%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW375+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 : n015.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 18:08:45 EDT 2024 % Result : Theorem 168.19s 168.04s % Output : CNFRefutation 168.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWW375+1 : TPTP v8.2.0. Released v5.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n015.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 06:20:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.56/0.62 start to proof:theBenchmark % 167.67/167.88 %------------------------------------------- % 167.67/167.88 % File :CSE---1.7 % 167.67/167.88 % Problem :theBenchmark % 167.67/167.88 % Transform :cnf % 167.67/167.88 % Format :tptp:raw % 167.67/167.88 % Command :java -jar mcs_scs.jar %d %s % 167.67/167.88 % 167.67/167.88 % Result :Theorem 147.580000s % 167.67/167.88 % Output :CNFRefutation 147.580000s % 167.67/167.88 %------------------------------------------- % 167.67/167.89 %------------------------------------------------------------------------------ % 167.67/167.89 % File : SWW375+1 : TPTP v8.2.0. Released v5.2.0. % 167.67/167.89 % Domain : Software Verification % 167.67/167.89 % Problem : Hoare's Logic with Procedures 435539, 5000 axioms selected % 167.67/167.89 % Version : Especial. % 167.67/167.89 % English : % 167.67/167.89 % 167.67/167.89 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 167.67/167.89 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 167.67/167.89 % Source : [Bla11] % 167.67/167.89 % Names : hoare_435539.5000.p [Bla11] % 167.67/167.89 % 167.67/167.89 % Status : Theorem % 167.67/167.89 % Rating : 0.42 v8.2.0, 0.39 v8.1.0, 0.42 v7.5.0, 0.47 v7.4.0, 0.50 v7.3.0, 0.45 v7.2.0, 0.41 v7.1.0, 0.57 v6.4.0, 0.54 v6.2.0, 0.64 v6.1.0, 0.73 v6.0.0, 0.65 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0 % 167.67/167.89 % Syntax : Number of formulae : 5230 (1752 unt; 0 def) % 167.67/167.89 % Number of atoms : 12494 (4548 equ) % 167.67/167.89 % Maximal formula atoms : 13 ( 2 avg) % 167.67/167.89 % Number of connectives : 8293 (1029 ~; 155 |; 711 &) % 167.67/167.89 % ( 880 <=>;5518 =>; 0 <=; 0 <~>) % 167.67/167.89 % Maximal formula depth : 22 ( 6 avg) % 167.67/167.89 % Maximal term depth : 19 ( 2 avg) % 167.67/167.89 % Number of predicates : 138 ( 137 usr; 2 prp; 0-7 aty) % 167.67/167.89 % Number of functors : 374 ( 374 usr; 63 con; 0-10 aty) % 167.67/167.89 % Number of variables : 16843 (16698 !; 145 ?) % 167.67/167.89 % SPC : FOF_THM_RFO_SEQ % 167.67/167.89 % 167.67/167.89 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 167.67/167.89 % 2011-03-01 12:48:51 % 167.67/167.89 %------------------------------------------------------------------------------ % 167.67/167.89 %----Relevant facts (4985) % 167.67/167.89 fof(fact_ext,axiom, % 167.67/167.89 ! [V_g_2,V_f_2] : % 167.67/167.89 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 167.67/167.89 => V_f_2 = V_g_2 ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_WT__bodiesD,axiom, % 167.67/167.89 ! [V_b,V_pn] : % 167.67/167.89 ( c_Com_OWT__bodies % 167.67/167.89 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 167.67/167.89 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_option_Oinject,axiom, % 167.67/167.89 ! [V_a_H_2,V_a_2,T_a] : % 167.67/167.89 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 167.67/167.89 <=> V_a_2 = V_a_H_2 ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_WT_Oequations_I7_J,axiom, % 167.67/167.89 ! [V_a_2] : % 167.67/167.89 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 167.67/167.89 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_state__not__singleton__def,axiom, % 167.67/167.89 ( c_Hoare__Mirabelle_Ostate__not__singleton % 167.67/167.89 <=> ? [B_s,B_t] : B_s != B_t ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_single__stateE,axiom, % 167.67/167.89 ( c_Hoare__Mirabelle_Ostate__not__singleton % 167.67/167.89 => ! [B_t] : % 167.67/167.89 ~ ! [B_s] : B_s = B_t ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_WTs__elim__cases_I7_J,axiom, % 167.67/167.89 ! [V_P] : % 167.67/167.89 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 167.67/167.89 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_option_Orecs_I2_J,axiom, % 167.67/167.89 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 167.67/167.89 % 167.67/167.89 fof(fact_option_Osimps_I5_J,axiom, % 167.67/167.89 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 167.67/167.89 % 167.67/167.89 fof(fact_is__none__code_I2_J,axiom, % 167.67/167.89 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ). % 167.67/167.89 % 167.67/167.89 fof(fact_map__comp__Some__iff,axiom, % 167.67/167.89 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 167.67/167.89 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) % 167.67/167.89 <=> ? [B_k_H] : % 167.67/167.89 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 167.67/167.89 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_map__comp__simps_I2_J,axiom, % 167.67/167.89 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 167.67/167.89 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 167.67/167.89 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_bind__runit,axiom, % 167.67/167.89 ! [V_x_2,T_a] : hAPP(hAPP(c_Option_Obind(T_a,T_a),V_x_2),c_Option_Ooption_OSome(T_a)) = V_x_2 ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I6_J,axiom, % 167.67/167.89 ! [V_pname_H_2,V_pname_2] : % 167.67/167.89 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 167.67/167.89 <=> V_pname_2 = V_pname_H_2 ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_bind__lunit,axiom, % 167.67/167.89 ! [V_f_2,V_x_2,T_a,T_b] : hAPP(hAPP(c_Option_Obind(T_b,T_a),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 167.67/167.89 % 167.67/167.89 fof(fact_WT_OBody,axiom, % 167.67/167.89 ! [V_pn] : % 167.67/167.89 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 167.67/167.89 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_WTs__elim__cases_I8_J,axiom, % 167.67/167.89 ! [V_a_2,V_P_2,V_X_2] : % 167.67/167.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2))) % 167.67/167.89 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_WT_Oequations_I8_J,axiom, % 167.67/167.89 ! [V_a3_2,V_a1_2,V_a2_2] : % 167.67/167.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 167.67/167.89 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_WT_OCall,axiom, % 167.67/167.89 ! [V_a_2,V_X_2,V_pn_2] : % 167.67/167.89 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2))) % 167.67/167.89 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_map__comp__None__iff,axiom, % 167.67/167.89 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 167.67/167.89 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.89 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 167.67/167.89 | ? [B_k_H] : % 167.67/167.89 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 167.67/167.89 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I70_J,axiom, % 167.67/167.89 ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2) ). % 167.67/167.89 % 167.67/167.89 fof(fact_the_Osimps,axiom, % 167.67/167.89 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 167.67/167.89 % 167.67/167.89 fof(fact_option_Orecs_I1_J,axiom, % 167.67/167.89 ! [V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 167.67/167.89 % 167.67/167.89 fof(fact_WTs__elim__cases_I4_J,axiom, % 167.67/167.89 ! [V_c2,V_c1] : % 167.67/167.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 167.67/167.89 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 167.67/167.89 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_WTs__elim__cases_I5_J,axiom, % 167.67/167.89 ! [V_c2_2,V_c1_2,V_b_2] : % 167.67/167.89 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 167.67/167.89 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 167.67/167.89 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 167.67/167.89 % 167.67/167.89 fof(fact_is__none__code_I1_J,axiom, % 167.67/167.89 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I12_J,axiom, % 167.67/167.89 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I20_J,axiom, % 167.67/167.89 ! [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) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I14_J,axiom, % 167.67/167.89 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I13_J,axiom, % 167.67/167.89 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I50_J,axiom, % 167.67/167.89 ! [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) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I44_J,axiom, % 167.67/167.89 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I21_J,axiom, % 167.67/167.89 ! [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 ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I15_J,axiom, % 167.67/167.89 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I51_J,axiom, % 167.67/167.89 ! [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) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I45_J,axiom, % 167.67/167.89 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 167.67/167.89 % 167.67/167.89 fof(fact_com_Osimps_I57_J,axiom, % 167.67/167.89 ! [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) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I56_J,axiom, % 167.67/167.90 ! [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) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I3_J,axiom, % 167.67/167.90 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 167.67/167.90 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 167.67/167.90 <=> ( V_com1_2 = V_com1_H_2 % 167.67/167.90 & V_com2_2 = V_com2_H_2 ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I7_J,axiom, % 167.67/167.90 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 167.67/167.90 ( 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) % 167.67/167.90 <=> ( V_vname_2 = V_vname_H_2 % 167.67/167.90 & V_pname_2 = V_pname_H_2 % 167.67/167.90 & V_fun_2 = V_fun_H_2 ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I4_J,axiom, % 167.67/167.90 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 167.67/167.90 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) % 167.67/167.90 <=> ( V_fun_2 = V_fun_H_2 % 167.67/167.90 & V_com1_2 = V_com1_H_2 % 167.67/167.90 & V_com2_2 = V_com2_H_2 ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I64_J,axiom, % 167.67/167.90 ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2 ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I67_J,axiom, % 167.67/167.90 ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I71_J,axiom, % 167.67/167.90 ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I68_J,axiom, % 167.67/167.90 ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_option_Osimps_I2_J,axiom, % 167.67/167.90 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 167.67/167.90 % 167.67/167.90 fof(fact_option_Osimps_I3_J,axiom, % 167.67/167.90 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 167.67/167.90 % 167.67/167.90 fof(fact_not__Some__eq,axiom, % 167.67/167.90 ! [T_a,V_x_2] : % 167.67/167.90 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 167.67/167.90 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_not__None__eq,axiom, % 167.67/167.90 ! [T_a,V_x_2] : % 167.67/167.90 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 167.67/167.90 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_option_Osimps_I4_J,axiom, % 167.67/167.90 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 167.67/167.90 % 167.67/167.90 fof(fact_bind__lzero,axiom, % 167.67/167.90 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Obind(T_b,T_a),c_Option_Ooption_ONone(T_b)),V_f_2) = c_Option_Ooption_ONone(T_a) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I63_J,axiom, % 167.67/167.90 ! [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) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I62_J,axiom, % 167.67/167.90 ! [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) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_Oequations_I5_J,axiom, % 167.67/167.90 ! [V_a2_2,V_a1_2,V_a3_2] : % 167.67/167.90 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 167.67/167.90 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 167.67/167.90 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_OIf,axiom, % 167.67/167.90 ! [V_b_2,V_c1_2,V_c0_2] : % 167.67/167.90 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 167.67/167.90 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 167.67/167.90 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I54_J,axiom, % 167.67/167.90 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I55_J,axiom, % 167.67/167.90 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_map__comp__simps_I1_J,axiom, % 167.67/167.90 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 167.67/167.90 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.90 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_Oequations_I4_J,axiom, % 167.67/167.90 ! [V_a2_2,V_a1_2] : % 167.67/167.90 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 167.67/167.90 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 167.67/167.90 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_OSemi,axiom, % 167.67/167.90 ! [V_c1,V_c0] : % 167.67/167.90 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 167.67/167.90 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 167.67/167.90 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I48_J,axiom, % 167.67/167.90 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I49_J,axiom, % 167.67/167.90 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_OSkip,axiom, % 167.67/167.90 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_Oequations_I1_J,axiom, % 167.67/167.90 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I19_J,axiom, % 167.67/167.90 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I18_J,axiom, % 167.67/167.90 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 167.67/167.90 % 167.67/167.90 fof(fact_is__none__def,axiom, % 167.67/167.90 ! [V_x_2,T_a] : % 167.67/167.90 ( c_Option_Ois__none(T_a,V_x_2) % 167.67/167.90 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_option_Oexhaust,axiom, % 167.67/167.90 ! [T_a,V_y] : % 167.67/167.90 ( V_y != c_Option_Ooption_ONone(T_a) % 167.67/167.90 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_map__add__SomeD,axiom, % 167.67/167.90 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 167.67/167.90 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.67/167.90 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.67/167.90 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.90 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_map__add__Some__iff,axiom, % 167.67/167.90 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 167.67/167.90 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.67/167.90 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.67/167.90 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.90 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Orecs_I1_J,axiom, % 167.67/167.90 ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2 ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Orecs_I4_J,axiom, % 167.67/167.90 ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Orecs_I8_J,axiom, % 167.67/167.90 ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Orecs_I5_J,axiom, % 167.67/167.90 ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WTs__elim__cases_I3_J,axiom, % 167.67/167.90 ! [V_ca_2,V_a_2,V_Y_2] : % 167.67/167.90 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) % 167.67/167.90 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Orecs_I7_J,axiom, % 167.67/167.90 ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_OBody,axiom, % 167.67/167.90 ! [V_s1,V_s0,V_pn] : % 167.67/167.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 167.67/167.90 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc__elim__cases_I6_J,axiom, % 167.67/167.90 ! [V_s1,V_s,V_P] : % 167.67/167.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 167.67/167.90 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_OIfFalse,axiom, % 167.67/167.90 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 167.67/167.90 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.90 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 167.67/167.90 => 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)) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_OIfTrue,axiom, % 167.67/167.90 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 167.67/167.90 ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.90 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 167.67/167.90 => 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)) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc__elim__cases_I5_J,axiom, % 167.67/167.90 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 167.67/167.90 ( 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)) % 167.67/167.90 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.90 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 167.67/167.90 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.90 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_OSemi,axiom, % 167.67/167.90 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 167.67/167.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 167.67/167.90 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 167.67/167.90 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_OSkip,axiom, % 167.67/167.90 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc__elim__cases_I1_J,axiom, % 167.67/167.90 ! [V_t,V_s] : % 167.67/167.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 167.67/167.90 => V_t = V_s ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com__det,axiom, % 167.67/167.90 ! [V_u,V_t,V_s,V_c] : % 167.67/167.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 167.67/167.90 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 167.67/167.90 => V_u = V_t ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Orecs_I3_J,axiom, % 167.67/167.90 ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Orecs_I2_J,axiom, % 167.67/167.90 ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I2_J,axiom, % 167.67/167.90 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 167.67/167.90 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) % 167.67/167.90 <=> ( V_loc_2 = V_loc_H_2 % 167.67/167.90 & V_fun_2 = V_fun_H_2 % 167.67/167.90 & V_com_2 = V_com_H_2 ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I1_J,axiom, % 167.67/167.90 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] : % 167.67/167.90 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) % 167.67/167.90 <=> ( V_vname_2 = V_vname_H_2 % 167.67/167.90 & V_fun_2 = V_fun_H_2 ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_map__add__assoc,axiom, % 167.67/167.90 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I23_J,axiom, % 167.67/167.90 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I22_J,axiom, % 167.67/167.90 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_Oequations_I5_J,axiom, % 167.67/167.90 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 167.67/167.90 ( 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)) % 167.67/167.90 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.90 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 167.67/167.90 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.90 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_Oequations_I6_J,axiom, % 167.67/167.90 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 167.67/167.90 ( 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)) % 167.67/167.90 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.90 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 167.67/167.90 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.90 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_Oequations_I4_J,axiom, % 167.67/167.90 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 167.67/167.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 167.67/167.90 <=> ? [B_s1] : % 167.67/167.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 167.67/167.90 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_evalc_Oequations_I1_J,axiom, % 167.67/167.90 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 167.67/167.90 % 167.67/167.90 fof(fact_map__add__None,axiom, % 167.67/167.90 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 167.67/167.90 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.90 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.90 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_map__add__find__right,axiom, % 167.67/167.90 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 167.67/167.90 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 167.67/167.90 => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I31_J,axiom, % 167.67/167.90 ! [V_fun_2,V_vname_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I30_J,axiom, % 167.67/167.90 ! [V_pname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_Oequations_I2_J,axiom, % 167.67/167.90 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_OAssign,axiom, % 167.67/167.90 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I41_J,axiom, % 167.67/167.90 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I40_J,axiom, % 167.67/167.90 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_OLocal,axiom, % 167.67/167.90 ! [V_a_2,V_Y_2,V_ca_2] : % 167.67/167.90 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 167.67/167.90 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_WT_Oequations_I3_J,axiom, % 167.67/167.90 ! [V_a1_2,V_a3_2,V_a2_2] : % 167.67/167.90 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 167.67/167.90 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I27_J,axiom, % 167.67/167.90 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I26_J,axiom, % 167.67/167.90 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I36_J,axiom, % 167.67/167.90 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 167.67/167.90 % 167.67/167.90 fof(fact_com_Osimps_I37_J,axiom, % 167.67/167.91 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I33_J,axiom, % 167.67/167.91 ! [V_fun_2,V_vname_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_OAss(V_vname_2,V_fun_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I32_J,axiom, % 167.67/167.91 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I25_J,axiom, % 167.67/167.91 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I24_J,axiom, % 167.67/167.91 ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I9_J,axiom, % 167.67/167.91 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I8_J,axiom, % 167.67/167.91 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I42_J,axiom, % 167.67/167.91 ! [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) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I43_J,axiom, % 167.67/167.91 ! [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) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I34_J,axiom, % 167.67/167.91 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I35_J,axiom, % 167.67/167.91 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I11_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I10_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_Oequations_I9_J,axiom, % 167.67/167.91 ! [V_a3_2,V_a2_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 167.67/167.91 <=> 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)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I65_J,axiom, % 167.67/167.91 ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I66_J,axiom, % 167.67/167.91 ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc__elim__cases_I4_J,axiom, % 167.67/167.91 ! [V_t,V_s,V_c2,V_c1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 167.67/167.91 => ~ ! [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 167.67/167.91 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_OAssign,axiom, % 167.67/167.91 ! [V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc__elim__cases_I2_J,axiom, % 167.67/167.91 ! [V_t_2,V_s_2,V_a_2,V_X_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2)) % 167.67/167.91 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_Oequations_I2_J,axiom, % 167.67/167.91 ! [V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__add__upd,axiom, % 167.67/167.91 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OBody,axiom, % 167.67/167.91 ! [V_s1,V_n,V_s0,V_pn] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_n),V_s1)) % 167.67/167.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),hAPP(c_Nat_OSuc,V_n)),V_s1)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_WTs__elim__cases_I6_J,axiom, % 167.67/167.91 ! [V_ca_2,V_b_2] : % 167.67/167.91 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) % 167.67/167.91 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I69_J,axiom, % 167.67/167.91 ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(V_f6_2,V_fun_2),V_com_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I9_J,axiom, % 167.67/167.91 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2)) % 167.67/167.91 <=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2),V_a4_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_OWhileFalse,axiom, % 167.67/167.91 ! [V_ca_2,V_s_2,V_b_2] : % 167.67/167.91 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.91 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_OWhileTrue,axiom, % 167.67/167.91 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] : % 167.67/167.91 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 167.67/167.91 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2)) % 167.67/167.91 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2)) % 167.67/167.91 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__add__le__mapE,axiom, % 167.67/167.91 ! [V_h_2,V_g_2,V_f_2,T_b,T_a] : % 167.67/167.91 ( c_Map_Omap__le(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2),V_h_2) % 167.67/167.91 => c_Map_Omap__le(T_a,T_b,V_g_2,V_h_2) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OWhileFalse,axiom, % 167.67/167.91 ! [V_n_2,V_ca_2,V_s_2,V_b_2] : % 167.67/167.91 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.91 => 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)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OWhileTrue,axiom, % 167.67/167.91 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] : % 167.67/167.91 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 167.67/167.91 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2)) % 167.67/167.91 => ( 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)) % 167.67/167.91 => 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)) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln__elim__cases_I5_J,axiom, % 167.67/167.91 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_n_2),V_t_2)) % 167.67/167.91 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.91 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 167.67/167.91 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.91 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OIfTrue,axiom, % 167.67/167.91 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 167.67/167.91 ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.91 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 167.67/167.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OIfFalse,axiom, % 167.67/167.91 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 167.67/167.91 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.91 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 167.67/167.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OSemi,axiom, % 167.67/167.91 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 167.67/167.91 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 167.67/167.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln__elim__cases_I1_J,axiom, % 167.67/167.91 ! [V_t,V_n,V_s] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 167.67/167.91 => V_t = V_s ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OSkip,axiom, % 167.67/167.91 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln__elim__cases_I2_J,axiom, % 167.67/167.91 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_n_2),V_t_2)) % 167.67/167.91 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OAssign,axiom, % 167.67/167.91 ! [V_n_2,V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_n_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I7_J,axiom, % 167.67/167.91 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2)) % 167.67/167.91 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.91 => ? [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 167.67/167.91 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2)) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I8_J,axiom, % 167.67/167.91 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2)) % 167.67/167.91 <=> ( ( V_a6_2 = V_a2_2 % 167.67/167.91 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 167.67/167.91 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.91 & ? [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 167.67/167.91 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2)) ) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln__Suc,axiom, % 167.67/167.91 ! [V_s_H,V_n,V_s,V_c] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 167.67/167.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__le__refl,axiom, % 167.67/167.91 ! [V_f_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,V_f_2,V_f_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I5_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 167.67/167.91 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 167.67/167.91 <=> ( V_fun_2 = V_fun_H_2 % 167.67/167.91 & V_com_2 = V_com_H_2 ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__le__upd,axiom, % 167.67/167.91 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_a] : % 167.67/167.91 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2) % 167.67/167.91 => c_Map_Omap__le(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_a_2),V_b_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_a_2),V_b_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__le__antisym,axiom, % 167.67/167.91 ! [V_g_2,V_f_2,T_b,T_a] : % 167.67/167.91 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2) % 167.67/167.91 => ( c_Map_Omap__le(T_a,T_b,V_g_2,V_f_2) % 167.67/167.91 => V_f_2 = V_g_2 ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__le__trans,axiom, % 167.67/167.91 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : % 167.67/167.91 ( c_Map_Omap__le(T_a,T_b,V_m1_2,V_m2_2) % 167.67/167.91 => ( c_Map_Omap__le(T_a,T_b,V_m2_2,V_m3_2) % 167.67/167.91 => c_Map_Omap__le(T_a,T_b,V_m1_2,V_m3_2) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_upd__None__map__le,axiom, % 167.67/167.91 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,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)),V_f_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I2_J,axiom, % 167.67/167.91 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),V_a4_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__le__imp__upd__le,axiom, % 167.67/167.91 ! [V_y_2,V_x_2,V_m2_2,V_m1_2,T_b,T_a] : % 167.67/167.91 ( c_Map_Omap__le(T_a,T_b,V_m1_2,V_m2_2) % 167.67/167.91 => c_Map_Omap__le(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m1_2),V_x_2),c_Option_Ooption_ONone(T_b)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m2_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__upd__Some__unfold,axiom, % 167.67/167.91 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 167.67/167.91 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 167.67/167.91 <=> ( ( V_x_2 = V_a_2 % 167.67/167.91 & V_b_2 = V_y_2 ) % 167.67/167.91 | ( V_x_2 != V_a_2 % 167.67/167.91 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__upd__triv,axiom, % 167.67/167.91 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 167.67/167.91 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 167.67/167.91 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__upd__eqD1,axiom, % 167.67/167.91 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 167.67/167.91 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) % 167.67/167.91 => V_x_2 = V_y_2 ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln__evalc,axiom, % 167.67/167.91 ! [V_t,V_n,V_s,V_c] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 167.67/167.91 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_eval__eq,axiom, % 167.67/167.91 ! [V_t_2,V_s_2,V_ca_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2)) % 167.67/167.91 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I6_J,axiom, % 167.67/167.91 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2)),V_a2_2),V_a4_2),V_a5_2)) % 167.67/167.91 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.91 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 167.67/167.91 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.91 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I5_J,axiom, % 167.67/167.91 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2)),V_a2_2),V_a4_2),V_a5_2)) % 167.67/167.91 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.91 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 167.67/167.91 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.91 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I4_J,axiom, % 167.67/167.91 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2)) % 167.67/167.91 <=> ? [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 167.67/167.91 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I1_J,axiom, % 167.67/167.91 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_Oequations_I8_J,axiom, % 167.67/167.91 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 167.67/167.91 <=> ( ( V_a5_2 = V_a2_2 % 167.67/167.91 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 167.67/167.91 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.91 & ? [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 167.67/167.91 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_Oequations_I7_J,axiom, % 167.67/167.91 ! [V_a2_2,V_a3_2,V_a1_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 167.67/167.91 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 167.67/167.91 => ? [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 167.67/167.91 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_WT_Oequations_I6_J,axiom, % 167.67/167.91 ! [V_a1_2,V_a2_2] : % 167.67/167.91 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 167.67/167.91 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_While,axiom, % 167.67/167.91 ! [V_b_2,V_ca_2] : % 167.67/167.91 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 167.67/167.91 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I58_J,axiom, % 167.67/167.91 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I59_J,axiom, % 167.67/167.91 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I53_J,axiom, % 167.67/167.91 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I52_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I28_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I29_J,axiom, % 167.67/167.91 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I46_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I47_J,axiom, % 167.67/167.91 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I60_J,axiom, % 167.67/167.91 ! [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) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I61_J,axiom, % 167.67/167.91 ! [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) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I39_J,axiom, % 167.67/167.91 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I38_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I16_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Osimps_I17_J,axiom, % 167.67/167.91 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 167.67/167.91 % 167.67/167.91 fof(fact_com_Orecs_I6_J,axiom, % 167.67/167.91 ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f6_2,V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__le__map__add,axiom, % 167.67/167.91 ! [V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,V_f_2,c_Map_Omap__add(T_a,T_b,V_g_2,V_f_2)) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__le__iff__map__add__commute,axiom, % 167.67/167.91 ! [V_g_2,V_f_2,T_b,T_a] : % 167.67/167.91 ( c_Map_Omap__le(T_a,T_b,V_f_2,c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)) % 167.67/167.91 <=> c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2) = c_Map_Omap__add(T_a,T_b,V_g_2,V_f_2) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_map__add__le__mapI,axiom, % 167.67/167.91 ! [V_g_2,V_h_2,V_f_2,T_b,T_a] : % 167.67/167.91 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_h_2) % 167.67/167.91 => ( c_Map_Omap__le(T_a,T_b,V_g_2,V_h_2) % 167.67/167.91 => ( c_Map_Omap__le(T_a,T_b,V_f_2,c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)) % 167.67/167.91 => c_Map_Omap__le(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2),V_h_2) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_fun__upd__triv,axiom, % 167.67/167.91 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln__elim__cases_I6_J,axiom, % 167.67/167.91 ! [V_s1,V_n,V_s,V_P] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1)) % 167.67/167.91 => ~ ! [B_n] : % 167.67/167.91 ( V_n = hAPP(c_Nat_OSuc,B_n) % 167.67/167.91 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),B_n),V_s1)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_fun__upd__idem,axiom, % 167.67/167.91 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 167.67/167.91 ( hAPP(V_f_2,V_x_2) = V_y_2 % 167.67/167.91 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_fun__upd__other,axiom, % 167.67/167.91 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 167.67/167.91 ( V_z_2 != V_x_2 % 167.67/167.91 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_fun__upd__twist,axiom, % 167.67/167.91 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] : % 167.67/167.91 ( V_a_2 != V_ca_2 % 167.67/167.91 => 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) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_fun__upd__apply,axiom, % 167.67/167.91 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 167.67/167.91 ( ( V_z_2 = V_x_2 % 167.67/167.91 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) % 167.67/167.91 & ( V_z_2 != V_x_2 % 167.67/167.91 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_fun__upd__same,axiom, % 167.67/167.91 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ). % 167.67/167.91 % 167.67/167.91 fof(fact_fun__upd__upd,axiom, % 167.67/167.91 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ). % 167.67/167.91 % 167.67/167.91 fof(fact_fun__upd__idem__iff,axiom, % 167.67/167.91 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 167.67/167.91 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 167.67/167.91 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln__elim__cases_I4_J,axiom, % 167.67/167.91 ! [V_t,V_n,V_s,V_c2,V_c1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_n),V_t)) % 167.67/167.91 => ~ ! [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s),V_n),B_s1)) % 167.67/167.91 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),B_s1),V_n),V_t)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_n__not__Suc__n,axiom, % 167.67/167.91 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 167.67/167.91 % 167.67/167.91 fof(fact_Suc__n__not__n,axiom, % 167.67/167.91 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 167.67/167.91 % 167.67/167.91 fof(fact_nat_Oinject,axiom, % 167.67/167.91 ! [V_nat_H_2,V_nat_2] : % 167.67/167.91 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 167.67/167.91 <=> V_nat_2 = V_nat_H_2 ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_Suc__inject,axiom, % 167.67/167.91 ! [V_y,V_x] : % 167.67/167.91 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 167.67/167.91 => V_x = V_y ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc__WHILE__case,axiom, % 167.67/167.91 ! [V_t_2,V_s_2,V_ca_2,V_b_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_t_2)) % 167.67/167.91 => ( ( V_t_2 = V_s_2 % 167.67/167.91 => hBOOL(hAPP(V_b_2,V_s_2)) ) % 167.67/167.91 => ~ ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.91 => ! [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),B_s1)) % 167.67/167.91 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),B_s1),V_t_2)) ) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln__WHILE__case,axiom, % 167.67/167.91 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_b_2] : % 167.67/167.91 ( 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_t_2)) % 167.67/167.91 => ( ( V_t_2 = V_s_2 % 167.67/167.91 => hBOOL(hAPP(V_b_2,V_s_2)) ) % 167.67/167.91 => ~ ( hBOOL(hAPP(V_b_2,V_s_2)) % 167.67/167.91 => ! [B_s1] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),V_n_2),B_s1)) % 167.67/167.91 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),B_s1),V_n_2),V_t_2)) ) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc__evaln,axiom, % 167.67/167.91 ! [V_t,V_s,V_c] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 167.67/167.91 => ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),B_n),V_t)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_Body__triple__valid__Suc,axiom, % 167.67/167.91 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 167.67/167.91 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) % 167.67/167.91 <=> c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_OLocal,axiom, % 167.67/167.91 ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_ca_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_s1_2)) % 167.67/167.91 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2)))) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_OLocal,axiom, % 167.67/167.91 ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_ca_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_n_2),V_s1_2)) % 167.67/167.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s0_2),V_n_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s0_2),V_Y_2)))) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_ran__map__upd,axiom, % 167.67/167.91 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 167.67/167.91 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.91 => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_vname_Osimps_I2_J,axiom, % 167.67/167.91 ! [V_loc_H_2,V_loc_2] : % 167.67/167.91 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2) % 167.67/167.91 <=> V_loc_2 = V_loc_H_2 ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_triple_Oinject,axiom, % 167.67/167.91 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 167.67/167.91 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 167.67/167.91 <=> ( V_fun1_2 = V_fun1_H_2 % 167.67/167.91 & V_com_2 = V_com_H_2 % 167.67/167.91 & V_fun2_2 = V_fun2_H_2 ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_triple__valid__def2,axiom, % 167.67/167.91 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] : % 167.67/167.91 ( 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)) % 167.67/167.91 <=> ! [B_Z,B_s] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 167.67/167.91 => ! [B_s_H] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H)) % 167.67/167.91 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evaln_Oequations_I3_J,axiom, % 167.67/167.91 ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),V_a5_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)))) % 167.67/167.91 <=> ? [B_s1] : % 167.67/167.91 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) % 167.67/167.91 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),V_a5_2),B_s1)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc_Oequations_I3_J,axiom, % 167.67/167.91 ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)))) % 167.67/167.91 <=> ? [B_s1] : % 167.67/167.91 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_a2_2),V_a3_2)) % 167.67/167.91 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),B_s1)) ) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_triple__valid__Suc,axiom, % 167.67/167.91 ! [V_t,V_n,T_a] : % 167.67/167.91 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 167.67/167.91 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 167.67/167.91 % 167.67/167.91 fof(fact_evalc__elim__cases_I3_J,axiom, % 167.67/167.91 ! [V_t_2,V_s_2,V_ca_2,V_a_2,V_Y_2] : % 167.67/167.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s_2),V_t_2)) % 167.67/167.91 => ~ ! [B_s1] : % 167.67/167.91 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2)) % 167.67/167.92 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_evaln__elim__cases_I3_J,axiom, % 167.67/167.92 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_a_2,V_Y_2] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s_2),V_n_2),V_t_2)) % 167.67/167.92 => ~ ! [B_s1] : % 167.67/167.92 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),hAPP(hAPP(c_Natural_Ogetlocs,V_s_2),V_Y_2)) % 167.67/167.92 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),V_n_2),B_s1)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_triple_Osimps_I2_J,axiom, % 167.67/167.92 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_triple_Orecs,axiom, % 167.67/167.92 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Orecs_I2_J,axiom, % 167.67/167.92 ! [V_loc_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__rec(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osimps_I6_J,axiom, % 167.67/167.92 ! [V_loc_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__case(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Body__triple__valid__0,axiom, % 167.67/167.92 ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insert__code,axiom, % 167.67/167.92 ! [V_x_2,V_A_2,V_y_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 167.67/167.92 <=> ( V_y_2 = V_x_2 % 167.67/167.92 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insert__commute,axiom, % 167.67/167.92 ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insert__absorb2,axiom, % 167.67/167.92 ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_evalc_OCall,axiom, % 167.67/167.92 ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pn_2] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2))),V_s1_2)) % 167.67/167.92 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_evaln_OCall,axiom, % 167.67/167.92 ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pn_2] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s0_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s0_2))),V_n_2),V_s1_2)) % 167.67/167.92 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_s0_2),V_n_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s1_2),hAPP(c_Natural_Ogetlocs,V_s0_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,V_s1_2),c_Com_ORes)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Zero__not__Suc,axiom, % 167.67/167.92 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat_Osimps_I2_J,axiom, % 167.67/167.92 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Suc__not__Zero,axiom, % 167.67/167.92 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat_Osimps_I3_J,axiom, % 167.67/167.92 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Zero__neq__Suc,axiom, % 167.67/167.92 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Suc__neq__Zero,axiom, % 167.67/167.92 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_evaln_Oequations_I10_J,axiom, % 167.67/167.92 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCall(V_a6_2,V_a1_2,V_a3_2)),V_a2_2),V_a4_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)))) % 167.67/167.92 <=> ? [B_s1] : % 167.67/167.92 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a5_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a5_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a6_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) % 167.67/167.92 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),V_a4_2),B_s1)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_evalc_Oequations_I10_J,axiom, % 167.67/167.92 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_a5_2,V_a1_2,V_a3_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)))) % 167.67/167.92 <=> ? [B_s1] : % 167.67/167.92 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a4_2),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,V_a4_2),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_a2_2))),V_a5_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) % 167.67/167.92 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_a2_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a3_2,V_a2_2))),B_s1)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_evalc__elim__cases_I7_J,axiom, % 167.67/167.92 ! [V_s1_2,V_s_2,V_a_2,V_P_2,V_X_2] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)),V_s_2),V_s1_2)) % 167.67/167.92 => ~ ! [B_s1] : % 167.67/167.92 ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) % 167.67/167.92 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_evaln__elim__cases_I7_J,axiom, % 167.67/167.92 ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_P_2,V_X_2] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)),V_s_2),V_n_2),V_s1_2)) % 167.67/167.92 => ~ ! [B_s1] : % 167.67/167.92 ( V_s1_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s1),hAPP(c_Natural_Ogetlocs,V_s_2))),V_X_2),hAPP(hAPP(c_Natural_Ogetlocs,B_s1),c_Com_ORes)) % 167.67/167.92 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P_2)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,V_s_2),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(V_a_2,V_s_2))),V_n_2),B_s1)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_triple_Osize_I1_J,axiom, % 167.67/167.92 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osize_I2_J,axiom, % 167.67/167.92 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_triple_Osize_I2_J,axiom, % 167.67/167.92 ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osize_I4_J,axiom, % 167.67/167.92 ! [V_loc] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osimps_I5_J,axiom, % 167.67/167.92 ! [V_glb_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__case(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Orecs_I1_J,axiom, % 167.67/167.92 ! [V_glb_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__rec(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I1_J,axiom, % 167.67/167.92 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I8_J,axiom, % 167.67/167.92 ! [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) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I2_J,axiom, % 167.67/167.92 ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osimps_I1_J,axiom, % 167.67/167.92 ! [V_glb_H_2,V_glb_2] : % 167.67/167.92 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2) % 167.67/167.92 <=> V_glb_2 = V_glb_H_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osize_I3_J,axiom, % 167.67/167.92 ! [V_glb] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osize_I1_J,axiom, % 167.67/167.92 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osimps_I3_J,axiom, % 167.67/167.92 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ). % 167.67/167.92 % 167.67/167.92 fof(fact_vname_Osimps_I4_J,axiom, % 167.67/167.92 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I7_J,axiom, % 167.67/167.92 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I3_J,axiom, % 167.67/167.92 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I4_J,axiom, % 167.67/167.92 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I5_J,axiom, % 167.67/167.92 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I6_J,axiom, % 167.67/167.92 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I9_J,axiom, % 167.67/167.92 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I16_J,axiom, % 167.67/167.92 ! [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) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I10_J,axiom, % 167.67/167.92 ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I15_J,axiom, % 167.67/167.92 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_option_Osize_I1_J,axiom, % 167.67/167.92 ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_zero__reorient,axiom, % 167.67/167.92 ! [V_x_2,T_a] : % 167.67/167.92 ( class_Groups_Ozero(T_a) % 167.67/167.92 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 167.67/167.92 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat__add__right__cancel,axiom, % 167.67/167.92 ! [V_n_2,V_k_2,V_m_2] : % 167.67/167.92 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) % 167.67/167.92 <=> V_m_2 = V_n_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat__add__left__cancel,axiom, % 167.67/167.92 ! [V_n_2,V_m_2,V_k_2] : % 167.67/167.92 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) % 167.67/167.92 <=> V_m_2 = V_n_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat__add__assoc,axiom, % 167.67/167.92 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat__add__left__commute,axiom, % 167.67/167.92 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat__add__commute,axiom, % 167.67/167.92 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ). % 167.67/167.92 % 167.67/167.92 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 167.67/167.92 ! [V_c,V_b,V_a,T_a] : % 167.67/167.92 ( class_Groups_Oab__semigroup__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__left__cancel,axiom, % 167.67/167.92 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 167.67/167.92 ( class_Groups_Ocancel__semigroup__add(T_a) % 167.67/167.92 => ( 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) % 167.67/167.92 <=> V_b_2 = V_ca_2 ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__right__cancel,axiom, % 167.67/167.92 ! [V_ca_2,V_a_2,V_b_2,T_a] : % 167.67/167.92 ( class_Groups_Ocancel__semigroup__add(T_a) % 167.67/167.92 => ( 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) % 167.67/167.92 <=> V_b_2 = V_ca_2 ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__left__imp__eq,axiom, % 167.67/167.92 ! [V_c,V_b,V_a,T_a] : % 167.67/167.92 ( class_Groups_Ocancel__semigroup__add(T_a) % 167.67/167.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 167.67/167.92 => V_b = V_c ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__imp__eq,axiom, % 167.67/167.92 ! [V_c,V_b,V_a,T_a] : % 167.67/167.92 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 167.67/167.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 167.67/167.92 => V_b = V_c ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__right__imp__eq,axiom, % 167.67/167.92 ! [V_c,V_a,V_b,T_a] : % 167.67/167.92 ( class_Groups_Ocancel__semigroup__add(T_a) % 167.67/167.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) % 167.67/167.92 => V_b = V_c ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__0__left,axiom, % 167.67/167.92 ! [V_a,T_a] : % 167.67/167.92 ( class_Groups_Omonoid__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__0,axiom, % 167.67/167.92 ! [V_a,T_a] : % 167.67/167.92 ( class_Groups_Ocomm__monoid__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_double__zero__sym,axiom, % 167.67/167.92 ! [V_a_2,T_a] : % 167.67/167.92 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.67/167.92 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 167.67/167.92 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__0__right,axiom, % 167.67/167.92 ! [V_a,T_a] : % 167.67/167.92 ( class_Groups_Omonoid__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add_Ocomm__neutral,axiom, % 167.67/167.92 ! [V_a,T_a] : % 167.67/167.92 ( class_Groups_Ocomm__monoid__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__eq__self__zero,axiom, % 167.67/167.92 ! [V_n,V_m] : % 167.67/167.92 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 167.67/167.92 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__is__0,axiom, % 167.67/167.92 ! [V_n_2,V_m_2] : % 167.67/167.92 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.92 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.92 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Nat_Oadd__0__right,axiom, % 167.67/167.92 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 167.67/167.92 % 167.67/167.92 fof(fact_plus__nat_Oadd__0,axiom, % 167.67/167.92 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__Suc__right,axiom, % 167.67/167.92 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__Suc,axiom, % 167.67/167.92 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__Suc__shift,axiom, % 167.67/167.92 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_option_Osize_I2_J,axiom, % 167.67/167.92 ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I14_J,axiom, % 167.67/167.92 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I13_J,axiom, % 167.67/167.92 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I12_J,axiom, % 167.67/167.92 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_com_Osize_I11_J,axiom, % 167.67/167.92 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__is__1,axiom, % 167.67/167.92 ! [V_n_2,V_m_2] : % 167.67/167.92 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.67/167.92 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.67/167.92 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.67/167.92 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.92 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_one__is__add,axiom, % 167.67/167.92 ! [V_n_2,V_m_2] : % 167.67/167.92 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) % 167.67/167.92 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.67/167.92 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.67/167.92 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.92 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat_Osize_I2_J,axiom, % 167.67/167.92 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat_Osize_I4_J,axiom, % 167.67/167.92 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_option_Osize_I4_J,axiom, % 167.67/167.92 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_option_Osize_I3_J,axiom, % 167.67/167.92 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 167.67/167.92 ! [V_a,T_a] : % 167.67/167.92 ( class_Rings_Ocomm__semiring__1(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 167.67/167.92 ! [V_a,T_a] : % 167.67/167.92 ( class_Rings_Ocomm__semiring__1(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__0__iff,axiom, % 167.67/167.92 ! [V_a_2,V_b_2,T_a] : % 167.67/167.92 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 167.67/167.92 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 167.67/167.92 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_double__eq__0__iff,axiom, % 167.67/167.92 ! [V_a_2,T_a] : % 167.67/167.92 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.67/167.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.67/167.92 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bool_Osize_I1_J,axiom, % 167.67/167.92 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bool_Osize_I2_J,axiom, % 167.67/167.92 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat_Osize_I1_J,axiom, % 167.67/167.92 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat__size,axiom, % 167.67/167.92 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 167.67/167.92 % 167.67/167.92 fof(fact_nat_Osize_I3_J,axiom, % 167.67/167.92 hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 167.67/167.92 ! [V_d,V_c,V_b,V_a,T_a] : % 167.67/167.92 ( class_Rings_Ocomm__semiring__1(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 167.67/167.92 ! [V_c,V_b,V_a,T_a] : % 167.67/167.92 ( class_Rings_Ocomm__semiring__1(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 167.67/167.92 ! [V_c,V_b,V_a,T_a] : % 167.67/167.92 ( class_Rings_Ocomm__semiring__1(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 167.67/167.92 ! [V_d,V_c,V_a,T_a] : % 167.67/167.92 ( class_Rings_Ocomm__semiring__1(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 167.67/167.92 ! [V_d,V_c,V_a,T_a] : % 167.67/167.92 ( class_Rings_Ocomm__semiring__1(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 167.67/167.92 ! [V_c,V_a,T_a] : % 167.67/167.92 ( class_Rings_Ocomm__semiring__1(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bool_Osize_I4_J,axiom, % 167.67/167.92 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bool_Osize_I3_J,axiom, % 167.67/167.92 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 167.67/167.92 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 167.67/167.92 ( class_Rings_Osemiring__1(T_a) % 167.67/167.92 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 167.67/167.92 ! [V_i_2,V_inc_2,T_a] : % 167.67/167.92 ( class_Rings_Osemiring__1(T_a) % 167.67/167.92 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_pair__box_Osize_I1_J,axiom, % 167.67/167.92 ! [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))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_hoare__derivs_OCall,axiom, % 167.67/167.92 ! [V_a_2,V_X_2,V_s_H_2,V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] : % 167.67/167.92 ( 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)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),hAPP(c_Natural_Ogetlocs,V_s_H_2)))),V_X_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Oloc,tc_Nat_Onat),c_Natural_Ogetlocs),c_Com_ORes))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.67/167.92 => 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_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ostate,tc_fun(tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),tc_Com_Ostate),c_Natural_Oupdate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Oloc,tc_Nat_Onat),tc_Com_Ostate),c_Natural_Osetlocs),c_Natural_Onewlocs))),c_Com_Ovname_OLoc(c_Com_OArg))),V_a_2)))),c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_sum_Osize_I1_J,axiom, % 167.67/167.92 ! [V_a_2,V_fb_2,V_fa_2,T_b,T_a] : c_Sum__Type_Osum_Osum__size(T_a,T_b,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInl(T_a,T_b),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_sum_Osize_I2_J,axiom, % 167.67/167.92 ! [V_b_2,V_fb_2,V_fa_2,T_b,T_a] : c_Sum__Type_Osum_Osum__size(T_a,T_b,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInr(T_b,T_a),V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fb_2,V_b_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_restrict__map__insert,axiom, % 167.67/167.92 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_ranI,axiom, % 167.67/167.92 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 167.67/167.92 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 167.67/167.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_equalityCE,axiom, % 167.67/167.92 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 167.67/167.92 ( V_A_2 = V_B_2 % 167.67/167.92 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.92 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 167.67/167.92 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_emptyE,axiom, % 167.67/167.92 ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insertE,axiom, % 167.67/167.92 ! [V_A_2,V_b_2,V_a_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 167.67/167.92 => ( V_a_2 != V_b_2 % 167.67/167.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insertCI,axiom, % 167.67/167.92 ! [V_b_2,V_B_2,V_a_2,T_a] : % 167.67/167.92 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 167.67/167.92 => V_a_2 = V_b_2 ) % 167.67/167.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_LoopF,axiom, % 167.67/167.92 ! [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)))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_derivs__insertD,axiom, % 167.67/167.92 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 167.67/167.92 ( 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)) % 167.67/167.92 => ( 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)))) % 167.67/167.92 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_hoare__derivs_Oinsert,axiom, % 167.67/167.92 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 167.67/167.92 ( 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)))) % 167.67/167.92 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 167.67/167.92 => 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)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_restrict__map__to__empty,axiom, % 167.67/167.92 ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.67/167.92 % 167.67/167.92 fof(fact_restrict__map__def,axiom, % 167.67/167.92 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) % 167.67/167.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_restrict__map__empty,axiom, % 167.67/167.92 ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.67/167.92 % 167.67/167.92 fof(fact_empty,axiom, % 167.67/167.92 ! [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))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 167.67/167.92 ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_pair__box_Oinject,axiom, % 167.67/167.92 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 167.67/167.92 ( 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) % 167.67/167.92 <=> ( V_a_2 = V_a_H_2 % 167.67/167.92 & V_b_2 = V_b_H_2 ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_cut,axiom, % 167.67/167.92 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 167.67/167.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 167.67/167.92 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_G_H_2) % 167.67/167.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_restrict__in,axiom, % 167.67/167.92 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_eq__mem__trans,axiom, % 167.67/167.92 ! [V_A_2,T_a,V_b_2,V_a_2] : % 167.67/167.92 ( V_a_2 = V_b_2 % 167.67/167.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 167.67/167.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_eqelem__imp__iff,axiom, % 167.67/167.92 ! [V_A_2,T_a,V_y_2,V_x_2] : % 167.67/167.92 ( V_x_2 = V_y_2 % 167.67/167.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.92 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_eqset__imp__iff,axiom, % 167.67/167.92 ! [V_x_2,T_a,V_B_2,V_A_2] : % 167.67/167.92 ( V_A_2 = V_B_2 % 167.67/167.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.92 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_equals0D,axiom, % 167.67/167.92 ! [V_a_2,T_a,V_A_2] : % 167.67/167.92 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.92 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_mem__def,axiom, % 167.67/167.92 ! [V_A_2,V_x_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.92 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_empty__iff,axiom, % 167.67/167.92 ! [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)))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_ex__in__conv,axiom, % 167.67/167.92 ! [V_A_2,T_a] : % 167.67/167.92 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.67/167.92 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_all__not__in__conv,axiom, % 167.67/167.92 ! [V_A_2,T_a] : % 167.67/167.92 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.67/167.92 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_fun__upd__def,axiom, % 167.67/167.92 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 167.67/167.92 ( ( V_x_2 = V_a_2 % 167.67/167.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 ) % 167.67/167.92 & ( V_x_2 != V_a_2 % 167.67/167.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_singletonE,axiom, % 167.67/167.92 ! [V_a_2,V_b_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.67/167.92 => V_b_2 = V_a_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_singleton__iff,axiom, % 167.67/167.92 ! [V_a_2,V_b_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.67/167.92 <=> V_b_2 = V_a_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_restrict__out,axiom, % 167.67/167.92 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bind__assoc,axiom, % 167.67/167.92 ! [V_g_2,V_f_2,V_x_2,T_c,T_a,T_b] : hAPP(hAPP(c_Option_Obind(T_b,T_a),hAPP(hAPP(c_Option_Obind(T_c,T_b),V_x_2),V_f_2)),V_g_2) = hAPP(hAPP(c_Option_Obind(T_c,T_a),V_x_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_Option_Ooption(T_a)),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_a)),tc_Option_Ooption(T_a)),T_c),c_Option_Obind(T_b,T_a)),V_f_2)),V_g_2)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_ran__empty,axiom, % 167.67/167.92 ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Ass,axiom, % 167.67/167.92 ! [V_a_2,V_X_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_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_hoare__derivs_Oequations_I8_J,axiom, % 167.67/167.92 ! [V_a4_2,V_a3_2,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),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_empty__upd__none,axiom, % 167.67/167.92 ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a) ). % 167.67/167.92 % 167.67/167.92 fof(fact_map__add__empty,axiom, % 167.67/167.92 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2 ). % 167.67/167.92 % 167.67/167.92 fof(fact_empty__map__add,axiom, % 167.67/167.92 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2 ). % 167.67/167.92 % 167.67/167.92 fof(fact_map__add__def,axiom, % 167.67/167.92 ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_map__le__empty,axiom, % 167.67/167.92 ! [V_g_2,T_b,T_a] : c_Map_Omap__le(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_g_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bind__rzero,axiom, % 167.67/167.92 ! [V_x_2,T_a,T_b] : hAPP(hAPP(c_Option_Obind(T_b,T_a),V_x_2),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Option_Ooption_ONone(T_a) ). % 167.67/167.92 % 167.67/167.92 fof(fact_map__comp__def,axiom, % 167.67/167.92 ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_map__comp__empty_I1_J,axiom, % 167.67/167.92 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.67/167.92 % 167.67/167.92 fof(fact_map__comp__empty_I2_J,axiom, % 167.67/167.92 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insertI1,axiom, % 167.67/167.92 ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insert__iff,axiom, % 167.67/167.92 ! [V_A_2,V_b_2,V_a_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 167.67/167.92 <=> ( V_a_2 = V_b_2 % 167.67/167.92 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insert__ident,axiom, % 167.67/167.92 ! [V_B_2,V_A_2,V_x_2,T_a] : % 167.67/167.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.67/167.92 => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2) % 167.67/167.92 <=> V_A_2 = V_B_2 ) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insertI2,axiom, % 167.67/167.92 ! [V_b_2,V_B_2,V_a_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 167.67/167.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insert__absorb,axiom, % 167.67/167.92 ! [V_A_2,V_a_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.67/167.92 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Comp,axiom, % 167.67/167.92 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_G_2,T_a] : % 167.67/167.92 ( 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)))) % 167.67/167.92 => ( 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)))) % 167.67/167.92 => 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)))) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 167.67/167.92 ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_hoare__derivs_OSkip,axiom, % 167.67/167.92 ! [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)))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_empty__not__insert,axiom, % 167.67/167.92 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_insert__not__empty,axiom, % 167.67/167.92 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_doubleton__eq__iff,axiom, % 167.67/167.92 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 167.67/167.92 ( 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)))) % 167.67/167.92 <=> ( ( V_a_2 = V_ca_2 % 167.67/167.92 & V_b_2 = V_d_2 ) % 167.67/167.92 | ( V_a_2 = V_d_2 % 167.67/167.92 & V_b_2 = V_ca_2 ) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_singleton__inject,axiom, % 167.67/167.92 ! [V_b_2,V_a_2,T_a] : % 167.67/167.92 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 167.67/167.92 => V_a_2 = V_b_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_hoare__derivs_OLocal,axiom, % 167.67/167.92 ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_ca_2,V_P_2,V_G_2,T_a] : % 167.67/167.92 ( 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),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),hAPP(hAPP(c_Natural_Ogetlocs,V_s_H_2),V_X_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 167.67/167.92 => 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_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2)))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_ca_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_map__upd__nonempty,axiom, % 167.67/167.92 ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ). % 167.67/167.92 % 167.67/167.92 fof(fact_weak__Body,axiom, % 167.67/167.92 ! [V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] : % 167.67/167.92 ( 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)))) % 167.67/167.92 => 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)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_BodyN,axiom, % 167.67/167.92 ! [V_G_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 167.67/167.92 ( 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)))) % 167.67/167.92 => 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)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_pair__box_Osize_I2_J,axiom, % 167.67/167.92 ! [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) ). % 167.67/167.92 % 167.67/167.92 fof(fact_pair__box_Orecs,axiom, % 167.67/167.92 ! [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) ). % 167.67/167.92 % 167.67/167.92 fof(fact_pair__box_Osimps_I2_J,axiom, % 167.67/167.92 ! [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) ). % 167.67/167.92 % 167.67/167.92 fof(fact_the__elem__eq,axiom, % 167.67/167.92 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ). % 167.67/167.92 % 167.67/167.92 fof(fact_Inl__not__Inr,axiom, % 167.67/167.92 ! [V_b,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b) ). % 167.67/167.92 % 167.67/167.92 fof(fact_sum_Osimps_I3_J,axiom, % 167.67/167.92 ! [V_b_H,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b_H) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Inr__not__Inl,axiom, % 167.67/167.92 ! [V_a,V_b,T_a,T_b] : hAPP(c_Sum__Type_OInr(T_b,T_a),V_b) != hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) ). % 167.67/167.92 % 167.67/167.92 fof(fact_sum_Osimps_I4_J,axiom, % 167.67/167.92 ! [V_a_1,V_b_H_1,T_a_1,T_b_1] : hAPP(c_Sum__Type_OInr(T_b_1,T_a_1),V_b_H_1) != hAPP(c_Sum__Type_OInl(T_a_1,T_b_1),V_a_1) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bot__fun__def,axiom, % 167.67/167.92 ! [V_x_2,T_b,T_a] : % 167.67/167.92 ( class_Orderings_Obot(T_a) % 167.67/167.92 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bot__empty__eq,axiom, % 167.67/167.92 ! [V_x_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 167.67/167.92 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bot__nat__def,axiom, % 167.67/167.92 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_eq__mem,axiom, % 167.67/167.92 ! [V_y_2,V_x_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 167.67/167.92 <=> V_x_2 = V_y_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Inr__inject,axiom, % 167.67/167.92 ! [V_y,V_x,T_a,T_b] : % 167.67/167.92 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y) % 167.67/167.92 => V_x = V_y ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_sum_Osimps_I2_J,axiom, % 167.67/167.92 ! [V_b_H_2,V_b_2,T_a,T_b] : % 167.67/167.92 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_b_2) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_b_H_2) % 167.67/167.92 <=> V_b_2 = V_b_H_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Inl__inject,axiom, % 167.67/167.92 ! [V_y,V_x,T_b,T_a] : % 167.67/167.92 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y) % 167.67/167.92 => V_x = V_y ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_sum_Osimps_I1_J,axiom, % 167.67/167.92 ! [V_a_H_2,V_a_2,T_b,T_a] : % 167.67/167.92 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_a_2) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_a_H_2) % 167.67/167.92 <=> V_a_2 = V_a_H_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_pred__equals__eq,axiom, % 167.67/167.92 ! [V_S_2,V_R_2,T_a] : % 167.67/167.92 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) % 167.67/167.92 <=> V_R_2 = V_S_2 ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_bot__apply,axiom, % 167.67/167.92 ! [V_x_2,T_b,T_a] : % 167.67/167.92 ( class_Orderings_Obot(T_a) % 167.67/167.92 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Projl_Osimps,axiom, % 167.67/167.92 ! [V_x,T_b,T_a] : c_Sum__Type_OProjl(T_a,T_b,hAPP(c_Sum__Type_OInl(T_a,T_b),V_x)) = V_x ). % 167.67/167.92 % 167.67/167.92 fof(fact_Projr_Osimps,axiom, % 167.67/167.92 ! [V_x,T_b,T_a] : c_Sum__Type_OProjr(T_a,T_b,hAPP(c_Sum__Type_OInr(T_b,T_a),V_x)) = V_x ). % 167.67/167.92 % 167.67/167.92 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 167.67/167.92 ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 167.67/167.92 % 167.67/167.92 fof(fact_sum_Osize_I3_J,axiom, % 167.67/167.92 ! [V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInl(T_a,T_b),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_sum_Osize_I4_J,axiom, % 167.67/167.92 ! [V_b,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_a),V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.92 % 167.67/167.92 fof(fact_MGT__BodyN,axiom, % 167.67/167.92 ! [V_G_2,V_pn_2] : % 167.67/167.92 ( 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)))) % 167.67/167.92 => 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)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_,axiom, % 167.67/167.92 ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_fun__upd__None__restrict,axiom, % 167.67/167.92 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 167.67/167.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.67/167.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) % 167.67/167.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.67/167.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_escape,axiom, % 167.67/167.92 ! [V_Q_2,V_ca_2,V_G_2,T_a,V_P_2] : % 167.67/167.92 ( ! [B_Z,B_s] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 167.67/167.92 => 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)))) ) % 167.67/167.92 => 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)))) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_dom__eq__singleton__conv,axiom, % 167.67/167.92 ! [V_x_2,V_f_2,T_b,T_a] : % 167.67/167.92 ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 167.67/167.92 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_DiffE,axiom, % 167.67/167.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.67/167.92 ( 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))) % 167.67/167.92 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_DiffI,axiom, % 167.67/167.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.67/167.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 167.67/167.92 => 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))) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_Diff__idemp,axiom, % 167.67/167.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.67/167.92 % 167.67/167.92 fof(fact_diff__eq__diff__eq,axiom, % 167.67/167.92 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 167.67/167.92 ( class_Groups_Oab__group__add(T_a) % 167.67/167.92 => ( 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) % 167.67/167.92 => ( V_a_2 = V_b_2 % 167.67/167.92 <=> V_ca_2 = V_d_2 ) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_diff__0__right,axiom, % 167.67/167.92 ! [V_a,T_a] : % 167.67/167.92 ( class_Groups_Ogroup__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_diff__self,axiom, % 167.67/167.92 ! [V_a,T_a] : % 167.67/167.92 ( class_Groups_Ogroup__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_eq__iff__diff__eq__0,axiom, % 167.67/167.92 ! [V_b_2,V_a_2,T_a] : % 167.67/167.92 ( class_Groups_Oab__group__add(T_a) % 167.67/167.92 => ( V_a_2 = V_b_2 % 167.67/167.92 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_right__minus__eq,axiom, % 167.67/167.92 ! [V_b_2,V_a_2,T_a] : % 167.67/167.92 ( class_Groups_Ogroup__add(T_a) % 167.67/167.92 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.67/167.92 <=> V_a_2 = V_b_2 ) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_dom__minus,axiom, % 167.67/167.92 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 167.67/167.92 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_diff__add__cancel,axiom, % 167.67/167.92 ! [V_b,V_a,T_a] : % 167.67/167.92 ( class_Groups_Ogroup__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_add__diff__cancel,axiom, % 167.67/167.92 ! [V_b,V_a,T_a] : % 167.67/167.92 ( class_Groups_Ogroup__add(T_a) % 167.67/167.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_DiffD2,axiom, % 167.67/167.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.67/167.92 ( 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))) % 167.67/167.92 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 167.67/167.92 % 167.67/167.92 fof(fact_DiffD1,axiom, % 167.67/167.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.67/167.92 ( 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))) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Diff__iff,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.67/167.93 ( 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))) % 167.67/167.93 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.93 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Diff__cancel,axiom, % 167.67/167.93 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Diff__empty,axiom, % 167.67/167.93 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 167.67/167.93 % 167.67/167.93 fof(fact_empty__Diff,axiom, % 167.67/167.93 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_map__le__def,axiom, % 167.67/167.93 ! [V_m_092_060_094isub_0622_2,V_m_092_060_094isub_0621_2,T_b,T_a] : % 167.67/167.93 ( c_Map_Omap__le(T_a,T_b,V_m_092_060_094isub_0621_2,V_m_092_060_094isub_0622_2) % 167.67/167.93 <=> ! [B_x] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Map_Odom(T_a,T_b,V_m_092_060_094isub_0621_2))) % 167.67/167.93 => hAPP(V_m_092_060_094isub_0621_2,B_x) = hAPP(V_m_092_060_094isub_0622_2,B_x) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_insert__Diff1,axiom, % 167.67/167.93 ! [V_A_2,V_B_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_insert__Diff__if,axiom, % 167.67/167.93 ! [V_A_2,V_B_2,V_x_2,T_a] : % 167.67/167.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) % 167.67/167.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_insert__Diff__single,axiom, % 167.67/167.93 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Diff__insert2,axiom, % 167.67/167.93 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Diff__insert,axiom, % 167.67/167.93 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.67/167.93 % 167.67/167.93 fof(fact_dom__fun__upd,axiom, % 167.67/167.93 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 167.67/167.93 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 167.67/167.93 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) % 167.67/167.93 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 167.67/167.93 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_domIff,axiom, % 167.67/167.93 ! [V_m_2,T_b,V_a_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 167.67/167.93 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_domI,axiom, % 167.67/167.93 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 167.67/167.93 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_insert__dom,axiom, % 167.67/167.93 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 167.67/167.93 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 167.67/167.93 => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 167.67/167.93 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 167.67/167.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 167.67/167.93 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 167.67/167.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 167.67/167.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 167.67/167.93 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 167.67/167.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 167.67/167.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_dom__empty,axiom, % 167.67/167.93 ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_dom__eq__empty__conv,axiom, % 167.67/167.93 ! [V_f_2,T_b,T_a] : % 167.67/167.93 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.93 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Diff__insert__absorb,axiom, % 167.67/167.93 ! [V_A_2,V_x_2,T_a] : % 167.67/167.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_insert__Diff,axiom, % 167.67/167.93 ! [V_A_2,V_a_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.67/167.93 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_MGT__def,axiom, % 167.67/167.93 ! [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)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_fun__upd__restrict,axiom, % 167.67/167.93 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_map__add__upd__left,axiom, % 167.67/167.93 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 167.67/167.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 167.67/167.93 => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_restrict__fun__upd,axiom, % 167.67/167.93 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 167.67/167.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.67/167.93 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) % 167.67/167.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.67/167.93 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_fun__upd__restrict__conv,axiom, % 167.67/167.93 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 167.67/167.93 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_elem__set,axiom, % 167.67/167.93 ! [V_xo_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 167.67/167.93 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_set__empty__eq,axiom, % 167.67/167.93 ! [V_xo_2,T_a] : % 167.67/167.93 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.93 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 167.67/167.93 ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_MGF__lemma1,axiom, % 167.67/167.93 ! [V_ca_2,V_G_2] : % 167.67/167.93 ( c_Hoare__Mirabelle_Ostate__not__singleton % 167.67/167.93 => ( ! [B_x] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 167.67/167.93 => 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)))) ) % 167.67/167.93 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 167.67/167.93 => 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)))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_MGF__complete,axiom, % 167.67/167.93 ! [V_Q_2,V_P_2,V_ca_2] : % 167.67/167.93 ( 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)))) % 167.67/167.93 => ( 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)))) % 167.67/167.93 => 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)))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_MGT__alternD,axiom, % 167.67/167.93 ! [V_ca_2,V_G_2] : % 167.67/167.93 ( c_Hoare__Mirabelle_Ostate__not__singleton % 167.67/167.93 => ( 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)))) % 167.67/167.93 => 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)))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 167.67/167.93 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2) % 167.67/167.93 => c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_fun__diff__def,axiom, % 167.67/167.93 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 167.67/167.93 ( class_Groups_Ominus(T_a) % 167.67/167.93 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_MGT__alternI,axiom, % 167.67/167.93 ! [V_ca_2,V_G_2] : % 167.67/167.93 ( 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)))) % 167.67/167.93 => 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)))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__apply,axiom, % 167.67/167.93 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 167.67/167.93 ( class_Groups_Ominus(T_a) % 167.67/167.93 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_ran__restrictD,axiom, % 167.67/167.93 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2)))) % 167.67/167.93 => ? [B_x] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.67/167.93 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_the__elem__def,axiom, % 167.67/167.93 ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 167.67/167.93 % 167.67/167.93 fof(fact_conseq1,axiom, % 167.67/167.93 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_G_2,T_a] : % 167.67/167.93 ( 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)))) % 167.67/167.93 => ( ! [B_Z,B_s] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 167.67/167.93 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 167.67/167.93 => 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)))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__0__eq__0,axiom, % 167.67/167.93 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__nat_Odiff__0,axiom, % 167.67/167.93 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__self__eq__0,axiom, % 167.67/167.93 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diffs0__imp__equal,axiom, % 167.67/167.93 ! [V_n,V_m] : % 167.67/167.93 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.93 => V_m = V_n ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Suc__diff__diff,axiom, % 167.67/167.93 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__Suc__Suc,axiom, % 167.67/167.93 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__add__inverse2,axiom, % 167.67/167.93 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__add__inverse,axiom, % 167.67/167.93 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__diff__left,axiom, % 167.67/167.93 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__cancel,axiom, % 167.67/167.93 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__cancel2,axiom, % 167.67/167.93 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 167.67/167.93 % 167.67/167.93 fof(fact_triple__valid__def,axiom, % 167.67/167.93 ! [V_t_2,V_n_2,T_a] : % 167.67/167.93 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 167.67/167.93 <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__add__0,axiom, % 167.67/167.93 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.67/167.93 % 167.67/167.93 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 167.67/167.93 ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 167.67/167.93 ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_hoare__sound,axiom, % 167.67/167.93 ! [V_ts_2,V_G_2,T_a] : % 167.67/167.93 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 167.67/167.93 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 167.67/167.93 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 167.67/167.93 ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 167.67/167.93 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.93 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 167.67/167.93 | ? [B_x,B_y] : % 167.67/167.93 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 167.67/167.93 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 167.67/167.93 & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_conseq2,axiom, % 167.67/167.93 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_G_2,T_a] : % 167.67/167.93 ( 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)))) % 167.67/167.93 => ( ! [B_Z,B_s] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 167.67/167.93 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 167.67/167.93 => 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)))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Option_Omap__def,axiom, % 167.67/167.93 ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_the__sym__eq__trivial,axiom, % 167.67/167.93 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 167.67/167.93 % 167.67/167.93 fof(fact_the__eq__trivial,axiom, % 167.67/167.93 ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 167.67/167.93 % 167.67/167.93 fof(fact_sum_Orecs_I1_J,axiom, % 167.67/167.93 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_a,T_b] : c_Sum__Type_Osum_Osum__rec(T_b,T_a,T_c,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2)) = hAPP(V_f1_2,V_a_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_sum_Orecs_I2_J,axiom, % 167.67/167.93 ! [V_b_2,V_f2_2,V_f1_2,T_c,T_a,T_b] : c_Sum__Type_Osum_Osum__rec(T_b,T_a,T_c,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2)) = hAPP(V_f2_2,V_b_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_restrict__upd__same,axiom, % 167.67/167.93 ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 167.67/167.93 % 167.67/167.93 fof(fact_restrict__complement__singleton__eq,axiom, % 167.67/167.93 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_InlI,axiom, % 167.67/167.93 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInl(T_a,T_b),V_a_2)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_ComplI,axiom, % 167.67/167.93 ! [V_A_2,V_ca_2,T_a] : % 167.67/167.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.93 => 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))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_InrI,axiom, % 167.67/167.93 ! [V_A_2,T_b,V_B_2,V_b_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_b,T_a)),hAPP(c_Sum__Type_OInr(T_a,T_b),V_b_2)),c_Sum__Type_OPlus(T_b,T_a,V_A_2,V_B_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__commute,axiom, % 167.67/167.93 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ). % 167.67/167.93 % 167.67/167.93 fof(fact_fun__Compl__def,axiom, % 167.67/167.93 ! [V_x_2,V_A_2,T_b,T_a] : % 167.67/167.93 ( class_Groups_Ouminus(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_compl__eq__compl__iff,axiom, % 167.67/167.93 ! [V_y_2,V_x_2,T_a] : % 167.67/167.93 ( class_Lattices_Oboolean__algebra(T_a) % 167.67/167.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 167.67/167.93 <=> V_x_2 = V_y_2 ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_uminus__apply,axiom, % 167.67/167.93 ! [V_x_2,V_A_2,T_b,T_a] : % 167.67/167.93 ( class_Groups_Ouminus(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_double__compl,axiom, % 167.67/167.93 ! [V_x,T_a] : % 167.67/167.93 ( class_Lattices_Oboolean__algebra(T_a) % 167.67/167.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Compl__eq__Compl__iff,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2) % 167.67/167.93 <=> V_A_2 = V_B_2 ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_double__complement,axiom, % 167.67/167.93 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 167.67/167.93 % 167.67/167.93 fof(fact_neg__equal__iff__equal,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 167.67/167.93 <=> V_a_2 = V_b_2 ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__equation__iff,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 167.67/167.93 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_equation__minus__iff,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 167.67/167.93 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__minus,axiom, % 167.67/167.93 ! [V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__zero,axiom, % 167.67/167.93 ! [T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_neg__0__equal__iff__equal,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 167.67/167.93 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_equal__neg__zero,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.67/167.93 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 167.67/167.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_neg__equal__0__iff__equal,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.67/167.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_neg__equal__zero,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.67/167.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 167.67/167.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__add__distrib,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oab__group__add(T_a) % 167.67/167.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__add,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__minus__cancel,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__add__cancel,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_ComplE,axiom, % 167.67/167.93 ! [V_A_2,V_ca_2,T_a] : % 167.67/167.93 ( 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))) % 167.67/167.93 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_ComplD,axiom, % 167.67/167.93 ! [V_A_2,V_ca_2,T_a] : % 167.67/167.93 ( 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))) % 167.67/167.93 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Compl__iff,axiom, % 167.67/167.93 ! [V_A_2,V_ca_2,T_a] : % 167.67/167.93 ( 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))) % 167.67/167.93 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__diff__eq,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oab__group__add(T_a) % 167.67/167.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_option__map__is__None,axiom, % 167.67/167.93 ! [V_opt_2,V_f_2,T_a,T_b] : % 167.67/167.93 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 167.67/167.93 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_option__map__None,axiom, % 167.67/167.93 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ). % 167.67/167.93 % 167.67/167.93 fof(fact_option__map__eq__Some,axiom, % 167.67/167.93 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 167.67/167.93 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 167.67/167.93 <=> ? [B_z] : % 167.67/167.93 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 167.67/167.93 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_option__map__Some,axiom, % 167.67/167.93 ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Plus__eq__empty__conv,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,T_b,T_a] : % 167.67/167.93 ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) % 167.67/167.93 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.93 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__unique,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 167.67/167.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_ab__left__minus,axiom, % 167.67/167.93 ! [V_a,T_a] : % 167.67/167.93 ( class_Groups_Oab__group__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_left__minus,axiom, % 167.67/167.93 ! [V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_eq__neg__iff__add__eq__0,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 167.67/167.93 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_right__minus,axiom, % 167.67/167.93 ! [V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__0,axiom, % 167.67/167.93 ! [V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__def,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_ab__diff__minus,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oab__group__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 167.67/167.93 ! [V_y,V_x,T_a] : % 167.67/167.93 ( class_Rings_Ocomm__ring__1(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__minus__eq__add,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Ogroup__add(T_a) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_dom__option__map,axiom, % 167.67/167.93 ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__Suc,axiom, % 167.67/167.93 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_surjective__sum,axiom, % 167.67/167.93 ! [V_f_2,T_b,T_c,T_a] : c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,hAPP(hAPP(c_COMBB(tc_sum(T_a,T_b),T_c,T_a),V_f_2),c_Sum__Type_OInl(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_sum(T_a,T_b),T_c,T_b),V_f_2),c_Sum__Type_OInr(T_b,T_a))) = V_f_2 ). % 167.67/167.93 % 167.67/167.93 fof(fact_fun__upd__image,axiom, % 167.67/167.93 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) % 167.67/167.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_PlusE,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,V_u_2,T_b,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(tc_sum(T_a,T_b)),V_u_2),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 167.67/167.93 => ( ! [B_x] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.67/167.93 => V_u_2 != hAPP(c_Sum__Type_OInl(T_a,T_b),B_x) ) % 167.67/167.93 => ~ ! [B_y] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_B_2)) % 167.67/167.93 => V_u_2 != hAPP(c_Sum__Type_OInr(T_b,T_a),B_y) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Suml_Osimps,axiom, % 167.67/167.93 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Sum__Type_OSuml(T_b,T_a,T_c,V_f_2),hAPP(c_Sum__Type_OInl(T_b,T_c),V_x_2)) = hAPP(V_f_2,V_x_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_the__inv__into__def,axiom, % 167.67/167.93 ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Ints__double__eq__0__iff,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Int_Oring__char__0(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.67/167.93 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.67/167.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__eq__if,axiom, % 167.67/167.93 ! [V_n,V_m] : % 167.67/167.93 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 167.67/167.93 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Sumr_Osimps,axiom, % 167.67/167.93 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Sum__Type_OSumr(T_b,T_a,T_c,V_f_2),hAPP(c_Sum__Type_OInr(T_b,T_c),V_x_2)) = hAPP(V_f_2,V_x_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__insert__iff,axiom, % 167.67/167.93 ! [V_B_2,V_x_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 167.67/167.93 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 167.67/167.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_order__refl,axiom, % 167.67/167.93 ! [V_x,T_a] : % 167.67/167.93 ( class_Orderings_Opreorder(T_a) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_equalityI,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.67/167.93 => V_A_2 = V_B_2 ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subsetD,axiom, % 167.67/167.93 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__eqI,axiom, % 167.67/167.93 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 167.67/167.93 ( V_b_2 = hAPP(V_f_2,V_x_2) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_empty__subsetI,axiom, % 167.67/167.93 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__diff__subset,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__image,axiom, % 167.67/167.93 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2)),V_A_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__ident,axiom, % 167.67/167.93 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 167.67/167.93 % 167.67/167.93 fof(fact_one__reorient,axiom, % 167.67/167.93 ! [V_x_2,T_a] : % 167.67/167.93 ( class_Groups_Oone(T_a) % 167.67/167.93 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 167.67/167.93 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__refl,axiom, % 167.67/167.93 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_set__eq__subset,axiom, % 167.67/167.93 ! [T_a,V_B_2,V_A_2] : % 167.67/167.93 ( V_A_2 = V_B_2 % 167.67/167.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__image__iff,axiom, % 167.67/167.93 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 167.67/167.93 <=> ? [B_AA] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 167.67/167.93 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_equalityD1,axiom, % 167.67/167.93 ! [T_a,V_B_2,V_A_2] : % 167.67/167.93 ( V_A_2 = V_B_2 % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_equalityD2,axiom, % 167.67/167.93 ! [T_a,V_B_2,V_A_2] : % 167.67/167.93 ( V_A_2 = V_B_2 % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__mono,axiom, % 167.67/167.93 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__trans,axiom, % 167.67/167.93 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_equalityE,axiom, % 167.67/167.93 ! [T_a,V_B_2,V_A_2] : % 167.67/167.93 ( V_A_2 = V_B_2 % 167.67/167.93 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_le__fun__def,axiom, % 167.67/167.93 ! [V_g_2,V_f_2,T_a,T_b] : % 167.67/167.93 ( class_Orderings_Oord(T_b) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.67/167.93 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_linorder__linear,axiom, % 167.67/167.93 ! [V_y,V_x,T_a] : % 167.67/167.93 ( class_Orderings_Olinorder(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_order__eq__iff,axiom, % 167.67/167.93 ! [V_y_2,V_x_2,T_a] : % 167.67/167.93 ( class_Orderings_Oorder(T_a) % 167.67/167.93 => ( V_x_2 = V_y_2 % 167.67/167.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_rev__predicate1D,axiom, % 167.67/167.93 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 167.67/167.93 ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 167.67/167.93 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_order__eq__refl,axiom, % 167.67/167.93 ! [V_y,V_x,T_a] : % 167.67/167.93 ( class_Orderings_Opreorder(T_a) % 167.67/167.93 => ( V_x = V_y % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_le__funD,axiom, % 167.67/167.93 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 167.67/167.93 ( class_Orderings_Oord(T_b) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_order__antisym__conv,axiom, % 167.67/167.93 ! [V_x_2,V_y_2,T_a] : % 167.67/167.93 ( class_Orderings_Oorder(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.93 <=> V_x_2 = V_y_2 ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_sum__case__weak__cong,axiom, % 167.67/167.93 ! [V_g_2,V_f_2,T_b,T_c,T_a,V_t_2,V_s_2] : % 167.67/167.93 ( V_s_2 = V_t_2 % 167.67/167.93 => hAPP(c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,V_f_2,V_g_2),V_s_2) = hAPP(c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,V_f_2,V_g_2),V_t_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_predicate1D,axiom, % 167.67/167.93 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 167.67/167.93 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 167.67/167.93 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_ord__eq__le__trans,axiom, % 167.67/167.93 ! [V_c,V_b,V_a,T_a] : % 167.67/167.93 ( class_Orderings_Oord(T_a) % 167.67/167.93 => ( V_a = V_b % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_xt1_I3_J,axiom, % 167.67/167.93 ! [V_c,V_b,V_a,T_a] : % 167.67/167.93 ( class_Orderings_Oorder(T_a) % 167.67/167.93 => ( V_a = V_b % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_ord__le__eq__trans,axiom, % 167.67/167.93 ! [V_c,V_b,V_a,T_a] : % 167.67/167.93 ( class_Orderings_Oord(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.67/167.93 => ( V_b = V_c % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_xt1_I4_J,axiom, % 167.67/167.93 ! [V_c,V_a,V_b,T_a] : % 167.67/167.93 ( class_Orderings_Oorder(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.67/167.93 => ( V_b = V_c % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_order__antisym,axiom, % 167.67/167.93 ! [V_y,V_x,T_a] : % 167.67/167.93 ( class_Orderings_Oorder(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.67/167.93 => V_x = V_y ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_order__trans,axiom, % 167.67/167.93 ! [V_z,V_y,V_x,T_a] : % 167.67/167.93 ( class_Orderings_Opreorder(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_xt1_I5_J,axiom, % 167.67/167.93 ! [V_x,V_y,T_a] : % 167.67/167.93 ( class_Orderings_Oorder(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.93 => V_x = V_y ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_xt1_I6_J,axiom, % 167.67/167.93 ! [V_z,V_x,V_y,T_a] : % 167.67/167.93 ( class_Orderings_Oorder(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_le__funE,axiom, % 167.67/167.93 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 167.67/167.93 ( class_Orderings_Oord(T_b) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_sum__case__inject,axiom, % 167.67/167.93 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_b,T_c,T_a] : % 167.67/167.93 ( c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,V_f1_2,V_f2_2) = c_Sum__Type_Osum_Osum__case(T_a,T_c,T_b,V_g1_2,V_g2_2) % 167.67/167.93 => ~ ( V_f1_2 = V_g1_2 % 167.67/167.93 => V_f2_2 != V_g2_2 ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_linorder__le__cases,axiom, % 167.67/167.93 ! [V_y,V_x,T_a] : % 167.67/167.93 ( class_Orderings_Olinorder(T_a) % 167.67/167.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Ints__1,axiom, % 167.67/167.93 ! [T_a] : % 167.67/167.93 ( class_Rings_Oring__1(T_a) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Sumr__inject,axiom, % 167.67/167.93 ! [V_g_2,V_f_2,T_a,T_c,T_b] : % 167.67/167.93 ( c_Sum__Type_OSumr(T_b,T_c,T_a,V_f_2) = c_Sum__Type_OSumr(T_b,T_c,T_a,V_g_2) % 167.67/167.93 => V_f_2 = V_g_2 ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Suml__inject,axiom, % 167.67/167.93 ! [V_g_2,V_f_2,T_b,T_c,T_a] : % 167.67/167.93 ( c_Sum__Type_OSuml(T_a,T_c,T_b,V_f_2) = c_Sum__Type_OSuml(T_a,T_c,T_b,V_g_2) % 167.67/167.93 => V_f_2 = V_g_2 ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__iff,axiom, % 167.67/167.93 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 167.67/167.93 <=> ? [B_x] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 167.67/167.93 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_imageI,axiom, % 167.67/167.93 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_rev__image__eqI,axiom, % 167.67/167.93 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_empty__is__image,axiom, % 167.67/167.93 ! [V_A_2,V_f_2,T_b,T_a] : % 167.67/167.93 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) % 167.67/167.93 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__empty,axiom, % 167.67/167.93 ! [V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__is__empty,axiom, % 167.67/167.93 ! [V_A_2,V_f_2,T_a,T_b] : % 167.67/167.93 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.93 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__insert,axiom, % 167.67/167.93 ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_sum__case__KK,axiom, % 167.67/167.93 ! [V_x_2,V_a_2,T_c,T_a,T_b] : hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_a_2),hAPP(c_COMBK(T_a,T_c),V_a_2)),V_x_2) = V_a_2 ). % 167.67/167.93 % 167.67/167.93 fof(fact_in__mono,axiom, % 167.67/167.93 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_set__rev__mp,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_set__mp,axiom, % 167.67/167.93 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__le__imp__le__left,axiom, % 167.67/167.93 ! [V_b,V_a,V_c,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__le__imp__le__right,axiom, % 167.67/167.93 ! [V_b,V_c,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__mono,axiom, % 167.67/167.93 ! [V_d,V_c,V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__left__mono,axiom, % 167.67/167.93 ! [V_c,V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__right__mono,axiom, % 167.67/167.93 ! [V_c,V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__le__cancel__left,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.67/167.93 => ( 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))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__le__cancel__right,axiom, % 167.67/167.93 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.67/167.93 => ( 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))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_bot__least,axiom, % 167.67/167.93 ! [V_x,T_a] : % 167.67/167.93 ( class_Orderings_Obot(T_a) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__eq__diff__less__eq,axiom, % 167.67/167.93 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.93 => ( 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) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__empty,axiom, % 167.67/167.93 ! [V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 167.67/167.93 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_insert__mono,axiom, % 167.67/167.93 ! [V_a_2,V_D_2,V_C_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__insertI2,axiom, % 167.67/167.93 ! [V_b_2,V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__insertI,axiom, % 167.67/167.93 ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 167.67/167.93 % 167.67/167.93 fof(fact_le__minus__iff,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__le__iff,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_neg__le__iff__le,axiom, % 167.67/167.93 ! [V_a_2,V_b_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_le__imp__neg__le,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_compl__le__compl__iff,axiom, % 167.67/167.93 ! [V_y_2,V_x_2,T_a] : % 167.67/167.93 ( class_Lattices_Oboolean__algebra(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_compl__mono,axiom, % 167.67/167.93 ! [V_y,V_x,T_a] : % 167.67/167.93 ( class_Lattices_Oboolean__algebra(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Diff__subset,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Diff__mono,axiom, % 167.67/167.93 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_double__diff,axiom, % 167.67/167.93 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.67/167.