191.46 inference(rename_variables,[],[3302])). % 191.49/191.46 cnf(13119,plain, % 191.49/191.46 (P4(f333(f333(f250(a1),f2(a1)),f333(f105(a1),x131191)))), % 191.49/191.46 inference(rename_variables,[],[3414])). % 191.49/191.46 cnf(13122,plain, % 191.49/191.46 (~P4(f333(f333(f335(x131221),x131222),f194(f890(x131221,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13125,plain, % 191.49/191.46 (~P4(f333(f333(f335(x131251),x131252),f194(f890(x131251,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13126,plain, % 191.49/191.46 (E(f333(f259(x131261,x131261),f260(x131261,x131262)),x131262)), % 191.49/191.46 inference(rename_variables,[],[3269])). % 191.49/191.46 cnf(13127,plain, % 191.49/191.46 (P28(x131271,x131271,f7(x131271),x131272)), % 191.49/191.46 inference(rename_variables,[],[3551])). % 191.49/191.46 cnf(13131,plain, % 191.49/191.46 (E(f333(f259(x131311,x131311),f260(x131311,x131312)),x131312)), % 191.49/191.46 inference(rename_variables,[],[3269])). % 191.49/191.46 cnf(13137,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x131371),f333(a117,x131371)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(13139,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x131391),x131391))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(13140,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),f2(a880)),x131401))), % 191.49/191.46 inference(rename_variables,[],[3335])). % 191.49/191.46 cnf(13143,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),x131431),f333(a117,x131431)))), % 191.49/191.46 inference(rename_variables,[],[3383])). % 191.49/191.46 cnf(13146,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),f2(a880)),x131461))), % 191.49/191.46 inference(rename_variables,[],[3335])). % 191.49/191.46 cnf(13150,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),f2(a880)),x131501))), % 191.49/191.46 inference(rename_variables,[],[3335])). % 191.49/191.46 cnf(13151,plain, % 191.49/191.46 (P4(f333(f333(f251(a880),f2(a880)),f333(a117,x131511)))), % 191.49/191.46 inference(rename_variables,[],[3395])). % 191.49/191.46 cnf(13152,plain, % 191.49/191.46 (E(f333(f259(x131521,x131521),f260(x131521,x131522)),x131522)), % 191.49/191.46 inference(rename_variables,[],[3269])). % 191.49/191.46 cnf(13155,plain, % 191.49/191.46 (P4(f333(f49(f333(f259(x131551,x131551),f260(x131551,f333(f333(f81(a880),f333(f333(f82(a880),f333(f262(a880,a880),f333(f333(f263(a880,a880),f2(a880)),x131552))),f333(a117,f333(f333(f81(a880),x131553),f333(f271(a880,a880),f333(f333(f263(a880,a880),f2(a880)),x131552)))))),f333(f271(a880,a880),f333(f333(f263(a880,a880),f2(a880)),x131552))))),f333(a117,f333(f333(f81(a880),x131553),f333(f271(a880,a880),f333(f333(f263(a880,a880),f2(a880)),x131552))))),f333(f333(f263(a880,a880),f2(a880)),x131552)))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,12539,12976,12986,12991,12995,13001,13004,13028,13127,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,12797,13049,4503,10466,10559,3372,3333,12586,3521,3230,4497,12715,13069,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2933,2943,2946,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3005,3015,3017,3018,3024,3026,3027,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,12851,13019,13126,13131,13152,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3144,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3191,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,12370,4521,12337,3302,11721,11724,12945,13045,13098,13102,13106,4570,11013,11083,11304,11307,3396,3711,3217,3297,3419,3635,3411,3386,3205,3206,10365,10672,4554,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,11207,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3496,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,13048,13053,13137,13143,3756,11616,3295,3395,11736,12646,13151,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,12726,13081,13085,13089,3888,3486,13082,3487,13086,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,12917,13097,3995,13101,4000,11025,12108,12181,12241,12285,12948,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,12985,12990,4579,10793,11161,12998,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,12966,13066,13139,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,12911,12980,13031,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,12900,12981,13023,13038,13041,13078,13122,13125,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,13062,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,12969,3335,10702,10853,10924,11650,11805,11994,12223,12793,13065,13140,13146,13150,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,4303,3806,3624,11612,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,12714,12975,13027,3750,10964,10970,10985,11921,12129,12401,3611,11187,12155,12267,12277,12345,12396,12404,12515,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,12390,13015,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,12276,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,10880,13052,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483,8484,8485,8631,8838,8862,8863,8943,8957,9011,9012,9116,9161,9184,9216,9257,9448,9734,9927,9973,9975,6054,6422,6423,6509,6524,6525,6932,7150,8557,8588,8774,8969,8970,9034,9035,9308,9309,9310,9311,9522,9816,10101,10185,10186,6491,8382,8383,8827,8845])). % 191.49/191.46 cnf(13171,plain, % 191.49/191.46 (E(f333(f333(f81(a880),f2(a880)),f844(f333(a117,f2(a880)),f2(a880))),f2(a880))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,12539,12976,12986,12991,12995,13001,13004,13028,13127,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,12797,13049,4503,10466,10559,3372,3333,12586,3521,3230,4497,12715,13069,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2931,2933,2943,2946,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3005,3015,3017,3018,3024,3026,3027,3030,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,12851,13019,13126,13131,13152,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3144,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3191,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,12370,4521,12337,3302,11721,11724,12945,13045,13098,13102,13106,4570,11013,11083,11304,11307,3396,3711,3217,3297,3419,3635,3411,3386,3205,3206,10365,10672,4554,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,11207,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3496,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,13048,13053,13137,13143,3756,11616,3295,3395,11736,12646,13151,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,12957,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,12726,13081,13085,13089,3888,3486,13082,3487,13086,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,12917,13097,3995,13101,4000,11025,12108,12181,12241,12285,12948,4001,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,12985,12990,4579,10793,11161,12998,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,12966,13066,13139,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,12911,12980,13031,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,12900,12981,13023,13038,13041,13078,13122,13125,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,13062,13119,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,12969,3335,10702,10853,10924,11650,11805,11994,12223,12793,13065,13140,13146,13150,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,4303,3806,3624,11612,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,12714,12975,13027,3750,10964,10970,10985,11921,12129,12401,3611,11187,12155,12267,12277,12345,12396,12404,12515,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,12390,13015,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,12276,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,10880,13052,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483,8484,8485,8631,8838,8862,8863,8943,8957,9011,9012,9116,9161,9184,9216,9257,9448,9734,9927,9973,9975,6054,6422,6423,6509,6524,6525,6932,7150,8557,8588,8774,8969,8970,9034,9035,9308,9309,9310,9311,9522,9816,10101,10185,10186,6491,8382,8383,8827,8845,9817,10184,4679,4681])). % 191.49/191.46 cnf(13225,plain, % 191.49/191.46 (P4(f333(f333(f251(a1),f2(a1)),f333(f76(a1),f79(a1))))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,12539,12976,12986,12991,12995,13001,13004,13028,13127,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,12797,13049,4503,10466,10559,3372,3333,12586,3521,3230,4497,12715,13069,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2931,2933,2943,2946,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3005,3015,3017,3018,3024,3026,3027,3030,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,12851,13019,13126,13131,13152,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3144,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3191,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,12370,4521,12337,3302,11721,11724,12945,13045,13098,13102,13106,4570,11013,11083,11304,11307,3396,3711,3217,3297,3419,3635,3411,3386,3205,3206,10365,10672,4554,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,11207,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3496,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,13048,13053,13137,13143,3756,11616,3295,3395,11736,12646,13151,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,12957,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,12726,13081,13085,13089,3888,3486,13082,3487,13086,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,12917,13097,3995,13101,4000,11025,12108,12181,12241,12285,12948,4001,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,12985,12990,4579,10793,11161,12998,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,12966,13066,13139,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,12911,12980,13031,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,12900,12981,13023,13038,13041,13078,13122