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Compl__subset__Compl__iff,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Compl__anti__mono,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_thin,axiom, % 167.67/167.93 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 167.67/167.93 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 167.67/167.93 => ( 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)) % 167.67/167.93 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_weaken,axiom, % 167.67/167.93 ! [V_ts_2,V_ts_H_2,V_G_2,T_a] : % 167.67/167.93 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_H_2) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 167.67/167.93 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_asm,axiom, % 167.67/167.93 ! [V_G_2,V_ts_2,T_a] : % 167.67/167.93 ( 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)) % 167.67/167.93 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_pred__subset__eq,axiom, % 167.67/167.93 ! [V_S_2,V_R_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Ints__odd__nonzero,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Int_Oring__char__0(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.67/167.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_insert__image,axiom, % 167.67/167.93 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__nonneg__nonneg,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__nonneg__eq__0__iff,axiom, % 167.67/167.93 ! [V_y_2,V_x_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 167.67/167.93 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.67/167.93 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.67/167.93 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__increasing,axiom, % 167.67/167.93 ! [V_c,V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__increasing2,axiom, % 167.67/167.93 ! [V_a,V_b,V_c,T_a] : % 167.67/167.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_add__nonpos__nonpos,axiom, % 167.67/167.93 ! [V_b,V_a,T_a] : % 167.67/167.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_le__iff__diff__le__0,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_minus__le__self__iff,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_neg__le__0__iff__le,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_le__minus__self__iff,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_neg__0__le__iff__le,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_insert__subset,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2)) % 167.67/167.93 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.67/167.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__insert,axiom, % 167.67/167.93 ! [V_B_2,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__singletonD,axiom, % 167.67/167.93 ! [V_x_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.67/167.93 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.93 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_One__nat__def,axiom, % 167.67/167.93 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Suc__eq__plus1__left,axiom, % 167.67/167.93 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Suc__eq__plus1,axiom, % 167.67/167.93 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__Suc__1,axiom, % 167.67/167.93 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__Suc__eq__diff__pred,axiom, % 167.67/167.93 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__constant__conv,axiom, % 167.67/167.93 ! [V_ca_2,T_b,T_a,V_A_2] : % 167.67/167.93 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.93 => 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)) ) % 167.67/167.93 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.93 => 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))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_subset__Compl__self__eq,axiom, % 167.67/167.93 ! [V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 167.67/167.93 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_sum_Osimps_I6_J,axiom, % 167.67/167.93 ! [V_b_2,V_f2_2,V_f1_2,T_c,T_a,T_b] : hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_a,T_c,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2)) = hAPP(V_f2_2,V_b_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_sum_Osimps_I5_J,axiom, % 167.67/167.93 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_a,T_b] : hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_a,T_c,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2)) = hAPP(V_f1_2,V_a_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_map__le__implies__dom__le,axiom, % 167.67/167.93 ! [V_g_2,V_f_2,T_b,T_a] : % 167.67/167.93 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),c_Map_Odom(T_a,T_b,V_g_2))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_nat__case__0,axiom, % 167.67/167.93 ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 167.67/167.93 % 167.67/167.93 fof(fact_nat__case__Suc,axiom, % 167.67/167.93 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Ints__0,axiom, % 167.67/167.93 ! [T_a] : % 167.67/167.93 ( class_Rings_Oring__1(T_a) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Ints__add,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Rings_Oring__1(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Ints__diff,axiom, % 167.67/167.93 ! [V_b_2,V_a_2,T_a] : % 167.67/167.93 ( class_Rings_Oring__1(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Ints__minus,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Rings_Oring__1(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__map__upd,axiom, % 167.67/167.93 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_image__constant,axiom, % 167.67/167.93 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => 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))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_diff__single__insert,axiom, % 167.67/167.93 ! [V_B_2,V_x_2,V_A_2,T_a] : % 167.67/167.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_zero__le__one,axiom, % 167.67/167.93 ! [T_a] : % 167.67/167.93 ( class_Rings_Olinordered__semidom(T_a) % 167.67/167.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_not__one__le__zero,axiom, % 167.67/167.93 ! [T_a] : % 167.67/167.93 ( class_Rings_Olinordered__semidom(T_a) % 167.67/167.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Body1,axiom, % 167.67/167.93 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 167.67/167.93 ( 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)) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 167.67/167.93 => 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)))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_flat__lub__def,axiom, % 167.67/167.93 ! [V_b_2,V_A_2,T_a] : % 167.67/167.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.67/167.93 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 167.67/167.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 167.67/167.93 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_zero__neq__one,axiom, % 167.67/167.93 ! [T_a] : % 167.67/167.93 ( class_Rings_Ozero__neq__one(T_a) % 167.67/167.93 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_one__neq__zero,axiom, % 167.67/167.93 ! [T_a] : % 167.67/167.93 ( class_Rings_Ozero__neq__one(T_a) % 167.67/167.93 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Body__sound__lemma,axiom, % 167.67/167.93 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 167.67/167.93 ( 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)) % 167.67/167.93 => 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)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_hoare__derivs_OBody,axiom, % 167.67/167.93 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 167.67/167.93 ( 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)) % 167.67/167.93 => 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)) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_Ints__odd__less__0,axiom, % 167.67/167.93 ! [V_a_2,T_a] : % 167.67/167.93 ( class_Rings_Olinordered__idom(T_a) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.67/167.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.67/167.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.67/167.93 % 167.67/167.93 fof(fact_less__zeroE,axiom, % 167.67/167.93 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.93 % 167.67/167.94 fof(fact_le0,axiom, % 167.67/167.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_lessI,axiom, % 167.67/167.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__mono,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup1CI,axiom, % 167.67/167.94 ! [T_a,V_A_2,V_x_2,V_B_2] : % 167.67/167.94 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 167.67/167.94 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 167.67/167.94 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup1E,axiom, % 167.67/167.94 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 167.67/167.94 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 167.67/167.94 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_UnCI,axiom, % 167.67/167.94 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 167.67/167.94 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) % 167.67/167.94 => 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))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_UnE,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.67/167.94 ( 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))) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_zero__less__Suc,axiom, % 167.67/167.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__diff__iff,axiom, % 167.67/167.94 ! [V_n_2,V_m_2,V_k_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_diff__less__mono,axiom, % 167.67/167.94 ! [V_c,V_b,V_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__le__lessD,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__less__Suc__eq,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 167.67/167.94 <=> V_n_2 = V_m_2 ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__leI,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__imp__less__Suc,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__le__eq,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__Suc__eq__le,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__eq__Suc__le,axiom, % 167.67/167.94 ! [V_m_2,V_n_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__supI2,axiom, % 167.67/167.94 ! [V_a,V_b,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__supI1,axiom, % 167.67/167.94 ! [V_b,V_a,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__apply,axiom, % 167.67/167.94 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 167.67/167.94 ( class_Lattices_Olattice(T_a) % 167.67/167.94 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__assoc,axiom, % 167.67/167.94 ! [V_z,V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_inf__sup__aci_I6_J,axiom, % 167.67/167.94 ! [V_z,V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Olattice(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup_Oassoc,axiom, % 167.67/167.94 ! [V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__left__commute,axiom, % 167.67/167.94 ! [V_z,V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_inf__sup__aci_I7_J,axiom, % 167.67/167.94 ! [V_z,V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Olattice(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup_Oleft__commute,axiom, % 167.67/167.94 ! [V_c,V_a,V_b,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__left__idem,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_inf__sup__aci_I8_J,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Olattice(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup_Oleft__idem,axiom, % 167.67/167.94 ! [V_b,V_a,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__commute,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_inf__sup__aci_I5_J,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Olattice(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup_Ocommute,axiom, % 167.67/167.94 ! [V_b,V_a,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__idem,axiom, % 167.67/167.94 ! [V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup_Oidem,axiom, % 167.67/167.94 ! [V_a,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__cases,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => ( V_x != V_y % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__asym,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_xt1_I10_J,axiom, % 167.67/167.94 ! [V_z,V_x,V_y,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__trans,axiom, % 167.67/167.94 ! [V_z,V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_xt1_I2_J,axiom, % 167.67/167.94 ! [V_c,V_a,V_b,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.67/167.94 => ( V_b = V_c % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_ord__less__eq__trans,axiom, % 167.67/167.94 ! [V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Orderings_Oord(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.67/167.94 => ( V_b = V_c % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_xt1_I1_J,axiom, % 167.67/167.94 ! [V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( V_a = V_b % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_ord__eq__less__trans,axiom, % 167.67/167.94 ! [V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Orderings_Oord(T_a) % 167.67/167.94 => ( V_a = V_b % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_xt1_I9_J,axiom, % 167.67/167.94 ! [V_a,V_b,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__asym_H,axiom, % 167.67/167.94 ! [V_b,V_a,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__imp__not__eq2,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => V_y != V_x ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__imp__not__eq,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => V_x != V_y ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__imp__not__less,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__not__sym,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__imp__neq,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => V_x != V_y ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup1I2,axiom, % 167.67/167.94 ! [V_A_2,T_a,V_x_2,V_B_2] : % 167.67/167.94 ( hBOOL(hAPP(V_B_2,V_x_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup1I1,axiom, % 167.67/167.94 ! [V_B_2,T_a,V_x_2,V_A_2] : % 167.67/167.94 ( hBOOL(hAPP(V_A_2,V_x_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__neqE,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( V_x != V_y % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__antisym__conv3,axiom, % 167.67/167.94 ! [V_x_2,V_y_2,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> V_x_2 = V_y_2 ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__less__linear,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 | V_x = V_y % 167.67/167.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__less__iff__gr__or__eq,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 167.67/167.94 | V_x_2 = V_y_2 ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__neq__iff,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( V_x_2 != V_y_2 % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__irrefl,axiom, % 167.67/167.94 ! [V_x,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__neqE__linordered__idom,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.67/167.94 => ( V_x != V_y % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_ball__Un,axiom, % 167.67/167.94 ! [V_P_2,V_B_2,V_A_2,T_a] : % 167.67/167.94 ( ! [B_x] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.67/167.94 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.67/167.94 <=> ( ! [B_x] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.67/167.94 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.67/167.94 & ! [B_x] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 167.67/167.94 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_bex__Un,axiom, % 167.67/167.94 ! [V_P_2,V_B_2,V_A_2,T_a] : % 167.67/167.94 ( ? [B_x] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 167.67/167.94 & hBOOL(hAPP(V_P_2,B_x)) ) % 167.67/167.94 <=> ( ? [B_x] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.67/167.94 & hBOOL(hAPP(V_P_2,B_x)) ) % 167.67/167.94 | ? [B_x] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 167.67/167.94 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__assoc,axiom, % 167.67/167.94 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__left__commute,axiom, % 167.67/167.94 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__left__absorb,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__commute,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__absorb,axiom, % 167.67/167.94 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__fun__def,axiom, % 167.67/167.94 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 167.67/167.94 ( class_Lattices_Olattice(T_a) % 167.67/167.94 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__eq__Suc__le__raw,axiom, % 167.67/167.94 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 167.67/167.94 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__supE,axiom, % 167.67/167.94 ! [V_x,V_b,V_a,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) % 167.67/167.94 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__mono,axiom, % 167.67/167.94 ! [V_d,V_b,V_c,V_a,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__least,axiom, % 167.67/167.94 ! [V_z,V_x,V_y,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__supI,axiom, % 167.67/167.94 ! [V_b,V_x,V_a,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__absorb1,axiom, % 167.67/167.94 ! [V_x,V_y,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__absorb2,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__supI2,axiom, % 167.67/167.94 ! [V_a,V_b,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__supI1,axiom, % 167.67/167.94 ! [V_b,V_a,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__sup__iff,axiom, % 167.67/167.94 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)),V_z_2)) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 167.67/167.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__iff__sup,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__ge2,axiom, % 167.67/167.94 ! [V_x,V_y,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_inf__sup__ord_I4_J,axiom, % 167.67/167.94 ! [V_x,V_y,T_a] : % 167.67/167.94 ( class_Lattices_Olattice(T_a) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__ge1,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Osemilattice__sup(T_a) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_inf__sup__ord_I3_J,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Lattices_Olattice(T_a) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__bot__left,axiom, % 167.67/167.94 ! [V_x,T_a] : % 167.67/167.94 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__bot__right,axiom, % 167.67/167.94 ! [V_x,T_a] : % 167.67/167.94 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__eq__bot__iff,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.67/167.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 167.67/167.94 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 167.67/167.94 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_UnI2,axiom, % 167.67/167.94 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 167.67/167.94 => 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))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_UnI1,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.94 => 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))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__iff,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.67/167.94 ( 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))) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.94 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__fun__def,axiom, % 167.67/167.94 ! [V_g_2,V_f_2,T_a,T_b] : % 167.67/167.94 ( class_Orderings_Oord(T_b) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 167.67/167.94 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_xt1_I8_J,axiom, % 167.67/167.94 ! [V_z,V_x,V_y,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__le__less__trans,axiom, % 167.67/167.94 ! [V_z,V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_xt1_I7_J,axiom, % 167.67/167.94 ! [V_z,V_x,V_y,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__le__trans,axiom, % 167.67/167.94 ! [V_z,V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_xt1_I11_J,axiom, % 167.67/167.94 ! [V_a,V_b,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.67/167.94 => ( V_a != V_b % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__le__neq__trans,axiom, % 167.67/167.94 ! [V_b,V_a,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.67/167.94 => ( V_a != V_b % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__le__imp__less__or__eq,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 | V_x = V_y ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__antisym__conv2,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> V_x_2 = V_y_2 ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__imp__le,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_leD,axiom, % 167.67/167.94 ! [V_x,V_y,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_xt1_I12_J,axiom, % 167.67/167.94 ! [V_b,V_a,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( V_a != V_b % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__neq__le__trans,axiom, % 167.67/167.94 ! [V_b,V_a,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( V_a != V_b % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__antisym__conv1,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> V_x_2 = V_y_2 ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__leE,axiom, % 167.67/167.94 ! [V_x,V_y,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_leI,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__le__less,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 | V_x_2 = V_y_2 ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__le__not__le,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Opreorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.94 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_order__less__le,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Oorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.94 & V_x_2 != V_y_2 ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__le__less__linear,axiom, % 167.67/167.94 ! [V_y,V_x,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.67/167.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__not__le,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_linorder__not__less,axiom, % 167.67/167.94 ! [V_y_2,V_x_2,T_a] : % 167.67/167.94 ( class_Orderings_Olinorder(T_a) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__empty,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.94 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.67/167.94 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__empty__right,axiom, % 167.67/167.94 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__empty__left,axiom, % 167.67/167.94 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 167.67/167.94 % 167.67/167.94 fof(fact_psubsetD,axiom, % 167.67/167.94 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__insert__right,axiom, % 167.67/167.94 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__insert__left,axiom, % 167.67/167.94 ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__less__cancel__right,axiom, % 167.67/167.94 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 167.67/167.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.67/167.94 => ( 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))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__less__cancel__left,axiom, % 167.67/167.94 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 167.67/167.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.67/167.94 => ( 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))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__strict__right__mono,axiom, % 167.67/167.94 ! [V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__strict__left__mono,axiom, % 167.67/167.94 ! [V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__strict__mono,axiom, % 167.67/167.94 ! [V_d,V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__less__imp__less__right,axiom, % 167.67/167.94 ! [V_b,V_c,V_a,T_a] : % 167.67/167.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__less__imp__less__left,axiom, % 167.67/167.94 ! [V_b,V_a,V_c,T_a] : % 167.67/167.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__mono,axiom, % 167.67/167.94 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__least,axiom, % 167.67/167.94 ! [V_B_2,V_C_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__absorb2,axiom, % 167.67/167.94 ! [V_A_2,V_B_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__absorb1,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_subset__Un__eq,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__upper2,axiom, % 167.67/167.94 ! [V_A_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__upper1,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_image__Un,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__psubset__empty,axiom, % 167.67/167.94 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_diff__eq__diff__less,axiom, % 167.67/167.94 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 167.67/167.94 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.94 => ( 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) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__Diff,axiom, % 167.67/167.94 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__Diff__cancel2,axiom, % 167.67/167.94 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Un__Diff__cancel,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.67/167.94 % 167.67/167.94 fof(fact_neg__less__iff__less,axiom, % 167.67/167.94 ! [V_a_2,V_b_2,T_a] : % 167.67/167.94 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_minus__less__iff,axiom, % 167.67/167.94 ! [V_b_2,V_a_2,T_a] : % 167.67/167.94 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__minus__iff,axiom, % 167.67/167.94 ! [V_b_2,V_a_2,T_a] : % 167.67/167.94 ( class_Groups_Oordered__ab__group__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_subset__psubset__trans,axiom, % 167.67/167.94 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_psubset__subset__trans,axiom, % 167.67/167.94 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_psubset__imp__subset,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_subset__iff__psubset__eq,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 | V_A_2 = V_B_2 ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_psubset__eq,axiom, % 167.67/167.94 ! [V_B_2,V_A_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.67/167.94 & V_A_2 != V_B_2 ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_gr0I,axiom, % 167.67/167.94 ! [V_n] : % 167.67/167.94 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_gr__implies__not0,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__nat__zero__code,axiom, % 167.67/167.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_neq0__conv,axiom, % 167.67/167.94 ! [V_n_2] : % 167.67/167.94 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__less0,axiom, % 167.67/167.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__0__eq,axiom, % 167.67/167.94 ! [V_n_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 167.67/167.94 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 167.67/167.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__less__eq,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__Suc__eq,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.67/167.94 | V_m_2 = V_n_2 ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__less__eq,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__less__less__Suc__eq,axiom, % 167.67/167.94 ! [V_m_2,V_n_2] : % 167.67/167.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 167.67/167.94 <=> V_n_2 = V_m_2 ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__antisym,axiom, % 167.67/167.94 ! [V_m,V_n] : % 167.67/167.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 167.67/167.94 => V_m = V_n ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__SucI,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__lessI,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__trans__Suc,axiom, % 167.67/167.94 ! [V_k,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__SucE,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => V_m = V_n ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__lessD,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__less__SucD,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__n__not__le__n,axiom, % 167.67/167.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__less__eq__eq,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__Suc__eq,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.67/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.67/167.94 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__le__mono,axiom, % 167.67/167.94 ! [V_m_2,V_n_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__SucI,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__SucE,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 167.67/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Suc__leD,axiom, % 167.67/167.94 ! [V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__lessD1,axiom, % 167.67/167.94 ! [V_k,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__add__eq__less,axiom, % 167.67/167.94 ! [V_n,V_m,V_l,V_k] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 167.67/167.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__less__mono,axiom, % 167.67/167.94 ! [V_l,V_k,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__less__mono1,axiom, % 167.67/167.94 ! [V_k,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_trans__less__add2,axiom, % 167.67/167.94 ! [V_m,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_trans__less__add1,axiom, % 167.67/167.94 ! [V_m,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_nat__add__left__cancel__less,axiom, % 167.67/167.94 ! [V_n_2,V_m_2,V_k_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__add__less2,axiom, % 167.67/167.94 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__add__less1,axiom, % 167.67/167.94 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__leE,axiom, % 167.67/167.94 ! [V_n,V_k,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 167.67/167.94 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__leD1,axiom, % 167.67/167.94 ! [V_n,V_k,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__leD2,axiom, % 167.67/167.94 ! [V_n,V_k,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__le__mono,axiom, % 167.67/167.94 ! [V_l,V_k,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__le__mono1,axiom, % 167.67/167.94 ! [V_k,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_trans__le__add2,axiom, % 167.67/167.94 ! [V_m,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_trans__le__add1,axiom, % 167.67/167.94 ! [V_m,V_j,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_nat__add__left__cancel__le,axiom, % 167.67/167.94 ! [V_n_2,V_m_2,V_k_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__iff__add,axiom, % 167.67/167.94 ! [V_n_2,V_m_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.67/167.94 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__add1,axiom, % 167.67/167.94 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__add2,axiom, % 167.67/167.94 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ). % 167.67/167.94 % 167.67/167.94 fof(fact_diff__less__mono2,axiom, % 167.67/167.94 ! [V_l,V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__imp__diff__less,axiom, % 167.67/167.94 ! [V_n,V_k,V_j] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_le__diff__iff,axiom, % 167.67/167.94 ! [V_n_2,V_m_2,V_k_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_Nat_Odiff__diff__eq,axiom, % 167.67/167.94 ! [V_n,V_m,V_k] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 167.67/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_eq__diff__iff,axiom, % 167.67/167.94 ! [V_n_2,V_m_2,V_k_2] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 167.67/167.94 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) % 167.67/167.94 <=> V_m_2 = V_n_2 ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_diff__diff__cancel,axiom, % 167.67/167.94 ! [V_n,V_i] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 167.67/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_diff__le__mono,axiom, % 167.67/167.94 ! [V_l,V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_diff__le__mono2,axiom, % 167.67/167.94 ! [V_l,V_n,V_m] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_diff__le__self,axiom, % 167.67/167.94 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 167.67/167.94 % 167.67/167.94 fof(fact_evaln__nonstrict,axiom, % 167.67/167.94 ! [V_m,V_t,V_n,V_s,V_c] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.67/167.94 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_pos__add__strict,axiom, % 167.67/167.94 ! [V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Rings_Olinordered__semidom(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_not__one__less__zero,axiom, % 167.67/167.94 ! [T_a] : % 167.67/167.94 ( class_Rings_Olinordered__semidom(T_a) % 167.67/167.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_zero__less__one,axiom, % 167.67/167.94 ! [T_a] : % 167.67/167.94 ( class_Rings_Olinordered__semidom(T_a) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__minus__self__iff,axiom, % 167.67/167.94 ! [V_a_2,T_a] : % 167.67/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_less__add__one,axiom, % 167.67/167.94 ! [V_a,T_a] : % 167.67/167.94 ( class_Rings_Olinordered__semidom(T_a) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_sup__Un__eq,axiom, % 167.67/167.94 ! [V_x_2,V_S_2,V_R_2,T_a] : % 167.67/167.94 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) % 167.67/167.94 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_zero__less__two,axiom, % 167.67/167.94 ! [T_a] : % 167.67/167.94 ( class_Rings_Olinordered__semidom(T_a) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__le__less__mono,axiom, % 167.67/167.94 ! [V_d,V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__less__le__mono,axiom, % 167.67/167.94 ! [V_d,V_c,V_b,V_a,T_a] : % 167.67/167.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.67/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 167.67/167.94 % 167.67/167.94 fof(fact_insert__is__Un,axiom, % 167.67/167.94 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2) ). % 167.67/167.94 % 167.67/167.94 fof(fact_add__neg__neg,axiom, % 167.67/167.94 ! [V_b,V_a,T_a] : % 167.67/167.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.67/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__pos__pos,axiom, % 167.88/167.94 ! [V_b,V_a,T_a] : % 167.88/167.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 167.88/167.94 ! [V_a_2,T_a] : % 167.88/167.94 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 167.88/167.94 ! [V_a_2,T_a] : % 167.88/167.94 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_even__less__0__iff,axiom, % 167.88/167.94 ! [V_a_2,T_a] : % 167.88/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__iff__diff__less__0,axiom, % 167.88/167.94 ! [V_b_2,V_a_2,T_a] : % 167.88/167.94 ( class_Groups_Oordered__ab__group__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_neg__0__less__iff__less,axiom, % 167.88/167.94 ! [V_a_2,T_a] : % 167.88/167.94 ( class_Groups_Oordered__ab__group__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_neg__less__0__iff__less,axiom, % 167.88/167.94 ! [V_a_2,T_a] : % 167.88/167.94 ( class_Groups_Oordered__ab__group__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_neg__less__nonneg,axiom, % 167.88/167.94 ! [V_a_2,T_a] : % 167.88/167.94 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_Diff__subset__conv,axiom, % 167.88/167.94 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_Diff__partition,axiom, % 167.88/167.94 ! [V_B_2,V_A_2,T_a] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.94 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__Suc__eq__0__disj,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 167.88/167.94 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.94 | ? [B_j] : % 167.88/167.94 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 167.88/167.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__Suc0,axiom, % 167.88/167.94 ! [V_n_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 167.88/167.94 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_gr0__conv__Suc,axiom, % 167.88/167.94 ! [V_n_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 167.88/167.94 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__gr__0,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) % 167.88/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 167.88/167.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__iff__Suc__add,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.88/167.94 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__add__Suc2,axiom, % 167.88/167.94 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__add__Suc1,axiom, % 167.88/167.94 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__less,axiom, % 167.88/167.94 ! [V_m,V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_zero__less__diff,axiom, % 167.88/167.94 ! [V_m_2,V_n_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__is__0__eq_H,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__is__0__eq,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__less__Suc,axiom, % 167.88/167.94 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ). % 167.88/167.94 % 167.88/167.94 fof(fact_Suc__diff__le,axiom, % 167.88/167.94 ! [V_m,V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__diff__inverse,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__diff__conv,axiom, % 167.88/167.94 ! [V_k_2,V_j_2,V_i_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__add__assoc2,axiom, % 167.88/167.94 ! [V_i,V_j,V_k] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__diff__assoc2,axiom, % 167.88/167.94 ! [V_i,V_j,V_k] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__add__assoc,axiom, % 167.88/167.94 ! [V_i,V_j,V_k] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__imp__diff__is__add,axiom, % 167.88/167.94 ! [V_k_2,V_j_2,V_i_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.88/167.94 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 167.88/167.94 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__add__diff__inverse2,axiom, % 167.88/167.94 ! [V_m,V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__diff__conv2,axiom, % 167.88/167.94 ! [V_i_2,V_j_2,V_k_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__diff__assoc,axiom, % 167.88/167.94 ! [V_i,V_j,V_k] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__add__diff__inverse,axiom, % 167.88/167.94 ! [V_m,V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__add__diff,axiom, % 167.88/167.94 ! [V_m,V_n,V_k] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__diff__conv,axiom, % 167.88/167.94 ! [V_i_2,V_k_2,V_j_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__diff__right,axiom, % 167.88/167.94 ! [V_i,V_j,V_k] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_Compl__Diff__eq,axiom, % 167.88/167.94 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 167.88/167.94 % 167.88/167.94 fof(fact_dom__map__add,axiom, % 167.88/167.94 ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__nonpos__neg,axiom, % 167.88/167.94 ! [V_b,V_a,T_a] : % 167.88/167.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__neg__nonpos,axiom, % 167.88/167.94 ! [V_b,V_a,T_a] : % 167.88/167.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__strict__increasing2,axiom, % 167.88/167.94 ! [V_c,V_b,V_a,T_a] : % 167.88/167.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__strict__increasing,axiom, % 167.88/167.94 ! [V_c,V_b,V_a,T_a] : % 167.88/167.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__nonneg__pos,axiom, % 167.88/167.94 ! [V_b,V_a,T_a] : % 167.88/167.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_add__pos__nonneg,axiom, % 167.88/167.94 ! [V_b,V_a,T_a] : % 167.88/167.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_Suc__pred,axiom, % 167.88/167.94 ! [V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.88/167.94 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__Suc__less,axiom, % 167.88/167.94 ! [V_i,V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_nat__diff__split__asm,axiom, % 167.88/167.94 ! [V_b_2,V_a_2,V_P_2] : % 167.88/167.94 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 167.88/167.94 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 167.88/167.94 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 167.88/167.94 | ? [B_d] : % 167.88/167.94 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 167.88/167.94 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_nat__diff__split,axiom, % 167.88/167.94 ! [V_b_2,V_a_2,V_P_2] : % 167.88/167.94 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 167.88/167.94 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 167.88/167.94 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 167.88/167.94 & ! [B_d] : % 167.88/167.94 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 167.88/167.94 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__Suc__diff__eq1,axiom, % 167.88/167.94 ! [V_m,V_j,V_k] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_diff__Suc__diff__eq2,axiom, % 167.88/167.94 ! [V_m,V_j,V_k] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 167.88/167.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_Suc__diff__1,axiom, % 167.88/167.94 ! [V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.88/167.94 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_Suc__pred_H,axiom, % 167.88/167.94 ! [V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.88/167.94 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_psubset__insert__iff,axiom, % 167.88/167.94 ! [V_B_2,V_x_2,V_A_2,T_a] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 167.88/167.94 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 167.88/167.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 167.88/167.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 167.88/167.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_sgn__neg,axiom, % 167.88/167.94 ! [V_a,T_a] : % 167.88/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.94 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_sgn__1__neg,axiom, % 167.88/167.94 ! [V_a_2,T_a] : % 167.88/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.94 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_sgn__if,axiom, % 167.88/167.94 ! [V_x,T_a] : % 167.88/167.94 ( class_Groups_Osgn__if(T_a) % 167.88/167.94 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.94 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.88/167.94 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.94 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.88/167.94 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 167.88/167.94 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.88/167.94 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 167.88/167.94 ! [V_n_2,T_a] : % 167.88/167.94 ( class_Rings_Osemiring__1(T_a) % 167.88/167.94 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_Groups_Oone__class_Oone(T_a)),V_n_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_convex__bound__lt,axiom, % 167.88/167.94 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 167.88/167.94 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 167.88/167.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_sgn__1__pos,axiom, % 167.88/167.94 ! [V_a_2,T_a] : % 167.88/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.94 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_sgn__pos,axiom, % 167.88/167.94 ! [V_a,T_a] : % 167.88/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.94 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_inj__on__insert,axiom, % 167.88/167.94 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 167.88/167.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 167.88/167.94 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.94 & ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_mult__eq__if,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.88/167.94 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_negative__zless,axiom, % 167.88/167.94 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 167.88/167.94 % 167.88/167.94 fof(fact_inj__on__empty,axiom, % 167.88/167.94 ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 167.88/167.94 % 167.88/167.94 fof(fact_inj__uminus,axiom, % 167.88/167.94 ! [V_A_2,T_a] : % 167.88/167.94 ( class_Groups_Oordered__ab__group__add(T_a) % 167.88/167.94 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__refl,axiom, % 167.88/167.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__square,axiom, % 167.88/167.94 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__cube,axiom, % 167.88/167.94 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ). % 167.88/167.94 % 167.88/167.94 fof(fact_nat__le__linear,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.88/167.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_nat__less__le,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.88/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.88/167.94 & V_m_2 != V_n_2 ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__eq__less__or__eq,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 167.88/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.88/167.94 | V_m_2 = V_n_2 ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_eq__imp__le,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( V_m = V_n % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__imp__le__nat,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_mult__le__mono1,axiom, % 167.88/167.94 ! [V_k,V_j,V_i] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_mult__le__mono2,axiom, % 167.88/167.94 ! [V_k,V_j,V_i] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__neq__implies__less,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.88/167.94 => ( V_m != V_n % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__trans,axiom, % 167.88/167.94 ! [V_k,V_j,V_i] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_le__antisym,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.88/167.94 => V_m = V_n ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_mult__le__mono,axiom, % 167.88/167.94 ! [V_l,V_k,V_j,V_i] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__or__eq__imp__le,axiom, % 167.88/167.94 ! [V_n,V_m] : % 167.88/167.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.88/167.94 | V_m = V_n ) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_zle__int,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_zmult__zless__mono2__lemma,axiom, % 167.88/167.94 ! [V_k,V_j,V_i] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_zless__int,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 167.88/167.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_nat__less__cases,axiom, % 167.88/167.94 ! [V_P_2,V_n_2,V_m_2] : % 167.88/167.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.88/167.94 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 167.88/167.94 => ( ( V_m_2 = V_n_2 % 167.88/167.94 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 167.88/167.94 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 167.88/167.94 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 167.88/167.94 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__not__refl3,axiom, % 167.88/167.94 ! [V_t,V_s] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 167.88/167.94 => V_s != V_t ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__not__refl2,axiom, % 167.88/167.94 ! [V_m,V_n] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 167.88/167.94 => V_m != V_n ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__irrefl__nat,axiom, % 167.88/167.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 167.88/167.94 % 167.88/167.94 fof(fact_linorder__neqE__nat,axiom, % 167.88/167.94 ! [V_y,V_x] : % 167.88/167.94 ( V_x != V_y % 167.88/167.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_nat__neq__iff,axiom, % 167.88/167.94 ! [V_n_2,V_m_2] : % 167.88/167.94 ( V_m_2 != V_n_2 % 167.88/167.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.88/167.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_less__not__refl,axiom, % 167.88/167.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 167.88/167.94 % 167.88/167.94 fof(fact_sgn__sgn,axiom, % 167.88/167.94 ! [V_a,T_a] : % 167.88/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.94 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_sgn__times,axiom, % 167.88/167.94 ! [V_b,V_a,T_a] : % 167.88/167.94 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.94 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_psubset__trans,axiom, % 167.88/167.94 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.88/167.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_inj__on__id2,axiom, % 167.88/167.94 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 167.88/167.94 % 167.88/167.94 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 167.88/167.94 ! [V_c,V_b,V_a,T_a] : % 167.88/167.94 ( class_Groups_Oab__semigroup__mult(T_a) % 167.88/167.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_inj__on__def,axiom, % 167.88/167.94 ! [V_A_2,V_f_2,T_b,T_a] : % 167.88/167.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.94 <=> ! [B_x] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.88/167.94 => ! [B_xa] : % 167.88/167.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 167.88/167.94 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 167.88/167.94 => B_x = B_xa ) ) ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_of__nat__mult,axiom, % 167.88/167.94 ! [V_n,V_m,T_a] : % 167.88/167.94 ( class_Rings_Osemiring__1(T_a) % 167.88/167.94 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_nat__mult__commute,axiom, % 167.88/167.94 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ). % 167.88/167.94 % 167.88/167.94 fof(fact_of__nat__eq__iff,axiom, % 167.88/167.94 ! [V_n_2,V_m_2,T_a] : % 167.88/167.94 ( class_Nat_Osemiring__char__0(T_a) % 167.88/167.94 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) % 167.88/167.94 <=> V_m_2 = V_n_2 ) ) ). % 167.88/167.94 % 167.88/167.94 fof(fact_nat__mult__assoc,axiom, % 167.88/167.94 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 167.88/167.94 % 167.88/167.94 fof(fact_int__mult,axiom, % 167.88/167.94 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ). % 167.88/167.94 % 167.88/167.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 167.88/167.94 ! [V_b,V_a,T_a] : % 167.88/167.94 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ). % 167.88/167.94 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 167.88/167.95 ! [V_ry,V_rx,V_lx,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 167.88/167.95 ! [V_ry,V_rx,V_lx,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zmult__int,axiom, % 167.88/167.95 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 167.88/167.95 ! [V_rx,V_ly,V_lx,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 167.88/167.95 ! [V_rx,V_ly,V_lx,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 167.88/167.95 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 167.88/167.95 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 167.88/167.95 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_times_Oidem,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__idem,axiom, % 167.88/167.95 ! [V_x,T_a] : % 167.88/167.95 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__left__idem,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__contraD,axiom, % 167.88/167.95 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => ( V_x_2 != V_y_2 % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.88/167.95 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__iff,axiom, % 167.88/167.95 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.88/167.95 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.88/167.95 <=> V_x_2 = V_y_2 ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__onD,axiom, % 167.88/167.95 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 167.88/167.95 => V_x_2 = V_y_2 ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__Suc,axiom, % 167.88/167.95 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 167.88/167.95 % 167.88/167.95 fof(fact_subset__inj__on,axiom, % 167.88/167.95 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.95 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__strict__subset,axiom, % 167.88/167.95 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__diff,axiom, % 167.88/167.95 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__Some,axiom, % 167.88/167.95 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2) ). % 167.88/167.95 % 167.88/167.95 fof(fact_negative__eq__positive,axiom, % 167.88/167.95 ! [V_m_2,V_n_2] : % 167.88/167.95 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) % 167.88/167.95 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.95 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__0,axiom, % 167.88/167.95 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__eq__0__conv,axiom, % 167.88/167.95 ! [V_n_2] : % 167.88/167.95 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.95 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__less__int__conv,axiom, % 167.88/167.95 ! [V_n_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__le__0__conv,axiom, % 167.88/167.95 ! [V_n_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.95 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__zle__neg,axiom, % 167.88/167.95 ! [V_m_2,V_n_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) % 167.88/167.95 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.95 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zless__iff__Suc__zadd,axiom, % 167.88/167.95 ! [V_z_2,V_w_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 167.88/167.95 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__Suc,axiom, % 167.88/167.95 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_negative__zless__0,axiom, % 167.88/167.95 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_not__zle__0__negative,axiom, % 167.88/167.95 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__zero__left,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Omult__zero(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__zero__right,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Omult__zero(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__eq__0__iff,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oring__no__zero__divisors(T_a) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_no__zero__divisors,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Ono__zero__divisors(T_a) % 167.88/167.95 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_divisors__zero,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Ono__zero__divisors(T_a) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__int,axiom, % 167.88/167.95 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__int__left,axiom, % 167.88/167.95 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ). % 167.88/167.95 % 167.88/167.95 fof(fact_crossproduct__eq,axiom, % 167.88/167.95 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 167.88/167.95 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) % 167.88/167.95 <=> ( V_w_2 = V_x_2 % 167.88/167.95 | V_y_2 = V_z_2 ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 167.88/167.95 ! [V_b,V_m,V_a,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 167.88/167.95 ! [V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_crossproduct__noteq,axiom, % 167.88/167.95 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 167.88/167.95 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 167.88/167.95 => ( ( V_a_2 != V_b_2 % 167.88/167.95 & V_ca_2 != V_d_2 ) % 167.88/167.95 <=> 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)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 167.88/167.95 ! [V_z,V_y,V_x,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_combine__common__factor,axiom, % 167.88/167.95 ! [V_c,V_b,V_e,V_a,T_a] : % 167.88/167.95 ( class_Rings_Osemiring(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__class_Odistrib,axiom, % 167.88/167.95 ! [V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zdiff__int,axiom, % 167.88/167.95 ! [V_m,V_n] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.88/167.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__le__iff,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__less__iff,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_less__imp__of__nat__less,axiom, % 167.88/167.95 ! [V_n,V_m,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__less__imp__less,axiom, % 167.88/167.95 ! [V_n,V_m,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__1__left,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__1,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__1__right,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult_Ocomm__neutral,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__Inr,axiom, % 167.88/167.95 ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(T_a,tc_sum(T_b,T_a),c_Sum__Type_OInr(T_a,T_b),V_A_2) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__0,axiom, % 167.88/167.95 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__0__right,axiom, % 167.88/167.95 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__is__0,axiom, % 167.88/167.95 ! [V_n_2,V_m_2] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.95 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.95 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 167.88/167.95 <=> ( V_m_2 = V_n_2 % 167.88/167.95 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__cancel2,axiom, % 167.88/167.95 ! [V_n_2,V_k_2,V_m_2] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) % 167.88/167.95 <=> ( V_m_2 = V_n_2 % 167.88/167.95 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__mono2,axiom, % 167.88/167.95 ! [V_k,V_j,V_i] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__mono1,axiom, % 167.88/167.95 ! [V_k,V_j,V_i] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__cancel2,axiom, % 167.88/167.95 ! [V_n_2,V_k_2,V_m_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 167.88/167.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 167.88/167.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__0__less__mult__iff,axiom, % 167.88/167.95 ! [V_n_2,V_m_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 167.88/167.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__le__cancel2,axiom, % 167.88/167.95 ! [V_n_2,V_k_2,V_m_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 167.88/167.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__le__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 167.88/167.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_square__eq__iff,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oidom(T_a) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) % 167.88/167.95 <=> ( V_a_2 = V_b_2 % 167.88/167.95 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_minus__mult__minus,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oring(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_minus__mult__commute,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oring(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_minus__mult__left,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oring(T_a) % 167.88/167.95 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_minus__mult__right,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oring(T_a) % 167.88/167.95 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Suc__mult__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) % 167.88/167.95 <=> V_m_2 = V_n_2 ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Suc__mult__less__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Suc__mult__le__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__1,axiom, % 167.88/167.95 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 167.88/167.95 % 167.88/167.95 fof(fact_add__mult__distrib2,axiom, % 167.88/167.95 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_add__mult__distrib,axiom, % 167.88/167.95 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__Inl,axiom, % 167.88/167.95 ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(T_a,tc_sum(T_a,T_b),c_Sum__Type_OInl(T_a,T_b),V_A_2) ). % 167.88/167.95 % 167.88/167.95 fof(fact_diff__mult__distrib2,axiom, % 167.88/167.95 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_diff__mult__distrib,axiom, % 167.88/167.95 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__mult__1,axiom, % 167.88/167.95 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__1__eq__mult__iff,axiom, % 167.88/167.95 ! [V_n_2,V_m_2] : % 167.88/167.95 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 167.88/167.95 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.88/167.95 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__mult__1__right,axiom, % 167.88/167.95 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__mult__eq__1__iff,axiom, % 167.88/167.95 ! [V_n_2,V_m_2] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.88/167.95 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.88/167.95 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__add__nat,axiom, % 167.88/167.95 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ). % 167.88/167.95 % 167.88/167.95 fof(fact_sgn0,axiom, % 167.88/167.95 ! [T_a] : % 167.88/167.95 ( class_Groups_Osgn__if(T_a) % 167.88/167.95 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_sgn__0__0,axiom, % 167.88/167.95 ! [V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__Un__image__eq__iff,axiom, % 167.88/167.95 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.95 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 167.88/167.95 <=> V_A_2 = V_B_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__Suc0__eq__1,axiom, % 167.88/167.95 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 167.88/167.95 % 167.88/167.95 fof(fact_split__mult__neg__le,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.88/167.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 167.88/167.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_split__mult__pos__le,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__ring(T_a) % 167.88/167.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 167.88/167.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__mono,axiom, % 167.88/167.95 ! [V_d,V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__mono_H,axiom, % 167.88/167.95 ! [V_d,V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__left__mono__neg,axiom, % 167.88/167.95 ! [V_c,V_a,V_b,T_a] : % 167.88/167.95 ( class_Rings_Oordered__ring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__right__mono__neg,axiom, % 167.88/167.95 ! [V_c,V_a,V_b,T_a] : % 167.88/167.95 ( class_Rings_Oordered__ring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__mult__left__mono,axiom, % 167.88/167.95 ! [V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__comm__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__left__mono,axiom, % 167.88/167.95 ! [V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__right__mono,axiom, % 167.88/167.95 ! [V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__nonpos__nonpos,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__ring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__nonpos__nonneg,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__nonneg__nonpos2,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__nonneg__nonpos,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__nonneg__nonneg,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__le__0__iff,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 167.88/167.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__le__mult__iff,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))) % 167.88/167.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 167.88/167.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__le__square,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__strict__left__mono__neg,axiom, % 167.88/167.95 ! [V_c,V_a,V_b,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__strict__right__mono__neg,axiom, % 167.88/167.95 ! [V_c,V_a,V_b,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__mult__strict__left__mono,axiom, % 167.88/167.95 ! [V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__strict__left__mono,axiom, % 167.88/167.95 ! [V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__strict__right__mono,axiom, % 167.88/167.95 ! [V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__neg__neg,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__neg__pos,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__cancel__left__neg,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__less__mult__pos2,axiom, % 167.88/167.95 ! [V_a,V_b,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__less__mult__pos,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__pos__neg2,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__pos__neg,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__pos__pos,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__cancel__left__pos,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__cancel__left__disj,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 167.88/167.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__cancel__right__disj,axiom, % 167.88/167.95 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 167.88/167.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_not__square__less__zero,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring(T_a) % 167.88/167.95 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_add__scale__eq__noteq,axiom, % 167.88/167.95 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 167.88/167.95 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 167.88/167.95 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 => ( ( V_a = V_b % 167.88/167.95 & V_c != V_d ) % 167.88/167.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_sum__squares__eq__zero__iff,axiom, % 167.88/167.95 ! [V_y_2,V_x_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_less__1__mult,axiom, % 167.88/167.95 ! [V_n,V_m,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_eq__add__iff1,axiom, % 167.88/167.95 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oring(T_a) % 167.88/167.95 => ( 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) % 167.88/167.95 <=> 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 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_eq__add__iff2,axiom, % 167.88/167.95 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oring(T_a) % 167.88/167.95 => ( 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) % 167.88/167.95 <=> 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) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__0__le__iff,axiom, % 167.88/167.95 ! [V_n,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__le__imp__of__nat,axiom, % 167.88/167.95 ! [V_m,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 167.88/167.95 ! [V_m,V_a,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 167.88/167.95 ! [V_a,V_m,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 167.88/167.95 ! [V_m,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__less__0__iff,axiom, % 167.88/167.95 ! [V_m,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__0,axiom, % 167.88/167.95 ! [T_a] : % 167.88/167.95 ( class_Rings_Osemiring__1(T_a) % 167.88/167.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 167.88/167.95 ! [V_x,T_a] : % 167.88/167.95 ( class_Rings_Ocomm__ring__1(T_a) % 167.88/167.95 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_square__eq__1__iff,axiom, % 167.88/167.95 ! [V_x_2,T_a] : % 167.88/167.95 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 167.88/167.95 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 167.88/167.95 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__eq__1__iff,axiom, % 167.88/167.95 ! [V_n_2,V_m_2] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.88/167.95 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.88/167.95 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_one__le__mult__iff,axiom, % 167.88/167.95 ! [V_n_2,V_m_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 167.88/167.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_one__less__mult,axiom, % 167.88/167.95 ! [V_m,V_n] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_n__less__n__mult__m,axiom, % 167.88/167.95 ! [V_m,V_n] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_n__less__m__mult__n,axiom, % 167.88/167.95 ! [V_m,V_n] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_the__inv__into__f__f,axiom, % 167.88/167.95 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.88/167.95 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_the__inv__into__f__eq,axiom, % 167.88/167.95 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 167.88/167.95 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__map__add__dom,axiom, % 167.88/167.95 ! [V_m_H_2,V_m_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2)) % 167.88/167.95 <=> c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__Suc__right,axiom, % 167.88/167.95 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__Suc,axiom, % 167.88/167.95 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__add,axiom, % 167.88/167.95 ! [V_n,V_m,T_a] : % 167.88/167.95 ( class_Rings_Osemiring__1(T_a) % 167.88/167.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__the__inv__into,axiom, % 167.88/167.95 ! [V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_the__inv__into__onto,axiom, % 167.88/167.95 ! [V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__diff,axiom, % 167.88/167.95 ! [V_m,V_n,T_a] : % 167.88/167.95 ( class_Rings_Oring__1(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 167.88/167.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__eq__self__implies__10,axiom, % 167.88/167.95 ! [V_n,V_m] : % 167.88/167.95 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 167.88/167.95 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 167.88/167.95 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__1,axiom, % 167.88/167.95 ! [T_a] : % 167.88/167.95 ( class_Rings_Osemiring__1(T_a) % 167.88/167.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Ints__mult,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oring__1(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Ints__of__nat,axiom, % 167.88/167.95 ! [V_n_2,T_a] : % 167.88/167.95 ( class_Rings_Oring__1(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__image__set__diff,axiom, % 167.88/167.95 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.88/167.95 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__fun__updI,axiom, % 167.88/167.95 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.88/167.95 => c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__left__le__imp__le,axiom, % 167.88/167.95 ! [V_b,V_a,V_c,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__right__le__imp__le,axiom, % 167.88/167.95 ! [V_b,V_c,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__imp__less__left,axiom, % 167.88/167.95 ! [V_b,V_a,V_c,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__left__less__imp__less,axiom, % 167.88/167.95 ! [V_b,V_a,V_c,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__imp__less__right,axiom, % 167.88/167.95 ! [V_b,V_c,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__right__less__imp__less,axiom, % 167.88/167.95 ! [V_b,V_c,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__le__less__imp__less,axiom, % 167.88/167.95 ! [V_d,V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__less__le__imp__less,axiom, % 167.88/167.95 ! [V_d,V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__strict__mono_H,axiom, % 167.88/167.95 ! [V_d,V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__strict__mono,axiom, % 167.88/167.95 ! [V_d,V_c,V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__le__cancel__left__neg,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__le__cancel__left__pos,axiom, % 167.88/167.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_sum__squares__le__zero__iff,axiom, % 167.88/167.95 ! [V_y_2,V_x_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_sum__squares__ge__zero,axiom, % 167.88/167.95 ! [V_y,V_x,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_sum__squares__gt__zero__iff,axiom, % 167.88/167.95 ! [V_y_2,V_x_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring__strict(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) % 167.88/167.95 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_not__sum__squares__lt__zero,axiom, % 167.88/167.95 ! [V_y,V_x,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__ring(T_a) % 167.88/167.95 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__left__le__one__le,axiom, % 167.88/167.95 ! [V_y,V_x,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_mult__right__le__one__le,axiom, % 167.88/167.95 ! [V_y,V_x,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_le__add__iff1,axiom, % 167.88/167.95 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oordered__ring(T_a) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> 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)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_le__add__iff2,axiom, % 167.88/167.95 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oordered__ring(T_a) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> 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))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_f__the__inv__into__f,axiom, % 167.88/167.95 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.88/167.95 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_less__add__iff1,axiom, % 167.88/167.95 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oordered__ring(T_a) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> 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)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_less__add__iff2,axiom, % 167.88/167.95 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Oordered__ring(T_a) % 167.88/167.95 => ( 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))) % 167.88/167.95 <=> 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))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_sgn__less,axiom, % 167.88/167.95 ! [V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_sgn__greater,axiom, % 167.88/167.95 ! [V_a_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__0__less__iff,axiom, % 167.88/167.95 ! [V_n_2,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_of__nat__Suc,axiom, % 167.88/167.95 ! [V_m,T_a] : % 167.88/167.95 ( class_Rings_Osemiring__1(T_a) % 167.88/167.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Plus__def,axiom, % 167.88/167.95 ! [V_B_2,V_A_2,T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_sum(T_a,T_b),c_Sum__Type_OInl(T_a,T_b)),V_A_2)),hAPP(c_Set_Oimage(T_b,tc_sum(T_a,T_b),c_Sum__Type_OInr(T_b,T_a)),V_B_2)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_the__inv__into__into,axiom, % 167.88/167.95 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_convex__bound__le,axiom, % 167.88/167.95 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__semiring__1(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__less__add__iff1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__less__add__iff2,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__le__add__iff1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__diff__add__eq1,axiom, % 167.88/167.95 ! [V_n,V_m,V_u,V_i,V_j] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 167.88/167.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__eq__add__iff1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 167.88/167.95 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__le__add__iff2,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__diff__add__eq2,axiom, % 167.88/167.95 ! [V_n,V_m,V_u,V_j,V_i] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 167.88/167.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__eq__add__iff2,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 167.88/167.95 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_negative__zle,axiom, % 167.88/167.95 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zle__diff1__eq,axiom, % 167.88/167.95 ! [V_z_2,V_w_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_negative__zle__0,axiom, % 167.88/167.95 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zsgn__def,axiom, % 167.88/167.95 ! [V_i] : % 167.88/167.95 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.95 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.88/167.95 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 167.88/167.95 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 167.88/167.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 167.88/167.95 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_not__int__zless__negative,axiom, % 167.88/167.95 ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zle__refl,axiom, % 167.88/167.95 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zmult__1,axiom, % 167.88/167.95 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 167.88/167.95 % 167.88/167.95 fof(fact_zmult__1__right,axiom, % 167.88/167.95 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 167.88/167.95 % 167.88/167.95 fof(fact_zle__linear,axiom, % 167.88/167.95 ! [V_w,V_z] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 167.88/167.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zless__le,axiom, % 167.88/167.95 ! [V_w_2,V_z_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 167.88/167.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 167.88/167.95 & V_z_2 != V_w_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zle__trans,axiom, % 167.88/167.95 ! [V_k,V_j,V_i] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zle__antisym,axiom, % 167.88/167.95 ! [V_w,V_z] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 167.88/167.95 => V_z = V_w ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__0__less__1,axiom, % 167.88/167.95 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__zle__int,axiom, % 167.88/167.95 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__one__le__iff__zero__less,axiom, % 167.88/167.95 ! [V_z_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_odd__less__0,axiom, % 167.88/167.95 ! [V_z_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_le__imp__0__less,axiom, % 167.88/167.95 ! [V_z] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_pos__zmult__eq__1__iff,axiom, % 167.88/167.95 ! [V_n_2,V_m_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.88/167.95 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.88/167.95 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__zless__mono,axiom, % 167.88/167.95 ! [V_z,V_z_H,V_w,V_w_H] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__left__mono,axiom, % 167.88/167.95 ! [V_k,V_j,V_i] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zless__imp__add1__zle,axiom, % 167.88/167.95 ! [V_z,V_w] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_add1__zle__eq,axiom, % 167.88/167.95 ! [V_z_2,V_w_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zless__add1__eq,axiom, % 167.88/167.95 ! [V_z_2,V_w_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 167.88/167.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 167.88/167.95 | V_w_2 = V_z_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zle__add1__eq__le,axiom, % 167.88/167.95 ! [V_z_2,V_w_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zle__iff__zadd,axiom, % 167.88/167.95 ! [V_z_2,V_w_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 167.88/167.95 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__strict__right__mono,axiom, % 167.88/167.95 ! [V_k,V_j,V_i] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zmult__zless__mono2,axiom, % 167.88/167.95 ! [V_k,V_j,V_i] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__less__0__conv,axiom, % 167.88/167.95 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zless__linear,axiom, % 167.88/167.95 ! [V_y,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 167.88/167.95 | V_x = V_y % 167.88/167.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_less__bin__lemma,axiom, % 167.88/167.95 ! [V_l_2,V_k_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zdiff__zmult__distrib,axiom, % 167.88/167.95 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zdiff__zmult__distrib2,axiom, % 167.88/167.95 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zmult__commute,axiom, % 167.88/167.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__int__eq,axiom, % 167.88/167.95 ! [V_n_2,V_m_2] : % 167.88/167.95 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) % 167.88/167.95 <=> V_m_2 = V_n_2 ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zmult__assoc,axiom, % 167.88/167.95 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__zmult__distrib,axiom, % 167.88/167.95 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__zmult__distrib2,axiom, % 167.88/167.95 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zmult__zminus,axiom, % 167.88/167.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_diff__int__def,axiom, % 167.88/167.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_diff__int__def__symmetric,axiom, % 167.88/167.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zminus__zadd__distrib,axiom, % 167.88/167.95 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__zminus__inverse2,axiom, % 167.88/167.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zminus__0,axiom, % 167.88/167.95 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zminus__zminus,axiom, % 167.88/167.95 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__commute,axiom, % 167.88/167.95 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__left__commute,axiom, % 167.88/167.95 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__assoc,axiom, % 167.88/167.95 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__0__right,axiom, % 167.88/167.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 167.88/167.95 % 167.88/167.95 fof(fact_zadd__0,axiom, % 167.88/167.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 167.88/167.95 % 167.88/167.95 fof(fact_odd__nonzero,axiom, % 167.88/167.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.95 % 167.88/167.95 fof(fact_int__0__neq__1,axiom, % 167.88/167.95 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__mult__eq__cancel__disj,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 167.88/167.95 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.95 | V_m_2 = V_n_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_left__add__mult__distrib,axiom, % 167.88/167.95 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__mult__less__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__mult__eq__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.88/167.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 167.88/167.95 <=> V_m_2 = V_n_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_nat__mult__le__cancel1,axiom, % 167.88/167.95 ! [V_n_2,V_m_2,V_k_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zdiff__int__split,axiom, % 167.88/167.95 ! [V_y_2,V_x_2,V_P_2] : % 167.88/167.95 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) % 167.88/167.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 167.88/167.95 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) % 167.88/167.95 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 167.88/167.95 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_self__quotient__aux2,axiom, % 167.88/167.95 ! [V_q,V_r,V_a] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.88/167.95 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_self__quotient__aux1,axiom, % 167.88/167.95 ! [V_q,V_r,V_a] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.88/167.95 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_q__pos__lemma,axiom, % 167.88/167.95 ! [V_r_H,V_q_H,V_b_H] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_q__neg__lemma,axiom, % 167.88/167.95 ! [V_r_H,V_q_H,V_b_H] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_unique__quotient__lemma,axiom, % 167.88/167.95 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zdiv__mono2__lemma,axiom, % 167.88/167.95 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zdiv__mono2__neg__lemma,axiom, % 167.88/167.95 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 167.88/167.95 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_unique__quotient__lemma__neg,axiom, % 167.88/167.95 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_inj__on__iff__surj,axiom, % 167.88/167.95 ! [V_A_H_2,T_b,T_a,V_A_2] : % 167.88/167.95 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.88/167.95 => ( ? [B_f] : % 167.88/167.95 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 167.88/167.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2)) ) % 167.88/167.95 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 167.88/167.95 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 167.88/167.95 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 167.88/167.95 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 167.88/167.95 ! [V_y_2,V_x_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 167.88/167.95 ! [V_y_2,V_x_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 167.88/167.95 ! [V_y,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 167.88/167.95 ! [V_A_2,V_x_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 167.88/167.95 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 167.88/167.95 ! [V_B_2,V_A_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 167.88/167.95 ! [V_B_2,V_A_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 167.88/167.95 ! [V_B_2,V_A_2] : % 167.88/167.95 ( V_A_2 = V_B_2 % 167.88/167.95 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 167.88/167.95 ! [V_y_2,V_x_2] : % 167.88/167.95 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) % 167.88/167.95 <=> V_x_2 = V_y_2 ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 167.88/167.95 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 167.88/167.95 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 167.88/167.95 ! [V_y,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 167.88/167.95 ! [V_P_2] : % 167.88/167.95 ( ! [B_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.88/167.95 => hBOOL(hAPP(V_P_2,B_x)) ) % 167.88/167.95 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 167.88/167.95 ! [V_P_2] : % 167.88/167.95 ( ? [B_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.88/167.95 & hBOOL(hAPP(V_P_2,B_x)) ) % 167.88/167.95 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 167.88/167.95 ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 167.88/167.95 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.88/167.95 % 167.88/167.95 fof(fact_small_H_Osimps,axiom, % 167.88/167.95 ! [V_f_2,V_i_2,V_d_2] : % 167.88/167.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 167.88/167.95 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 167.88/167.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 167.88/167.95 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_tsub__def,axiom, % 167.88/167.95 ! [V_x,V_y] : % 167.88/167.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 167.88/167.95 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 167.88/167.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 167.88/167.95 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_termination__basic__simps_I3_J,axiom, % 167.88/167.95 ! [V_z,V_y,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_termination__basic__simps_I4_J,axiom, % 167.88/167.95 ! [V_y,V_z,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_termination__basic__simps_I5_J,axiom, % 167.88/167.95 ! [V_y,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_termination__basic__simps_I1_J,axiom, % 167.88/167.95 ! [V_z,V_y,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_termination__basic__simps_I2_J,axiom, % 167.88/167.95 ! [V_y,V_z,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 167.88/167.95 ! [V_y,V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_tsub__eq,axiom, % 167.88/167.95 ! [V_x,V_y] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 167.88/167.95 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 167.88/167.95 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ). % 167.88/167.95 % 167.88/167.95 fof(fact_decr__mult__lemma,axiom, % 167.88/167.95 ! [V_k_2,V_P_2,V_d_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 167.88/167.95 => ( ! [B_x] : % 167.88/167.95 ( hBOOL(hAPP(V_P_2,B_x)) % 167.88/167.95 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 167.88/167.95 => ! [B_x] : % 167.88/167.95 ( hBOOL(hAPP(V_P_2,B_x)) % 167.88/167.95 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_negD,axiom, % 167.88/167.95 ! [V_x] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.95 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_incr__mult__lemma,axiom, % 167.88/167.95 ! [V_k_2,V_P_2,V_d_2] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 167.88/167.95 => ( ! [B_x] : % 167.88/167.95 ( hBOOL(hAPP(V_P_2,B_x)) % 167.88/167.95 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 167.88/167.95 => ! [B_x] : % 167.88/167.95 ( hBOOL(hAPP(V_P_2,B_x)) % 167.88/167.95 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_ex__least__nat__less,axiom, % 167.88/167.95 ! [V_n_2,V_P_2] : % 167.88/167.95 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 167.88/167.95 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 167.88/167.95 => ? [B_k] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 167.88/167.95 & ! [B_i] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 167.88/167.95 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 167.88/167.95 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__less__imp__eq__int,axiom, % 167.88/167.95 ! [V_k] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 167.88/167.95 => ? [B_n] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 167.88/167.95 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_incr__lemma,axiom, % 167.88/167.95 ! [V_x,V_z,V_d] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_decr__lemma,axiom, % 167.88/167.95 ! [V_z,V_x,V_d] : % 167.88/167.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__idempotent,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__le__D1,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__ge__self,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__zero,axiom, % 167.88/167.95 ! [T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__eq__0,axiom, % 167.88/167.95 ! [V_a_2,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__add__abs,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__mult__self,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__mult,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__minus__commute,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__one,axiom, % 167.88/167.95 ! [T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__minus__cancel,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__of__nat,axiom, % 167.88/167.95 ! [V_n,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__int__eq,axiom, % 167.88/167.95 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__ge__zero,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__le__zero__iff,axiom, % 167.88/167.95 ! [V_a_2,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__of__nonneg,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__not__less__zero,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_zero__less__abs__iff,axiom, % 167.88/167.95 ! [V_a_2,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2))) % 167.88/167.95 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__of__pos,axiom, % 167.88/167.95 ! [V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.95 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__triangle__ineq,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__mult__less,axiom, % 167.88/167.95 ! [V_d,V_b,V_c,V_a,T_a] : % 167.88/167.95 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 167.88/167.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__triangle__ineq3,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__triangle__ineq2,axiom, % 167.88/167.95 ! [V_b,V_a,T_a] : % 167.88/167.95 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 167.88/167.95 % 167.88/167.95 fof(fact_abs__triangle__ineq2__sym,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__ge__minus__self,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__le__iff,axiom, % 167.88/167.96 ! [V_b_2,V_a_2,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 167.88/167.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__leI,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__le__D2,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__less__iff,axiom, % 167.88/167.96 ! [V_b_2,V_a_2,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 167.88/167.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__zmult__eq__1,axiom, % 167.88/167.96 ! [V_n,V_m] : % 167.88/167.96 ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_mult__sgn__abs,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__sgn,axiom, % 167.88/167.96 ! [V_k,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__mult__pos,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__eq__mult,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Rings_Oordered__ring__abs(T_a) % 167.88/167.96 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 167.88/167.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__triangle__ineq4,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__diff__triangle__ineq,axiom, % 167.88/167.96 ! [V_d,V_c,V_b,V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__minus__le__zero,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__of__nonpos,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__if,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Groups_Oabs__if(T_a) % 167.88/167.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__of__neg,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_zabs__less__one__iff,axiom, % 167.88/167.96 ! [V_z_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 167.88/167.96 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_zabs__def,axiom, % 167.88/167.96 ! [V_i] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat0__intermed__int__val,axiom, % 167.88/167.96 ! [V_k_2,V_f_2,V_n_2] : % 167.88/167.96 ( ! [B_i] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 167.88/167.96 => ? [B_i] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 167.88/167.96 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_int__val__lemma,axiom, % 167.88/167.96 ! [V_k_2,V_f_2,V_n_2] : % 167.88/167.96 ( ! [B_i] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 167.88/167.96 => ? [B_i] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 167.88/167.96 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__on__diff__nat,axiom, % 167.88/167.96 ! [V_k_2,V_N_2] : % 167.88/167.96 ( ! [B_x] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 167.88/167.96 => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_expand__Suc,axiom, % 167.88/167.96 ! [V_v] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__on__Un,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.96 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.96 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.88/167.96 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__intermed__int__val,axiom, % 167.88/167.96 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 167.88/167.96 ( ! [B_i] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 167.88/167.96 => ? [B_i] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 167.88/167.96 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__mult__distrib__neg,axiom, % 167.88/167.96 ! [V_z_H,V_z] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.96 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf1I,axiom, % 167.88/167.96 ! [T_a,V_B_2,V_x_2,V_A_2] : % 167.88/167.96 ( hBOOL(hAPP(V_A_2,V_x_2)) % 167.88/167.96 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf1E,axiom, % 167.88/167.96 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 167.88/167.96 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 167.88/167.96 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_IntI,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 167.88/167.96 => 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))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_IntE,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.88/167.96 ( 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))) % 167.88/167.96 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.88/167.96 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__fun__def,axiom, % 167.88/167.96 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__absorb,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__commute,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__left__absorb,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__left__commute,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__assoc,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__reorient,axiom, % 167.88/167.96 ! [V_x_2,V_w_2,T_a] : % 167.88/167.96 ( class_Int_Onumber(T_a) % 167.88/167.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 167.88/167.96 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__number__of,axiom, % 167.88/167.96 ! [V_y_2,V_x_2,T_a] : % 167.88/167.96 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.96 & class_Int_Oring__char__0(T_a) ) % 167.88/167.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 167.88/167.96 <=> V_x_2 = V_y_2 ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf1D1,axiom, % 167.88/167.96 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 167.88/167.96 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf1D2,axiom, % 167.88/167.96 ! [V_x_2,V_B_2,V_A_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 167.88/167.96 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf_Oidem,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__idem,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf_Ocommute,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__aci_I1_J,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__commute,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf_Oleft__idem,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__aci_I4_J,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__left__idem,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf_Oleft__commute,axiom, % 167.88/167.96 ! [V_c,V_a,V_b,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__aci_I3_J,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__left__commute,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf_Oassoc,axiom, % 167.88/167.96 ! [V_c,V_b,V_a,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__aci_I2_J,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__assoc,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__apply,axiom, % 167.88/167.96 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__ord_I1_J,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__le1,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__ord_I2_J,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__le2,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__iff__inf,axiom, % 167.88/167.96 ! [V_y_2,V_x_2,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.88/167.96 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__inf__iff,axiom, % 167.88/167.96 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2))) % 167.88/167.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__infI1,axiom, % 167.88/167.96 ! [V_b,V_x,V_a,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__infI2,axiom, % 167.88/167.96 ! [V_a,V_x,V_b,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__absorb1,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__absorb2,axiom, % 167.88/167.96 ! [V_x,V_y,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__infI,axiom, % 167.88/167.96 ! [V_b,V_a,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__greatest,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__mono,axiom, % 167.88/167.96 ! [V_d,V_b,V_c,V_a,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__infE,axiom, % 167.88/167.96 ! [V_b,V_a,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) % 167.88/167.96 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.88/167.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__infI1,axiom, % 167.88/167.96 ! [V_b,V_x,V_a,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__infI2,axiom, % 167.88/167.96 ! [V_a,V_x,V_b,T_a] : % 167.88/167.96 ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__bot__right,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__bot__left,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Obounded__lattice__bot(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__absorb,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_sup__inf__absorb,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__distrib1,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Odistrib__lattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_sup__inf__distrib1,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Odistrib__lattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__sup__distrib2,axiom, % 167.88/167.96 ! [V_x,V_z,V_y,T_a] : % 167.88/167.96 ( class_Lattices_Odistrib__lattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_sup__inf__distrib2,axiom, % 167.88/167.96 ! [V_x,V_z,V_y,T_a] : % 167.88/167.96 ( class_Lattices_Odistrib__lattice(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__iff,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.88/167.96 ( 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))) % 167.88/167.96 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_IntD1,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.88/167.96 ( 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))) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_IntD2,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 167.88/167.96 ( 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))) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__empty__left,axiom, % 167.88/167.96 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__empty__right,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_disjoint__iff__not__equal,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : % 167.88/167.96 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.88/167.96 <=> ! [B_x] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 167.88/167.96 => ! [B_xa] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 167.88/167.96 => B_x != B_xa ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__int,axiom, % 167.88/167.96 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 167.88/167.96 % 167.88/167.96 fof(fact_insert__inter__insert,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__lower1,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__lower2,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__absorb2,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__absorb1,axiom, % 167.88/167.96 ! [V_A_2,V_B_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__greatest,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_C_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__mono,axiom, % 167.88/167.96 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__Un__distrib,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Un__Int__distrib,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__Un__distrib2,axiom, % 167.88/167.96 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Un__Int__distrib2,axiom, % 167.88/167.96 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Un__Int__crazy,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__Int__distrib,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__Diff,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__Int__distrib2,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__Int2,axiom, % 167.88/167.96 ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__on__Int,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 167.88/167.96 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 167.88/167.96 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__nat__number__of__lemma,axiom, % 167.88/167.96 ! [V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_restrict__restrict,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__Int__eq,axiom, % 167.88/167.96 ! [V_x_2,V_S_2,V_R_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_distrib__inf__le,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_distrib__sup__le,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Olattice(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__number__of__eq__not__less,axiom, % 167.88/167.96 ! [V_w_2,V_v_2,T_a] : % 167.88/167.96 ( ( class_Int_Onumber(T_a) % 167.88/167.96 & class_Orderings_Olinorder(T_a) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 167.88/167.96 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_compl__inf__bot,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__compl__bot,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_diff__eq,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_left__distrib__number__of,axiom, % 167.88/167.96 ! [V_v,V_b,V_a,T_b] : % 167.88/167.96 ( ( class_Int_Onumber(T_b) % 167.88/167.96 & class_Rings_Osemiring(T_b) ) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_right__distrib__number__of,axiom, % 167.88/167.96 ! [V_c,V_b,V_v,T_b] : % 167.88/167.96 ( ( class_Int_Onumber(T_b) % 167.88/167.96 & class_Rings_Osemiring(T_b) ) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_compl__inf,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_compl__sup,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__0,axiom, % 167.88/167.96 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 167.88/167.96 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_left__diff__distrib__number__of,axiom, % 167.88/167.96 ! [V_v,V_b,V_a,T_b] : % 167.88/167.96 ( ( class_Int_Onumber(T_b) % 167.88/167.96 & class_Rings_Oring(T_b) ) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_right__diff__distrib__number__of,axiom, % 167.88/167.96 ! [V_c,V_b,V_v,T_b] : % 167.88/167.96 ( ( class_Int_Onumber(T_b) % 167.88/167.96 & class_Rings_Oring(T_b) ) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__number__of,axiom, % 167.88/167.96 ! [V_y_2,V_x_2,T_a] : % 167.88/167.96 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.96 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__number__of,axiom, % 167.88/167.96 ! [V_y_2,V_x_2,T_a] : % 167.88/167.96 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.96 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__nat__nat__iff,axiom, % 167.88/167.96 ! [V_z_H_2,V_z_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 167.88/167.96 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 167.88/167.96 <=> V_z_2 = V_z_H_2 ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_ex__nat,axiom, % 167.88/167.96 ! [V_P_2] : % 167.88/167.96 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.88/167.96 <=> ? [B_x] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.88/167.96 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_all__nat,axiom, % 167.88/167.96 ! [V_P_2] : % 167.88/167.96 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 167.88/167.96 <=> ! [B_x] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 167.88/167.96 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 167.88/167.96 ! [V_y_2,V_x_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 167.88/167.96 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 167.88/167.96 <=> V_x_2 = V_y_2 ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__number__of__left,axiom, % 167.88/167.96 ! [V_z,V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__number__of__eq,axiom, % 167.88/167.96 ! [V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__add,axiom, % 167.88/167.96 ! [V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__insert__right,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_a_2,T_a] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__insert__left,axiom, % 167.88/167.96 ! [V_B_2,V_C_2,V_a_2,T_a] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__insert__right__if0,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_a_2,T_a] : % 167.88/167.96 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__insert__left__if0,axiom, % 167.88/167.96 ! [V_B_2,V_C_2,V_a_2,T_a] : % 167.88/167.96 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__insert__right__if1,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_a_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__insert__left__if1,axiom, % 167.88/167.96 ! [V_B_2,V_C_2,V_a_2,T_a] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__mult,axiom, % 167.88/167.96 ! [V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_arith__simps_I32_J,axiom, % 167.88/167.96 ! [V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_mult__number__of__left,axiom, % 167.88/167.96 ! [V_z,V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__diff,axiom, % 167.88/167.96 ! [V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_arith__simps_I30_J,axiom, % 167.88/167.96 ! [V_w,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__minus,axiom, % 167.88/167.96 ! [V_w,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_image__Int__subset,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 167.88/167.96 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__disjoint,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__triv,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : % 167.88/167.96 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Un__Int__assoc__eq,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : % 167.88/167.96 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Un__Diff__Int,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__Un,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__Int,axiom, % 167.88/167.96 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__disjoint2,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__disjoint,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Ints__number__of,axiom, % 167.88/167.96 ! [V_w_2,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__Int,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__Un,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__eq,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__Compl,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__int__nat__set__return__embed,axiom, % 167.88/167.96 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ). % 167.88/167.96 % 167.88/167.96 fof(fact_dom__restrict,axiom, % 167.88/167.96 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 167.88/167.96 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__le__0,axiom, % 167.88/167.96 ! [V_z] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.96 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__0__iff,axiom, % 167.88/167.96 ! [V_i_2] : % 167.88/167.96 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__mono__iff,axiom, % 167.88/167.96 ! [V_w_2,V_z_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_zless__nat__conj,axiom, % 167.88/167.96 ! [V_z_2,V_w_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 167.88/167.