,13125,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,13062,13119,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,12969,3335,10702,10853,10924,11650,11805,11994,12223,12793,13065,13140,13146,13150,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,4303,3806,3624,11612,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,12714,12975,13027,3750,10964,10970,10985,11921,12129,12401,3611,11187,12155,12267,12277,12345,12396,12404,12515,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,12390,13015,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,12276,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,10880,13052,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483,8484,8485,8631,8838,8862,8863,8943,8957,9011,9012,9116,9161,9184,9216,9257,9448,9734,9927,9973,9975,6054,6422,6423,6509,6524,6525,6932,7150,8557,8588,8774,8969,8970,9034,9035,9308,9309,9310,9311,9522,9816,10101,10185,10186,6491,8382,8383,8827,8845,9817,10184,4679,4681,4682,4736,4744,4879,4895,4896,4924,4925,4954,5009,5071,5128,5177,5205,5241,5243,5250,5252,5253,5279,5354,5375,5509,5573,5574,5575,5693])). % 191.49/191.46 cnf(13245,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),f333(a117,f333(f333(f81(a880),x132451),x132452))),f333(a117,x132452)))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,12539,12976,12986,12991,12995,13001,13004,13028,13127,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,12797,13049,4503,10466,10559,3372,3333,12586,3521,3230,4497,12715,13069,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2931,2933,2943,2946,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3005,3015,3017,3018,3024,3026,3027,3030,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,12851,13019,13126,13131,13152,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3144,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3191,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,12370,4521,12337,3302,11721,11724,12945,13045,13098,13102,13106,4570,11013,11083,11304,11307,3396,3711,3217,3297,3419,3635,3411,3386,3205,3206,10365,10672,4554,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,11207,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3496,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,13048,13053,13137,13143,3756,11616,3295,3395,11736,12646,13151,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,12957,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,12726,13081,13085,13089,3888,3486,13082,3487,13086,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,12917,13097,3995,13101,4000,11025,12108,12181,12241,12285,12948,4001,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,12985,12990,4579,10793,11161,12998,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,12966,13066,13139,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,12911,12980,13031,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,12900,12981,13023,13038,13041,13078,13122,13125,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,13062,13119,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,12969,3335,10702,10853,10924,11650,11805,11994,12223,12793,13065,13140,13146,13150,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,4303,3806,3624,11612,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,12714,12975,13027,3750,10964,10970,10985,11921,12129,12401,3611,11187,12155,12267,12277,12345,12396,12404,12515,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,12390,13015,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,12276,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,10880,13052,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483,8484,8485,8631,8838,8862,8863,8943,8957,9011,9012,9116,9161,9184,9216,9257,9448,9734,9927,9973,9975,6054,6422,6423,6509,6524,6525,6932,7150,8557,8588,8774,8969,8970,9034,9035,9308,9309,9310,9311,9522,9816,10101,10185,10186,6491,8382,8383,8827,8845,9817,10184,4679,4681,4682,4736,4744,4879,4895,4896,4924,4925,4954,5009,5071,5128,5177,5205,5241,5243,5250,5252,5253,5279,5354,5375,5509,5573,5574,5575,5693,5694,5719,5720,5724,5777,5783,5785,5794,5800,5872])). % 191.49/191.46 cnf(13255,plain, % 191.49/191.46 (~P4(f333(f63(x132551),f41(f890(x132551,a874),f258(f890(f890(x132551,a874),a874)))))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,12539,12976,12986,12991,12995,13001,13004,13028,13127,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,12797,13049,4503,10466,10559,3372,3333,12586,3521,3230,4497,12715,13069,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2931,2933,2943,2946,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3005,3015,3017,3018,3024,3026,3027,3030,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,12851,13019,13126,13131,13152,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3144,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3191,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,12370,4521,12337,3302,11721,11724,12945,13045,13098,13102,13106,4570,11013,11083,11304,11307,3396,3711,3217,3297,3419,3635,3411,3386,3205,3206,10365,10672,4554,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,11207,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3496,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,13048,13053,13137,13143,3756,11616,3295,3395,11736,12646,13151,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,12957,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,12726,13081,13085,13089,3888,3486,13082,3487,13086,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,12917,13097,3995,13101,4000,11025,12108,12181,12241,12285,12948,4001,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,12985,12990,4579,10793,11161,12998,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,12966,13066,13139,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,12911,12980,13031,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,12900,12981,13023,13038,13041,13078,13122,13125,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,13062,13119,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,12969,3335,10702,10853,10924,11650,11805,11994,12223,12793,13065,13140,13146,13150,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,4303,3806,3624,11612,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,12714,12975,13027,3750,10964,10970,10985,11921,12129,12401,3611,11187,12155,12267,12277,12345,12396,12404,12515,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,12390,13015,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,12276,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,10880,13052,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483,8484,8485,8631,8838,8862,8863,8943,8957,9011,9012,9116,9161,9184,9216,9257,9448,9734,9927,9973,9975,6054,6422,6423,6509,6524,6525,6932,7150,8557,8588,8774,8969,8970,9034,9035,9308,9309,9310,9311,9522,9816,10101,10185,10186,6491,8382,8383,8827,8845,9817,10184,4679,4681,4682,4736,4744,4879,4895,4896,4924,4925,4954,5009,5071,5128,5177,5205,5241,5243,5250,5252,5253,5279,5354,5375,5509,5573,5574,5575,5693,5694,5719,5720,5724,5777,5783,5785,5794,5800,5872,5949,6014,6077,6100,6266])). % 191.49/191.46 cnf(13269,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),f2(a880)),f194(a880)))), % 191.49/191.46 inference(scs_inference,[],[4500,3551,11078,12111,12211,12306,12341,12349,12362,12417,12537,12539,12976,12986,12991,12995,13001,13004,13028,13127,3561,12175,12630,12632,3562,12245,3279,12574,12576,3280,12580,3248,12490,4522,4523,11698,4248,12597,12600,3283,12624,3122,3142,12637,3185,12552,4506,3613,4487,10241,10244,10254,10265,10373,10376,10379,10482,10595,10899,11063,11066,11264,11354,11361,11375,11426,11429,11536,11583,11599,11900,11925,11937,11969,12067,12171,12178,12333,12387,12524,12647,12797,13049,4503,10466,10559,3372,3333,12586,3521,3230,4497,12715,13069,2898,2905,2906,2912,2913,2919,2920,2924,2925,2927,2930,2931,2933,2943,2946,2949,2952,2953,2961,2964,2966,2967,2969,2970,2972,2973,2974,2976,2977,2983,2984,2990,2993,3004,3005,3015,3017,3018,3024,3026,3027,3030,3032,3033,3046,3047,3053,3054,3056,3057,3058,3077,3084,3101,3184,4483,3650,3155,11351,3293,3356,3266,3269,10238,10247,10308,10311,10400,10403,10696,11366,11369,11481,11523,11528,11628,12085,12282,12470,12526,12531,12533,12550,12556,12568,12570,12572,12595,12620,12851,13019,13126,13131,13152,3636,3880,3243,11625,12365,12369,12373,3254,3768,11010,11631,4068,3144,3145,3965,4499,4510,3856,11402,3371,3210,3176,3686,12614,3171,3973,3191,3691,4466,12512,3153,3154,3132,3159,3190,3326,12059,12201,12420,12493,3375,10848,12172,3241,3242,3264,10507,3418,4578,10436,3938,4512,10299,10463,11261,12329,12366,12370,4521,12337,3302,11721,11724,12945,13045,13098,13102,13106,4570,11013,11083,11304,11307,3396,3711,3217,3297,3419,3635,3411,3386,3205,3206,10365,10672,4554,3475,3198,3123,3226,11393,4081,12352,12482,3941,11019,11145,11196,12316,12322,12431,12434,12457,4592,10951,11150,11255,11277,11312,11318,12261,4593,11052,11153,11258,4594,11156,11207,4595,11210,4596,3225,3514,12214,12258,12336,3675,4369,4370,3496,3615,3653,3823,3583,12834,12838,12842,12846,12856,3866,12208,3499,3745,3383,10384,10502,10573,10634,10637,10675,10769,11003,11896,11959,12035,12076,12137,12140,12461,12653,12711,12742,12754,12796,12817,12873,12879,13048,13053,13137,13143,3756,11616,3295,3395,11736,12646,13151,3577,4560,10276,10279,10305,10777,10790,10909,11327,11785,11793,12011,12014,12102,12264,12356,12658,12661,12678,12681,12703,12755,12923,12928,12952,12957,4574,11500,11531,11566,11596,12764,12768,3743,3523,3524,12684,12687,12690,12693,12723,12726,13081,13085,13089,3888,3486,13082,3487,13086,3341,3342,3316,4557,3204,4508,3702,4218,4006,3506,4577,4075,11272,3634,3355,11745,11748,12182,12286,12441,4045,4005,11889,12229,3950,10845,12047,12070,12242,12464,12917,13097,3995,13101,4000,11025,12108,12181,12241,12285,12948,4001,3676,11899,12042,12116,12162,4034,3693,11022,11088,11169,11229,12