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__number__of__diff1,axiom, % 167.88/167.96 ! [V_c,V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 167.88/167.96 ! [V_y_2,V_x_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__1,axiom, % 167.88/167.96 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__0__le,axiom, % 167.88/167.96 ! [V_z] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_int__eq__iff,axiom, % 167.88/167.96 ! [V_z_2,V_m_2] : % 167.88/167.96 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 167.88/167.96 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_int__nat__eq,axiom, % 167.88/167.96 ! [V_z] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_zless__nat__eq__int__zless,axiom, % 167.88/167.96 ! [V_z_2,V_m_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_minus__number__of__mult,axiom, % 167.88/167.96 ! [V_z,V_w,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__zminus__int,axiom, % 167.88/167.96 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.88/167.96 % 167.88/167.96 fof(fact_diff__number__of__eq,axiom, % 167.88/167.96 ! [V_w,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__on__image__Int,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 167.88/167.96 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__abs__mult__distrib,axiom, % 167.88/167.96 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_disjoint__eq__subset__Compl,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,T_a] : % 167.88/167.96 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_map__add__comm,axiom, % 167.88/167.96 ! [V_m2_2,V_m1_2,T_b,T_a] : % 167.88/167.96 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 167.88/167.96 => c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_zero__less__nat__eq,axiom, % 167.88/167.96 ! [V_z_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__less__eq__zless,axiom, % 167.88/167.96 ! [V_z_2,V_w_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 167.88/167.96 ! [V_y_2,V_x_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_abs__number__of,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.96 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__eq__iff2,axiom, % 167.88/167.96 ! [V_w_2,V_m_2] : % 167.88/167.96 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 167.88/167.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.88/167.96 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.88/167.96 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__eq__iff,axiom, % 167.88/167.96 ! [V_m_2,V_w_2] : % 167.88/167.96 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 167.88/167.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.88/167.96 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.88/167.96 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__le__eq__zle,axiom, % 167.88/167.96 ! [V_z_2,V_w_2] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.88/167.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_split__nat,axiom, % 167.88/167.96 ! [V_i_2,V_P_2] : % 167.88/167.96 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 167.88/167.96 <=> ( ! [B_n] : % 167.88/167.96 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 167.88/167.96 => hBOOL(hAPP(V_P_2,B_n)) ) % 167.88/167.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.96 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__add__distrib,axiom, % 167.88/167.96 ! [V_z_H,V_z] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 167.88/167.96 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 167.88/167.96 ! [V_y,V_x] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__mult__distrib,axiom, % 167.88/167.96 ! [V_z_H,V_z] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.96 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 167.88/167.96 ! [V_y,V_x] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__number__of__diff2,axiom, % 167.88/167.96 ! [V_w,V_c,V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__diff__distrib,axiom, % 167.88/167.96 ! [V_z,V_z_H] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 167.88/167.96 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 167.88/167.96 ! [V_y,V_x] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_one__less__nat__eq,axiom, % 167.88/167.96 ! [V_z_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__less__iff,axiom, % 167.88/167.96 ! [V_m_2,V_w_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 167.88/167.96 ! [V_z] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.96 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__aux__def,axiom, % 167.88/167.96 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__morphism__nat__int,axiom, % 167.88/167.96 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__of__nat,axiom, % 167.88/167.96 ! [V_k,T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nitpick_Oint__lcm__def,axiom, % 167.88/167.96 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.88/167.96 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__is__id,axiom, % 167.88/167.96 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 167.88/167.96 % 167.88/167.96 fof(fact_int__number__of__def,axiom, % 167.88/167.96 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__eq__iff,axiom, % 167.88/167.96 ! [V_z_2,V_w_2,T_a] : % 167.88/167.96 ( class_Int_Oring__char__0(T_a) % 167.88/167.96 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 167.88/167.96 <=> V_w_2 = V_z_2 ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.88/167.96 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__eq__number__of__int__code,axiom, % 167.88/167.96 ! [V_l_2,V_k_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__number__of__int__code,axiom, % 167.88/167.96 ! [V_l_2,V_k_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_plus__numeral__code_I9_J,axiom, % 167.88/167.96 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_times__numeral__code_I5_J,axiom, % 167.88/167.96 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_minus__numeral__code_I5_J,axiom, % 167.88/167.96 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__number__of__eq,axiom, % 167.88/167.96 ! [V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__eq,axiom, % 167.88/167.96 ! [V_k,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__int__eq,axiom, % 167.88/167.96 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.88/167.96 => ( V_A_2 = V_B_2 % 167.88/167.96 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__number__of,axiom, % 167.88/167.96 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__number__of__def,axiom, % 167.88/167.96 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__0,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__0__eq__iff,axiom, % 167.88/167.96 ! [V_z_2,T_a] : % 167.88/167.96 ( class_Int_Oring__char__0(T_a) % 167.88/167.96 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 167.88/167.96 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__eq__0__iff,axiom, % 167.88/167.96 ! [V_z_2,T_a] : % 167.88/167.96 ( class_Int_Oring__char__0(T_a) % 167.88/167.96 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.96 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 167.88/167.96 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__le__iff,axiom, % 167.88/167.96 ! [V_z_2,V_w_2,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__less__iff,axiom, % 167.88/167.96 ! [V_z_2,V_w_2,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__add,axiom, % 167.88/167.96 ! [V_z,V_w,T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__mult,axiom, % 167.88/167.96 ! [V_z,V_w,T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__1,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__diff,axiom, % 167.88/167.96 ! [V_z,V_w,T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__of__nat__eq,axiom, % 167.88/167.96 ! [V_n,T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__minus,axiom, % 167.88/167.96 ! [V_z,T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Ints__of__int,axiom, % 167.88/167.96 ! [V_z_2,T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__set__def,axiom, % 167.88/167.96 ! [V_S_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_S_2) % 167.88/167.96 <=> ! [B_x] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 167.88/167.96 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_minus__numeral__code_I6_J,axiom, % 167.88/167.96 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_int__eq__iff__number__of,axiom, % 167.88/167.96 ! [V_v_2,V_m_2] : % 167.88/167.96 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) % 167.88/167.96 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__nat__int__set__return__embed,axiom, % 167.88/167.96 ! [V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 167.88/167.96 ! [V_B_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( c_Nat__Transfer_Onat__set(V_B_2) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 167.88/167.96 ! [V_x_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__le__0__iff,axiom, % 167.88/167.96 ! [V_z_2,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__0__le__iff,axiom, % 167.88/167.96 ! [V_z_2,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__less__0__iff,axiom, % 167.88/167.96 ! [V_z_2,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__int__0__less__iff,axiom, % 167.88/167.96 ! [V_z_2,T_a] : % 167.88/167.96 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__nat__nat,axiom, % 167.88/167.96 ! [V_z,T_a] : % 167.88/167.96 ( class_Rings_Oring__1(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 167.88/167.96 ! [V_A_2,V_x_2] : % 167.88/167.96 ( c_Nat__Transfer_Ois__nat(V_x_2) % 167.88/167.96 => ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_of__nat__number__of__eq,axiom, % 167.88/167.96 ! [V_v,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_compl__unique,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 167.88/167.96 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 167.88/167.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__number__of__eq,axiom, % 167.88/167.96 ! [V_y_2,V_x_2,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 167.88/167.96 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_mult__nat__number__of,axiom, % 167.88/167.96 ! [V_v_H,V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__number__of__mult__left,axiom, % 167.88/167.96 ! [V_k,V_v_H,V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_UNIV__I,axiom, % 167.88/167.96 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_not__neg__number__of__Pls,axiom, % 167.88/167.96 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_iszero__Numeral0,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_top__apply,axiom, % 167.88/167.96 ! [V_x_2,T_b,T_a] : % 167.88/167.96 ( class_Orderings_Otop(T_a) % 167.88/167.96 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_UNIV__Plus__UNIV,axiom, % 167.88/167.96 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_UNIV__not__empty,axiom, % 167.88/167.96 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Pls__def,axiom, % 167.88/167.96 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.96 % 167.88/167.96 fof(fact_rel__simps_I19_J,axiom, % 167.88/167.96 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_rel__simps_I2_J,axiom, % 167.88/167.96 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_subset__UNIV,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__Pls__right,axiom, % 167.88/167.96 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__Pls,axiom, % 167.88/167.96 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 167.88/167.96 % 167.88/167.96 fof(fact_Un__UNIV__left,axiom, % 167.88/167.96 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Un__UNIV__right,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__UNIV__left,axiom, % 167.88/167.96 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 167.88/167.96 % 167.88/167.96 fof(fact_Int__UNIV__right,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 167.88/167.96 % 167.88/167.96 fof(fact_mult__Pls,axiom, % 167.88/167.96 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__eq,axiom, % 167.88/167.96 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.88/167.96 <=> V_x_2 = V_y_2 ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_injD,axiom, % 167.88/167.96 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 167.88/167.96 => V_x_2 = V_y_2 ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__int,axiom, % 167.88/167.96 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_diff__bin__simps_I1_J,axiom, % 167.88/167.96 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 167.88/167.96 % 167.88/167.96 fof(fact_minus__Pls,axiom, % 167.88/167.96 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 167.88/167.96 % 167.88/167.96 fof(fact_not__neg__0,axiom, % 167.88/167.96 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_not__neg__int,axiom, % 167.88/167.96 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_not__neg__1,axiom, % 167.88/167.96 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 167.88/167.96 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_range__composition,axiom, % 167.88/167.96 ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 167.88/167.96 ! [V_y,V_x] : % 167.88/167.96 ( c_Nat__Transfer_Ois__nat(V_x) % 167.88/167.96 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.88/167.96 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 167.88/167.96 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 167.88/167.96 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 167.88/167.96 ! [V_y,V_x] : % 167.88/167.96 ( c_Nat__Transfer_Ois__nat(V_x) % 167.88/167.96 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.88/167.96 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__fun,axiom, % 167.88/167.96 ! [T_c,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_top__greatest,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Orderings_Otop(T_a) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_sup__top__left,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Obounded__lattice__top(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_sup__top__right,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Obounded__lattice__top(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__top__left,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Obounded__lattice__top(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__top__right,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Obounded__lattice__top(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__eq__top__iff,axiom, % 167.88/167.96 ! [V_y_2,V_x_2,T_a] : % 167.88/167.96 ( class_Lattices_Obounded__lattice__top(T_a) % 167.88/167.96 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 167.88/167.96 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 167.88/167.96 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_UNIV__option__conv,axiom, % 167.88/167.96 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_iszero__def,axiom, % 167.88/167.96 ! [V_z_2,T_a] : % 167.88/167.96 ( class_Rings_Osemiring__1(T_a) % 167.88/167.96 => ( c_Int_Oiszero(T_a,V_z_2) % 167.88/167.96 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_iszero__0,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Rings_Osemiring__1(T_a) % 167.88/167.96 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_not__iszero__1,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Rings_Osemiring__1(T_a) % 167.88/167.96 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__Pls,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_semiring__norm_I112_J,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__numeral__0__right,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__numeral__0,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_rangeI,axiom, % 167.88/167.96 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_range__eqI,axiom, % 167.88/167.96 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 167.88/167.96 ( V_b_2 = hAPP(V_f_2,V_x_2) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_bin__less__0__simps_I1_J,axiom, % 167.88/167.96 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_semiring__norm_I113_J,axiom, % 167.88/167.96 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__number__of__Pls,axiom, % 167.88/167.96 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.88/167.96 % 167.88/167.96 fof(fact_zero__is__num__zero,axiom, % 167.88/167.96 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Diff__UNIV,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 167.88/167.96 ! [V_y,V_x] : % 167.88/167.96 ( c_Nat__Transfer_Ois__nat(V_x) % 167.88/167.96 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.88/167.96 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__image__eq__iff,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 167.88/167.96 <=> V_A_2 = V_B_2 ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__UNIV__eq,axiom, % 167.88/167.96 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__empty__eq,axiom, % 167.88/167.96 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__partition2,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__partition,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Compl__eq__Diff__UNIV,axiom, % 167.88/167.96 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2) ). % 167.88/167.96 % 167.88/167.96 fof(fact_not__neg__eq__ge__0,axiom, % 167.88/167.96 ! [V_x_2] : % 167.88/167.96 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_neg__def,axiom, % 167.88/167.96 ! [V_Z_2] : % 167.88/167.96 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_neg__nat,axiom, % 167.88/167.96 ! [V_z] : % 167.88/167.96 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 167.88/167.96 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__special_I1_J,axiom, % 167.88/167.96 ! [V_y_2,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 167.88/167.96 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__special_I3_J,axiom, % 167.88/167.96 ! [V_x_2,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.96 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__singleton,axiom, % 167.88/167.96 ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_not__neg__nat,axiom, % 167.88/167.96 ! [V_z] : % 167.88/167.96 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_the__inv__f__f,axiom, % 167.88/167.96 ! [V_x_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__of__nat,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Nat_Osemiring__char__0(T_a) % 167.88/167.96 => c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_dom__const,axiom, % 167.88/167.96 ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_is__nat__def,axiom, % 167.88/167.96 ! [V_x_2] : % 167.88/167.96 ( c_Nat__Transfer_Ois__nat(V_x_2) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_compl__bot__eq,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_compl__top__eq,axiom, % 167.88/167.96 ! [T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_sup__compl__top,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_compl__sup__top,axiom, % 167.88/167.96 ! [V_x,T_a] : % 167.88/167.96 ( class_Lattices_Oboolean__algebra(T_a) % 167.88/167.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_range__ex1__eq,axiom, % 167.88/167.96 ! [V_b_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) % 167.88/167.96 <=> ? [B_x] : % 167.88/167.96 ( V_b_2 = hAPP(V_f_2,B_x) % 167.88/167.96 & ! [B_y] : % 167.88/167.96 ( V_b_2 = hAPP(V_f_2,B_y) % 167.88/167.96 => B_y = B_x ) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__image__mem__iff,axiom, % 167.88/167.96 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__number__of__0,axiom, % 167.88/167.96 ! [V_v_2] : % 167.88/167.96 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__0__number__of,axiom, % 167.88/167.96 ! [V_v_2] : % 167.88/167.96 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of2,axiom, % 167.88/167.96 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__nat__number__of,axiom, % 167.88/167.96 ! [V_v_H_2,V_v_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 167.88/167.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 167.88/167.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__nat__number__of,axiom, % 167.88/167.96 ! [V_v_H_2,V_v_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) % 167.88/167.96 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__image__subset__iff,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_image__Int,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_image__set__diff,axiom, % 167.88/167.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_surj__Compl__image__subset,axiom, % 167.88/167.96 ! [V_A_2,V_f_2,T_a,T_b] : % 167.88/167.96 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 167.88/167.96 ! [V_x_2,V_A_2] : % 167.88/167.96 ( c_Nat__Transfer_Onat__set(V_A_2) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 167.88/167.96 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_neg__imp__number__of__eq__0,axiom, % 167.88/167.96 ! [V_v] : % 167.88/167.96 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_neg__zminus__int,axiom, % 167.88/167.96 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__special_I1_J,axiom, % 167.88/167.96 ! [V_y_2,T_a] : % 167.88/167.96 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.96 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__special_I3_J,axiom, % 167.88/167.96 ! [V_x_2,T_a] : % 167.88/167.96 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.96 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__special_I1_J,axiom, % 167.88/167.96 ! [V_y_2,T_a] : % 167.88/167.96 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.96 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__special_I3_J,axiom, % 167.88/167.96 ! [V_x_2,T_a] : % 167.88/167.96 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.96 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__0__number__of,axiom, % 167.88/167.96 ! [V_v_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_add__nat__number__of,axiom, % 167.88/167.96 ! [V_v_H,V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inj__image__Compl__subset,axiom, % 167.88/167.96 ! [V_A_2,V_f_2,T_b,T_a] : % 167.88/167.96 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_diff__nat__number__of,axiom, % 167.88/167.96 ! [V_v_2,V_v_H_2] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__nat__number__of,axiom, % 167.88/167.96 ! [V_v_H_2,V_v_2] : % 167.88/167.96 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2) % 167.88/167.96 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 167.88/167.96 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 167.88/167.96 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__number__of__add__left,axiom, % 167.88/167.96 ! [V_k,V_v_H,V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_int__nat__number__of,axiom, % 167.88/167.96 ! [V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_diff__nat__eq__if,axiom, % 167.88/167.96 ! [V_z_2,V_z_H_2] : % 167.88/167.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Suc__nat__number__of__add,axiom, % 167.88/167.96 ! [V_n,V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__case__add__eq__if,axiom, % 167.88/167.96 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Suc__nat__number__of,axiom, % 167.88/167.96 ! [V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.96 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__Suc__number__of,axiom, % 167.88/167.96 ! [V_v_2,V_n_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__number__of__Suc,axiom, % 167.88/167.96 ! [V_n_2,V_v_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__number__of__add__1,axiom, % 167.88/167.96 ! [V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_top1I,axiom, % 167.88/167.96 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_succ__pred,axiom, % 167.88/167.96 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 167.88/167.96 % 167.88/167.96 fof(fact_le__iff__pred__less,axiom, % 167.88/167.96 ! [V_l_2,V_k_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_pred__def,axiom, % 167.88/167.96 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_succ__def,axiom, % 167.88/167.96 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__succ,axiom, % 167.88/167.96 ! [V_k,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_number__of__pred,axiom, % 167.88/167.96 ! [V_w,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_neg__number__of__pred__iff__0,axiom, % 167.88/167.96 ! [V_v_2] : % 167.88/167.96 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 167.88/167.96 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Suc__diff__number__of,axiom, % 167.88/167.96 ! [V_m,V_v] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Suc__eq__number__of,axiom, % 167.88/167.96 ! [V_v_2,V_n_2] : % 167.88/167.96 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_eq__number__of__Suc,axiom, % 167.88/167.96 ! [V_n_2,V_v_2] : % 167.88/167.96 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__case__number__of,axiom, % 167.88/167.96 ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__number__of__diff__1,axiom, % 167.88/167.96 ! [V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__Suc__number__of,axiom, % 167.88/167.96 ! [V_v_2,V_n_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_less__number__of__Suc,axiom, % 167.88/167.96 ! [V_n_2,V_v_2] : % 167.88/167.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) % 167.88/167.96 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__1__add__number__of,axiom, % 167.88/167.96 ! [V_v] : % 167.88/167.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 167.88/167.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 167.88/167.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__rec__add__eq__if,axiom, % 167.88/167.96 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_nat__rec__number__of,axiom, % 167.88/167.96 ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__Suc__number__of,axiom, % 167.88/167.96 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__number__of__Suc,axiom, % 167.88/167.96 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_Nats__number__of,axiom, % 167.88/167.96 ! [V_w_2,T_a] : % 167.88/167.96 ( class_Int_Onumber__ring(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 167.88/167.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_iso__tuple__UNIV__I,axiom, % 167.88/167.96 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 167.88/167.96 % 167.88/167.96 fof(fact_inf__nat__def,axiom, % 167.88/167.96 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf_Oidem,axiom, % 167.88/167.96 ! [V_a,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf_Ocommute,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf__commute,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 167.88/167.96 ! [V_b,V_a,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf__left__idem,axiom, % 167.88/167.96 ! [V_y,V_x,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 167.88/167.96 ! [V_c,V_a,V_b,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf__left__commute,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf_Oassoc,axiom, % 167.88/167.96 ! [V_c,V_b,V_a,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__max_Oinf__assoc,axiom, % 167.88/167.96 ! [V_z,V_y,V_x,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ). % 167.88/167.96 % 167.88/167.96 fof(fact_min__le__iff__disj,axiom, % 167.88/167.96 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.88/167.96 ( class_Orderings_Olinorder(T_a) % 167.88/167.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 167.88/167.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 167.88/167.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__le1,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__le2,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__iff__inf,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.88/167.97 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__inf__iff,axiom, % 167.88/167.97 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2))) % 167.88/167.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.88/167.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__infI1,axiom, % 167.88/167.97 ! [V_b,V_x,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__infI2,axiom, % 167.88/167.97 ! [V_a,V_x,V_b,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__absorb1,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__absorb2,axiom, % 167.88/167.97 ! [V_x,V_y,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__infI,axiom, % 167.88/167.97 ! [V_b,V_a,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__greatest,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__mono,axiom, % 167.88/167.97 ! [V_d,V_b,V_c,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__infE,axiom, % 167.88/167.97 ! [V_b,V_a,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) % 167.88/167.97 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.88/167.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__less__iff__conj,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,V_z_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2))) % 167.88/167.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 167.88/167.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__less__iff__disj,axiom, % 167.88/167.97 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 167.88/167.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 167.88/167.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oless__infI1,axiom, % 167.88/167.97 ! [V_b,V_x,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oless__infI2,axiom, % 167.88/167.97 ! [V_a,V_x,V_b,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__add__distrib__left,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__diff__distrib__left,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Groups_Oordered__ab__group__add(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_inf__min,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( ( class_Lattices_Osemilattice__inf(T_a) % 167.88/167.97 & class_Orderings_Olinorder(T_a) ) % 167.88/167.97 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__0L,axiom, % 167.88/167.97 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__0R,axiom, % 167.88/167.97 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__Suc__Suc,axiom, % 167.88/167.97 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__diff,axiom, % 167.88/167.97 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__number__of,axiom, % 167.88/167.97 ! [V_v,V_u,T_b] : % 167.88/167.97 ( ( class_Int_Onumber(T_b) % 167.88/167.97 & class_Orderings_Oord(T_b) ) % 167.88/167.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__rec__0,axiom, % 167.88/167.97 ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__rec__Suc,axiom, % 167.88/167.97 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),V_nat_2)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nats__0,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nats__add,axiom, % 167.88/167.97 ! [V_b_2,V_a_2,T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nats__mult,axiom, % 167.88/167.97 ! [V_b_2,V_a_2,T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nats__1,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_of__nat__in__Nats,axiom, % 167.88/167.97 ! [V_n_2,T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__Suc1,axiom, % 167.88/167.97 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__Suc2,axiom, % 167.88/167.97 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__ord__min,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Orderings_Oord(T_a) % 167.88/167.97 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__number__of__Suc,axiom, % 167.88/167.97 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__Suc__number__of,axiom, % 167.88/167.97 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_inj__vimage__singleton,axiom, % 167.88/167.97 ! [V_a_2,V_f_2,T_b,T_a] : % 167.88/167.97 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__number__of__Bit1,axiom, % 167.88/167.97 ! [V_w_2] : % 167.88/167.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.88/167.97 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.88/167.97 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_eq__special_I4_J,axiom, % 167.88/167.97 ! [V_x_2,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 167.88/167.97 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimageI,axiom, % 167.88/167.97 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 167.88/167.97 ( hAPP(V_f_2,V_a_2) = V_b_2 % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__ident,axiom, % 167.88/167.97 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__assoc,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup_Oassoc,axiom, % 167.88/167.97 ! [V_c,V_b,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__left__commute,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup_Oleft__commute,axiom, % 167.88/167.97 ! [V_c,V_a,V_b,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__left__idem,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup_Oleft__idem,axiom, % 167.88/167.97 ! [V_b,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__commute,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup_Ocommute,axiom, % 167.88/167.97 ! [V_b,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup_Oidem,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I51_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 167.88/167.97 <=> V_k_2 = V_l_2 ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__code,axiom, % 167.88/167.97 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 167.88/167.97 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_sup__nat__def,axiom, % 167.88/167.97 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__supE,axiom, % 167.88/167.97 ! [V_x,V_b,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) % 167.88/167.97 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.88/167.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__mono,axiom, % 167.88/167.97 ! [V_d,V_b,V_c,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__least,axiom, % 167.88/167.97 ! [V_z,V_x,V_y,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__supI,axiom, % 167.88/167.97 ! [V_b,V_x,V_a,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__absorb1,axiom, % 167.88/167.97 ! [V_x,V_y,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__absorb2,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__supI2,axiom, % 167.88/167.97 ! [V_a,V_b,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__supI1,axiom, % 167.88/167.97 ! [V_b,V_a,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__sup__iff,axiom, % 167.88/167.97 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 167.88/167.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 167.88/167.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Ole__iff__sup,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 167.88/167.97 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_le__maxI2,axiom, % 167.88/167.97 ! [V_x,V_y,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_le__maxI1,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_le__max__iff__disj,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,V_z_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 167.88/167.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 167.88/167.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oless__supI2,axiom, % 167.88/167.97 ! [V_a,V_b,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oless__supI1,axiom, % 167.88/167.97 ! [V_b,V_a,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__less__iff__conj,axiom, % 167.88/167.97 ! [V_z_2,V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 167.88/167.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 167.88/167.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__max__iff__disj,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,V_z_2,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 167.88/167.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 167.88/167.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__add__distrib__left,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__diff__distrib__left,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Groups_Oordered__ab__group__add(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimageI2,axiom, % 167.88/167.97 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimageD,axiom, % 167.88/167.97 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__eq,axiom, % 167.88/167.97 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_sup__max,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( ( class_Lattices_Osemilattice__sup(T_a) % 167.88/167.97 & class_Orderings_Olinorder(T_a) ) % 167.88/167.97 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__0R,axiom, % 167.88/167.97 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__0L,axiom, % 167.88/167.97 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__Suc__Suc,axiom, % 167.88/167.97 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__empty,axiom, % 167.88/167.97 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 167.88/167.97 ! [V_x,V_z,V_y,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__inf__distrib2,axiom, % 167.88/167.97 ! [V_x,V_z,V_y,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__inf__distrib1,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Oinf__sup__absorb,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Osup__inf__absorb,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I34_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__eq__int__code_I16_J,axiom, % 167.88/167.97 ! [V_k2_2,V_k1_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__int__code_I16_J,axiom, % 167.88/167.97 ! [V_k2_2,V_k1_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I17_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__mono,axiom, % 167.88/167.97 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I46_J,axiom, % 167.88/167.97 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I39_J,axiom, % 167.88/167.97 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__UNIV,axiom, % 167.88/167.97 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__Un,axiom, % 167.88/167.97 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__Int,axiom, % 167.88/167.97 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__Diff,axiom, % 167.88/167.97 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__Compl,axiom, % 167.88/167.97 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__number__of,axiom, % 167.88/167.97 ! [V_v,V_u,T_b] : % 167.88/167.97 ( ( class_Int_Onumber(T_b) % 167.88/167.97 & class_Orderings_Oord(T_b) ) % 167.88/167.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Odistrib__sup__le,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_min__max_Odistrib__inf__le,axiom, % 167.88/167.97 ! [V_z,V_y,V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_minus__max__eq__min,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.88/167.97 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_minus__min__eq__max,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Groups_Olinordered__ab__group__add(T_a) % 167.88/167.97 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_bin__less__0__simps_I4_J,axiom, % 167.88/167.97 ! [V_w_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__minus__add__max,axiom, % 167.88/167.97 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I22_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I12_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_image__vimage__subset,axiom, % 167.88/167.97 ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_surj__image__vimage__eq,axiom, % 167.88/167.97 ! [V_A_2,V_f_2,T_a,T_b] : % 167.88/167.97 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.88/167.97 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Bit1__def,axiom, % 167.88/167.97 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ). % 167.88/167.97 % 167.88/167.97 fof(fact_neg__number__of__Bit1,axiom, % 167.88/167.97 ! [V_w_2] : % 167.88/167.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 167.88/167.97 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_minus__Bit1,axiom, % 167.88/167.97 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_iszero__number__of__Bit1,axiom, % 167.88/167.97 ! [V_w,T_a] : % 167.88/167.97 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.97 & class_Int_Oring__char__0(T_a) ) % 167.88/167.97 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_succ__Pls,axiom, % 167.88/167.97 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__Suc2,axiom, % 167.88/167.97 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__Suc1,axiom, % 167.88/167.97 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ). % 167.88/167.97 % 167.88/167.97 fof(fact_number__of__Bit1,axiom, % 167.88/167.97 ! [V_w,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__singleton__eq,axiom, % 167.88/167.97 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 167.88/167.97 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mult__numeral__1__right,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mult__numeral__1,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_numeral__1__eq__1,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_semiring__norm_I110_J,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__insert,axiom, % 167.88/167.97 ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I5_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I29_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__subsetD,axiom, % 167.88/167.97 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 167.88/167.97 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)),V_A_2)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_image__vimage__eq,axiom, % 167.88/167.97 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_inj__vimage__image__eq,axiom, % 167.88/167.97 ! [V_A_2,V_f_2,T_b,T_a] : % 167.88/167.97 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.97 => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_one__is__num__one,axiom, % 167.88/167.97 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Numeral1__eq1__nat,axiom, % 167.88/167.97 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__numeral__1__eq__1,axiom, % 167.88/167.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 167.88/167.97 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_not__iszero__Numeral1,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__const,axiom, % 167.88/167.97 ! [T_b,V_A_2,V_ca_2,T_a] : % 167.88/167.97 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.88/167.97 => 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)) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.88/167.97 => 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)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_numeral__1__eq__Suc__0,axiom, % 167.88/167.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_numeral__3__eq__3,axiom, % 167.88/167.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 167.88/167.97 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Suc3__eq__add__3,axiom, % 167.88/167.97 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__subsetI,axiom, % 167.88/167.97 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 167.88/167.97 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),V_A_2)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 167.88/167.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 167.88/167.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_vimage__if,axiom, % 167.88/167.97 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] : % 167.88/167.97 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.88/167.97 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 167.88/167.97 => 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)) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 167.88/167.97 => 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 ) ) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 167.88/167.97 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 167.88/167.97 => 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) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 167.88/167.97 => 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)) ) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_le__special_I4_J,axiom, % 167.88/167.97 ! [V_x_2,T_a] : % 167.88/167.97 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.97 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_le__special_I2_J,axiom, % 167.88/167.97 ! [V_y_2,T_a] : % 167.88/167.97 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.97 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__special_I2_J,axiom, % 167.88/167.97 ! [V_y_2,T_a] : % 167.88/167.97 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.97 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__special_I4_J,axiom, % 167.88/167.97 ! [V_x_2,T_a] : % 167.88/167.97 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.97 & class_Rings_Olinordered__idom(T_a) ) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_add__special_I3_J,axiom, % 167.88/167.97 ! [V_v,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_add__special_I2_J,axiom, % 167.88/167.97 ! [V_w,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Suc__diff__eq__diff__pred,axiom, % 167.88/167.97 ! [V_m,V_n] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) % 167.88/167.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_diff__special_I1_J,axiom, % 167.88/167.97 ! [V_w,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_diff__special_I2_J,axiom, % 167.88/167.97 ! [V_v,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_eq__special_I2_J,axiom, % 167.88/167.97 ! [V_y_2,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 167.88/167.97 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_dual__min,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_of__nat__double,axiom, % 167.88/167.97 ! [V_x,T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_max__ord__max,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Orderings_Oord(T_a) % 167.88/167.97 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__number__of__odd__number__of,axiom, % 167.88/167.97 ! [V_v_2,V_w_2,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(T_a))) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zpower__number__of__odd,axiom, % 167.88/167.97 ! [V_z_2,V_w_2] : % 167.88/167.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 167.88/167.97 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_int__power,axiom, % 167.88/167.97 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zpower__int,axiom, % 167.88/167.97 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I48_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 167.88/167.97 <=> V_k_2 = V_l_2 ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_of__int__power,axiom, % 167.88/167.97 ! [V_n,V_z,T_a] : % 167.88/167.97 ( class_Rings_Oring__1(T_a) % 167.88/167.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 167.88/167.97 ! [V_q,V_y,V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__number__of__even,axiom, % 167.88/167.97 ! [V_w_2,V_z_2,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__eq__int__code_I13_J,axiom, % 167.88/167.97 ! [V_k2_2,V_k1_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I31_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I14_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__int__code_I13_J,axiom, % 167.88/167.97 ! [V_k2_2,V_k1_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Bit0__Pls,axiom, % 167.88/167.97 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I38_J,axiom, % 167.88/167.97 ! [V_l_2] : % 167.88/167.97 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 167.88/167.97 <=> c_Int_OPls = V_l_2 ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I44_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 167.88/167.97 <=> V_k_2 = c_Int_OPls ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I49_J,axiom, % 167.88/167.97 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I50_J,axiom, % 167.88/167.97 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 167.88/167.97 % 167.88/167.97 fof(fact_add__Bit0__Bit0,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Bit0__def,axiom, % 167.88/167.97 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 167.88/167.97 ! [V_q,V_p,V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zpower__zpower,axiom, % 167.88/167.97 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zpower__number__of__even,axiom, % 167.88/167.97 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mult__Bit0,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_diff__bin__simps_I7_J,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_minus__Bit0,axiom, % 167.88/167.97 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 167.88/167.97 ! [V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 167.88/167.97 ! [V_n,V_x] : % 167.88/167.97 ( c_Nat__Transfer_Ois__nat(V_x) % 167.88/167.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__power__eq,axiom, % 167.88/167.97 ! [V_n,V_z] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 167.88/167.97 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 167.88/167.97 ! [V_n,V_x] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__number__of__even__number__of,axiom, % 167.88/167.97 ! [V_w_2,V_v_2,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__power2,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__eq__power2,axiom, % 167.88/167.97 ! [V_a_2,T_a] : % 167.88/167.97 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 167.88/167.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 167.88/167.97 ! [V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__eq__square,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_one__power2,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__minus,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Rings_Oring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__even__eq,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_abs__power2,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__abs,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 167.88/167.97 ! [V_q,V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 167.88/167.97 ! [V_q,V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 167.88/167.97 ! [V_q,V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 167.88/167.97 ! [V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 167.88/167.97 ! [V_q,V_p,V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_bin__less__0__simps_I3_J,axiom, % 167.88/167.97 ! [V_w_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 167.88/167.97 ! [V_n,V_x] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I27_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I21_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__eq__int__code_I14_J,axiom, % 167.88/167.97 ! [V_k2_2,V_k1_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I32_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I4_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I10_J,axiom, % 167.88/167.97 ! [V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I16_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__int__code_I15_J,axiom, % 167.88/167.97 ! [V_k2_2,V_k1_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_add__Bit0__Bit1,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_add__Bit1__Bit0,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zpower__zadd__distrib,axiom, % 167.88/167.97 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_diff__bin__simps_I3_J,axiom, % 167.88/167.97 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_diff__bin__simps_I9_J,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_diff__bin__simps_I10_J,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Ints__power,axiom, % 167.88/167.97 ! [V_n_2,V_a_2,T_a] : % 167.88/167.97 ( class_Rings_Oring__1(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_neg__number__of__Bit0,axiom, % 167.88/167.97 ! [V_w_2] : % 167.88/167.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 167.88/167.97 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_pred__Bit0,axiom, % 167.88/167.97 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_pred__Bit1,axiom, % 167.88/167.97 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 167.88/167.97 % 167.88/167.97 fof(fact_iszero__number__of__Bit0,axiom, % 167.88/167.97 ! [V_w_2,T_a] : % 167.88/167.97 ( ( class_Int_Onumber__ring(T_a) % 167.88/167.97 & class_Int_Oring__char__0(T_a) ) % 167.88/167.97 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 167.88/167.97 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__eq__imp__eq,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.88/167.97 => V_x = V_y ) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__le__imp__le,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__le__power2,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__less__0,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__less__power2,axiom, % 167.88/167.97 ! [V_a_2,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 167.88/167.97 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_sum__power2__eq__zero__iff,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.97 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.97 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__eq__square__number__of,axiom, % 167.88/167.97 ! [V_w,T_b] : % 167.88/167.97 ( ( class_Groups_Omonoid__mult(T_b) % 167.88/167.97 & class_Int_Onumber(T_b) ) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_succ__Bit1,axiom, % 167.88/167.97 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_succ__Bit0,axiom, % 167.88/167.97 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__eq__1__iff,axiom, % 167.88/167.97 ! [V_a_2,T_a] : % 167.88/167.97 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 167.88/167.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) % 167.88/167.97 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 167.88/167.97 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 167.88/167.97 ! [V_n,V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__minus__even,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Oring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__number__of__Bit0,axiom, % 167.88/167.97 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__nat__number__of,axiom, % 167.88/167.97 ! [V_n,V_v] : % 167.88/167.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__nat__number__of__number__of,axiom, % 167.88/167.97 ! [V_w,V_v] : % 167.88/167.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__less__imp__less,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_sum__power2__ge__zero,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_sum__power2__le__zero__iff,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.97 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.97 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_sum__power2__gt__zero__iff,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 167.88/167.97 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.97 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_not__sum__power2__lt__zero,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__sum,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__le__even__power_H,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__odd__eq,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 167.88/167.97 ! [V_n,V_x,T_a] : % 167.88/167.97 ( class_Rings_Ocomm__semiring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__minus1__even,axiom, % 167.88/167.97 ! [V_n,T_a] : % 167.88/167.97 ( class_Rings_Oring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_number__of__Bit0,axiom, % 167.88/167.97 ! [V_w,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I15_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__int__code_I14_J,axiom, % 167.88/167.97 ! [V_k2_2,V_k1_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_rel__simps_I33_J,axiom, % 167.88/167.97 ! [V_l_2,V_k_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__eq__int__code_I15_J,axiom, % 167.88/167.97 ! [V_k2_2,V_k1_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mult__Bit1,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__le__zpower__abs,axiom, % 167.88/167.97 ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_diff__bin__simps_I8_J,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power2__diff,axiom, % 167.88/167.97 ! [V_y,V_x,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_odd__0__le__power__imp__0__le,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_odd__power__less__zero,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_add__Bit1__Bit1,axiom, % 167.88/167.97 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__minus1__odd,axiom, % 167.88/167.97 ! [V_n,T_a] : % 167.88/167.97 ( class_Rings_Oring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Sup__fin_Oidem,axiom, % 167.88/167.97 ! [V_x,T_a] : % 167.88/167.97 ( class_Lattices_Olattice(T_a) % 167.88/167.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Inf__fin_Oidem,axiom, % 167.88/167.97 ! [V_x,T_a] : % 167.88/167.97 ( class_Lattices_Olattice(T_a) % 167.88/167.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Min_Oidem,axiom, % 167.88/167.97 ! [V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Max_Oidem,axiom, % 167.88/167.97 ! [V_x,T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_double__number__of__Bit0,axiom, % 167.88/167.97 ! [V_w,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power3__eq__cube,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_number__of1,axiom, % 167.88/167.97 ! [V_n] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) % 167.88/167.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__eq__if,axiom, % 167.88/167.97 ! [V_p,V_m] : % 167.88/167.97 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 167.88/167.97 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_dual__max,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Orderings_Olinorder(T_a) % 167.88/167.97 => c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__less__zpower__abs__iff,axiom, % 167.88/167.97 ! [V_n_2,V_x_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) % 167.88/167.97 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.97 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 167.88/167.97 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mult__2,axiom, % 167.88/167.97 ! [V_z,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mult__2__right,axiom, % 167.88/167.97 ! [V_z,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_one__add__one__is__two,axiom, % 167.88/167.97 ! [T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_numeral__2__eq__2,axiom, % 167.88/167.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_semiring__norm_I115_J,axiom, % 167.88/167.97 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 167.88/167.97 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_add__2__eq__Suc,axiom, % 167.88/167.97 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_add__2__eq__Suc_H,axiom, % 167.88/167.97 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__mult__2,axiom, % 167.88/167.97 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__mult__2__right,axiom, % 167.88/167.97 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ). % 167.88/167.97 % 167.88/167.97 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 167.88/167.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 167.88/167.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__1__add__1,axiom, % 167.88/167.97 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_less__2__cases,axiom, % 167.88/167.97 ! [V_n] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) % 167.88/167.97 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.97 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__2,axiom, % 167.88/167.97 hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__number__of__odd,axiom, % 167.88/167.97 ! [V_z_2,V_w_2,T_a] : % 167.88/167.97 ( class_Int_Onumber__ring(T_a) % 167.88/167.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(T_a))) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__strict__mono,axiom, % 167.88/167.97 ! [V_n,V_b,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_one__less__power,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__le__imp__le__exp,axiom, % 167.88/167.97 ! [V_n,V_m,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__increasing__iff,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,V_b_2,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__decreasing,axiom, % 167.88/167.97 ! [V_a,V_N,V_n,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_field__power__not__zero,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 167.88/167.97 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 167.88/167.97 ! [V_m_2,V_x_2] : % 167.88/167.97 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 167.88/167.97 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.97 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__Suc__0,axiom, % 167.88/167.97 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__power__less__imp__less,axiom, % 167.88/167.97 ! [V_n,V_m,V_i] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__zero__less__power__iff,axiom, % 167.88/167.97 ! [V_n_2,V_x_2] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) % 167.88/167.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 167.88/167.97 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__commutes,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__mult__distrib,axiom, % 167.88/167.97 ! [V_n,V_b,V_a,T_a] : % 167.88/167.97 ( class_Groups_Ocomm__monoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__one,axiom, % 167.88/167.97 ! [V_n,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_of__nat__power,axiom, % 167.88/167.97 ! [V_n,V_m,T_a] : % 167.88/167.97 ( class_Rings_Osemiring__1(T_a) % 167.88/167.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__mult,axiom, % 167.88/167.97 ! [V_n,V_m,V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__abs,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__one__right,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__le__power,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__mono,axiom, % 167.88/167.97 ! [V_n,V_b,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__less__power,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__eq__0__iff,axiom, % 167.88/167.97 ! [V_n_2,V_a_2,T_a] : % 167.88/167.97 ( ( class_Power_Opower(T_a) % 167.88/167.97 & class_Rings_Omult__zero(T_a) % 167.88/167.97 & class_Rings_Ono__zero__divisors(T_a) % 167.88/167.97 & class_Rings_Ozero__neq__one(T_a) ) % 167.88/167.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.97 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 167.88/167.97 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_one__le__power,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__0__Suc,axiom, % 167.88/167.97 ! [V_n,T_a] : % 167.88/167.97 ( ( class_Power_Opower(T_a) % 167.88/167.97 & class_Rings_Osemiring__0(T_a) ) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__inject__exp,axiom, % 167.88/167.97 ! [V_n_2,V_m_2,V_a_2,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 167.88/167.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) % 167.88/167.97 <=> V_m_2 = V_n_2 ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__Suc2,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__Suc,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Power_Opower(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_nat__one__le__power,axiom, % 167.88/167.97 ! [V_n,V_i] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__0,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Power_Opower(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__add,axiom, % 167.88/167.97 ! [V_n,V_m,V_a,T_a] : % 167.88/167.97 ( class_Groups_Omonoid__mult(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_abs__power__minus,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__less__imp__less__base,axiom, % 167.88/167.97 ! [V_b,V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__inject__base,axiom, % 167.88/167.97 ! [V_b,V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.97 => V_a = V_b ) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__le__imp__le__base,axiom, % 167.88/167.97 ! [V_b,V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)))) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__less__power__Suc,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__gt1__lemma,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__0__left,axiom, % 167.88/167.97 ! [V_n,T_a] : % 167.88/167.97 ( ( class_Power_Opower(T_a) % 167.88/167.97 & class_Rings_Osemiring__0(T_a) ) % 167.88/167.97 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) % 167.88/167.97 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__gt1,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__strict__increasing,axiom, % 167.88/167.97 ! [V_a,V_N,V_n,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__less__imp__less__exp,axiom, % 167.88/167.97 ! [V_n,V_m,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__strict__increasing__iff,axiom, % 167.88/167.97 ! [V_y_2,V_x_2,V_b_2,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 167.88/167.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zero__le__power__abs,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__idom(T_a) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__increasing,axiom, % 167.88/167.97 ! [V_a,V_N,V_n,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__minus,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Oring__1(T_a) % 167.88/167.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__Suc__less,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__eq__imp__eq__base,axiom, % 167.88/167.97 ! [V_b,V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 167.88/167.97 => V_a = V_b ) ) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__Suc__less__one,axiom, % 167.88/167.97 ! [V_n,V_a,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_power__strict__decreasing,axiom, % 167.88/167.97 ! [V_a,V_N,V_n,T_a] : % 167.88/167.97 ( class_Rings_Olinordered__semidom(T_a) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 167.88/167.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 167.88/167.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_neg__zmod__mult__2,axiom, % 167.88/167.97 ! [V_b,V_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.97 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zmod__number__of__Bit1,axiom, % 167.88/167.97 ! [V_v,V_w] : % 167.88/167.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.88/167.97 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 167.88/167.97 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_of__int__num,axiom, % 167.88/167.97 ! [V_k_2,T_a] : % 167.88/167.97 ( class_Rings_Oring__1(T_a) % 167.88/167.97 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 167.88/167.97 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 167.88/167.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 167.88/167.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_pos__zmod__mult__2,axiom, % 167.88/167.97 ! [V_b,V_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.88/167.97 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_pos__zdiv__mult__2,axiom, % 167.88/167.97 ! [V_b,V_a] : % 167.88/167.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 167.88/167.97 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b),V_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zdiv__zminus__zminus,axiom, % 167.88/167.97 ! [V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zdiv__zminus2,axiom, % 167.88/167.97 ! [V_b,V_a] : hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zmod__zmult1__eq,axiom, % 167.88/167.97 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zmod__simps_I3_J,axiom, % 167.88/167.97 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zdiff__zmod__right,axiom, % 167.88/167.97 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zdiff__zmod__left,axiom, % 167.88/167.97 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zminus__zmod,axiom, % 167.88/167.97 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zmod__zminus__zminus,axiom, % 167.88/167.97 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zmod__zminus2,axiom, % 167.88/167.97 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__minus__eq,axiom, % 167.88/167.97 ! [V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Oring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__minus__cong,axiom, % 167.88/167.97 ! [V_a_H,V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Oring__div(T_a) % 167.88/167.97 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__0,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__by__0,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__self,axiom, % 167.88/167.97 ! [V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__add__self2,axiom, % 167.88/167.97 ! [V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__add__self1,axiom, % 167.88/167.97 ! [V_a,V_b,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__add__right__eq,axiom, % 167.88/167.97 ! [V_c,V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__add__left__eq,axiom, % 167.88/167.97 ! [V_c,V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__add__eq,axiom, % 167.88/167.97 ! [V_c,V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zmod__simps_I2_J,axiom, % 167.88/167.97 ! [V_c,V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zmod__simps_I1_J,axiom, % 167.88/167.97 ! [V_b,V_c,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__add__cong,axiom, % 167.88/167.97 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 167.88/167.97 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__mult__right__eq,axiom, % 167.88/167.97 ! [V_c,V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__mult__left__eq,axiom, % 167.88/167.97 ! [V_c,V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__mult__eq,axiom, % 167.88/167.97 ! [V_c,V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__mult__mult1,axiom, % 167.88/167.97 ! [V_b,V_a,V_c,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__mult__mult2,axiom, % 167.88/167.97 ! [V_b,V_c,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_zmod__simps_I4_J,axiom, % 167.88/167.97 ! [V_b,V_c,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__mult__cong,axiom, % 167.88/167.97 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 167.88/167.97 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 167.88/167.97 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 167.88/167.97 ! [V_b,V_a,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)),V_b)) = V_a ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__div__equality2,axiom, % 167.88/167.97 ! [V_a,V_b,T_a] : % 167.88/167.97 ( class_Divides_Osemiring__div(T_a) % 167.88/167.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 167.88/167.97 % 167.88/167.97 fof(fact_mod__div__equality,axiom, % 167.88/167.97 ! [V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_div__mod__equality2,axiom, % 167.88/167.98 ! [V_c,V_a,V_b,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_div__mod__equality,axiom, % 167.88/167.98 ! [V_c,V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zmod__zdiv__equality,axiom, % 167.88/167.98 ! [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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zdiv__zmult1__eq,axiom, % 167.88/167.98 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b),V_c))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zdiv__zmod__equality,axiom, % 167.88/167.98 ! [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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zdiv__zmod__equality2,axiom, % 167.88/167.98 ! [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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__mod__trivial,axiom, % 167.88/167.98 ! [V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zmod__zdiv__trivial,axiom, % 167.88/167.98 ! [V_b,V_a] : hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__div__trivial,axiom, % 167.88/167.98 ! [V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => hAPP(c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_DIVISION__BY__ZERO,axiom, % 167.88/167.98 ! [V_a] : % 167.88/167.98 ( hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.98 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zdiv__zadd1__eq,axiom, % 167.88/167.98 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_c)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b),V_c))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zmult__div__cancel,axiom, % 167.88/167.98 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zmod__zdiv__equality_H,axiom, % 167.88/167.98 ! [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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m),V_n)),V_n)) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__diff__cong,axiom, % 167.88/167.98 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 167.88/167.98 ( class_Divides_Oring__div(T_a) % 167.88/167.98 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 167.88/167.98 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__diff__eq,axiom, % 167.88/167.98 ! [V_c,V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Oring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__diff__left__eq,axiom, % 167.88/167.98 ! [V_c,V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Oring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__diff__right__eq,axiom, % 167.88/167.98 ! [V_c,V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Oring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zmod__self,axiom, % 167.88/167.98 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zmod__zero,axiom, % 167.88/167.98 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zdiv__zero,axiom, % 167.88/167.98 ! [V_b] : hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 167.88/167.98 % 167.88/167.98 fof(fact_div__by__0,axiom, % 167.88/167.98 ! [V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_div__0,axiom, % 167.88/167.98 ! [V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => hAPP(c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_div__by__1,axiom, % 167.88/167.98 ! [V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 167.88/167.98 ! [V_y,V_x] : % 167.88/167.98 ( c_Nat__Transfer_Ois__nat(V_x) % 167.88/167.98 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.88/167.98 => c_Nat__Transfer_Ois__nat(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y)) ) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 167.88/167.98 ! [V_y,V_x] : % 167.88/167.98 ( c_Nat__Transfer_Ois__nat(V_x) % 167.88/167.98 => ( c_Nat__Transfer_Ois__nat(V_y) % 167.88/167.98 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zpower__zmod,axiom, % 167.88/167.98 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__mult__self1__is__0,axiom, % 167.88/167.98 ! [V_a,V_b,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__mult__self2__is__0,axiom, % 167.88/167.98 ! [V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zmod__zmult2__eq,axiom, % 167.88/167.98 ! [V_b,V_a,V_c] : % 167.88/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 167.88/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__mult__self1,axiom, % 167.88/167.98 ! [V_b,V_c,V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__mult__self2,axiom, % 167.88/167.98 ! [V_c,V_b,V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_mod__by__1,axiom, % 167.88/167.98 ! [V_a,T_a] : % 167.88/167.98 ( class_Divides_Osemiring__div(T_a) % 167.88/167.98 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zdiv__zminus2__eq__if,axiom, % 167.88/167.98 ! [V_a,V_b] : % 167.88/167.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.98 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)) ) % 167.88/167.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 167.88/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 167.88/167.98 % 167.88/167.98 fof(fact_zdiv__zminus1__eq__if,axiom, % 167.88/167.98 ! [V_a,V_b] : % 168.02/167.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)) ) % 168.02/167.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 168.02/167.98 ! [V_y,V_x] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__neg__pos__less0,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 168.02/167.98 ! [V_a_2,V_b_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 168.02/167.98 ! [V_a_2,V_b_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__self,axiom, % 168.02/167.98 ! [V_a] : % 168.02/167.98 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__le__nonneg__dividend,axiom, % 168.02/167.98 ! [V_k,V_m] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 168.02/167.98 ! [V_y,V_x] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 168.02/167.98 => 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))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_neg__mod__bound,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => 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))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pos__mod__bound,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__number__of__Bit0,axiom, % 168.02/167.98 ! [V_w,V_v] : 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(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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__eq__0__iff,axiom, % 168.02/167.98 ! [V_d_2,V_m_2] : % 168.02/167.98 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__zminus1__not__zero,axiom, % 168.02/167.98 ! [V_l,V_k] : % 168.02/167.98 ( 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) % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__zminus2__not__zero,axiom, % 168.02/167.98 ! [V_l,V_k] : % 168.02/167.98 ( 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) % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__mult1,axiom, % 168.02/167.98 ! [V_b,V_a,V_c,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__mult2,axiom, % 168.02/167.98 ! [V_b,V_a,V_c,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__self1__is__id,axiom, % 168.02/167.98 ! [V_a,V_b,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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 ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__self2__is__id,axiom, % 168.02/167.98 ! [V_a,V_b,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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 ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__mult1__if,axiom, % 168.02/167.98 ! [V_b,V_a,V_c,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__self,axiom, % 168.02/167.98 ! [V_a,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__neg__lemma,axiom, % 168.02/167.98 ! [V_n_2,V_P_2,V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(V_P_2,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))) % 168.02/167.98 <=> ! [B_i,B_j] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 & 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) ) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__pos__lemma,axiom, % 168.02/167.98 ! [V_n_2,V_P_2,V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(V_P_2,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))) % 168.02/167.98 <=> ! [B_i,B_j] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 168.02/167.98 & 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) ) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__eq__0__iff,axiom, % 168.02/167.98 ! [V_k_2,V_i_2] : % 168.02/167.98 ( hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 168.02/167.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 168.02/167.98 ! [V_a_2,V_b_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 168.02/167.98 ! [V_i_2,V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2),V_k_2))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 168.02/167.98 ! [V_b_2,V_a_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2))) % 168.02/167.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__mono2,axiom, % 168.02/167.98 ! [V_b,V_b_H,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b_H))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__nonneg__neg__le0,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__pos__pos__trivial,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 168.02/167.98 ! [V_a_2,V_b_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2),V_b_2))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__nonpos__pos__le0,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__mono2__neg,axiom, % 168.02/167.98 ! [V_b,V_b_H,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b_H)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__neg__neg__trivial,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__mono1,axiom, % 168.02/167.98 ! [V_b,V_a_H,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H),V_b))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__mono1__neg,axiom, % 168.02/167.98 ! [V_b,V_a_H,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H),V_b)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_int__div__less__self,axiom, % 168.02/167.98 ! [V_k,V_x] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_k)),V_x)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__zmult2__eq,axiom, % 168.02/167.98 ! [V_b,V_a,V_c] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b)),V_c) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pos__mod__sign,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => 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))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pos__mod__conj,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => ( 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))) % 168.02/167.98 & 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__pos__pos__trivial,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_neg__mod__sign,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => 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))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_neg__mod__conj,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( 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))) % 168.02/167.98 & 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))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__neg__neg__trivial,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__zminus1__eq__if,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__zminus2__eq__if,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__self2,axiom, % 168.02/167.98 ! [V_c,V_a,V_b,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__self1,axiom, % 168.02/167.98 ! [V_c,V_a,V_b,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__add__self2,axiom, % 168.02/167.98 ! [V_a,V_b,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__add__self1,axiom, % 168.02/167.98 ! [V_a,V_b,T_a] : % 168.02/167.98 ( class_Divides_Osemiring__div(T_a) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(T_a,V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__pos__neg__trivial,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( 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))) % 168.02/167.98 => 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) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__rel__div__eq,axiom, % 168.02/167.98 ! [V_r_1,V_y,V_b_1,V_a_1] : % 168.02/167.98 ( 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) % 168.02/167.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 168.02/167.98 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1),V_b_1) = V_y ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__zdiv,axiom, % 168.02/167.98 ! [V_k_2,V_n_2,V_P_2] : % 168.02/167.98 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2),V_k_2))) % 168.02/167.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 168.02/167.98 => ! [B_i] : % 168.02/167.98 ( ? [B_j] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 168.02/167.98 & 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) ) % 168.02/167.98 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 168.02/167.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ! [B_i] : % 168.02/167.98 ( ? [B_j] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 & 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) ) % 168.02/167.98 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__rel__mod__eq,axiom, % 168.02/167.98 ! [V_y,V_q_1,V_b_1,V_a_1] : % 168.02/167.98 ( 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) % 168.02/167.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 168.02/167.98 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmult2__lemma__aux2,axiom, % 168.02/167.98 ! [V_q,V_r,V_b,V_c] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => 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))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmult2__lemma__aux1,axiom, % 168.02/167.98 ! [V_q,V_r,V_b,V_c] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => 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))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmult2__lemma__aux4,axiom, % 168.02/167.98 ! [V_q,V_b,V_r,V_c] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 168.02/167.98 => 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))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmult2__lemma__aux3,axiom, % 168.02/167.98 ! [V_q,V_b,V_r,V_c] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 168.02/167.98 => 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))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__zmod,axiom, % 168.02/167.98 ! [V_k_2,V_n_2,V_P_2] : % 168.02/167.98 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 168.02/167.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 168.02/167.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 168.02/167.98 => ! [B_i,B_j] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 168.02/167.98 & 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) ) % 168.02/167.98 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 168.02/167.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ! [B_i,B_j] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 & 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) ) % 168.02/167.98 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__number__of__Bit0,axiom, % 168.02/167.98 ! [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))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__number__of__Bit1,axiom, % 168.02/167.98 ! [V_v,V_w] : % 168.02/167.98 ( ( 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))) % 168.02/167.98 => 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(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)) ) % 168.02/167.98 & ( ~ 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))) % 168.02/167.98 => 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(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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_int__power__div__base,axiom, % 168.02/167.98 ! [V_k,V_m] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 168.02/167.98 => 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)))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_neg__zdiv__mult__2,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => 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(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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_z3div__def,axiom, % 168.02/167.98 ! [V_k,V_l] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 168.02/167.98 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k),V_l) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 168.02/167.98 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_z3mod__def,axiom, % 168.02/167.98 ! [V_k,V_l] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 168.02/167.98 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_power__power__power,axiom, % 168.02/167.98 ! [T_a] : % 168.02/167.98 ( class_Power_Opower(T_a) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_power__m1__odd,axiom, % 168.02/167.98 ! [V_n,T_a] : % 168.02/167.98 ( class_Int_Onumber__ring(T_a) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_power__m1__even,axiom, % 168.02/167.98 ! [V_n,T_a] : % 168.02/167.98 ( class_Int_Onumber__ring(T_a) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__mult2__eq,axiom, % 168.02/167.98 ! [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(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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult1__eq,axiom, % 168.02/167.98 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b),V_c))),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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mod__equality_H,axiom, % 168.02/167.98 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mult__div__cancel,axiom, % 168.02/167.98 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Divides_Omod__div__equality_H,axiom, % 168.02/167.98 ! [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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),V_n)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__add1__eq,axiom, % 168.02/167.98 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a),V_c)),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b),V_c))),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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__mult__distrib2,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__mult__distrib,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__less__eq__dividend,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__less,axiom, % 168.02/167.98 ! [V_n,V_m] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult2__eq,axiom, % 168.02/167.98 ! [V_c,V_b,V_a] : 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a),V_b)),V_c) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__le__dividend,axiom, % 168.02/167.98 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),V_m)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__le__mono,axiom, % 168.02/167.98 ! [V_k,V_n,V_m] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_k)),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n),V_k))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I42_J,axiom, % 168.02/167.98 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I45_J,axiom, % 168.02/167.98 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 168.02/167.98 % 168.02/167.98 fof(fact_Bit1__Min,axiom, % 168.02/167.98 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I43_J,axiom, % 168.02/167.98 ! [V_l_2] : % 168.02/167.98 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 168.02/167.98 <=> c_Int_OMin = V_l_2 ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I47_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 168.02/167.98 <=> V_k_2 = c_Int_OMin ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I40_J,axiom, % 168.02/167.98 c_Int_OMin != c_Int_OPls ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I37_J,axiom, % 168.02/167.98 c_Int_OPls != c_Int_OMin ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I7_J,axiom, % 168.02/167.98 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I24_J,axiom, % 168.02/167.98 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__1,axiom, % 168.02/167.98 ! [V_m] : 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 ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__less,axiom, % 168.02/167.98 ! [V_n,V_m] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_nat__mult__div__cancel__disj,axiom, % 168.02/167.98 ! [V_n,V_m,V_k] : % 168.02/167.98 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__Suc,axiom, % 168.02/167.98 ! [V_n,V_m] : % 168.02/167.98 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.02/167.98 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__1,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__less__divisor,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__eq__0__iff,axiom, % 168.02/167.98 ! [V_d_2,V_m_2] : % 168.02/167.98 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__if,axiom, % 168.02/167.98 ! [V_n,V_m] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => 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) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__geq,axiom, % 168.02/167.98 ! [V_n,V_m] : % 168.02/167.98 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__mult__self3,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_le__mod__geq,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 168.02/167.98 ! [V_y,V_x] : 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x),V_y)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__int,axiom, % 168.02/167.98 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a),V_b)) = 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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_bin__less__0__simps_I2_J,axiom, % 168.02/167.98 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I23_J,axiom, % 168.02/167.98 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I20_J,axiom, % 168.02/167.98 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I26_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I30_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I3_J,axiom, % 168.02/167.98 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I6_J,axiom, % 168.02/167.98 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I13_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I9_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I28_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I8_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__int,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_eq__number__of__Pls__Min,axiom, % 168.02/167.98 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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Int_OMin__def,axiom, % 168.02/167.98 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mult__Min,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_neg__number__of__Min,axiom, % 168.02/167.98 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pred__Pls,axiom, % 168.02/167.98 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 168.02/167.98 % 168.02/167.98 fof(fact_add__Min__right,axiom, % 168.02/167.98 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 168.02/167.98 % 168.02/167.98 fof(fact_add__Min,axiom, % 168.02/167.98 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pred__Min,axiom, % 168.02/167.98 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 168.02/167.98 % 168.02/167.98 fof(fact_nonzero__number__of__Min,axiom, % 168.02/167.98 ! [T_a] : % 168.02/167.98 ( class_Int_Onumber__ring(T_a) % 168.02/167.98 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_succ__Min,axiom, % 168.02/167.98 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 168.02/167.98 % 168.02/167.98 fof(fact_diff__bin__simps_I2_J,axiom, % 168.02/167.98 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__le__mono2,axiom, % 168.02/167.98 ! [V_k,V_n,V_m] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k),V_n)),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k),V_m))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_nat__mult__div__cancel1,axiom, % 168.02/167.98 ! [V_n,V_m,V_k] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__self1__is__m,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => 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 ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mult__self__is__m,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => 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 ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__less__dividend,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),V_m)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__le__divisor,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__mult__self4,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mult__minus1,axiom, % 168.02/167.98 ! [V_z,T_a] : % 168.02/167.98 ( class_Int_Onumber__ring(T_a) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mult__minus1__right,axiom, % 168.02/167.98 ! [V_z,T_a] : % 168.02/167.98 ( class_Int_Onumber__ring(T_a) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_arith__simps_I31_J,axiom, % 168.02/167.98 ! [T_a] : % 168.02/167.98 ( class_Int_Onumber__ring(T_a) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_number__of__Min,axiom, % 168.02/167.98 ! [T_a] : % 168.02/167.98 ( class_Int_Onumber__ring(T_a) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_abs__minus__one,axiom, % 168.02/167.98 ! [T_a] : % 168.02/167.98 ( ( class_Int_Onumber__ring(T_a) % 168.02/167.98 & class_Rings_Olinordered__idom(T_a) ) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I11_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rel__simps_I25_J,axiom, % 168.02/167.98 ! [V_k_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 168.02/167.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__minus1__right,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_diff__bin__simps_I4_J,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_minus__Min,axiom, % 168.02/167.98 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmult__eq__1__iff,axiom, % 168.02/167.98 ! [V_n_2,V_m_2] : % 168.02/167.98 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 168.02/167.98 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 168.02/167.98 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 168.02/167.98 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 168.02/167.98 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 168.02/167.98 ! [V_n,V_m] : % 168.02/167.98 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 168.02/167.98 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 168.02/167.98 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_diff__bin__simps_I5_J,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_diff__bin__simps_I6_J,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_power_Opower_Opower__0,axiom, % 168.02/167.98 ! [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 ). % 168.02/167.98 % 168.02/167.98 fof(fact_power_Opower_Opower__Suc,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_of__int__m1,axiom, % 168.02/167.98 ! [T_a] : % 168.02/167.98 ( class_Int_Onumber__ring(T_a) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zdiv__minus1__right,axiom, % 168.02/167.98 ! [V_a] : 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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__if,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = hAPP(c_Nat_OSuc,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)) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__geq,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = hAPP(c_Nat_OSuc,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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__div,axiom, % 168.02/167.98 ! [V_k_2,V_n_2,V_P_2] : % 168.02/167.98 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2),V_k_2))) % 168.02/167.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 168.02/167.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 => ! [B_i,B_j] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 168.02/167.98 => ( 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) % 168.02/167.98 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_nat__div__distrib,axiom, % 168.02/167.98 ! [V_y,V_x] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 168.02/167.98 => hAPP(c_Int_Onat,hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 168.02/167.98 ! [V_y,V_x] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 168.02/167.98 => 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x),V_y)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__lemma,axiom, % 168.02/167.98 ! [V_q,V_b,V_r,V_c] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 168.02/167.98 => 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))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__mod,axiom, % 168.02/167.98 ! [V_k_2,V_n_2,V_P_2] : % 168.02/167.98 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 168.02/167.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 168.02/167.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 => ! [B_i,B_j] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 168.02/167.98 => ( 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) % 168.02/167.98 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Suc__times__mod__eq,axiom, % 168.02/167.98 ! [V_m,V_k] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_nat__mod__distrib,axiom, % 168.02/167.98 ! [V_y,V_x] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 168.02/167.98 ! [V_y,V_x] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_abs__power__minus__one,axiom, % 168.02/167.98 ! [V_n,T_a] : % 168.02/167.98 ( ( class_Int_Onumber__ring(T_a) % 168.02/167.98 & class_Rings_Olinordered__idom(T_a) ) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__eq__minus1,axiom, % 168.02/167.98 ! [V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_le__div__geq,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = hAPP(c_Nat_OSuc,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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__div_H,axiom, % 168.02/167.98 ! [V_n_2,V_m_2,V_P_2] : % 168.02/167.98 ( hBOOL(hAPP(V_P_2,hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2),V_n_2))) % 168.02/167.98 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 168.02/167.98 | ? [B_q] : % 168.02/167.98 ( 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)) % 168.02/167.98 & 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)))) % 168.02/167.98 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__div__lemma,axiom, % 168.02/167.98 ! [V_m_2,V_q_2,V_n_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 168.02/167.98 => ( ( 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)) % 168.02/167.98 & 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)))) ) % 168.02/167.98 <=> V_q_2 = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2),V_n_2) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__Suc__eq__div__add3,axiom, % 168.02/167.98 ! [V_n,V_m] : 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(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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Suc__div__eq__add3__div,axiom, % 168.02/167.98 ! [V_n,V_m] : 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(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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 168.02/167.98 ! [V_v,V_m] : 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(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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div2__Suc__Suc,axiom, % 168.02/167.98 ! [V_m] : 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(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))))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_add__self__div__2,axiom, % 168.02/167.98 ! [V_m] : 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 ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__Suc__eq__mod__add3,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Suc__mod__eq__add3__mod,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod2__Suc__Suc,axiom, % 168.02/167.98 ! [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)))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__nat__number__of,axiom, % 168.02/167.98 ! [V_v_H,V_v] : % 168.02/167.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 168.02/167.98 => 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(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))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod__nat__number__of,axiom, % 168.02/167.98 ! [V_v_H,V_v] : % 168.02/167.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 168.02/167.98 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 168.02/167.98 => 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))) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__pos__neg__trivial,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( 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))) % 168.02/167.98 => 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) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmod__minus1,axiom, % 168.02/167.98 ! [V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__2__gt__zero,axiom, % 168.02/167.98 ! [V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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)))))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_one__div__nat__number__of,axiom, % 168.02/167.98 ! [V_v_H] : 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(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))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mod2__gr__0,axiom, % 168.02/167.98 ! [V_m_2] : % 168.02/167.98 ( 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)))))) % 168.02/167.98 <=> 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Suc__n__div__2__gt__zero,axiom, % 168.02/167.98 ! [V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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)))))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_one__mod__nat__number__of,axiom, % 168.02/167.98 ! [V_v_H] : % 168.02/167.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 168.02/167.98 => 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))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_int__of__code,axiom, % 168.02/167.98 ! [V_k] : % 168.02/167.98 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 168.02/167.98 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 168.02/167.98 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 168.02/167.98 => ( ( 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) % 168.02/167.98 => 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(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)))))) ) % 168.02/167.98 & ( 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) % 168.02/167.98 => 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(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)) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Nitpick_Onat__lcm__def,axiom, % 168.02/167.98 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = 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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_one__code__numeral__code,axiom, % 168.02/167.98 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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__rel__def,axiom, % 168.02/167.98 ! [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))))))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_code__numeral__zero__minus__one,axiom, % 168.02/167.98 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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_nat__gcd_Osimps,axiom, % 168.02/167.98 ! [V_x,V_y] : % 168.02/167.98 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 168.02/167.98 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__correct,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zero__code__numeral__code,axiom, % 168.02/167.98 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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Nitpick_Oint__gcd__def,axiom, % 168.02/167.98 ! [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)))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_small__int__def,axiom, % 168.02/167.98 ! [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))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Nitpick_OFrac__def,axiom, % 168.02/167.98 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)))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_nat__of__aux__code,axiom, % 168.02/167.98 ! [V_n,V_i] : % 168.02/167.98 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 168.02/167.98 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 168.02/167.98 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_full__small__int__def,axiom, % 168.02/167.98 ! [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))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmult2__lemma,axiom, % 168.02/167.98 ! [V_c,V_r,V_q,V_b,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 168.02/167.98 => 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(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)))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_code__numeral_Osize_I1_J,axiom, % 168.02/167.98 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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_adjust__eq,axiom, % 168.02/167.98 ! [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))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_inf__Int__eq2,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 <=> 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))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pred__equals__eq2,axiom, % 168.02/167.98 ! [V_S_2,V_R_2,T_b,T_a] : % 168.02/167.98 ( 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) % 168.02/167.98 <=> V_R_2 = V_S_2 ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_bot__empty__eq2,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 <=> 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)))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pred__subset__eq2,axiom, % 168.02/167.98 ! [V_S_2,V_R_2,T_b,T_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 <=> 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_sup__Un__eq2,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 <=> 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))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_small__prod__def,axiom, % 168.02/167.98 ! [V_d_2,V_f_2,T_a,T_b] : % 168.02/167.98 ( ( class_Smallcheck_Osmall(T_b) % 168.02/167.98 & class_Smallcheck_Osmall(T_a) ) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_unique__remainder,axiom, % 168.02/167.98 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( 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))) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => V_r = V_r_H ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_unique__quotient,axiom, % 168.02/167.98 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( 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))) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => V_q = V_q_H ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_self__remainder,axiom, % 168.02/167.98 ! [V_r,V_q,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__rel__0,axiom, % 168.02/167.98 ! [V_b] : % 168.02/167.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_self__quotient,axiom, % 168.02/167.98 ! [V_r,V_q,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__rel__mod,axiom, % 168.02/167.98 ! [V_r,V_q,V_b,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__rel__div,axiom, % 168.02/167.98 ! [V_r,V_q,V_b,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a),V_b) = V_q ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__mod__div,axiom, % 168.02/167.98 ! [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(c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__rel__div__mod,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),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)))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zadd1__lemma,axiom, % 168.02/167.98 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( 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))) % 168.02/167.98 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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(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)))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zminus1__lemma,axiom, % 168.02/167.98 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 168.02/167.98 ( 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))) % 168.02/167.98 => 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))))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__relI,axiom, % 168.02/167.98 ! [V_r,V_q,V_b,V_a] : % 168.02/167.98 ( 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) % 168.02/167.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 168.02/167.