066,12130,12382,12454,12467,12985,12990,4579,10793,11161,12998,3312,10393,10489,10620,10682,11473,11692,11739,11773,11869,11924,12123,12289,3313,10751,10796,10799,10832,10856,10893,10931,10967,11940,11943,11946,11949,12143,12146,12149,12152,12222,12393,12437,12704,12729,12806,12813,12820,12825,12828,12831,12864,12876,12894,12938,12963,12966,13066,13139,3314,10422,10477,10687,10772,10896,11579,11776,11788,11875,11886,11907,11912,11952,11974,11989,12720,12870,12897,12924,12929,12953,3315,3391,12096,12784,12835,12839,12843,12847,12857,12861,4556,10339,10431,10544,10568,10814,10859,10869,11545,11646,11667,11670,11673,11689,11831,11834,11837,11840,11936,11955,11958,11968,12023,12026,12029,12032,12103,12193,12196,12292,12295,12355,12386,12423,12505,3470,10640,10904,10948,11218,11296,11461,11701,12332,12508,12911,12980,13031,4572,10823,10835,10940,10958,10961,11016,11102,11110,11126,11164,11181,11190,11226,11267,11287,11290,11293,11321,11334,11337,11718,11754,12017,12020,12054,12097,12126,12270,12313,12319,12405,12408,12427,12481,12487,12496,12518,12783,12800,12803,12900,12981,13023,13038,13041,13078,13122,13125,3377,10669,10699,10708,11247,11800,12424,12438,12765,12769,12772,3414,13062,13119,3408,3827,3765,10342,11619,11649,12747,4569,10296,10663,10666,11105,11123,11582,11637,11681,11702,11806,11843,11846,11849,11852,12969,3335,10702,10853,10924,11650,11805,11994,12223,12793,13065,13140,13146,13150,3787,11751,12700,3529,4567,3798,3834,4546,4548,4549,3286,3287,4547,4550,4551,4590,4303,3806,3624,11612,4226,11480,4581,10270,10273,10525,10576,10579,10584,10990,11455,11705,11809,4591,11184,11301,11343,4012,12253,3905,11340,11676,11680,11742,12340,12348,12430,12714,12975,13027,3750,10964,10970,10985,11921,12129,12401,3611,11187,12155,12267,12277,12345,12396,12404,12515,3648,4079,3752,10705,11041,11193,11223,11234,12235,12344,12390,13015,3580,10626,10629,10711,10883,3579,4584,11613,4580,12668,4585,10762,10862,11172,11324,11458,11486,12217,12226,12273,12451,4180,10838,12238,12250,12276,4087,3786,12521,3731,3732,4582,10318,10321,10657,10660,11497,11677,12460,4583,11593,11686,3754,10623,10880,13052,4019,4588,4610,4615,4622,4638,4687,4689,4718,4735,4742,4743,4782,4812,4818,4901,4926,4927,4987,4988,5010,5011,5024,5028,5050,5057,5074,5077,5078,5079,5084,5085,5106,5131,5132,5142,5152,5197,5198,5206,5216,5220,5222,5232,5234,5240,5244,5245,5260,5267,5270,5271,5272,5276,5313,5326,5333,5335,5336,5340,5341,5342,5350,5353,5357,5358,5359,5366,5370,5371,5372,5380,5384,5385,5386,5391,5404,5413,5425,5427,5435,5436,5440,5444,5469,5475,5485,5486,5501,5511,5533,5539,5555,5556,5559,5578,5586,5587,5592,5593,5603,5604,5618,5622,5631,5632,5634,5649,5654,5664,5665,5677,5684,5698,5702,5705,5711,5712,5713,5716,5721,5758,5759,5762,5764,5767,5768,5769,5771,5773,5775,5780,5787,5802,5816,5821,5822,5835,5836,5841,5845,5847,5852,5893,5905,5914,5918,5929,5932,5933,5941,5955,5961,5979,5982,5994,6021,6035,6060,6080,6081,6084,6099,6101,6102,6104,6117,6118,6121,6123,6126,6127,6139,6145,6146,6147,6151,6153,6191,6192,6197,6200,6209,6245,6247,6249,6251,6260,6262,6264,6270,6272,6278,6281,6289,6296,6297,6298,6302,6324,6325,6326,6328,6334,6337,6373,6374,6378,6379,6380,6381,6382,6383,6384,6391,6424,6425,6434,6455,6456,6475,6478,6489,6490,6496,6521,6523,6539,6576,6579,6580,6633,6658,6700,6720,6729,6730,6731,6732,6751,6752,6758,6765,6768,6770,6772,6773,6774,6776,6790,6801,6803,6804,6815,6818,6868,6879,6881,6885,6900,6901,6937,6950,6981,7015,7069,7096,7151,7172,7181,7184,7239,7249,7303,7305,7313,7321,7324,7325,7344,7350,7352,7400,7410,7413,7429,7478,7479,7483,7526,7527,7545,7609,7628,7651,7673,7687,7703,7713,7721,7722,7751,7754,7756,7766,7804,7816,7841,7894,7924,7955,8001,8017,8033,8034,8115,8169,8188,8211,8230,8254,8349,8351,8357,8375,8379,8395,8414,8425,8427,8444,8450,8454,8477,8489,8490,8505,8507,8516,8517,8518,8519,8520,8538,8539,8540,8548,8562,8563,8575,8579,8581,8582,8583,8591,8595,8623,8624,8648,8661,8664,8681,8703,8704,8705,8718,8719,8720,8741,8752,8761,8762,8763,8764,8766,8788,8789,8802,8847,8853,8860,8873,8878,8880,8883,8884,8889,8898,8977,9008,9009,9010,9025,9037,9041,9062,9063,9110,9113,9142,9189,9190,9191,9204,9229,9243,9249,9252,9277,9278,9306,9373,9401,9402,9403,9428,9429,9445,9463,9469,9492,9521,9543,9551,9552,9553,9554,9567,9569,9574,9613,9614,9620,9621,9669,9670,9702,9711,9721,9723,9724,9733,9752,9762,9793,9822,9827,9879,9917,9918,9919,9928,9929,9934,9948,9967,9972,9984,10036,10114,10115,10201,10222,2,8,9,4625,4626,4644,4675,4676,4678,4706,4712,4713,4722,4771,4773,4803,4817,4847,4860,4941,4942,4955,4975,5031,5032,5035,5036,5038,5040,5041,5053,5054,5064,5075,5076,5082,5101,5102,5119,5124,5125,5126,5127,5130,5138,5141,5147,5212,5218,5219,5226,5257,5268,5274,5292,5312,5319,5320,5321,5330,5339,5346,5348,5349,5355,5362,5363,5376,5377,5378,5379,5381,5382,5387,5388,5389,5390,5421,5422,5423,5431,5432,5433,5434,5480,5482,5484,5518,5520,5521,5523,5524,5526,5527,5529,5538,5543,5545,5546,5547,5548,5549,5550,5557,5567,5570,5581,5597,5598,5601,5612,5614,5615,5616,5641,5651,5667,5668,5678,5679,5681,5683,5688,5723,5727,5729,5789,5823,5824,5828,5834,5837,5838,5839,5840,5846,5857,5858,5860,5861,5869,5890,5921,5936,5939,5940,5942,5951,5972,5973,5974,5977,5978,5996,6007,6008,6037,6038,6042,6062,6065,6069,6088,6093,6094,6119,6122,6130,6138,6144,6150,6157,6158,6159,6160,6194,6210,6263,6299,6300,6321,6322,6327,6330,6331,6335,6339,6348,6366,6386,6387,6392,6402,6417,6437,6443,6445,6460,6461,6463,6464,6466,6468,6469,6470,6472,6474,6477,6483,6484,6485,6486,6492,6494,6533,6538,6553,6554,6555,6556,6591,6596,6598,6603,6604,6612,6616,6629,6654,6655,6656,6657,6668,6673,6690,6694,6713,6746,6747,6748,6753,6761,6782,6784,6786,6788,6791,6797,6799,6812,6819,6854,6857,6858,6871,6872,6873,6874,6890,6892,6909,6935,6958,6969,6971,6972,6974,6976,6977,7012,7013,7018,7019,7020,7021,7023,7025,7050,7059,7060,7071,7081,7120,7130,7134,7141,7152,7153,7158,7160,7166,7175,7188,7205,7223,7225,7242,7288,7290,7291,7292,7299,7304,7320,7364,7397,7411,7428,7461,7464,7487,7511,7528,7531,7532,7542,7559,7560,7562,7564,7566,7568,7592,7617,7618,7650,7652,7653,7654,7659,7679,7688,7699,7704,7710,7712,7718,7729,7730,7732,7753,7762,7787,7854,7855,7897,7905,7906,7926,7927,7944,7945,8009,8010,8011,8037,8073,8080,8083,8092,8104,8138,8144,8151,8164,8183,8190,8210,8252,8282,8294,8312,8315,8342,8366,8428,8429,8433,8435,8455,8542,8543,8544,8545,8598,8627,8663,8680,8730,8781,8784,8799,8806,8844,8866,8894,8895,8911,8912,9043,9047,9060,9070,9099,9101,9104,9108,9111,9112,9127,9128,9151,9157,9169,9215,9233,9295,9296,9298,9364,9370,9398,9405,9406,9409,9410,9427,9441,9450,9462,9476,9477,9479,9481,9519,9655,9697,9698,9745,9799,9905,9906,9950,10012,10091,10105,10203,3,2634,2636,2637,2638,2640,2643,2645,2647,2648,2649,2650,2653,2654,2655,2657,2660,2665,2666,2667,2678,2679,2680,2683,2685,2690,2691,2693,2694,2695,2696,2700,2709,2710,2711,2720,2721,2722,2726,2727,2730,2732,2733,2734,2745,2746,2749,2750,2751,2756,2757,2758,2773,2774,2775,2780,2781,2782,2788,2804,2805,2807,2809,2818,2827,2829,2830,2832,2850,2851,2869,2875,2876,2881,5249,5311,5407,5493,5494,5495,5568,5666,5697,5730,5746,5748,5754,5817,5818,5819,5820,5826,5859,5991,6036,6059,6096,6136,6279,6286,6319,6320,6338,6341,6343,6350,6351,6352,6353,6354,6355,6356,6357,6439,6506,6507,6589,6623,6624,6665,6666,6798,6811,6882,6883,6887,6910,6933,6941,6943,6991,7016,7017,7033,7034,7035,7070,7114,7115,7212,7270,7271,7272,7273,7287,7314,7369,7370,7379,7385,7387,7399,7431,7432,7433,7434,7572,7573,7579,7580,7582,7584,7795,7797,7798,7814,7852,7921,7962,8020,8042,8043,8061,8122,8223,8292,8293,8295,8327,8391,8392,8463,8482,8483,8484,8485,8631,8838,8862,8863,8943,8957,9011,9012,9116,9161,9184,9216,9257,9448,9734,9927,9973,9975,6054,6422,6423,6509,6524,6525,6932,7150,8557,8588,8774,8969,8970,9034,9035,9308,9309,9310,9311,9522,9816,10101,10185,10186,6491,8382,8383,8827,8845,9817,10184,4679,4681,4682,4736,4744,4879,4895,4896,4924,4925,4954,5009,5071,5128,5177,5205,5241,5243,5250,5252,5253,5279,5354,5375,5509,5573,5574,5575,5693,5694,5719,5720,5724,5777,5783,5785,5794,5800,5872,5949,6014,6077,6100,6266,6385,6536,6738,6739,6880,6944,6984])). % 191.49/191.46 cnf(13399,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x133991),x133991))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(13408,plain, % 191.49/191.46 (~E(f333(f333(f106(a880),f333(a117,x134081)),x134081),f333(a117,x134081))), % 191.49/191.46 inference(rename_variables,[],[11516])). % 191.49/191.46 cnf(13414,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x134141),x134142)),x134141))), % 191.49/191.46 inference(rename_variables,[],[4583])). % 191.49/191.46 cnf(13423,plain, % 191.49/191.46 (P4(f333(f333(f251(a1),f333(f333(f3(a1),x134231),f79(a1))),x134231))), % 191.49/191.46 inference(rename_variables,[],[10771])). % 191.49/191.46 cnf(13440,plain, % 191.49/191.46 (~P4(f333(f333(f335(a880),x134401),f333(f256(a880),f2(a880))))), % 191.49/191.46 inference(rename_variables,[],[11766])). % 191.49/191.46 cnf(13445,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x134451,a874)),x134452),x134452))), % 191.49/191.46 inference(rename_variables,[],[3611])). % 191.49/191.46 cnf(13448,plain, % 191.49/191.46 (~P37(x134481,x134482,x134483,f333(f333(f155(x134484,x134481),x134485),f333(a117,f118(x134484))),f118(x134482))), % 191.49/191.46 inference(rename_variables,[],[11198])). % 191.49/191.46 cnf(13451,plain, % 191.49/191.46 (E(f333(f259(x134511,x134511),f260(x134511,x134512)),x134512)), % 191.49/191.46 inference(rename_variables,[],[3269])). % 191.49/191.46 cnf(13459,plain, % 191.49/191.46 (~P4(f333(f333(f194(f890(x134591,f890(x134592,a874))),x134593),x134594))), % 191.49/191.46 inference(rename_variables,[],[4585])). % 191.49/191.46 cnf(13481,plain, % 191.49/191.46 (~P4(f333(f333(f335(a880),x134811),f333(f256(a880),f2(a880))))), % 191.49/191.46 inference(rename_variables,[],[11766])). % 