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 168.02/167.98 => 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))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_zmult1__lemma,axiom, % 168.02/167.98 ! [V_a,V_r,V_q,V_c,V_b] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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(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)))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_adjust__def,axiom, % 168.02/167.98 ! [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))))))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pair__imageI,axiom, % 168.02/167.98 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 => 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))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_norm__frac_Osimps,axiom, % 168.02/167.98 ! [V_a_2,V_b_2] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 168.02/167.98 => 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)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b_2))) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 168.02/167.98 ! [V_w] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( ( 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)))) % 168.02/167.98 => 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))) ) % 168.02/167.98 & ( ~ 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)))) % 168.02/167.98 => 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)))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_prod__caseI,axiom, % 168.02/167.98 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 168.02/167.98 => 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))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_sup2E,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_sup2CI,axiom, % 168.02/167.98 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 168.02/167.98 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_inf2I,axiom, % 168.02/167.98 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_inf2E,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 168.02/167.98 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_mem__splitI,axiom, % 168.02/167.98 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 168.02/167.98 => 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)))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_splitI,axiom, % 168.02/167.98 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 168.02/167.98 => 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))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_bot2E,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_swap__inj__on,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_splitD_H,axiom, % 168.02/167.98 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_sup2I1,axiom, % 168.02/167.98 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_sup2I2,axiom, % 168.02/167.98 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_less__by__empty,axiom, % 168.02/167.98 ! [V_B_2,T_a,V_A_2] : % 168.02/167.98 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 168.02/167.98 => 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_predicate2D,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_rev__predicate2D,axiom, % 168.02/167.98 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 168.02/167.98 => ( 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)) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_inf2D1,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_inf2D2,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__paired__All,axiom, % 168.02/167.98 ! [T_b,T_a,V_P_2] : % 168.02/167.98 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 168.02/167.98 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Pair__eq,axiom, % 168.02/167.98 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/167.98 ( 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) % 168.02/167.98 <=> ( V_a_2 = V_a_H_2 % 168.02/167.98 & V_b_2 = V_b_H_2 ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Pair__inject,axiom, % 168.02/167.98 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 168.02/167.98 ( 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) % 168.02/167.98 => ~ ( V_a = V_a_H % 168.02/167.98 => V_b != V_b_H ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__weak__cong,axiom, % 168.02/167.98 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 168.02/167.98 ( V_p_2 = V_q_2 % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negDivAlg__correct,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__twice,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__conv,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_prod_Osimps_I2_J,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_splitD,axiom, % 168.02/167.98 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negDivAlg__div__mod,axiom, % 168.02/167.98 ! [V_l,V_k] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 168.02/167.98 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negDivAlg__minus1,axiom, % 168.02/167.98 ! [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))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__eta,axiom, % 168.02/167.98 ! [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 ). % 168.02/167.98 % 168.02/167.98 fof(fact_The__split__eq,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_split__paired__The,axiom, % 168.02/167.98 ! [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)))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negDivAlg_Osimps,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( ( ( 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))) % 168.02/167.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( ~ ( 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))) % 168.02/167.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.98 => 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))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negDivAlg__eqn__number__of,axiom, % 168.02/167.98 ! [V_w,V_v] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( ( 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)))) % 168.02/167.98 => 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))) ) % 168.02/167.98 & ( ~ 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)))) % 168.02/167.98 => 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)))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negDivAlg__eqn,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => ( ( 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))) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( ~ 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))) % 168.02/167.98 => 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))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_in__rel__def,axiom, % 168.02/167.98 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 168.02/167.98 <=> 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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_div__mod__code__numeral__def,axiom, % 168.02/167.98 ! [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(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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_Nitpick_Orefl_H__def,axiom, % 168.02/167.98 ! [V_r_2,T_a] : % 168.02/167.98 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 168.02/167.98 <=> ! [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)) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 168.02/167.98 ! [V_w] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( ( 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))) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( ~ 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))) % 168.02/167.98 => 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)))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_posDivAlg__0,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_posDivAlg__correct,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_posDivAlg__div__mod,axiom, % 168.02/167.98 ! [V_l,V_k] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 168.02/167.98 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_posDivAlg__eqn__number__of,axiom, % 168.02/167.98 ! [V_w,V_v] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( ( 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))) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( ~ 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))) % 168.02/167.98 => 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)))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_posDivAlg__eqn,axiom, % 168.02/167.98 ! [V_a,V_b] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 168.02/167.98 => 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))) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_posDivAlg_Osimps,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 168.02/167.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 168.02/167.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.98 => 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))) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__def,axiom, % 168.02/167.98 ! [V_b,V_a] : % 168.02/167.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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))) ) ) ) ) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 168.02/167.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.98 => 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))) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__nat__step,axiom, % 168.02/167.98 ! [V_m,V_n] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 168.02/167.98 => 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(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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__pdivmod,axiom, % 168.02/167.98 ! [V_l_2,V_k_2] : % 168.02/167.98 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)))) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__code,axiom, % 168.02/167.98 ! [V_l_2,V_k_2] : % 168.02/167.98 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)))) ) ) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negateSnd__def,axiom, % 168.02/167.98 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_apsnd__conv,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__nat__zero,axiom, % 168.02/167.98 ! [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) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__nat__base,axiom, % 168.02/167.98 ! [V_n,V_m] : % 168.02/167.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.02/167.98 => 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) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_negateSnd__eq,axiom, % 168.02/167.98 ! [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)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__nat__div__mod,axiom, % 168.02/167.98 ! [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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__int__rel__neg,axiom, % 168.02/167.98 ! [V_qr,V_b,V_a] : % 168.02/167.98 ( 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)) % 168.02/167.98 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__nat__if,axiom, % 168.02/167.98 ! [V_m_2,V_n_2] : % 168.02/167.98 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 168.02/167.98 => 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) ) % 168.02/167.98 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pdivmod__def,axiom, % 168.02/167.98 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),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))) ). % 168.02/167.98 % 168.02/167.98 fof(fact_pdivmod__posDivAlg,axiom, % 168.02/167.98 ! [V_k,V_l] : % 168.02/167.98 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)) ) % 168.02/167.98 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.98 => 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)) ) ) ). % 168.02/167.98 % 168.02/167.98 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 168.02/167.98 ! [V_c,V_r,V_q,V_b,V_a] : % 168.02/167.98 ( 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))) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 168.02/167.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 168.02/167.99 => 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(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)))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 168.02/167.99 ! [V_a,V_r,V_q,V_c,V_b] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 168.02/167.99 => 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(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)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_negDivAlg_Opsimps,axiom, % 168.02/167.99 ! [V_b_2,V_a_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ( ( 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))) % 168.02/167.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.99 => 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)) ) % 168.02/167.99 & ( ~ ( 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))) % 168.02/167.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.99 => 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_small_H_Opsimps,axiom, % 168.02/167.99 ! [V_i_2,V_d_2,V_f_2] : % 168.02/167.99 ( 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)))) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 168.02/167.99 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_accp_Osimps,axiom, % 168.02/167.99 ! [V_a_2,V_r_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 168.02/167.99 <=> ! [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 168.02/167.99 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_accp_Oequations,axiom, % 168.02/167.99 ! [V_a_2,V_r_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 168.02/167.99 <=> ! [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 168.02/167.99 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_accp__downward,axiom, % 168.02/167.99 ! [V_a_2,V_b_2,V_r_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 168.02/167.99 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_divmod__nat__rel__unique,axiom, % 168.02/167.99 ! [V_qr_H,V_qr,V_n,V_m] : % 168.02/167.99 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 168.02/167.99 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 168.02/167.99 => V_qr = V_qr_H ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 168.02/167.99 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_divmod__nat__eq,axiom, % 168.02/167.99 ! [V_qr,V_n,V_m] : % 168.02/167.99 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 168.02/167.99 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_divmod__nat__def,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_accp__subset,axiom, % 168.02/167.99 ! [V_R2_2,V_R1_2,T_a] : % 168.02/167.99 ( 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)) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__eq,axiom, % 168.02/167.99 ! [V_r,V_q,V_n,V_m] : % 168.02/167.99 ( 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))) % 168.02/167.99 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__eq,axiom, % 168.02/167.99 ! [V_r,V_q,V_n,V_m] : % 168.02/167.99 ( 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))) % 168.02/167.99 => hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n) = V_q ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_divmod__nat__rel,axiom, % 168.02/167.99 ! [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(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_divmod__nat__rel__add1__eq,axiom, % 168.02/167.99 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( 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))) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 168.02/167.99 => 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(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)))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_posDivAlg_Opsimps,axiom, % 168.02/167.99 ! [V_b_2,V_a_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 168.02/167.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.99 => 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) ) % 168.02/167.99 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 168.02/167.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.99 => 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_norm__frac_Opsimps,axiom, % 168.02/167.99 ! [V_b_2,V_a_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => 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)) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.99 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 168.02/167.99 => 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)) ) % 168.02/167.99 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 168.02/167.99 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 168.02/167.99 => 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)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b_2))) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_negDivAlg_Opinduct,axiom, % 168.02/167.99 ! [V_P_2,V_a1_2,V_a0_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ! [B_a,B_b] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ( ~ ( 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))) % 168.02/167.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.99 => 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))) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_small_H_Opinduct,axiom, % 168.02/167.99 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 168.02/167.99 ( 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)))) % 168.02/167.99 => ( ! [B_f,B_d,B_i] : % 168.02/167.99 ( 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)))) % 168.02/167.99 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 168.02/167.99 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 168.02/167.99 => 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)))) ) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_posDivAlg_Opinduct,axiom, % 168.02/167.99 ! [V_P_2,V_a1_2,V_a0_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ! [B_a,B_b] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 168.02/167.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 168.02/167.99 => 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))) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_nat__gcd_Opsimps,axiom, % 168.02/167.99 ! [V_y_2,V_x_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.99 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 168.02/167.99 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__pos__neg__1__number__of,axiom, % 168.02/167.99 ! [V_w] : % 168.02/167.99 ( 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))) % 168.02/167.99 => 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))))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_in__measure,axiom, % 168.02/167.99 ! [V_f_2,V_y_2,V_x_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_snd__conv,axiom, % 168.02/167.99 ! [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 ). % 168.02/167.99 % 168.02/167.99 fof(fact_snd__eqD,axiom, % 168.02/167.99 ! [V_a,V_y,V_x,T_a,T_b] : % 168.02/167.99 ( 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 % 168.02/167.99 => V_y = V_a ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_snd__apsnd,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_apsnd__eq__conv,axiom, % 168.02/167.99 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 168.02/167.99 ( 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) % 168.02/167.99 <=> 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_snd__def,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__int__def,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__neg__pos,axiom, % 168.02/167.99 ! [V_b,V_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__pos__pos,axiom, % 168.02/167.99 ! [V_b,V_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__pos__pos__1__number__of,axiom, % 168.02/167.99 ! [V_w] : % 168.02/167.99 ( 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))) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__pos__neg,axiom, % 168.02/167.99 ! [V_b,V_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => 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)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__neg__neg,axiom, % 168.02/167.99 ! [V_b,V_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => 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)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_norm__frac_Opinduct,axiom, % 168.02/167.99 ! [V_P_2,V_a1_2,V_a0_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ! [B_a,B_b] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => 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))) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__pos__neg__1__number__of,axiom, % 168.02/167.99 ! [V_w] : % 168.02/167.99 ( 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))) % 168.02/167.99 => 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))))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_nat__gcd_Opinduct,axiom, % 168.02/167.99 ! [V_P_2,V_a1_2,V_a0_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ! [B_x,B_y] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 168.02/167.99 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mlex__leq,axiom, % 168.02/167.99 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Pair__fst__snd__eq,axiom, % 168.02/167.99 ! [T_b,T_a,V_t_2,V_s_2] : % 168.02/167.99 ( V_s_2 = V_t_2 % 168.02/167.99 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 168.02/167.99 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_prod__eqI,axiom, % 168.02/167.99 ! [V_q,V_p,T_b,T_a] : % 168.02/167.99 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 168.02/167.99 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 168.02/167.99 => V_p = V_q ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_fst__eqD,axiom, % 168.02/167.99 ! [V_a,V_y,V_x,T_b,T_a] : % 168.02/167.99 ( 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 % 168.02/167.99 => V_x = V_a ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_fst__conv,axiom, % 168.02/167.99 ! [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 ). % 168.02/167.99 % 168.02/167.99 fof(fact_fst__apsnd,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_fst__def,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_pair__collapse,axiom, % 168.02/167.99 ! [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 ). % 168.02/167.99 % 168.02/167.99 fof(fact_surjective__pairing,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_prod__case__beta,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__int__def,axiom, % 168.02/167.99 ! [V_b,V_a] : 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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mod__nat__def,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_split__beta,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_split__comp__eq,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_split__def,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_The__split,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__neg__pos,axiom, % 168.02/167.99 ! [V_b,V_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__pos__pos,axiom, % 168.02/167.99 ! [V_b,V_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__pos__pos__1__number__of,axiom, % 168.02/167.99 ! [V_w] : % 168.02/167.99 ( 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))) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__pos__neg,axiom, % 168.02/167.99 ! [V_b,V_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => 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)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__neg__neg,axiom, % 168.02/167.99 ! [V_b,V_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 168.02/167.99 => 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)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mlex__less,axiom, % 168.02/167.99 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 168.02/167.99 ( 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))) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_prod__size__simp,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_exI__realizer,axiom, % 168.02/167.99 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 168.02/167.99 => 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)))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_conjI__realizer,axiom, % 168.02/167.99 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 168.02/167.99 ( hBOOL(hAPP(V_P_2,V_p_2)) % 168.02/167.99 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 168.02/167.99 => ( 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)))) % 168.02/167.99 & 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)))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_code__numeral_Osize_I2_J,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_code__numeral_Oinject,axiom, % 168.02/167.99 ! [V_code__numeral_H_2,V_code__numeral_2] : % 168.02/167.99 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 168.02/167.99 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_code__numeral_Osimps_I2_J,axiom, % 168.02/167.99 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 168.02/167.99 % 168.02/167.99 fof(fact_code__numeral_Osimps_I3_J,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_div__nat__def,axiom, % 168.02/167.99 ! [V_n,V_m] : 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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Suc__code__numeral__minus__one,axiom, % 168.02/167.99 ! [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 ). % 168.02/167.99 % 168.02/167.99 fof(fact_divmod__nat__rel__def,axiom, % 168.02/167.99 ! [V_qr_2,V_n_2,V_m_2] : % 168.02/167.99 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 168.02/167.99 <=> ( 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)) % 168.02/167.99 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.99 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.02/167.99 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 & 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)) ) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 & 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))) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_code__numeral_Osize_I4_J,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_prod_Orecs,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_in__lex__prod,axiom, % 168.02/167.99 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( 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)) % 168.02/167.99 | ( V_a_2 = V_a_H_2 % 168.02/167.99 & 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_apfst__apsnd,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_apfst__conv,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_apfst__eq__conv,axiom, % 168.02/167.99 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 168.02/167.99 ( 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) % 168.02/167.99 <=> 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_fst__apfst,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_snd__apfst,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_apsnd__apfst__commute,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_code__numeral_Osize_I3_J,axiom, % 168.02/167.99 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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_apsnd__apfst,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_same__fstI,axiom, % 168.02/167.99 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 168.02/167.99 ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_pair__lessI2,axiom, % 168.02/167.99 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_code__numeral_Osimps_I5_J,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_accp__acc__eq,axiom, % 168.02/167.99 ! [V_x_2,V_r_2,T_a] : % 168.02/167.99 ( 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)) % 168.02/167.99 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_acc__subset,axiom, % 168.02/167.99 ! [V_R2_2,V_R1_2,T_a] : % 168.02/167.99 ( 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)) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_acc__downward,axiom, % 168.02/167.99 ! [V_a_2,V_r_2,V_b_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 168.02/167.99 => ( 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)) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_acc_Osimps,axiom, % 168.02/167.99 ! [V_r_2,V_a_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 168.02/167.99 <=> ! [B_x] : % 168.02/167.99 ( 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)) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_pair__lessI1,axiom, % 168.02/167.99 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_code__numeral_Osimps_I4_J,axiom, % 168.02/167.99 ! [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 ). % 168.02/167.99 % 168.02/167.99 fof(fact_pair__leqI2,axiom, % 168.02/167.99 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_smin__insertI,axiom, % 168.02/167.99 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_smax__insertI,axiom, % 168.02/167.99 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_pair__leqI1,axiom, % 168.02/167.99 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_smin__emptyI,axiom, % 168.02/167.99 ! [V_X_2] : % 168.02/167.99 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_wmax__insertI,axiom, % 168.02/167.99 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_wmin__insertI,axiom, % 168.02/167.99 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_wmin__emptyI,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__strict__def,axiom, % 168.02/167.99 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__weak__def,axiom, % 168.02/167.99 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)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_max__weak__def,axiom, % 168.02/167.99 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)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__rpair__set,axiom, % 168.02/167.99 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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_max__rpair__set,axiom, % 168.02/167.99 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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_less__than__iff,axiom, % 168.02/167.99 ! [V_y_2,V_x_2] : % 168.02/167.99 ( 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)) % 168.02/167.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_pair__less__def,axiom, % 168.02/167.99 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 168.02/167.99 % 168.02/167.99 fof(fact_max__strict__def,axiom, % 168.02/167.99 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 168.02/167.99 % 168.02/167.99 fof(fact_max__ext__additive,axiom, % 168.02/167.99 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ( 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))) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_max__extp__max__ext__eq,axiom, % 168.02/167.99 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 168.02/167.99 ( 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) % 168.02/167.99 <=> 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mlex__prod__def,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_intrel__iff,axiom, % 168.02/167.99 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 168.02/167.99 ( 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)) % 168.02/167.99 <=> 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) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_rp__inv__image__rp,axiom, % 168.02/167.99 ! [V_f_2,T_b,V_P_2,T_a] : % 168.02/167.99 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 168.02/167.99 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_rp__inv__image__def,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_in__inv__image,axiom, % 168.02/167.99 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_equiv__intrel__iff,axiom, % 168.02/167.99 ! [V_y_2,V_x_2] : % 168.02/167.99 ( 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)))) % 168.02/167.99 <=> 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_wmax__emptyI,axiom, % 168.02/167.99 ! [V_X_2] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_smax__emptyI,axiom, % 168.02/167.99 ! [V_Y_2] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 168.02/167.99 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Image__mono,axiom, % 168.02/167.99 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 168.02/167.99 ( 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)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Image__Int__subset,axiom, % 168.02/167.99 ! [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)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Image__Un,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Image__empty,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Un__Image,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_rev__ImageI,axiom, % 168.02/167.99 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Image__iff,axiom, % 168.02/167.99 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 168.02/167.99 <=> ? [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/167.99 & 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Image__singleton__iff,axiom, % 168.02/167.99 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 168.02/167.99 ( 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)))))) % 168.02/167.99 <=> 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_measure__def,axiom, % 168.02/167.99 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Diff,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Int,axiom, % 168.02/167.99 ! [V_G_2,V_F_2,T_a] : % 168.02/167.99 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/167.99 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__imageI,axiom, % 168.02/167.99 ! [V_h_2,T_b,V_F_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite_OinsertI,axiom, % 168.02/167.99 ! [V_a_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite_OemptyI,axiom, % 168.02/167.99 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_infinite__UNIV__nat,axiom, % 168.02/167.99 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 168.02/167.99 ! [V_A_2] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 168.02/167.99 <=> 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 168.02/167.99 ! [V_A_2] : % 168.02/167.99 ( c_Nat__Transfer_Onat__set(V_A_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 168.02/167.99 <=> 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__code,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Finite__Set_Ofinite(T_a) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Finite__Set_Ofinite(T_a) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__dom__body,axiom, % 168.02/167.99 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__range__updI,axiom, % 168.02/167.99 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( 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))))) % 168.02/167.99 => 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))))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite_Oequations_I1_J,axiom, % 168.02/167.99 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__insert,axiom, % 168.02/167.99 ! [V_A_2,V_a_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 168.02/167.99 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__subset,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_rev__finite__subset,axiom, % 168.02/167.99 ! [V_A_2,V_B_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__fun__UNIVD2,axiom, % 168.02/167.99 ! [T_b,T_a] : % 168.02/167.99 ( 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)))) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__UNIV,axiom, % 168.02/167.99 ! [T_a] : % 168.02/167.99 ( class_Finite__Set_Ofinite(T_a) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__UnI,axiom, % 168.02/167.99 ! [V_G_2,V_F_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Un,axiom, % 168.02/167.99 ! [V_G_2,V_F_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/167.99 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Diff2,axiom, % 168.02/167.99 ! [V_A_2,V_B_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Plus__iff,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_b,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Plus,axiom, % 168.02/167.99 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__PlusD_I1_J,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_b,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__PlusD_I2_J,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_b,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__surj,axiom, % 168.02/167.99 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Diff__insert,axiom, % 168.02/167.99 ! [V_B_2,V_a_2,V_A_2,T_a] : % 168.02/167.99 ( 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)))) % 168.02/167.99 <=> 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__imageD,axiom, % 168.02/167.99 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 168.02/167.99 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__compl,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 168.02/167.99 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Prod__UNIV,axiom, % 168.02/167.99 ! [T_b,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 168.02/167.99 => 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)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__range__imageI,axiom, % 168.02/167.99 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 168.02/167.99 ( 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))))) % 168.02/167.99 => 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))))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Plus__UNIV__iff,axiom, % 168.02/167.99 ! [T_b,T_a] : % 168.02/167.99 ( 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)))) % 168.02/167.99 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/167.99 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_endo__inj__surj,axiom, % 168.02/167.99 ! [V_f_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 168.02/167.99 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__surj__inj,axiom, % 168.02/167.99 ! [V_f_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__UNIV__inj__surj,axiom, % 168.02/167.99 ! [V_f_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/167.99 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__UNIV__surj__inj,axiom, % 168.02/167.99 ! [V_f_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/167.99 => ( 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)) % 168.02/167.99 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__option__UNIV,axiom, % 168.02/167.99 ! [T_a] : % 168.02/167.99 ( 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)))) % 168.02/167.99 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__vimageD,axiom, % 168.02/167.99 ! [V_F_2,V_h_2,T_b,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 168.02/167.99 => ( 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)) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__vimageI,axiom, % 168.02/167.99 ! [V_h_2,T_b,V_F_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/167.99 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_in__finite__psubset,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/167.99 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_of__int,axiom, % 168.02/167.99 ! [V_j_2,V_i_2,T_a] : % 168.02/167.99 ( class_Rings_Oring__1(T_a) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_One__int__def,axiom, % 168.02/167.99 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))))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mult,axiom, % 168.02/167.99 ! [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))))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_infinite__UNIV__int,axiom, % 168.02/167.99 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_minus,axiom, % 168.02/167.99 ! [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))))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Zero__int__def,axiom, % 168.02/167.99 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))))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_int__def,axiom, % 168.02/167.99 ! [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))))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_add,axiom, % 168.02/167.99 ! [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))))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_nat,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_less,axiom, % 168.02/167.99 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 168.02/167.99 ( 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))))))) % 168.02/167.99 <=> 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_le,axiom, % 168.02/167.99 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 168.02/167.99 ( 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))))))) % 168.02/167.99 <=> 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_irrefl__def,axiom, % 168.02/167.99 ! [V_r_2,T_a] : % 168.02/167.99 ( c_Relation_Oirrefl(T_a,V_r_2) % 168.02/167.99 <=> ! [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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__pointwise,axiom, % 168.02/167.99 ! [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] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 168.02/167.99 => ( ! [B_p] : % 168.02/167.99 ( 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)))) % 168.02/167.99 => 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)))) ) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__image__simple_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 168.02/167.99 => 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)))))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__one_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__image__simple_Oempty,axiom, % 168.02/167.99 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.02/167.99 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__one_Osingleton,axiom, % 168.02/167.99 ! [V_x_2,V_F_2,V_f_2,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.02/167.99 => 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 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__image__simple_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__image__simple_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__one_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/167.99 => 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)))))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__one_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__one_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__one_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_eq__Abs__Integ,axiom, % 168.02/167.99 ! [V_z_2] : % 168.02/167.99 ~ ! [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))))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 168.02/167.99 ! [V_N_2] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 168.02/167.99 <=> ? [B_m] : % 168.02/167.99 ! [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__nat__set__iff__bounded,axiom, % 168.02/167.99 ! [V_N_2] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 168.02/167.99 <=> ? [B_m] : % 168.02/167.99 ! [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Field__insert,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Field__empty,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_mono__Field,axiom, % 168.02/167.99 ! [V_s_2,V_r_2,T_a] : % 168.02/167.99 ( 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)) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Field__Un,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__Field,axiom, % 168.02/167.99 ! [V_r_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_ord_OatMost__iff,axiom, % 168.02/167.99 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 168.02/167.99 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_ord_OatLeast__iff,axiom, % 168.02/167.99 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 168.02/167.99 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_ord_OlessThan__iff,axiom, % 168.02/167.99 ! [V_k_2,V_less_2,V_i_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 168.02/167.99 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_ord_OgreaterThan__iff,axiom, % 168.02/167.99 ! [V_k_2,V_less_2,V_i_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 168.02/167.99 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 168.02/167.99 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 168.02/167.99 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_ord_OatLeastLessThan__iff,axiom, % 168.02/167.99 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 168.02/167.99 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 168.02/167.99 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 168.02/167.99 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_ord_OatLeastAtMost__iff,axiom, % 168.02/167.99 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 168.02/167.99 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__le__Sup,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_minus__Max__eq__Min,axiom, % 168.02/167.99 ! [V_S_2,T_a] : % 168.02/167.99 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/167.99 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_minus__Min__eq__Max,axiom, % 168.02/167.99 ! [V_S_2,T_a] : % 168.02/167.99 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/167.99 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Osingleton,axiom, % 168.02/167.99 ! [V_x_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => 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 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Osingleton,axiom, % 168.02/167.99 ! [V_x_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => 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 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Osingleton,axiom, % 168.02/167.99 ! [V_x_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => 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 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Osingleton,axiom, % 168.02/167.99 ! [V_x_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => 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 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max__ge,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min__le,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min__in,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max__in,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Oin__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_sup__Inf__absorb,axiom, % 168.02/167.99 ! [V_a_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/167.99 => 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 ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_inf__Sup__absorb,axiom, % 168.02/167.99 ! [V_a_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/167.99 => 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 ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Oin__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Oin__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Oin__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max__mono,axiom, % 168.02/167.99 ! [V_N_2,V_M_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 168.02/167.99 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/167.99 => 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))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min__antimono,axiom, % 168.02/167.99 ! [V_N_2,V_M_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 168.02/167.99 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/167.99 => 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))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Oinsert__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Oinsert__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min__insert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max__insert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Osubset__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Osubset__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Osubset__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Ounion__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Osubset__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Ounion__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min__Un,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max__Un,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => 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 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => 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 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Max_Oclosed,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( ! [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)))))) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Min_Oclosed,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( ! [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)))))) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Inf__fin_Oclosed,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( ! [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)))))) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Sup__fin_Oclosed,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Lattices_Olattice(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( ! [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)))))) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__one_Oclosed,axiom, % 168.02/167.99 ! [V_A_2,V_F_2,V_f_2,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( ! [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)))))) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Diff__singleton,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 168.02/167.99 ! [V_A_2] : % 168.02/167.99 ( c_Nat__Transfer_Onat__set(V_A_2) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Plus,axiom, % 168.02/167.99 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__UNIV__unit,axiom, % 168.02/167.99 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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Plus__conv__if,axiom, % 168.02/167.99 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/167.99 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 168.02/167.99 => 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)) ) % 168.02/167.99 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 168.02/167.99 => 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) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card_Oempty,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__infinite,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/167.99 => ( 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))) % 168.02/167.99 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__image,axiom, % 168.02/167.99 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/167.99 => 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) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__le__Sup,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__eq__0__iff,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.99 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__ge__0__finite,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__insert__le,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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)))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__seteq,axiom, % 168.02/167.99 ! [V_A_2,V_B_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 => V_A_2 = V_B_2 ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__mono,axiom, % 168.02/167.99 ! [V_A_2,V_B_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__image__le,axiom, % 168.02/167.99 ! [V_f_2,T_b,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_inj__on__iff__eq__card,axiom, % 168.02/167.99 ! [V_f_2,T_b,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/167.99 <=> 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) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_eq__card__imp__inj__on,axiom, % 168.02/167.99 ! [V_f_2,T_b,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( 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) % 168.02/167.99 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_pigeonhole,axiom, % 168.02/167.99 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_psubset__card__mono,axiom, % 168.02/167.99 ! [V_A_2,V_B_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 168.02/167.99 ! [V_x_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => 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 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 168.02/167.99 ! [V_x_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => 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 ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__insert__if,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__insert__disjoint,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__gt__0__iff,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__UNIV__card__ge__0,axiom, % 168.02/167.99 ! [T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/167.99 => 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))))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Un__Int,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__bij__eq,axiom, % 168.02/167.99 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/167.99 => ( 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)) % 168.02/167.99 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 168.02/167.99 => ( 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)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/167.99 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Diff__subset,axiom, % 168.02/167.99 ! [V_A_2,V_B_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Diff__subset__Int,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( 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))) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_diff__card__le__card__Diff,axiom, % 168.02/167.99 ! [V_A_2,V_B_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => 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)))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__UNIV__bool,axiom, % 168.02/167.99 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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__psubset,axiom, % 168.02/167.99 ! [V_A_2,V_B_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_Osup__Inf__absorb,axiom, % 168.02/167.99 ! [V_a_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/167.99 => 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 ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 168.02/167.99 ! [V_a_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/167.99 => 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 ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__insert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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)))))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Un__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Diff1__le,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__inj__on__le,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/167.99 => ( 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)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/167.99 => 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_inj__on__iff__card__le,axiom, % 168.02/167.99 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/167.99 => ( ? [B_f] : % 168.02/167.99 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 168.02/167.99 & 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)) ) % 168.02/167.99 <=> 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Suc__Diff1,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Diff2__less,axiom, % 168.02/167.99 ! [V_y_2,V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 168.02/167.99 => 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Diff1__less,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => 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 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( 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)) % 168.02/167.99 => 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 ) % 168.02/167.99 & ( 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)) % 168.02/167.99 => 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)))))) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Diff__insert,axiom, % 168.02/167.99 ! [V_B_2,V_a_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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)))))) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__fun__UNIVD1,axiom, % 168.02/167.99 ! [T_b,T_a] : % 168.02/167.99 ( 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)))) % 168.02/167.99 => ( 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)) % 168.02/167.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card_Oremove,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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)))))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Diff__singleton__if,axiom, % 168.02/167.99 ! [V_x_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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)) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card_Ounion__inter__neutral,axiom, % 168.02/167.99 ! [V_B_2,V_A_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( ( ? [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))) % 168.02/167.99 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( ! [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)))))) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 168.02/167.99 ! [V_A_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => ( ! [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)))))) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__Suc__eq,axiom, % 168.02/167.99 ! [V_k_2,V_A_2,T_a] : % 168.02/167.99 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 168.02/167.99 <=> ? [B_b,B_B] : % 168.02/167.99 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 168.02/167.99 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 168.02/167.99 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 168.02/167.99 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/167.99 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_card__greaterThanLessThan__int,axiom, % 168.02/167.99 ! [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)))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__gen__delta,axiom, % 168.02/167.99 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/167.99 => 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)))) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_fold__Un__disjoint,axiom, % 168.02/167.99 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 168.02/167.99 ! [V_N_2,V_h_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => ( ! [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)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/167.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_finite__greaterThanLessThan__int,axiom, % 168.02/167.99 ! [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))) ). % 168.02/167.99 % 168.02/167.99 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 168.02/167.99 ! [V_A_2,V_f_2,T_a] : % 168.02/167.99 ( ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/167.99 & class_Groups_Ocomm__monoid__mult(T_a) ) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_OF__eq,axiom, % 168.02/167.99 ! [V_g_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Oeq__fold,axiom, % 168.02/167.99 ! [V_g_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_of__nat__setprod,axiom, % 168.02/167.99 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 168.02/167.99 & class_Rings_Osemiring__1(T_a) ) % 168.02/167.99 => 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) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_int__setprod,axiom, % 168.02/167.99 ! [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) ). % 168.02/167.99 % 168.02/167.99 fof(fact_of__int__setprod,axiom, % 168.02/167.99 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 168.02/167.99 & class_Rings_Oring__1(T_a) ) % 168.02/167.99 => 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) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 168.02/167.99 ! [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)) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__1,axiom, % 168.02/167.99 ! [V_A_2,T_b,T_a] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.02/167.99 => 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) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__timesf,axiom, % 168.02/167.99 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_abs__setprod,axiom, % 168.02/167.99 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( class_Fields_Olinordered__field(T_a) % 168.02/167.99 => 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) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_fold__image__empty,axiom, % 168.02/167.99 ! [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 ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__zero__iff,axiom, % 168.02/167.99 ! [V_f_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( ( class_Rings_Ocomm__semiring__1(T_b) % 168.02/167.99 & class_Rings_Ono__zero__divisors(T_b) ) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( 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) % 168.02/167.99 <=> ? [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/167.99 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__zero,axiom, % 168.02/167.99 ! [V_f_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Rings_Ocomm__semiring__1(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ? [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/167.99 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 168.02/167.99 => 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) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__empty,axiom, % 168.02/167.99 ! [V_f_2,T_b,T_a] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.02/167.99 => 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) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Oempty,axiom, % 168.02/167.99 ! [V_g_2,T_b,T_a] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.02/167.99 => 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) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__infinite,axiom, % 168.02/167.99 ! [V_f_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Oinfinite,axiom, % 168.02/167.99 ! [V_g_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__eq__1__iff,axiom, % 168.02/167.99 ! [V_f_2,V_F_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/167.99 => ( 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) % 168.02/167.99 <=> ! [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 168.02/167.99 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 168.02/167.99 ! [V_f_2,V_A_2,T_a] : % 168.02/167.99 ( ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/167.99 & class_Groups_Ocomm__monoid__mult(T_a) ) % 168.02/167.99 => ( c_Nat__Transfer_Onat__set(V_A_2) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Odistrib,axiom, % 168.02/167.99 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__pos__nat__iff,axiom, % 168.02/167.99 ! [V_f_2,V_S_2,T_a] : % 168.02/167.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/167.99 => ( 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))) % 168.02/167.99 <=> ! [B_x] : % 168.02/167.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 168.02/167.99 => 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))) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 168.02/167.99 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/167.99 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/167.99 => 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) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_greaterThanLessThan__empty,axiom, % 168.02/167.99 ! [V_k_2,V_l_2,T_a] : % 168.02/167.99 ( class_Orderings_Oorder(T_a) % 168.02/167.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_image__uminus__greaterThanLessThan,axiom, % 168.02/167.99 ! [V_y_2,V_x_2,T_a] : % 168.02/167.99 ( class_Groups_Oordered__ab__group__add(T_a) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__delta_H,axiom, % 168.02/167.99 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/167.99 => 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) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/167.99 => 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) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__delta,axiom, % 168.02/167.99 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/167.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/167.99 => 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) ) % 168.02/167.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/167.99 => 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) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__constant,axiom, % 168.02/167.99 ! [V_y_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__insert,axiom, % 168.02/167.99 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Oinsert,axiom, % 168.02/167.99 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Ounion__inter,axiom, % 168.02/167.99 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__Un__Int,axiom, % 168.02/167.99 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_fold__image__distrib,axiom, % 168.02/167.99 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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)) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_fold__image__insert,axiom, % 168.02/167.99 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Oab__semigroup__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/167.99 => 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)) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_Int__greaterThanLessThan,axiom, % 168.02/167.99 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/167.99 ( class_Orderings_Olinorder(T_a) % 168.02/167.99 => 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)) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Oinsert__remove,axiom, % 168.02/167.99 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => 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)))))) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Ounion__disjoint,axiom, % 168.02/167.99 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod__Un__disjoint,axiom, % 168.02/167.99 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/167.99 => ( 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)) % 168.02/167.99 => 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)) ) ) ) ) ). % 168.02/167.99 % 168.02/167.99 fof(fact_setprod_Oremove,axiom, % 168.02/167.99 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 168.02/167.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/167.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.00 => 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)))))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_fold__image__Un__Int,axiom, % 168.02/168.00 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__eq__fold__image,axiom, % 168.02/168.00 ! [V_f_2,T_b,V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__def,axiom, % 168.02/168.00 ! [V_A_2,T_a] : % 168.02/168.00 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card_Oeq__fold__g,axiom, % 168.02/168.00 ! [V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_comm__monoid__big_OF__eq,axiom, % 168.02/168.00 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 168.02/168.00 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/168.00 => 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) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/168.00 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_fold__image__Un__one,axiom, % 168.02/168.00 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.02/168.00 => ( ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setprod_Ounion__inter__neutral,axiom, % 168.02/168.00 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.00 => ( ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setprod__Un__one,axiom, % 168.02/168.00 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.02/168.00 => ( ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__greaterThanLessThan,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__greaterThanLessThan,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_comm__monoid__big_Oinfinite,axiom, % 168.02/168.00 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 168.02/168.00 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/168.00 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 168.02/168.00 ! [V_f_2,V_A_2,T_a] : % 168.02/168.00 ( ! [B_x] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.00 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I4_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setprod__diff1,axiom, % 168.02/168.00 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Fields_Ofield(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.00 => 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) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__greaterThanAtMost,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__greaterThanAtMost__int,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_diff__divide__distrib,axiom, % 168.02/168.00 ! [V_c,V_b,V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_power__divide,axiom, % 168.02/168.00 ! [V_n,V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_add__divide__distrib,axiom, % 168.02/168.00 ! [V_c,V_b,V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_times__divide__eq__right,axiom, % 168.02/168.00 ! [V_c,V_b,V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_minus__divide__left,axiom, % 168.02/168.00 ! [V_b,V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__1,axiom, % 168.02/168.00 ! [V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__zero__left,axiom, % 168.02/168.00 ! [V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__zero,axiom, % 168.02/168.00 ! [V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_nonzero__eq__divide__eq,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 168.02/168.00 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_nonzero__divide__eq__eq,axiom, % 168.02/168.00 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 168.02/168.00 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__eq__imp,axiom, % 168.02/168.00 ! [V_a,V_b,V_c,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 168.02/168.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_eq__divide__imp,axiom, % 168.02/168.00 ! [V_b,V_a,V_c,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 168.02/168.00 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_right__inverse__eq,axiom, % 168.02/168.00 ! [V_a_2,V_b_2,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 168.02/168.00 <=> V_a_2 = V_b_2 ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__self,axiom, % 168.02/168.00 ! [V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__self__if,axiom, % 168.02/168.00 ! [V_a,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 168.02/168.00 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 168.02/168.00 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_nonzero__minus__divide__divide,axiom, % 168.02/168.00 ! [V_a,V_b,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_nonzero__minus__divide__right,axiom, % 168.02/168.00 ! [V_a,V_b,T_a] : % 168.02/168.00 ( class_Rings_Odivision__ring(T_a) % 168.02/168.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_nonzero__power__divide,axiom, % 168.02/168.00 ! [V_n,V_a,V_b,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_power__one__over,axiom, % 168.02/168.00 ! [V_n,V_a,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setprod__dividef,axiom, % 168.02/168.00 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_greaterThanAtMost__empty,axiom, % 168.02/168.00 ! [V_k_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_greaterThanAtMost__empty__iff,axiom, % 168.02/168.00 ! [V_l_2,V_k_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 168.02/168.00 ! [V_l_2,V_k_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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) % 168.02/168.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I20_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_eq__divide__eq__number__of1,axiom, % 168.02/168.00 ! [V_w_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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 ) % 168.02/168.00 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_eq__divide__eq__number__of,axiom, % 168.02/168.00 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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) % 168.02/168.00 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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 ) % 168.02/168.00 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__eq__eq__number__of,axiom, % 168.02/168.00 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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) % 168.02/168.00 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) % 168.02/168.00 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__eq__eq__number__of1,axiom, % 168.02/168.00 ! [V_a_2,V_w_2,V_b_2,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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 % 168.02/168.00 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I14_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__Numeral0,axiom, % 168.02/168.00 ! [V_x,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber__ring(T_a) ) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__Numeral1,axiom, % 168.02/168.00 ! [V_x,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield(T_a) % 168.02/168.00 & class_Int_Onumber__ring(T_a) ) % 168.02/168.00 => 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 ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__numeral__1,axiom, % 168.02/168.00 ! [V_a,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield(T_a) % 168.02/168.00 & class_Int_Onumber__ring(T_a) ) % 168.02/168.00 => 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 ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__minus1,axiom, % 168.02/168.00 ! [V_x,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber__ring(T_a) ) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__greaterThanAtMost,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__less__eq__number__of1,axiom, % 168.02/168.00 ! [V_a_2,V_w_2,V_b_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> ( ( 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))) % 168.02/168.00 => 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)))) ) % 168.02/168.00 & ( ~ 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))) % 168.02/168.00 => ( ( 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))) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ 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))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__less__eq__number__of,axiom, % 168.02/168.00 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_less__divide__eq__number__of,axiom, % 168.02/168.00 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_less__divide__eq__number__of1,axiom, % 168.02/168.00 ! [V_w_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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)))) % 168.02/168.00 <=> ( ( 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))) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ 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))) % 168.02/168.00 => ( ( 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))) % 168.02/168.00 => 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)))) ) % 168.02/168.00 & ( ~ 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))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_power__diff,axiom, % 168.02/168.00 ! [V_m,V_n,V_a,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_minus1__divide,axiom, % 168.02/168.00 ! [V_x,T_a] : % 168.02/168.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber__ring(T_a) ) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Int__greaterThanAtMost,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I10_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__le__eq__number__of1,axiom, % 168.02/168.00 ! [V_a_2,V_w_2,V_b_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> ( ( 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))) % 168.02/168.00 => 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)))) ) % 168.02/168.00 & ( ~ 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))) % 168.02/168.00 => ( ( 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))) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ 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))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__le__eq__number__of,axiom, % 168.02/168.00 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_le__divide__eq__number__of,axiom, % 168.02/168.00 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_le__divide__eq__number__of1,axiom, % 168.02/168.00 ! [V_w_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber(T_a) ) % 168.02/168.00 => ( 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)))) % 168.02/168.00 <=> ( ( 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))) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ 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))) % 168.02/168.00 => ( ( 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))) % 168.02/168.00 => 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)))) ) % 168.02/168.00 & ( ~ 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))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__greaterThanAtMost__int,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I16_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_half__gt__zero__iff,axiom, % 168.02/168.00 ! [V_r_2,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber__ring(T_a) ) % 168.02/168.00 => ( 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)))))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_half__gt__zero,axiom, % 168.02/168.00 ! [V_r,T_a] : % 168.02/168.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 & class_Int_Onumber__ring(T_a) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 168.02/168.00 => 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)))))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_le__divide__eq,axiom, % 168.02/168.00 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__le__eq,axiom, % 168.02/168.00 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_pos__le__divide__eq,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_times__divide__times__eq,axiom, % 168.02/168.00 ! [V_w,V_z,V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_minus__divide__right,axiom, % 168.02/168.00 ! [V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_minus__divide__divide,axiom, % 168.02/168.00 ! [V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_abs__divide,axiom, % 168.02/168.00 ! [V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__right__mono__neg,axiom, % 168.02/168.00 ! [V_c,V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__right__mono,axiom, % 168.02/168.00 ! [V_c,V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__le__0__iff,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 168.02/168.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_zero__le__divide__iff,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 168.02/168.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_zero__less__divide__iff,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 168.02/168.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__less__0__iff,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 168.02/168.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__pos__pos,axiom, % 168.02/168.00 ! [V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__pos__neg,axiom, % 168.02/168.00 ! [V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__neg__pos,axiom, % 168.02/168.00 ! [V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__neg__neg,axiom, % 168.02/168.00 ! [V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__strict__right__mono,axiom, % 168.02/168.00 ! [V_c,V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__strict__right__mono__neg,axiom, % 168.02/168.00 ! [V_c,V_a,V_b,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_eq__divide__eq,axiom, % 168.02/168.00 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 168.02/168.00 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) % 168.02/168.00 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__eq__eq,axiom, % 168.02/168.00 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 168.02/168.00 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) % 168.02/168.00 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_mult__divide__mult__cancel__right,axiom, % 168.02/168.00 ! [V_b,V_a,V_c,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_mult__divide__mult__cancel__left,axiom, % 168.02/168.00 ! [V_b,V_a,V_c,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_frac__eq__eq,axiom, % 168.02/168.00 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( 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) % 168.02/168.00 <=> 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) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_nonzero__abs__divide,axiom, % 168.02/168.00 ! [V_a,V_b,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__nonneg__pos,axiom, % 168.02/168.00 ! [V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__nonneg__neg,axiom, % 168.02/168.00 ! [V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_frac__less2,axiom, % 168.02/168.00 ! [V_z,V_w,V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 168.02/168.00 => 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))) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_frac__less,axiom, % 168.02/168.00 ! [V_z,V_w,V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 168.02/168.00 => 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))) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_frac__le,axiom, % 168.02/168.00 ! [V_z,V_w,V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 168.02/168.00 => 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))) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__nonpos__pos,axiom, % 168.02/168.00 ! [V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__nonpos__neg,axiom, % 168.02/168.00 ! [V_y,V_x,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_less__divide__eq,axiom, % 168.02/168.00 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__less__eq,axiom, % 168.02/168.00 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_pos__less__divide__eq,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_pos__divide__less__eq,axiom, % 168.02/168.00 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_mult__imp__div__pos__less,axiom, % 168.02/168.00 ! [V_z,V_x,V_y,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => ( 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))) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_mult__imp__less__div__pos,axiom, % 168.02/168.00 ! [V_x,V_z,V_y,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => ( 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)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_neg__less__divide__eq,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_neg__divide__less__eq,axiom, % 168.02/168.00 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__strict__left__mono,axiom, % 168.02/168.00 ! [V_c,V_a,V_b,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.02/168.00 => ( 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))) % 168.02/168.00 => 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))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__strict__left__mono__neg,axiom, % 168.02/168.00 ! [V_c,V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( 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))) % 168.02/168.00 => 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))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_add__frac__eq,axiom, % 168.02/168.00 ! [V_w,V_x,V_z,V_y,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__add__eq__iff,axiom, % 168.02/168.00 ! [V_y,V_x,V_z,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_add__frac__num,axiom, % 168.02/168.00 ! [V_z,V_x,V_y,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_add__divide__eq__iff,axiom, % 168.02/168.00 ! [V_y,V_x,V_z,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_add__num__frac,axiom, % 168.02/168.00 ! [V_x,V_z,V_y,T_a] : % 168.02/168.00 ( class_Fields_Ofield__inverse__zero(T_a) % 168.02/168.00 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_diff__divide__eq__iff,axiom, % 168.02/168.00 ! [V_y,V_x,V_z,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__diff__eq__iff,axiom, % 168.02/168.00 ! [V_y,V_x,V_z,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_diff__frac__eq,axiom, % 168.02/168.00 ! [V_w,V_x,V_z,V_y,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_less__half__sum,axiom, % 168.02/168.00 ! [V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.02/168.00 => 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))))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_gt__half__sum,axiom, % 168.02/168.00 ! [V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_abs__div__pos,axiom, % 168.02/168.00 ! [V_x,V_y,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__left__mono__neg,axiom, % 168.02/168.00 ! [V_c,V_b,V_a,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( 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))) % 168.02/168.00 => 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))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_divide__left__mono,axiom, % 168.02/168.00 ! [V_c,V_a,V_b,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.02/168.00 => ( 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))) % 168.02/168.00 => 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))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_neg__divide__le__eq,axiom, % 168.02/168.00 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_neg__le__divide__eq,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_mult__imp__le__div__pos,axiom, % 168.02/168.00 ! [V_x,V_z,V_y,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => ( 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)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_mult__imp__div__pos__le,axiom, % 168.02/168.00 ! [V_z,V_x,V_y,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.02/168.00 => ( 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))) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_pos__divide__le__eq,axiom, % 168.02/168.00 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 168.02/168.00 ( class_Fields_Olinordered__field(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setprod__Un,axiom, % 168.02/168.00 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Fields_Ofield(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.00 => ( ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 168.02/168.00 => 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))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 168.02/168.00 ! [V_N_2,V_h_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( ! [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)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Max_Ohom__commute,axiom, % 168.02/168.00 ! [V_N_2,V_h_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( ! [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)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Min_Ohom__commute,axiom, % 168.02/168.00 ! [V_N_2,V_h_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( ! [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)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Inf__fin_Ohom__commute,axiom, % 168.02/168.00 ! [V_N_2,V_h_2,T_a] : % 168.02/168.00 ( class_Lattices_Olattice(T_a) % 168.02/168.00 => ( ! [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)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Sup__fin_Ohom__commute,axiom, % 168.02/168.00 ! [V_N_2,V_h_2,T_a] : % 168.02/168.00 ( class_Lattices_Olattice(T_a) % 168.02/168.00 => ( ! [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)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.00 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ImageE,axiom, % 168.02/168.00 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 168.02/168.00 => ~ ! [B_x] : % 168.02/168.00 ( 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)) % 168.02/168.00 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setprod__mono__one__right,axiom, % 168.02/168.00 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 168.02/168.00 => ( ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 168.02/168.00 => 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) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setprod__mono__one__left,axiom, % 168.02/168.00 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 168.02/168.00 => ( ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 168.02/168.00 => 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) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__Pow,axiom, % 168.02/168.00 ! [V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__empty__induct,axiom, % 168.02/168.00 ! [V_P_2,V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 168.02/168.00 => ( ! [B_a,B_A] : % 168.02/168.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 168.02/168.00 => ( hBOOL(hAPP(V_P_2,B_A)) % 168.02/168.00 => 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)))))) ) ) ) % 168.02/168.00 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I19_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__atLeastAtMost,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__atLeastAtMost__int,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_PowI,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Cantors__paradox,axiom, % 168.02/168.00 ! [V_A_2,T_a] : % 168.02/168.00 ~ ? [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__Pow__surj,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 168.02/168.00 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__bottom,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__iff,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_PowD,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 168.02/168.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__top,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__Int__eq,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__mono,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Un__Pow__subset,axiom, % 168.02/168.00 ! [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)))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__not__empty,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__Pow__iff,axiom, % 168.02/168.00 ! [V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 168.02/168.00 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__empty,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__add__atLeastAtMost,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__Suc__atLeastAtMost,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__insert,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Pow__UNIV,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 168.02/168.00 ! [V_n_2,V_m_2] : % 168.02/168.00 ( c_Nat__Transfer_Ois__nat(V_m_2) % 168.02/168.00 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 168.02/168.00 => 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))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastAtMostSuc__conv,axiom, % 168.02/168.00 ! [V_n_2,V_m_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 168.02/168.00 ! [V_y_2,V_x_2] : % 168.02/168.00 ( c_Nat__Transfer_Ois__nat(V_x_2) % 168.02/168.00 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastatMost__empty__iff2,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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) % 168.02/168.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastatMost__empty__iff,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastatMost__empty,axiom, % 168.02/168.00 ! [V_a_2,V_b_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastatMost__subset__iff,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 168.02/168.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastAtMost__singleton,axiom, % 168.02/168.00 ! [V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastAtMost__singleton__iff,axiom, % 168.02/168.00 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( V_a_2 = V_b_2 % 168.02/168.00 & V_b_2 = V_ca_2 ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastAtMost__singleton_H,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( V_a_2 = V_b_2 % 168.02/168.00 => 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))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__uminus__atLeastAtMost,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__Pow__mono,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( 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)) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 168.02/168.00 ! [V_y_2,V_x_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 168.02/168.00 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__atLeastAtMost,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Int__atLeastAtMost,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastatMost__psubset__iff,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 168.02/168.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 168.02/168.00 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2)) % 168.02/168.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I22_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I16_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I12_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I13_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_simp__from__to,axiom, % 168.02/168.00 ! [V_i_2,V_j_2] : % 168.02/168.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__atLeastAtMost__int,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I5_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_bset_I8_J,axiom, % 168.02/168.00 ! [V_B_2,V_t_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ( 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)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 168.02/168.00 => 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))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_aset_I6_J,axiom, % 168.02/168.00 ! [V_A_2,V_t_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ( 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)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_aset_I4_J,axiom, % 168.02/168.00 ! [V_A_2,V_t_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( B_x != V_t_2 % 168.02/168.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_all__nat__less,axiom, % 168.02/168.00 ! [V_P_2,V_n_2] : % 168.02/168.00 ( ! [B_m] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 168.02/168.00 => hBOOL(hAPP(V_P_2,B_m)) ) % 168.02/168.00 <=> ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ex__nat__less,axiom, % 168.02/168.00 ! [V_P_2,V_n_2] : % 168.02/168.00 ( ? [B_m] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 168.02/168.00 & hBOOL(hAPP(V_P_2,B_m)) ) % 168.02/168.00 <=> ? [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Powp__Pow__eq,axiom, % 168.02/168.00 ! [V_x_2,V_A_2,T_a] : % 168.02/168.00 ( 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)) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Powp__mono,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,T_a] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_bset_I4_J,axiom, % 168.02/168.00 ! [V_B_2,V_t_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( B_x != V_t_2 % 168.02/168.00 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_bset_I7_J,axiom, % 168.02/168.00 ! [V_B_2,V_t_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 168.02/168.00 => 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))) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_aset_I5_J,axiom, % 168.02/168.00 ! [V_A_2,V_t_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_bset_I3_J,axiom, % 168.02/168.00 ! [V_B_2,V_t_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ( 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)) % 168.02/168.00 => ( ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xa] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 168.02/168.00 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 168.02/168.00 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_aset_I3_J,axiom, % 168.02/168.00 ! [V_A_2,V_t_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ( 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)) % 168.02/168.00 => ( ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xa] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 168.02/168.00 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 168.02/168.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_aset_I8_J,axiom, % 168.02/168.00 ! [V_t_2,V_A_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_bset_I6_J,axiom, % 168.02/168.00 ! [V_t_2,V_B_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_periodic__finite__ex,axiom, % 168.02/168.00 ! [V_P_2,V_d_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 168.02/168.00 => ( ! [B_x,B_k] : % 168.02/168.00 ( hBOOL(hAPP(V_P_2,B_x)) % 168.02/168.00 <=> 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)))) ) % 168.02/168.00 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 168.02/168.00 <=> ? [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_bset_I5_J,axiom, % 168.02/168.00 ! [V_t_2,V_B_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_aset_I7_J,axiom, % 168.02/168.00 ! [V_t_2,V_A_2,V_D_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 168.02/168.00 => ! [B_x] : % 168.02/168.00 ( ! [B_xa] : % 168.02/168.00 ( 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))) % 168.02/168.00 => ! [B_xb] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 168.02/168.00 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 168.02/168.00 ! [V_x_2,V_y_2,V_ca_2] : % 168.02/168.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 168.02/168.00 => 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))) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__atLeastLessThan,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__atMost,axiom, % 168.02/168.00 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atMost__eq__iff,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 168.02/168.00 <=> V_x_2 = V_y_2 ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__eq__iff,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 168.02/168.00 => ( 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) % 168.02/168.00 <=> ( V_a_2 = V_ca_2 % 168.02/168.00 & V_b_2 = V_d_2 ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( 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) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 168.02/168.00 => V_a_2 = V_ca_2 ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( 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) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 168.02/168.00 => V_b_2 = V_d_2 ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_all__nat__less__eq,axiom, % 168.02/168.00 ! [V_P_2,V_n_2] : % 168.02/168.00 ( ! [B_m] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 168.02/168.00 => hBOOL(hAPP(V_P_2,B_m)) ) % 168.02/168.00 <=> ! [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ex__nat__less__eq,axiom, % 168.02/168.00 ! [V_P_2,V_n_2] : % 168.02/168.00 ( ? [B_m] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 168.02/168.00 & hBOOL(hAPP(V_P_2,B_m)) ) % 168.02/168.00 <=> ? [B_x] : % 168.02/168.00 ( 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))) % 168.02/168.00 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan0,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__atLeastLessThan,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__Suc__atLeastLessThan,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__empty,axiom, % 168.02/168.00 ! [V_a_2,V_b_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__empty__iff,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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)) % 168.02/168.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__empty__iff2,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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) % 168.02/168.00 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__subset__iff,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 168.02/168.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 168.02/168.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I17_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__diff,axiom, % 168.02/168.00 ! [V_m_2,V_n_2,V_i_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I11_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeast0AtMost,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__add__atLeastLessThan,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__atMost,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atMost__Suc,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atMost__iff,axiom, % 168.02/168.00 ! [V_k_2,V_i_2,T_a] : % 168.02/168.00 ( class_Orderings_Oord(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atMost__subset__iff,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__singleton,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I21_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThan__add__Un,axiom, % 168.02/168.00 ! [V_k_2,V_j_2,V_i_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I15_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Int__atLeastLessThan,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_subset__card__intvl__is__intvl,axiom, % 168.02/168.00 ! [V_k_2,V_A_2] : % 168.02/168.00 ( 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))))) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I9_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__uminus__atLeastLessThan,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__uminus__greaterThanAtMost,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThanSuc,axiom, % 168.02/168.00 ! [V_n_2,V_m_2] : % 168.02/168.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atMost__0,axiom, % 168.02/168.00 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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Int__atLeastAtMostR1,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_b_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Int__atLeastAtMostL1,axiom, % 168.02/168.00 ! [V_d_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I9_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I3_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I1_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I15_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I6_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I3_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I18_J,axiom, % 168.02/168.00 ! [V_u_2,V_m_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_greaterThan__0,axiom, % 168.02/168.00 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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I7_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_folding__one__idem_Ounion__idem,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/168.00 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => 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)) ) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__lessThan,axiom, % 168.02/168.00 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__atLeastLessThan__int,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__lessThan,axiom, % 168.02/168.00 ! [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 ). % 168.02/168.00 % 168.02/168.00 fof(fact_lessThan__eq__iff,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 168.02/168.00 <=> V_x_2 = V_y_2 ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_greaterThan__eq__iff,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 168.02/168.00 <=> V_x_2 = V_y_2 ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_folding__one__idem_Oidem,axiom, % 168.02/168.00 ! [V_x_2,V_F_2,V_f_2,T_a] : % 168.02/168.00 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.02/168.00 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__uminus__greaterThan,axiom, % 168.02/168.00 ! [V_x_2,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__uminus__lessThan,axiom, % 168.02/168.00 ! [V_x_2,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeast0LessThan,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_lessThan__0,axiom, % 168.02/168.00 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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_lessThan__Suc,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_lessThan__Suc__atMost,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__atLeastZeroLessThan__int,axiom, % 168.02/168.00 ! [V_u_2] : % 168.02/168.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_lessThan__iff,axiom, % 168.02/168.00 ! [V_k_2,V_i_2,T_a] : % 168.02/168.00 ( class_Orderings_Oord(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_lessThan__subset__iff,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_greaterThan__iff,axiom, % 168.02/168.00 ! [V_k_2,V_i_2,T_a] : % 168.02/168.00 ( class_Orderings_Oord(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_greaterThan__subset__iff,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_lessThan__strict__subset__iff,axiom, % 168.02/168.00 ! [V_n_2,V_m_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Compl__greaterThan,axiom, % 168.02/168.00 ! [V_k_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Compl__atMost,axiom, % 168.02/168.00 ! [V_k_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__add__int__atLeastLessThan,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__atLeastZeroLessThan__int,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_card__atLeastLessThan__int,axiom, % 168.02/168.00 ! [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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_folding__one__idem_Oin__idem,axiom, % 168.02/168.00 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/168.00 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.00 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_single__Diff__lessThan,axiom, % 168.02/168.00 ! [V_k_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I8_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I4_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I2_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I7_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I11_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I5_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_greaterThan__Suc,axiom, % 168.02/168.00 ! [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)))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 168.02/168.00 ! [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))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I2_J,axiom, % 168.02/168.00 ! [V_u_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 168.02/168.00 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/168.00 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_folding__one__idem_Osubset__idem,axiom, % 168.02/168.00 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.02/168.00 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/168.00 => 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) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I10_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_arith__series__int,axiom, % 168.02/168.00 ! [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)))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I12_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I13_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__abs,axiom, % 168.02/168.00 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__abs__ge__zero,axiom, % 168.02/168.00 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__divide__distrib,axiom, % 168.02/168.00 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_abs__setsum__abs,axiom, % 168.02/168.00 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__0,axiom, % 168.02/168.00 ! [V_A_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__addf,axiom, % 168.02/168.00 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__right__distrib,axiom, % 168.02/168.00 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 168.02/168.00 ( class_Rings_Osemiring__0(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__left__distrib,axiom, % 168.02/168.00 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Rings_Osemiring__0(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__product,axiom, % 168.02/168.00 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Rings_Osemiring__0(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__negf,axiom, % 168.02/168.00 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Oab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__commute,axiom, % 168.02/168.00 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_of__int__setsum,axiom, % 168.02/168.00 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Rings_Oring__1(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_of__nat__setsum,axiom, % 168.02/168.00 ! [V_A_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Rings_Osemiring__1(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__subtractf,axiom, % 168.02/168.00 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Oab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeast__eq__iff,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 168.02/168.00 <=> V_x_2 = V_y_2 ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__empty,axiom, % 168.02/168.00 ! [V_f_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum_Oempty,axiom, % 168.02/168.00 ! [V_g_2,T_b,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum_Oinfinite,axiom, % 168.02/168.00 ! [V_g_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__infinite,axiom, % 168.02/168.00 ! [V_f_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum_Odistrib,axiom, % 168.02/168.00 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__lessThan__Suc,axiom, % 168.02/168.00 ! [V_n_2,V_f_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 168.02/168.00 ! [V_n_2,V_m_2,V_f_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 168.02/168.00 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 168.02/168.00 ! [V_n_2,V_m_2,V_f_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 168.02/168.00 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__add__nat__ivl,axiom, % 168.02/168.00 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__diff__nat__ivl,axiom, % 168.02/168.00 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 168.02/168.00 ( class_Groups_Oab__group__add(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeast__iff,axiom, % 168.02/168.00 ! [V_k_2,V_i_2,T_a] : % 168.02/168.00 ( class_Orderings_Oord(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__delta,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/168.00 => 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) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/168.00 => 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) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__delta_H,axiom, % 168.02/168.00 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/168.00 => 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) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 168.02/168.00 => 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) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeast__subset__iff,axiom, % 168.02/168.00 ! [V_y_2,V_x_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => ( 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))) % 168.02/168.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeast__0,axiom, % 168.02/168.00 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)) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__constant,axiom, % 168.02/168.00 ! [V_A_2,V_y_2,T_b,T_a] : % 168.02/168.00 ( class_Rings_Osemiring__1(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__atMost__Suc,axiom, % 168.02/168.00 ! [V_n_2,V_f_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => 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))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Compl__atLeast,axiom, % 168.02/168.00 ! [V_k_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Compl__lessThan,axiom, % 168.02/168.00 ! [V_k_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum_Oinsert,axiom, % 168.02/168.00 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__insert,axiom, % 168.02/168.00 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/168.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeast__Suc__greaterThan,axiom, % 168.02/168.00 ! [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) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__Un__Int,axiom, % 168.02/168.00 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__diff,axiom, % 168.02/168.00 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Oab__group__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum_Oeq__fold,axiom, % 168.02/168.00 ! [V_g_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum_OF__eq,axiom, % 168.02/168.00 ! [V_g_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 168.02/168.00 ! [V_k_2,V_f_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 168.02/168.00 => 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)) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__head__upt__Suc,axiom, % 168.02/168.00 ! [V_f_2,V_n_2,V_m_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.00 => 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))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__head__Suc,axiom, % 168.02/168.00 ! [V_f_2,V_n_2,V_m_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.00 => 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))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__restrict__set,axiom, % 168.02/168.00 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum_Oinsert__remove,axiom, % 168.02/168.00 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => 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)))))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__Un__disjoint,axiom, % 168.02/168.00 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.00 => ( 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)) % 168.02/168.00 => 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)) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__Un,axiom, % 168.02/168.00 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Oab__group__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__un_I14_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 168.02/168.00 => 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) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I8_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Int__atLeastAtMostR2,axiom, % 168.02/168.00 ! [V_d_2,V_ca_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_Int__atLeastAtMostL2,axiom, % 168.02/168.00 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 168.02/168.00 ( class_Orderings_Olinorder(T_a) % 168.02/168.00 => 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) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__op__ivl__Suc,axiom, % 168.02/168.00 ! [V_f_2,V_m_2,V_n_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 168.02/168.00 => 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) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__cl__ivl__Suc,axiom, % 168.02/168.00 ! [V_f_2,V_m_2,V_n_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 168.02/168.00 => 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) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 168.02/168.00 => 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))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__head,axiom, % 168.02/168.00 ! [V_P_2,V_n_2,V_m_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.00 => 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))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_ivl__disj__int_I6_J,axiom, % 168.02/168.00 ! [V_u_2,V_l_2,T_a] : % 168.02/168.00 ( class_Orderings_Oorder(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__uminus__atMost,axiom, % 168.02/168.00 ! [V_x_2,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_image__uminus__atLeast,axiom, % 168.02/168.00 ! [V_x_2,T_a] : % 168.02/168.00 ( class_Groups_Oordered__ab__group__add(T_a) % 168.02/168.00 => 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)) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_atLeast__Suc,axiom, % 168.02/168.00 ! [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)))) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__ub__add__nat,axiom, % 168.02/168.00 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.00 => ( 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)))) % 168.02/168.00 => 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)))) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum_Oremove,axiom, % 168.02/168.00 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.00 => 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)))))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__diff1_H,axiom, % 168.02/168.00 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.00 => 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)))))) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__diff1__ring,axiom, % 168.02/168.00 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Rings_Oring(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.00 => 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)) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_setsum__diff1,axiom, % 168.02/168.00 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 168.02/168.00 ( class_Groups_Oab__group__add(T_b) % 168.02/168.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.00 => 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)) ) % 168.02/168.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.00 => 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) ) ) ) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_arith__series__general,axiom, % 168.02/168.00 ! [V_n_2,V_d_2,V_a_2,T_a] : % 168.02/168.00 ( class_Rings_Ocomm__semiring__1(T_a) % 168.02/168.00 => 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)))) ) ). % 168.02/168.00 % 168.02/168.00 fof(fact_geometric__sum,axiom, % 168.02/168.00 ! [V_n_2,V_x_2,T_a] : % 168.02/168.00 ( class_Fields_Ofield(T_a) % 168.02/168.00 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 168.02/168.00 => 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))) ) ) ). % 168.02/168.00 % 168.02/168.01 fof(fact_gauss__sum,axiom, % 168.02/168.01 ! [V_n_2,T_a] : % 168.02/168.01 ( class_Rings_Ocomm__semiring__1(T_a) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__natinterval__difff,axiom, % 168.02/168.01 ! [V_f_2,V_n_2,V_m_2,T_a] : % 168.02/168.01 ( class_Groups_Oab__group__add(T_a) % 168.02/168.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.01 => 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)))) ) % 168.02/168.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_atMost__Int__atLeast,axiom, % 168.02/168.01 ! [V_n_2,T_a] : % 168.02/168.01 ( class_Orderings_Oorder(T_a) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_ivl__disj__un_I1_J,axiom, % 168.02/168.01 ! [V_l_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__mono2,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Oordered__comm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.01 => ( ! [B_b] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 168.02/168.01 => 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))) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__bounded,axiom, % 168.02/168.01 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 168.02/168.01 & class_Rings_Osemiring__1(T_b) ) % 168.02/168.01 => ( ! [B_i] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum_Ounion__inter__neutral,axiom, % 168.02/168.01 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__eq__0__iff,axiom, % 168.02/168.01 ! [V_f_2,V_F_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/168.01 => ( 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) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 168.02/168.01 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_card__eq__setsum,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_int__setsum,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__eq__Suc0__iff,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( 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)) % 168.02/168.01 <=> ? [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 168.02/168.01 & ! [B_xa] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 168.02/168.01 => ( B_x != B_xa % 168.02/168.01 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__eq__1__iff,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( 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) % 168.02/168.01 <=> ? [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 168.02/168.01 & ! [B_xa] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 168.02/168.01 => ( B_x != B_xa % 168.02/168.01 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 168.02/168.01 ! [V_k_2,V_f_2] : % 168.02/168.01 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__diff__nat,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,V_B_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 168.02/168.01 ! [V_A_2,V_f_2,T_a] : % 168.02/168.01 ( ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.01 & class_Groups_Ocomm__monoid__mult(T_a) ) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__diff1__nat,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,V_a_2,T_a] : % 168.02/168.01 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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)) ) % 168.02/168.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__Un__nat,axiom, % 168.02/168.01 ! [V_f_2,V_B_2,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,T_a] : % 168.02/168.01 ( ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.01 & class_Groups_Ocomm__monoid__mult(T_a) ) % 168.02/168.01 => ( c_Nat__Transfer_Onat__set(V_A_2) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_arith__series__nat,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,T_a] : % 168.02/168.01 ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__Un__zero,axiom, % 168.02/168.01 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__mono3,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 168.02/168.01 ( ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 168.02/168.01 => 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))) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__nonneg__leq__bound,axiom, % 168.02/168.01 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Oordered__ab__group__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 168.02/168.01 => ( ! [B_i] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 168.02/168.01 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__nonneg__0,axiom, % 168.02/168.01 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Oordered__ab__group__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 168.02/168.01 => ( ! [B_i] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 168.02/168.01 => ( 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) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 168.02/168.01 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_sum__diff__distrib,axiom, % 168.02/168.01 ! [V_n_2,V_P_2,V_Q_2] : % 168.02/168.01 ( ! [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))) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__mono__zero__left,axiom, % 168.02/168.01 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 168.02/168.01 => 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) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__mono__zero__right,axiom, % 168.02/168.01 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 168.02/168.01 => 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) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__subset__induct,axiom, % 168.02/168.01 ! [V_P_2,V_A_2,V_F_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/168.01 => ( ! [B_a,B_F] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 168.02/168.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 168.02/168.01 => ( hBOOL(hAPP(V_P_2,B_F)) % 168.02/168.01 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 168.02/168.01 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__strict__mono,axiom, % 168.02/168.01 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 168.02/168.01 => 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))) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_field__le__mult__one__interval,axiom, % 168.02/168.01 ! [V_y,V_x,T_a] : % 168.02/168.01 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 168.02/168.01 => ( ! [B_z] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 168.02/168.01 => 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)) ) ) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__Plus,axiom, % 168.02/168.01 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_c) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/168.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(T_a,T_b),T_c),V_f_2),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(tc_sum(T_a,T_b),T_c,T_a,V_f_2),c_Sum__Type_OInl(T_a,T_b))),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(tc_sum(T_a,T_b),T_c,T_b,V_f_2),c_Sum__Type_OInr(T_b,T_a))),V_B_2)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_image__compose,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_apfst__compose,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__upd__comp,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_vimage__compose,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_o__def,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Option_Omap_Ocomp,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_o__assoc,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_o__apply,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_o__eq__dest,axiom, % 168.02/168.01 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 168.02/168.01 ( 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) % 168.02/168.01 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_o__eq__elim,axiom, % 168.02/168.01 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 168.02/168.01 ( 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) % 168.02/168.01 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_comp__cong,axiom, % 168.02/168.01 ! [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] : % 168.02/168.01 ( 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)) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_o__eq__dest__lhs,axiom, % 168.02/168.01 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 168.02/168.01 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2 % 168.02/168.01 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_K__record__comp,axiom, % 168.02/168.01 ! [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 ). % 168.02/168.01 % 168.02/168.01 fof(fact_Option_Omap_Ocompositionality,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_option__map__comp,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_inj__on__imageI2,axiom, % 168.02/168.01 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 168.02/168.01 ( 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) % 168.02/168.01 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_apsnd__compose,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_comp__surj,axiom, % 168.02/168.01 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 168.02/168.01 ( 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)) % 168.02/168.01 => ( 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)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_comp__inj__on__iff,axiom, % 168.02/168.01 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 <=> 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_comp__inj__on,axiom, % 168.02/168.01 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_inj__on__imageI,axiom, % 168.02/168.01 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 168.02/168.01 ( 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) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_inj__comp,axiom, % 168.02/168.01 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 168.02/168.01 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__reindex,axiom, % 168.02/168.01 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_c) % 168.02/168.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setprod__reindex,axiom, % 168.02/168.01 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__mult(T_c) % 168.02/168.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setprod__reindex__cong,axiom, % 168.02/168.01 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__mult(T_c) % 168.02/168.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/168.01 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 168.02/168.01 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 168.02/168.01 => 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) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum_Oreindex,axiom, % 168.02/168.01 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setprod_Oreindex,axiom, % 168.02/168.01 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_the__inv__into__comp,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 168.02/168.01 => ( 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)))) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold__image__reindex,axiom, % 168.02/168.01 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 168.02/168.01 ( class_Groups_Oab__semigroup__mult(T_c) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Oremove,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__image_Oreindex,axiom, % 168.02/168.01 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/168.01 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ounion,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => ( 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)) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_option__map__o__sum__case,axiom, % 168.02/168.01 ! [V_h_2,V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_sum(T_a,T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),c_Sum__Type_Osum_Osum__case(T_a,tc_Option_Ooption(T_d),T_b,V_g_2,V_h_2)) = c_Sum__Type_Osum_Osum__case(T_a,tc_Option_Ooption(T_c),T_b,hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_a,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_g_2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_h_2)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 168.02/168.01 ! [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] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ocommute__comp,axiom, % 168.02/168.01 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ocommute__left__comp,axiom, % 168.02/168.01 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_option__map__o__empty,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__image_Odistrib,axiom, % 168.02/168.01 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_split__comp,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_option__map__o__map__upd,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ocommute__comp_H,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ocommute__left__comp_H,axiom, % 168.02/168.01 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ocommute__comp_H_H,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 168.02/168.01 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__image_Oeq__fold,axiom, % 168.02/168.01 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Oinsert,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Ounion__inter,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding_Oinsert__remove,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Loop__sound__lemma,axiom, % 168.02/168.01 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => 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)))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_hoare__derivs_OIf,axiom, % 168.02/168.01 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => ( 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)))) % 168.02/168.01 => 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)))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Loop,axiom, % 168.02/168.01 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => 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)))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_peek__and__def,axiom, % 168.02/168.01 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 168.02/168.01 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 168.02/168.01 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__reindex__nonzero,axiom, % 168.02/168.01 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_c) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 168.02/168.01 => ! [B_y] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 168.02/168.01 => ( B_x != B_y % 168.02/168.01 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 168.02/168.01 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__idem_Ounion__idem,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__idem_Oidem__left__comp,axiom, % 168.02/168.01 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__idem_Oidem__comp,axiom, % 168.02/168.01 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__idem_Oin__comp__idem,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__idem_Oinsert__idem,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_strong__setprod__reindex__cong,axiom, % 168.02/168.01 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__mult(T_c) % 168.02/168.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/168.01 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => 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) ) % 168.02/168.01 => 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) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 168.02/168.01 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 168.02/168.01 ( ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.01 & class_Groups_Ocomm__monoid__mult(T_a) ) % 168.02/168.01 => ( V_A_2 = V_B_2 % 168.02/168.01 => ( c_Nat__Transfer_Onat__set(V_B_2) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 168.02/168.01 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 168.02/168.01 => 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) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equiv__class__nondisjoint,axiom, % 168.02/168.01 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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))))))) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equiv__intrel,axiom, % 168.02/168.01 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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equiv__class__self,axiom, % 168.02/168.01 ! [V_a_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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)))))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equiv__class__eq,axiom, % 168.02/168.01 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 => 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)))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equiv__class__eq__iff,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 <=> ( 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)))) % 168.02/168.01 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_eq__equiv__class,axiom, % 168.02/168.01 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_eq__equiv__class__iff,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 168.02/168.01 => ( 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)))) % 168.02/168.01 <=> 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equiv__class__subset,axiom, % 168.02/168.01 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 => 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)))))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_subset__equiv__class,axiom, % 168.02/168.01 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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)))))) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_card__quotient__disjoint,axiom, % 168.02/168.01 ! [V_r_2,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( 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) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_eq__equiv__class__iff2,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 168.02/168.01 => ( 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) % 168.02/168.01 <=> 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_singleton__quotient,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotient__empty,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotient__is__empty2,axiom, % 168.02/168.01 ! [V_r_2,V_A_2,T_a] : % 168.02/168.01 ( 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) % 168.02/168.01 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotient__is__empty,axiom, % 168.02/168.01 ! [V_r_2,V_A_2,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotient__disj,axiom, % 168.02/168.01 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( V_X_2 = V_Y_2 % 168.02/168.01 | 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotient__diff1,axiom, % 168.02/168.01 ! [V_a_2,V_A_2,V_r_2,T_a] : % 168.02/168.01 ( 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) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotientI,axiom, % 168.02/168.01 ! [V_r_2,V_A_2,V_x_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotient__eq__iff,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 168.02/168.01 => ( V_X_2 = V_Y_2 % 168.02/168.01 <=> 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)) ) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotient__eqI,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 168.02/168.01 => ( 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)) % 168.02/168.01 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotientE,axiom, % 168.02/168.01 ! [V_r_2,V_A_2,V_X_2,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 => ~ ! [B_x] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Integ__def,axiom, % 168.02/168.01 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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equivp__equiv,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 168.02/168.01 <=> 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_identity__equivp,axiom, % 168.02/168.01 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equivp__def,axiom, % 168.02/168.01 ! [V_R_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 168.02/168.01 <=> ! [B_x,B_y] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 168.02/168.01 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equivp__reflp,axiom, % 168.02/168.01 ! [V_x_2,V_R_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 168.02/168.01 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equivp__symp,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_R_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equivp__transp,axiom, % 168.02/168.01 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_quotient__def,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold__graph__permute__diff,axiom, % 168.02/168.01 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 168.02/168.01 ( class_Groups_Oab__semigroup__mult(T_a) % 168.02/168.01 => ( 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)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 168.02/168.01 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 168.02/168.01 ( ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.01 & class_Groups_Ocomm__monoid__mult(T_a) ) % 168.02/168.01 => ( V_A_2 = V_B_2 % 168.02/168.01 => ( c_Nat__Transfer_Onat__set(V_B_2) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 168.02/168.01 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 168.02/168.01 => 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) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP1__I,axiom, % 168.02/168.01 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__o,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__UN,axiom, % 168.02/168.01 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( 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))) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold__graph__imp__finite,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_empty__fold__graphE,axiom, % 168.02/168.01 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 => V_x_2 = V_z_2 ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold__graph_OemptyI,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold__graph_Oequations_I1_J,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Image__UN,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP1__iff,axiom, % 168.02/168.01 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> ? [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP__UN__eq,axiom, % 168.02/168.01 ! [V_x_2,V_r_2,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold__graph_OinsertI,axiom, % 168.02/168.01 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 168.02/168.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Image__eq__UN,axiom, % 168.02/168.01 ! [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))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold__graph__insert__swap,axiom, % 168.02/168.01 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 168.02/168.01 ( class_Groups_Oab__semigroup__mult(T_a) % 168.02/168.01 => ( 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)) % 168.02/168.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 168.02/168.01 => 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))) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Diff1__fold__graph,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__I,axiom, % 168.02/168.01 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__Pow__subset,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_vimage__eq__UN,axiom, % 168.02/168.01 ! [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))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__lessThan__UNIV,axiom, % 168.02/168.01 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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__atMost__UNIV,axiom, % 168.02/168.01 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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__atLeast__UNIV,axiom, % 168.02/168.01 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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__UN__finite__eq,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_ball__UN,axiom, % 168.02/168.01 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/168.01 ( ! [B_x] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hBOOL(hAPP(V_P_2,B_x)) ) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.01 => ! [B_xa] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 168.02/168.01 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__le__add__shift,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP__commute,axiom, % 168.02/168.01 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 168.02/168.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__UN__flatten,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__simps_I9_J,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__extend__simps_I9_J,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__le__eq__Un0,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP__le__iff,axiom, % 168.02/168.01 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 168.02/168.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.01 => ( 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)) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_less__SUP__iff,axiom, % 168.02/168.01 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 168.02/168.01 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.01 & class_Orderings_Olinorder(T_a) ) % 168.02/168.01 => ( 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))) % 168.02/168.01 <=> ? [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__iff,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 <=> ? [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP__const,axiom, % 168.02/168.01 ! [V_M_2,T_a,V_A_2,T_b] : % 168.02/168.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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 ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UNION__empty__conv_I2_J,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.01 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__constant,axiom, % 168.02/168.01 ! [V_ca_2,T_b,T_a,V_A_2] : % 168.02/168.01 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) % 168.02/168.01 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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 ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__empty2,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UNION__empty__conv_I1_J,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,T_a] : % 168.02/168.01 ( 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) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.01 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__subset__iff,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__extend__simps_I10_J,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_image__UN,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__simps_I10_J,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__Un,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__Un__distrib,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__simps_I5_J,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__simps_I4_J,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__extend__simps_I5_J,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Int__UN__distrib,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__extend__simps_I4_J,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Int__UN__distrib2,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUPR__apply,axiom, % 168.02/168.01 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 168.02/168.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__simps_I6_J,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__extend__simps_I6_J,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_vimage__UN,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP__subset,axiom, % 168.02/168.01 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_le__SUPI,axiom, % 168.02/168.01 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 168.02/168.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__insert__distrib,axiom, % 168.02/168.01 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__upper,axiom, % 168.02/168.01 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__absorb,axiom, % 168.02/168.01 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__simps_I1_J,axiom, % 168.02/168.01 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 168.02/168.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) % 168.02/168.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__singleton,axiom, % 168.02/168.01 ! [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 ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__extend__simps_I1_J,axiom, % 168.02/168.01 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 168.02/168.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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))) ) % 168.02/168.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__simps_I3_J,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) % 168.02/168.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__simps_I2_J,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) % 168.02/168.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__extend__simps_I3_J,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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 ) % 168.02/168.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__extend__simps_I2_J,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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 ) % 168.02/168.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__insert,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_image__eq__UN,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_minus__int__def,axiom, % 168.02/168.01 ! [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))))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__equiv__class,axiom, % 168.02/168.01 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__equiv__class2,axiom, % 168.02/168.01 ! [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] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 168.02/168.01 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 168.02/168.01 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 168.02/168.01 => 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) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP2__I,axiom, % 168.02/168.01 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Rep__Integ__inject,axiom, % 168.02/168.01 ! [V_y_2,V_x_2] : % 168.02/168.01 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 168.02/168.01 <=> V_x_2 = V_y_2 ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Rep__Integ__inverse,axiom, % 168.02/168.01 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 168.02/168.01 % 168.02/168.01 fof(fact_congruent2__implies__congruent,axiom, % 168.02/168.01 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 168.02/168.01 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Rep__Integ,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP__UN__eq2,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_congruent2D,axiom, % 168.02/168.01 ! [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] : % 168.02/168.01 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 => ( 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)) % 168.02/168.01 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_congruentD,axiom, % 168.02/168.01 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_congruent2__implies__congruent__UN,axiom, % 168.02/168.01 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 168.02/168.01 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 168.02/168.01 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_nat__def,axiom, % 168.02/168.01 ! [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)))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__equiv__class__inject,axiom, % 168.02/168.01 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 168.02/168.01 => ( 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) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => ! [B_y] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 168.02/168.01 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 168.02/168.01 => 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)) ) ) ) % 168.02/168.01 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__equiv__class__type2,axiom, % 168.02/168.01 ! [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] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 168.02/168.01 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 168.02/168.01 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( ! [B_x1] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 168.02/168.01 => ! [B_x2] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 168.02/168.01 => 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)) ) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__equiv__class__type,axiom, % 168.02/168.01 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 168.02/168.01 => ( 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))) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SUP2__iff,axiom, % 168.02/168.01 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> ? [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__finite2__subset,axiom, % 168.02/168.01 ! [V_B_2,V_k_2,V_A_2,T_a] : % 168.02/168.01 ( ! [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))) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1Set_Ointros,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 168.02/168.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__finite2__eq,axiom, % 168.02/168.01 ! [V_B_2,V_k_2,V_A_2,T_a] : % 168.02/168.01 ( ! [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) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_empty__fold1SetE,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1Set__nonempty,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_f_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 168.02/168.01 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1Set__sing,axiom, % 168.02/168.01 ! [V_b_2,V_a_2,V_f_2,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> V_a_2 = V_b_2 ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__finite__subset,axiom, % 168.02/168.01 ! [V_C_2,V_A_2,T_a] : % 168.02/168.01 ( ! [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)) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Id__on__def,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_type__definition__Integ,axiom, % 168.02/168.01 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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Id__on__def_H,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Id__on__empty,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Image__Id__on,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Id__on__eqI,axiom, % 168.02/168.01 ! [V_A_2,T_a,V_b_2,V_a_2] : % 168.02/168.01 ( V_a_2 = V_b_2 % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Id__on__iff,axiom, % 168.02/168.01 ! [V_A_2,V_y_2,V_x_2,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 <=> ( V_x_2 = V_y_2 % 168.02/168.01 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_type__definition_ORep__range,axiom, % 168.02/168.01 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 168.02/168.01 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 168.02/168.01 => 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 ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_type__definition_OAbs__image,axiom, % 168.02/168.01 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 168.02/168.01 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_type__definition_OAbs__inject,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 168.02/168.01 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 168.02/168.01 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 168.02/168.01 <=> V_x_2 = V_y_2 ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_type__definition_ORep__inverse,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 168.02/168.01 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 168.02/168.01 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_type__definition_ORep__inject,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 168.02/168.01 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 168.02/168.01 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 168.02/168.01 <=> V_x_2 = V_y_2 ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_type__definition_ORep,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 168.02/168.01 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_type__definition_OAbs__inverse,axiom, % 168.02/168.01 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 168.02/168.01 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 168.02/168.01 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Id__onE,axiom, % 168.02/168.01 ! [V_A_2,V_ca_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) % 168.02/168.01 => ~ ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_max__extp_Oequations,axiom, % 168.02/168.01 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 168.02/168.01 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 168.02/168.01 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 168.02/168.01 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 168.02/168.01 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 & ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 168.02/168.01 => ? [B_xa] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_max__ext_Ointros,axiom, % 168.02/168.01 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 168.02/168.01 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 168.02/168.01 => ? [B_xa] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 168.02/168.01 & 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)) ) ) % 168.02/168.01 => 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))) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Nitpick_Ozero__frac__def,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1Set_Oequations,axiom, % 168.02/168.01 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> ? [B_a,B_A] : % 168.02/168.01 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 168.02/168.01 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 168.02/168.01 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_insert__fold1SetE,axiom, % 168.02/168.01 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 => ~ ! [B_a,B_A] : % 168.02/168.01 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Nitpick_Oone__frac__def,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Nitpick_Ofrac__def,axiom, % 168.02/168.01 ! [V_b,V_a,T_a] : c_Nitpick_Ofrac(T_a,V_a,V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_image__split__eq__Sigma,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__Un,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_a] : % 168.02/168.01 ( class_Groups_Oab__semigroup__mult(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( 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)) % 168.02/168.01 => 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)) ) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__antimono,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => 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))) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SigmaI,axiom, % 168.02/168.01 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Times__eq__cancel2,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 168.02/168.01 => ( 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)) % 168.02/168.01 <=> V_A_2 = V_B_2 ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__Diff__distrib2,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Times__Diff__distrib1,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__Diff__distrib1,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__empty1,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_card__cartesian__product,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__cartesian__product,axiom, % 168.02/168.01 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__empty2,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Times__empty,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Compl__Times__UNIV2,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Compl__Times__UNIV1,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setprod__cartesian__product,axiom, % 168.02/168.01 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__Un__distrib1,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Times__Un__distrib1,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__Un__distrib2,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_swap__product,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__singleton__def,axiom, % 168.02/168.01 ! [V_a_2,V_f_2,T_a,V_g_2] : % 168.02/168.01 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 168.02/168.01 => 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 ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__singleton,axiom, % 168.02/168.01 ! [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 ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__cartesian__product,axiom, % 168.02/168.01 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/168.01 => 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)))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_equiv__type,axiom, % 168.02/168.01 ! [V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.01 => 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)))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__Int__distrib1,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Times__Int__distrib1,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__Int__distrib2,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Id__on__subset__Times,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UNIV__Times__UNIV,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SigmaE2,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SigmaD2,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SigmaD1,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_mem__Sigma__iff,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__one_Oeq__fold,axiom, % 168.02/168.01 ! [V_A_2,V_F_2,V_f_2,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_card__cartesian__product__singleton,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Times__subset__cancel2,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 168.02/168.01 => ( 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)))) % 168.02/168.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Image__subset,axiom, % 168.02/168.01 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__cartesian__productD1,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__cartesian__productD2,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_b,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fst__image__times,axiom, % 168.02/168.01 ! [V_A_2,T_b,T_a,V_B_2] : % 168.02/168.01 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) % 168.02/168.01 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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 ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_snd__image__times,axiom, % 168.02/168.01 ! [V_B_2,T_b,T_a,V_A_2] : % 168.02/168.01 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) % 168.02/168.01 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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 ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__def,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sup__fin_OF__eq,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( class_Lattices_Olattice(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Inf__fin_OF__eq,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( class_Lattices_Olattice(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Min_OF__eq,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Max_OF__eq,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_insert__times__insert,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__equiv__class,axiom, % 168.02/168.01 ! [V_X_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( 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)))) % 168.02/168.01 => ( 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))) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_vimage__Times,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_UN__Times__distrib,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Sigma__def,axiom, % 168.02/168.01 ! [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))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__belowI,axiom, % 168.02/168.01 ! [V_a_2,V_A_2,T_a] : % 168.02/168.01 ( class_Lattices_Osemilattice__inf(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__quotient,axiom, % 168.02/168.01 ! [V_r_2,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( 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)))) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_below__fold1__iff,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,T_a] : % 168.02/168.01 ( class_Lattices_Osemilattice__inf(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( 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))) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_min__max_Ofold1__belowI,axiom, % 168.02/168.01 ! [V_a_2,V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__insert__idem,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,T_a] : % 168.02/168.01 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_min__max_Obelow__fold1__iff,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( 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))) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__below__iff,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( 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)) % 168.02/168.01 <=> ? [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__Un2,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_a] : % 168.02/168.01 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_strict__below__fold1__iff,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( 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))) % 168.02/168.01 <=> ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__strict__below__iff,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( 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)) % 168.02/168.01 <=> ? [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__insert,axiom, % 168.02/168.01 ! [V_x_2,V_A_2,T_a] : % 168.02/168.01 ( class_Groups_Oab__semigroup__mult(T_a) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_semilattice__big_OF__eq,axiom, % 168.02/168.01 ! [V_A_2,V_F_2,V_f_2,T_a] : % 168.02/168.01 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 168.02/168.01 ! [V_A_2,V_I_2,T_b,T_a] : % 168.02/168.01 ? [B_f] : % 168.02/168.01 ( 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)) % 168.02/168.01 & 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold__image__Sigma,axiom, % 168.02/168.01 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__mult(T_c) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setprod__Sigma,axiom, % 168.02/168.01 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__mult(T_c) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__Sigma,axiom, % 168.02/168.01 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_c) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_card__SigmaI,axiom, % 168.02/168.01 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fold1__in,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( class_Groups_Oab__semigroup__mult(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( ! [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)))))) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__SigmaI,axiom, % 168.02/168.01 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( ! [B_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_hom__fold1__commute,axiom, % 168.02/168.01 ! [V_N_2,V_h_2,T_a] : % 168.02/168.01 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.02/168.01 => ( ! [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)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.01 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SigmaE,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 => ~ ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => ! [B_y] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 168.02/168.01 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair__surj,axiom, % 168.02/168.01 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 168.02/168.01 ( 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)) % 168.02/168.01 => ( 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)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair__inj__on,axiom, % 168.02/168.01 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.02/168.01 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair__imageI,axiom, % 168.02/168.01 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/168.01 ( 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)) % 168.02/168.01 => 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))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fst__comp__map__pair,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair_Ocomp,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair__compose,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair_Ocompositionality,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_snd__comp__map__pair,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_snd__prod__fun,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair__ident,axiom, % 168.02/168.01 ! [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 ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair__simp,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fst__map__pair,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair__def,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_map__pair__surj__on,axiom, % 168.02/168.01 ! [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] : % 168.02/168.01 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 168.02/168.01 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_prod__fun__imageE,axiom, % 168.02/168.01 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] : % 168.02/168.01 ( 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))) % 168.02/168.01 => ~ ! [B_x,B_y] : % 168.02/168.01 ( 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)) % 168.02/168.01 => ~ 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__on__def,axiom, % 168.02/168.01 ! [V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.02/168.01 <=> ( 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)))) % 168.02/168.01 & ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setprod__pos__nat,axiom, % 168.02/168.01 ! [V_f_2,V_S_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 168.02/168.01 => 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))) ) % 168.02/168.01 => 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))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__on__Id__on,axiom, % 168.02/168.01 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__on__empty,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__on__Un,axiom, % 168.02/168.01 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__on__Int,axiom, % 168.02/168.01 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__onD,axiom, % 168.02/168.01 ! [V_a_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__onD2,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__onD1,axiom, % 168.02/168.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 168.02/168.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.02/168.01 => ( 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)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_refl__onI,axiom, % 168.02/168.01 ! [V_A_2,V_r_2,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.01 => 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)) ) % 168.02/168.01 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__one__idem_Ohom__commute,axiom, % 168.02/168.01 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.02/168.01 => ( ! [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)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.01 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Rep__Integ__cases,axiom, % 168.02/168.01 ! [V_y_2] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 168.02/168.01 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Rep__Integ__induct,axiom, % 168.02/168.01 ! [V_P_2,V_y_2] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 168.02/168.01 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 168.02/168.01 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hAPP(V_g_2,B_x) = V_z_2 ) % 168.02/168.01 => 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)) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__left__comm__idem__remove,axiom, % 168.02/168.01 ! [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))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__left__comm__idem__sup,axiom, % 168.02/168.01 ! [T_a] : % 168.02/168.01 ( class_Lattices_Osemilattice__sup(T_a) % 168.02/168.01 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__left__comm__idem__inf,axiom, % 168.02/168.01 ! [T_a] : % 168.02/168.01 ( class_Lattices_Osemilattice__inf(T_a) % 168.02/168.01 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 168.02/168.01 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 168.02/168.01 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.02/168.01 => 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)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__left__comm__idem__insert,axiom, % 168.02/168.01 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__left__comm__idem,axiom, % 168.02/168.01 ! [T_a] : % 168.02/168.01 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.02/168.01 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 168.02/168.01 ! [T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 168.02/168.01 ! [T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 168.02/168.01 ! [V_x_2,V_f_2,T_b,T_a] : % 168.02/168.01 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_card__less__Suc2,axiom, % 168.02/168.01 ! [V_i_2,V_M_2] : % 168.02/168.01 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 168.02/168.01 => 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))))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_card__less,axiom, % 168.02/168.01 ! [V_i_2,V_M_2] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 168.02/168.01 => 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) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_card__less__Suc,axiom, % 168.02/168.01 ! [V_i_2,V_M_2] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 168.02/168.01 => 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))))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_CollectI,axiom, % 168.02/168.01 ! [T_a,V_a_2,V_P_2] : % 168.02/168.01 ( hBOOL(hAPP(V_P_2,V_a_2)) % 168.02/168.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__Collect__conjI,axiom, % 168.02/168.01 ! [V_Q_2,V_P_2,T_a] : % 168.02/168.01 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 168.02/168.01 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 168.02/168.01 => 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)))) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__Collect__less__nat,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__Collect__le__nat,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__split,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_SetCompr__Sigma__eq,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__neg__eq,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_vimage__Collect__eq,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_CollectE,axiom, % 168.02/168.01 ! [V_P_2,V_a_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 168.02/168.01 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_CollectD,axiom, % 168.02/168.01 ! [V_P_2,V_a_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 168.02/168.01 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_mem__Collect__eq,axiom, % 168.02/168.01 ! [V_P_2,V_a_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 168.02/168.01 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__mem__eq,axiom, % 168.02/168.01 ! [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 ). % 168.02/168.01 % 168.02/168.01 fof(fact_insert__Collect,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__Collect__disjI,axiom, % 168.02/168.01 ! [V_Q_2,V_P_2,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 168.02/168.01 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_empty__Collect__eq,axiom, % 168.02/168.01 ! [V_P_2,T_a] : % 168.02/168.01 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 168.02/168.01 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__empty__eq,axiom, % 168.02/168.01 ! [V_P_2,T_a] : % 168.02/168.01 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_empty__def,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__disj__eq,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__conj__eq,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__def,axiom, % 168.02/168.01 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 168.02/168.01 % 168.02/168.01 fof(fact_UNIV__def,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_insert__compr,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_insert__compr__raw,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Un__def,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Int__Collect,axiom, % 168.02/168.01 ! [V_P_2,V_A_2,V_x_2,T_a] : % 168.02/168.01 ( 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)))) % 168.02/168.01 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.01 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Int__def,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_singleton__conv2,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_singleton__conv,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__conv__if2,axiom, % 168.02/168.01 ! [T_a,V_a_2,V_P_2] : % 168.02/168.01 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 168.02/168.01 => 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))) ) % 168.02/168.01 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__conv__if,axiom, % 168.02/168.01 ! [T_a,V_a_2,V_P_2] : % 168.02/168.01 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 168.02/168.01 => 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))) ) % 168.02/168.01 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_set__diff__eq,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__Collect__not,axiom, % 168.02/168.01 ! [V_P_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 168.02/168.01 => ( 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)))) % 168.02/168.01 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_insert__def,axiom, % 168.02/168.01 ! [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) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Compl__eq,axiom, % 168.02/168.01 ! [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))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_vimage__def,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Collect__imp__eq,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_dom__def,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__M__bounded__by__nat,axiom, % 168.02/168.01 ! [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))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__setsum__restrict,axiom, % 168.02/168.01 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_c) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 168.02/168.01 => 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) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_if__image__distrib,axiom, % 168.02/168.01 ! [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))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_dom__if,axiom, % 168.02/168.01 ! [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)))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_nat__seg__image__imp__finite,axiom, % 168.02/168.01 ! [V_n_2,V_f_2,T_a,V_A_2] : % 168.02/168.01 ( 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))) % 168.02/168.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__restrict__set_H,axiom, % 168.02/168.01 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__image__gen,axiom, % 168.02/168.01 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.01 => 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)) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_Image__singleton,axiom, % 168.02/168.01 ! [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)) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__cases,axiom, % 168.02/168.01 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 168.02/168.01 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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))))) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_dom__override__on,axiom, % 168.02/168.01 ! [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))))) ). % 168.02/168.01 % 168.02/168.01 fof(fact_setsum__multicount,axiom, % 168.02/168.01 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 168.02/168.01 => ( ! [B_x] : % 168.02/168.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 168.02/168.01 => 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 ) % 168.02/168.01 => 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)) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 168.02/168.01 ! [V_B_2,V_A_2,T_a] : % 168.02/168.01 ( class_Orderings_Olinorder(T_a) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.01 => 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))))))) ) ) ) ) ) ). % 168.02/168.01 % 168.02/168.01 fof(fact_finite__Collect__subsets,axiom, % 168.02/168.01 ! [V_A_2,T_a] : % 168.02/168.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.01 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Pow__Compl,axiom, % 168.02/168.02 ! [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))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Pow__def,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__Collect__bounded__ex,axiom, % 168.02/168.02 ! [V_Q_2,T_b,V_P_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 168.02/168.02 => ( 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))))) % 168.02/168.02 <=> ! [B_y] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,B_y)) % 168.02/168.02 => 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)))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__image__set,axiom, % 168.02/168.02 ! [V_f_2,T_b,V_P_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 168.02/168.02 => 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))))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_override__on__apply__notin,axiom, % 168.02/168.02 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 168.02/168.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_override__on__apply__in,axiom, % 168.02/168.02 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_override__on__emptyset,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_inj__graph,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_override__on__def,axiom, % 168.02/168.02 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 168.02/168.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.02 => 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) ) % 168.02/168.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__psubset__def,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_ran__def,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inv__image__def,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_add__Min__commute,axiom, % 168.02/168.02 ! [V_k_2,V_N_2,T_a] : % 168.02/168.02 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.02 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_add__Max__commute,axiom, % 168.02/168.02 ! [V_k_2,V_N_2,T_a] : % 168.02/168.02 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.02/168.02 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sup__Inf1__distrib,axiom, % 168.02/168.02 ! [V_x_2,V_A_2,T_a] : % 168.02/168.02 ( class_Lattices_Odistrib__lattice(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sup__Inf2__distrib,axiom, % 168.02/168.02 ! [V_B_2,V_A_2,T_a] : % 168.02/168.02 ( class_Lattices_Odistrib__lattice(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))))) ) ) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inf__Sup1__distrib,axiom, % 168.02/168.02 ! [V_x_2,V_A_2,T_a] : % 168.02/168.02 ( class_Lattices_Odistrib__lattice(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inf__Sup2__distrib,axiom, % 168.02/168.02 ! [V_B_2,V_A_2,T_a] : % 168.02/168.02 ( class_Lattices_Odistrib__lattice(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))))) ) ) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 168.02/168.02 ! [V_x_2,V_A_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 168.02/168.02 ! [V_x_2,V_A_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 168.02/168.02 ! [V_B_2,V_A_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.02/168.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 => 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))))))) ) ) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nitpick_Oprod__def,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_int__ge__less__than__def,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_int__ge__less__than2__def,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_reflp__def,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Predicate_Oreflp(T_a,V_r_2) % 168.02/168.02 <=> 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_setsum__mult__setsum__if__inj,axiom, % 168.02/168.02 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 168.02/168.02 ( class_Rings_Osemiring__0(T_c) % 168.02/168.02 => ( 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))) % 168.02/168.02 => 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))))))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_setsum__multicount__gen,axiom, % 168.02/168.02 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 168.02/168.02 => ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 168.02/168.02 => 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) ) % 168.02/168.02 => 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) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inj__on__id,axiom, % 168.02/168.02 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__pair_Oidentity,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__pair_Oid,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_apfst__id,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_id__def,axiom, % 168.02/168.02 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 168.02/168.02 % 168.02/168.02 fof(fact_id__apply,axiom, % 168.02/168.02 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 168.02/168.02 % 168.02/168.02 fof(fact_Option_Omap_Oid,axiom, % 168.02/168.02 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_reflpE,axiom, % 168.02/168.02 ! [V_x_2,V_r_2,T_a] : % 168.02/168.02 ( c_Predicate_Oreflp(T_a,V_r_2) % 168.02/168.02 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_apsnd__id,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Option_Omap_Oidentity,axiom, % 168.02/168.02 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_of__int__eq__id,axiom, % 168.02/168.02 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 168.02/168.02 % 168.02/168.02 fof(fact_vimage__id,axiom, % 168.02/168.02 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 168.02/168.02 % 168.02/168.02 fof(fact_id__o,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_o__id,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_o__eq__id__dest,axiom, % 168.02/168.02 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 168.02/168.02 ( 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) % 168.02/168.02 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_image__id,axiom, % 168.02/168.02 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 168.02/168.02 % 168.02/168.02 fof(fact_surj__id,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_folding_Oempty,axiom, % 168.02/168.02 ! [V_F_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.02/168.02 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_apfst__def,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_apsnd__def,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_split__Pair,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_setsum__reindex__id,axiom, % 168.02/168.02 ! [V_B_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.02 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_setprod__reindex__id,axiom, % 168.02/168.02 ! [V_B_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.02/168.02 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__conv__nat__seg__image,axiom, % 168.02/168.02 ! [V_A_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 <=> ? [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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__def,axiom, % 168.02/168.02 ! [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))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__Collect__split,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__compI,axiom, % 168.02/168.02 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_RangeI,axiom, % 168.02/168.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__UNION__distrib,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__UNION__distrib2,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__Id__on,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__mono,axiom, % 168.02/168.02 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__distrib2,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__distrib,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__empty1,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__empty2,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_O__assoc,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_union__comp__emptyR,axiom, % 168.02/168.02 ! [V_C_2,V_B_2,V_A_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_union__comp__emptyL,axiom, % 168.02/168.02 ! [V_B_2,V_C_2,V_A_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__empty,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__empty__iff,axiom, % 168.02/168.02 ! [V_r_2,T_a,T_b] : % 168.02/168.02 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_rel__comp__subset__Sigma,axiom, % 168.02/168.02 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => ( 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)))) % 168.02/168.02 => 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)))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__Un__eq,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__Range,axiom, % 168.02/168.02 ! [V_r_2,T_b,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 168.02/168.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_snd__eq__Range,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__iff,axiom, % 168.02/168.02 ! [V_r_2,T_b,V_a_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 168.02/168.02 <=> ? [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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__insert,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__Int__subset,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Range__Diff__subset,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_max__ext__compat,axiom, % 168.02/168.02 ! [V_S_2,V_R_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_min__ext__compat,axiom, % 168.02/168.02 ! [V_S_2,V_R_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_RangeP__Range__eq,axiom, % 168.02/168.02 ! [V_x_2,V_r_2,T_b,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_RangeE,axiom, % 168.02/168.02 ! [V_r_2,T_b,V_b_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 168.02/168.02 => ~ ! [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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_RangeP_Ointros,axiom, % 168.02/168.02 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 168.02/168.02 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_RangeP_Oequations,axiom, % 168.02/168.02 ! [V_a2_2,V_r_2,T_b,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 168.02/168.02 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_pred__comp__rel__comp__eq,axiom, % 168.02/168.02 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 <=> 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_reduction__pairI,axiom, % 168.02/168.02 ! [V_S_2,V_R_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__less__than,axiom, % 168.02/168.02 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 168.02/168.02 % 168.02/168.02 fof(fact_pred__comp_Ointros,axiom, % 168.02/168.02 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 168.02/168.02 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 168.02/168.02 => c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__empty,axiom, % 168.02/168.02 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__inv__image,axiom, % 168.02/168.02 ! [V_f_2,T_b,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__lex__prod,axiom, % 168.02/168.02 ! [V_rb_2,T_b,V_ra_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_ra_2) % 168.02/168.02 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 168.02/168.02 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__measure,axiom, % 168.02/168.02 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__comp__self,axiom, % 168.02/168.02 ! [V_R_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 168.02/168.02 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_min__ext__wf,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__subset,axiom, % 168.02/168.02 ! [V_p_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => ( 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)) % 168.02/168.02 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_acc__wfD,axiom, % 168.02/168.02 ! [V_x_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__acc__iff,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__finite__psubset,axiom, % 168.02/168.02 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__mlex,axiom, % 168.02/168.02 ! [V_f_2,V_R_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 168.02/168.02 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__Int1,axiom, % 168.02/168.02 ! [V_r_H_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__Int2,axiom, % 168.02/168.02 ! [V_r_H_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_max__ext__wf,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_pred__comp_Oequations,axiom, % 168.02/168.02 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 168.02/168.02 ( c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a1_2,V_a3_2) % 168.02/168.02 <=> ? [B_b] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 168.02/168.02 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__pair__less,axiom, % 168.02/168.02 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__irrefl,axiom, % 168.02/168.02 ! [V_a_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => ~ 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__asym,axiom, % 168.02/168.02 ! [V_x_2,V_a_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => ( 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)) % 168.02/168.02 => ~ 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__not__sym,axiom, % 168.02/168.02 ! [V_x_2,V_a_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => ( 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)) % 168.02/168.02 => ~ 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__not__refl,axiom, % 168.02/168.02 ! [V_a_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => ~ 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__int__ge__less__than,axiom, % 168.02/168.02 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__int__ge__less__than2,axiom, % 168.02/168.02 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__less,axiom, % 168.02/168.02 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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__no__loop,axiom, % 168.02/168.02 ! [V_R_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__union__merge,axiom, % 168.02/168.02 ! [V_S_2,V_R_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 <=> 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 <=> ~ ? [B_f] : % 168.02/168.02 ! [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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wfE__pf,axiom, % 168.02/168.02 ! [V_A_2,V_R_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 168.02/168.02 => ( 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))) % 168.02/168.02 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__union__compatible,axiom, % 168.02/168.02 ! [V_S_2,V_R_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 168.02/168.02 => ( c_Wellfounded_Owf(T_a,V_S_2) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf,axiom, % 168.02/168.02 ! [T_a] : % 168.02/168.02 ( class_Orderings_Owellorder(T_a) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_reduction__pair__def,axiom, % 168.02/168.02 ! [V_P_2,T_a] : % 168.02/168.02 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 168.02/168.02 <=> ( 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)) % 168.02/168.02 & 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_reduction__pair__lemma,axiom, % 168.02/168.02 ! [V_S_2,V_R_2,V_P_2,T_a] : % 168.02/168.02 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 168.02/168.02 => ( 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))) % 168.02/168.02 => ( 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))) % 168.02/168.02 => ( c_Wellfounded_Owf(T_a,V_S_2) % 168.02/168.02 => 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)) ) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__map__pair__image,axiom, % 168.02/168.02 ! [V_f_2,T_b,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__lenlex,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__Un,axiom, % 168.02/168.02 ! [V_s_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => ( c_Wellfounded_Owf(T_a,V_s_2) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_DomainI,axiom, % 168.02/168.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__Id__on,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__empty__iff,axiom, % 168.02/168.02 ! [V_r_2,T_b,T_a] : % 168.02/168.02 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__empty,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__mono,axiom, % 168.02/168.02 ! [V_s_2,V_r_2,T_b,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__Un__eq,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__Domain,axiom, % 168.02/168.02 ! [V_r_2,T_b,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 168.02/168.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_fst__eq__Domain,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__iff,axiom, % 168.02/168.02 ! [V_r_2,T_b,V_a_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 168.02/168.02 <=> ? [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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__insert,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__Int__subset,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__Diff__subset,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Field__def,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Domain__Collect__split,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_pred__nat__def,axiom, % 168.02/168.02 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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_DomainP__Domain__eq,axiom, % 168.02/168.02 ! [V_x_2,V_r_2,T_b,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_DomainP_Ointros,axiom, % 168.02/168.02 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 168.02/168.02 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_DomainP_Oequations,axiom, % 168.02/168.02 ! [V_a1_2,V_r_2,T_b,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 168.02/168.02 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__pred__nat,axiom, % 168.02/168.02 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__lex,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__lexn,axiom, % 168.02/168.02 ! [V_n_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lex__def,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexn_Osimps_I1_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_DomainE,axiom, % 168.02/168.02 ! [V_r_2,T_b,V_a_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 168.02/168.02 => ~ ! [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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__same__fst,axiom, % 168.02/168.02 ! [T_a,V_R_2,T_b,V_P_2] : % 168.02/168.02 ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,B_x)) % 168.02/168.02 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 168.02/168.02 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__if__measure,axiom, % 168.02/168.02 ! [T_a,V_g_2,V_f_2,V_P_2] : % 168.02/168.02 ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,B_x)) % 168.02/168.02 => 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))) ) % 168.02/168.02 => 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))))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wfP__def,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 168.02/168.02 <=> 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wfP__empty,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wfP__subset,axiom, % 168.02/168.02 ! [V_p_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 168.02/168.02 => ( 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)) % 168.02/168.02 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_accp__wfPD,axiom, % 168.02/168.02 ! [V_x_2,V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 168.02/168.02 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wfP__accp__iff,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 168.02/168.02 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__in__rel,axiom, % 168.02/168.02 ! [V_R_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 168.02/168.02 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wfP__wf__eq,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wfP__acyclicP,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_pigeonhole__infinite,axiom, % 168.02/168.02 ! [V_f_2,T_b,V_A_2,T_a] : % 168.02/168.02 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 168.02/168.02 => ? [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.02 & ~ 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)))))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__acyclic,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_acyclic__subset,axiom, % 168.02/168.02 ! [V_r_2,V_s_2,T_a] : % 168.02/168.02 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 168.02/168.02 => ( 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)) % 168.02/168.02 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__acyclic__wf,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 168.02/168.02 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 168.02/168.02 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_wf__iff__acyclic__if__finite,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 168.02/168.02 => ( c_Wellfounded_Owf(T_a,V_r_2) % 168.02/168.02 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nitpick_Owf_H__def,axiom, % 168.02/168.02 ! [V_r_2,T_a] : % 168.02/168.02 ( c_Nitpick_Owf_H(T_a,V_r_2) % 168.02/168.02 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 168.02/168.02 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 168.02/168.02 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_refl__on__def_H,axiom, % 168.02/168.02 ! [V_r_2,V_A_2,T_a] : % 168.02/168.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.02/168.02 <=> ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 168.02/168.02 => 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)) ) % 168.02/168.02 & ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.02 => 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)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_ball__empty,axiom, % 168.02/168.02 ! [V_P_2,T_a,B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/168.02 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_ball__UNIV,axiom, % 168.02/168.02 ! [V_P_2,T_a] : % 168.02/168.02 ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 168.02/168.02 => hBOOL(hAPP(V_P_2,B_x)) ) % 168.02/168.02 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Powp__def,axiom, % 168.02/168.02 ! [V_B_2,V_A_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 168.02/168.02 <=> ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 168.02/168.02 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_congruent__def,axiom, % 168.02/168.02 ! [V_f_2,V_r_2,T_b,T_a] : % 168.02/168.02 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 168.02/168.02 <=> ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Abs__Integ__induct,axiom, % 168.02/168.02 ! [V_x_2,V_P_2] : % 168.02/168.02 ( ! [B_y] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 168.02/168.02 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 168.02/168.02 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Abs__Integ__cases,axiom, % 168.02/168.02 ! [V_x_2] : % 168.02/168.02 ~ ! [B_y] : % 168.02/168.02 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 168.02/168.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_triples__valid__Suc,axiom, % 168.02/168.02 ! [V_n_2,V_ts_2,T_a] : % 168.02/168.02 ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 168.02/168.02 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 168.02/168.02 => ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 168.02/168.02 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_hoare__valids__def,axiom, % 168.02/168.02 ! [V_ts_2,V_G_2,T_a] : % 168.02/168.02 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) % 168.02/168.02 <=> ! [B_n] : % 168.02/168.02 ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_G_2)) % 168.02/168.02 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 168.02/168.02 => ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 168.02/168.02 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__range__map__of__map__add,axiom, % 168.02/168.02 ! [V_l_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( 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))))) % 168.02/168.02 => 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))))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__UN__I,axiom, % 168.02/168.02 ! [V_B_2,T_b,V_A_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => ( ! [B_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 168.02/168.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__dom__map__of,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__range__map__of,axiom, % 168.02/168.02 ! [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))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__add__map__of__foldr,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__mapk__SomeI,axiom, % 168.02/168.02 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 168.02/168.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 168.02/168.02 => ( 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) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inj__mapI,axiom, % 168.02/168.02 ! [V_f_2,T_b,T_a] : % 168.02/168.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inj__map,axiom, % 168.02/168.02 ! [V_f_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inj__map__eq__map,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 168.02/168.02 => ( 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) % 168.02/168.02 <=> V_xs_2 = V_ys_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inj__mapD,axiom, % 168.02/168.02 ! [V_f_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__injective,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 168.02/168.02 => V_xs_2 = V_ys_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_foldr__map,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_List_Omap_Ocomp,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__comp__map,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_List_Omap_Ocompositionality,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__map,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__ident,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 168.02/168.02 % 168.02/168.02 fof(fact_List_Omap_Oidentity,axiom, % 168.02/168.02 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_List_Omap_Oid,axiom, % 168.02/168.02 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__map,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__map__restrict,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_body__def,axiom, % 168.02/168.02 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__set,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__map,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__eq__conv,axiom, % 168.02/168.02 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( 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) % 168.02/168.02 <=> ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 168.02/168.02 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_infinite__UNIV__listI,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_WT__bodies__def,axiom, % 168.02/168.02 ( c_Com_OWT__bodies % 168.02/168.02 <=> ! [B_x] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__inj__on,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( 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))) % 168.02/168.02 => V_xs_2 = V_ys_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_inj__on__map__eq__map,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( 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) % 168.02/168.02 <=> V_xs_2 = V_ys_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__fun__upd,axiom, % 168.02/168.02 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 168.02/168.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__eq__dom,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,T_b,T_a] : % 168.02/168.02 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__is__SomeD,axiom, % 168.02/168.02 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 168.02/168.02 ( 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) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__SomeD,axiom, % 168.02/168.02 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 168.02/168.02 ( 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) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_dom__map__of__conv__image__fst,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__eq__None__iff,axiom, % 168.02/168.02 ! [V_x_2,V_xys_2,T_a,T_b] : % 168.02/168.02 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 168.02/168.02 <=> ~ 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__map__keys,axiom, % 168.02/168.02 ! [V_m_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 168.02/168.02 => 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 ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_ran__distinct,axiom, % 168.02/168.02 ! [V_al_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__map__of__compr,axiom, % 168.02/168.02 ! [V_xs_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__map,axiom, % 168.02/168.02 ! [V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 168.02/168.02 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 168.02/168.02 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__inject__set,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( 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))) % 168.02/168.02 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 168.02/168.02 <=> 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) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Some__eq__map__of__iff,axiom, % 168.02/168.02 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( 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) % 168.02/168.02 <=> 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__eq__Some__iff,axiom, % 168.02/168.02 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( 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) % 168.02/168.02 <=> 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__is__SomeI,axiom, % 168.02/168.02 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( 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))) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_greaterThanLessThan__upto,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_weak__map__of__SomeI,axiom, % 168.02/168.02 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ? [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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__upto,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_atLeastAtMost__upto,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__upto,axiom, % 168.02/168.02 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_atLeastLessThan__upto,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_greaterThanAtMost__upto,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nat__list__def,axiom, % 168.02/168.02 ! [V_l_2] : % 168.02/168.02 ( c_List_Onat__list(V_l_2) % 168.02/168.02 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__remove1__eq,axiom, % 168.02/168.02 ! [V_x_2,V_xs_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_remove1__commute,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__remove1,axiom, % 168.02/168.02 ! [V_x,V_xs,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.02/168.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_in__set__remove1,axiom, % 168.02/168.02 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 168.02/168.02 ( V_a_2 != V_b_2 % 168.02/168.02 => ( 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)))) % 168.02/168.02 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_notin__set__remove1,axiom, % 168.02/168.02 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => ~ 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_remove1__idem,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__remove1__subset,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sorted__list__of__set__remove,axiom, % 168.02/168.02 ! [V_x_2,V_A_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__zip__map,axiom, % 168.02/168.02 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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)) ) % 168.02/168.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__zipI1,axiom, % 168.02/168.02 ! [V_ys,T_b,V_xs,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.02/168.02 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__zipI2,axiom, % 168.02/168.02 ! [V_xs,T_b,V_ys,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 168.02/168.02 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__same__conv__map,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__map__fst__snd,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__zip__map2,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__zip__map,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_in__set__zipE,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__zip__rightD,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__zip__leftD,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__same,axiom, % 168.02/168.02 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 & V_a_2 = V_b_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__map2,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__map1,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__map__map,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sorted__list__of__set__insert,axiom, % 168.02/168.02 ! [V_x_2,V_A_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => 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)))))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__zip__upd,axiom, % 168.02/168.02 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( 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) % 168.02/168.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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)) ) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__zip,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexn__length,axiom, % 168.02/168.02 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 168.02/168.02 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__insort,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( class_Orderings_Olinorder(T_b) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_neq__if__length__neq,axiom, % 168.02/168.02 ! [V_ys,V_xs,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => V_xs != V_ys ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__left__comm,axiom, % 168.02/168.02 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__key__left__comm,axiom, % 168.02/168.02 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__eq__imp__length__eq,axiom, % 168.02/168.02 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( 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) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__map,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_remove1__insort,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => 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 ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__insort,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( class_Orderings_Olinorder(T_b) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_card__length,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_card__distinct,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__card,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__zip__inject,axiom, % 168.02/168.02 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( 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) % 168.02/168.02 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 168.02/168.02 => ( 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)) % 168.02/168.02 => V_ys_2 = V_zs_2 ) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__fst__zip,axiom, % 168.02/168.02 ! [V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => 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 ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__snd__zip,axiom, % 168.02/168.02 ! [V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => 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 ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__insort,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( class_Orderings_Olinorder(T_b) % 168.02/168.02 => ( 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))) % 168.02/168.02 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__pos__if__in__set,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__eq__conv,axiom, % 168.02/168.02 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 168.02/168.02 <=> ( 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 % 168.02/168.02 & 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 ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lenlex__conv,axiom, % 168.02/168.02 ! [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)))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lenlex__def,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__lists__length__eq,axiom, % 168.02/168.02 ! [V_n_2,V_A_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => 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))))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__eq__iff__zip__eq,axiom, % 168.02/168.02 ! [T_a,V_ys_2,V_xs_2] : % 168.02/168.02 ( V_xs_2 = V_ys_2 % 168.02/168.02 <=> ( 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) % 168.02/168.02 & ! [B_x] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__zip__is__None,axiom, % 168.02/168.02 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( 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) % 168.02/168.02 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__zip__is__Some,axiom, % 168.02/168.02 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 <=> ? [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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__remove1,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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)) ) % 168.02/168.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_dom__map__of__zip,axiom, % 168.02/168.02 ! [V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_finite__lists__length__le,axiom, % 168.02/168.02 ! [V_n_2,V_A_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => 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))))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__iff__zip,axiom, % 168.02/168.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( 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) % 168.02/168.02 & ! [B_x] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => 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)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__sublist,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__eq__len,axiom, % 168.02/168.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__sublistI,axiom, % 168.02/168.02 ! [V_I_2,V_xs_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__mono,axiom, % 168.02/168.02 ! [V_s_2,V_r_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_in__set__sublistD,axiom, % 168.02/168.02 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_notin__set__sublistI,axiom, % 168.02/168.02 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => ~ 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__sublist__subset,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrelp__listrel__eq,axiom, % 168.02/168.02 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 <=> 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexn_Osimps_I2_J,axiom, % 168.02/168.02 ! [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)))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_impossible__Cons,axiom, % 168.02/168.02 ! [V_x,V_ys,V_xs,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__ConsD,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => ( V_y_2 = V_x_2 % 168.02/168.02 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__Cons__Cons,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__subset__Cons,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_List_Oset_Osimps_I2_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_foldr_Osimps_I2_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrelp_OCons,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 168.02/168.02 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrelp_Oequations_I2_J,axiom, % 168.02/168.02 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 168.02/168.02 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Oinject,axiom, % 168.02/168.02 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 <=> ( V_a_2 = V_a_H_2 % 168.02/168.02 & V_list_2 = V_list_H_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_not__Cons__self2,axiom, % 168.02/168.02 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 168.02/168.02 % 168.02/168.02 fof(fact_not__Cons__self,axiom, % 168.02/168.02 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map_Osimps_I2_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_remove1_Osimps_I2_J,axiom, % 168.02/168.02 ! [V_xs,T_a,V_y,V_x] : % 168.02/168.02 ( ( V_x = V_y % 168.02/168.02 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 168.02/168.02 & ( V_x != V_y % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__key_Osimps_I2_J,axiom, % 168.02/168.02 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( ( 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))) % 168.02/168.02 => 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)) ) % 168.02/168.02 & ( ~ 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))) % 168.02/168.02 => 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)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct_Osimps_I2_J,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 168.02/168.02 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__Cons__code_I2_J,axiom, % 168.02/168.02 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 168.02/168.02 ( ( V_l = V_k % 168.02/168.02 => 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) ) % 168.02/168.02 & ( V_l != V_k % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Osize_I4_J,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel_OCons,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => ( 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))) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of_Osimps_I2_J,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Cons__in__lex,axiom, % 168.02/168.02 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( ( 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)) % 168.02/168.02 & 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) ) % 168.02/168.02 | ( V_x_2 = V_y_2 % 168.02/168.02 & 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))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__Cons,axiom, % 168.02/168.02 ! [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))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__Cons__def,axiom, % 168.02/168.02 ! [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)))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__Cons1,axiom, % 168.02/168.02 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ~ ! [B_y,B_ys] : % 168.02/168.02 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 168.02/168.02 => ( 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)) % 168.02/168.02 => ~ 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))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__Cons2,axiom, % 168.02/168.02 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ~ ! [B_x,B_xs] : % 168.02/168.02 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 168.02/168.02 => ( 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)) % 168.02/168.02 => ~ 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))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__insert__insort__key,axiom, % 168.02/168.02 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( ~ 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)))) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexord__cons__cons,axiom, % 168.02/168.02 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( 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)) % 168.02/168.02 | ( V_a_2 = V_b_2 % 168.02/168.02 & 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))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__insort__insert,axiom, % 168.02/168.02 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 168.02/168.02 ( class_Orderings_Olinorder(T_b) % 168.02/168.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__insert__triv,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__insort__insert,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__insert__key__triv,axiom, % 168.02/168.02 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( 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)))) % 168.02/168.02 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexord__lex,axiom, % 168.02/168.02 ! [V_r_2,V_y_2,V_x_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( 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))) % 168.02/168.02 & 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__insert__insort,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__zip,axiom, % 168.02/168.02 ! [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)))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Osize_I2_J,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__Cons__Suc,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__Cons__0,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__zip,axiom, % 168.02/168.02 ! [V_ys,T_b,V_xs,T_a,V_i] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( 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))) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__eq__iff__nth__eq,axiom, % 168.02/168.02 ! [T_a,V_ys_2,V_xs_2] : % 168.02/168.02 ( V_xs_2 = V_ys_2 % 168.02/168.02 <=> ( 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) % 168.02/168.02 & ! [B_i] : % 168.02/168.02 ( 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))) % 168.02/168.