191.49/191.46 cnf(13484,plain, % 191.49/191.46 (~E(f333(f333(f152(x134841),x134842),x134843),x134843)), % 191.49/191.46 inference(rename_variables,[],[4512])). % 191.49/191.46 cnf(13487,plain, % 191.49/191.46 (P4(f333(f333(f251(a1),f333(f333(f3(a1),x134871),f79(a1))),x134871))), % 191.49/191.46 inference(rename_variables,[],[10771])). % 191.49/191.46 cnf(13494,plain, % 191.49/191.46 (~P4(f333(f333(f335(f889(x134941,x134941)),x134942),f260(x134941,f194(f890(x134941,a874)))))), % 191.49/191.46 inference(rename_variables,[],[10957])). % 191.49/191.46 cnf(13499,plain, % 191.49/191.46 (P4(f333(f333(f251(a1),f333(f333(f3(a1),x134991),f79(a1))),x134991))), % 191.49/191.46 inference(rename_variables,[],[10771])). % 191.49/191.46 cnf(13509,plain, % 191.49/191.46 (~P4(f333(f333(f335(x135091),x135092),f194(f890(x135091,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13512,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x135121,a874)),f333(f173(x135121),f171(x135121,x135122,x135123))),f333(f173(x135121),x135123)))), % 191.49/191.46 inference(rename_variables,[],[4000])). % 191.49/191.46 cnf(13526,plain, % 191.49/191.46 (~P4(f333(f333(f335(x135261),x135262),f333(f313(x135261,x135263,x135264),f194(f890(x135263,a874)))))), % 191.49/191.46 inference(rename_variables,[],[10960])). % 191.49/191.46 cnf(13534,plain, % 191.49/191.46 (~E(f333(f333(f106(a880),f333(a117,x135341)),x135341),f333(a117,x135341))), % 191.49/191.46 inference(rename_variables,[],[11516])). % 191.49/191.46 cnf(13545,plain, % 191.49/191.46 (~E(f333(f333(f152(x135451),x135452),x135453),x135453)), % 191.49/191.46 inference(rename_variables,[],[4512])). % 191.49/191.46 cnf(13556,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x135561),f333(f333(f81(a880),x135561),x135562)))), % 191.49/191.46 inference(rename_variables,[],[3579])). % 191.49/191.46 cnf(13559,plain, % 191.49/191.46 (~E(f333(f333(f311(x135591),x135592),x135593),f194(f890(x135591,a874)))), % 191.49/191.46 inference(rename_variables,[],[4543])). % 191.49/191.46 cnf(13568,plain, % 191.49/191.46 (~P4(f333(f333(f335(f889(x135681,x135681)),x135682),f260(x135681,f194(f890(x135681,a874)))))), % 191.49/191.46 inference(rename_variables,[],[10957])). % 191.49/191.46 cnf(13573,plain, % 191.49/191.46 (~P4(f333(f333(f335(x135731),x135732),f194(f890(x135731,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13576,plain, % 191.49/191.46 (~P4(f333(f333(f335(x135761),x135762),f194(f890(x135761,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13593,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x135931,a874)),f333(f173(x135931),f171(x135931,x135932,x135933))),f333(f173(x135931),x135933)))), % 191.49/191.46 inference(rename_variables,[],[4000])). % 191.49/191.46 cnf(13596,plain, % 191.49/191.46 (~P4(f333(f333(f335(x135961),x135962),f194(f890(x135961,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13613,plain, % 191.49/191.46 (~P4(f333(f333(f335(x136131),x136132),f194(f890(x136131,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13634,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x136341),x136342)),x136341))), % 191.49/191.46 inference(rename_variables,[],[4583])). % 191.49/191.46 cnf(13639,plain, % 191.49/191.46 (~P4(f333(f333(f335(f889(x136391,x136391)),x136392),f260(x136391,f194(f890(x136391,a874)))))), % 191.49/191.46 inference(rename_variables,[],[10957])). % 191.49/191.46 cnf(13659,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x136591,a874)),x136592),x136592))), % 191.49/191.46 inference(rename_variables,[],[3611])). % 191.49/191.46 cnf(13668,plain, % 191.49/191.46 (~E(f333(f333(f152(x136681),x136682),x136683),x136683)), % 191.49/191.46 inference(rename_variables,[],[4512])). % 191.49/191.46 cnf(13677,plain, % 191.49/191.46 (~P4(f333(f333(f335(f889(x136771,x136771)),x136772),f260(x136771,f194(f890(x136771,a874)))))), % 191.49/191.46 inference(rename_variables,[],[10957])). % 191.49/191.46 cnf(13680,plain, % 191.49/191.46 (~P4(f333(f333(f335(a880),x136801),f333(f256(a880),f2(a880))))), % 191.49/191.46 inference(rename_variables,[],[11766])). % 191.49/191.46 cnf(13690,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x136901),x136901))), % 191.49/191.46 inference(rename_variables,[],[3313])). % 191.49/191.46 cnf(13693,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x136931,a874)),f333(f173(x136931),f171(x136931,x136932,x136933))),f333(f173(x136931),x136933)))), % 191.49/191.46 inference(rename_variables,[],[4000])). % 191.49/191.46 cnf(13698,plain, % 191.49/191.46 (~P4(f333(f333(f194(f890(x136981,f890(x136982,a874))),x136983),x136984))), % 191.49/191.46 inference(rename_variables,[],[4585])). % 191.49/191.46 cnf(13717,plain, % 191.49/191.46 (P4(f333(f333(f335(x137171),f333(x137172,x137173)),f333(f312(x137174,x137171,x137172),f258(f890(x137174,a874)))))), % 191.49/191.46 inference(rename_variables,[],[3905])). % 191.49/191.46 cnf(13737,plain, % 191.49/191.46 (~P4(f333(f333(f251(a880),f333(f333(f81(a880),x137371),x137372)),x137371))), % 191.49/191.46 inference(rename_variables,[],[4583])). % 191.49/191.46 cnf(13740,plain, % 191.49/191.46 (E(f333(x137401,f557(f333(x137401,x137402),f333(f242(x137403),x137402),x137401,x137404,x137403)),f333(x137401,x137402))), % 191.49/191.46 inference(rename_variables,[],[11136])). % 191.49/191.46 cnf(13750,plain, % 191.49/191.46 (~E(f333(f333(f152(x137501),x137502),x137503),x137503)), % 191.49/191.46 inference(rename_variables,[],[4512])). % 191.49/191.46 cnf(13755,plain, % 191.49/191.46 (~E(f333(f333(f152(x137551),x137552),x137553),x137553)), % 191.49/191.46 inference(rename_variables,[],[4512])). % 191.49/191.46 cnf(13770,plain, % 191.49/191.46 (~P4(f333(f333(f335(x137701),x137702),f194(f890(x137701,a874))))), % 191.49/191.46 inference(rename_variables,[],[4572])). % 191.49/191.46 cnf(13782,plain, % 191.49/191.46 (~P4(f333(f333(f335(f889(f881(x137821),f881(x137821))),f333(f333(f263(f881(x137821),f881(x137821)),x137822),f118(x137821))),f146(x137821,x137823)))), % 191.49/191.46 inference(rename_variables,[],[4592])). % 191.49/191.46 cnf(13789,plain, % 191.49/191.46 (~P4(f333(f333(f335(f889(x137891,x137891)),x137892),f260(x137891,f194(f890(x137891,a874)))))), % 191.49/191.46 inference(rename_variables,[],[10957])). % 191.49/191.46 cnf(13800,plain, % 191.49/191.46 (~E(f333(f333(f152(x138001),x138002),x138003),x138003)), % 191.49/191.46 inference(rename_variables,[],[4512])). % 191.49/191.46 cnf(13806,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x138061),f333(f333(f81(a880),x138061),x138062)))), % 191.49/191.46 inference(rename_variables,[],[3579])). % 191.49/191.46 cnf(13814,plain, % 191.49/191.46 (~P4(f333(f333(f335(a880),x138141),f333(f256(a880),f2(a880))))), % 191.49/191.46 inference(rename_variables,[],[11766])). % 191.49/191.46 cnf(13822,plain, % 191.49/191.46 (~P4(f333(f333(f194(f890(x138221,f890(x138222,a874))),x138223),x138224))), % 191.49/191.46 inference(rename_variables,[],[4585])). % 191.49/191.46 cnf(13829,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),x138291),f333(f333(f82(a880),x138291),x138291)))), % 191.49/191.46 inference(rename_variables,[],[3580])). % 191.49/191.46 cnf(13866,plain, % 191.49/191.46 (P4(f333(f333(f250(f890(x138661,a874)),f333(f173(x138661),f171(x138661,x138662,x138663))),f333(f173(x138661),x138663)))), % 191.49/191.46 inference(rename_variables,[],[4000])). % 191.49/191.46 cnf(13945,plain, % 191.49/191.46 (P4(f333(f333(f250(a880),f2(a880)),x139451))), % 191.49/191.46 inference(rename_variables,[],[3335])). % 191.49/191.46 cnf(13952,plain, % 191.49/191.46 ($false), % 191.49/191.46 inference(scs_inference,[],[3743,4045,3888,4081,3101,4584,4546,3313,13399,13690,3316,4557,3941,3391,4547,3408,3756,4592,13782,4572,13509,13573,13576,13596,13613,13770,3395,4000,13512,13593,13693,13866,3905,13717,4503,4512,13484,13545,13668,13750,13755,13800,4590,3295,4075,3314,3765,3335,13945,3624,3750,3611,13445,13659,3752,3580,13829,3579,13556,13806,4180,3754,3269,13451,3243,3154,4593,4596,4556,4569,4580,4585,13459,13698,13822,4582,4583,13414,13634,13737,4588,3521,11516,13408,13534,10325,13055,11386,10594,11200,11951,12719,11826,11331,13225,12225,10625,10609,12484,10947,13155,11168,10911,10771,13423,13487,13499,10942,11233,11192,11136,13740,13171,10307,12974,11309,3376,3253,10994,12962,12965,13245,10728,13269,11652,12159,11918,12266,10292,11766,13440,13481,13680,13814,12717,11122,10957,13494,13568,13639,13677,13789,10960,13526,11163,12025,12046,11286,12503,13255,12416,11198,13448,11202,2909,4543,13559,2,9,8,8853,9038,4988,5539,5664,6773,6868,10201,9917,6123,6247,5354,5918,7371,5533,7303,5131,9543,5698,6900,8664,6738,5260,9521,9733,8033,7172,5821,5955,6379,8357,5994,6981,9469,5342,6337,5677,8782,4622,5835,7816,8375,9189,4812,5632,5719,9204,5357,7804,8623,9252,9274,5350,7687,5665,7751,8520,8517,9918,6391,6879,5050,6102,4818,8883,9191,5009,7324,5077,5370,6272,6496,10114,5271,6700,9402,9984,6325,5272,5444,5573,8563,9613,9620,8575,5511,7721,7938,8766,9929,7722,6060,5085,5979,6118,6425,6490,8519,5132,5333,9463,4879,8017,5071,5384,6100,5366,6014,5603,7955,9711,5764,7344,5341,5780,6297,8425,5575,7894,8898,5555,5486,6278,6950,9306,5767,7413,9569,5841,6077,8188,8648,6579,8427,5436,4689,5011,6770,7015,5326,5556,6373,5142,4682,6191,6580,7069,8583,9429,5634,7766,4782,6768,9062,9243,4987,6084,6455,7609,8548,9948,6262,7526,8847,8414,8661,4679,4735,7756,7325,9793,5705,6815,7429,5279,4927,5702,8579,6881,7440,9403,5941,6296,6765,8539,9551,6539,6101,6478,7479,6245,5222,6266,8518,8788,9229,5244,5622,8349,8450,6801,5079,5836,6374,5206,5386,5787,6147,6658,7527,8889,7924,8230,5785,8762,9190,5509,5872,6021,8115,9621,5353,6126,6117,6146,5604,7181,9567,6260,6080,4718]), % 191.49/191.46 ['proof']). % 191.49/191.47 % SZS output end Proof % 191.49/191.47 % Total time :171.580000s %------------------------------------------------------------------------------