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__size__map,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth_Osimps,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_all__set__conv__all__nth,axiom, % 168.02/168.02 ! [V_P_2,V_xs_2,T_a] : % 168.02/168.02 ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => hBOOL(hAPP(V_P_2,B_x)) ) % 168.02/168.02 <=> ! [B_i] : % 168.02/168.02 ( 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))) % 168.02/168.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__map,axiom, % 168.02/168.02 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__conv__nth,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 <=> ! [B_i] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ! [B_j] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( B_i != B_j % 168.02/168.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__eq__iff__index__eq,axiom, % 168.02/168.02 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => ( 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))) % 168.02/168.02 => ( 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))) % 168.02/168.02 => ( 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) % 168.02/168.02 <=> V_i_2 = V_j_2 ) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_in__set__conv__nth,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 <=> ? [B_i] : % 168.02/168.02 ( 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))) % 168.02/168.02 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__mem,axiom, % 168.02/168.02 ! [V_xs_2,T_a,V_n_2] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__Cons_H,axiom, % 168.02/168.02 ! [V_xs,V_x,T_a,V_n] : % 168.02/168.02 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 168.02/168.02 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__conv__nth,axiom, % 168.02/168.02 ! [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))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__Cons__number__of,axiom, % 168.02/168.02 ! [V_xs,V_x,T_a,V_v] : % 168.02/168.02 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 => 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 ) % 168.02/168.02 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__size__estimation,axiom, % 168.02/168.02 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__size__estimation_H,axiom, % 168.02/168.02 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__sublist,axiom, % 168.02/168.02 ! [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))))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__iff__nth,axiom, % 168.02/168.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( 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) % 168.02/168.02 & ! [B_n] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexord__take__index__conv,axiom, % 168.02/168.02 ! [V_r_2,V_y_2,V_x_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( ( 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))) % 168.02/168.02 & 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 ) % 168.02/168.02 | ? [B_i] : % 168.02/168.02 ( 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)))) % 168.02/168.02 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 168.02/168.02 & 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)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__list__update,axiom, % 168.02/168.02 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => ( ~ 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)))))) % 168.02/168.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__list__update__neq,axiom, % 168.02/168.02 ! [V_x,V_xs,T_a,V_j,V_i] : % 168.02/168.02 ( V_i != V_j % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__id,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__take,axiom, % 168.02/168.02 ! [V_xs,T_a,V_n,V_i] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__all,axiom, % 168.02/168.02 ! [V_n,V_xs,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__beyond,axiom, % 168.02/168.02 ! [V_x,V_i,V_xs,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__take__subset,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__take,axiom, % 168.02/168.02 ! [V_i,V_xs,T_a] : % 168.02/168.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.02/168.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__update,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__map,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__overwrite,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__swap,axiom, % 168.02/168.02 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 168.02/168.02 ( V_i != V_i_H % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__take,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_update__zip,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__zip,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__update,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__take,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__list__update,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_in__set__takeD,axiom, % 168.02/168.02 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__code_I2_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update_Osimps_I2_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__code_I3_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__Suc__Cons,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sublist__upt__eq__take,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__take__subset__set__take,axiom, % 168.02/168.02 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__update__subsetI,axiom, % 168.02/168.02 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__update__subset__insert,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__list__update,axiom, % 168.02/168.02 ! [V_x,V_j,V_xs,T_a,V_i] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( ( V_i = V_j % 168.02/168.02 => 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 ) % 168.02/168.02 & ( V_i != V_j % 168.02/168.02 => 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) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__same__conv,axiom, % 168.02/168.02 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 168.02/168.02 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__list__update__eq,axiom, % 168.02/168.02 ! [V_x,V_xs,T_a,V_i] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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 ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__update__memI,axiom, % 168.02/168.02 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__upd__upds__conv__if,axiom, % 168.02/168.02 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 168.02/168.02 ( ( 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)))) % 168.02/168.02 => 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) ) % 168.02/168.02 & ( ~ 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)))) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__subset,axiom, % 168.02/168.02 ! [V_A_2,V_r_2,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => 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))))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__add__upds,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__le__upds,axiom, % 168.02/168.02 ! [V_bs_2,V_as_2,V_g_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( c_Map_Omap__le(T_a,T_b,V_f_2,V_g_2) % 168.02/168.02 => c_Map_Omap__le(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_f_2,V_as_2,V_bs_2),c_Map_Omap__upds(T_a,T_b,V_g_2,V_as_2,V_bs_2)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lists__mono,axiom, % 168.02/168.02 ! [V_B_2,V_A_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__upds__apply__nontin,axiom, % 168.02/168.02 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lists__UNIV,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_equiv__listrel,axiom, % 168.02/168.02 ! [V_r_2,V_A_2,T_a] : % 168.02/168.02 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__refl__on,axiom, % 168.02/168.02 ! [V_r_2,V_A_2,T_a] : % 168.02/168.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__upds__Cons,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Cons__in__lists__iff,axiom, % 168.02/168.02 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.02/168.02 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_in__lists__conv__set,axiom, % 168.02/168.02 ! [V_A_2,V_xs_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 168.02/168.02 <=> ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__upds__list__update2__drop,axiom, % 168.02/168.02 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => ( 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))) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__upds__twist,axiom, % 168.02/168.02 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 168.02/168.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lists__eq__set,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_restrict__map__upds,axiom, % 168.02/168.02 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( 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)) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_dom__map__upds,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel1__subset__listrel,axiom, % 168.02/168.02 ! [V_r_H_2,V_r_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 168.02/168.02 => 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexord__linear,axiom, % 168.02/168.02 ! [V_y_2,V_x_2,V_r_2,T_a] : % 168.02/168.02 ( ! [B_a,B_b] : % 168.02/168.02 ( 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)) % 168.02/168.02 | B_a = B_b % 168.02/168.02 | 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)) ) % 168.02/168.02 => ( 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))) % 168.02/168.02 | V_x_2 = V_y_2 % 168.02/168.02 | 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))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Cons__acc__listrel1I,axiom, % 168.02/168.02 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 168.02/168.02 => ( 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)))) % 168.02/168.02 => 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)))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel1__mono,axiom, % 168.02/168.02 ! [V_s_2,V_r_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel1I2,axiom, % 168.02/168.02 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel1__eq__len,axiom, % 168.02/168.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lists__accI,axiom, % 168.02/168.02 ! [V_r_2,V_xs_2,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lists__accD,axiom, % 168.02/168.02 ! [V_r_2,V_xs_2,T_a] : % 168.02/168.02 ( 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)))) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Cons__listrel1__Cons,axiom, % 168.02/168.02 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( ( 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)) % 168.02/168.02 & V_xs_2 = V_ys_2 ) % 168.02/168.02 | ( V_x_2 = V_y_2 % 168.02/168.02 & 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))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel1I1,axiom, % 168.02/168.02 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 168.02/168.02 ( 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)) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel1__iff__update,axiom, % 168.02/168.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ? [B_y,B_n] : % 168.02/168.02 ( 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)) % 168.02/168.02 & 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))) % 168.02/168.02 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexord__irreflexive,axiom, % 168.02/168.02 ! [V_y_2,V_r_2,T_a] : % 168.02/168.02 ( ! [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)) % 168.02/168.02 => ~ 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__setsum__nth,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__size__pointwise,axiom, % 168.02/168.02 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 168.02/168.02 ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 168.02/168.02 ! [V_ns_2] : % 168.02/168.02 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 <=> ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 168.02/168.02 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__simps_I2_J,axiom, % 168.02/168.02 ! [V_xs,V_x,T_a] : % 168.02/168.02 ( class_Groups_Omonoid__add(T_a) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_elem__le__listsum__nat,axiom, % 168.02/168.02 ! [V_ns,V_k] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__0,axiom, % 168.02/168.02 ! [V_xs_2,T_b,T_a] : % 168.02/168.02 ( class_Groups_Omonoid__add(T_a) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__addf,axiom, % 168.02/168.02 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__const__mult,axiom, % 168.02/168.02 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] : % 168.02/168.02 ( class_Rings_Osemiring__0(T_a) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__mult__const,axiom, % 168.02/168.02 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( class_Rings_Osemiring__0(T_a) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__subtractf,axiom, % 168.02/168.02 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( class_Groups_Oab__group__add(T_a) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__update__nat,axiom, % 168.02/168.02 ! [V_n,V_ns,V_k] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__abs,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_uminus__listsum__map,axiom, % 168.02/168.02 ! [V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( class_Groups_Oab__group__add(T_a) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__size__conv__listsum,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__listsum__conv__Setsum,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 168.02/168.02 ! [V_f_2,V_xs_2,T_a,T_b] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 168.02/168.02 ! [V_l_2,V_k_2,V_f_2,T_a] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 168.02/168.02 ! [V_j_2,V_i_2,V_f_2,T_a] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__triv,axiom, % 168.02/168.02 ! [V_xs_2,V_r_2,T_b,T_a] : % 168.02/168.02 ( class_Rings_Osemiring__1(T_a) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__map__remove1,axiom, % 168.02/168.02 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => 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)))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nitpick_Osetsum_H__def,axiom, % 168.02/168.02 ! [V_f_2,V_A_2,T_a,T_b] : % 168.02/168.02 ( class_Groups_Ocomm__monoid__add(T_b) % 168.02/168.02 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => 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))))) ) % 168.02/168.02 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__mono,axiom, % 168.02/168.02 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 168.02/168.02 ( ( class_Groups_Omonoid__add(T_b) % 168.02/168.02 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 168.02/168.02 => ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 168.02/168.02 => 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)))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_someI,axiom, % 168.02/168.02 ! [T_a,V_x_2,V_P_2] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/168.02 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_tfl__some,axiom, % 168.02/168.02 ! [T_a,B_P] : % 168.02/168.02 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 168.02/168.02 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_someI__ex,axiom, % 168.02/168.02 ! [T_a,V_P_2] : % 168.02/168.02 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 168.02/168.02 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_some__eq__ex,axiom, % 168.02/168.02 ! [T_a,V_P_2] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 168.02/168.02 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_some__eq__trivial,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_some__sym__eq__trivial,axiom, % 168.02/168.02 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 168.02/168.02 % 168.02/168.02 fof(fact_exE__some,axiom, % 168.02/168.02 ! [T_a,V_ca_2,V_P_2] : % 168.02/168.02 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 168.02/168.02 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 168.02/168.02 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nitpick_Ocard_H__def,axiom, % 168.02/168.02 ! [V_A_2,T_a] : % 168.02/168.02 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => 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)))) ) % 168.02/168.02 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.02 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_LeastM__def,axiom, % 168.02/168.02 ! [V_P_2,V_m_2,T_a,T_b] : % 168.02/168.02 ( class_Orderings_Oord(T_b) % 168.02/168.02 => 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))))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_LeastM__nat__le,axiom, % 168.02/168.02 ! [T_a,V_m_2,V_x_2,V_P_2] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/168.02 => 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))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_LeastM__nat__lemma,axiom, % 168.02/168.02 ! [V_m_2,T_a,V_k_2,V_P_2] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,V_k_2)) % 168.02/168.02 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 168.02/168.02 & ! [B_y] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,B_y)) % 168.02/168.02 => 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))) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_split__paired__Eps,axiom, % 168.02/168.02 ! [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)))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Eps__split__eq,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Eps__split,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_GreatestM__def,axiom, % 168.02/168.02 ! [V_P_2,V_m_2,T_a,T_b] : % 168.02/168.02 ( class_Orderings_Oord(T_b) % 168.02/168.02 => 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))))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_butlast__take,axiom, % 168.02/168.02 ! [V_xs,T_a,V_n] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_LeastM__natI,axiom, % 168.02/168.02 ! [V_m_2,T_a,V_k_2,V_P_2] : % 168.02/168.02 ( hBOOL(hAPP(V_P_2,V_k_2)) % 168.02/168.02 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__butlast,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_in__set__butlastD,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 168.02/168.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__butlast,axiom, % 168.02/168.02 ! [V_xs,T_a,V_n] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__butlast,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_butlast__conv__take,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_butlast__list__update,axiom, % 168.02/168.02 ! [V_x,V_xs,T_a,V_k] : % 168.02/168.02 ( ( 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)) % 168.02/168.02 => 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) ) % 168.02/168.02 & ( 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)) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Greatest__def,axiom, % 168.02/168.02 ! [T_a] : % 168.02/168.02 ( class_Orderings_Oord(T_a) % 168.02/168.02 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_nth__take__lemma,axiom, % 168.02/168.02 ! [V_ys,V_xs,T_a,V_k] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( 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))) % 168.02/168.02 => ( ! [B_i] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 168.02/168.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 168.02/168.02 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__Cons__number__of,axiom, % 168.02/168.02 ! [V_xs,V_x,T_a,V_v] : % 168.02/168.02 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 => 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) ) % 168.02/168.02 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_partition__set,axiom, % 168.02/168.02 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lists_ONil,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__Nil1,axiom, % 168.02/168.02 ! [V_r_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__Nil2,axiom, % 168.02/168.02 ! [V_r_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Osimps_I3_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Osimps_I2_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__key_Osimps_I1_J,axiom, % 168.02/168.02 ! [V_x_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( class_Orderings_Olinorder(T_b) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_upto__empty,axiom, % 168.02/168.02 ! [V_i,V_j] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 168.02/168.02 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sublist__nil,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_partition_Osimps_I1_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__Nil,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip_Osimps_I1_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_foldr_Osimps_I1_J,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of__Cons__code_I1_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_remove1_Osimps_I1_J,axiom, % 168.02/168.02 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct_Osimps_I1_J,axiom, % 168.02/168.02 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_insort__not__Nil,axiom, % 168.02/168.02 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( class_Orderings_Olinorder(T_b) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrelp_Oequations_I1_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrelp_ONil,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Osize_I1_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__upds__Nil1,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__upds__Nil2,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__Nil,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__eq__Nil,axiom, % 168.02/168.02 ! [V_xs_2,V_n_2,T_a] : % 168.02/168.02 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 168.02/168.02 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__0,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sorted__list__of__set__empty,axiom, % 168.02/168.02 ! [T_a] : % 168.02/168.02 ( class_Orderings_Olinorder(T_a) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__nonempty,axiom, % 168.02/168.02 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 168.02/168.02 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 168.02/168.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update_Osimps_I1_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list__update__code_I1_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__is__Nil__conv,axiom, % 168.02/168.02 ! [V_xs_2,V_f_2,T_a,T_b] : % 168.02/168.02 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 168.02/168.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map_Osimps_I1_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nil__is__map__conv,axiom, % 168.02/168.02 ! [V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.02 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 168.02/168.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Osize_I3_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__0__conv,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__empty,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__empty2,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 168.02/168.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_List_Oset_Osimps_I1_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__simps_I1_J,axiom, % 168.02/168.02 ! [T_a] : % 168.02/168.02 ( class_Groups_Omonoid__add(T_a) % 168.02/168.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_distinct__butlast,axiom, % 168.02/168.02 ! [T_a,V_xs] : % 168.02/168.02 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.02/168.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_butlast_Osimps_I1_J,axiom, % 168.02/168.02 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 168.02/168.02 % 168.02/168.02 fof(fact_butlast_Osimps_I2_J,axiom, % 168.02/168.02 ! [V_x,T_a,V_xs] : % 168.02/168.02 ( ( V_xs = c_List_Olist_ONil(T_a) % 168.02/168.02 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 168.02/168.02 & ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sublist__empty,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__of_Osimps_I1_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__greater__0__conv,axiom, % 168.02/168.02 ! [V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__1__Cons,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_not__Nil__listrel1,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_not__listrel1__Nil,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel_ONil,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lexord__Nil__right,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nil2__notin__lex,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nil__notin__lex,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_partition__P,axiom, % 168.02/168.02 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 168.02/168.02 => hBOOL(hAPP(V_P_2,B_x)) ) % 168.02/168.02 & ! [B_x] : % 168.02/168.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 168.02/168.02 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__Cons,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_upto_Osimps,axiom, % 168.02/168.02 ! [V_j,V_i] : % 168.02/168.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 168.02/168.02 => 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)) ) % 168.02/168.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 168.02/168.02 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_sublist__singleton,axiom, % 168.02/168.02 ! [V_x_2,T_a,V_A_2] : % 168.02/168.02 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 168.02/168.02 => 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)) ) % 168.02/168.02 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_partition_Osimps_I2_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_lists__empty,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_take__Cons_H,axiom, % 168.02/168.02 ! [V_xs,V_x,T_a,V_n] : % 168.02/168.02 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 => 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) ) % 168.02/168.02 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_upto__rec__number__of,axiom, % 168.02/168.02 ! [V_n,V_m] : % 168.02/168.02 ( ( 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))) % 168.02/168.02 => 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))) ) % 168.02/168.02 & ( ~ 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))) % 168.02/168.02 => 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) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listrel__Nil,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__Cons__sing__Nil,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_upto_Opsimps,axiom, % 168.02/168.02 ! [V_j_2,V_i_2] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 168.02/168.02 => 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)) ) % 168.02/168.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 168.02/168.02 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_anamorph_Osimps,axiom, % 168.02/168.02 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 168.02/168.02 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 168.02/168.02 => 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) ) % 168.02/168.02 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 168.02/168.02 => 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))))),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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listset_Osimps_I1_J,axiom, % 168.02/168.02 ! [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))) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__Cons,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Osimps_I5_J,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_list_Osimps_I4_J,axiom, % 168.02/168.02 ! [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 ). % 168.02/168.02 % 168.02/168.02 fof(fact_listset_Osimps_I2_J,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__Cons1,axiom, % 168.02/168.02 ! [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) ). % 168.02/168.02 % 168.02/168.02 fof(fact_upto_Opinduct,axiom, % 168.02/168.02 ! [V_P_2,V_a1_2,V_a0_2] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( ! [B_i,B_j] : % 168.02/168.02 ( 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))) % 168.02/168.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 168.02/168.02 => 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)) ) % 168.02/168.02 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 168.02/168.02 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__upds__append1,axiom, % 168.02/168.02 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 => 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)))) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append1__eq__conv,axiom, % 168.02/168.02 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( V_xs_2 = V_ys_2 % 168.02/168.02 & V_x_2 = V_y_2 ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_Cons__eq__append__conv,axiom, % 168.02/168.02 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 168.02/168.02 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 168.02/168.02 | ? [B_ys_H] : % 168.02/168.02 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 168.02/168.02 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__eq__Cons__conv,axiom, % 168.02/168.02 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 168.02/168.02 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 168.02/168.02 | ? [B_ys_H] : % 168.02/168.02 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 168.02/168.02 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_eq__Nil__appendI,axiom, % 168.02/168.02 ! [T_a,V_ys,V_xs] : % 168.02/168.02 ( V_xs = V_ys % 168.02/168.02 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__self__conv2,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 168.02/168.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__self__conv,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 168.02/168.02 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__is__Nil__conv,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 168.02/168.02 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 168.02/168.02 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_self__append__conv2,axiom, % 168.02/168.02 ! [V_xs_2,T_a,V_ys_2] : % 168.02/168.02 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 168.02/168.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_self__append__conv,axiom, % 168.02/168.02 ! [V_ys_2,T_a,V_xs_2] : % 168.02/168.02 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 168.02/168.02 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__Nil2,axiom, % 168.02/168.02 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 168.02/168.02 % 168.02/168.02 fof(fact_Nil__is__append__conv,axiom, % 168.02/168.02 ! [V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 168.02/168.02 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 168.02/168.02 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__Nil,axiom, % 168.02/168.02 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 168.02/168.02 % 168.02/168.02 fof(fact_butlast__append,axiom, % 168.02/168.02 ! [V_xs,T_a,V_ys] : % 168.02/168.02 ( ( V_ys = c_List_Olist_ONil(T_a) % 168.02/168.02 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 168.02/168.02 & ( V_ys != c_List_Olist_ONil(T_a) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_listsum__append,axiom, % 168.02/168.02 ! [V_ys,V_xs,T_a] : % 168.02/168.02 ( class_Groups_Omonoid__add(T_a) % 168.02/168.02 => 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)) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_zip__append,axiom, % 168.02/168.02 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => ( 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) % 168.02/168.02 => 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)) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_length__append,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_set__append,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_map__append,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_fun__upds__append__drop,axiom, % 168.02/168.02 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_fun__upds__append2__drop,axiom, % 168.02/168.02 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.02/168.02 ( 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) % 168.02/168.02 => 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) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__in__lists__conv,axiom, % 168.02/168.02 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.02 ( 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))) % 168.02/168.02 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 168.02/168.02 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__assoc,axiom, % 168.02/168.02 ! [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)) ). % 168.02/168.02 % 168.02/168.02 fof(fact_append__eq__append__conv2,axiom, % 168.02/168.03 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.03 ( 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) % 168.02/168.03 <=> ? [B_us] : % 168.02/168.03 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 168.02/168.03 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 168.02/168.03 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 168.02/168.03 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_same__append__eq,axiom, % 168.02/168.03 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.03 ( 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) % 168.02/168.03 <=> V_ys_2 = V_zs_2 ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__same__eq,axiom, % 168.02/168.03 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 168.02/168.03 ( 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) % 168.02/168.03 <=> V_ys_2 = V_zs_2 ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__eq__appendI,axiom, % 168.02/168.03 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 168.02/168.03 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 168.02/168.03 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 168.02/168.03 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__of__append,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldr__append,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Cons__eq__appendI,axiom, % 168.02/168.03 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 168.02/168.03 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 168.02/168.03 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 168.02/168.03 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__Cons,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__append__length,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__append__length__plus,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_take__append,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_list__update__append1,axiom, % 168.02/168.03 ! [V_x,V_ys,V_xs,T_a,V_i] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_list__update__length,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_remove1__append,axiom, % 168.02/168.03 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => 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) ) % 168.02/168.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_in__set__butlast__appendI,axiom, % 168.02/168.03 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 168.02/168.03 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 168.02/168.03 => 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))))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_butlast__snoc,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__listrel1I,axiom, % 168.02/168.03 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.03 ( ( ( 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))) % 168.02/168.03 & V_us_2 = V_vs_2 ) % 168.02/168.03 | ( V_xs_2 = V_ys_2 % 168.02/168.03 & 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))) ) ) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_lexord__append__leftI,axiom, % 168.02/168.03 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_distinct__append,axiom, % 168.02/168.03 ! [V_ys_2,V_xs_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 168.02/168.03 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.03 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 168.02/168.03 & 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__append,axiom, % 168.02/168.03 ! [V_ys,V_xs,T_a,V_n] : % 168.02/168.03 ( ( 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))) % 168.02/168.03 => 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) ) % 168.02/168.03 & ( ~ 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))) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_list__update__append,axiom, % 168.02/168.03 ! [V_x,V_ys,V_xs,T_a,V_n] : % 168.02/168.03 ( ( 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))) % 168.02/168.03 => 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) ) % 168.02/168.03 & ( ~ 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))) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sublist__append,axiom, % 168.02/168.03 ! [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)))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listrel1I,axiom, % 168.02/168.03 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 => ( 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)) % 168.02/168.03 => ( 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)) % 168.02/168.03 => 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))) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_lexord__append__left__rightI,axiom, % 168.02/168.03 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_take__Suc__conv__app__nth,axiom, % 168.02/168.03 ! [V_xs,T_a,V_i] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_snoc__listrel1__snoc__iff,axiom, % 168.02/168.03 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 <=> ( ( 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))) % 168.02/168.03 & V_x_2 = V_y_2 ) % 168.02/168.03 | ( V_xs_2 = V_ys_2 % 168.02/168.03 & 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)) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sublist__Cons,axiom, % 168.02/168.03 ! [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)))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listrel1E,axiom, % 168.02/168.03 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => ~ ! [B_x,B_y] : % 168.02/168.03 ( 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)) % 168.02/168.03 => ! [B_us,B_vs] : % 168.02/168.03 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 168.02/168.03 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_lexord__append__leftD,axiom, % 168.02/168.03 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => ( ! [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)) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate1__def,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upd__conv__take__nth__drop,axiom, % 168.02/168.03 ! [V_a,V_xs,T_a,V_i] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__take__drop__id,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate1__is__Nil__conv,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 168.02/168.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__Nil,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__butlast,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_butlast__drop,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_set__drop__subset,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_in__set__dropD,axiom, % 168.02/168.03 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 168.02/168.03 ( 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)))) % 168.02/168.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__drop,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__rotate1,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_set__rotate1,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__map,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_take__drop,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__take,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_distinct__drop,axiom, % 168.02/168.03 ! [V_i,V_xs,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.02/168.03 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_distinct1__rotate,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 168.02/168.03 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__0,axiom, % 168.02/168.03 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__drop,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__zip,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__via__drop,axiom, % 168.02/168.03 ! [V_ys,V_y,V_xs,V_n,T_a] : % 168.02/168.03 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 168.02/168.03 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__1__Cons,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__Suc__Cons,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_set__drop__subset__set__drop,axiom, % 168.02/168.03 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 168.02/168.03 => 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)))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__eq__Nil,axiom, % 168.02/168.03 ! [V_xs_2,V_n_2,T_a] : % 168.02/168.03 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 168.02/168.03 <=> 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__all,axiom, % 168.02/168.03 ! [V_n,V_xs,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__append,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__eq__conv__conj,axiom, % 168.02/168.03 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 168.02/168.03 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 168.02/168.03 <=> ( 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) % 168.02/168.03 & 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__Cons,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__Cons_H,axiom, % 168.02/168.03 ! [V_xs,V_x,T_a,V_n] : % 168.02/168.03 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.03 => 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) ) % 168.02/168.03 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__drop,axiom, % 168.02/168.03 ! [V_xs,T_a,V_i,V_n] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__eq__append__conv__if,axiom, % 168.02/168.03 ! [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] : % 168.02/168.03 ( 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) % 168.02/168.03 <=> ( ( 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))) % 168.02/168.03 => ( 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) % 168.02/168.03 & 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) ) ) % 168.02/168.03 & ( ~ 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))) % 168.02/168.03 => ( 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 % 168.02/168.03 & 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 ) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__drop_H,axiom, % 168.02/168.03 ! [V_xs,T_a,V_i] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__simps,axiom, % 168.02/168.03 ! [V_xs,V_x,T_b,T_a] : % 168.02/168.03 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 168.02/168.03 & 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__Cons__number__of,axiom, % 168.02/168.03 ! [V_xs,V_x,T_a,V_v] : % 168.02/168.03 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.03 => 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) ) % 168.02/168.03 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_take__add,axiom, % 168.02/168.03 ! [V_xs,T_a,V_j,V_i] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate1__length01,axiom, % 168.02/168.03 ! [V_xs,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_zip__append1,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_zip__append2,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_id__take__nth__drop,axiom, % 168.02/168.03 ! [V_xs,T_a,V_i] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_take__hd__drop,axiom, % 168.02/168.03 ! [V_xs,T_a,V_n] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd__drop__conv__nth,axiom, % 168.02/168.03 ! [V_n,T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => ( 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))) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd_Osimps,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd__map,axiom, % 168.02/168.03 ! [V_f_2,T_b,T_a,V_xs_2] : % 168.02/168.03 ( V_xs_2 != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd__append,axiom, % 168.02/168.03 ! [V_ys,T_a,V_xs] : % 168.02/168.03 ( ( V_xs = c_List_Olist_ONil(T_a) % 168.02/168.03 => 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) ) % 168.02/168.03 & ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd__append2,axiom, % 168.02/168.03 ! [V_ys,T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd__in__set,axiom, % 168.02/168.03 ! [T_a,V_xs_2] : % 168.02/168.03 ( V_xs_2 != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd__conv__nth,axiom, % 168.02/168.03 ! [T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate1__hd__tl,axiom, % 168.02/168.03 ! [T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd__rotate__conv__nth,axiom, % 168.02/168.03 ! [V_n,T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_tl__drop,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__tl,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__is__Nil__conv,axiom, % 168.02/168.03 ! [V_xs_2,V_n_2,T_a] : % 168.02/168.03 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 168.02/168.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_tl_Osimps_I1_J,axiom, % 168.02/168.03 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__rotate,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_set__rotate,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__tl,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__map,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_distinct__tl,axiom, % 168.02/168.03 ! [V_xs,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.02/168.03 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_distinct__rotate,axiom, % 168.02/168.03 ! [V_xs_2,V_n_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 168.02/168.03 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__rotate,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_tl_Osimps_I2_J,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate1__rotate__swap,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_tl__append2,axiom, % 168.02/168.03 ! [V_ys,T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_take__tl,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__conv__mod,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__Suc,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__Suc,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_tl__append,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate0,axiom, % 168.02/168.03 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__add,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__id,axiom, % 168.02/168.03 ! [V_xs,T_a,V_n] : % 168.02/168.03 ( 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) % 168.02/168.03 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__length01,axiom, % 168.02/168.03 ! [V_n,V_xs,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__tl,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_tl__take,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_take__Suc,axiom, % 168.02/168.03 ! [V_n,T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rotate__drop__take,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_fold1__set,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.02/168.03 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_lexord__append__rightI,axiom, % 168.02/168.03 ! [V_r_2,V_x_2,T_a,V_y_2] : % 168.02/168.03 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__Cons,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_start__le__sum,axiom, % 168.02/168.03 ! [V_ns_2,V_n_2,V_m_2] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldr__conv__foldl,axiom, % 168.02/168.03 ! [V_a_2,V_xs_2,T_a] : % 168.02/168.03 ( class_Groups_Oab__semigroup__add(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__assoc,axiom, % 168.02/168.03 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 168.02/168.03 ( class_Groups_Osemigroup__add(T_a) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__absorb0,axiom, % 168.02/168.03 ! [V_zs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Groups_Omonoid__add(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__map,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__Nil,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__append,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsum__foldl,axiom, % 168.02/168.03 ! [T_a] : % 168.02/168.03 ( class_Groups_Omonoid__add(T_a) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__foldr1,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( class_Groups_Omonoid__add(T_a) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__foldr1__lemma,axiom, % 168.02/168.03 ! [V_xs_2,V_a_2,T_a] : % 168.02/168.03 ( class_Groups_Omonoid__add(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sum__eq__0__conv,axiom, % 168.02/168.03 ! [V_ns_2,V_m_2] : % 168.02/168.03 ( 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) % 168.02/168.03 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.03 & ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 168.02/168.03 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Sup__fin__set__fold,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Lattices_Olattice(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Inf__fin__set__fold,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Lattices_Olattice(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Min__fin__set__fold,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Max__fin__set__fold,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_min__max_OInf__fin__set__fold,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_min__max_OSup__fin__set__fold,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_SUPR__set__fold,axiom, % 168.02/168.03 ! [V_f_2,V_xs_2,T_b,T_a] : % 168.02/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__upds__fold__map__upd,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_elem__le__sum,axiom, % 168.02/168.03 ! [V_ns_2,V_n_2] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_lexord__Nil__left,axiom, % 168.02/168.03 ! [V_r_2,V_y_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__list__update,axiom, % 168.02/168.03 ! [V_x,V_k,T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => ( ( 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)) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 168.02/168.03 & ( 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)) % 168.02/168.03 => 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) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last_Osimps,axiom, % 168.02/168.03 ! [V_x,T_a,V_xs] : % 168.02/168.03 ( ( V_xs = c_List_Olist_ONil(T_a) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 168.02/168.03 & ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__ConsR,axiom, % 168.02/168.03 ! [V_x,T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__ConsL,axiom, % 168.02/168.03 ! [V_x,T_a,V_xs] : % 168.02/168.03 ( V_xs = c_List_Olist_ONil(T_a) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__map,axiom, % 168.02/168.03 ! [V_f_2,T_b,T_a,V_xs_2] : % 168.02/168.03 ( V_xs_2 != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__appendL,axiom, % 168.02/168.03 ! [V_xs,T_a,V_ys] : % 168.02/168.03 ( V_ys = c_List_Olist_ONil(T_a) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__appendR,axiom, % 168.02/168.03 ! [V_xs,T_a,V_ys] : % 168.02/168.03 ( V_ys != c_List_Olist_ONil(T_a) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__append,axiom, % 168.02/168.03 ! [V_xs,T_a,V_ys] : % 168.02/168.03 ( ( V_ys = c_List_Olist_ONil(T_a) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 168.02/168.03 & ( V_ys != c_List_Olist_ONil(T_a) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__in__set,axiom, % 168.02/168.03 ! [T_a,V_as_2] : % 168.02/168.03 ( V_as_2 != c_List_Olist_ONil(T_a) % 168.02/168.03 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__snoc,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__drop,axiom, % 168.02/168.03 ! [V_xs,T_a,V_n] : % 168.02/168.03 ( 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))) % 168.02/168.03 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_snoc__eq__iff__butlast,axiom, % 168.02/168.03 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 168.02/168.03 ( 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 % 168.02/168.03 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 168.02/168.03 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 168.02/168.03 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__butlast__last__id,axiom, % 168.02/168.03 ! [T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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 ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__conv__nth,axiom, % 168.02/168.03 ! [T_a,V_xs] : % 168.02/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_lists_Osimps,axiom, % 168.02/168.03 ! [V_A_2,V_a_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 168.02/168.03 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 168.02/168.03 | ? [B_a,B_l] : % 168.02/168.03 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 168.02/168.03 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 168.02/168.03 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INFI__set__fold,axiom, % 168.02/168.03 ! [V_f_2,V_xs_2,T_b,T_a] : % 168.02/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF2__E,axiom, % 168.02/168.03 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 168.02/168.03 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF2__D,axiom, % 168.02/168.03 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.03 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF1__E,axiom, % 168.02/168.03 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 168.02/168.03 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF1__D,axiom, % 168.02/168.03 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.03 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__E,axiom, % 168.02/168.03 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 168.02/168.03 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__D,axiom, % 168.02/168.03 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 168.02/168.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_finite__INT,axiom, % 168.02/168.03 ! [V_A_2,T_b,V_I_2,T_a] : % 168.02/168.03 ( ? [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 168.02/168.03 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I10_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I10_J,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF__INT__eq2,axiom, % 168.02/168.03 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 <=> 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__subset__iff,axiom, % 168.02/168.03 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_le__INF__iff,axiom, % 168.02/168.03 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 168.02/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.03 => ( 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))) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Image__INT__subset,axiom, % 168.02/168.03 ! [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)))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__lower,axiom, % 168.02/168.03 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__absorb,axiom, % 168.02/168.03 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__insert,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I1_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.03 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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 ) % 168.02/168.03 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I2_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.03 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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 ) % 168.02/168.03 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF__const,axiom, % 168.02/168.03 ! [V_M_2,T_a,V_A_2,T_b] : % 168.02/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.02/168.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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 ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I5_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I5_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__empty,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__constant,axiom, % 168.02/168.03 ! [V_ca_2,T_b,T_a,V_A_2] : % 168.02/168.03 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) % 168.02/168.03 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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 ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF__INT__eq,axiom, % 168.02/168.03 ! [V_x_2,V_r_2,T_b,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 <=> 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__insert__distrib,axiom, % 168.02/168.03 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__iff,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Collect__ball__eq,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_a,T_b] : % 168.02/168.03 ( 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)) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.03 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a] : % 168.02/168.03 ( 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) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.03 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I7_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I6_J,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I7_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Un__INT__distrib,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I6_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Un__INT__distrib2,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF__less__iff,axiom, % 168.02/168.03 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 168.02/168.03 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.03 & class_Orderings_Olinorder(T_a) ) % 168.02/168.03 => ( 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)) % 168.02/168.03 <=> ? [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.02/168.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_vimage__INT,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Pow__INT__eq,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INFI__apply,axiom, % 168.02/168.03 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 168.02/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF__commute,axiom, % 168.02/168.03 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 168.02/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I9_J,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I9_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_UN__extend__simps_I7_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_UN__simps_I7_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Compl__UN,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Compl__INT,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INFI__bool__eq,axiom, % 168.02/168.03 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__Int__distrib,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__Un,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF__subset,axiom, % 168.02/168.03 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 168.02/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INTER__def,axiom, % 168.02/168.03 ! [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)))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I2_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.03 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) % 168.02/168.03 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I1_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.03 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) % 168.02/168.03 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Collect__all__eq,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I3_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.03 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) % 168.02/168.03 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I3_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.03 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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) ) % 168.02/168.03 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__extend__simps_I4_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.03 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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 ) % 168.02/168.03 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF__leI,axiom, % 168.02/168.03 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 168.02/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__greaterThan__UNIV,axiom, % 168.02/168.03 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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INT__simps_I4_J,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 168.02/168.03 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) % 168.02/168.03 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose__aux__max,axiom, % 168.02/168.03 ! [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)))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_lists__Int__eq,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsp_ONil,axiom, % 168.02/168.03 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF1__iff,axiom, % 168.02/168.03 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.03 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_INF2__iff,axiom, % 168.02/168.03 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.02/168.03 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__append,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_append__in__listsp__conv,axiom, % 168.02/168.03 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 168.02/168.03 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 168.02/168.03 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsp_Oequations_I1_J,axiom, % 168.02/168.03 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter_Osimps_I1_J,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__empty__conv,axiom, % 168.02/168.03 ! [V_xs_2,V_P_2,T_a] : % 168.02/168.03 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_partition__filter1,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__filter__le,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__is__subset,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__map,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_in__listsp__conv__set,axiom, % 168.02/168.03 ! [V_xs_2,V_A_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__id__conv,axiom, % 168.02/168.03 ! [V_xs_2,V_P_2,T_a] : % 168.02/168.03 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sum__length__filter__compl,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsp__inf__eq,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsp__infI,axiom, % 168.02/168.03 ! [V_B_2,V_l_2,V_A_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 168.02/168.03 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__insort__triv,axiom, % 168.02/168.03 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 168.02/168.03 ( class_Orderings_Olinorder(T_b) % 168.02/168.03 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_distinct__filter,axiom, % 168.02/168.03 ! [V_P_2,V_xs_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.03 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_remove1__filter__not,axiom, % 168.02/168.03 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 168.02/168.03 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__remove1,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsp__conj__eq,axiom, % 168.02/168.03 ! [V_x_2,V_B_2,V_A_2,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 168.02/168.03 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__filter,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsp_Oequations_I2_J,axiom, % 168.02/168.03 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 168.02/168.03 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 168.02/168.03 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter_Osimps_I2_J,axiom, % 168.02/168.03 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 168.02/168.03 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/168.03 => 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)) ) % 168.02/168.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_partition__filter2,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_set__filter,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__filter__map,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__filter__less,axiom, % 168.02/168.03 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_partition__filter__conv,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsp__mono,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_set__minus__filter__out,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__in__sublist,axiom, % 168.02/168.03 ! [V_s_2,V_xs_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsp__lists__eq,axiom, % 168.02/168.03 ! [V_x_2,V_A_2,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__filter__conv__card,axiom, % 168.02/168.03 ! [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))))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_lists__IntI,axiom, % 168.02/168.03 ! [V_B_2,V_A_2,V_l_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__filter__def,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose__max__length,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose_Osimps_I2_J,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose__map__map,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__filter__simps_I2_J,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose__empty,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 168.02/168.03 <=> ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 168.02/168.03 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose_Osimps_I1_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__of__filter__in,axiom, % 168.02/168.03 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 168.02/168.03 ( 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) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__filter__simps_I1_J,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sublist__shift__lemma__Suc,axiom, % 168.02/168.03 ! [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)))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__transpose,axiom, % 168.02/168.03 ! [V_xs_2,T_a,V_i_2] : % 168.02/168.03 ( 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)))) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__transpose,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__filter__map__filter,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_insort__key__remove1,axiom, % 168.02/168.03 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 168.02/168.03 ( class_Orderings_Olinorder(T_b) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 168.02/168.03 => ( 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 % 168.02/168.03 => 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 ) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sublist__def,axiom, % 168.02/168.03 ! [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))))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted_ONil,axiom, % 168.02/168.03 ! [T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__single,axiom, % 168.02/168.03 ! [V_x,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__filter,axiom, % 168.02/168.03 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__map__same,axiom, % 168.02/168.03 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__same,axiom, % 168.02/168.03 ! [V_xs_2,V_g_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__insort__insert__key,axiom, % 168.02/168.03 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__drop,axiom, % 168.02/168.03 ! [V_n,V_xs,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 168.02/168.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_drop__upt,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_hd__upt,axiom, % 168.02/168.03 ! [V_j,V_i] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__Suc__append,axiom, % 168.02/168.03 ! [V_j,V_i] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__Suc,axiom, % 168.02/168.03 ! [V_j,V_i] : % 168.02/168.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => 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))) ) % 168.02/168.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__add__eq__append,axiom, % 168.02/168.03 ! [V_k,V_j,V_i] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__eq__Nil__conv,axiom, % 168.02/168.03 ! [V_j_2,V_i_2] : % 168.02/168.03 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 168.02/168.03 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.02/168.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__conv__Nil,axiom, % 168.02/168.03 ! [V_i,V_j] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 168.02/168.03 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted_Oequations_I1_J,axiom, % 168.02/168.03 ! [T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__0,axiom, % 168.02/168.03 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__butlast,axiom, % 168.02/168.03 ! [V_xs,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( V_xs != c_List_Olist_ONil(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 168.02/168.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__Suc__upt,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__distinct__set__unique,axiom, % 168.02/168.03 ! [V_ys_2,V_xs_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.02/168.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 168.02/168.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 168.02/168.03 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 168.02/168.03 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__map__remove1,axiom, % 168.02/168.03 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 168.02/168.03 => 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))) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__insort__key,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( 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))) % 168.02/168.03 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__take,axiom, % 168.02/168.03 ! [V_n,V_xs,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 168.02/168.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__insort,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( 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)) % 168.02/168.03 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_distinct__upt,axiom, % 168.02/168.03 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__remove1,axiom, % 168.02/168.03 ! [V_a,V_xs,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 168.02/168.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__upt,axiom, % 168.02/168.03 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__upto,axiom, % 168.02/168.03 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__list__of__set__range,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__insort__insert,axiom, % 168.02/168.03 ! [V_x_2,V_xs_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_take__upt,axiom, % 168.02/168.03 ! [V_n,V_m,V_i] : % 168.02/168.03 ( 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)) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__conv__Cons,axiom, % 168.02/168.03 ! [V_j,V_i] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__many,axiom, % 168.02/168.03 ! [V_zs,V_y,V_x,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 168.02/168.03 => 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))) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__many__eq,axiom, % 168.02/168.03 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( 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))) % 168.02/168.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.02/168.03 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__rec,axiom, % 168.02/168.03 ! [V_j,V_i] : % 168.02/168.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => 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)) ) % 168.02/168.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__tl,axiom, % 168.02/168.03 ! [V_xs,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 168.02/168.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_atLeastLessThan__upt,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_set__upt,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__upt,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__Cons,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 168.02/168.03 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.02/168.03 & ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__append,axiom, % 168.02/168.03 ! [V_ys_2,V_xs_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 168.02/168.03 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.02/168.03 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 168.02/168.03 & ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => ! [B_xa] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 168.02/168.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__rec__number__of,axiom, % 168.02/168.03 ! [V_n,V_m] : % 168.02/168.03 ( ( 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))) % 168.02/168.03 => 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))) ) % 168.02/168.03 & ( ~ 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))) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_upt__eq__Cons__conv,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 168.02/168.03 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 168.02/168.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 168.02/168.03 & V_i_2 = V_x_2 % 168.02/168.03 & 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 ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_last__upt,axiom, % 168.02/168.03 ! [V_j,V_i] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_filter__insort,axiom, % 168.02/168.03 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 168.02/168.03 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.02/168.03 => 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)) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__nth,axiom, % 168.02/168.03 ! [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 ). % 168.02/168.03 % 168.02/168.03 fof(fact_atLeastAtMost__upt,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_atLeast__upt,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 168.02/168.03 ! [V_n_2,V_m_2,V_f_2,T_a] : % 168.02/168.03 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 168.02/168.03 ! [V_n_2,V_m_2,V_f_2,T_a] : % 168.02/168.03 ( class_Groups_Ocomm__monoid__add(T_a) % 168.02/168.03 => 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))) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__upt,axiom, % 168.02/168.03 ! [V_j,V_k,V_i] : % 168.02/168.03 ( 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)) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_greaterThanAtMost__upt,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted_Oequations_I2_J,axiom, % 168.02/168.03 ! [V_a1_2,V_a2_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 168.02/168.03 <=> ( ! [B_x] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 168.02/168.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 168.02/168.03 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_greaterThanLessThan__upt,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_nth__map__upt,axiom, % 168.02/168.03 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__list__of__set,axiom, % 168.02/168.03 ! [V_A_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.02/168.03 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 168.02/168.03 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 168.02/168.03 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_atMost__upto,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_insort__remove1,axiom, % 168.02/168.03 ! [V_xs_2,V_a_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.02/168.03 => 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 ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__equals__nth__mono,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.02/168.03 <=> ! [B_j] : % 168.02/168.03 ( 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))) % 168.02/168.03 => ! [B_i] : % 168.02/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 168.02/168.03 => 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))) ) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sorted__nth__mono,axiom, % 168.02/168.03 ! [V_j,V_i,V_xs,T_a] : % 168.02/168.03 ( class_Orderings_Olinorder(T_a) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 168.02/168.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.02/168.03 => ( 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))) % 168.02/168.03 => 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))) ) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_map__sorted__distinct__set__unique,axiom, % 168.02/168.03 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 168.02/168.03 ( class_Orderings_Olinorder(T_b) % 168.02/168.03 => ( 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))) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 168.02/168.03 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 168.02/168.03 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 168.02/168.03 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 168.02/168.03 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 168.02/168.03 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_sublist__shift__lemma,axiom, % 168.02/168.03 ! [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))))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose__rectangle,axiom, % 168.02/168.03 ! [V_n_2,T_a,V_xs_2] : % 168.02/168.03 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 168.02/168.03 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.02/168.03 => ( ! [B_i] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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 ) % 168.02/168.03 => 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)) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose_Opsimps_I2_J,axiom, % 168.02/168.03 ! [V_xss_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => 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) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose_Opsimps_I1_J,axiom, % 168.02/168.03 ! [T_a] : % 168.02/168.03 ( 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)))) % 168.02/168.03 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose__column,axiom, % 168.02/168.03 ! [V_i_2,V_xs_2,T_a] : % 168.02/168.03 ( 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))) % 168.02/168.03 => ( 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))) % 168.02/168.03 => 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) ) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_transpose__aux__filter__head,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_inj__on__rev,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rev__is__Nil__conv,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 168.02/168.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_Nil__is__rev__conv,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 168.02/168.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rev_Osimps_I1_J,axiom, % 168.02/168.03 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rev__concat,axiom, % 168.02/168.03 ! [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))) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rev__map,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rev__singleton__conv,axiom, % 168.02/168.03 ! [V_x_2,V_xs_2,T_a] : % 168.02/168.03 ( 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)) % 168.02/168.03 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_singleton__rev__conv,axiom, % 168.02/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.02/168.03 ( 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) % 168.02/168.03 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_concat__conv__foldl,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rev__foldl__cons,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__conv__concat,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_distinct__rev,axiom, % 168.02/168.03 ! [V_xs_2,T_a] : % 168.02/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 168.02/168.03 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 168.02/168.03 % 168.02/168.03 fof(fact_concat__append,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_rev__append,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldl__foldr,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_foldr__foldl,axiom, % 168.02/168.03 ! [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)) ). % 168.02/168.03 % 168.02/168.03 fof(fact_concat_Osimps_I1_J,axiom, % 168.02/168.03 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 168.02/168.03 % 168.02/168.03 fof(fact_length__rev,axiom, % 168.02/168.03 ! [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) ). % 168.02/168.03 % 168.02/168.03 fof(fact_listsum__rev,axiom, % 168.19/168.03 ! [V_xs,T_a] : % 168.19/168.03 ( class_Groups_Ocomm__monoid__add(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__rev__ident,axiom, % 168.19/168.03 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__swap,axiom, % 168.19/168.03 ! [V_ys_2,V_xs_2,T_a] : % 168.19/168.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 168.19/168.03 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__is__rev__conv,axiom, % 168.19/168.03 ! [V_ys_2,V_xs_2,T_a] : % 168.19/168.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 168.19/168.03 <=> V_xs_2 = V_ys_2 ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_set__rev,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_zip__rev,axiom, % 168.19/168.03 ! [V_ys,T_b,V_xs,T_a] : % 168.19/168.03 ( 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) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__filter,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_concat_Osimps_I2_J,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_concat__eq__Nil__conv,axiom, % 168.19/168.03 ! [V_xss_2,T_a] : % 168.19/168.03 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 168.19/168.03 <=> ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 168.19/168.03 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Nil__eq__concat__conv,axiom, % 168.19/168.03 ! [V_xss_2,T_a] : % 168.19/168.03 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 168.19/168.03 <=> ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 168.19/168.03 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_map__concat,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_filter__concat,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__eq__Cons__iff,axiom, % 168.19/168.03 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 168.19/168.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 168.19/168.03 <=> 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev_Osimps_I2_J,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__concat,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_set__concat,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_hd__rev,axiom, % 168.19/168.03 ! [T_a,V_xs] : % 168.19/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.19/168.03 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_last__rev,axiom, % 168.19/168.03 ! [T_a,V_xs] : % 168.19/168.03 ( V_xs != c_List_Olist_ONil(T_a) % 168.19/168.03 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__transpose,axiom, % 168.19/168.03 ! [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)))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__take,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__drop,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rotate__rev,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_transpose_Osimps_I3_J,axiom, % 168.19/168.03 ! [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))))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__nth,axiom, % 168.19/168.03 ! [V_xs,T_a,V_n] : % 168.19/168.03 ( 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))) % 168.19/168.03 => 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_concat__injective,axiom, % 168.19/168.03 ! [V_ys_2,V_xs_2,T_a] : % 168.19/168.03 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 168.19/168.03 => ( 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) % 168.19/168.03 => ( ! [B_x] : % 168.19/168.03 ( 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)))) % 168.19/168.03 => 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)) ) % 168.19/168.03 => V_xs_2 = V_ys_2 ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_concat__eq__concat__iff,axiom, % 168.19/168.03 ! [V_ys_2,V_xs_2,T_a] : % 168.19/168.03 ( ! [B_x] : % 168.19/168.03 ( 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)))) % 168.19/168.03 => 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)) ) % 168.19/168.03 => ( 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) % 168.19/168.03 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 168.19/168.03 <=> V_xs_2 = V_ys_2 ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_rev__update,axiom, % 168.19/168.03 ! [V_y,V_xs,T_a,V_k] : % 168.19/168.03 ( 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))) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_concat__map__singleton,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__rev__nth__mono,axiom, % 168.19/168.03 ! [V_j,V_i,V_xs,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.19/168.03 => ( 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))) % 168.19/168.03 => 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))) ) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_foldr__max__sorted,axiom, % 168.19/168.03 ! [V_y_2,V_xs_2,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 168.19/168.03 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 168.19/168.03 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 168.19/168.03 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 168.19/168.03 => 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) ) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_transpose_Opsimps_I3_J,axiom, % 168.19/168.03 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => 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))))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__transpose__sorted,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 168.19/168.03 => 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) ) % 168.19/168.03 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 168.19/168.03 => 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))) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_transpose__column__length,axiom, % 168.19/168.03 ! [V_i_2,V_xs_2,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => ( 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))) % 168.19/168.03 => 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)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_transpose__aux__filter__tail,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_nth__nth__transpose__sorted,axiom, % 168.19/168.03 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => ( 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)))) % 168.19/168.03 => ( 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)))) % 168.19/168.03 => 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) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_transpose__transpose,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 168.19/168.03 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__map,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_zip__takeWhile__fst,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_zip__takeWhile__snd,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__eq__all__conv,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,T_a] : % 168.19/168.03 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 168.19/168.03 <=> ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_set__takeWhileD,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 168.19/168.03 ( 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)))) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__takeWhile__le,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__eq__take,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_distinct__takeWhile,axiom, % 168.19/168.03 ! [V_P_2,V_xs_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.19/168.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile_Osimps_I2_J,axiom, % 168.19/168.03 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 168.19/168.03 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.03 => 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)) ) % 168.19/168.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.03 => 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) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__takeWhile,axiom, % 168.19/168.03 ! [V_P_2,V_xs_2,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.19/168.03 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile_Osimps_I1_J,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__tail,axiom, % 168.19/168.03 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 168.19/168.03 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_return__list__def,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__append1,axiom, % 168.19/168.03 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.03 => 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) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__nth,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 168.19/168.03 ( 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)))) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_nth__length__takeWhile,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => ~ 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))))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_map__upds__def,axiom, % 168.19/168.03 ! [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)))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__not__last,axiom, % 168.19/168.03 ! [T_a,V_xs_2] : % 168.19/168.03 ( V_xs_2 != c_List_Olist_ONil(T_a) % 168.19/168.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.19/168.03 => 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) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 168.19/168.03 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => ( 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))) % 168.19/168.03 => 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) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_transfer__nat__int__list__return__embed,axiom, % 168.19/168.03 ! [V_l] : % 168.19/168.03 ( c_List_Onat__list(V_l) % 168.19/168.03 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__remdups__concat,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_distinct__remdups,axiom, % 168.19/168.03 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__remdups__leq,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remdups__map__remdups,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_set__remdups,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remove1__remdups,axiom, % 168.19/168.03 ! [V_x,V_xs,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remdups__eq__nil__iff,axiom, % 168.19/168.03 ! [V_x_2,T_a] : % 168.19/168.03 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 168.19/168.03 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remdups__eq__nil__right__iff,axiom, % 168.19/168.03 ! [V_x_2,T_a] : % 168.19/168.03 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 168.19/168.03 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remdups_Osimps_I1_J,axiom, % 168.19/168.03 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__remdups,axiom, % 168.19/168.03 ! [V_l,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 168.19/168.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remdups__id__iff__distinct,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 168.19/168.03 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_distinct__remdups__id,axiom, % 168.19/168.03 ! [V_xs,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.19/168.03 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__remdups__eq,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( 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) % 168.19/168.03 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remdups__remdups,axiom, % 168.19/168.03 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remdups__filter,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_embed__list__def,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_remdups_Osimps_I2_J,axiom, % 168.19/168.03 ! [V_xs_2,V_x_2,T_a] : % 168.19/168.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => 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) ) % 168.19/168.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => 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)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__remdups__card__conv,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__neq__rev,axiom, % 168.19/168.03 ! [V_x_2,V_xs_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile__neq__rev,axiom, % 168.19/168.03 ! [V_x_2,V_xs_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__dropWhile__le,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_distinct__dropWhile,axiom, % 168.19/168.03 ! [V_P_2,V_xs_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.19/168.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile_Osimps_I2_J,axiom, % 168.19/168.03 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 168.19/168.03 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.03 => 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) ) % 168.19/168.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.03 => 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) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__dropWhile,axiom, % 168.19/168.03 ! [V_P_2,V_xs_2,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.19/168.03 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile_Osimps_I1_J,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile__eq__Nil__conv,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,T_a] : % 168.19/168.03 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 168.19/168.03 <=> ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__dropWhile__id,axiom, % 168.19/168.03 ! [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 ). % 168.19/168.03 % 168.19/168.03 fof(fact_hd__dropWhile,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,T_a] : % 168.19/168.03 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 168.19/168.03 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile__map,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile__append1,axiom, % 168.19/168.03 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.03 => 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) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile__eq__Cons__conv,axiom, % 168.19/168.03 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 168.19/168.03 ( 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) % 168.19/168.03 <=> ( 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)) % 168.19/168.03 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile__eq__drop,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_dropWhile__nth,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 168.19/168.03 ( 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)))) % 168.19/168.03 => 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)))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_listsum__map__filter,axiom, % 168.19/168.03 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 168.19/168.03 ( class_Groups_Omonoid__add(T_b) % 168.19/168.03 => ( ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.03 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 168.19/168.03 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 168.19/168.03 => 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)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__nth__monoI,axiom, % 168.19/168.03 ! [V_xs,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => ( ! [B_i,B_j] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 168.19/168.03 => ( 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))) % 168.19/168.03 => 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))) ) ) % 168.19/168.03 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_n__lists_Osimps_I2_J,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__sublists,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_distinct__n__lists,axiom, % 168.19/168.03 ! [V_n,V_xs,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.19/168.03 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_distinct__set__sublists,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 168.19/168.03 => 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)))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__n__lists,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__n__lists__elem,axiom, % 168.19/168.03 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 168.19/168.03 ( 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)))) % 168.19/168.03 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sublists__powset,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sublists_Osimps_I1_J,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_n__lists_Osimps_I1_J,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_n__lists__Nil,axiom, % 168.19/168.03 ! [T_a,V_n] : % 168.19/168.03 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.19/168.03 => 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))) ) % 168.19/168.03 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.19/168.03 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sublists_Osimps_I2_J,axiom, % 168.19/168.03 ! [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))))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_set__n__lists,axiom, % 168.19/168.03 ! [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)))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_product_Osimps_I2_J,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__the__def,axiom, % 168.19/168.03 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 168.19/168.03 % 168.19/168.03 fof(fact_product_Osimps_I1_J,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_distinct__product,axiom, % 168.19/168.03 ! [V_ys,T_b,V_xs,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.19/168.03 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 168.19/168.03 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_product__list__set,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_map__of__zip__enum__inject,axiom, % 168.19/168.03 ! [V_ys_2,V_xs_2,T_a,T_b] : % 168.19/168.03 ( ( class_Enum_Oenum(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) ) % 168.19/168.03 => ( 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)) % 168.19/168.03 => ( 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)) % 168.19/168.03 => ( 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))) % 168.19/168.03 => V_xs_2 = V_ys_2 ) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sort__foldl__insort,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__prod__def,axiom, % 168.19/168.03 ! [T_b,T_a] : % 168.19/168.03 ( ( class_Enum_Oenum(T_a) % 168.19/168.03 & class_Enum_Oenum(T_b) ) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__distinct,axiom, % 168.19/168.03 ! [T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__option__def,axiom, % 168.19/168.03 ! [T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__sum__def,axiom, % 168.19/168.03 ! [T_b,T_a] : % 168.19/168.03 ( ( class_Enum_Oenum(T_a) % 168.19/168.03 & class_Enum_Oenum(T_b) ) % 168.19/168.03 => c_Enum_Oenum__class_Oenum(tc_sum(T_a,T_b)) = hAPP(hAPP(c_List_Oappend(tc_sum(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_a,tc_sum(T_a,T_b)),c_Sum__Type_OInl(T_a,T_b)),c_Enum_Oenum__class_Oenum(T_a))),hAPP(hAPP(c_List_Omap(T_b,tc_sum(T_a,T_b)),c_Sum__Type_OInr(T_b,T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_distinct__sort,axiom, % 168.19/168.03 ! [V_xs_2,V_f_2,T_a,T_b] : % 168.19/168.03 ( class_Orderings_Olinorder(T_b) % 168.19/168.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 168.19/168.03 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_filter__sort,axiom, % 168.19/168.03 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 168.19/168.03 ( class_Orderings_Olinorder(T_b) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__sort,axiom, % 168.19/168.03 ! [V_xs_2,V_f_2,T_a,T_b] : % 168.19/168.03 ( class_Orderings_Olinorder(T_b) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__sort,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sort__key__simps_I1_J,axiom, % 168.19/168.03 ! [V_f_2,T_a,T_b] : % 168.19/168.03 ( class_Orderings_Olinorder(T_b) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_set__sort,axiom, % 168.19/168.03 ! [V_xs_2,V_f_2,T_a,T_b] : % 168.19/168.03 ( class_Orderings_Olinorder(T_b) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_in__enum,axiom, % 168.19/168.03 ! [V_x_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_UNIV__enum,axiom, % 168.19/168.03 ! [T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__UNIV,axiom, % 168.19/168.03 ! [T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__sort__key,axiom, % 168.19/168.03 ! [V_xs_2,V_f_2,T_b,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sort__key__simps_I2_J,axiom, % 168.19/168.03 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 168.19/168.03 ( class_Orderings_Olinorder(T_b) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__fun__code,axiom, % 168.19/168.03 ! [T_b,T_a] : % 168.19/168.03 ( ( class_Enum_Oenum(T_a) % 168.19/168.03 & class_HOL_Oequal(T_a) % 168.19/168.03 & class_Enum_Oenum(T_b) ) % 168.19/168.03 => 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__fun__def,axiom, % 168.19/168.03 ! [T_b,T_a] : % 168.19/168.03 ( ( class_Enum_Oenum(T_a) % 168.19/168.03 & class_Enum_Oenum(T_b) ) % 168.19/168.03 => 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_all__n__lists__def,axiom, % 168.19/168.03 ! [V_n_2,V_P_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 168.19/168.03 <=> ! [B_x] : % 168.19/168.03 ( 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))))) % 168.19/168.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_ex__n__lists__def,axiom, % 168.19/168.03 ! [V_n_2,V_P_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 168.19/168.03 <=> ? [B_x] : % 168.19/168.03 ( 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))))) % 168.19/168.03 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__all__fun__def,axiom, % 168.19/168.03 ! [V_P_2,T_a,T_b] : % 168.19/168.03 ( ( class_Enum_Oenum(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 168.19/168.03 <=> 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__ex__fun__def,axiom, % 168.19/168.03 ! [V_P_2,T_a,T_b] : % 168.19/168.03 ( ( class_Enum_Oenum(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 168.19/168.03 <=> 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_all__code,axiom, % 168.19/168.03 ! [V_P_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 168.19/168.03 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_exists__code,axiom, % 168.19/168.03 ! [V_P_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 168.19/168.03 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__all,axiom, % 168.19/168.03 ! [V_P_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 168.19/168.03 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__ex,axiom, % 168.19/168.03 ! [V_P_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 168.19/168.03 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__ex__option__def,axiom, % 168.19/168.03 ! [V_P_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 168.19/168.03 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 168.19/168.03 | 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)))) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__all__option__def,axiom, % 168.19/168.03 ! [V_P_2,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 168.19/168.03 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 168.19/168.03 & 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)))) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__ex__sum__def,axiom, % 168.19/168.03 ! [V_P_2,T_b,T_a] : % 168.19/168.03 ( ( class_Enum_Oenum(T_a) % 168.19/168.03 & class_Enum_Oenum(T_b) ) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_sum(T_a,T_b)),V_P_2)) % 168.19/168.03 <=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_sum(T_a,T_b),tc_HOL_Obool,T_a),V_P_2),c_Sum__Type_OInl(T_a,T_b)))) % 168.19/168.03 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_sum(T_a,T_b),tc_HOL_Obool,T_b),V_P_2),c_Sum__Type_OInr(T_b,T_a)))) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__all__sum__def,axiom, % 168.19/168.03 ! [V_P_2,T_b,T_a] : % 168.19/168.03 ( ( class_Enum_Oenum(T_a) % 168.19/168.03 & class_Enum_Oenum(T_b) ) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_sum(T_a,T_b)),V_P_2)) % 168.19/168.03 <=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_sum(T_a,T_b),tc_HOL_Obool,T_a),V_P_2),c_Sum__Type_OInl(T_a,T_b)))) % 168.19/168.03 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_sum(T_a,T_b),tc_HOL_Obool,T_b),V_P_2),c_Sum__Type_OInr(T_b,T_a)))) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__ex__prod__def,axiom, % 168.19/168.03 ! [V_P_2,T_a,T_b] : % 168.19/168.03 ( ( class_Enum_Oenum(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 168.19/168.03 <=> 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))))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__all__prod__def,axiom, % 168.19/168.03 ! [V_P_2,T_a,T_b] : % 168.19/168.03 ( ( class_Enum_Oenum(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 168.19/168.03 <=> 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))))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_order__fun_I1_J,axiom, % 168.19/168.03 ! [V_g_2,V_f_2,T_a,T_b] : % 168.19/168.03 ( ( class_Orderings_Oorder(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 168.19/168.03 <=> 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_order__fun_I2_J,axiom, % 168.19/168.03 ! [V_g_2,V_f_2,T_a,T_b] : % 168.19/168.03 ( ( class_Orderings_Oorder(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 168.19/168.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 168.19/168.03 & 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)))) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__ex__fun__code,axiom, % 168.19/168.03 ! [V_P_2,T_a,T_b] : % 168.19/168.03 ( ( class_Enum_Oenum(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) % 168.19/168.03 & class_HOL_Oequal(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 168.19/168.03 <=> 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_enum__all__fun__code,axiom, % 168.19/168.03 ! [V_P_2,T_a,T_b] : % 168.19/168.03 ( ( class_Enum_Oenum(T_b) % 168.19/168.03 & class_Enum_Oenum(T_a) % 168.19/168.03 & class_HOL_Oequal(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 168.19/168.03 <=> 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_image__INT,axiom, % 168.19/168.03 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 168.19/168.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 168.19/168.03 => ( ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 168.19/168.03 => 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)) ) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 168.19/168.03 => 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)) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_map__of__zip__enum__is__Some,axiom, % 168.19/168.03 ! [V_x,V_ys,T_b,T_a] : % 168.19/168.03 ( class_Enum_Oenum(T_a) % 168.19/168.03 => ( 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)) % 168.19/168.03 => ? [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) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__eq__filter,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,T_a] : % 168.19/168.03 ( ! [B_x] : % 168.19/168.03 ( 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)))) % 168.19/168.03 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 168.19/168.03 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_inj__on__mapI,axiom, % 168.19/168.03 ! [V_A_2,V_f_2,T_b,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_UnionI,axiom, % 168.19/168.03 ! [V_A_2,V_C_2,V_X_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 168.19/168.03 => 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_UNION__eq__Union__image,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__image__eq,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_image__Union,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Field__Union,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_INT__simps_I8_J,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_INT__extend__simps_I8_J,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__disjoint,axiom, % 168.19/168.03 ! [V_A_2,V_C_2,T_a] : % 168.19/168.03 ( 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)) % 168.19/168.03 <=> ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 168.19/168.03 => 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)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__upper,axiom, % 168.19/168.03 ! [V_A_2,V_x_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.19/168.03 => 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))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__mono,axiom, % 168.19/168.03 ! [V_B_2,V_A_2,T_a] : % 168.19/168.03 ( 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)) % 168.19/168.03 => 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__le__iff,axiom, % 168.19/168.03 ! [V_b_2,V_A_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => ( 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)) % 168.19/168.03 <=> ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.19/168.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__quotient,axiom, % 168.19/168.03 ! [V_r_2,V_A_2,T_a] : % 168.19/168.03 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.19/168.03 => 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 ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__upper,axiom, % 168.19/168.03 ! [V_A_2,V_B_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.19/168.03 => 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_finite__UnionD,axiom, % 168.19/168.03 ! [V_A_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 168.19/168.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__empty,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__insert,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__Pow__eq,axiom, % 168.19/168.03 ! [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 ). % 168.19/168.03 % 168.19/168.03 fof(fact_less__Sup__iff,axiom, % 168.19/168.03 ! [V_S_2,V_a_2,T_a] : % 168.19/168.03 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 & class_Orderings_Olinorder(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 168.19/168.03 <=> ? [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 168.19/168.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_subset__Pow__Union,axiom, % 168.19/168.03 ! [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)))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__Un__distrib,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__UNIV,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__insert,axiom, % 168.19/168.03 ! [V_A_2,V_a_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__singleton,axiom, % 168.19/168.03 ! [V_a_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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 ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__empty,axiom, % 168.19/168.03 ! [T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__UNIV,axiom, % 168.19/168.03 ! [T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sigma__Union,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Domain__Union,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_vimage__Union,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_UN__simps_I8_J,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_UN__extend__simps_I8_J,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__def,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Range__Union,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Int__Union,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Int__Union2,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Un__eq__Union,axiom, % 168.19/168.03 ! [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))))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Un__Union__image,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Union__Int__subset,axiom, % 168.19/168.03 ! [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)))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__binary,axiom, % 168.19/168.03 ! [V_b_2,V_a_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__fin__Sup,axiom, % 168.19/168.03 ! [V_A_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.19/168.03 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__set__fold,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_finite__Union,axiom, % 168.19/168.03 ! [V_A_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 168.19/168.03 => ( ! [B_M] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 168.19/168.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 168.19/168.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_insert__partition,axiom, % 168.19/168.03 ! [V_F_2,V_x_2,T_a] : % 168.19/168.03 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 168.19/168.03 => ( ! [B_x] : % 168.19/168.03 ( 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))) % 168.19/168.03 => ! [B_xa] : % 168.19/168.03 ( 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))) % 168.19/168.03 => ( B_x != B_xa % 168.19/168.03 => 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)) ) ) ) % 168.19/168.03 => 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)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_takeWhile__eq__take__P__nth,axiom, % 168.19/168.03 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 168.19/168.03 ( ! [B_i] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 168.19/168.03 => ( 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))) % 168.19/168.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 168.19/168.03 => ( ( 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))) % 168.19/168.03 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 168.19/168.03 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_length__takeWhile__less__P__nth,axiom, % 168.19/168.03 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 168.19/168.03 ( ! [B_i] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 168.19/168.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 168.19/168.03 => ( 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))) % 168.19/168.03 => 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)))) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Sup__Inf,axiom, % 168.19/168.03 ! [V_A_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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)))))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__Sup,axiom, % 168.19/168.03 ! [V_A_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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))))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_finite__Inter,axiom, % 168.19/168.03 ! [V_M_2,T_a] : % 168.19/168.03 ( ? [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 168.19/168.03 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 168.19/168.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_InterD,axiom, % 168.19/168.03 ! [V_X_2,V_C_2,V_A_2,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 168.19/168.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_InterE,axiom, % 168.19/168.03 ! [V_X_2,V_C_2,V_A_2,T_a] : % 168.19/168.03 ( 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))) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 168.19/168.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__eq,axiom, % 168.19/168.03 ! [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)))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__singleton,axiom, % 168.19/168.03 ! [V_a_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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 ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__empty,axiom, % 168.19/168.03 ! [T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__UNIV,axiom, % 168.19/168.03 ! [T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__insert,axiom, % 168.19/168.03 ! [V_A_2,V_a_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__Un__distrib,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__UNIV,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__less__iff,axiom, % 168.19/168.03 ! [V_a_2,V_S_2,T_a] : % 168.19/168.03 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 & class_Orderings_Olinorder(T_a) ) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 168.19/168.03 <=> ? [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 168.19/168.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__lower,axiom, % 168.19/168.03 ! [V_A_2,V_B_2,T_a] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_le__Inf__iff,axiom, % 168.19/168.03 ! [V_A_2,V_b_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => ( 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))) % 168.19/168.03 <=> ! [B_x] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.19/168.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__empty,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__anti__mono,axiom, % 168.19/168.03 ! [V_A_2,V_B_2,T_a] : % 168.19/168.03 ( 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)) % 168.19/168.03 => 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))) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__insert,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__lower,axiom, % 168.19/168.03 ! [V_A_2,V_x_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.19/168.03 => 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)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__image__eq,axiom, % 168.19/168.03 ! [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) ). % 168.19/168.03 % 168.19/168.03 fof(fact_INTER__eq__Inter__image,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__def,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Un__Inter,axiom, % 168.19/168.03 ! [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)) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Int__eq__Inter,axiom, % 168.19/168.03 ! [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))))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Int__Inter__image,axiom, % 168.19/168.03 ! [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))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inter__Un__subset,axiom, % 168.19/168.03 ! [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)))) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__binary,axiom, % 168.19/168.03 ! [V_b_2,V_a_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__fin__Inf,axiom, % 168.19/168.03 ! [V_A_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.19/168.03 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_Inf__set__fold,axiom, % 168.19/168.03 ! [V_xs_2,T_a] : % 168.19/168.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__def,axiom, % 168.19/168.03 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.03 <=> ( 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) % 168.19/168.03 & ! [B_x] : % 168.19/168.03 ( 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)))) % 168.19/168.03 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_sorted_Osimps,axiom, % 168.19/168.03 ! [V_a_2,T_a] : % 168.19/168.03 ( class_Orderings_Olinorder(T_a) % 168.19/168.03 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 168.19/168.03 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 168.19/168.03 | ? [B_xs,B_x] : % 168.19/168.03 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 168.19/168.03 & ! [B_xa] : % 168.19/168.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 168.19/168.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 168.19/168.03 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__appendI,axiom, % 168.19/168.03 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 168.19/168.03 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2) % 168.19/168.03 => 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)) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__append,axiom, % 168.19/168.03 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.19/168.03 ( 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) % 168.19/168.03 => ( 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)) % 168.19/168.03 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.03 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__Cons,axiom, % 168.19/168.03 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( 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)) % 168.19/168.03 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 168.19/168.03 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__map1,axiom, % 168.19/168.03 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 168.19/168.03 ( 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) % 168.19/168.03 <=> 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__map2,axiom, % 168.19/168.03 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( 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)) % 168.19/168.03 <=> 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__eq,axiom, % 168.19/168.03 ! [T_a,V_ys_2,V_xs_2] : % 168.19/168.03 ( V_xs_2 = V_ys_2 % 168.19/168.03 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__lengthD,axiom, % 168.19/168.03 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.03 => 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) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__dropI,axiom, % 168.19/168.03 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__takeI,axiom, % 168.19/168.03 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.03 => 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)) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__Nil,axiom, % 168.19/168.03 ! [V_ys_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 168.19/168.03 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 168.19/168.03 % 168.19/168.03 fof(fact_list__all2__Nil2,axiom, % 168.19/168.03 ! [V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 168.19/168.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2__rev,axiom, % 168.19/168.04 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2__rev1,axiom, % 168.19/168.04 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 168.19/168.04 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2__conv__all__nth,axiom, % 168.19/168.04 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.04 <=> ( 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) % 168.19/168.04 & ! [B_i] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2__nthD,axiom, % 168.19/168.04 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2__nthD2,axiom, % 168.19/168.04 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2__update__cong,axiom, % 168.19/168.04 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 168.19/168.04 => 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)) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2__update__cong2,axiom, % 168.19/168.04 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 168.19/168.04 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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)) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2I,axiom, % 168.19/168.04 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 168.19/168.04 ( ! [B_x] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 168.19/168.04 => ( 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) % 168.19/168.04 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_card__partition,axiom, % 168.19/168.04 ! [V_k_2,V_C_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 168.19/168.04 => ( ! [B_c] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 168.19/168.04 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 168.19/168.04 => ( ! [B_c1] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 168.19/168.04 => ! [B_c2] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 168.19/168.04 => ( B_c1 != B_c2 % 168.19/168.04 => 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)) ) ) ) % 168.19/168.04 => 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)) ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_all__nth__imp__all__set,axiom, % 168.19/168.04 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 168.19/168.04 ( ! [B_i] : % 168.19/168.04 ( 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))) % 168.19/168.04 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_map__removeAll__inj__on,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_removeAll__append,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_removeAll_Osimps_I2_J,axiom, % 168.19/168.04 ! [V_xs,T_a,V_y,V_x] : % 168.19/168.04 ( ( V_x = V_y % 168.19/168.04 => 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) ) % 168.19/168.04 & ( V_x != V_y % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_distinct__removeAll,axiom, % 168.19/168.04 ! [V_x,V_xs,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.19/168.04 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_removeAll__filter__not,axiom, % 168.19/168.04 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 168.19/168.04 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_removeAll__filter__not__eq,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_removeAll_Osimps_I1_J,axiom, % 168.19/168.04 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 168.19/168.04 % 168.19/168.04 fof(fact_removeAll__id,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,T_a] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_distinct__remove1__removeAll,axiom, % 168.19/168.04 ! [V_x,V_xs,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.19/168.04 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_map__removeAll__inj,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 168.19/168.04 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 168.19/168.04 => 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_set__removeAll,axiom, % 168.19/168.04 ! [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)))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_List_Oinsert__def,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,T_a] : % 168.19/168.04 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 168.19/168.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_not__in__set__insert,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,T_a] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_insert__remdups,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_distinct__insert,axiom, % 168.19/168.04 ! [V_x,V_xs,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 168.19/168.04 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_in__set__insert,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_List_Oset__insert,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_insert__Nil,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_concat__map__maps,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_maps__def,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_maps__simps_I2_J,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_maps__simps_I1_J,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_distinct__concat,axiom, % 168.19/168.04 ! [V_xs_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 168.19/168.04 => ( ! [B_ys] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 168.19/168.04 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 168.19/168.04 => ( ! [B_ys] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 168.19/168.04 => ! [B_zs] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 168.19/168.04 => ( B_ys != B_zs % 168.19/168.04 => 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)) ) ) ) % 168.19/168.04 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_measures__lesseq,axiom, % 168.19/168.04 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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)))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_wf__measures,axiom, % 168.19/168.04 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_in__measures_I1_J,axiom, % 168.19/168.04 ! [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))))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_measures__def,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_in__measures_I2_J,axiom, % 168.19/168.04 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 <=> ( 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))) % 168.19/168.04 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 168.19/168.04 & 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))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_measures__less,axiom, % 168.19/168.04 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_inj__on__Inter,axiom, % 168.19/168.04 ! [V_f_2,T_b,T_a,V_S_2] : % 168.19/168.04 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 168.19/168.04 => ( ! [B_A] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 168.19/168.04 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Inter__subset,axiom, % 168.19/168.04 ! [V_B_2,V_A_2,T_a] : % 168.19/168.04 ( ! [B_X] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 168.19/168.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_foldl__apply,axiom, % 168.19/168.04 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 168.19/168.04 ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => 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)) ) % 168.19/168.04 => 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_inj__on__INTER,axiom, % 168.19/168.04 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 168.19/168.04 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.19/168.04 => ( ! [B_i] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 168.19/168.04 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_zip__obtain__same__length,axiom, % 168.19/168.04 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 168.19/168.04 ( ( 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)) % 168.19/168.04 => 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)))) ) % 168.19/168.04 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_map__of__eqI,axiom, % 168.19/168.04 ! [V_ys_2,V_xs_2,T_b,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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) ) % 168.19/168.04 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_wfP__SUP,axiom, % 168.19/168.04 ! [T_a,V_r_2,T_b] : % 168.19/168.04 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 168.19/168.04 => ( ! [B_i,B_j] : % 168.19/168.04 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 168.19/168.04 => 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)) ) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_dropWhile__append2,axiom, % 168.19/168.04 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 168.19/168.04 ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => hBOOL(hAPP(V_P_2,B_x)) ) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__all2__all__nthI,axiom, % 168.19/168.04 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 168.19/168.04 ( 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) % 168.19/168.04 => ( ! [B_n] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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))) ) % 168.19/168.04 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_finite__map__freshness,axiom, % 168.19/168.04 ! [V_f_2,T_b,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 168.19/168.04 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 168.19/168.04 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_mem__splitE,axiom, % 168.19/168.04 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ~ ! [B_x,B_y] : % 168.19/168.04 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 168.19/168.04 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_mem__splitI2,axiom, % 168.19/168.04 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 168.19/168.04 ( ! [B_a,B_b] : % 168.19/168.04 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_finite__sorted__distinct__unique,axiom, % 168.19/168.04 ! [V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ? [B_x] : % 168.19/168.04 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 168.19/168.04 & c_List_Olinorder__class_Osorted(T_a,B_x) % 168.19/168.04 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 168.19/168.04 & ! [B_y] : % 168.19/168.04 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 168.19/168.04 & c_List_Olinorder__class_Osorted(T_a,B_y) % 168.19/168.04 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 168.19/168.04 => B_y = B_x ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_setsum__SucD,axiom, % 168.19/168.04 ! [V_n_2,V_A_2,V_f_2,T_a] : % 168.19/168.04 ( 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) % 168.19/168.04 => ? [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.19/168.04 & 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_nat__mod__eq__lemma,axiom, % 168.19/168.04 ! [V_y,V_n,V_x] : % 168.19/168.04 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 168.19/168.04 => ? [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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_takeWhile__append2,axiom, % 168.19/168.04 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 168.19/168.04 ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => hBOOL(hAPP(V_P_2,B_x)) ) % 168.19/168.04 => 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_insort__is__Cons,axiom, % 168.19/168.04 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 168.19/168.04 ( class_Orderings_Olinorder(T_b) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_wfI__pf,axiom, % 168.19/168.04 ! [V_R_2,T_a] : % 168.19/168.04 ( ! [B_A] : % 168.19/168.04 ( 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))) % 168.19/168.04 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 168.19/168.04 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_filter__eq__Cons__iff,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 168.19/168.04 ( 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) % 168.19/168.04 <=> ? [B_us,B_vs] : % 168.19/168.04 ( 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)) % 168.19/168.04 & ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 168.19/168.04 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 168.19/168.04 & hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.04 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Cons__eq__filter__iff,axiom, % 168.19/168.04 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 168.19/168.04 ( 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) % 168.19/168.04 <=> ? [B_us,B_vs] : % 168.19/168.04 ( 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)) % 168.19/168.04 & ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 168.19/168.04 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 168.19/168.04 & hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.04 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Sigma__mono,axiom, % 168.19/168.04 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.19/168.04 => 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))) ) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_not__acc__down,axiom, % 168.19/168.04 ! [V_R_2,V_x_2,T_a] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 168.19/168.04 => ~ ! [B_z] : % 168.19/168.04 ( 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)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_acc_OaccI,axiom, % 168.19/168.04 ! [V_r_2,V_x_2,T_a] : % 168.19/168.04 ( ! [B_y] : % 168.19/168.04 ( 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)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold__image__1,axiom, % 168.19/168.04 ! [V_f_2,V_S_2,T_a,T_b] : % 168.19/168.04 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 168.19/168.04 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 168.19/168.04 => 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) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_card_Oneutral,axiom, % 168.19/168.04 ! [V_A_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.19/168.04 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.19/168.04 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__ball__nth,axiom, % 168.19/168.04 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => hBOOL(hAPP(V_P_2,B_x)) ) % 168.19/168.04 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_max__ext_Osimps,axiom, % 168.19/168.04 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 168.19/168.04 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 168.19/168.04 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.19/168.04 & ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 168.19/168.04 => ? [B_xa] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 168.19/168.04 & 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)) ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_mod__induct__0,axiom, % 168.19/168.04 ! [V_i_2,V_P_2,V_p_2] : % 168.19/168.04 ( ! [B_i] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 168.19/168.04 => ( hBOOL(hAPP(V_P_2,B_i)) % 168.19/168.04 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 168.19/168.04 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 168.19/168.04 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_sorted_OCons,axiom, % 168.19/168.04 ! [V_x_2,V_xs_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 168.19/168.04 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 168.19/168.04 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_InterI,axiom, % 168.19/168.04 ! [V_A_2,V_C_2,T_a] : % 168.19/168.04 ( ! [B_X] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold__image__cong,axiom, % 168.19/168.04 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 168.19/168.04 ( class_Groups_Oab__semigroup__mult(T_b) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.19/168.04 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 168.19/168.04 => 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) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Max__eqI,axiom, % 168.19/168.04 ! [V_x_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( ! [B_y] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.19/168.04 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Min__eqI,axiom, % 168.19/168.04 ! [V_x_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( ! [B_y] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.19/168.04 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_wf__no__infinite__down__chainE,axiom, % 168.19/168.04 ! [V_f_2,V_r_2,T_a] : % 168.19/168.04 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.19/168.04 => ~ ! [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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__ex__length,axiom, % 168.19/168.04 ! [V_xs_2,V_P_2,T_a] : % 168.19/168.04 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 168.19/168.04 <=> ? [B_n] : % 168.19/168.04 ( 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))) % 168.19/168.04 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_setsum__reindex__cong,axiom, % 168.19/168.04 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 168.19/168.04 ( class_Groups_Ocomm__monoid__add(T_c) % 168.19/168.04 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.19/168.04 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 168.19/168.04 => ( ! [B_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 168.19/168.04 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 168.19/168.04 => 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) ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__ex__simps_I2_J,axiom, % 168.19/168.04 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__ex__rev,axiom, % 168.19/168.04 ! [V_xs_2,V_P_2,T_a] : % 168.19/168.04 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 168.19/168.04 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__ex__iff,axiom, % 168.19/168.04 ! [V_xs_2,V_P_2,T_a] : % 168.19/168.04 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 168.19/168.04 <=> ? [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__ex__append,axiom, % 168.19/168.04 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 168.19/168.04 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 168.19/168.04 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 168.19/168.04 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_list__ex__simps_I1_J,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 168.19/168.04 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 168.19/168.04 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.19/168.04 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_scomp__unfold,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_setsum__ivl__cong,axiom, % 168.19/168.04 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] : % 168.19/168.04 ( ( class_Groups_Ocomm__monoid__add(T_b) % 168.19/168.04 & class_Orderings_Oord(T_a) ) % 168.19/168.04 => ( V_a_2 = V_ca_2 % 168.19/168.04 => ( V_b_2 = V_d_2 % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x)) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 168.19/168.04 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 168.19/168.04 => 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)) ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_scomp__def,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_scomp__apply,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_scomp__Pair,axiom, % 168.19/168.04 ! [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 ). % 168.19/168.04 % 168.19/168.04 fof(fact_Pair__scomp,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_scomp__scomp,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_iterate_Osimps,axiom, % 168.19/168.04 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 168.19/168.04 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 168.19/168.04 => 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) ) % 168.19/168.04 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_less__eq,axiom, % 168.19/168.04 ! [V_n_2,V_m_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_acyclic__def,axiom, % 168.19/168.04 ! [V_r_2,T_a] : % 168.19/168.04 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 168.19/168.04 <=> ! [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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_less__than__def,axiom, % 168.19/168.04 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 168.19/168.04 % 168.19/168.04 fof(fact_wf__trancl,axiom, % 168.19/168.04 ! [V_r_2,T_a] : % 168.19/168.04 ( c_Wellfounded_Owf(T_a,V_r_2) % 168.19/168.04 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl_Or__into__trancl,axiom, % 168.19/168.04 ! [V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__subset__Field2,axiom, % 168.19/168.04 ! [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))))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_r__into__trancl_H,axiom, % 168.19/168.04 ! [V_r_2,V_p_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__empty,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__domain,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__range,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_finite__trancl,axiom, % 168.19/168.04 ! [V_r_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 168.19/168.04 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_r__r__into__trancl,axiom, % 168.19/168.04 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( 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)) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__into__trancl2,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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)) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__trans,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__mono,axiom, % 168.19/168.04 ! [V_s_2,V_r_2,V_p_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 168.19/168.04 => ( 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)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__unfold,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__subset__Sigma,axiom, % 168.19/168.04 ! [V_A_2,V_r_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__Int__subset,axiom, % 168.19/168.04 ! [V_s_2,V_r_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( 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)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_log_Osimps,axiom, % 168.19/168.04 ! [V_i,V_b] : % 168.19/168.04 ( ( ( 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))) % 168.19/168.04 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 168.19/168.04 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 168.19/168.04 & ( ~ ( 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))) % 168.19/168.04 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 168.19/168.04 => 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(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral,V_i),V_b))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_minus__shift__def,axiom, % 168.19/168.04 ! [V_r,V_l,V_k] : % 168.19/168.04 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 168.19/168.04 => 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) ) % 168.19/168.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_inc__shift__def,axiom, % 168.19/168.04 ! [V_k,V_v] : % 168.19/168.04 ( ( V_v = V_k % 168.19/168.04 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 168.19/168.04 & ( V_v != V_k % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_select,axiom, % 168.19/168.04 ! [V_s_2,T_a,V_xs_2] : % 168.19/168.04 ( V_xs_2 != c_List_Olist_ONil(T_a) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_select__weight__member,axiom, % 168.19/168.04 ! [V_s_2,V_xs_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_select__weigth__select,axiom, % 168.19/168.04 ! [T_a,V_xs_2] : % 168.19/168.04 ( V_xs_2 != c_List_Olist_ONil(T_a) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_select__weight__cons__zero,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_select__weigth__drop__zero,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_pick__member,axiom, % 168.19/168.04 ! [V_xs_2,T_a,V_i_2] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_pick_Osimps,axiom, % 168.19/168.04 ! [V_xs,V_x,T_a,V_i] : % 168.19/168.04 ( ( 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))) % 168.19/168.04 => 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) ) % 168.19/168.04 & ( ~ 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_pick__drop__zero,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_select__weight__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_pick__same,axiom, % 168.19/168.04 ! [V_xs_2,T_a,V_l_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_one__code__numeral__def,axiom, % 168.19/168.04 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_times__code__numeral__code,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 168.19/168.04 ! [V_m_2,V_n_2] : % 168.19/168.04 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 168.19/168.04 <=> V_n_2 = V_m_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 168.19/168.04 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(fact_zero__code__numeral__def,axiom, % 168.19/168.04 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_code__numeral_Oof__nat__inject,axiom, % 168.19/168.04 ! [V_y_2,V_x_2] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 168.19/168.04 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 168.19/168.04 <=> V_x_2 = V_y_2 ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_number__of__code__numeral__def,axiom, % 168.19/168.04 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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_less__eq__code__numeral__code,axiom, % 168.19/168.04 ! [V_m_2,V_n_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_plus__code__numeral__code,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_less__code__numeral__code,axiom, % 168.19/168.04 ! [V_m_2,V_n_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_code__numeral__not__eq__zero,axiom, % 168.19/168.04 ! [V_i_2] : % 168.19/168.04 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 168.19/168.04 <=> 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_range,axiom, % 168.19/168.04 ! [V_s,V_k] : % 168.19/168.04 ( 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)) % 168.19/168.04 => 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_select__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__insert,axiom, % 168.19/168.04 ! [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)))))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_r__into__rtrancl,axiom, % 168.19/168.04 ! [V_r_2,V_p_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl_Ortrancl__refl,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__into__rtrancl,axiom, % 168.19/168.04 ! [V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_listrel__rtrancl__refl,axiom, % 168.19/168.04 ! [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)))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 168.19/168.04 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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)))) % 168.19/168.04 => 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)))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_nat__of__of__nat,axiom, % 168.19/168.04 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 168.19/168.04 % 168.19/168.04 fof(fact_of__nat__nat__of,axiom, % 168.19/168.04 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 168.19/168.04 % 168.19/168.04 fof(fact_nat__of__inverse,axiom, % 168.19/168.04 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 168.19/168.04 % 168.19/168.04 fof(fact_times__code__numeral__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_type__definition__code__numeral,axiom, % 168.19/168.04 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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_listrel__rtrancl__trans,axiom, % 168.19/168.04 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => ( 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)))) % 168.19/168.04 => 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)))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__trans,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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)) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__eq__or__trancl,axiom, % 168.19/168.04 ! [V_R_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> ( V_x_2 = V_y_2 % 168.19/168.04 | ( V_x_2 != V_y_2 % 168.19/168.04 & 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))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__into__trancl2,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtranclD,axiom, % 168.19/168.04 ! [V_R_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( V_a_2 = V_b_2 % 168.19/168.04 | ( V_a_2 != V_b_2 % 168.19/168.04 & 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))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__into__trancl1,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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)) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__rtrancl__trancl,axiom, % 168.19/168.04 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__trancl__trancl,axiom, % 168.19/168.04 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__mono,axiom, % 168.19/168.04 ! [V_s_2,V_r_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__subset,axiom, % 168.19/168.04 ! [V_S_2,V_R_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( 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))) % 168.19/168.04 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__subset__rtrancl,axiom, % 168.19/168.04 ! [V_s_2,V_r_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__Un__subset,axiom, % 168.19/168.04 ! [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)))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Image__closed__trancl,axiom, % 168.19/168.04 ! [V_X_2,V_r_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_less__code__numeral__def,axiom, % 168.19/168.04 ! [V_m_2,V_n_2] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 168.19/168.04 <=> 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_less__eq__code__numeral__def,axiom, % 168.19/168.04 ! [V_m_2,V_n_2] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 168.19/168.04 <=> 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 168.19/168.04 ! [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)))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_nat__of__code,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_nat__of__number,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_int__of__def,axiom, % 168.19/168.04 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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_code__numeral_Onat__of__inject,axiom, % 168.19/168.04 ! [V_y_2,V_x_2] : % 168.19/168.04 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 168.19/168.04 <=> V_x_2 = V_y_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 168.19/168.04 ! [V_l_2,V_k_2] : % 168.19/168.04 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 168.19/168.04 <=> V_k_2 = V_l_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_nat__of,axiom, % 168.19/168.04 ! [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)))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__idemp,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__Un__rtrancl,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__idemp__self__comp,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_r__comp__rtrancl__eq,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Domain__rtrancl,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Range__rtrancl,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_in__rtrancl__UnI,axiom, % 168.19/168.04 ! [V_S_2,V_R_2,V_x_2,T_a] : % 168.19/168.04 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 168.19/168.04 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_refl__rtrancl,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__unfold__left,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__unfold__right,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__trancl__absorb,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__rtrancl__absorb,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_nat__of__aux__def,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 168.19/168.04 ! [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)))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Not__Domain__rtrancl,axiom, % 168.19/168.04 ! [V_y_2,V_R_2,V_x_2,T_a] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 168.19/168.04 => ( 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))) % 168.19/168.04 <=> V_x_2 = V_y_2 ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_acc__downwards,axiom, % 168.19/168.04 ! [V_b_2,V_r_2,V_a_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 168.19/168.04 => ( 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))) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_acc__downwards__aux,axiom, % 168.19/168.04 ! [V_r_2,V_a_2,V_b_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_wf__insert,axiom, % 168.19/168.04 ! [V_r_2,V_x_2,V_y_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 168.19/168.04 & ~ 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 168.19/168.04 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__listrel1__eq__len,axiom, % 168.19/168.04 ! [V_r_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_acyclic__insert,axiom, % 168.19/168.04 ! [V_r_2,V_x_2,V_y_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 168.19/168.04 & ~ 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_listrel__reflcl__if__listrel1,axiom, % 168.19/168.04 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 168.19/168.04 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Suc__code__numeral__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_minus__code__numeral__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_of__nat__inverse,axiom, % 168.19/168.04 ! [V_y_2] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 168.19/168.04 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_plus__code__numeral__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_div__code__numeral__def,axiom, % 168.19/168.04 ! [V_m,V_n] : hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral,V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_pred__nat__trancl__eq__le,axiom, % 168.19/168.04 ! [V_n_2,V_m_2] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_mod__code__numeral__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__subset__Sigma__aux,axiom, % 168.19/168.04 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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)))) % 168.19/168.04 => ( V_a_2 = V_b_2 % 168.19/168.04 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_code__numeral__decr,axiom, % 168.19/168.04 ! [V_k] : % 168.19/168.04 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_subtract__code__numeral__code,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_subtract__code__numeral__def,axiom, % 168.19/168.04 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(fact_minus__code__numeral__code,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_irrefl__tranclI,axiom, % 168.19/168.04 ! [V_x_2,V_r_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ~ 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_sequence__trans,axiom, % 168.19/168.04 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 168.19/168.04 ( ! [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))) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__converseD,axiom, % 168.19/168.04 ! [V_r_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__converseI,axiom, % 168.19/168.04 ! [V_r_2,V_x_2,V_y_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__converse,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__iff,axiom, % 168.19/168.04 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converseI,axiom, % 168.19/168.04 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converseD,axiom, % 168.19/168.04 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_in__listrel1__converse,axiom, % 168.19/168.04 ! [V_r_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 <=> 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__converseI,axiom, % 168.19/168.04 ! [V_r_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__converseD,axiom, % 168.19/168.04 ! [V_r_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__UNION,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__INTER,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__Int,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_listrel1__converse,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_refl__on__converse,axiom, % 168.19/168.04 ! [V_r_2,V_A_2,T_a] : % 168.19/168.04 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 168.19/168.04 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_equiv__comp__eq,axiom, % 168.19/168.04 ! [V_r_2,V_A_2,T_a] : % 168.19/168.04 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 168.19/168.04 => 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 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__rel__comp,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__Un,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__Id__on,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__converse,axiom, % 168.19/168.04 ! [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 ). % 168.19/168.04 % 168.19/168.04 fof(fact_Field__converse,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_acyclic__converse,axiom, % 168.19/168.04 ! [V_r_2,T_a] : % 168.19/168.04 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 168.19/168.04 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_finite__converse,axiom, % 168.19/168.04 ! [V_r_2,T_b,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 168.19/168.04 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Range__def,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Domain__converse,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Range__converse,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__inv__image,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_wf__converse__trancl,axiom, % 168.19/168.04 ! [V_r_2,T_a] : % 168.19/168.04 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 168.19/168.04 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__converse,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Image__subset__eq,axiom, % 168.19/168.04 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 <=> 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))))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_refl__on__comp__subset,axiom, % 168.19/168.04 ! [V_r_2,V_A_2,T_a] : % 168.19/168.04 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 168.19/168.04 => 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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_comp__equivI,axiom, % 168.19/168.04 ! [V_A_2,V_r_2,T_a] : % 168.19/168.04 ( 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 % 168.19/168.04 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 168.19/168.04 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_finite__acyclic__wf__converse,axiom, % 168.19/168.04 ! [V_r_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 168.19/168.04 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 168.19/168.04 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__def,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Image__INT__eq,axiom, % 168.19/168.04 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 168.19/168.04 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 168.19/168.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_reflcl__set__eq,axiom, % 168.19/168.04 ! [V_y_2,V_x_2,V_r_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 <=> 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_IdI,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_converse__Id,axiom, % 168.19/168.04 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Range__Id,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_refl__Id,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Domain__Id,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_single__valued__Id,axiom, % 168.19/168.04 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Id__O__R,axiom, % 168.19/168.04 ! [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 ). % 168.19/168.04 % 168.19/168.04 fof(fact_R__O__Id,axiom, % 168.19/168.04 ! [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 ). % 168.19/168.04 % 168.19/168.04 fof(fact_single__valued__rel__comp,axiom, % 168.19/168.04 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 168.19/168.04 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 168.19/168.04 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_single__valued__Id__on,axiom, % 168.19/168.04 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Image__Id,axiom, % 168.19/168.04 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 168.19/168.04 % 168.19/168.04 fof(fact_single__valued__subset,axiom, % 168.19/168.04 ! [V_s_2,V_r_2,T_b,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 168.19/168.04 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_pair__in__Id__conv,axiom, % 168.19/168.04 ! [V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> V_a_2 = V_b_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_single__valuedD,axiom, % 168.19/168.04 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 168.19/168.04 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 168.19/168.04 => ( 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)) % 168.19/168.04 => ( 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)) % 168.19/168.04 => V_y_2 = V_z_2 ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_single__valued__def,axiom, % 168.19/168.04 ! [V_r_2,T_b,T_a] : % 168.19/168.04 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 168.19/168.04 <=> ! [B_x,B_y] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ! [B_z] : % 168.19/168.04 ( 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)) % 168.19/168.04 => B_y = B_z ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__empty,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__reflcl__absorb,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__reflcl,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__r__diff__Id,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_pair__leq__def,axiom, % 168.19/168.04 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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__reflcl,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_reflcl__trancl,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__unfold,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_refl__reflcl,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Id__def,axiom, % 168.19/168.04 ! [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))))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_irrefl__diff__Id,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_single__valued__confluent,axiom, % 168.19/168.04 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 168.19/168.04 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 168.19/168.04 => ( 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))) % 168.19/168.04 => ( 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))) % 168.19/168.04 => ( 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))) % 168.19/168.04 | 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))) ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Image__Int__eq,axiom, % 168.19/168.04 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 168.19/168.04 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 168.19/168.04 => 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__Int__subset,axiom, % 168.19/168.04 ! [V_r_2,V_s_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( 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)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_total__on__diff__Id,axiom, % 168.19/168.04 ! [V_r_2,V_A_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 168.19/168.04 ! [V_R_2,V_p_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 168.19/168.04 => 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)))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_total__on__converse,axiom, % 168.19/168.04 ! [V_r_2,V_A_2,T_a] : % 168.19/168.04 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 168.19/168.04 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_relpow_Osimps_I1_J,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_single__valued__rel__pow,axiom, % 168.19/168.04 ! [V_n_2,V_R_2,T_a] : % 168.19/168.04 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 168.19/168.04 => 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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_funpow_Osimps_I1_J,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_funpow_Osimps_I2_J,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_comp__funpow,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__power,axiom, % 168.19/168.04 ! [V_R_2,V_p_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 168.19/168.04 <=> ? [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))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__imp__rtrancl,axiom, % 168.19/168.04 ! [V_R_2,V_n_2,V_p_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_funpow__add,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__0__E,axiom, % 168.19/168.04 ! [V_R_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => V_x_2 = V_y_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__0__I,axiom, % 168.19/168.04 ! [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))) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__Suc__I2,axiom, % 168.19/168.04 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ( 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))) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__Suc__I,axiom, % 168.19/168.04 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( 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)) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__add,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_wf__exp,axiom, % 168.19/168.04 ! [V_R_2,V_n_2,T_a] : % 168.19/168.04 ( 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)) % 168.19/168.04 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_funpow__swap1,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_total__on__empty,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__1,axiom, % 168.19/168.04 ! [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 ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__commute,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_relpow_Osimps_I2_J,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_funpow__mult,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(fact_trancl__power,axiom, % 168.19/168.04 ! [V_R_2,V_p_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 168.19/168.04 <=> ? [B_n] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 168.19/168.04 & 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_total__on__def,axiom, % 168.19/168.04 ! [V_r_2,V_A_2,T_a] : % 168.19/168.04 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 168.19/168.04 <=> ! [B_x] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.19/168.04 => ! [B_xa] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 168.19/168.04 => ( B_x != B_xa % 168.19/168.04 => ( 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)) % 168.19/168.04 | 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)) ) ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_funpow__code__def,axiom, % 168.19/168.04 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__E,axiom, % 168.19/168.04 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.19/168.04 => V_x_2 != V_z_2 ) % 168.19/168.04 => ~ ! [B_y,B_m] : % 168.19/168.04 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 168.19/168.04 => ( 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))) % 168.19/168.04 => ~ 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)) ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rotate__def,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__E2,axiom, % 168.19/168.04 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.19/168.04 => V_x_2 != V_z_2 ) % 168.19/168.04 => ~ ! [B_y,B_m] : % 168.19/168.04 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 168.19/168.04 => ( 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)) % 168.19/168.04 => ~ 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))) ) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_acyclicI,axiom, % 168.19/168.04 ! [V_r_2,T_a] : % 168.19/168.04 ( ! [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))) % 168.19/168.04 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_pos__not__random__dseq__def,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__Un__separatorE,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ! [B_y] : % 168.19/168.04 ( 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)) % 168.19/168.04 => B_x = B_y ) ) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rtrancl__Un__separator__converseE,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 168.19/168.04 ( 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)))) % 168.19/168.04 => ( ! [B_x] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ! [B_y] : % 168.19/168.04 ( 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)) % 168.19/168.04 => B_y = B_x ) ) % 168.19/168.04 => 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__Suc__E,axiom, % 168.19/168.04 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ~ ! [B_y] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ~ 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__Suc__D2,axiom, % 168.19/168.04 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ? [B_y] : % 168.19/168.04 ( 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)) % 168.19/168.04 & 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_rel__pow__Suc__E2,axiom, % 168.19/168.04 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ~ ! [B_y] : % 168.19/168.04 ( 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)) % 168.19/168.04 => ~ 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_tranclD2,axiom, % 168.19/168.04 ! [V_R_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ? [B_z] : % 168.19/168.04 ( 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))) % 168.19/168.04 & 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_tranclD,axiom, % 168.19/168.04 ! [V_R_2,V_y_2,V_x_2,T_a] : % 168.19/168.04 ( 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))) % 168.19/168.04 => ? [B_z] : % 168.19/168.04 ( 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)) % 168.19/168.04 & 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))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_IdE,axiom, % 168.19/168.04 ! [V_p_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 168.19/168.04 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_in__set__conv__decomp,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 <=> ? [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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_in__set__conv__decomp__first,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 <=> ? [B_ys] : % 168.19/168.04 ( ? [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)) % 168.19/168.04 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_in__set__conv__decomp__last,axiom, % 168.19/168.04 ! [V_xs_2,V_x_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 168.19/168.04 <=> ? [B_ys,B_zs] : % 168.19/168.04 ( 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)) % 168.19/168.04 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_mod__div__decomp,axiom, % 168.19/168.04 ! [V_b,V_a,T_a] : % 168.19/168.04 ( class_Divides_Osemiring__div(T_a) % 168.19/168.04 => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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)) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 168.19/168.04 ! [V_x_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.19/168.04 => 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) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_sup__Sup__fold__sup,axiom, % 168.19/168.04 ! [V_B_2,V_A_2,T_a] : % 168.19/168.04 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold__sup__insert,axiom, % 168.19/168.04 ! [V_a_2,V_b_2,V_A_2,T_a] : % 168.19/168.04 ( class_Lattices_Osemilattice__sup(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_union__fold__insert,axiom, % 168.19/168.04 ! [V_B_2,V_A_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_sup__SUPR__fold__sup,axiom, % 168.19/168.04 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 168.19/168.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 168.19/168.04 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 168.19/168.04 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 168.19/168.04 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 168.19/168.04 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_inf__Inf__fold__inf,axiom, % 168.19/168.04 ! [V_B_2,V_A_2,T_a] : % 168.19/168.04 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold__inf__insert,axiom, % 168.19/168.04 ! [V_a_2,V_b_2,V_A_2,T_a] : % 168.19/168.04 ( class_Lattices_Osemilattice__inf(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_min__max_Ofold__inf__insert,axiom, % 168.19/168.04 ! [V_a_2,V_b_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_min__max_Ofold__sup__insert,axiom, % 168.19/168.04 ! [V_a_2,V_b_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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)) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_folding_Oeq__fold,axiom, % 168.19/168.04 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 168.19/168.04 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold__image__def,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold__empty,axiom, % 168.19/168.04 ! [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 ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold__def,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 168.19/168.04 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.19/168.04 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_inf__INFI__fold__inf,axiom, % 168.19/168.04 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 168.19/168.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 168.19/168.04 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 168.19/168.04 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_sup__le__fold__sup,axiom, % 168.19/168.04 ! [V_b_2,V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Lattices_Osemilattice__sup(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.19/168.04 => 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))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold__inf__le__inf,axiom, % 168.19/168.04 ! [V_b_2,V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Lattices_Osemilattice__inf(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.19/168.04 => 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))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 168.19/168.04 ! [V_b_2,V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.19/168.04 => 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))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_min__max_Osup__le__fold__sup,axiom, % 168.19/168.04 ! [V_b_2,V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.19/168.04 => 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))) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Sup__fold__sup,axiom, % 168.19/168.04 ! [V_A_2,T_a] : % 168.19/168.04 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Inf__fold__inf,axiom, % 168.19/168.04 ! [V_A_2,T_a] : % 168.19/168.04 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_fold1__eq__fold__idem,axiom, % 168.19/168.04 ! [V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 168.19/168.04 ! [V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Lattices_Olattice(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 168.19/168.04 ! [V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Lattices_Olattice(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Min_Oeq__fold__idem_H,axiom, % 168.19/168.04 ! [V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_Max_Oeq__fold__idem_H,axiom, % 168.19/168.04 ! [V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 168.19/168.04 ! [V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 168.19/168.04 ! [V_a_2,V_A_2,T_a] : % 168.19/168.04 ( class_Orderings_Olinorder(T_a) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_minus__fold__remove,axiom, % 168.19/168.04 ! [V_B_2,V_A_2,T_a] : % 168.19/168.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_folding__one_Oeq__fold_H,axiom, % 168.19/168.04 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.19/168.04 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.19/168.04 => 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) ) ) ) ). % 168.19/168.04 % 168.19/168.04 fof(fact_SUPR__fold__sup,axiom, % 168.19/168.04 ! [V_f_2,V_A_2,T_a,T_b] : % 168.19/168.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 168.19/168.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.19/168.04 => 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) ) ) ). % 168.19/168.04 % 168.19/168.04 %----Arity declarations (220) % 168.19/168.04 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 168.19/168.04 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Lattices_Obounded__lattice(T_1) % 168.19/168.04 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 168.19/168.04 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Lattices_Obounded__lattice(T_1) % 168.19/168.04 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Lattices_Obounded__lattice(T_1) % 168.19/168.04 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Lattices_Olattice(T_1) % 168.19/168.04 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Lattices_Olattice(T_1) % 168.19/168.04 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Lattices_Odistrib__lattice(T_1) % 168.19/168.04 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Lattices_Oboolean__algebra(T_1) % 168.19/168.04 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Orderings_Opreorder,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Orderings_Opreorder(T_1) % 168.19/168.04 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Finite__Set_Ofinite,axiom, % 168.19/168.04 ! [T_1,T_2] : % 168.19/168.04 ( ( class_Finite__Set_Ofinite(T_2) % 168.19/168.04 & class_Finite__Set_Ofinite(T_1) ) % 168.19/168.04 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Lattices_Olattice,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Lattices_Olattice(T_1) % 168.19/168.04 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Orderings_Oorder,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Orderings_Oorder(T_1) % 168.19/168.04 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Orderings_Otop,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Orderings_Otop(T_1) % 168.19/168.04 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Orderings_Oord,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Orderings_Oord(T_1) % 168.19/168.04 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Orderings_Obot,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Orderings_Obot(T_1) % 168.19/168.04 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Groups_Ouminus,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Groups_Ouminus(T_1) % 168.19/168.04 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Groups_Ominus,axiom, % 168.19/168.04 ! [T_2,T_1] : % 168.19/168.04 ( class_Groups_Ominus(T_1) % 168.19/168.04 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__HOL_Oequal,axiom, % 168.19/168.04 ! [T_1,T_2] : % 168.19/168.04 ( ( class_Enum_Oenum(T_2) % 168.19/168.04 & class_HOL_Oequal(T_1) ) % 168.19/168.04 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_fun__Enum_Oenum,axiom, % 168.19/168.04 ! [T_1,T_2] : % 168.19/168.04 ( ( class_Enum_Oenum(T_2) % 168.19/168.04 & class_Enum_Oenum(T_1) ) % 168.19/168.04 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_Com_Ocom) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 168.19/168.04 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 168.19/168.04 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 168.19/168.04 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 168.19/168.04 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 168.19/168.04 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 168.19/168.04 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 168.19/168.04 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 168.19/168.04 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 168.19/168.04 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 168.19/168.04 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 168.19/168.04 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 168.19/168.04 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 168.19/168.04 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 168.19/168.04 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 168.19/168.04 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 168.19/168.04 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 168.19/168.04 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 168.19/168.04 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 168.19/168.04 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 168.19/168.04 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 168.19/168.04 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 168.19/168.04 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 168.19/168.04 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 168.19/168.04 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 168.19/168.04 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 168.19/168.04 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 168.19/168.04 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 168.19/168.04 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 168.19/168.04 class_Divides_Osemiring__div(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 168.19/168.04 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 168.19/168.04 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 168.19/168.04 class_Groups_Oab__group__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 168.19/168.04 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 168.19/168.04 class_Rings_Oordered__ring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 168.19/168.04 class_Orderings_Opreorder(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 168.19/168.04 class_Orderings_Olinorder(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 168.19/168.04 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 168.19/168.04 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 168.19/168.04 class_Groups_Omonoid__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 168.19/168.04 class_Smallcheck_Osmall(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 168.19/168.04 class_Rings_Osemiring__1(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 168.19/168.04 class_Rings_Osemiring__0(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 168.19/168.04 class_Lattices_Olattice(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 168.19/168.04 class_Groups_Ogroup__add(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 168.19/168.04 class_Divides_Oring__div(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 168.19/168.04 class_Rings_Omult__zero(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 168.19/168.04 class_Orderings_Oorder(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 168.19/168.04 class_Int_Oring__char__0(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 168.19/168.04 class_Int_Onumber__ring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 168.19/168.04 class_Rings_Osemiring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Orderings_Oord,axiom, % 168.19/168.04 class_Orderings_Oord(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 168.19/168.04 class_Groups_Ouminus(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 168.19/168.04 class_Groups_Osgn__if(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 168.19/168.04 class_Groups_Oabs__if(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 168.19/168.04 class_Rings_Oring__1(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Ominus,axiom, % 168.19/168.04 class_Groups_Ominus(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Power_Opower,axiom, % 168.19/168.04 class_Power_Opower(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Ozero,axiom, % 168.19/168.04 class_Groups_Ozero(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oring,axiom, % 168.19/168.04 class_Rings_Oring(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Rings_Oidom,axiom, % 168.19/168.04 class_Rings_Oidom(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Int_Onumber,axiom, % 168.19/168.04 class_Int_Onumber(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__Groups_Oone,axiom, % 168.19/168.04 class_Groups_Oone(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Int__Oint__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_Int_Oint) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 168.19/168.04 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 168.19/168.04 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 168.19/168.04 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 168.19/168.04 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 168.19/168.04 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 168.19/168.04 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 168.19/168.04 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 168.19/168.04 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 168.19/168.04 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 168.19/168.04 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 168.19/168.04 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 168.19/168.04 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 168.19/168.04 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 168.19/168.04 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 168.19/168.04 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 168.19/168.04 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 168.19/168.04 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 168.19/168.04 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 168.19/168.04 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 168.19/168.04 class_Orderings_Owellorder(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 168.19/168.04 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 168.19/168.04 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 168.19/168.04 class_Orderings_Opreorder(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 168.19/168.04 class_Orderings_Olinorder(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 168.19/168.04 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 168.19/168.04 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 168.19/168.04 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 168.19/168.04 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 168.19/168.04 class_Lattices_Olattice(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 168.19/168.04 class_Rings_Omult__zero(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 168.19/168.04 class_Orderings_Oorder(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 168.19/168.04 class_Rings_Osemiring(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 168.19/168.04 class_Orderings_Oord(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 168.19/168.04 class_Orderings_Obot(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 168.19/168.04 class_Groups_Ominus(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Power_Opower,axiom, % 168.19/168.04 class_Power_Opower(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 168.19/168.04 class_Groups_Ozero(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Int_Onumber,axiom, % 168.19/168.04 class_Int_Onumber(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__Groups_Oone,axiom, % 168.19/168.04 class_Groups_Oone(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_Nat_Onat) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 168.19/168.04 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 168.19/168.04 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 168.19/168.04 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 168.19/168.04 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 168.19/168.04 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 168.19/168.04 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 168.19/168.04 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 168.19/168.04 class_Orderings_Opreorder(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 168.19/168.04 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 168.19/168.04 class_Lattices_Olattice(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 168.19/168.04 class_Orderings_Oorder(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 168.19/168.04 class_Orderings_Otop(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 168.19/168.04 class_Orderings_Oord(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 168.19/168.04 class_Orderings_Obot(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 168.19/168.04 class_Groups_Ouminus(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 168.19/168.04 class_Groups_Ominus(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 168.19/168.04 class_Enum_Oenum(tc_HOL_Obool) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_Com_Ostate) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Com__Ovname__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_Com_Ovname) ). % 168.19/168.04 % 168.19/168.04 fof(arity_List__Olist__HOL_Oequal,axiom, % 168.19/168.04 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 168.19/168.04 % 168.19/168.04 fof(arity_sum__Finite__Set_Ofinite,axiom, % 168.19/168.04 ! [T_1,T_2] : % 168.19/168.04 ( ( class_Finite__Set_Ofinite(T_2) % 168.19/168.04 & class_Finite__Set_Ofinite(T_1) ) % 168.19/168.04 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_sum__HOL_Oequal,axiom, % 168.19/168.04 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 168.19/168.04 % 168.19/168.04 fof(arity_sum__Enum_Oenum,axiom, % 168.19/168.04 ! [T_1,T_2] : % 168.19/168.04 ( ( class_Enum_Oenum(T_2) % 168.19/168.04 & class_Enum_Oenum(T_1) ) % 168.19/168.04 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 168.19/168.04 ! [T_1] : % 168.19/168.04 ( class_Finite__Set_Ofinite(T_1) % 168.19/168.04 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 168.19/168.04 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 168.19/168.04 ! [T_1] : % 168.19/168.04 ( class_Enum_Oenum(T_1) % 168.19/168.04 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom, % 168.19/168.04 ! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)) ). % 168.19/168.04 % 168.19/168.04 fof(arity_prod__Finite__Set_Ofinite,axiom, % 168.19/168.04 ! [T_1,T_2] : % 168.19/168.04 ( ( class_Finite__Set_Ofinite(T_2) % 168.19/168.04 & class_Finite__Set_Ofinite(T_1) ) % 168.19/168.04 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_prod__Smallcheck_Osmall,axiom, % 168.19/168.04 ! [T_1,T_2] : % 168.19/168.04 ( ( class_Smallcheck_Osmall(T_2) % 168.19/168.04 & class_Smallcheck_Osmall(T_1) ) % 168.19/168.04 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_prod__HOL_Oequal,axiom, % 168.19/168.04 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 168.19/168.04 % 168.19/168.04 fof(arity_prod__Enum_Oenum,axiom, % 168.19/168.04 ! [T_1,T_2] : % 168.19/168.04 ( ( class_Enum_Oenum(T_2) % 168.19/168.04 & class_Enum_Oenum(T_1) ) % 168.19/168.04 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 168.19/168.04 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 168.19/168.04 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 168.19/168.04 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 168.19/168.04 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 168.19/168.04 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 168.19/168.04 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 168.19/168.04 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 168.19/168.04 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 168.19/168.04 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 168.19/168.04 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 168.19/168.04 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 168.19/168.04 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 168.19/168.04 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 168.19/168.04 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 168.19/168.04 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 168.19/168.04 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 168.19/168.04 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 168.19/168.04 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 168.19/168.04 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 168.19/168.04 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 168.19/168.04 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 168.19/168.04 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 168.19/168.04 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 168.19/168.04 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 168.19/168.04 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 168.19/168.04 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 168.19/168.04 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 168.19/168.04 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 168.19/168.04 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 168.19/168.04 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 168.19/168.04 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 168.19/168.04 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 168.19/168.04 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 168.19/168.04 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 168.19/168.04 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 168.19/168.04 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 168.19/168.04 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 168.19/168.04 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 168.19/168.04 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 168.19/168.04 % 168.19/168.04 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 168.19/168.04 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 168.19/168.04 % 168.19/168.04 %----Helper facts (20) % 168.19/168.04 fof(help_c__COMBI__1,axiom, % 168.19/168.04 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 168.19/168.04 % 168.19/168.04 fof(help_c__COMBK__1,axiom, % 168.19/168.04 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 168.19/168.04 % 168.19/168.04 fof(help_c__COMBB__1,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__COMBC__1,axiom, % 168.19/168.04 ! [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) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__COMBS__1,axiom, % 168.19/168.04 ! [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)) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fequal__1,axiom, % 168.19/168.04 ! [V_y_2,V_x_2] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 168.19/168.04 | V_x_2 = V_y_2 ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fequal__2,axiom, % 168.19/168.04 ! [V_y_2,V_x_2] : % 168.19/168.04 ( V_x_2 != V_y_2 % 168.19/168.04 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fFalse__1,axiom, % 168.19/168.04 ~ hBOOL(c_fFalse) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fTrue__1,axiom, % 168.19/168.04 hBOOL(c_fTrue) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fNot__1,axiom, % 168.19/168.04 ! [V_P_2] : % 168.19/168.04 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 168.19/168.04 | ~ hBOOL(V_P_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fNot__2,axiom, % 168.19/168.04 ! [V_P_2] : % 168.19/168.04 ( ~ ~ hBOOL(V_P_2) % 168.19/168.04 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fconj__1,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2] : % 168.19/168.04 ( ~ hBOOL(V_P_2) % 168.19/168.04 | ~ hBOOL(V_Q_2) % 168.19/168.04 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fconj__2,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 168.19/168.04 | hBOOL(V_P_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fconj__3,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 168.19/168.04 | hBOOL(V_Q_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fdisj__1,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2] : % 168.19/168.04 ( ~ hBOOL(V_P_2) % 168.19/168.04 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fdisj__2,axiom, % 168.19/168.04 ! [V_P_2,V_Q_2] : % 168.19/168.04 ( ~ hBOOL(V_Q_2) % 168.19/168.04 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fdisj__3,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 168.19/168.04 | hBOOL(V_P_2) % 168.19/168.04 | hBOOL(V_Q_2) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fimplies__1,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2] : % 168.19/168.04 ( hBOOL(V_P_2) % 168.19/168.04 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fimplies__2,axiom, % 168.19/168.04 ! [V_P_2,V_Q_2] : % 168.19/168.04 ( ~ hBOOL(V_Q_2) % 168.19/168.04 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 168.19/168.04 % 168.19/168.04 fof(help_c__fimplies__3,axiom, % 168.19/168.04 ! [V_Q_2,V_P_2] : % 168.19/168.04 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 168.19/168.04 | ~ hBOOL(V_P_2) % 168.19/168.04 | hBOOL(V_Q_2) ) ). % 168.19/168.04 % 168.19/168.04 %----Conjectures (5) % 168.19/168.04 fof(conj_0,hypothesis, % 168.19/168.04 c_Hoare__Mirabelle_Ostate__not__singleton ). % 168.19/168.04 % 168.19/168.04 fof(conj_1,hypothesis, % 168.19/168.04 c_Com_OWT__bodies ). % 168.19/168.04 % 168.19/168.04 fof(conj_2,hypothesis, % 168.19/168.04 hBOOL(hAPP(c_Com_OWT,v_c)) ). % 168.19/168.04 % 168.19/168.04 fof(conj_3,hypothesis, % 168.19/168.04 hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ). % 168.19/168.04 % 168.19/168.04 fof(conj_4,conjecture, % 168.19/168.04 hBOOL(hAPP(c_Com_OWT,v_y)) ). % 168.19/168.04 % 168.19/168.04 %------------------------------------------------------------------------------ % 168.19/168.04 %------------------------------------------- % 168.19/168.04 % Proof found % 168.19/168.04 % SZS status Theorem for theBenchmark % 168.19/168.04 % SZS output start Proof % 168.19/168.05 %ClaNum:10078(EqnAxiom:2785) % 168.19/168.05 %VarNum:69831(SingletonVarNum:20554) % 168.19/168.05 %MaxLitNum:8 % 168.19/168.05 %MaxfuncDepth:15 % 168.19/168.05 %SharedTerms:1103 % 168.19/168.05 %goalClause: 4401 % 168.19/168.05 %singleGoalClaCount:1 % 168.19/168.05 [2786]P1(a5000) % 168.19/168.05 [2787]P4(a5000) % 168.19/168.05 [2791]P22(a186) % 168.19/168.05 [2792]P23(a849) % 168.19/168.05 [2793]P23(a1) % 168.19/168.05 [2794]P23(a111) % 168.19/168.05 [2795]P24(a849) % 168.19/168.05 [2796]P24(a1) % 168.19/168.05 [2797]P24(a111) % 168.19/168.05 [2798]P62(a849) % 168.19/168.05 [2799]P62(a1) % 168.19/168.05 [2800]P62(a111) % 168.19/168.05 [2801]P63(a849) % 168.19/168.05 [2802]P63(a1) % 168.19/168.05 [2803]P63(a111) % 168.19/168.05 [2804]P66(a849) % 168.19/168.05 [2805]P66(a1) % 168.19/168.05 [2806]P66(a111) % 168.19/168.05 [2807]P67(a849) % 168.19/168.05 [2808]P67(a1) % 168.19/168.05 [2809]P67(a111) % 168.19/168.05 [2810]P68(a1) % 168.19/168.05 [2811]P84(a849) % 168.19/168.05 [2812]P84(a1) % 168.19/168.05 [2813]P84(a111) % 168.19/168.05 [2814]P109(a849) % 168.19/168.05 [2815]P109(a1) % 168.19/168.05 [2816]P110(a849) % 168.19/168.05 [2817]P110(a1) % 168.19/168.05 [2818]P110(a111) % 168.19/168.05 [2819]P85(a849) % 168.19/168.05 [2820]P85(a842) % 168.19/168.05 [2821]P25(a1) % 168.19/168.05 [2822]P69(a1) % 168.19/168.05 [2823]P71(a849) % 168.19/168.05 [2824]P71(a842) % 168.19/168.05 [2825]P71(a1) % 168.19/168.05 [2826]P71(a111) % 168.19/168.05 [2827]P73(a842) % 168.19/168.05 [2828]P73(a1) % 168.19/168.05 [2829]P86(a842) % 168.19/168.05 [2830]P100(a1) % 168.19/168.05 [2831]P87(a1) % 168.19/168.05 [2832]P101(a849) % 168.19/168.05 [2833]P101(a842) % 168.19/168.05 [2834]P101(a1) % 168.19/168.05 [2835]P101(a111) % 168.19/168.05 [2836]P74(a849) % 168.19/168.05 [2837]P74(a1) % 168.19/168.05 [2838]P74(a111) % 168.19/168.05 [2839]P102(a849) % 168.19/168.05 [2840]P102(a842) % 168.19/168.05 [2841]P102(a1) % 168.19/168.05 [2842]P102(a111) % 168.19/168.05 [2843]P103(a849) % 168.19/168.05 [2844]P103(a1) % 168.19/168.05 [2845]P103(a111) % 168.19/168.05 [2846]P104(a849) % 168.19/168.05 [2847]P104(a842) % 168.19/168.05 [2848]P104(a1) % 168.19/168.05 [2849]P104(a111) % 168.19/168.05 [2850]P111(a1) % 168.19/168.05 [2851]P76(a849) % 168.19/168.05 [2852]P76(a1) % 168.19/168.05 [2853]P76(a111) % 168.19/168.05 [2854]P77(a849) % 168.19/168.05 [2855]P77(a1) % 168.19/168.05 [2856]P77(a111) % 168.19/168.05 [2857]P78(a1) % 168.19/168.05 [2858]P80(a849) % 168.19/168.05 [2859]P80(a1) % 168.19/168.05 [2860]P80(a111) % 168.19/168.05 [2861]P112(a849) % 168.19/168.05 [2862]P112(a1) % 168.19/168.05 [2863]P112(a111) % 168.19/168.05 [2864]P136(a849) % 168.19/168.05 [2865]P136(a1) % 168.19/168.05 [2866]P136(a111) % 168.19/168.05 [2867]P113(a1) % 168.19/168.05 [2868]P92(a849) % 168.19/168.05 [2869]P92(a842) % 168.19/168.05 [2870]P92(a1) % 168.19/168.05 [2871]P93(a849) % 168.19/168.05 [2872]P93(a842) % 168.19/168.05 [2873]P93(a1) % 168.19/168.05 [2874]P94(a842) % 168.19/168.05 [2875]P81(a849) % 168.19/168.05 [2876]P81(a1) % 168.19/168.05 [2877]P81(a111) % 168.19/168.05 [2878]P82(a1) % 168.19/168.05 [2879]P120(a1) % 168.19/168.05 [2880]P64(a849) % 168.19/168.05 [2881]P64(a1) % 168.19/168.05 [2882]P64(a111) % 168.19/168.05 [2883]P99(a849) % 168.19/168.05 [2884]P99(a1) % 168.19/168.05 [2885]P99(a111) % 168.19/168.05 [2886]P123(a849) % 168.19/168.05 [2887]P123(a1) % 168.19/168.05 [2888]P123(a111) % 168.19/168.05 [2889]P132(a1) % 168.19/168.05 [2890]P125(a849) % 168.19/168.05 [2891]P125(a1) % 168.19/168.05 [2892]P125(a111) % 168.19/168.05 [2893]P134(a849) % 168.19/168.05 [2894]P134(a1) % 168.19/168.05 [2895]P134(a111) % 168.19/168.05 [2896]P108(a849) % 168.19/168.05 [2897]P108(a1) % 168.19/168.05 [2898]P108(a111) % 168.19/168.05 [2899]P75(a849) % 168.19/168.05 [2900]P75(a1) % 168.19/168.05 [2901]P75(a111) % 168.19/168.05 [2902]P70(a849) % 168.19/168.05 [2903]P70(a1) % 168.19/168.05 [2904]P70(a111) % 168.19/168.05 [2905]P114(a1) % 168.19/168.05 [2906]P126(a1) % 168.19/168.05 [2907]P127(a849) % 168.19/168.05 [2908]P127(a1) % 168.19/168.05 [2909]P127(a111) % 168.19/168.05 [2910]P128(a1) % 168.19/168.05 [2911]P130(a849) % 168.19/168.05 [2912]P130(a1) % 168.19/168.05 [2913]P130(a111) % 168.19/168.05 [2914]P129(a849) % 168.19/168.05 [2915]P129(a1) % 168.19/168.05 [2916]P129(a111) % 168.19/168.05 [2917]P118(a1) % 168.19/168.05 [2918]P119(a1) % 168.19/168.05 [2919]P117(a849) % 168.19/168.05 [2920]P117(a1) % 168.19/168.05 [2921]P117(a111) % 168.19/168.05 [2922]P124(a849) % 168.19/168.05 [2923]P124(a1) % 168.19/168.05 [2924]P124(a111) % 168.19/168.05 [2925]P133(a1) % 168.19/168.05 [2926]P121(a849) % 168.19/168.05 [2927]P121(a1) % 168.19/168.05 [2928]P121(a111) % 168.19/168.05 [2929]P122(a1) % 168.19/168.05 [2930]P79(a1) % 168.19/168.05 [2931]P131(a1) % 168.19/168.05 [2932]P65(a1) % 168.19/168.05 [2933]P88(a849) % 168.19/168.05 [2934]P88(a1) % 168.19/168.05 [2935]P88(a111) % 168.19/168.05 [2936]P90(a1) % 168.19/168.05 [2937]P98(a849) % 168.19/168.05 [2938]P98(a842) % 168.19/168.05 [2939]P98(a1) % 168.19/168.05 [2940]P96(a849) % 168.19/168.05 [2941]P96(a842) % 168.19/168.05 [2942]P96(a1) % 168.19/168.05 [2943]P105(a842) % 168.19/168.05 [2944]P97(a842) % 168.19/168.05 [2945]P106(a849) % 168.19/168.05 [2946]P106(a1) % 168.19/168.05 [2947]P106(a111) % 168.19/168.05 [2948]P135(a849) % 168.19/168.05 [2949]P135(a1) % 168.19/168.05 [2950]P135(a111) % 168.19/168.05 [2951]P26(a1) % 168.19/168.05 [2952]P55(a849) % 168.19/168.05 [2953]P55(a1) % 168.19/168.05 [2954]P55(a111) % 168.19/168.05 [2955]P137(a1) % 168.19/168.05 [2956]P137(a852) % 168.19/168.05 [2957]P56(a842) % 168.19/168.05 [2958]P56(a852) % 168.19/168.05 [2959]P27(a842) % 168.19/168.05 [2960]P72(a849) % 168.19/168.05 [2961]P72(a1) % 168.19/168.05 [2962]P72(a111) % 168.19/168.05 [2963]P107(a849) % 168.19/168.05 [2964]P83(a849) % 168.19/168.05 [2965]P83(a1) % 168.19/168.05 [2966]P83(a111) % 168.19/168.05 [2967]P57(a842) % 168.19/168.05 [2968]P57(a852) % 168.19/168.05 [2969]P89(a843) % 168.19/168.05 [2970]P89(a849) % 168.19/168.05 [2971]P89(a844) % 168.19/168.05 [2972]P89(a842) % 168.19/168.05 [2973]P89(a845) % 168.19/168.05 [2974]P89(a1) % 168.19/168.05 [2975]P89(a313) % 168.19/168.05 [2976]P89(a111) % 168.19/168.05 [2977]P89(a852) % 168.19/168.05 [2978]P95(a842) % 168.19/168.05 [2994]P37(a849,a229) % 168.19/168.05 [2995]P37(a849,a307) % 168.19/168.05 [4378]~E(a109,a92) % 168.19/168.05 [4379]~P22(a187) % 168.19/168.05 [2788]E(f2(a1),a92) % 168.19/168.05 [2789]E(f112(a111),a3) % 168.19/168.05 [2790]E(f21(a111),a22) % 168.19/168.05 [2979]E(f34(a23),f2(a849)) % 168.19/168.05 [2980]E(f93(a186),f2(a849)) % 168.19/168.05 [2981]E(f93(a187),f2(a849)) % 168.19/168.05 [2982]E(f188(a849),f2(a849)) % 168.19/168.05 [2983]E(f113(a849),f223(a849)) % 168.19/168.05 [2984]E(f122(a849),f224(a849)) % 168.19/168.05 [2985]E(f114(a1),f39(a1)) % 168.19/168.05 [2986]P28(f2(a1)) % 168.19/168.05 [2987]P28(f87(a1)) % 168.19/168.05 [3034]P22(f317(a24,a23)) % 168.19/168.05 [3035]P22(f317(a24,a855)) % 168.19/168.05 [3051]P37(f857(a849,a849),a45) % 168.19/168.05 [3402]E(f310(a849,a849,a229,a229),a45) % 168.19/168.05 [4380]~E(f87(a1),f2(a1)) % 168.19/168.05 [4401]~P22(f317(a24,a859)) % 168.19/168.05 [2988]E(f123(f2(a849)),f2(a849)) % 168.19/168.05 [2989]E(f4(f2(a111)),f2(a849)) % 168.19/168.05 [2999]E(f317(f88(a1),a92),a92) % 168.19/168.05 [3003]E(f317(a3,f2(a849)),f2(a111)) % 168.19/168.05 [3004]E(f317(a124,f2(a849)),f87(a849)) % 168.19/168.05 [3005]E(f317(a116,f87(a1)),f87(a849)) % 168.19/168.05 [3006]E(f317(a3,f87(a849)),f87(a111)) % 168.19/168.05 [3008]E(f317(f115(a1),a92),f2(a1)) % 168.19/168.05 [3009]E(f317(f115(a111),a92),f2(a111)) % 168.19/168.05 [3010]E(f317(a116,f2(a1)),f2(a849)) % 168.19/168.05 [3011]E(f317(f189(a843),a23),f2(a849)) % 168.19/168.05 [3012]E(f317(f189(a842),a186),f2(a849)) % 168.19/168.05 [3013]E(f317(f189(a842),a187),f2(a849)) % 168.19/168.05 [3014]E(f317(f115(a849),a92),f2(a849)) % 168.19/168.05 [3019]E(f317(f88(a1),f87(a1)),a109) % 168.19/168.05 [3027]E(f317(f189(a111),f2(a111)),f2(a849)) % 168.19/168.05 [3028]E(f317(f88(a1),f2(a1)),f2(a1)) % 168.19/168.05 [3029]E(f317(f112(a1),f2(a849)),f2(a1)) % 168.19/168.05 [3030]E(f317(f112(a1),f87(a849)),f87(a1)) % 168.19/168.05 [3038]E(f317(f217(a843),a859),f317(a27,a860)) % 168.19/168.05 [3046]E(f317(a116,f87(a1)),f317(a124,f2(a849))) % 168.19/168.05 [3048]E(f317(f171(a846,a843),a28),a27) % 168.19/168.05 [3049]E(f308(f857(a849,a849),a45),a46) % 168.19/168.05 [3050]E(f309(f857(a849,a849),a45),a47) % 168.19/168.05 [3073]E(f317(f231(a849),f2(a849)),f188(f858(a849,a842))) % 168.19/168.05 [3074]E(f317(f232(a849),f2(a849)),f233(f858(a849,a842))) % 168.19/168.05 [3084]P39(f188(f858(a1,a842))) % 168.19/168.05 [3116]E(f317(f317(f21(a111),f2(a111)),f87(a111)),f2(a111)) % 168.19/168.05 [3189]P22(f317(f317(f226(a1),a109),f2(a1))) % 168.19/168.05 [3215]P22(f317(f317(f225(a1),f2(a1)),f87(a1))) % 168.19/168.05 [3216]P22(f317(f317(f226(a1),f2(a1)),f87(a1))) % 168.19/168.05 [3395]P22(f317(f71(a846),f177(a846,a843,a27))) % 168.19/168.05 [3432]E(f317(f317(f265(a849,a849,a849),a307),f284(a849,a307)),a229) % 168.19/168.05 [3474]P40(a1,a849,a116,f317(f225(a1),f2(a1))) % 168.19/168.05 [3478]E(f317(f317(f51(a849,f858(a849,a842)),f233(f858(a849,a842))),f277(a849)),f233(f858(a849,a842))) % 168.19/168.05 [3479]E(f317(f317(f51(a849,f858(a849,a842)),f233(f858(a849,a842))),f231(a849)),f233(f858(a849,a842))) % 168.19/168.05 [3480]E(f317(f317(f51(a849,f858(a849,a842)),f233(f858(a849,a842))),f232(a849)),f233(f858(a849,a842))) % 168.19/168.05 [3481]E(f317(f317(f52(a849,f858(a849,a842)),f233(f858(a849,a842))),f280(a849)),f188(f858(a849,a842))) % 168.19/168.05 [3495]P19(a849,a1,f112(a1),f233(f858(a849,a842))) % 168.19/168.05 [3638]E(f317(f82(a849,a111,a1,a3),a116),f115(a111)) % 168.19/168.05 [3865]P51(a111,a849,a19,a3,f233(f858(a849,a842))) % 168.19/168.05 [3874]P51(a1,f858(f857(a849,a849),a842),a118,a98,a110) % 168.19/168.05 [4141]E(f248(a1,a1,a1,a1,f39(a1),f88(a1)),a60) % 168.19/168.05 [4414]~E(f317(f115(a1),a109),f317(f115(a1),a92)) % 168.19/168.05 [4415]~P22(f317(a193,f2(a1))) % 168.19/168.05 [4416]~P22(f317(a193,f87(a1))) % 168.19/168.05 [4473]~P22(f317(f317(f226(a1),a92),f2(a1))) % 168.19/168.05 [3066]E(f317(f317(f21(a1),a109),a109),a92) % 168.19/168.05 [3082]E(f317(f112(a1),f317(a124,f2(a849))),f87(a1)) % 168.19/168.05 [3140]E(f317(f54(a852),f233(f858(a852,a842))),f87(a849)) % 168.19/168.05 [3164]P22(f317(a193,f317(f115(a1),a109))) % 168.19/168.05 [3166]P22(f317(f317(f225(a1),a109),a92)) % 168.19/168.05 [3168]P22(f317(f317(f226(a1),a109),a92)) % 168.19/168.05 [3226]E(f317(f317(f286(a849),f2(a849)),f188(f858(a849,a842))),f317(f277(a849),f2(a849))) % 168.19/168.05 [3285]P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),a92))) % 168.19/168.05 [3299]E(f317(f287(a849,a849,a124),f233(f858(a849,a842))),f317(f280(a849),f2(a849))) % 168.19/168.05 [3337]P6(f857(a849,a849),f233(f858(f857(a849,a849),a842)),a120) % 168.19/168.05 [3646]E(f317(f82(a849,a1,a111,f112(a1)),a19),a20) % 168.19/168.05 [3704]P37(a849,f317(f230(f857(a849,a849)),f317(f247(a849,a849,a842),f226(a849)))) % 168.19/168.05 [4464]~P22(f317(a193,f317(f115(a1),a92))) % 168.19/168.05 [4465]~P22(f317(f317(f225(a1),a92),a109)) % 168.19/168.05 [4466]~P22(f317(f317(f226(a1),a92),a92)) % 168.19/168.05 [4467]~P22(f317(f317(f226(a1),a92),a109)) % 168.19/168.05 [4468]~P22(f317(f317(f226(a1),a109),a109)) % 168.19/168.05 [4483]~P22(f317(f71(a849),f233(f858(a849,a842)))) % 168.19/168.05 [4484]~P22(f317(f71(a1),f233(f858(a1,a842)))) % 168.19/168.05 [4311]E(f317(f247(a1,a1,a842),f317(f317(f8(f858(a1,a842),f858(a1,a842),a1),f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f226(a1),f2(a1))))),f317(f317(f7(a1,a1,f858(a1,a842)),f317(f317(f8(f858(a1,f858(a1,a842)),f858(a1,f858(a1,a842)),a1),f7(a1,a1,a842)),f317(f317(f8(f858(a1,a1),f858(a1,f858(a1,a842)),a1),f317(f8(a1,f858(a1,a842),a1),a314)),a199))),f87(a1)))),a204) % 168.19/168.05 [3375]E(f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109),f317(f88(a1),a109)) % 168.19/168.05 [3417]E(f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109),f317(f317(f21(a1),a92),a109)) % 168.19/168.05 [3574]E(f317(f317(f70(f857(a849,a849)),f233(f858(f857(a849,a849),a842))),a120),a110) % 168.19/168.05 [3602]E(f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f87(a1)) % 168.19/168.05 [3603]E(f317(f115(a111),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f87(a111)) % 168.19/168.05 [3604]E(f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f87(a849)) % 168.19/168.05 [3608]E(f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(a124,f2(a849))) % 168.19/168.05 [4002]E(f317(f317(f122(f858(f857(f857(a849,a849),f857(a849,a849)),a842)),a45),f284(f857(a849,a849),f188(f858(f857(f857(a849,a849),f857(a849,a849)),a842)))),a79) % 168.19/168.05 [4075]E(f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),f2(a849)),f2(a849))),f188(f858(f857(a849,a849),a842))))),f2(a1)) % 168.19/168.05 [4076]E(f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),f87(a849)),f2(a849))),f188(f858(f857(a849,a849),a842))))),f87(a1)) % 168.19/168.05 [4092]E(f317(f230(f857(a849,a849)),f317(f247(a849,a849,a842),f317(f317(f8(a849,f858(a849,a842),a849),f317(f7(a849,a849,a842),a314)),a124))),a307) % 168.19/168.05 [4060]E(f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),f317(a124,f317(a124,f2(a849)))) % 168.19/168.05 [4063]E(f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),f317(f317(f89(a849),f87(a849)),f87(a849))) % 168.19/168.05 [4064]E(f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),f317(f54(a842),f233(f858(a842,a842)))) % 168.19/168.05 [4127]P28(f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))) % 168.19/168.05 [4203]P20(f858(f857(a849,a849),a842),f317(f317(f237(f858(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a842),f858(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a842)),a46),a80)) % 168.19/168.05 [4204]P20(f858(f857(a849,a849),a842),f317(f317(f237(f858(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a842),f858(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a842)),a47),a78)) % 168.19/168.05 [4243]E(f317(f317(f122(f858(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a842)),f309(f857(a849,a849),a79)),f317(f317(f286(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),f188(f858(f857(a849,a849),a842))),f188(f858(f857(a849,a849),a842)))),f188(f858(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a842)))),a78) % 168.19/168.05 [4244]E(f317(f317(f122(f858(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a842)),f308(f857(a849,a849),a79)),f317(f317(f286(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),f188(f858(f857(a849,a849),a842))),f188(f858(f857(a849,a849),a842)))),f188(f858(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a842)))),a80) % 168.19/168.05 [4129]E(f317(a116,f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(a124,f317(a124,f2(a849)))) % 168.19/168.05 [4180]E(f317(f112(a1),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))) % 168.19/168.05 [4215]P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.19/168.05 [4216]E(f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109)),f317(a124,f317(a124,f317(a124,f2(a849))))) % 168.19/168.05 [4257]P28(f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))) % 168.19/168.05 [4283]E(f317(f112(a1),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))),f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))) % 168.19/168.05 [4298]P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109)))) % 168.19/168.05 [2996]P5(x29961,a314) % 168.19/168.05 [3403]P19(a849,a849,a124,x34031) % 168.19/168.05 [2990]P89(f853(x29901)) % 168.19/168.05 [2991]P89(f848(x29911)) % 168.19/168.05 [2992]P89(f850(x29921)) % 168.19/168.05 [2993]P89(f851(x29931)) % 168.19/168.05 [3015]P37(a1,f117(x30151)) % 168.19/168.05 [3016]P37(a1,f119(x30161)) % 168.19/168.05 [3018]P38(x30181,f191(x30181)) % 168.19/168.05 [3070]P37(f858(x30701,a842),f283(x30701)) % 168.19/168.05 [3107]E(f55(a1,x31071,x31071),f2(a1)) % 168.19/168.05 [3161]P11(x31611,f858(x31611,a842),f286(x31611)) % 168.19/168.05 [4384]~E(f317(a29,x43841),a23) % 168.19/168.05 [4386]~E(f317(a124,x43861),x43861) % 168.19/168.05 [4398]~E(f317(a124,x43981),f2(a849)) % 168.19/168.05 [2997]E(f42(f40(x29971)),f2(a849)) % 168.19/168.05 [2998]E(f42(f41(x29981)),f2(a849)) % 168.19/168.05 [3000]E(f317(f189(a849),x30001),x30001) % 168.19/168.05 [3001]E(f317(f115(a1),x30011),x30011) % 168.19/168.05 [3017]E(f317(a98,f318(x30171)),x30171) % 168.19/168.05 [3031]E(f126(x30311,f125(x30311)),f125(x30311)) % 168.19/168.05 [3032]E(f146(x30321,f125(x30321)),f125(x30321)) % 168.19/168.05 [3036]E(f317(f189(a844),f40(x30361)),f2(a849)) % 168.19/168.05 [3037]E(f317(f189(a844),f41(x30371)),f2(a849)) % 168.19/168.05 [3039]E(f34(f317(a29,x30391)),f2(a849)) % 168.19/168.05 [3043]E(f317(f162(x30431),f125(x30431)),f125(x30431)) % 168.19/168.05 [3044]E(f317(f165(x30441),f125(x30441)),f125(x30441)) % 168.19/168.05 [3045]E(f317(f163(x30451),f125(x30451)),f125(x30451)) % 168.19/168.05 [3052]E(f317(f115(a1),x30521),f317(f114(a1),x30521)) % 168.19/168.05 [3053]E(f317(a98,f317(a118,x30531)),x30531) % 168.19/168.05 [3055]E(f317(a3,f317(a19,x30551)),x30551) % 168.19/168.05 [3056]E(f317(a19,f317(a3,x30561)),x30561) % 168.19/168.05 [3057]P28(f317(f112(a1),x30571)) % 168.19/168.05 [3062]E(f317(f189(f853(x30621)),f191(x30621)),f2(a849)) % 168.19/168.05 [3063]E(f317(f189(f850(x30631)),f125(x30631)),f2(a849)) % 168.19/168.05 [3068]E(f317(f189(a843),f317(a29,x30681)),f2(a849)) % 168.19/168.05 [3069]E(f317(f48(a1,x30691),f2(a1)),f2(a1)) % 168.19/168.05 [3080]E(f218(x30801,f191(x30801)),f188(f858(x30801,a842))) % 168.19/168.05 [3087]E(f317(f317(f89(a849),x30871),f2(a849)),x30871) % 168.19/168.05 [3088]E(f317(f317(f89(a1),x30881),f2(a1)),x30881) % 168.19/168.05 [3089]E(f317(f317(f21(a849),x30891),f2(a849)),x30891) % 168.19/168.05 [3090]E(f317(f317(f90(a849),x30901),f87(a849)),x30901) % 168.19/168.05 [3091]E(f317(f317(f90(a1),x30911),f87(a1)),x30911) % 168.19/168.05 [3092]E(f317(f317(f224(a849),x30921),f2(a849)),x30921) % 168.19/168.05 [3093]E(f317(f317(f90(a849),x30931),f2(a849)),f2(a849)) % 168.19/168.05 [3094]E(f317(f317(f223(a849),x30941),f2(a849)),f2(a849)) % 168.19/168.05 [3100]E(f317(f166(x31001),f125(x31001)),f188(f858(x31001,a842))) % 168.19/168.05 [3103]P22(f317(f131(x31031),f125(x31031))) % 168.19/168.05 [3108]E(f317(f192(x31081,x31081),f5(x31081)),f39(f853(x31081))) % 168.19/168.05 [3109]E(f317(f192(x31091,x31091),f39(x31091)),f39(f853(x31091))) % 168.19/168.05 [3110]E(f317(f148(x31101,x31101),f5(x31101)),f39(f850(x31101))) % 168.19/168.05 [3111]E(f317(f148(x31111,x31111),f39(x31111)),f39(f850(x31111))) % 168.19/168.05 [3112]E(f55(a1,x31121,f2(a1)),x31121) % 168.19/168.05 [3113]E(f317(f225(a849),f317(a124,x31131)),f317(f226(a849),x31131)) % 168.19/168.05 [3114]E(f317(f231(a849),f317(a124,x31141)),f317(f277(a849),x31141)) % 168.19/168.05 [3115]E(f317(f232(a849),f317(a124,x31151)),f317(f280(a849),x31151)) % 168.19/168.05 [3117]E(f55(a1,f2(a1),x31171),f2(a1)) % 168.19/168.05 [3124]E(f317(f317(f89(a849),x31241),f87(a849)),f317(a124,x31241)) % 168.19/168.05 [3134]E(f317(f278(a849,x31341),f2(a849)),f188(f858(a849,a842))) % 168.19/168.05 [3147]E(f279(a849,f2(a849),x31471),f317(f277(a849),x31471)) % 168.19/168.05 [3192]E(f317(f317(f21(a849),f317(a124,x31921)),f87(a849)),x31921) % 168.19/168.05 [3205]E(f56(f2(a1),x32051),f317(f317(f237(a1,a1),f2(a1)),f2(a1))) % 168.19/168.05 [3258]P22(f317(f317(f226(a849),x32581),f317(a124,x32581))) % 168.19/168.05 [3272]P22(f317(f317(f226(a849),f2(a849)),f317(a124,x32721))) % 168.19/168.05 [3562]E(f317(f317(f21(a111),f317(a3,f317(a124,f317(a19,x35621)))),f87(a111)),x35621) % 168.19/168.05 [3630]P22(f317(f317(f225(a1),f317(f88(a1),f317(f112(a1),x36301))),f2(a1))) % 168.19/168.05 [3782]P22(f317(f317(f226(a1),f317(f88(a1),f317(f112(a1),f317(a124,x37821)))),f2(a1))) % 168.19/168.05 [4422]~E(f233(f858(x44221,a842)),f188(f858(x44221,a842))) % 168.19/168.05 [4476]~P22(f317(f317(f226(a849),x44761),f2(a849))) % 168.19/168.05 [4492]~P22(f317(f317(f226(a1),f317(f112(a1),x44921)),f2(a1))) % 168.19/168.05 [3067]E(f173(x30671,f125(f850(x30671))),f125(f850(x30671))) % 168.19/168.05 [3071]E(f317(f317(f90(a1),a92),x30711),a92) % 168.19/168.05 [3072]E(f317(f317(f89(a1),a92),x30721),x30721) % 168.19/168.05 [3075]E(f317(a116,f317(f112(a1),x30751)),x30751) % 168.19/168.05 [3076]E(f317(f317(f89(a1),x30761),a92),x30761) % 168.19/168.05 [3077]E(f317(f317(f21(a1),x30771),a92),x30771) % 168.19/168.05 [3079]E(f317(f48(a1,f2(a1)),x30791),f2(a1)) % 168.19/168.05 [3081]E(f317(f317(f21(a849),x30811),x30811),f2(a849)) % 168.19/168.05 [3085]E(f317(f88(a1),f317(f88(a1),x30851)),x30851) % 168.19/168.05 [3086]E(f317(f54(a849),f317(f231(a849),x30861)),x30861) % 168.19/168.05 [3095]E(f317(f317(f89(a849),f2(a849)),x30951),x30951) % 168.19/168.05 [3096]E(f317(f317(f89(a1),f2(a1)),x30961),x30961) % 168.19/168.05 [3097]E(f317(f317(f90(a849),f87(a849)),x30971),x30971) % 168.19/168.05 [3098]E(f317(f317(f90(a1),f87(a1)),x30981),x30981) % 168.19/168.05 [3099]E(f317(f317(f224(a849),f2(a849)),x30991),x30991) % 168.19/168.05 [3104]E(f317(f317(f21(a849),f2(a849)),x31041),f2(a849)) % 168.19/168.05 [3105]E(f317(f317(f90(a849),f2(a849)),x31051),f2(a849)) % 168.19/168.05 [3106]E(f317(f317(f223(a849),f2(a849)),x31061),f2(a849)) % 168.19/168.05 [3122]E(f317(f278(a849,f2(a849)),x31221),f317(f231(a849),x31221)) % 168.19/168.05 [3123]E(f317(f317(f90(a1),a109),x31231),f317(f88(a1),x31231)) % 168.19/168.05 [3126]E(f317(a116,f317(f115(a1),x31261)),f317(f115(a849),x31261)) % 168.19/168.05 [3127]E(f317(a19,f317(f115(a111),x31271)),f317(f115(a849),x31271)) % 168.19/168.05 [3128]E(f317(f54(a849),f317(f277(a849),x31281)),f317(a124,x31281)) % 168.19/168.05 [3138]E(f317(f317(f89(a849),f87(a849)),x31381),f317(a124,x31381)) % 168.19/168.05 [3142]E(f317(f84(a1),f317(f112(a1),x31421)),f317(f112(a1),x31421)) % 168.19/168.05 [3143]E(f317(f114(a1),f317(f112(a1),x31431)),f317(f112(a1),x31431)) % 168.19/168.05 [3146]E(f317(f48(a849,x31461),f317(a124,f2(a849))),x31461) % 168.19/168.05 [3149]E(f317(f54(x31491),f188(f858(x31491,a842))),f2(a849)) % 168.19/168.05 [3160]E(f317(f48(a1,x31601),f317(f115(a1),a109)),f317(f88(a1),x31601)) % 168.19/168.05 [3162]E(f55(a849,x31621,f317(a124,f2(a849))),f2(a849)) % 168.19/168.05 [3163]E(f55(a1,x31631,f317(f115(a1),a109)),f2(a1)) % 168.19/168.05 [3179]E(f133(a849,f317(f278(a849,x31791),f2(a849))),f125(a849)) % 168.19/168.05 [3180]E(f317(f317(f21(a1),x31801),f87(a1)),f317(f317(f89(a1),x31801),a109)) % 168.19/168.05 [3181]E(f317(f317(f89(a1),x31811),f87(a1)),f317(f317(f21(a1),x31811),a109)) % 168.19/168.05 [3186]P22(f317(f317(f194(a23),x31861),x31861)) % 168.19/168.05 [3187]P22(f317(f317(f225(a849),x31871),x31871)) % 168.19/168.05 [3188]P22(f317(f317(f225(a1),x31881),x31881)) % 168.19/168.05 [3193]E(f317(f88(a1),f317(f115(a1),x31931)),f317(f115(a1),f317(f88(a1),x31931))) % 168.19/168.05 [3195]P22(f317(f71(a849),f317(f277(a849),x31951))) % 168.19/168.05 [3196]P22(f317(f71(a849),f317(f231(a849),x31961))) % 168.19/168.05 [3204]E(f155(x32041,f233(f858(x32041,a842))),f233(f858(f850(x32041),a842))) % 168.19/168.05 [3208]P22(f317(f317(f225(a849),f2(a849)),x32081)) % 168.19/168.05 [3219]E(f317(f317(f89(a849),f123(x32191)),f317(a124,f2(a849))),f123(f317(a124,x32191))) % 168.19/168.05 [3220]E(f317(f230(x32201),f317(f16(a842,x32201),a187)),f188(f858(x32201,a842))) % 168.19/168.05 [3221]E(f317(f230(x32211),f317(f16(a842,x32211),a186)),f233(f858(x32211,a842))) % 168.19/168.05 [3225]E(f317(f317(f286(a849),x32251),f317(f231(a849),x32251)),f317(f231(a849),f317(a124,x32251))) % 168.19/168.05 [3237]E(f317(f317(f89(a1),f87(a1)),f317(f112(a1),x32371)),f317(f112(a1),f317(a124,x32371))) % 168.19/168.05 [3240]E(f317(f317(f145(f850(x32401)),f125(x32401)),f125(f850(x32401))),f63(x32401,f125(x32401))) % 168.19/168.05 [3261]E(f188(f858(f857(x32611,x32611),a842)),f235(x32611,f188(f858(x32611,a842)))) % 168.19/168.05 [3262]E(f317(f285(x32621),f233(f858(x32621,a842))),f233(f858(f858(x32621,a842),a842))) % 168.19/168.05 [3263]E(f317(f88(f858(x32631,a842)),f188(f858(x32631,a842))),f233(f858(x32631,a842))) % 168.19/168.05 [3264]E(f317(f88(f858(x32641,a842)),f233(f858(x32641,a842))),f188(f858(x32641,a842))) % 168.19/168.05 [3266]P22(f317(f71(x32661),f188(f858(x32661,a842)))) % 168.19/168.05 [3268]E(f317(f278(a849,x32681),f317(a124,x32681)),f317(f317(f286(a849),x32681),f188(f858(a849,a842)))) % 168.19/168.05 [3269]E(f94(f857(a849,a849),f57(x32691,f2(a849))),f317(f317(f237(a849,a849),f2(a849)),x32691)) % 168.19/168.05 [3284]E(f317(f317(f286(a849),f317(a124,x32841)),f317(f277(a849),x32841)),f317(f277(a849),f317(a124,x32841))) % 168.19/168.05 [3288]P37(x32881,f188(f858(f857(x32881,x32881),a842))) % 168.19/168.05 [3293]P22(f317(f317(f225(a1),f2(a1)),f317(f112(a1),x32931))) % 168.19/168.05 [3301]E(f317(f317(f89(a849),f317(f189(a849),x33011)),f317(a124,f2(a849))),f317(f189(a849),f317(a124,x33011))) % 168.19/168.05 [3410]P39(f317(f287(a849,a1,f112(a1)),x34101)) % 168.19/168.05 [3446]P45(x34461,f188(f858(x34461,a842)),f188(f858(f857(x34461,x34461),a842))) % 168.19/168.05 [3471]E(f317(f317(f237(a1,a1),f317(f115(a1),a109)),f317(f317(f21(a1),x34711),f87(a1))),f59(f317(f115(a1),a109),x34711)) % 168.19/168.05 [3519]P54(x35191,f317(f16(f858(x35191,a842),x35191),f317(f16(a842,x35191),a187))) % 168.19/168.05 [3718]P22(f317(f317(f319(f858(f857(a849,a849),a842)),f318(x37181)),a110)) % 168.19/168.05 [3742]P22(f317(f317(f319(f858(f857(a849,a849),a842)),f317(a118,x37421)),a110)) % 168.19/168.05 [3883]P19(x38831,f858(x38831,a842),f317(f317(f7(x38831,f858(x38831,a842),f858(x38831,a842)),f286(x38831)),f188(f858(x38831,a842))),f233(f858(x38831,a842))) % 168.19/168.05 [4418]~E(f317(f317(f89(a1),x44181),x44181),a109) % 168.19/168.05 [4463]~E(f317(a3,f317(a124,f317(a19,x44631))),f2(a111)) % 168.19/168.05 [4469]~P22(f317(a193,f317(f112(a1),x44691))) % 168.19/168.05 [4472]~P22(f317(f317(f226(a849),x44721),x44721)) % 168.19/168.05 [4485]~P22(f317(f317(f225(a849),f317(a124,x44851)),x44851)) % 168.19/168.05 [3211]E(f317(a116,f317(f88(a1),f317(f112(a1),x32111))),f2(a849)) % 168.19/168.05 [3213]E(f317(f317(f89(a1),f317(f88(a1),x32131)),x32131),f2(a1)) % 168.19/168.05 [3218]E(f317(f54(a1),f317(f278(a1,f2(a1)),x32181)),f317(a116,x32181)) % 168.19/168.05 [3230]E(f317(f317(f238(a849),f317(a124,f2(a849))),x32301),f317(a124,f2(a849))) % 168.19/168.05 [3334]E(f317(f261(x33341),f188(f858(f857(x33341,x33341),a842))),f188(f858(x33341,a842))) % 168.19/168.05 [3342]E(f49(f858(x33421,a842),f188(f858(f858(x33421,a842),a842))),f188(f858(x33421,a842))) % 168.19/168.05 [3343]E(f49(f858(x33431,a842),f233(f858(f858(x33431,a842),a842))),f233(f858(x33431,a842))) % 168.19/168.05 [3344]E(f50(f858(x33441,a842),f188(f858(f858(x33441,a842),a842))),f233(f858(x33441,a842))) % 168.19/168.05 [3345]E(f50(f858(x33451,a842),f233(f858(f858(x33451,a842),a842))),f188(f858(x33451,a842))) % 168.19/168.05 [3393]E(f317(f317(f286(f850(x33931)),f125(x33931)),f188(f858(f850(x33931),a842))),f155(x33931,f188(f858(x33931,a842)))) % 168.19/168.05 [3394]E(f317(f317(f286(f850(x33941)),f125(x33941)),f188(f858(f850(x33941),a842))),f156(x33941,f125(f858(x33941,a842)))) % 168.19/168.05 [3431]E(f317(f317(f89(a849),f4(x34311)),f317(a124,f2(a849))),f4(f317(a3,f317(a124,f317(a19,x34311))))) % 168.19/168.05 [3463]E(f317(f54(a1),f317(f287(a849,a1,f112(a1)),x34631)),f317(f54(a849),x34631)) % 168.19/168.05 [3466]P22(f317(f317(f225(a849),x34661),f317(f317(f90(a849),x34661),x34661))) % 168.19/168.05 [3489]E(f317(f48(a849,f317(a124,f2(a849))),f317(f115(a849),x34891)),f317(a116,f317(f48(a1,f87(a1)),f317(f115(a1),x34891)))) % 168.19/168.05 [3501]E(f317(f287(a1,a849,a116),f279(a1,f2(a1),f317(f112(a1),x35011))),f317(f277(a849),x35011)) % 168.19/168.05 [3516]E(f317(f166(a849),f133(a849,f317(f278(a849,f2(a849)),f317(a124,x35161)))),f317(f277(a849),x35161)) % 168.19/168.05 [3517]E(f317(f317(f89(a849),f317(f189(a111),x35171)),f317(a124,f2(a849))),f317(f189(a111),f317(a3,f317(a124,f317(a19,x35171))))) % 168.19/168.05 [3536]E(f317(f287(a1,a849,a116),f317(f287(a849,a1,f112(a1)),x35361)),x35361) % 168.19/168.05 [3564]E(f317(f317(f286(a849),f2(a849)),f317(f287(a849,a849,a124),f317(f231(a849),x35641))),f317(f231(a849),f317(a124,x35641))) % 168.19/168.05 [3573]P49(x35731,x35731,f284(x35731,f188(f858(f857(x35731,x35731),a842)))) % 168.19/168.05 [3579]P22(f317(a193,f317(f88(a1),f317(f112(a1),f317(a124,x35791))))) % 168.19/168.05 [3590]E(f317(f317(f21(f858(a849,a842)),f317(f232(a849),x35901)),f317(f317(f286(a849),x35901),f188(f858(a849,a842)))),f317(f232(a849),f317(a124,x35901))) % 168.19/168.05 [3605]E(f317(f317(f89(a1),f317(f317(f21(a1),a92),x36051)),f317(f317(f21(a1),a92),x36051)),f317(f317(f21(a1),a92),f317(f317(f89(a1),x36051),x36051))) % 168.19/168.05 [3619]E(f317(f317(f286(f858(x36191,a842)),f188(f858(x36191,a842))),f188(f858(f858(x36191,a842),a842))),f317(f285(x36191),f188(f858(x36191,a842)))) % 168.19/168.05 [3647]E(f317(f317(f21(f858(a849,a842)),f317(f280(a849),x36471)),f317(f317(f286(a849),f317(a124,x36471)),f188(f858(a849,a842)))),f317(f280(a849),f317(a124,x36471))) % 168.19/168.05 [3655]E(f317(f317(f286(f853(x36551)),f191(x36551)),f317(f287(x36551,f853(x36551),f217(x36551)),f233(f858(x36551,a842)))),f233(f858(f853(x36551),a842))) % 168.19/168.05 [3755]E(f317(f115(a849),f317(f317(f89(a1),x37551),x37551)),f317(f317(f95(a849,a849),f317(f115(a849),x37551)),f317(f317(f18(a849,a849,a849),f89(a849)),f5(a849)))) % 168.19/168.05 [4152]P11(x41521,f858(x41521,a842),f317(f317(f8(f858(x41521,a842),f858(f858(x41521,a842),f858(x41521,a842)),x41521),f317(f7(f858(x41521,a842),f858(x41521,a842),f858(x41521,a842)),f21(f858(x41521,a842)))),f317(f317(f7(x41521,f858(x41521,a842),f858(x41521,a842)),f286(x41521)),f188(f858(x41521,a842))))) % 168.19/168.05 [4242]E(f317(f230(f857(a1,a1)),f317(f247(a1,a1,a842),f317(f317(f8(f858(a1,a842),f858(a1,a842),a1),f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f225(a1),x42421)))),f226(a1)))),f119(x42421)) % 168.19/168.05 [4274]E(f317(f230(f857(a1,a1)),f317(f247(a1,a1,a842),f317(f317(f18(a1,f858(a1,a842),f858(a1,a842)),f317(f317(f8(f858(a842,a842),f858(f858(a1,a842),f858(a1,a842)),a1),f8(a842,a842,a1)),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f225(a1),x42741)))),f226(a1)))),f117(x42741)) % 168.19/168.05 [4323]E(f317(f230(f857(f858(x43231,a842),f858(x43231,a842))),f317(f247(f858(x43231,a842),f858(x43231,a842),a842),f317(f317(f7(f858(x43231,a842),f858(f858(x43231,a842),a842),f858(f858(x43231,a842),a842)),f317(f317(f8(f858(f858(x43231,a842),f858(a842,a842)),f858(f858(f858(x43231,a842),a842),f858(f858(x43231,a842),a842)),f858(x43231,a842)),f18(f858(x43231,a842),a842,a842)),f317(f317(f8(f858(f858(x43231,a842),a842),f858(f858(x43231,a842),f858(a842,a842)),f858(x43231,a842)),f317(f8(a842,f858(a842,a842),f858(x43231,a842)),a315)),f226(f858(x43231,a842))))),f71(x43231)))),f283(x43231)) % 168.19/168.05 [4489]~P22(f317(f71(f850(x44891)),f233(f858(f850(x44891),a842)))) % 168.19/168.05 [4502]~P22(f317(f317(f225(a1),f2(a1)),f317(f88(a1),f317(f112(a1),f317(a124,x45021))))) % 168.19/168.05 [3369]E(f317(f317(f21(a1),f317(f317(f89(a1),x33691),a109)),a109),x33691) % 168.19/168.05 [3387]E(f317(f166(a849),f133(a849,f317(f278(a849,f2(a849)),x33871))),f317(f231(a849),x33871)) % 168.19/168.05 [3624]E(f317(f317(f89(a1),f317(f317(f89(a1),f87(a1)),x36241)),x36241),f317(f317(f21(a1),f317(f317(f89(a1),x36241),x36241)),a109)) % 168.19/168.05 [3672]E(f317(f263(x36721,x36721),f284(x36721,f188(f858(f857(x36721,x36721),a842)))),f284(x36721,f188(f858(f857(x36721,x36721),a842)))) % 168.19/168.05 [3721]P22(f317(f317(f225(a849),x37211),f317(f317(f90(a849),x37211),f317(f317(f90(a849),x37211),x37211)))) % 168.19/168.05 [4006]P22(f317(f71(a849),f317(f230(a849),f317(f317(f7(a849,a849,a842),f225(a849)),x40061)))) % 168.19/168.05 [4007]P22(f317(f71(a849),f317(f230(a849),f317(f317(f7(a849,a849,a842),f226(a849)),x40071)))) % 168.19/168.05 [4293]E(f317(f230(f857(x42931,x42931)),f317(f317(f8(f858(x42931,a842),a842,f857(x42931,x42931)),f96(x42931)),f317(f317(f7(f857(x42931,x42931),f858(x42931,f857(x42931,x42931)),f858(x42931,a842)),f317(f317(f8(f858(f857(x42931,x42931),a842),f858(f858(x42931,f857(x42931,x42931)),f858(x42931,a842)),f857(x42931,x42931)),f8(f857(x42931,x42931),a842,x42931)),a314)),f317(f317(f18(x42931,x42931,f857(x42931,x42931)),f237(x42931,x42931)),f5(x42931))))),f284(x42931,f188(f858(f857(x42931,x42931),a842)))) % 168.19/168.05 [4491]~E(f317(f317(f21(a1),f317(f317(f89(a1),x44911),x44911)),a109),a92) % 168.19/168.05 [4493]~E(f317(f317(f89(a1),f317(f317(f89(a1),f87(a1)),x44931)),x44931),f2(a1)) % 168.19/168.05 [3771]E(f317(f317(f89(a1),f317(f317(f21(a1),a109),x37711)),f317(f317(f21(a1),a109),x37711)),f317(f317(f21(a1),a109),f317(f317(f21(a1),f317(f317(f89(a1),x37711),x37711)),a109))) % 168.19/168.05 [3891]E(f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),a109),x38911)),f317(f317(f21(a1),a109),x38911))),a109),f317(f317(f21(a1),a109),f317(f317(f89(a1),x38911),x38911))) % 168.19/168.05 [3927]E(f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f89(a1),x39271),a109)),f317(f317(f89(a1),x39271),a109))),a109),f317(f317(f89(a1),f317(f317(f89(a1),x39271),x39271)),a109)) % 168.19/168.05 [3963]E(f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),a109),x39631)),f317(f317(f21(a1),a109),x39631))),a109),f317(f317(f21(a1),a92),f317(f317(f21(a1),f317(f317(f89(a1),x39631),x39631)),a109))) % 168.19/168.05 [4072]E(f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x40721),f2(a849))),f188(f858(f857(a849,a849),a842))))),f317(f112(a1),x40721)) % 168.19/168.05 [4081]E(f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),f322(x40811)),f358(x40811))),f188(f858(f857(a849,a849),a842))))),x40811) % 168.19/168.05 [4115]E(f317(f230(a1),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f225(a1),f2(a1)))),x41151)),f317(f287(a849,a1,f112(a1)),f317(f230(a849),f317(f317(f8(a1,a842,a849),x41151),f112(a1))))) % 168.19/168.05 [4160]P39(f317(f230(a1),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f225(a1),f2(a1)))),x41601))) % 168.19/168.05 [4183]P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),x41831),f188(f858(f857(a849,a849),a842)))),a80)) % 168.19/168.05 [4189]E(f317(f287(a1,a849,a116),f317(f230(a1),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f225(a1),f2(a1)))),f317(f317(f8(a849,a842,a1),x41891),a116)))),f317(f230(a849),x41891)) % 168.19/168.05 [4337]E(f290(a849,f317(f317(f51(f857(a849,a849),f858(a849,a842)),f317(a118,x43371)),f317(f247(a849,a849,f858(a849,a842)),f317(f317(f7(a849,f858(a849,a842),f858(a849,f858(a849,a842))),f317(f317(f8(f858(a849,f858(f858(a849,a842),f858(a849,a842))),f858(f858(a849,a842),f858(a849,f858(a849,a842))),a849),f7(a849,f858(a849,a842),f858(a849,a842))),f317(f317(f8(f858(a849,a849),f858(a849,f858(f858(a849,a842),f858(a849,a842))),a849),f317(f8(a849,f858(f858(a849,a842),f858(a849,a842)),a849),f286(a849))),f21(a849)))),f188(f858(a849,a842)))))),f317(a116,x43371)) % 168.19/168.05 [3814]E(f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),x38141),x38141)),a109)),a109),f317(f317(f89(a1),x38141),x38141)) % 168.19/168.05 [3866]E(f317(f317(f21(a1),f317(f317(f21(a1),f317(f317(f89(a1),x38661),x38661)),a109)),a109),f317(f317(f89(a1),f317(f317(f21(a1),x38661),a109)),f317(f317(f21(a1),x38661),a109))) % 168.19/168.05 [4089]E(f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f89(a1),f317(f88(a1),x40891)),a109)),f317(f317(f89(a1),f317(f88(a1),x40891)),a109))),a109),f317(f88(a1),f317(f317(f21(a1),f317(f317(f89(a1),x40891),x40891)),a109))) % 168.19/168.05 [4130]E(f317(f317(f89(a849),x41301),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(a124,f317(a124,x41301))) % 168.19/168.05 [4131]E(f317(f317(f90(a849),x41311),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f89(a849),x41311),x41311)) % 168.19/168.05 [4132]E(f317(f48(a849,f317(f317(f89(a849),x41321),x41321)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x41321) % 168.19/168.05 [4218]E(f55(a849,f317(a124,f317(a124,x42181)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f55(a849,x42181,f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.19/168.05 [4354]E(f317(a98,f317(f317(f51(f857(a849,a849),f858(f857(a849,a849),a842)),f317(a118,x43541)),f317(f247(a849,a849,f858(f857(a849,a849),a842)),f317(f317(f8(f858(a849,f858(f857(a849,a849),a842)),f858(a849,f858(f857(a849,a849),a842)),a849),f317(f8(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842),a849),f262(f857(a849,a849),f857(a849,a849),a120))),f317(f317(f7(a849,f858(f857(a849,a849),a842),f858(a849,f858(f857(a849,a849),a842))),f317(f317(f8(f858(a849,f858(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f858(f858(f857(a849,a849),a842),f858(a849,f858(f857(a849,a849),a842))),a849),f7(a849,f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f8(f858(a849,f857(a849,a849)),f858(a849,f858(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),a849),f317(f8(f857(a849,a849),f858(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),a849),f286(f857(a849,a849)))),f317(f7(a849,a849,f857(a849,a849)),f237(a849,a849))))),f188(f858(f857(a849,a849),a842))))))),f317(f88(a1),x43541)) % 168.19/168.05 [4213]E(f317(f317(f89(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x42131),f317(a124,f317(a124,x42131))) % 168.19/168.05 [4214]E(f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x42141),f317(f317(f89(a849),x42141),x42141)) % 168.19/168.05 [4247]E(f317(f48(a849,f317(a124,f317(a124,x42471))),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(a124,f317(f48(a849,x42471),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.19/168.05 [4299]E(f317(f317(f89(a849),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))),x42991),f317(a124,f317(a124,f317(a124,x42991)))) % 168.19/168.05 [4374]E(f317(f247(a1,a1,f857(a1,a1)),f317(f317(f18(a1,f858(a1,f857(a1,a1)),f858(a1,f857(a1,a1))),f317(f317(f8(f858(a1,f858(f857(a1,a1),f857(a1,a1))),f858(f858(a1,f857(a1,a1)),f858(a1,f857(a1,a1))),a1),f18(a1,f857(a1,a1),f857(a1,a1))),f317(f317(f8(f858(a1,f857(a1,a1)),f858(a1,f858(f857(a1,a1),f857(a1,a1))),a1),f317(f18(a1,f857(a1,a1),f858(f857(a1,a1),f857(a1,a1))),f317(f317(f8(a842,f858(f857(a1,a1),f858(f857(a1,a1),f857(a1,a1))),a1),f108(f857(a1,a1))),f317(f317(f8(a1,a842,a1),f317(f225(a1),f2(a1))),f317(f317(f7(a1,a1,a1),f21(a1)),x43741))))),f317(f317(f7(a1,f858(a1,a1),f858(a1,f857(a1,a1))),f317(f317(f8(f858(a1,f857(a1,a1)),f858(f858(a1,a1),f858(a1,f857(a1,a1))),a1),f8(a1,f857(a1,a1),a1)),f317(f317(f8(a1,f858(a1,f857(a1,a1)),a1),f237(a1,a1)),f317(f317(f7(a1,a1,a1),f317(f317(f8(a1,f858(a1,a1),a1),f89(a1)),f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f87(a1))))),f317(f317(f7(a1,a1,a1),f21(a1)),x43741))))),f317(f317(f8(a1,f858(a1,f857(a1,a1)),a1),f237(a1,a1)),f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))))),f53(x43741)) % 168.19/168.05 [3040]P89(f854(x30401,x30402)) % 168.19/168.05 [3041]P89(f856(x30411,x30412)) % 168.19/168.05 [3042]P89(f857(x30421,x30422)) % 168.19/168.05 [3060]P29(a1,f172(x30601,x30602)) % 168.19/168.05 [3061]P37(x30611,f147(x30611,x30612)) % 168.19/168.05 [3156]P45(x31561,x31562,f235(x31561,x31562)) % 168.19/168.05 [3157]P49(x31571,x31571,f235(x31571,x31572)) % 168.19/168.05 [3434]P19(x34341,x34341,f5(x34341),x34342) % 168.19/168.05 [3435]P19(x34351,x34351,f39(x34351),x34352) % 168.19/168.05 [3441]P33(x34411,x34412,f125(x34411),f125(x34411)) % 168.19/168.05 [3442]P19(x34421,f853(x34421),f217(x34421),x34422) % 168.19/168.05 [3451]P19(f850(x34511),f850(x34511),f163(x34511),x34512) % 168.19/168.05 [4382]~E(f41(x43821),f40(x43822)) % 168.19/168.05 [4390]~E(f36(x43901,x43902),a23) % 168.19/168.05 [4391]~E(f30(x43911,x43912),a23) % 168.19/168.05 [4392]~E(f35(x43921,x43922),a23) % 168.19/168.05 [4431]~P34(x44311,x44312,f125(x44311)) % 168.19/168.05 [3020]E(f317(f5(x30201),x30202),x30202) % 168.19/168.05 [3021]E(f317(f230(x30211),x30212),x30212) % 168.19/168.05 [3023]E(f317(f39(x30231),x30232),x30232) % 168.19/168.05 [3047]E(f34(f30(x30471,x30472)),f2(a849)) % 168.19/168.05 [3058]E(f94(x30581,f317(a314,x30582)),x30582) % 168.19/168.05 [3059]E(f99(x30591,f317(a314,x30592)),x30592) % 168.19/168.05 [3078]E(f317(f189(a843),f30(x30781,x30782)),f2(a849)) % 168.19/168.05 [3083]E(f317(f130(x30831,x30832),f125(x30831)),f125(x30831)) % 168.19/168.05 [3101]E(f146(x31011,f146(x31011,x31012)),f146(x31011,x31012)) % 168.19/168.05 [3102]E(f284(x31021,f284(x31021,x31022)),f284(x31021,x31022)) % 168.19/168.05 [3120]E(f317(f317(f127(x31201),x31202),f125(x31201)),x31202) % 168.19/168.05 [3129]E(f317(f317(f167(x31291),x31292),f125(x31291)),f125(x31291)) % 168.19/168.05 [3130]E(f317(f317(f132(x31301),x31302),f125(x31301)),f125(x31301)) % 168.19/168.05 [3132]E(f219(x31321,x31322,f191(x31321)),f2(a849)) % 168.19/168.05 [3133]E(f149(x31331,x31332,f125(x31331)),f2(a849)) % 168.19/168.05 [3135]E(f164(x31351,x31352,f125(x31351)),f125(x31351)) % 168.19/168.05 [3136]E(f170(x31361,x31362,f125(x31361)),f125(x31361)) % 168.19/168.05 [3137]E(f168(x31371,f125(x31371),x31372),f125(x31371)) % 168.19/168.05 [3141]E(f317(f166(x31411),f146(x31411,x31412)),f317(f166(x31411),x31412)) % 168.19/168.05 [3144]E(f317(f234(x31441,x31441),f235(x31441,x31442)),x31442) % 168.19/168.05 [3145]E(f317(f236(x31451,x31451),f235(x31451,x31452)),x31452) % 168.19/168.05 [3154]P22(f317(a24,f30(x31541,x31542))) % 168.19/168.05 [3155]E(f317(f263(x31551,x31551),f235(x31551,x31552)),f235(x31551,x31552)) % 168.19/168.05 [3169]E(f284(f850(x31691),f151(x31691,x31692)),f152(x31691,f284(x31691,x31692))) % 168.19/168.05 [3171]P22(f317(f131(a1),f172(x31711,x31712))) % 168.19/168.05 [3177]E(f317(f234(x31771,x31771),f284(x31771,x31772)),f233(f858(x31771,a842))) % 168.19/168.05 [3178]E(f317(f236(x31781,x31781),f284(x31781,x31782)),f233(f858(x31781,a842))) % 168.19/168.05 [3182]P22(f317(f131(x31821),f146(x31821,x31822))) % 168.19/168.05 [3184]P22(f317(f154(x31841,x31842),f125(x31841))) % 168.19/168.05 [3191]E(f317(f166(a1),f172(x31911,x31912)),f279(a1,x31911,x31912)) % 168.19/168.05 [3194]E(f317(f317(f196(x31941,x31941),x31942),f217(x31941)),x31942) % 168.19/168.05 [3206]P50(x32061,f188(f858(x32061,a842)),x32062) % 168.19/168.05 [3212]E(f317(f278(a849,x32121),f317(a124,x32122)),f279(a849,x32121,x32122)) % 168.19/168.05 [3229]E(f317(f317(f145(x32291),x32292),f125(x32291)),f134(x32291,x32292,f125(x32291))) % 168.19/168.05 [3242]E(f279(a849,f317(a124,x32421),x32422),f281(a849,x32421,x32422)) % 168.19/168.05 [3245]P45(x32451,f233(f858(x32451,a842)),f284(x32451,x32452)) % 168.19/168.05 [3312]E(f317(f317(f21(a849),x33121),f317(a124,x33122)),f317(f54(a849),f282(a849,x33122,x33121))) % 168.19/168.05 [3370]E(f161(x33701,x33702,f125(x33701)),f317(f317(f237(f850(x33701),f850(x33701)),f125(x33701)),f125(x33701))) % 168.19/168.05 [3391]E(f317(f247(x33911,x33912,f857(x33911,x33912)),f237(x33911,x33912)),f39(f857(x33911,x33912))) % 168.19/168.05 [3396]P22(f317(f317(f319(f850(x33961)),f125(x33961)),f155(x33961,x33962))) % 168.19/168.05 [3397]E(f317(f189(f850(x33971)),f126(x33971,x33972)),f317(f317(f21(a849),f317(f189(f850(x33971)),x33972)),f87(a849))) % 168.19/168.05 [3404]P22(f317(f71(a849),f282(a849,x34041,x34042))) % 168.19/168.05 [3405]P22(f317(f71(a849),f281(a849,x34051,x34052))) % 168.19/168.05 [3406]P22(f317(f71(a849),f279(a849,x34061,x34062))) % 168.19/168.05 [3407]P22(f317(f71(a1),f282(a1,x34071,x34072))) % 168.19/168.05 [3408]P22(f317(f71(a1),f281(a1,x34081,x34082))) % 168.19/168.05 [3409]P22(f317(f71(a1),f279(a1,x34091,x34092))) % 168.19/168.05 [3514]E(f317(f287(a849,a849,a124),f279(a849,x35141,x35142)),f279(a849,f317(a124,x35141),f317(a124,x35142))) % 168.19/168.05 [3533]E(f317(f317(f265(x35331,x35331,x35331),f284(x35331,x35332)),f284(x35331,x35332)),f284(x35331,x35332)) % 168.19/168.05 [3572]E(f317(f317(f237(a849,a849),f317(f48(a849,x35721),x35722)),f55(a849,x35721,x35722)),f94(f857(a849,a849),f57(x35721,x35722))) % 168.19/168.05 [3643]P22(f317(f317(f226(a849),f317(f317(f21(a849),x36431),x36432)),f317(a124,x36431))) % 168.19/168.05 [3714]E(f317(f317(f89(a1),f317(f317(f90(a1),x37141),f317(f48(a1,x37142),x37141))),f55(a1,x37142,x37141)),x37142) % 168.19/168.05 [3745]E(f317(f317(f51(a849,f858(f857(f850(x37451),f850(x37451)),a842)),f233(f858(a849,a842))),f137(x37451,x37452)),f139(x37451,x37452)) % 168.19/168.05 [3978]P22(f317(f317(f319(f857(f850(x39781),f850(x39781))),f317(f317(f237(f850(x39781),f850(x39781)),f125(x39781)),f125(x39781))),f152(x39781,x39782))) % 168.19/168.05 [4143]E(f248(x41431,x41431,x41432,x41432,f5(x41431),f5(x41432)),f39(f857(x41431,x41432))) % 168.19/168.05 [4145]E(f248(x41451,x41451,x41452,x41452,f39(x41451),f39(x41452)),f39(f857(x41451,x41452))) % 168.19/168.05 [4400]~E(f317(f217(x44001),x44002),f191(x44001)) % 168.19/168.05 [4419]~P38(x44191,f317(f217(x44191),x44192)) % 168.19/168.05 [3118]E(f317(f222(x31181),f317(f217(x31181),x31182)),x31182) % 168.19/168.05 [3119]E(f317(f163(x31191),f317(f163(x31191),x31192)),x31192) % 168.19/168.05 [3121]E(f317(f317(f132(x31211),f2(a849)),x31212),x31212) % 168.19/168.05 [3131]E(f317(f317(f167(x31311),f2(a849)),x31312),f125(x31311)) % 168.19/168.05 [3139]E(f317(f317(f127(x31391),f125(x31391)),x31392),x31392) % 168.19/168.05 [3148]E(f317(f189(f853(x31481)),f317(f217(x31481),x31482)),f2(a849)) % 168.19/168.05 [3150]E(f49(f858(x31501,a842),f317(f285(x31501),x31502)),x31502) % 168.19/168.05 [3151]E(f317(f166(x31511),f317(f162(x31511),x31512)),f317(f166(x31511),x31512)) % 168.19/168.05 [3152]E(f317(f166(x31521),f317(f163(x31521),x31522)),f317(f166(x31521),x31522)) % 168.19/168.05 [3159]E(f317(f317(f21(a111),x31591),x31592),f317(f317(a22,x31591),x31592)) % 168.19/168.05 [3172]E(f317(f317(f89(a849),x31721),x31722),f317(f317(f89(a849),x31722),x31721)) % 168.19/168.05 [3173]E(f317(f317(f89(a1),x31731),x31732),f317(f317(f89(a1),x31732),x31731)) % 168.19/168.05 [3174]E(f317(f317(f90(a849),x31741),x31742),f317(f317(f90(a849),x31742),x31741)) % 168.19/168.05 [3175]E(f317(f317(f90(a1),x31751),x31752),f317(f317(f90(a1),x31752),x31751)) % 168.19/168.05 [3199]E(f317(f317(f182(x31991,x31991),f2(a849)),x31992),f39(x31991)) % 168.19/168.05 [3200]E(f317(f189(f850(x32001)),f317(f162(x32001),x32002)),f317(f189(f850(x32001)),x32002)) % 168.19/168.05 [3201]E(f317(f189(f850(x32011)),f317(f163(x32011),x32012)),f317(f189(f850(x32011)),x32012)) % 168.19/168.05 [3202]E(f168(x32021,x32022,f188(f858(a849,a842))),f125(x32021)) % 168.19/168.05 [3203]E(f317(f317(f148(x32031,x32031),f5(x32031)),x32032),x32032) % 168.19/168.05 [3222]E(f317(f189(f850(x32221)),f146(x32221,x32222)),f317(f54(x32221),f317(f166(x32221),x32222))) % 168.19/168.05 [3223]E(f34(f35(x32231,x32232)),f317(f317(f89(a849),f34(x32232)),f317(a124,f2(a849)))) % 168.19/168.05 [3224]E(f317(f261(x32241),f317(f263(x32241,x32241),x32242)),f317(f261(x32241),x32242)) % 168.19/168.05 [3228]P22(f317(f71(x32281),f317(f166(x32281),x32282))) % 168.19/168.05 [3236]E(f317(f317(f89(a1),x32361),f317(f88(a1),x32362)),f317(f317(f21(a1),x32361),x32362)) % 168.19/168.05 [3244]P18(x32441,x32442,f188(f858(f848(x32441),a842))) % 168.19/168.05 [3248]E(f317(f287(x32481,x32481,f5(x32481)),x32482),x32482) % 168.19/168.05 [3249]E(f317(f287(x32491,x32491,f39(x32491)),x32492),x32492) % 168.19/168.05 [3250]E(f317(f289(x32501,x32501,f5(x32501)),x32502),x32502) % 168.19/168.05 [3251]E(f317(f289(x32511,x32511,f39(x32511)),x32512),x32512) % 168.19/168.05 [3252]P22(f317(f233(f858(x32521,a842)),x32522)) % 168.19/168.05 [3254]E(f317(f54(a849),f317(f278(a849,x32541),x32542)),f317(f317(f21(a849),x32542),x32541)) % 168.19/168.05 [3255]E(f317(f278(a849,f317(a124,x32551)),x32552),f282(a849,x32551,x32552)) % 168.19/168.05 [3267]E(f317(f317(f286(x32671),x32672),f188(f858(x32671,a842))),f317(f230(x32671),f317(a314,x32672))) % 168.19/168.05 [3273]E(f317(f317(f286(x32731),x32732),f188(f858(x32731,a842))),f218(x32731,f317(f217(x32731),x32732))) % 168.19/168.05 [3276]E(f284(x32761,f317(f263(x32761,x32761),x32762)),f317(f263(x32761,x32761),f284(x32761,x32762))) % 168.19/168.05 [3280]E(f317(f317(f89(a849),f317(a124,x32801)),x32802),f317(f317(f89(a849),x32801),f317(a124,x32802))) % 168.19/168.05 [3281]E(f317(f317(f21(a849),f317(a124,x32811)),f317(a124,x32812)),f317(f317(f21(a849),x32811),x32812)) % 168.19/168.05 [3286]E(f64(x32861,f2(a849),x32862),f317(f317(f145(f850(x32861)),f125(x32861)),f125(f850(x32861)))) % 168.19/168.05 [3287]E(f317(f54(a849),f281(a849,x32871,x32872)),f317(f317(f21(a849),x32872),x32871)) % 168.19/168.05 [3290]E(f317(f48(a1,f317(f88(a1),x32901)),f317(f88(a1),x32902)),f317(f48(a1,x32901),x32902)) % 168.19/168.05 [3298]P37(x32981,f317(f317(f264(a849,x32981),a229),x32982)) % 168.19/168.05 [3300]P29(a849,f133(a849,f317(f278(a849,x33001),x33002))) % 168.19/168.05 [3302]P22(f317(f71(a849),f317(f278(a849,x33021),x33022))) % 168.19/168.05 [3303]P22(f317(f71(a1),f317(f278(a1,x33031),x33032))) % 168.19/168.05 [3306]E(f317(f263(f850(x33061),f850(x33061)),f151(x33061,x33062)),f151(x33061,f317(f263(x33061,x33061),x33062))) % 168.19/168.05 [3307]E(f317(f189(a843),f35(x33071,x33072)),f317(f317(f89(a849),f317(f189(a843),x33072)),f317(a124,f2(a849)))) % 168.19/168.05 [3309]E(f317(f278(a1,x33091),f317(f317(f89(a1),x33092),f87(a1))),f279(a1,x33091,x33092)) % 168.19/168.05 [3311]E(f317(f244(a849,a849),f94(f857(a849,a849),f57(x33111,x33112))),f317(f48(a849,x33111),x33112)) % 168.19/168.05 [3319]E(f179(x33191,x33192,f317(f16(f853(x33192),x33191),f191(x33192))),f188(f858(x33192,a842))) % 168.19/168.05 [3320]E(f177(x33201,x33202,f317(f16(f853(x33202),x33201),f191(x33202))),f188(f858(x33201,a842))) % 168.19/168.05 [3321]E(f317(f317(f182(f857(x33211,x33211),a842),f87(a849)),x33212),x33212) % 168.19/168.05 [3323]E(f317(f317(f21(f858(x33231,a842)),x33232),f188(f858(x33231,a842))),x33232) % 168.19/168.05 [3324]E(f317(f317(f122(f858(x33241,a842)),x33242),f188(f858(x33241,a842))),x33242) % 168.19/168.05 [3325]E(f317(f317(f113(f858(x33251,a842)),x33252),f233(f858(x33251,a842))),x33252) % 168.19/168.05 [3332]E(f291(x33321,f317(a20,x33322),f317(f88(a1),f317(a20,x33322))),f317(f317(f294(a1),x33321),x33322)) % 168.19/168.05 [3333]E(f279(a1,f317(f317(f89(a1),x33331),f87(a1)),x33332),f281(a1,x33331,x33332)) % 168.19/168.05 [3338]E(f317(f246(a849,a849),f94(f857(a849,a849),f57(x33381,x33382))),f55(a849,x33381,x33382)) % 168.19/168.05 [3346]E(f292(x33461,f317(a20,x33462),f317(f88(a1),f317(a20,x33462))),f293(a1,x33461,x33462)) % 168.19/168.05 [3349]P22(f317(f317(f319(x33491),x33492),f233(f858(x33491,a842)))) % 168.19/168.05 [3355]E(f317(f317(f21(a849),f317(a124,x33551)),x33552),f317(f54(a849),f279(a849,x33552,x33551))) % 168.19/168.05 [3377]E(f317(f48(a1,f317(f112(a1),x33771)),f317(f112(a1),x33772)),f317(f112(a1),f317(f48(a849,x33771),x33772))) % 168.19/168.05 [3383]E(f317(f317(f21(f858(x33831,a842)),x33832),f233(f858(x33831,a842))),f188(f858(x33831,a842))) % 168.19/168.05 [3384]E(f317(f317(f122(f858(x33841,a842)),x33842),f233(f858(x33841,a842))),f233(f858(x33841,a842))) % 168.19/168.05 [3385]E(f317(f317(f113(f858(x33851,a842)),x33852),f188(f858(x33851,a842))),f188(f858(x33851,a842))) % 168.19/168.05 [3399]E(f55(a1,f317(f88(a1),x33991),f317(f88(a1),x33992)),f317(f88(a1),f55(a1,x33991,x33992))) % 168.19/168.05 [3400]E(f55(a1,f317(f112(a1),x34001),f317(f112(a1),x34002)),f317(f112(a1),f55(a849,x34001,x34002))) % 168.19/168.05 [3411]E(f317(f189(f850(x34111)),f317(f165(x34111),x34112)),f317(f317(f21(a849),f317(f189(f850(x34111)),x34112)),f87(a849))) % 168.19/168.05 [3414]E(f317(f48(a1,f55(a1,x34141,x34142)),x34142),f2(a1)) % 168.19/168.05 [3439]E(f317(a3,f317(f48(a849,f317(a19,x34391)),f317(a19,x34392))),f317(f48(a111,x34391),x34392)) % 168.19/168.05 [3444]E(f317(a3,f55(a849,f317(a19,x34441),f317(a19,x34442))),f55(a111,x34441,x34442)) % 168.19/168.05 [3456]E(f317(f317(f90(a849),x34561),f317(f48(a849,x34562),x34561)),f317(f317(f21(a849),x34562),f55(a849,x34562,x34561))) % 168.19/168.05 [3457]E(f317(f317(f90(a1),x34571),f317(f48(a1,x34572),x34571)),f317(f317(f21(a1),x34572),f55(a1,x34572,x34571))) % 168.19/168.05 [3483]E(f317(a3,f317(f317(f89(a849),f317(a19,x34831)),f317(a19,x34832))),f317(f317(f89(a111),x34831),x34832)) % 168.19/168.05 [3484]E(f317(a3,f317(f317(f21(a849),f317(a19,x34841)),f317(a19,x34842))),f317(f317(f21(a111),x34841),x34842)) % 168.19/168.05 [3485]E(f317(a3,f317(f317(f90(a849),f317(a19,x34851)),f317(a19,x34852))),f317(f317(f90(a111),x34851),x34852)) % 168.19/168.05 [3493]E(f317(f287(a849,a849,a124),f317(f278(a849,x34931),x34932)),f317(f278(a849,f317(a124,x34931)),f317(a124,x34932))) % 168.19/168.05 [3518]P22(f317(f57(x35181,x35182),f94(f857(a849,a849),f57(x35181,x35182)))) % 168.19/168.05 [3539]E(f317(f317(f89(a849),f317(f317(f89(a849),f34(x35391)),f34(x35392))),f317(a124,f2(a849))),f34(f36(x35391,x35392))) % 168.19/168.05 [3540]E(f55(a849,f317(a124,f55(a849,x35401,x35402)),x35402),f55(a849,f317(a124,x35401),x35402)) % 168.19/168.05 [3554]E(f317(f317(f51(f858(x35541,a842),f858(x35541,a842)),x35542),f5(f858(x35541,a842))),f49(f858(x35541,a842),x35542)) % 168.19/168.05 [3555]E(f317(f317(f52(f858(x35551,a842),f858(x35551,a842)),x35552),f5(f858(x35551,a842))),f50(f858(x35551,a842),x35552)) % 168.19/168.05 [3556]E(f317(f287(f850(x35561),f858(x35561,a842),f166(x35561)),f317(f166(f850(x35561)),f63(x35561,x35562))),f317(f285(x35561),f317(f166(x35561),x35562))) % 168.19/168.05 [3559]P22(f317(f317(f319(f858(x35591,a842)),x35592),f317(f285(x35591),x35592))) % 168.19/168.05 [3563]E(f55(a1,f317(f88(a1),f55(a1,x35631,x35632)),x35632),f55(a1,f317(f88(a1),x35631),x35632)) % 168.19/168.05 [3575]P22(f317(f317(f225(f858(x35751,a842)),x35752),f233(f858(x35751,a842)))) % 168.19/168.05 [3577]E(f317(f317(f265(x35771,x35771,x35771),f284(x35771,x35772)),f284(x35771,f284(x35771,x35772))),f284(x35771,x35772)) % 168.19/168.05 [3578]E(f317(f317(f122(f858(x35781,a842)),f317(f236(x35781,x35781),x35782)),f317(f234(x35781,x35781),x35782)),f317(f261(x35781),x35782)) % 168.19/168.05 [3598]E(f298(x35981,x35982,f233(f858(x35981,a842)),f233(f858(x35982,a842))),f233(f858(f856(x35981,x35982),a842))) % 168.19/168.05 [3648]P22(f317(f317(f225(a849),f55(a849,x36481,x36482)),x36481)) % 168.19/168.05 [3670]P22(f317(f317(f225(a1),f317(f88(a1),f317(f112(a1),x36701))),f317(f112(a1),x36702))) % 168.19/168.05 [3695]P22(f317(f317(f319(f858(x36951,a842)),f188(f858(x36951,a842))),f317(f285(x36951),x36952))) % 168.19/168.05 [3700]E(f284(x37001,f317(f317(f265(x37001,x37001,x37001),x37002),f284(x37001,x37002))),f284(x37001,x37002)) % 168.19/168.05 [3703]E(f317(f317(f265(x37031,x37031,x37031),f284(x37031,x37032)),x37032),f317(f317(f265(x37031,x37031,x37031),x37032),f284(x37031,x37032))) % 168.19/168.05 [3705]E(f317(a116,f317(f317(f89(a1),f317(f317(f21(a1),x37051),x37052)),f87(a1))),f317(f54(a1),f279(a1,x37052,x37051))) % 168.19/168.05 [3722]E(f317(f234(x37221,x37221),f317(f317(f265(x37221,x37221,x37221),x37222),f284(x37221,x37222))),f317(f234(x37221,x37221),x37222)) % 168.19/168.05 [3723]E(f317(f236(x37231,x37231),f317(f317(f265(x37231,x37231,x37231),x37232),f284(x37231,x37232))),f317(f236(x37231,x37231),x37232)) % 168.19/168.05 [3739]E(f317(f317(f89(a849),f317(f317(f89(a849),f317(f189(a843),x37391)),f317(f189(a843),x37392))),f317(a124,f2(a849))),f317(f189(a843),f36(x37391,x37392))) % 168.19/168.05 [3750]P19(a849,a849,f317(f317(f7(a849,a849,a849),f89(a849)),x37501),x37502) % 168.19/168.05 [3752]P29(a849,f317(f163(a849),f317(f317(f148(f850(x37521),a849),f189(f850(x37521))),f173(x37521,x37522)))) % 168.19/168.05 [3802]P22(f317(f317(f226(a1),f317(f88(a1),f317(f112(a1),f317(a124,x38021)))),f317(f112(a1),x38022))) % 168.19/168.05 [3846]E(f317(f136(f850(x38461),x38461,f317(f7(x38461,f850(x38461),f850(x38461)),f145(x38461)),f125(x38461)),x38462),f317(f163(x38461),x38462)) % 168.19/168.05 [3898]P22(f317(f317(f225(f858(f857(f850(x38981),f850(x38981)),a842)),f152(x38981,x38982)),f284(f850(x38981),f151(x38981,x38982)))) % 168.19/168.05 [3899]P22(f317(f57(x38991,x38992),f317(f317(f237(a849,a849),f317(f48(a849,x38991),x38992)),f55(a849,x38991,x38992)))) % 168.19/168.05 [3941]P22(f317(f317(f225(f858(f857(f850(x39411),f850(x39411)),a842)),f151(x39411,f284(x39411,x39412))),f284(f850(x39411),f151(x39411,x39412)))) % 168.19/168.05 [4172]E(f317(f317(f249(f857(a111,a111),a111,f857(a111,a111),f857(x41721,f857(a111,a111))),f253(f317(f160(a111),f317(f317(f148(f857(a111,x41721),a111),f244(a111,x41721)),x41722)))),f317(f317(f8(x41721,f858(f857(a111,a111),f857(x41721,f857(a111,a111))),a111),f237(x41721,f857(a111,a111))),f254(x41721,x41722))),f252(x41721,x41722)) % 168.19/168.05 [4353]E(f317(f247(f858(f857(x43531,x43531),a842),f858(f857(x43531,x43531),a842),f858(f858(x43532,x43531),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842)))),f317(f317(f7(f858(f857(x43531,x43531),a842),f858(f858(f857(x43531,x43531),a842),f858(f858(x43532,x43531),f858(f857(x43532,x43532),a842))),f858(f858(f857(x43531,x43531),a842),f858(f858(x43532,x43531),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842))))),f317(f317(f8(f858(f858(f858(x43532,x43531),f858(f857(x43532,x43532),a842)),f858(f858(x43532,x43531),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842)))),f858(f858(f858(f857(x43531,x43531),a842),f858(f858(x43532,x43531),f858(f857(x43532,x43532),a842))),f858(f858(f857(x43531,x43531),a842),f858(f858(x43532,x43531),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842))))),f858(f857(x43531,x43531),a842)),f8(f858(f858(x43532,x43531),f858(f857(x43532,x43532),a842)),f858(f858(x43532,x43531),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842))),f858(f857(x43531,x43531),a842))),f317(f317(f8(f858(f858(x43532,x43531),f858(f858(f857(x43532,x43532),a842),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842)))),f858(f858(f858(x43532,x43531),f858(f857(x43532,x43532),a842)),f858(f858(x43532,x43531),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842)))),f858(f857(x43531,x43531),a842)),f18(f858(x43532,x43531),f858(f857(x43532,x43532),a842),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842)))),f317(f317(f8(f858(f858(x43532,x43531),f858(f857(x43532,x43532),a842)),f858(f858(x43532,x43531),f858(f858(f857(x43532,x43532),a842),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842)))),f858(f857(x43531,x43531),a842)),f317(f8(f858(f857(x43532,x43532),a842),f858(f858(f857(x43532,x43532),a842),f857(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842))),f858(x43532,x43531)),f237(f858(f857(x43532,x43532),a842),f858(f857(x43532,x43532),a842)))),f264(x43531,x43532))))),f264(x43531,x43532))),f83(x43531,x43532)) % 168.19/168.05 [4470]~E(f317(f285(x44701),x44702),f188(f858(f858(x44701,a842),a842))) % 168.19/168.05 [4488]~P22(f317(f317(f319(x44881),x44882),f188(f858(x44881,a842)))) % 168.19/168.05 [4497]~P22(f317(f317(f226(f858(x44971,a842)),x44972),f188(f858(x44971,a842)))) % 168.19/168.05 [3257]E(f317(f317(f21(a849),x32571),f317(f317(f89(a849),x32571),x32572)),f2(a849)) % 168.19/168.05 [3259]E(f317(f317(f122(f858(x32591,a842)),x32592),x32592),x32592) % 168.19/168.05 [3260]E(f317(f317(f113(f858(x32601,a842)),x32602),x32602),x32602) % 168.19/168.05 [3289]E(f317(f48(a1,f317(f88(a1),x32891)),x32892),f317(f48(a1,x32891),f317(f88(a1),x32892))) % 168.19/168.05 [3291]E(f317(f317(f21(f858(x32911,a842)),x32912),x32912),f188(f858(x32911,a842))) % 168.19/168.05 [3294]E(f317(f137(x32941,x32942),f2(a849)),f188(f858(f857(f850(x32941),f850(x32941)),a842))) % 168.19/168.05 [3295]E(f317(f317(f89(a849),x32951),f317(a124,x32952)),f317(a124,f317(f317(f89(a849),x32951),x32952))) % 168.19/168.05 [3308]E(f195(f317(f112(a1),x33081),f317(f112(a1),x33082)),f317(f112(a1),f317(f317(f21(a849),x33081),x33082))) % 168.19/168.05 [3314]E(f317(f54(a1),f317(f278(a1,x33141),x33142)),f317(a116,f317(f317(f21(a1),x33142),x33141))) % 168.19/168.05 [3317]E(f317(f317(f89(a849),f317(a124,x33171)),x33172),f317(a124,f317(f317(f89(a849),x33171),x33172))) % 168.19/168.05 [3322]E(f317(f88(f858(x33221,a842)),f317(f88(f858(x33221,a842)),x33222)),x33222) % 168.19/168.05 [3335]E(f173(x33351,f317(f317(f145(f850(x33351)),f125(x33351)),x33352)),f173(x33351,x33352)) % 168.19/168.05 [3339]E(f317(f317(f89(a849),x33391),f317(f317(f90(a849),x33391),x33392)),f317(f317(f90(a849),x33391),f317(a124,x33392))) % 168.19/168.05 [3347]E(f317(f317(a22,f317(a3,x33471)),f317(a3,x33472)),f317(a3,f317(f317(f21(a849),x33471),x33472))) % 168.19/168.05 [3361]E(f317(f317(f90(a1),f317(f88(a1),x33611)),x33612),f317(f88(a1),f317(f317(f90(a1),x33611),x33612))) % 168.19/168.05 [3363]E(f317(f317(f238(a1),f317(f112(a1),x33631)),x33632),f317(f112(a1),f317(f317(f238(a849),x33631),x33632))) % 168.19/168.05 [3364]E(f317(f317(f89(a111),f317(a3,x33641)),f317(a3,x33642)),f317(a3,f317(f317(f89(a849),x33641),x33642))) % 168.19/168.05 [3365]E(f317(f317(f90(a111),f317(a3,x33651)),f317(a3,x33652)),f317(a3,f317(f317(f90(a849),x33651),x33652))) % 168.19/168.05 [3366]E(f317(f317(f223(a849),f317(a124,x33661)),f317(a124,x33662)),f317(a124,f317(f317(f223(a849),x33661),x33662))) % 168.19/168.05 [3367]E(f317(f317(f224(a849),f317(a124,x33671)),f317(a124,x33672)),f317(a124,f317(f317(f224(a849),x33671),x33672))) % 168.19/168.05 [3373]E(f317(f166(a849),f133(a849,f317(f278(a849,x33731),x33732))),f317(f278(a849,x33731),x33732)) % 168.19/168.05 [3374]E(f290(x33741,f317(f317(f286(x33741),x33742),f188(f858(x33741,a842)))),x33742) % 168.19/168.05 [3381]E(f317(f234(x33811,x33812),f188(f858(f857(x33811,x33812),a842))),f188(f858(x33812,a842))) % 168.19/168.05 [3382]E(f317(f236(x33821,x33822),f188(f858(f857(x33821,x33822),a842))),f188(f858(x33821,a842))) % 168.19/168.05 [3386]E(f317(a116,f317(f317(f21(a1),x33861),x33862)),f317(f54(a1),f281(a1,x33862,x33861))) % 168.19/168.05 [3390]E(f317(f317(f89(a849),x33901),f317(f317(f90(a849),x33902),x33901)),f317(f317(f90(a849),f317(a124,x33902)),x33901)) % 168.19/168.05 [3392]E(f317(f317(f70(x33921),f188(f858(x33921,a842))),x33922),f188(f858(f858(x33921,a842),a842))) % 168.19/168.05 [3401]E(f317(f189(f850(a849)),f133(a849,f317(f278(a849,x34011),x34012))),f317(f317(f21(a849),x34012),x34011)) % 168.19/168.05 [3418]E(f317(f317(f122(f858(x34181,a842)),f188(f858(x34181,a842))),x34182),x34182) % 168.19/168.05 [3419]E(f317(f317(f113(f858(x34191,a842)),f233(f858(x34191,a842))),x34192),x34192) % 168.19/168.05 [3420]E(f317(f317(f89(a1),f317(f88(a1),x34201)),f317(f88(a1),x34202)),f317(f88(a1),f317(f317(f89(a1),x34201),x34202))) % 168.19/168.05 [3424]E(f317(f317(f89(a1),f317(f112(a1),x34241)),f317(f112(a1),x34242)),f317(f112(a1),f317(f317(f89(a849),x34241),x34242))) % 168.19/168.05 [3425]E(f317(f317(f89(a1),f317(f115(a1),x34251)),f317(f115(a1),x34252)),f317(f115(a1),f317(f317(f89(a1),x34251),x34252))) % 168.19/168.05 [3427]E(f317(f317(f90(a1),f317(f112(a1),x34271)),f317(f112(a1),x34272)),f317(f112(a1),f317(f317(f90(a849),x34271),x34272))) % 168.19/168.05 [3428]E(f317(f317(f90(a1),f317(f115(a1),x34281)),f317(f115(a1),x34282)),f317(f115(a1),f317(f317(f90(a1),x34281),x34282))) % 168.19/168.05 [3445]E(f317(f317(f6(x34451,a849),f317(f16(a849,x34451),f87(a849))),x34452),f317(f54(x34451),x34452)) % 168.19/168.05 [3458]E(f317(f88(a1),f55(a1,f317(f88(a1),x34581),x34582)),f55(a1,x34581,f317(f88(a1),x34582))) % 168.19/168.05 [3460]E(f317(f166(a1),f172(x34601,f317(f317(f21(a1),x34602),f87(a1)))),f317(f278(a1,x34601),x34602)) % 168.19/168.05 [3464]P22(f317(f317(f225(a849),x34641),f317(f317(f89(a849),x34642),x34641))) % 168.19/168.05 [3465]P22(f317(f317(f225(a849),x34651),f317(f317(f89(a849),x34651),x34652))) % 168.19/168.05 [3468]E(f317(f317(f21(f858(x34681,a842)),f188(f858(x34681,a842))),x34682),f188(f858(x34681,a842))) % 168.19/168.05 [3469]E(f317(f317(f122(f858(x34691,a842)),f233(f858(x34691,a842))),x34692),f233(f858(x34691,a842))) % 168.19/168.05 [3470]E(f317(f317(f113(f858(x34701,a842)),f188(f858(x34701,a842))),x34702),f188(f858(x34701,a842))) % 168.19/168.05 [3475]E(f317(f317(f237(a1,a1),x34751),f317(f88(a1),x34752)),f317(a60,f317(f317(f237(a1,a1),x34751),x34752))) % 168.19/168.05 [3476]E(f317(f278(a1,f317(f317(f89(a1),x34761),f87(a1))),x34762),f282(a1,x34761,x34762)) % 168.19/168.05 [3490]E(f317(f166(a1),f172(f317(f317(f89(a1),x34901),f87(a1)),x34902)),f281(a1,x34901,x34902)) % 168.19/168.05 [3494]P22(f317(f317(f225(f858(x34941,a842)),x34942),x34942)) % 168.19/168.05 [3499]E(f317(f317(f122(f858(x34991,a842)),x34992),f317(f88(f858(x34991,a842)),x34992)),f233(f858(x34991,a842))) % 168.19/168.05 [3500]E(f317(f317(f113(f858(x35001,a842)),x35002),f317(f88(f858(x35001,a842)),x35002)),f188(f858(x35001,a842))) % 168.19/168.05 [3507]E(f317(f317(f21(a849),f317(f317(f21(a849),x35071),f87(a849))),x35072),f317(f317(f21(a849),x35071),f317(a124,x35072))) % 168.19/168.05 [3511]E(f317(f317(f21(f858(x35111,a842)),f233(f858(x35111,a842))),x35112),f317(f88(f858(x35111,a842)),x35112)) % 168.19/168.05 [3512]E(f317(f317(f21(a1),f317(f115(a1),x35121)),f317(f115(a1),x35122)),f317(f115(a1),f317(f317(f89(a1),x35121),f317(f88(a1),x35122)))) % 168.19/168.05 [3523]E(f317(f166(a849),f133(a849,f317(f278(a849,x35231),f317(a124,x35232)))),f279(a849,x35231,x35232)) % 168.19/168.05 [3529]E(f317(f317(f90(a849),f317(f48(a849,x35291),x35292)),x35292),f317(f317(f21(a849),x35291),f55(a849,x35291,x35292))) % 168.19/168.05 [3531]P22(f317(f317(f317(f317(a197,a23),x35311),x35312),x35311)) % 168.19/168.05 [3537]E(f317(f189(f850(f850(x35371))),f63(x35371,x35372)),f317(f317(f238(a849),f317(a124,f317(a124,f2(a849)))),f317(f189(f850(x35371)),x35372))) % 168.19/168.05 [3557]E(f317(f317(f182(f857(x35571,x35571),a842),f2(a849)),x35572),f284(x35571,f188(f858(f857(x35571,x35571),a842)))) % 168.19/168.05 [3561]P22(f317(f131(a849),f133(a849,f317(f278(a849,x35611),x35612)))) % 168.19/168.05 [3568]P22(f317(f317(f225(a849),f317(f48(a849,x35681),x35682)),x35681)) % 168.19/168.05 [3576]E(f317(f287(a1,a849,a116),f279(a1,f317(f112(a1),x35761),f317(f112(a1),x35762))),f279(a849,x35761,x35762)) % 168.19/168.05 [3586]E(f184(a849,f2(a849),f5(a849),f317(f317(f21(a849),x35861),x35862)),f317(f317(f21(a849),x35861),f317(a124,x35862))) % 168.19/168.05 [3587]E(f317(a116,f317(f317(f21(a1),x35871),f317(f317(f89(a1),x35872),f87(a1)))),f317(f54(a1),f282(a1,x35872,x35871))) % 168.19/168.05 [3620]E(f317(f317(f148(a849,a849),a124),f133(a849,f317(f278(a849,x36201),x36202))),f133(a849,f317(f278(a849,f317(a124,x36201)),f317(a124,x36202)))) % 168.19/168.05 [3628]E(f317(f166(a1),f172(f317(f317(f89(a1),x36281),f87(a1)),f317(f317(f21(a1),x36282),f87(a1)))),f282(a1,x36281,x36282)) % 168.19/168.05 [3639]P22(f317(f317(f225(f858(x36391,a842)),f188(f858(x36391,a842))),x36392)) % 168.19/168.05 [3644]E(f94(x36441,f317(f317(f7(x36441,x36441,a842),a314),x36442)),x36442) % 168.19/168.05 [3645]E(f99(x36451,f317(f317(f7(x36451,x36451,a842),a314),x36452)),x36452) % 168.19/168.05 [3649]E(f317(f166(a849),f133(a849,f317(f278(a849,f317(a124,x36491)),f317(a124,x36492)))),f281(a849,x36491,x36492)) % 168.19/168.05 [3673]E(f317(f317(f245(x36731,x36732),f233(f858(x36731,a842))),f317(f16(f858(x36732,a842),x36731),f233(f858(x36732,a842)))),f233(f858(f857(x36731,x36732),a842))) % 168.19/168.05 [3709]E(f317(f230(x37091),f317(f317(f8(a842,a842,x37091),a312),x37092)),f317(f88(f858(x37091,a842)),f317(f230(x37091),x37092))) % 168.19/168.05 [3712]E(f317(f230(x37121),f317(f317(f7(x37121,x37121,a842),a314),x37122)),f317(f317(f286(x37121),x37122),f188(f858(x37121,a842)))) % 168.19/168.05 [3719]E(f317(f317(f89(a1),f317(f317(f89(a1),x37191),x37191)),f317(f317(f89(a1),x37192),x37192)),f317(f317(f89(a1),f317(f317(f89(a1),x37191),x37192)),f317(f317(f89(a1),x37191),x37192))) % 168.19/168.05 [3720]E(f317(f317(f21(a1),f317(f317(f89(a1),x37201),x37201)),f317(f317(f89(a1),x37202),x37202)),f317(f317(f89(a1),f317(f317(f21(a1),x37201),x37202)),f317(f317(f21(a1),x37201),x37202))) % 168.19/168.05 [3736]P22(f317(f317(f225(a849),f317(f54(x37361),f317(f166(x37361),x37362))),f317(f189(f850(x37361)),x37362))) % 168.19/168.05 [3737]P22(f317(f317(f225(a849),f317(f189(f850(x37371)),f146(x37371,x37372))),f317(f189(f850(x37371)),x37372))) % 168.19/168.05 [3746]E(f317(f230(x37461),f317(f317(f7(x37461,f858(x37461,a842),a842),f319(x37461)),x37462)),x37462) % 168.19/168.05 [3767]E(f317(f317(f167(x37671),f317(f317(f21(a849),f317(f189(f850(x37671)),x37672)),f87(a849))),x37672),f126(x37671,x37672)) % 168.19/168.05 [3783]E(f317(f317(f237(a1,a1),f317(f48(a1,f317(f84(a1),x37831)),f317(f84(a1),x37832))),f55(a1,f317(f84(a1),x37831),f317(f84(a1),x37832))),f62(x37831,x37832)) % 168.19/168.05 [3790]E(f184(a849,f2(a849),f317(f317(f8(a849,a849,a849),a124),f317(f223(a849),x37901)),x37902),f317(f317(f223(a849),f317(a124,x37901)),x37902)) % 168.19/168.05 [3794]E(f49(f858(x37941,a842),f317(f287(f858(f857(x37941,x37941),a842),f858(x37941,a842),f261(x37941)),x37942)),f317(f261(x37941),f49(f858(f857(x37941,x37941),a842),x37942))) % 168.19/168.05 [3795]E(f184(a849,f317(a124,x37951),f317(f317(f8(a849,a849,a849),a124),f317(f224(a849),x37951)),x37952),f317(f317(f224(a849),f317(a124,x37951)),x37952)) % 168.19/168.05 [3817]P22(f317(f317(f225(f858(f858(x38171,a842),a842)),x38172),f317(f285(x38171),f49(f858(x38171,a842),x38172)))) % 168.19/168.05 [3851]E(f317(f317(f51(x38511,f858(x38511,a842)),x38512),f317(f317(f7(x38511,f858(x38511,a842),f858(x38511,a842)),f286(x38511)),f188(f858(x38511,a842)))),x38512) % 168.19/168.05 [3852]E(f317(f317(f265(x38521,x38521,x38521),f317(f263(x38521,x38521),x38522)),f284(x38521,f317(f263(x38521,x38521),x38522))),f317(f263(x38521,x38521),f317(f317(f265(x38521,x38521,x38521),x38522),f284(x38521,x38522)))) % 168.19/168.05 [3922]E(f317(f166(x39221),f317(f136(f850(x39221),f850(x39221),f127(x39221),f125(x39221)),x39222)),f317(f317(f51(f850(x39221),f858(x39221,a842)),f317(f166(f850(x39221)),x39222)),f166(x39221))) % 168.19/168.05 [3952]E(f317(f317(f122(f858(f857(x39521,x39521),a842)),f284(x39521,f188(f858(f857(x39521,x39521),a842)))),f317(f317(f265(x39521,x39521,x39521),f284(x39521,x39522)),x39522)),f284(x39521,x39522)) % 168.19/168.05 [3989]E(f317(f317(f175(x39891,x39891),x39892),x39892),f317(f317(f148(x39891,f857(x39891,x39891)),f317(f317(f18(x39891,x39891,f857(x39891,x39891)),f237(x39891,x39891)),f5(x39891))),x39892)) % 168.19/168.05 [4108]E(f317(f136(a849,f850(x41081),f317(f7(f850(x41081),a849,a849),f317(f317(f8(a849,f858(a849,a849),f850(x41081)),f224(a849)),f189(f850(x41081)))),f2(a849)),f317(f163(f850(x41081)),x41082)),f317(f189(f850(f850(x41081))),f173(x41081,x41082))) % 168.19/168.05 [4188]E(f317(f317(f264(f857(a849,f850(x41881)),f850(x41881)),f310(a849,f850(x41881),a229,f139(x41881,x41882))),f317(f317(f18(f850(x41881),f850(x41881),f857(a849,f850(x41881))),f317(f317(f8(a849,f858(f850(x41881),f857(a849,f850(x41881))),f850(x41881)),f237(a849,f850(x41881))),f189(f850(x41881)))),f5(f850(x41881)))),f140(x41881,x41882)) % 168.19/168.05 [4313]E(f317(f230(x43131),f317(f317(f8(f858(f858(x43131,a842),a842),a842,x43131),f97(f858(x43131,a842))),f317(f317(f8(f858(f858(x43131,a842),a842),f858(f858(x43131,a842),a842),x43131),f317(f18(f858(x43131,a842),a842,a842),f317(f317(f8(a842,f858(a842,a842),f858(x43131,a842)),a320),f317(f317(f7(f858(x43131,a842),f858(f858(x43131,a842),a842),a842),f319(f858(x43131,a842))),x43132)))),f319(x43131)))),f50(f858(x43131,a842),x43132)) % 168.19/168.05 [4498]~P22(f317(f317(f226(a1),f317(f112(a1),x44981)),f317(f88(a1),f317(f112(a1),x44982)))) % 168.19/168.05 [3388]E(f317(f317(f21(a849),f317(f317(f89(a849),x33881),x33882)),x33882),x33881) % 168.19/168.05 [3389]E(f317(f317(f21(a849),f317(f317(f89(a849),x33891),x33892)),x33891),x33892) % 168.19/168.05 [3459]E(f317(f317(f89(a849),f317(f317(f21(a849),x34591),x34592)),x34592),f317(f317(f224(a849),x34591),x34592)) % 168.19/168.05 [3591]E(f317(f166(a849),f133(a849,f317(f278(a849,f317(a124,x35911)),x35912))),f282(a849,x35911,x35912)) % 168.19/168.05 [3597]E(f317(f112(a1),f198(f317(a116,f317(f84(a1),x35971)),f317(a116,f317(f84(a1),x35972)))),f317(f317(a199,x35971),x35972)) % 168.19/168.05 [3599]E(f317(f317(f122(f858(x35991,a842)),f317(f88(f858(x35991,a842)),x35992)),x35992),f233(f858(x35991,a842))) % 168.19/168.05 [3600]E(f317(f317(f113(f858(x36001,a842)),f317(f88(f858(x36001,a842)),x36002)),x36002),f188(f858(x36001,a842))) % 168.19/168.05 [3617]P22(f317(f317(f225(a849),f317(f317(f21(a849),x36171),x36172)),x36171)) % 168.19/168.05 [3625]E(f317(f317(f21(a849),x36251),f317(f317(f90(a849),f317(f48(a849,x36251),x36252)),x36252)),f55(a849,x36251,x36252)) % 168.19/168.05 [3626]E(f317(f317(f21(a1),x36261),f317(f317(f90(a1),f317(f48(a1,x36261),x36262)),x36262)),f55(a1,x36261,x36262)) % 168.19/168.05 [3641]P22(f317(f317(f226(a849),x36411),f317(a124,f317(f317(f89(a849),x36412),x36411)))) % 168.19/168.05 [3642]P22(f317(f317(f226(a849),x36421),f317(a124,f317(f317(f89(a849),x36421),x36422)))) % 168.19/168.05 [3659]E(f317(f317(f90(a849),f317(a116,f317(f84(a1),x36591))),f317(a116,f317(f84(a1),x36592))),f317(a116,f317(f84(a1),f317(f317(f90(a1),x36591),x36592)))) % 168.19/168.05 [3669]P22(f317(f317(f225(a1),f2(a1)),f317(f317(f238(a1),f317(f84(a1),x36691)),x36692))) % 168.19/168.05 [3741]E(f317(f262(f850(x37411),f850(x37411),f152(x37411,x37412)),f317(f317(f286(f850(x37411)),f125(x37411)),f188(f858(f850(x37411),a842)))),f317(f317(f286(f850(x37411)),f125(x37411)),f188(f858(f850(x37411),a842)))) % 168.19/168.05 [3763]E(f317(f317(f122(f858(f857(x37631,x37631),a842)),f284(x37631,x37632)),f284(x37631,f188(f858(f857(x37631,x37631),a842)))),f284(x37631,x37632)) % 168.19/168.05 [3778]E(f317(f48(a1,f317(f115(a1),f317(f317(f89(a1),x37781),x37781))),f317(f115(a1),f317(f317(f89(a1),x37782),x37782))),f317(f48(a1,f317(f115(a1),x37781)),f317(f115(a1),x37782))) % 168.19/168.05 [3841]E(f317(f317(f238(a1),x38411),f317(f115(a849),f317(f317(f89(a1),x38412),x38412))),f317(f317(f95(a1,a1),f317(f317(f238(a1),x38411),f317(f115(a849),x38412))),f317(f317(f18(a1,a1,a1),f90(a1)),f5(a1)))) % 168.19/168.05 [3847]E(f317(f230(f858(x38471,a842)),f317(f317(f7(f858(x38471,a842),f858(x38471,a842),a842),f225(f858(x38471,a842))),x38472)),f317(f285(x38471),x38472)) % 168.19/168.05 [3863]E(f317(f317(f148(a1,a849),a116),f317(f317(f127(a1),f317(f317(f148(a849,a1),f112(a1)),x38631)),f317(f317(f148(a849,a1),f112(a1)),x38632))),f317(f317(f127(a849),x38631),x38632)) % 168.19/168.05 [3897]E(f317(f287(a1,a1,f317(f317(f7(a1,a1,a1),f89(a1)),x38971)),f317(f278(a1,f2(a1)),f317(f317(f21(a1),x38972),x38971))),f317(f278(a1,x38971),x38972)) % 168.19/168.05 [3900]P46(x39001,f317(f317(f21(f858(f857(x39001,x39001),a842)),x39002),f284(x39001,f188(f858(f857(x39001,x39001),a842))))) % 168.19/168.05 [3919]E(f317(f189(f850(x39191)),f317(f136(f850(x39191),f850(x39191),f127(x39191),f125(x39191)),x39192)),f317(f160(a849),f317(f317(f148(f850(x39191),a849),f189(f850(x39191))),x39192))) % 168.19/168.05 [3925]P45(x39251,f233(f858(x39251,a842)),f317(f317(f122(f858(f857(x39251,x39251),a842)),x39252),f284(x39251,f188(f858(f857(x39251,x39251),a842))))) % 168.19/168.05 [3968]E(f184(a849,f2(a849),f317(f317(f8(a849,a849,a849),a124),f317(f317(f7(a849,a849,a849),f223(a849)),x39681)),x39682),f317(f317(f223(a849),x39682),f317(a124,x39681))) % 168.19/168.05 [3971]E(f184(a849,f317(a124,x39711),f317(f317(f8(a849,a849,a849),a124),f317(f317(f7(a849,a849,a849),f224(a849)),x39711)),x39712),f317(f317(f224(a849),x39712),f317(a124,x39711))) % 168.19/168.05 [3974]E(f317(f287(x39741,f850(x39741),f317(f317(f7(x39741,f850(x39741),f850(x39741)),f145(x39741)),f125(x39741))),x39742),f169(x39741,x39742,f317(f317(f286(f850(x39741)),f125(x39741)),f188(f858(f850(x39741),a842))))) % 168.19/168.05 [3975]E(f317(f317(f122(f858(f857(x39751,x39751),a842)),f317(f317(f265(x39751,x39751,x39751),x39752),f284(x39751,x39752))),f284(x39751,f188(f858(f857(x39751,x39751),a842)))),f284(x39751,x39752)) % 168.19/168.05 [3983]P22(f317(f317(f225(f858(f857(x39831,x39831),a842)),f235(x39831,x39832)),f317(f317(f245(x39831,x39831),x39832),f317(f16(f858(x39831,a842),x39831),x39832)))) % 168.19/168.05 [3987]E(f317(f287(a1,a849,a116),f317(f317(f122(f858(a1,a842)),f317(f287(a849,a1,f112(a1)),x39871)),f317(f287(a849,a1,f112(a1)),x39872))),f317(f317(f122(f858(a849,a842)),x39871),x39872)) % 168.19/168.05 [3988]E(f317(f287(a1,a849,a116),f317(f317(f113(f858(a1,a842)),f317(f287(a849,a1,f112(a1)),x39881)),f317(f287(a849,a1,f112(a1)),x39882))),f317(f317(f113(f858(a849,a842)),x39881),x39882)) % 168.19/168.05 [3992]E(f317(f230(x39921),f317(f317(f8(a842,a842,x39921),a312),f317(f317(f7(x39921,f858(x39921,a842),a842),f319(x39921)),x39922))),f317(f88(f858(x39921,a842)),x39922)) % 168.19/168.05 [4019]E(f317(f136(f850(x40191),f850(x40191),f127(x40191),f125(x40191)),f317(f317(f148(f850(x40191),f850(x40191)),f163(x40191)),f317(f163(f850(x40191)),x40192))),f317(f163(x40191),f317(f136(f850(x40191),f850(x40191),f127(x40191),f125(x40191)),x40192))) % 168.19/168.05 [4048]E(f317(f317(f51(a849,f858(f857(x40481,x40481),a842)),f233(f858(a849,a842))),f317(f317(f7(a849,f858(f857(x40481,x40481),a842),f858(f857(x40481,x40481),a842)),f182(f857(x40481,x40481),a842)),x40482)),f284(x40481,x40482)) % 168.19/168.05 [4073]E(f94(x40731,f317(f317(f8(f858(x40731,a842),a842,x40731),f317(a314,x40732)),f317(f317(f7(x40731,f858(x40731,a842),f858(x40731,a842)),f286(x40731)),f188(f858(x40731,a842))))),f290(x40731,x40732)) % 168.19/168.05 [4080]E(f317(f189(f850(x40801)),f146(x40801,f317(f136(f850(x40801),f850(x40801),f127(x40801),f125(x40801)),x40802))),f317(f54(x40801),f317(f317(f51(f850(x40801),f858(x40801,a842)),f317(f166(f850(x40801)),x40802)),f166(x40801)))) % 168.19/168.05 [4096]E(f317(f317(f122(f858(f857(x40961,x40961),a842)),x40962),f317(f317(f265(x40961,x40961,x40961),f317(f317(f265(x40961,x40961,x40961),x40962),f284(x40961,x40962))),x40962)),f317(f317(f265(x40961,x40961,x40961),x40962),f284(x40961,x40962))) % 168.19/168.05 [4117]P22(f317(f317(f225(f858(f857(x41171,x41171),a842)),f317(f317(f265(x41171,x41171,x41171),x41172),f284(x41171,x41172))),f317(f317(f245(x41171,x41171),f317(f261(x41171),x41172)),f317(f16(f858(x41171,a842),x41171),f317(f261(x41171),x41172))))) % 168.19/168.05 [4161]E(f317(f230(f850(x41611)),f317(f317(f7(f850(x41611),f858(x41611,a842),a842),f317(f317(f8(f858(x41611,a842),f858(f858(x41611,a842),a842),f850(x41611)),f225(f858(x41611,a842))),f166(x41611))),x41612)),f155(x41611,x41612)) % 168.19/168.05 [4174]E(f317(f150(f850(x41741),x41741,f125(x41741),f317(f317(f8(f850(x41741),f858(f850(x41741),f850(x41741)),x41741),f317(f7(f850(x41741),f850(x41741),f850(x41741)),f127(x41741))),f317(f317(f7(x41741,f850(x41741),f850(x41741)),f145(x41741)),f125(x41741)))),x41742),f317(f162(x41741),x41742)) % 168.19/168.05 [4217]P19(f858(x42171,x42172),f858(f857(x42171,x42172),a842),f317(f317(f8(f858(f857(x42171,x42172),a842),f858(f857(x42171,x42172),a842),f858(x42171,x42172)),f230(f857(x42171,x42172))),f317(f317(f8(f858(x42171,f858(x42172,a842)),f858(f857(x42171,x42172),a842),f858(x42171,x42172)),f247(x42171,x42172,a842)),f317(f8(x42172,f858(x42172,a842),x42171),f317(f7(x42172,x42172,a842),a314)))),f233(f858(f858(x42171,x42172),a842))) % 168.19/168.05 [4222]E(f55(a1,f317(f115(a1),f317(f317(f89(a1),x42221),x42221)),f317(f115(a1),f317(f317(f89(a1),x42222),x42222))),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f55(a1,f317(f115(a1),x42221),f317(f115(a1),x42222)))) % 168.19/168.05 [4264]E(f317(f317(f51(x42641,f858(f857(x42641,x42641),a842)),x42642),f317(f317(f7(x42641,f858(f857(x42641,x42641),a842),f858(f857(x42641,x42641),a842)),f317(f317(f8(f857(x42641,x42641),f858(f858(f857(x42641,x42641),a842),f858(f857(x42641,x42641),a842)),x42641),f286(f857(x42641,x42641))),f317(f317(f18(x42641,x42641,f857(x42641,x42641)),f237(x42641,x42641)),f5(x42641)))),f188(f858(f857(x42641,x42641),a842)))),f235(x42641,x42642)) % 168.19/168.05 [4348]E(f317(f230(f858(x43481,a842)),f317(f317(f8(f858(f858(x43481,a842),a842),a842,f858(x43481,a842)),f96(f858(x43481,a842))),f317(f317(f7(f858(x43481,a842),f858(f858(x43481,a842),a842),f858(f858(x43481,a842),a842)),f317(f317(f8(f858(f858(x43481,a842),f858(a842,a842)),f858(f858(f858(x43481,a842),a842),f858(f858(x43481,a842),a842)),f858(x43481,a842)),f18(f858(x43481,a842),a842,a842)),f317(f317(f8(f858(f858(x43481,a842),a842),f858(f858(x43481,a842),f858(a842,a842)),f858(x43481,a842)),f317(f8(a842,f858(a842,a842),f858(x43481,a842)),a315)),f317(f317(f7(f858(x43481,a842),f858(f858(x43481,a842),f858(x43481,a842)),f858(f858(x43481,a842),a842)),f317(f317(f8(f858(f858(x43481,a842),a842),f858(f858(f858(x43481,a842),f858(x43481,a842)),f858(f858(x43481,a842),a842)),f858(x43481,a842)),f8(f858(x43481,a842),a842,f858(x43481,a842))),a314)),f88(f858(x43481,a842)))))),f317(f317(f8(f858(f858(x43481,a842),a842),a842,f858(x43481,a842)),f317(f319(f858(x43481,a842)),x43482)),f285(x43481))))),f317(f285(x43481),f317(f88(f858(x43481,a842)),x43482))) % 168.19/168.05 [4495]~E(f317(f317(f89(a1),x44951),x44951),f317(f317(f21(a1),f317(f317(f89(a1),x44952),x44952)),a109)) % 168.19/168.05 [4500]~P22(f317(f317(f226(a849),f317(f317(f89(a849),x45001),x45002)),x45002)) % 168.19/168.05 [4501]~P22(f317(f317(f226(a849),f317(f317(f89(a849),x45011),x45012)),x45011)) % 168.19/168.05 [3710]E(f317(f317(f148(a849,x37101),f317(f159(x37101),x37102)),f133(a849,f317(f278(a849,f2(a849)),f317(f189(f850(x37101)),x37102)))),x37102) % 168.19/168.05 [3775]E(f317(f262(x37751,x37751,f284(x37751,f188(f858(f857(x37751,x37751),a842)))),x37752),x37752) % 168.19/168.05 [3901]E(f284(x39011,f317(f317(f21(f858(f857(x39011,x39011),a842)),x39012),f284(x39011,f188(f858(f857(x39011,x39011),a842))))),f284(x39011,x39012)) % 168.19/168.05 [3902]E(f284(x39021,f317(f317(f122(f858(f857(x39021,x39021),a842)),x39022),f284(x39021,f188(f858(f857(x39021,x39021),a842))))),f284(x39021,x39022)) % 168.19/168.05 [3955]E(f317(f317(f21(a1),f317(f317(f21(a1),f317(f317(f89(a1),x39551),x39551)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),x39552),x39552)),a109)),f317(f317(f89(a1),f317(f317(f21(a1),x39551),x39552)),f317(f317(f21(a1),x39551),x39552))) % 168.19/168.05 [3997]E(f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f89(a1),x39971),x39972)),f317(f317(f89(a1),x39971),x39972))),a109),f317(f317(f89(a1),f317(f317(f89(a1),x39971),x39971)),f317(f317(f21(a1),f317(f317(f89(a1),x39972),x39972)),a109))) % 168.19/168.05 [4023]E(f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),x40231),x40231)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),x40232),x40232)),a109)),f317(f317(f89(a1),f317(f317(f89(a1),x40231),f317(f317(f21(a1),x40232),a109))),f317(f317(f89(a1),x40231),f317(f317(f21(a1),x40232),a109)))) % 168.19/168.05 [4034]E(f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f89(a1),x40341),x40342)),f317(f317(f89(a1),x40341),x40342))),a109),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),x40341),x40341)),a109)),f317(f317(f89(a1),x40342),x40342))) % 168.19/168.05 [4035]E(f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),x40351),x40352)),f317(f317(f21(a1),x40351),x40352))),a109),f317(f317(f21(a1),f317(f317(f21(a1),f317(f317(f89(a1),x40351),x40351)),a109)),f317(f317(f89(a1),x40352),x40352))) % 168.19/168.05 [4091]E(f317(f112(a1),f317(f48(a849,f317(f317(f90(a849),f317(a116,f317(f84(a1),x40911))),f317(a116,f317(f84(a1),x40912)))),f198(f317(a116,f317(f84(a1),x40911)),f317(a116,f317(f84(a1),x40912))))),f207(x40911,x40912)) % 168.19/168.05 [4136]E(f317(f317(f249(f857(a111,a111),a111,f857(a111,a111),f857(x41361,f857(a111,a111))),f253(f317(a3,f317(f189(f850(x41361)),x41362)))),f317(f317(f8(x41361,f858(f857(a111,a111),f857(x41361,f857(a111,a111))),a111),f237(x41361,f857(a111,a111))),f317(f317(f8(a849,x41361,a111),f317(f159(x41361),x41362)),a19))),f259(x41361,x41362)) % 168.19/168.05 [4223]E(f317(f136(a849,f850(x42231),f317(f7(f850(x42231),a849,a849),f317(f317(f8(a849,f858(a849,a849),f850(x42231)),f224(a849)),f189(f850(x42231)))),f2(a849)),f317(f163(f850(x42231)),f173(x42231,x42232))),f317(f189(f850(f850(x42231))),f317(f130(f850(x42231),f317(f317(f8(a842,a842,f850(x42231)),a312),f317(f317(f7(f850(x42231),f850(x42231),a842),a314),f125(x42231)))),x42232))) % 168.19/168.05 [4229]E(f317(f317(f51(a849,f858(x42291,a842)),f233(f858(a849,a842))),f317(f317(f7(a849,f858(a849,f858(x42291,a842)),f858(x42291,a842)),f317(f317(f8(f858(a849,a842),f858(f858(a849,f858(x42291,a842)),f858(x42291,a842)),a849),f51(a849,f858(x42291,a842))),f278(a849,f2(a849)))),x42292)),f317(f317(f51(a849,f858(x42291,a842)),f233(f858(a849,a842))),x42292)) % 168.19/168.05 [4248]P22(f317(f71(a849),f317(f230(a849),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),x42481)),f317(f317(f7(a849,a849,a842),f226(a849)),x42482))))) % 168.19/168.05 [4357]E(f317(f230(f857(f850(x43571),f850(x43571))),f317(f247(f850(x43571),f850(x43571),a842),f317(f317(f18(f850(x43571),f858(f850(x43571),a842),f858(f850(x43571),a842)),f317(f317(f8(f858(f850(x43571),f858(a842,a842)),f858(f858(f850(x43571),a842),f858(f850(x43571),a842)),f850(x43571)),f18(f850(x43571),a842,a842)),f317(f317(f8(f858(f850(x43571),a842),f858(f850(x43571),f858(a842,a842)),f850(x43571)),f317(f8(a842,f858(a842,a842),f850(x43571)),a316)),f317(f317(f7(f850(x43571),f858(f850(x43571),a849),f858(f850(x43571),a842)),f317(f317(f8(f858(a849,a842),f858(f858(f850(x43571),a849),f858(f850(x43571),a842)),f850(x43571)),f8(a849,a842,f850(x43571))),f317(f317(f8(a849,f858(a849,a842),f850(x43571)),f226(a849)),f189(f850(x43571))))),f189(f850(x43571)))))),f317(f317(f18(f850(x43571),f858(f850(x43571),a842),f858(f850(x43571),a842)),f317(f317(f8(f858(f850(x43571),f858(a842,a842)),f858(f858(f850(x43571),a842),f858(f850(x43571),a842)),f850(x43571)),f18(f850(x43571),a842,a842)),f317(f317(f8(f858(f850(x43571),a842),f858(f850(x43571),f858(a842,a842)),f850(x43571)),f317(f8(a842,f858(a842,a842),f850(x43571)),a315)),f317(f317(f7(f850(x43571),f858(f850(x43571),a849),f858(f850(x43571),a842)),f317(f317(f8(f858(a849,a842),f858(f858(f850(x43571),a849),f858(f850(x43571),a842)),f850(x43571)),f8(a849,a842,f850(x43571))),f317(f317(f8(a849,f858(a849,a842),f850(x43571)),a314),f189(f850(x43571))))),f189(f850(x43571)))))),f317(f317(f7(f850(x43571),f858(f857(f850(x43571),f850(x43571)),a842),f858(f850(x43571),a842)),f317(f317(f8(f858(f850(x43571),f858(f858(f857(f850(x43571),f850(x43571)),a842),a842)),f858(f858(f857(f850(x43571),f850(x43571)),a842),f858(f850(x43571),a842)),f850(x43571)),f7(f850(x43571),f858(f857(f850(x43571),f850(x43571)),a842),a842)),f317(f317(f8(f858(f850(x43571),f857(f850(x43571),f850(x43571))),f858(f850(x43571),f858(f858(f857(f850(x43571),f850(x43571)),a842),a842)),f850(x43571)),f317(f8(f857(f850(x43571),f850(x43571)),f858(f858(f857(f850(x43571),f850(x43571)),a842),a842),f850(x43571)),f319(f857(f850(x43571),f850(x43571))))),f237(f850(x43571),f850(x43571))))),f139(x43571,x43572)))))),f140(x43571,x43572)) % 168.19/168.05 [4026]E(f317(f317(f89(a1),f317(f317(f89(a1),f317(f317(f90(a1),x40261),x40262)),f317(f317(f90(a1),x40261),x40262))),x40262),f317(f317(f90(a1),f317(f317(f21(a1),f317(f317(f89(a1),x40261),x40261)),a109)),x40262)) % 168.19/168.05 [4134]E(f317(a116,f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x41341),x41342)),f188(f858(f857(a849,a849),a842)))))),f317(f317(f21(a849),x41341),x41342)) % 168.19/168.05 [4139]E(f317(f317(f265(x41391,x41391,x41391),f317(f317(f122(f858(f857(x41391,x41391),a842)),x41392),f284(x41391,f188(f858(f857(x41391,x41391),a842))))),f284(x41391,f317(f317(f122(f858(f857(x41391,x41391),a842)),x41392),f284(x41391,f188(f858(f857(x41391,x41391),a842)))))),f284(x41391,x41392)) % 168.19/168.05 [4181]E(f252(x41811,f317(f130(f857(a111,x41811),f317(f247(a111,x41811,a842),f317(f317(f8(a842,f858(x41811,a842),a111),f16(a842,x41811)),f317(f226(a111),f2(a111))))),x41812)),f252(x41811,x41812)) % 168.19/168.05 [4182]E(f254(x41821,f317(f130(f857(a111,x41821),f317(f247(a111,x41821,a842),f317(f317(f8(a842,f858(x41821,a842),a111),f16(a842,x41821)),f317(f226(a111),f2(a111))))),x41822)),f254(x41821,x41822)) % 168.19/168.05 [4184]E(f317(f88(a1),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x41841),x41842)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x41842),x41841)),f188(f858(f857(a849,a849),a842)))))) % 168.19/168.05 [4240]E(f317(f317(f264(f850(a849),x42401),f139(a849,a229)),f317(f317(f7(x42401,f850(f858(x42401,a849)),f850(a849)),f317(f317(f8(f858(f858(x42401,a849),a849),f858(f850(f858(x42401,a849)),f850(a849)),x42401),f148(f858(x42401,a849),a849)),f317(f7(f858(x42401,a849),x42401,a849),f5(f858(x42401,a849))))),x42402)),f147(x42401,x42402)) % 168.19/168.05 [4261]E(f317(f317(f95(a1,a849),f317(f115(a1),f317(f317(f89(a1),x42611),a109))),f317(f317(f18(a1,a849,a849),f317(f317(f7(a1,a849,f858(a849,a849)),f317(f317(f8(a842,f858(a849,f858(a849,a849)),a1),f108(a849)),a193)),f2(a849))),f317(f317(f8(a849,a849,a1),a124),f317(f317(f8(a849,a849,a1),f317(f223(a849),x42612)),a116)))),f317(f317(f223(a849),f317(a124,x42612)),f317(f115(a849),x42611))) % 168.19/168.05 [4262]E(f317(f317(f95(a1,a849),f317(f115(a1),f317(f317(f89(a1),x42621),a109))),f317(f317(f18(a1,a849,a849),f317(f317(f7(a1,a849,f858(a849,a849)),f317(f317(f8(a842,f858(a849,f858(a849,a849)),a1),f108(a849)),a193)),f317(a124,x42622))),f317(f317(f8(a849,a849,a1),a124),f317(f317(f8(a849,a849,a1),f317(f224(a849),x42622)),a116)))),f317(f317(f224(a849),f317(a124,x42622)),f317(f115(a849),x42621))) % 168.19/168.05 [4281]E(f317(f136(f850(x42811),f850(x42811),f127(x42811),f125(x42811)),f317(f317(f148(f850(x42811),f850(x42811)),f150(f850(x42811),x42811,f125(x42811),f317(f317(f8(f850(x42811),f858(f850(x42811),f850(x42811)),x42811),f16(f850(x42811),f850(x42811))),f317(f317(f7(x42811,f850(x42811),f850(x42811)),f145(x42811)),f125(x42811))))),x42812)),f317(f317(f148(f850(x42811),x42811),f135(x42811)),f317(f130(f850(x42811),f317(f317(f8(a842,a842,f850(x42811)),a312),f317(f317(f7(f850(x42811),f850(x42811),a842),a314),f125(x42811)))),x42812))) % 168.19/168.05 [4338]E(f317(f247(a1,a1,a842),f317(f317(f7(a1,f858(a1,a842),f858(a1,a842)),f317(f317(f8(f858(a1,f858(a842,a842)),f858(f858(a1,a842),f858(a1,a842)),a1),f18(a1,a842,a842)),f317(f317(f8(f858(a1,a842),f858(a1,f858(a842,a842)),a1),f317(f8(a842,f858(a842,a842),a1),a315)),f317(f317(f8(f858(a1,a1),f858(a1,a842),a1),f317(f8(a1,a842,a1),f317(a314,x43381))),f317(f317(f8(a1,f858(a1,a1),a1),f89(a1)),f317(f90(a1),x43382)))))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),f317(a320,f317(f317(f226(a1),f2(a1)),x43382))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f225(a1),f2(a1)))),f317(f317(f7(a1,a1,a842),f226(a1)),x43382))))),f317(f317(f8(a842,a842,a1),f317(a320,f317(a312,f317(f317(f226(a1),f2(a1)),x43382)))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f226(a1),x43382))),f317(f317(f7(a1,a1,a842),f225(a1)),f2(a1))))))),f58(x43381,x43382)) % 168.19/168.05 [4340]E(f317(f230(x43401),f317(f317(f8(f858(a849,a842),a842,x43401),f96(a849)),f317(f317(f7(x43401,f858(a849,a842),f858(a849,a842)),f317(f317(f8(f858(a849,f858(a842,a842)),f858(f858(a849,a842),f858(a849,a842)),x43401),f18(a849,a842,a842)),f317(f317(f8(f858(a849,a842),f858(a849,f858(a842,a842)),x43401),f317(f8(a842,f858(a842,a842),a849),a315)),f317(f317(f7(x43401,f858(a849,x43401),f858(a849,a842)),f317(f317(f8(f858(x43401,a842),f858(f858(a849,x43401),f858(a849,a842)),x43401),f8(x43401,a842,a849)),a314)),f317(f159(x43401),x43402))))),f317(f317(f7(a849,a849,a842),f226(a849)),f317(f189(f850(x43401)),x43402))))),f317(f166(x43401),x43402)) % 168.19/168.05 [4151]E(f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),x41511),a109)),x41512)),f317(f317(f21(a1),f317(f317(f89(a1),x41511),a109)),x41512))),a109),f317(f317(f21(a1),f317(f317(f89(a1),x41511),x41511)),f317(f317(f21(a1),f317(f317(f89(a1),x41512),x41512)),a109))) % 168.19/168.05 [4276]E(f317(f136(f850(f850(x42761)),f850(f850(x42761)),f127(f850(x42761)),f125(f850(x42761))),f317(f317(f148(f850(x42761),f850(f850(x42761))),f150(f850(f850(x42761)),x42761,f125(f850(x42761)),f317(f16(f858(f850(x42761),f850(f850(x42761))),x42761),f317(f317(f7(f850(x42761),f850(f850(x42761)),f850(f850(x42761))),f145(f850(x42761))),f125(f850(x42761)))))),x42762)),f317(f317(f148(f850(x42761),f850(x42761)),f165(x42761)),f317(f130(f850(x42761),f317(f317(f8(a842,a842,f850(x42761)),a312),f317(f317(f7(f850(x42761),f850(x42761),a842),a314),f125(x42761)))),x42762))) % 168.19/168.05 [4286]E(f317(f317(f95(a1,a849),f317(f115(a1),f317(f317(f89(a1),x42861),a109))),f317(f317(f18(a1,a849,a849),f317(f317(f7(a1,a849,f858(a849,a849)),f317(f317(f8(a842,f858(a849,f858(a849,a849)),a1),f108(a849)),a193)),f2(a849))),f317(f317(f8(a849,a849,a1),a124),f317(f317(f7(a1,a849,a849),f317(f317(f8(a849,f858(a849,a849),a1),f223(a849)),a116)),x42862)))),f317(f317(f223(a849),f317(f115(a849),x42861)),f317(a124,x42862))) % 168.19/168.05 [4287]E(f317(f317(f95(a1,a849),f317(f115(a1),f317(f317(f89(a1),x42871),a109))),f317(f317(f18(a1,a849,a849),f317(f317(f7(a1,a849,f858(a849,a849)),f317(f317(f8(a842,f858(a849,f858(a849,a849)),a1),f108(a849)),a193)),f317(a124,x42872))),f317(f317(f8(a849,a849,a1),a124),f317(f317(f7(a1,a849,a849),f317(f317(f8(a849,f858(a849,a849),a1),f224(a849)),a116)),x42872)))),f317(f317(f224(a849),f317(f115(a849),x42871)),f317(a124,x42872))) % 168.19/168.05 [4275]E(f317(f247(x42751,x42751,a842),f317(f317(f18(x42751,a842,f858(x42751,a842)),f317(f317(f8(f858(x42751,f858(a842,a842)),f858(a842,f858(x42751,a842)),x42751),f7(x42751,a842,a842)),f317(f317(f8(f858(x42751,a842),f858(x42751,f858(a842,a842)),x42751),f317(f8(a842,f858(a842,a842),x42751),a315)),a314))),x42752)),f235(x42751,x42752)) % 168.19/168.05 [4318]E(f317(f48(a849,x43181),f317(f317(f89(a849),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))),x43182)),f317(f48(a849,x43181),f317(a124,f317(a124,f317(a124,x43182))))) % 168.19/168.05 [4319]E(f55(a849,x43191,f317(f317(f89(a849),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))),x43192)),f55(a849,x43191,f317(a124,f317(a124,f317(a124,x43192))))) % 168.19/168.05 [4320]E(f55(a849,f317(f317(f89(a849),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))),x43201),x43202),f55(a849,f317(a124,f317(a124,f317(a124,x43201))),x43202)) % 168.19/168.05 [4331]E(f128(f317(x43311,f317(f317(f90(a111),f317(f115(a111),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))),x43312))),f317(f205(x43311),x43312)) % 168.19/168.05 [4332]E(f317(f48(a849,f317(f317(f89(a849),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))),x43321)),x43322),f317(f48(a849,f317(a124,f317(a124,f317(a124,x43321)))),x43322)) % 168.19/168.05 [3416]P32(x34161,x34162,x34163,x34163) % 168.19/168.05 [3497]P19(x34971,f856(x34972,x34971),f297(x34971,x34972),x34973) % 168.19/168.05 [3498]P19(x34981,f856(x34981,x34982),f288(x34981,x34982),x34983) % 168.19/168.05 [4402]~E(f36(x44021,x44022),f317(a29,x44023)) % 168.19/168.05 [4403]~E(f30(x44031,x44032),f317(a29,x44033)) % 168.19/168.05 [4404]~E(f35(x44041,x44042),f317(a29,x44043)) % 168.19/168.05 [4405]~E(f317(a29,x44051),f36(x44052,x44053)) % 168.19/168.05 [4406]~E(f317(a29,x44061),f30(x44062,x44063)) % 168.19/168.05 [4407]~E(f317(a29,x44071),f35(x44072,x44073)) % 168.19/168.05 [4426]~E(f31(x44261,x44262,x44263),a23) % 168.19/168.05 [4427]~E(f33(x44271,x44272,x44273),a23) % 168.19/168.05 [4428]~E(f32(x44281,x44282,x44283),a23) % 168.19/168.05 [3197]E(f317(f317(f192(x31971,x31972),x31973),f191(x31971)),f191(x31972)) % 168.19/168.05 [3198]E(f317(f317(f148(x31981,x31982),x31983),f125(x31981)),f125(x31982)) % 168.19/168.05 [3217]E(f34(f31(x32171,x32172,x32173)),f2(a849)) % 168.19/168.05 [3238]E(f317(f183(x32381,x32382,x32383),f2(a849)),x32382) % 168.19/168.05 [3239]E(f317(f189(a843),f31(x32391,x32392,x32393)),f2(a849)) % 168.19/168.05 [3241]E(f317(f317(f175(x32411,x32412),x32413),f125(x32412)),f125(f857(x32411,x32412))) % 168.19/168.05 [3279]E(f94(x32791,f72(x32791,x32792,x32793)),f317(f73(x32791,x32792),x32793)) % 168.19/168.05 [3331]E(f134(x33311,x33312,f146(x33311,x33313)),f146(x33311,f134(x33311,x33312,x33313))) % 168.19/168.05 [3351]E(f317(f244(f850(x33511),f850(x33511)),f161(x33511,x33512,x33513)),f317(f130(x33511,x33512),x33513)) % 168.19/168.05 [3429]E(f184(x34291,x34292,x34293,f2(a849)),x34292) % 168.19/168.05 [3430]E(f17(x34301,x34302,x34303,f2(a111)),x34302) % 168.19/168.05 [3436]E(f157(x34361,x34362,x34363,f125(x34361)),f125(x34362)) % 168.19/168.05 [3437]E(f158(x34371,x34372,x34373,f125(x34371)),f125(x34372)) % 168.19/168.05 [3443]E(f317(f317(f159(x34431),f317(f317(f145(x34431),x34432),x34433)),f2(a849)),x34432) % 168.19/168.05 [3477]E(f69(x34771,x34772,f125(x34771),x34773),f125(f857(x34771,x34772))) % 168.19/168.05 [3496]P19(x34961,x34962,x34963,f188(f858(x34961,a842))) % 168.19/168.05 [3543]P32(x35431,x35432,f317(f16(f853(x35432),x35431),f191(x35432)),x35433) % 168.19/168.05 [3651]E(f317(f82(x36511,x36512,x36511,x36513),f39(x36511)),x36513) % 168.19/168.05 [3832]P22(f317(f317(f319(f857(x38321,x38321)),f317(f317(f237(x38321,x38321),x38322),x38322)),f284(x38321,x38323))) % 168.19/168.05 [4505]~P22(f317(f317(f319(f857(f850(x45051),f850(x45051))),f317(f317(f237(f850(x45051),f850(x45051)),x45052),f125(x45051))),f139(x45051,x45053))) % 168.19/168.05 [4506]~P22(f317(f317(f319(f857(f850(x45061),f850(x45061))),f317(f317(f237(f850(x45061),f850(x45061)),x45062),f125(x45061))),f141(x45061,x45063))) % 168.19/168.05 [4507]~P22(f317(f317(f319(f857(f850(x45071),f850(x45071))),f317(f317(f237(f850(x45071),f850(x45071)),x45072),f125(x45071))),f151(x45071,x45073))) % 168.19/168.05 [4508]~P22(f317(f317(f319(f857(f850(x45081),f850(x45081))),f317(f317(f237(f850(x45081),f850(x45081)),f125(x45081)),x45082)),f139(x45081,x45083))) % 168.19/168.05 [4509]~P22(f317(f317(f319(f857(f850(x45091),f850(x45091))),f317(f317(f237(f850(x45091),f850(x45091)),f125(x45091)),x45092)),f151(x45091,x45093))) % 168.19/168.05 [3210]E(f317(f317(f196(x32101,x32102),f191(x32101)),x32103),f191(x32102)) % 168.19/168.05 [3227]E(f317(f263(x32271,x32272),f317(f263(x32272,x32271),x32273)),x32273) % 168.19/168.05 [3246]E(f296(x32461,x32462,f317(f288(x32461,x32462),x32463)),x32463) % 168.19/168.05 [3247]E(f299(x32471,x32472,f317(f297(x32472,x32471),x32473)),x32473) % 168.19/168.05 [3253]E(f317(f317(f175(x32531,x32532),f125(x32531)),x32533),f125(f857(x32531,x32532))) % 168.19/168.05 [3256]E(f168(x32561,x32562,f317(f231(a849),x32563)),f317(f317(f167(x32561),x32563),x32562)) % 168.19/168.05 [3270]E(f317(f189(f856(x32701,x32702)),f317(f288(x32701,x32702),x32703)),f2(a849)) % 168.19/168.05 [3271]E(f317(f189(f856(x32711,x32712)),f317(f297(x32712,x32711),x32713)),f2(a849)) % 168.19/168.05 [3275]E(f146(x32751,f317(f130(x32751,x32752),x32753)),f317(f130(x32751,x32752),f146(x32751,x32753))) % 168.19/168.05 [3277]E(f317(f234(x32771,x32772),f317(f263(x32772,x32771),x32773)),f317(f236(x32772,x32771),x32773)) % 168.19/168.05 [3278]E(f317(f236(x32781,x32782),f317(f263(x32782,x32781),x32783)),f317(f234(x32782,x32781),x32783)) % 168.19/168.05 [3296]E(f317(f130(x32961,x32962),f317(f163(x32961),x32963)),f317(f163(x32961),f317(f130(x32961,x32962),x32963))) % 168.19/168.05 [3310]E(f317(f317(f132(x33101),x33102),f317(f165(x33101),x33103)),f317(f317(f132(x33101),f317(a124,x33102)),x33103)) % 168.19/168.05 [3326]E(f34(f32(x33261,x33262,x33263)),f317(f317(f89(a849),f34(x33263)),f317(a124,f2(a849)))) % 168.19/168.05 [3327]E(f317(f287(x33271,x33272,x33273),f188(f858(x33271,a842))),f188(f858(x33272,a842))) % 168.19/168.05 [3328]E(f317(f289(x33281,x33282,x33283),f188(f858(x33282,a842))),f188(f858(x33281,a842))) % 168.19/168.05 [3329]E(f317(f289(x33291,x33292,x33293),f233(f858(x33292,a842))),f233(f858(x33291,a842))) % 168.19/168.05 [3330]E(f317(f262(x33301,x33302,x33303),f188(f858(x33301,a842))),f188(f858(x33302,a842))) % 168.19/168.05 [3350]E(f317(f317(f196(x33501,x33502),x33503),f317(f16(f853(x33502),x33501),f191(x33502))),f191(x33502)) % 168.19/168.05 [3359]E(f317(f317(f286(x33591),x33592),f317(f166(x33591),x33593)),f317(f166(x33591),f134(x33591,x33592,x33593))) % 168.19/168.05 [3371]E(f219(x33711,x33712,f317(f217(x33711),x33713)),f317(f317(f89(a849),f317(x33712,x33713)),f317(a124,f2(a849)))) % 168.19/168.05 [3447]E(f317(f189(a843),f32(x34471,x34472,x34473)),f317(f317(f89(a849),f317(f189(a843),x34473)),f317(a124,f2(a849)))) % 168.19/168.05 [3448]E(f317(f287(f857(x34481,x34482),x34482,f246(x34481,x34482)),x34483),f317(f234(x34481,x34482),x34483)) % 168.19/168.05 [3449]E(f317(f287(f857(x34491,x34492),x34491,f244(x34491,x34492)),x34493),f317(f236(x34491,x34492),x34493)) % 168.19/168.05 [3522]E(f317(f317(f237(x35221,x35222),f317(f244(x35221,x35222),x35223)),f317(f246(x35221,x35222),x35223)),x35223) % 168.19/168.05 [3532]E(f317(f317(f247(x35321,x35322,x35321),f16(x35321,x35322)),x35323),f317(f244(x35321,x35322),x35323)) % 168.19/168.05 [3552]E(f178(x35521,x35522,x35523,f317(f16(f853(x35522),x35521),f191(x35522))),x35523) % 168.19/168.05 [3553]E(f178(x35531,x35532,f317(f16(f853(x35532),x35531),f191(x35532)),x35533),x35533) % 168.19/168.05 [3606]E(f34(f33(x36061,x36062,x36063)),f317(f317(f89(a849),f317(f317(f89(a849),f34(x36062)),f34(x36063))),f317(a124,f2(a849)))) % 168.19/168.05 [3654]E(f317(f82(x36541,x36541,x36542,f39(x36541)),x36543),x36543) % 168.19/168.05 [3766]P22(f317(f317(f194(f30(x37661,x37662)),x37663),f317(f317(f317(a200,x37663),x37661),f317(x37662,x37663)))) % 168.19/168.05 [3768]E(f317(f189(a843),f33(x37681,x37682,x37683)),f317(f317(f89(a849),f317(f317(f89(a849),f317(f189(a843),x37682)),f317(f189(a843),x37683))),f317(a124,f2(a849)))) % 168.19/168.05 [3842]P22(f317(f317(f225(f858(x38421,a842)),f317(f166(x38421),f317(f130(x38421,x38422),x38423))),f317(f166(x38421),x38423))) % 168.19/168.05 [3888]P22(f317(f317(f225(f858(x38881,a842)),f317(f166(x38881),f317(f317(f167(x38881),x38882),x38883))),f317(f166(x38881),x38883))) % 168.19/168.05 [3889]P22(f317(f317(f225(f858(x38891,a842)),f317(f166(x38891),f317(f317(f132(x38891),x38892),x38893))),f317(f166(x38891),x38893))) % 168.19/168.05 [3893]P22(f317(f317(f225(f858(x38931,a842)),f317(f166(x38931),f164(x38931,x38932,x38933))),f317(f166(x38931),x38933))) % 168.19/168.05 [3894]P22(f317(f317(f225(f858(x38941,a842)),f317(f166(x38941),f168(x38941,x38942,x38943))),f317(f166(x38941),x38942))) % 168.19/168.05 [3917]P19(f857(x39171,x39172),f857(x39172,x39171),f317(f247(x39171,x39172,f857(x39172,x39171)),f317(f7(x39172,x39171,f857(x39172,x39171)),f237(x39172,x39171))),x39173) % 168.19/168.05 [3930]E(f317(f317(f317(f182(f850(x39301),f850(x39301)),f55(a849,x39302,f317(f189(f850(x39301)),x39303))),f162(x39301)),x39303),f317(f317(f317(f182(f850(x39301),f850(x39301)),x39302),f162(x39301)),x39303)) % 168.19/168.05 [3972]P22(f317(f317(f319(f857(f850(x39721),f850(x39721))),f317(f317(f237(f850(x39721),f850(x39721)),x39722),x39722)),f152(x39721,f284(x39721,x39723)))) % 168.19/168.05 [4119]E(f94(f857(x41191,x41192),f317(f317(f18(f857(x41191,x41192),x41192,a842),f317(f317(f8(x41191,f858(x41192,a842),f857(x41191,x41192)),x41193),f244(x41191,x41192))),f246(x41191,x41192))),f94(f857(x41191,x41192),f317(f247(x41191,x41192,a842),x41193))) % 168.19/168.05 [4120]E(f99(f857(x41201,x41202),f317(f317(f18(f857(x41201,x41202),x41202,a842),f317(f317(f8(x41201,f858(x41202,a842),f857(x41201,x41202)),x41203),f244(x41201,x41202))),f246(x41201,x41202))),f99(f857(x41201,x41202),f317(f247(x41201,x41202,a842),x41203))) % 168.19/168.05 [4158]E(f317(f317(f264(f857(a849,x41581),x41581),f310(a849,x41581,a229,x41582)),f317(f317(f18(x41581,x41581,f857(a849,x41581)),f317(f317(f8(a849,f858(x41581,f857(a849,x41581)),x41581),f237(a849,x41581)),x41583)),f5(x41581))),f311(x41581,x41583,x41582)) % 168.19/168.05 [4225]E(f317(f248(x42251,x42251,x42252,x42252,f5(x42251),f5(x42252)),x42253),x42253) % 168.19/168.05 [4297]E(f317(f136(f850(f850(x42971)),f850(f850(x42971)),f127(f850(x42971)),f125(f850(x42971))),f317(f317(f148(f850(x42971),f850(f850(x42971))),f317(f317(f7(f850(x42971),f850(x42971),f850(f850(x42971))),f317(f317(f8(f858(x42971,f850(x42971)),f858(f850(x42971),f850(f850(x42971))),f850(x42971)),f148(x42971,f850(x42971))),f317(f7(x42971,f850(x42971),f850(x42971)),f145(x42971)))),x42972)),f64(x42971,x42973,x42972))),f64(x42971,f317(a124,x42973),x42972)) % 168.19/168.05 [4421]~E(f317(f317(f145(x44211),x44212),x44213),x44213) % 168.19/168.05 [4430]~E(f317(f317(f145(x44301),x44302),x44303),f125(x44301)) % 168.19/168.05 [4457]~E(f317(f317(f286(x44571),x44572),x44573),f188(f858(x44571,a842))) % 168.19/168.05 [4486]~E(f317(f287(x44861,f858(x44861,a842),x44862),x44863),f317(f285(x44861),x44863)) % 168.19/168.05 [3232]E(f317(f317(f153(x32321,f125(x32321)),x32322),x32323),f125(x32321)) % 168.19/168.05 [3233]E(f317(f135(x32331),f317(f317(f145(x32331),x32332),x32333)),x32332) % 168.19/168.05 [3234]E(f317(f165(x32341),f317(f317(f145(x32341),x32342),x32343)),x32343) % 168.19/168.05 [3282]E(f317(f317(f132(x32821),f87(a849)),f317(f317(f145(x32821),x32822),x32823)),x32823) % 168.19/168.05 [3316]E(f126(x33161,f317(f317(f132(x33161),x33162),x33163)),f317(f317(f132(x33161),x33162),f126(x33161,x33163))) % 168.19/168.05 [3318]E(f317(f317(f153(x33181,x33182),x33183),f317(f317(f159(x33181),x33182),x33183)),x33182) % 168.19/168.05 [3341]E(f317(f317(f286(x33411),x33412),f317(f317(f286(x33411),x33412),x33413)),f317(f317(f286(x33411),x33412),x33413)) % 168.19/168.05 [3353]E(f317(f317(f171(x33531,x33532),f125(f857(x33531,x33532))),x33533),f191(x33532)) % 168.19/168.05 [3356]E(f317(f317(f286(x33561),x33562),f317(f166(x33561),x33563)),f317(f166(x33561),f317(f317(f145(x33561),x33562),x33563))) % 168.19/168.05 [3358]E(f317(f317(f132(x33581),x33582),f317(f165(x33581),x33583)),f317(f165(x33581),f317(f317(f132(x33581),x33582),x33583))) % 168.19/168.05 [3368]E(f317(f317(f167(x33681),f87(a849)),f317(f317(f145(x33681),x33682),x33683)),f317(f317(f145(x33681),x33682),f125(x33681))) % 168.19/168.05 [3415]E(f317(f73(x34151,x34152),f317(f317(f286(x34151),x34153),f188(f858(x34151,a842)))),x34153) % 168.19/168.05 [3461]E(f317(f317(f89(a849),x34611),f317(f317(f89(a849),x34612),x34613)),f317(f317(f89(a849),x34612),f317(f317(f89(a849),x34611),x34613))) % 168.19/168.05 [3462]E(f317(f317(f89(a1),x34621),f317(f317(f89(a1),x34622),x34623)),f317(f317(f89(a1),x34622),f317(f317(f89(a1),x34621),x34623))) % 168.19/168.05 [3467]E(f317(f317(f245(x34671,x34672),f188(f858(x34671,a842))),x34673),f188(f858(f857(x34671,x34672),a842))) % 168.19/168.05 [3487]E(f317(f317(f122(f858(x34871,a842)),x34872),x34873),f317(f317(f122(f858(x34871,a842)),x34873),x34872)) % 168.19/168.05 [3488]E(f317(f317(f113(f858(x34881,a842)),x34882),x34883),f317(f317(f113(f858(x34881,a842)),x34883),x34882)) % 168.19/168.05 [3491]E(f317(f317(f127(x34911),x34912),f317(f317(f145(x34911),x34913),f125(x34911))),f317(f162(x34911),f317(f317(f145(x34911),x34913),x34912))) % 168.19/168.05 [3492]E(f317(f317(f127(x34921),f317(f163(x34921),x34922)),f317(f163(x34921),x34923)),f317(f163(x34921),f317(f317(f127(x34921),x34923),x34922))) % 168.19/168.05 [3502]E(f317(f165(x35021),f317(f317(f167(x35021),f317(a124,x35022)),x35023)),f317(f317(f167(x35021),x35022),f317(f165(x35021),x35023))) % 168.19/168.05 [3506]E(f317(f48(a849,x35061),f317(f317(f90(a849),x35062),x35063)),f317(f48(a849,f317(f48(a849,x35061),x35062)),x35063)) % 168.19/168.05 [3509]P22(f317(f317(f319(x35091),x35092),f317(f317(f286(x35091),x35092),x35093))) % 168.19/168.05 [3513]E(f317(f317(f52(x35131,f858(x35132,a842)),f188(f858(x35131,a842))),x35133),f233(f858(x35132,a842))) % 168.19/168.05 [3515]E(f317(f262(x35151,x35151,f235(x35151,x35152)),x35153),f317(f317(f113(f858(x35151,a842)),x35152),x35153)) % 168.19/168.05 [3528]E(f317(f189(f850(x35281)),f317(f317(f145(x35281),x35282),x35283)),f317(f317(f89(a849),f317(f189(f850(x35281)),x35283)),f317(a124,f2(a849)))) % 168.19/168.05 [3534]E(f126(x35341,f317(f317(f127(x35341),x35342),f317(f317(f145(x35341),x35343),f125(x35341)))),x35342) % 168.19/168.05 [3535]E(f138(x35351,f317(f317(f127(x35351),x35352),f317(f317(f145(x35351),x35353),f125(x35351)))),x35353) % 168.19/168.05 [3541]E(f317(f317(f127(x35411),f317(f317(f167(x35411),x35412),x35413)),f317(f317(f132(x35411),x35412),x35413)),x35413) % 168.19/168.05 [3550]E(f317(f317(f21(a849),f317(f317(f89(a849),x35501),x35502)),f317(f317(f89(a849),x35503),x35502)),f317(f317(f21(a849),x35501),x35503)) % 168.19/168.05 [3551]E(f317(f317(f21(a849),f317(f317(f89(a849),x35511),x35512)),f317(f317(f89(a849),x35511),x35513)),f317(f317(f21(a849),x35512),x35513)) % 168.19/168.05 [3558]E(f317(f317(f127(x35581),f317(f163(x35581),x35582)),f317(f317(f145(x35581),x35583),f125(x35581))),f317(f163(x35581),f317(f317(f145(x35581),x35583),x35582))) % 168.19/168.05 [3560]E(f317(f317(f89(a849),f317(f189(f850(x35601)),x35602)),f317(f189(f850(x35601)),x35603)),f317(f189(f850(x35601)),f317(f317(f127(x35601),x35602),x35603))) % 168.19/168.05 [3567]E(f317(f317(f122(f858(x35671,a842)),f317(f166(x35671),x35672)),f317(f166(x35671),x35673)),f317(f166(x35671),f317(f317(f127(x35671),x35672),x35673))) % 168.19/168.05 [3569]E(f55(a849,f317(f317(f90(a849),x35691),x35692),f317(f317(f90(a849),x35691),x35693)),f317(f317(f90(a849),x35691),f55(a849,x35692,x35693))) % 168.19/168.05 [3583]E(f317(f317(f167(x35831),f317(f317(f21(a849),x35832),f87(a849))),f317(f165(x35831),x35833)),f317(f165(x35831),f317(f317(f167(x35831),x35832),x35833))) % 168.19/168.05 [3588]E(f317(f317(f113(f858(x35881,a842)),x35882),f317(f88(f858(x35881,a842)),x35883)),f317(f317(f21(f858(x35881,a842)),x35882),x35883)) % 168.19/168.05 [3589]E(f317(f317(f21(f858(x35891,a842)),x35892),f317(f88(f858(x35891,a842)),x35893)),f317(f317(f113(f858(x35891,a842)),x35892),x35893)) % 168.19/168.05 [3610]E(f317(f317(f245(x36101,x36102),x36103),f317(f16(f858(x36102,a842),x36101),f188(f858(x36102,a842)))),f188(f858(f857(x36101,x36102),a842))) % 168.19/168.05 [3612]E(f317(f317(f89(a849),f317(f317(f90(a849),x36121),x36122)),f317(f317(f90(a849),x36121),x36123)),f317(f317(f90(a849),x36121),f317(f317(f89(a849),x36122),x36123))) % 168.19/168.05 [3613]E(f317(f317(f21(a849),f317(f317(f90(a849),x36131),x36132)),f317(f317(f90(a849),x36131),x36133)),f317(f317(f90(a849),x36131),f317(f317(f21(a849),x36132),x36133))) % 168.19/168.05 [3614]E(f317(f317(f89(a1),f317(f317(f90(a1),x36141),x36142)),f317(f317(f90(a1),x36141),x36143)),f317(f317(f90(a1),x36141),f317(f317(f89(a1),x36142),x36143))) % 168.19/168.05 [3615]E(f317(f317(f21(a1),f317(f317(f90(a1),x36151),x36152)),f317(f317(f90(a1),x36151),x36153)),f317(f317(f90(a1),x36151),f317(f317(f21(a1),x36152),x36153))) % 168.19/168.05 [3616]E(f317(f317(f90(a1),f317(f317(f238(a1),x36161),x36162)),f317(f317(f238(a1),x36161),x36163)),f317(f317(f238(a1),x36161),f317(f317(f89(a849),x36162),x36163))) % 168.19/168.05 [3629]E(f317(f317(f51(x36291,f858(x36292,a842)),x36293),f317(f16(f858(x36292,a842),x36291),f188(f858(x36292,a842)))),f188(f858(x36292,a842))) % 168.19/168.05 [3631]E(f55(a849,f317(f317(f90(a849),x36311),x36312),f317(f317(f90(a849),x36313),x36312)),f317(f317(f90(a849),f55(a849,x36311,x36313)),x36312)) % 168.19/168.05 [3635]E(f55(a1,f317(f317(f21(a1),x36351),f55(a1,x36352,x36353)),x36353),f55(a1,f317(f317(f21(a1),x36351),x36352),x36353)) % 168.19/168.05 [3636]E(f55(a1,f317(f317(f90(a1),x36361),f55(a1,x36362,x36363)),x36363),f55(a1,f317(f317(f90(a1),x36361),x36362),x36363)) % 168.19/168.05 [3637]P22(f317(f317(f225(f858(x36371,a842)),x36372),f317(f317(f286(x36371),x36373),x36372))) % 168.19/168.05 [3640]E(f317(f287(f857(x36401,x36402),x36401,f244(x36401,x36402)),f317(f166(f857(x36401,x36402)),x36403)),f177(x36401,x36402,f317(f171(x36401,x36402),x36403))) % 168.19/168.05 [3687]P22(f317(f71(x36871),f177(x36871,x36872,f317(f171(x36871,x36872),x36873)))) % 168.19/168.05 [3715]E(f317(f317(f52(f858(x37151,a842),f858(x37151,a842)),x37152),f317(f122(f858(x37151,a842)),x37153)),f317(f317(f122(f858(x37151,a842)),x37153),f50(f858(x37151,a842),x37152))) % 168.19/168.05 [3716]E(f317(f317(f51(f858(x37161,a842),f858(x37161,a842)),x37162),f317(f113(f858(x37161,a842)),x37163)),f317(f317(f113(f858(x37161,a842)),x37163),f49(f858(x37161,a842),x37162))) % 168.19/168.05 [3726]E(f317(f166(x37261),f317(f317(f317(f182(f850(x37261),f850(x37261)),x37262),f162(x37261)),x37263)),f317(f166(x37261),x37263)) % 168.19/168.05 [3730]E(f317(f317(f167(x37301),f317(f189(f850(x37301)),f170(x37301,x37302,x37303))),x37303),f170(x37301,x37302,x37303)) % 168.19/168.05 [3731]E(f177(x37311,x37312,f317(f317(f8(x37312,f853(x37312),x37311),f217(x37312)),x37313)),f233(f858(x37311,a842))) % 168.19/168.05 [3735]E(f317(f189(f850(x37351)),f317(f317(f317(f182(f850(x37351),f850(x37351)),x37352),f162(x37351)),x37353)),f317(f189(f850(x37351)),x37353)) % 168.19/168.05 [3738]E(f317(f317(f247(x37381,x37382,x37382),f317(f16(f858(x37382,x37382),x37381),f5(x37382))),x37383),f317(f246(x37381,x37382),x37383)) % 168.19/168.05 [3743]E(f55(a1,f317(f317(f21(a1),f55(a1,x37431,x37432)),x37433),x37432),f55(a1,f317(f317(f21(a1),x37431),x37433),x37432)) % 168.19/168.05 [3744]E(f55(a1,f317(f317(f238(a1),f55(a1,x37441,x37442)),x37443),x37442),f55(a1,f317(f317(f238(a1),x37441),x37443),x37442)) % 168.19/168.05 [3748]E(f317(f317(f51(f858(f857(x37481,x37482),a842),f858(x37482,a842)),x37483),f234(x37481,x37482)),f317(f234(x37481,x37482),f49(f858(f857(x37481,x37482),a842),x37483))) % 168.19/168.05 [3749]E(f317(f317(f51(f858(f857(x37491,x37492),a842),f858(x37491,a842)),x37493),f236(x37491,x37492)),f317(f236(x37491,x37492),f49(f858(f857(x37491,x37492),a842),x37493))) % 168.19/168.05 [3780]E(f317(f82(x37801,x37801,x37801,x37802),f317(f317(f182(x37801,x37801),x37803),x37802)),f317(f317(f182(x37801,x37801),f317(a124,x37803)),x37802)) % 168.19/168.05 [3791]E(f220(f853(x37911),x37912,f191(x37911),f317(f317(f8(x37911,f853(x37911),x37912),f217(x37911)),x37913)),f317(f192(x37912,x37911),x37913)) % 168.19/168.05 [3797]E(f317(f317(f132(x37971),f317(f317(f21(a849),f317(f189(f850(x37971)),x37972)),x37973)),f317(f163(x37971),x37972)),f317(f163(x37971),f317(f317(f167(x37971),x37973),x37972))) % 168.19/168.05 [3798]E(f317(f317(f167(x37981),f317(f317(f21(a849),f317(f189(f850(x37981)),x37982)),x37983)),f317(f163(x37981),x37982)),f317(f163(x37981),f317(f317(f132(x37981),x37983),x37982))) % 168.19/168.05 [3801]E(f317(f317(f89(a849),f317(f160(a849),f317(f317(f148(x38011,a849),x38012),x38013))),f317(f189(f850(x38011)),x38013)),f149(x38011,x38012,x38013)) % 168.19/168.05 [3818]E(f317(f162(x38181),f317(f317(f317(f182(f850(x38181),f850(x38181)),x38182),f162(x38181)),x38183)),f317(f317(f317(f182(f850(x38181),f850(x38181)),f317(a124,x38182)),f162(x38181)),x38183)) % 168.19/168.05 [3833]P22(f317(f317(f225(a849),f317(f189(f850(x38331)),f317(f130(x38331,x38332),x38333))),f317(f189(f850(x38331)),x38333))) % 168.19/168.05 [3850]E(f317(f317(f122(f858(f858(x38501,a842),a842)),f317(f285(x38501),x38502)),f317(f287(f858(x38501,a842),f858(x38501,a842),f317(f286(x38501),x38503)),f317(f285(x38501),x38502))),f317(f285(x38501),f317(f317(f286(x38501),x38503),x38502))) % 168.19/168.05 [3870]P18(x38701,x38702,f317(f317(f286(f848(x38701)),f317(f317(f317(f100(x38701),x38703),a23),x38703)),f188(f858(f848(x38701),a842)))) % 168.19/168.05 [3885]P22(f317(f317(f225(a849),f317(f189(f850(x38851)),f170(x38851,x38852,x38853))),f317(f189(f850(x38851)),x38853))) % 168.19/168.05 [3892]E(f317(f236(x38921,x38922),f317(f230(f857(x38921,x38922)),f317(f247(x38921,x38922,a842),x38923))),f317(f230(x38921),f317(f317(f8(f858(x38922,a842),a842,x38921),f96(x38922)),x38923))) % 168.19/168.05 [3905]E(f317(f287(a849,a849,f317(f317(f7(a849,a849,a849),f89(a849)),x39051)),f279(a849,x39052,x39053)),f279(a849,f317(f317(f89(a849),x39052),x39051),f317(f317(f89(a849),x39053),x39051))) % 168.19/168.05 [3907]P22(f317(f71(f853(x39071)),f317(f287(x39072,f853(x39071),f317(f171(x39072,x39071),x39073)),f233(f858(x39072,a842))))) % 168.19/168.05 [3920]E(f317(f287(a849,a849,f317(f317(f7(a849,a849,a849),f89(a849)),x39201)),f317(f278(a849,x39202),x39203)),f317(f278(a849,f317(f317(f89(a849),x39202),x39201)),f317(f317(f89(a849),x39203),x39201))) % 168.19/168.05 [3921]E(f317(f317(f89(a849),f317(f317(f90(a849),x39211),f55(a849,f317(f48(a849,x39212),x39211),x39213))),f55(a849,x39212,x39211)),f55(a849,x39212,f317(f317(f90(a849),x39211),x39213))) % 168.19/168.05 [3938]E(f317(f317(f175(x39381,x39382),f317(f317(f148(f857(x39381,x39382),x39381),f244(x39381,x39382)),x39383)),f317(f317(f148(f857(x39381,x39382),x39382),f246(x39381,x39382)),x39383)),x39383) % 168.19/168.05 [3956]E(f317(f317(f127(x39561),x39562),f317(f136(f850(x39561),f850(x39561),f127(x39561),f125(x39561)),x39563)),f317(f136(f850(x39561),f850(x39561),f127(x39561),x39562),x39563)) % 168.19/168.05 [3976]P22(f317(f317(f319(f857(x39761,x39761)),f317(f317(f237(x39761,x39761),x39762),x39762)),f317(f317(f182(f857(x39761,x39761),a842),f2(a849)),x39763))) % 168.19/168.05 [3982]E(f317(f230(x39821),f317(f317(f8(f858(x39822,a842),a842,x39821),f96(x39822)),f317(f7(x39822,x39821,a842),x39823))),f317(f234(x39822,x39821),f317(f230(f857(x39822,x39821)),f317(f247(x39822,x39821,a842),x39823)))) % 168.19/168.05 [4003]E(f317(f317(f122(f858(x40031,a842)),f317(f317(f51(a849,f858(x40031,a842)),f279(a849,f87(a849),x40032)),x40033)),f317(x40033,f2(a849))),f317(f317(f51(a849,f858(x40031,a842)),f317(f277(a849),x40032)),x40033)) % 168.19/168.05 [4018]E(f317(f136(f850(x40181),f850(x40181),f127(x40181),f125(x40181)),f317(f317(f148(f850(x40181),f850(x40181)),f130(x40181,x40182)),x40183)),f317(f130(x40181,x40182),f317(f136(f850(x40181),f850(x40181),f127(x40181),f125(x40181)),x40183))) % 168.19/168.05 [4021]E(f317(f246(f850(x40211),f850(x40211)),f161(x40211,x40212,x40213)),f317(f130(x40211,f317(f82(a842,a842,x40211,a312),x40212)),x40213)) % 168.19/168.05 [4039]E(f317(f317(f52(x40391,f858(x40392,a842)),f233(f858(x40391,a842))),f317(f317(f8(f858(x40392,a842),f858(x40392,a842),x40391),f230(x40392)),f317(f7(x40392,x40391,a842),x40393))),f317(f230(x40392),f317(f317(f8(f858(x40391,a842),a842,x40392),f97(x40391)),x40393))) % 168.19/168.05 [4055]E(f317(f317(f89(a1),f317(f317(f89(a1),f317(f317(f90(a1),x40551),f317(f48(a1,x40552),x40551))),f55(a1,x40552,x40551))),x40553),f317(f317(f89(a1),x40552),x40553)) % 168.19/168.05 [4103]E(f317(f317(f89(a1),f317(f317(f89(a1),f317(f317(f90(a1),f317(f48(a1,x41031),x41032)),x41032)),f55(a1,x41031,x41032))),x41033),f317(f317(f89(a1),x41031),x41033)) % 168.19/168.05 [4137]E(f94(f857(x41371,x41372),f317(f247(x41371,x41372,a842),f317(f317(f8(f858(x41372,f857(x41371,x41372)),f858(x41372,a842),x41371),f317(f8(f857(x41371,x41372),a842,x41372),x41373)),f237(x41371,x41372)))),f94(f857(x41371,x41372),x41373)) % 168.19/168.05 [4138]E(f99(f857(x41381,x41382),f317(f247(x41381,x41382,a842),f317(f317(f8(f858(x41382,f857(x41381,x41382)),f858(x41382,a842),x41381),f317(f8(f857(x41381,x41382),a842,x41382),x41383)),f237(x41381,x41382)))),f99(f857(x41381,x41382),x41383)) % 168.19/168.05 [4169]P22(f317(f317(f225(f858(x41691,a842)),f49(f858(x41691,a842),f317(f317(f113(f858(f858(x41691,a842),a842)),x41692),x41693))),f317(f317(f113(f858(x41691,a842)),f49(f858(x41691,a842),x41692)),f49(f858(x41691,a842),x41693)))) % 168.19/168.05 [4170]E(f317(f163(x41701),f317(f317(f317(f182(f850(x41701),f850(x41701)),f317(f317(f21(a849),f317(f189(f850(x41701)),x41702)),f55(a849,x41703,f317(f189(f850(x41701)),x41702)))),f162(x41701)),x41702)),f317(f317(f317(f182(f850(x41701),f850(x41701)),x41703),f162(x41701)),f317(f163(x41701),x41702))) % 168.19/168.05 [4185]E(f317(f230(x41851),f317(f317(f8(a842,a842,x41851),a312),f317(f317(f7(x41851,f853(x41852),a842),f317(f317(f8(f853(x41852),f858(f853(x41852),a842),x41851),a314),x41853)),f191(x41852)))),f177(x41851,x41852,x41853)) % 168.19/168.05 [4210]P22(f317(f317(f225(a849),f317(f189(f850(x42101)),f317(f317(f132(x42101),f317(f189(f850(x42101)),f170(x42101,x42102,x42103))),x42103))),f317(f189(f850(x42101)),x42103))) % 168.19/168.05 [4250]E(f317(f230(x42501),f317(f317(f8(f858(x42502,a842),a842,x42501),f96(x42502)),f317(f317(f8(f853(x42501),f858(x42502,a842),x42501),f317(f7(x42502,f853(x42501),a842),f317(f317(f8(f853(x42501),f858(f853(x42501),a842),x42502),a314),x42503))),f217(x42501)))),f179(x42502,x42501,x42503)) % 168.19/168.05 [4499]~P22(f317(f72(x44991,x44992,f188(f858(x44991,a842))),x44993)) % 168.19/168.05 [4504]~P22(f317(f317(f319(f857(x45041,x45041)),f317(f317(f237(x45041,x45041),x45042),x45043)),f147(x45041,f125(f858(x45041,a849))))) % 168.19/168.05 [3503]E(f317(f189(f850(x35031)),f317(f317(f167(x35031),x35032),x35033)),f317(f317(f223(a849),f317(f189(f850(x35031)),x35033)),x35032)) % 168.19/168.05 [3504]E(f317(f189(f850(x35041)),f317(f317(f132(x35041),x35042),x35043)),f317(f317(f21(a849),f317(f189(f850(x35041)),x35043)),x35042)) % 168.19/168.05 [3527]E(f317(f189(f850(f850(x35271))),f64(x35271,x35272,x35273)),f317(f317(f238(a849),f317(f189(f850(x35271)),x35273)),x35272)) % 168.19/168.05 [3544]E(f317(f317(f89(a849),f317(f317(f89(a849),x35441),x35442)),x35443),f317(f317(f89(a849),x35441),f317(f317(f89(a849),x35442),x35443))) % 168.19/168.05 [3545]E(f317(f317(f89(a1),f317(f317(f89(a1),x35451),x35452)),x35453),f317(f317(f89(a1),x35451),f317(f317(f89(a1),x35452),x35453))) % 168.19/168.05 [3546]E(f317(f317(f21(a849),f317(f317(f21(a849),x35461),x35462)),x35463),f317(f317(f21(a849),x35461),f317(f317(f89(a849),x35462),x35463))) % 168.19/168.05 [3547]E(f317(f317(f90(a849),f317(f317(f90(a849),x35471),x35472)),x35473),f317(f317(f90(a849),x35471),f317(f317(f90(a849),x35472),x35473))) % 168.19/168.05 [3548]E(f317(f317(f90(a1),f317(f317(f90(a1),x35481),x35482)),x35483),f317(f317(f90(a1),x35481),f317(f317(f90(a1),x35482),x35483))) % 168.19/168.05 [3549]E(f317(f317(f238(a1),f317(f317(f238(a1),x35491),x35492)),x35493),f317(f317(f238(a1),x35491),f317(f317(f90(a849),x35492),x35493))) % 168.19/168.05 [3565]E(f156(x35651,f317(f317(f145(f858(x35651,a842)),x35652),x35653)),f169(x35651,x35652,f156(x35651,x35653))) % 168.19/168.05 [3611]E(f317(f317(f21(a849),f317(f317(f21(a849),x36111),x36112)),x36113),f317(f317(f21(a849),f317(f317(f21(a849),x36111),x36113)),x36112)) % 168.19/168.05 [3618]E(f317(f317(f113(f858(x36181,a842)),x36182),f317(f317(f21(f858(x36181,a842)),x36183),x36182)),f188(f858(x36181,a842))) % 168.19/168.05 [3660]E(f49(f858(x36601,a842),f317(f317(f286(f858(x36601,a842)),x36602),x36603)),f317(f317(f122(f858(x36601,a842)),x36602),f49(f858(x36601,a842),x36603))) % 168.19/168.05 [3661]E(f50(f858(x36611,a842),f317(f317(f286(f858(x36611,a842)),x36612),x36613)),f317(f317(f113(f858(x36611,a842)),x36612),f50(f858(x36611,a842),x36613))) % 168.19/168.05 [3663]E(f317(f317(f89(a849),f317(f317(f90(a849),x36631),x36632)),f317(f317(f90(a849),x36633),x36632)),f317(f317(f90(a849),f317(f317(f89(a849),x36631),x36633)),x36632)) % 168.19/168.05 [3664]E(f317(f317(f21(a849),f317(f317(f90(a849),x36641),x36642)),f317(f317(f90(a849),x36643),x36642)),f317(f317(f90(a849),f317(f317(f21(a849),x36641),x36643)),x36642)) % 168.19/168.05 [3665]E(f317(f317(f89(a1),f317(f317(f90(a1),x36651),x36652)),f317(f317(f90(a1),x36653),x36652)),f317(f317(f90(a1),f317(f317(f89(a1),x36651),x36653)),x36652)) % 168.19/168.05 [3667]E(f317(f317(f21(a1),f317(f317(f90(a1),x36671),x36672)),f317(f317(f90(a1),x36673),x36672)),f317(f317(f90(a1),f317(f317(f21(a1),x36671),x36673)),x36672)) % 168.19/168.05 [3668]E(f317(f317(f223(a849),f317(f317(f21(a849),x36681),x36682)),f317(f317(f21(a849),x36683),x36682)),f317(f317(f21(a849),f317(f317(f223(a849),x36681),x36683)),x36682)) % 168.19/168.05 [3690]E(f317(f317(f113(f858(f850(x36901),a842)),f154(x36901,x36902)),f154(x36901,x36903)),f154(x36901,f317(f317(f113(f858(x36901,a842)),x36902),x36903))) % 168.19/168.05 [3692]E(f317(f317(f122(f858(x36921,a842)),x36922),f317(f317(f21(f858(x36921,a842)),x36923),x36922)),f317(f317(f122(f858(x36921,a842)),x36922),x36923)) % 168.19/168.05 [3693]E(f317(f317(f122(f858(x36931,a842)),x36932),f317(f317(f122(f858(x36931,a842)),x36932),x36933)),f317(f317(f122(f858(x36931,a842)),x36932),x36933)) % 168.19/168.05 [3694]E(f317(f317(f113(f858(x36941,a842)),x36942),f317(f317(f113(f858(x36941,a842)),x36942),x36943)),f317(f317(f113(f858(x36941,a842)),x36942),x36943)) % 168.19/168.05 [3706]E(f317(f317(f265(x37061,x37062,x37062),x37063),f284(x37062,f188(f858(f857(x37062,x37062),a842)))),x37063) % 168.19/168.05 [3711]E(f317(f317(f122(f858(x37111,a842)),f317(f317(f286(x37111),x37112),f188(f858(x37111,a842)))),x37113),f317(f317(f286(x37111),x37112),x37113)) % 168.19/168.05 [3729]E(f317(f317(f21(a849),f317(f317(f21(a849),f317(a124,x37291)),x37292)),f317(a124,x37293)),f317(f317(f21(a849),f317(f317(f21(a849),x37291),x37292)),x37293)) % 168.19/168.05 [3760]E(f317(f317(f113(f858(f858(x37601,a842),a842)),f317(f285(x37601),x37602)),f317(f285(x37601),x37603)),f317(f285(x37601),f317(f317(f113(f858(x37601,a842)),x37602),x37603))) % 168.19/168.05 [3764]E(f317(f317(f122(f858(x37641,a842)),f317(f88(f858(x37641,a842)),x37642)),x37643),f317(f88(f858(x37641,a842)),f317(f317(f21(f858(x37641,a842)),x37642),x37643))) % 168.19/168.05 [3777]E(f317(f317(f286(x37771),x37772),f317(f317(f21(f858(x37771,a842)),x37773),f317(f317(f286(x37771),x37772),f188(f858(x37771,a842))))),f317(f317(f286(x37771),x37772),x37773)) % 168.19/168.05 [3788]P22(f317(f317(f225(f858(x37881,a842)),x37882),f317(f317(f122(f858(x37881,a842)),x37883),x37882))) % 168.19/168.05 [3789]P22(f317(f317(f225(f858(x37891,a842)),x37892),f317(f317(f122(f858(x37891,a842)),x37892),x37893))) % 168.19/168.05 [3792]E(f317(f317(f113(f858(x37921,a842)),f317(f88(f858(x37921,a842)),x37922)),f317(f88(f858(x37921,a842)),x37923)),f317(f88(f858(x37921,a842)),f317(f317(f122(f858(x37921,a842)),x37922),x37923))) % 168.19/168.05 [3793]E(f317(f317(f122(f858(x37931,a842)),f317(f88(f858(x37931,a842)),x37932)),f317(f88(f858(x37931,a842)),x37933)),f317(f88(f858(x37931,a842)),f317(f317(f113(f858(x37931,a842)),x37932),x37933))) % 168.19/168.05 [3805]P22(f317(f317(f225(f858(x38051,a842)),f317(f166(x38051),x38052)),f317(f166(x38051),f317(f317(f145(x38051),x38053),x38052)))) % 168.19/168.05 [3815]E(f317(f317(f122(f858(x38151,a842)),f317(f317(f21(f858(x38151,a842)),x38152),x38153)),f317(f317(f113(f858(x38151,a842)),x38152),x38153)),x38152) % 168.19/168.05 [3872]E(f317(f317(f9(x38721,a1),f317(f317(f8(a849,a1,x38721),f112(a1)),x38722)),x38723),f317(f112(a1),f317(f317(f9(x38721,a849),x38722),x38723))) % 168.19/168.05 [3873]E(f317(f317(f6(x38731,a1),f317(f317(f8(a849,a1,x38731),f112(a1)),x38732)),x38733),f317(f112(a1),f317(f317(f6(x38731,a849),x38732),x38733))) % 168.19/168.05 [3923]E(f317(f317(f127(x39231),f170(x39231,x39232,x39233)),f317(f317(f132(x39231),f317(f189(f850(x39231)),f170(x39231,x39232,x39233))),x39233)),x39233) % 168.19/168.05 [3928]E(f317(f88(f858(f857(x39281,x39282),a842)),f317(f317(f245(x39281,x39282),x39283),f317(f16(f858(x39282,a842),x39281),f233(f858(x39282,a842))))),f317(f317(f245(x39281,x39282),f317(f88(f858(x39281,a842)),x39283)),f317(f16(f858(x39282,a842),x39281),f233(f858(x39282,a842))))) % 168.19/168.05 [3929]E(f317(f88(f858(f857(x39291,x39292),a842)),f317(f317(f245(x39291,x39292),f233(f858(x39291,a842))),f317(f16(f858(x39292,a842),x39291),x39293))),f317(f317(f245(x39291,x39292),f233(f858(x39291,a842))),f317(f16(f858(x39292,a842),x39291),f317(f88(f858(x39292,a842)),x39293)))) % 168.19/168.05 [3977]E(f317(f317(f51(f858(x39771,a842),f858(x39771,a842)),x39772),f317(f317(f7(f858(x39771,a842),f858(x39771,a842),f858(x39771,a842)),f113(f858(x39771,a842))),x39773)),f317(f317(f113(f858(x39771,a842)),f49(f858(x39771,a842),x39772)),x39773)) % 168.19/168.05 [3984]E(f317(f136(f850(x39841),f850(x39841),f127(x39841),f125(x39841)),f317(f317(f145(f850(x39841)),x39842),x39843)),f317(f317(f127(x39841),x39842),f317(f136(f850(x39841),f850(x39841),f127(x39841),f125(x39841)),x39843))) % 168.19/168.05 [3998]E(f317(f317(f89(a849),f317(f317(f90(a849),x39981),f317(f48(a849,x39982),x39983))),f317(f48(a849,f317(f317(f90(a849),x39981),f55(a849,x39982,x39983))),x39983)),f317(f48(a849,f317(f317(f90(a849),x39981),x39982)),x39983)) % 168.19/168.05 [3999]E(f317(f317(f89(a1),f317(f317(f90(a1),x39991),f317(f48(a1,x39992),x39993))),f317(f48(a1,f317(f317(f90(a1),x39991),f55(a1,x39992,x39993))),x39993)),f317(f48(a1,f317(f317(f90(a1),x39991),x39992)),x39993)) % 168.19/168.05 [4009]E(f317(f317(f286(f858(x40091,a842)),f317(f262(x40091,x40091,x40092),f317(f317(f286(x40091),x40093),f188(f858(x40091,a842))))),f188(f858(f858(x40091,a842),a842))),f317(f317(f70(x40091),f317(f317(f286(x40091),x40093),f188(f858(x40091,a842)))),x40092)) % 168.19/168.05 [4058]E(f317(f317(f21(f858(x40581,a842)),f317(f166(x40581),x40582)),f317(f317(f286(x40581),x40583),f188(f858(x40581,a842)))),f317(f166(x40581),f317(f130(x40581,f317(f317(f8(a842,a842,x40581),a312),f317(a314,x40583))),x40582))) % 168.19/168.05 [4107]E(f317(f317(f127(x41071),f317(f136(f850(x41071),f850(x41071),f127(x41071),f125(x41071)),x41072)),f317(f136(f850(x41071),f850(x41071),f127(x41071),f125(x41071)),x41073)),f317(f136(f850(x41071),f850(x41071),f127(x41071),f125(x41071)),f317(f317(f127(f850(x41071)),x41072),x41073))) % 168.19/168.05 [4110]E(f317(f317(f89(a849),f317(f317(f89(a849),f317(f48(a849,x41101),x41102)),f317(f48(a849,x41103),x41102))),f317(f48(a849,f317(f317(f89(a849),f55(a849,x41101,x41102)),f55(a849,x41103,x41102))),x41102)),f317(f48(a849,f317(f317(f89(a849),x41101),x41103)),x41102)) % 168.19/168.05 [4111]E(f317(f317(f89(a1),f317(f317(f89(a1),f317(f48(a1,x41111),x41112)),f317(f48(a1,x41113),x41112))),f317(f48(a1,f317(f317(f89(a1),f55(a1,x41111,x41112)),f55(a1,x41113,x41112))),x41112)),f317(f48(a1,f317(f317(f89(a1),x41111),x41113)),x41112)) % 168.19/168.05 [4113]E(f317(f317(f237(f850(x41131),f850(x41131)),f317(f130(x41131,x41132),x41133)),f317(f130(x41131,f317(f82(a842,a842,x41131,a312),x41132)),x41133)),f161(x41131,x41132,x41133)) % 168.19/168.05 [4173]E(f317(f317(f113(f858(f850(x41731),a842)),f317(f317(f7(f850(x41731),f858(f850(x41731),a842),a842),f319(f850(x41731))),f155(x41731,x41732))),f317(f317(f7(f850(x41731),f858(f850(x41731),a842),a842),f319(f850(x41731))),f155(x41731,x41733))),f154(x41731,f317(f317(f113(f858(x41731,a842)),f317(f317(f7(x41731,f858(x41731,a842),a842),f319(x41731)),x41732)),f317(f317(f7(x41731,f858(x41731,a842),a842),f319(x41731)),x41733)))) % 168.19/168.05 [4187]E(f317(f230(x41871),f317(f317(f18(x41871,a842,a842),f317(f317(f8(a842,f858(a842,a842),x41871),a316),f317(f317(f7(x41871,x41871,a842),a314),x41872))),f317(f317(f7(x41871,f858(x41871,a842),a842),f319(x41871)),x41873))),f317(f317(f286(x41871),x41872),x41873)) % 168.19/168.05 [4207]E(f317(f317(f95(f850(f850(x42071)),f850(f850(x42071))),f63(x42071,x42072)),f317(f317(f18(f850(f850(x42071)),f850(f850(x42071)),f850(f850(x42071))),f317(f317(f8(f850(f850(x42071)),f858(f850(f850(x42071)),f850(f850(x42071))),f850(f850(x42071))),f127(f850(x42071))),f317(f148(f850(x42071),f850(x42071)),f317(f145(x42071),x42073)))),f5(f850(f850(x42071))))),f63(x42071,f317(f317(f145(x42071),x42073),x42072))) % 168.19/168.05 [4211]E(f317(f230(x42111),f317(f317(f18(x42111,a842,a842),f317(f317(f8(a842,f858(a842,a842),x42111),a316),f317(f317(f7(x42111,f858(x42111,a842),a842),f319(x42111)),x42112))),f317(f317(f7(x42111,f858(x42111,a842),a842),f319(x42111)),x42113))),f317(f317(f122(f858(x42111,a842)),x42112),x42113)) % 168.19/168.05 [4212]E(f317(f230(x42121),f317(f317(f18(x42121,a842,a842),f317(f317(f8(a842,f858(a842,a842),x42121),a315),f317(f317(f7(x42121,f858(x42121,a842),a842),f319(x42121)),x42122))),f317(f317(f7(x42121,f858(x42121,a842),a842),f319(x42121)),x42123))),f317(f317(f113(f858(x42121,a842)),x42122),x42123)) % 168.19/168.05 [4300]E(f317(f317(f51(x43001,f858(f858(x43001,a842),a842)),x43002),f317(f317(f7(x43001,f858(f858(x43001,a842),a842),f858(f858(x43001,a842),a842)),f317(f317(f8(f858(x43001,a842),f858(f858(f858(x43001,a842),a842),f858(f858(x43001,a842),a842)),x43001),f286(f858(x43001,a842))),f317(f317(f8(f858(x43001,a842),f858(x43001,a842),x43001),f262(x43001,x43001,x43003)),f317(f317(f7(x43001,f858(x43001,a842),f858(x43001,a842)),f286(x43001)),f188(f858(x43001,a842)))))),f188(f858(f858(x43001,a842),a842)))),f317(f317(f70(x43001),x43002),x43003)) % 168.19/168.05 [4304]E(f317(f230(f850(x43041)),f317(f317(f18(f850(x43041),a842,a842),f317(f317(f8(a842,f858(a842,a842),f850(x43041)),a315),f317(f317(f7(f850(x43041),a849,a842),f317(f317(f8(a849,f858(a849,a842),f850(x43041)),a314),f189(f850(x43041)))),x43042))),f317(f317(f7(f850(x43041),f858(x43041,a842),a842),f317(f317(f8(f858(x43041,a842),f858(f858(x43041,a842),a842),f850(x43041)),f225(f858(x43041,a842))),f166(x43041))),f317(f166(x43041),x43043)))),f317(f166(f850(x43041)),f64(x43041,x43042,x43043))) % 168.19/168.05 [3679]E(f55(a849,f317(f317(f89(a849),f317(f317(f90(a849),x36791),x36792)),x36793),x36792),f55(a849,x36793,x36792)) % 168.19/168.05 [3728]E(f133(a849,f317(f278(a849,f317(f317(f89(a849),x37281),x37282)),x37283)),f317(f317(f132(a849),x37282),f133(a849,f317(f278(a849,x37281),x37283)))) % 168.19/168.05 [3776]E(f317(f317(f89(a1),f317(f112(a1),x37761)),f317(f317(f89(a1),f317(f112(a1),x37762)),x37763)),f317(f317(f89(a1),f317(f112(a1),f317(f317(f89(a849),x37761),x37762))),x37763)) % 168.19/168.05 [3784]E(f317(f317(f21(f858(x37841,a842)),f317(f317(f21(f858(x37841,a842)),x37842),x37843)),x37843),f317(f317(f21(f858(x37841,a842)),x37842),x37843)) % 168.19/168.05 [3785]E(f317(f317(f122(f858(x37851,a842)),f317(f317(f21(f858(x37851,a842)),x37852),x37853)),x37853),f317(f317(f122(f858(x37851,a842)),x37852),x37853)) % 168.19/168.05 [3806]E(f317(f317(f265(x38061,x38061,x38062),f284(x38061,f188(f858(f857(x38061,x38061),a842)))),x38063),x38063) % 168.19/168.05 [3812]E(f317(f317(f122(f858(x38121,a842)),f317(f261(x38121),x38122)),f317(f261(x38121),x38123)),f317(f261(x38121),f317(f317(f122(f858(f857(x38121,x38121),a842)),x38122),x38123))) % 168.19/168.05 [3823]E(f252(x38231,f317(f317(f145(f857(a111,x38231)),f317(f317(f237(a111,x38231),f2(a111)),x38232)),x38233)),f252(x38231,x38233)) % 168.19/168.05 [3826]E(f317(f317(f122(f858(x38261,a842)),f49(f858(x38261,a842),x38262)),f49(f858(x38261,a842),x38263)),f49(f858(x38261,a842),f317(f317(f122(f858(f858(x38261,a842),a842)),x38262),x38263))) % 168.19/168.05 [3827]E(f317(f317(f113(f858(x38271,a842)),f50(f858(x38271,a842),x38272)),f50(f858(x38271,a842),x38273)),f50(f858(x38271,a842),f317(f317(f122(f858(f858(x38271,a842),a842)),x38272),x38273))) % 168.19/168.05 [3864]E(f317(f317(f265(x38641,x38641,x38641),f317(f317(f182(f857(x38641,x38641),a842),x38642),x38643)),x38643),f317(f317(f182(f857(x38641,x38641),a842),f317(a124,x38642)),x38643)) % 168.19/168.05 [3913]P22(f317(f317(f225(f858(x39131,a842)),f317(f317(f21(f858(x39131,a842)),x39132),x39133)),x39132)) % 168.19/168.05 [3914]P22(f317(f317(f225(f858(x39141,a842)),f317(f317(f113(f858(x39141,a842)),x39142),x39143)),x39143)) % 168.19/168.05 [3915]P22(f317(f317(f225(f858(x39151,a842)),f317(f317(f113(f858(x39151,a842)),x39152),x39153)),x39152)) % 168.19/168.05 [3940]E(f284(x39401,f317(f317(f122(f858(f857(x39401,x39401),a842)),f284(x39401,x39402)),f284(x39401,x39403))),f284(x39401,f317(f317(f122(f858(f857(x39401,x39401),a842)),x39402),x39403))) % 168.19/168.05 [3943]E(f49(f858(x39431,a842),f317(f317(f286(f858(x39431,a842)),x39432),f317(f317(f286(f858(x39431,a842)),x39433),f188(f858(f858(x39431,a842),a842))))),f317(f317(f122(f858(x39431,a842)),x39432),x39433)) % 168.19/168.05 [3944]E(f50(f858(x39441,a842),f317(f317(f286(f858(x39441,a842)),x39442),f317(f317(f286(f858(x39441,a842)),x39443),f188(f858(f858(x39441,a842),a842))))),f317(f317(f113(f858(x39441,a842)),x39442),x39443)) % 168.19/168.05 [3950]E(f317(f317(f265(x39501,x39501,x39501),f317(f317(f182(f857(x39501,x39501),a842),x39502),x39503)),x39503),f317(f317(f265(x39501,x39501,x39501),x39503),f317(f317(f182(f857(x39501,x39501),a842),x39502),x39503))) % 168.19/168.05 [4022]E(f317(f317(f122(f858(x40221,a842)),f317(f230(x40221),f317(f317(f7(x40221,x40221,a842),a314),x40222))),x40223),f317(f317(f286(x40221),x40222),x40223)) % 168.19/168.05 [4024]E(f317(a116,f317(f317(f9(x40241,a1),f317(f317(f8(a849,a1,x40241),f112(a1)),x40242)),x40243)),f317(f317(f9(x40241,a849),x40242),x40243)) % 168.19/168.05 [4025]E(f317(a116,f317(f317(f6(x40251,a1),f317(f317(f8(a849,a1,x40251),f112(a1)),x40252)),x40253)),f317(f317(f6(x40251,a849),x40252),x40253)) % 168.19/168.05 [4104]E(f317(f150(f850(x41041),x41041,f317(f165(x41041),x41042),f317(f16(f858(f850(x41041),f850(x41041)),x41041),f317(f317(f7(f850(x41041),f850(x41041),f850(x41041)),f127(x41041)),x41042))),x41043),f317(f165(x41041),f317(f317(f127(x41041),x41043),x41042))) % 168.19/168.05 [4133]P22(f317(f317(f225(f858(f858(x41331,a842),a842)),f317(f317(f122(f858(f858(x41331,a842),a842)),f317(f285(x41331),x41332)),f317(f285(x41331),x41333))),f317(f285(x41331),f317(f317(f122(f858(x41331,a842)),x41332),x41333)))) % 168.19/168.05 [4230]E(f317(f230(x42301),f317(f317(f18(x42301,a842,a842),f317(f317(f8(a842,f858(a842,a842),x42301),a315),f317(f317(f7(x42301,f858(x42301,a842),a842),f319(x42301)),x42302))),f317(f317(f8(a842,a842,x42301),a312),f317(f317(f7(x42301,f858(x42301,a842),a842),f319(x42301)),x42303)))),f317(f317(f21(f858(x42301,a842)),x42302),x42303)) % 168.19/168.05 [4251]E(f317(f54(a849),f317(f230(a849),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),f317(f317(f7(a849,a849,a842),f226(a849)),f317(f189(f850(x42511)),x42512)))),f317(f317(f8(x42511,a842,a849),x42513),f317(f159(x42511),x42512))))),f317(f189(f850(x42511)),f317(f130(x42511,x42513),x42512))) % 168.19/168.05 [4253]E(f317(f189(f850(x42531)),f168(x42531,x42532,x42533)),f317(f54(a849),f317(f230(a849),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),f317(f317(f7(a849,a849,a842),f226(a849)),f317(f189(f850(x42531)),x42532)))),f317(f317(f7(a849,f858(a849,a842),a842),f319(a849)),x42533))))) % 168.19/168.05 [4343]E(f317(f317(f113(f858(f857(f850(x43431),f850(x43431)),a842)),f317(f287(f857(f857(x43431,f850(x43431)),f857(x43431,f850(x43431))),f857(f850(x43431),f850(x43431)),f248(f857(x43431,f850(x43431)),f850(x43431),f857(x43431,f850(x43431)),f850(x43431),f317(f247(x43431,f850(x43431),f850(x43431)),f145(x43431)),f317(f247(x43431,f850(x43431),f850(x43431)),f145(x43431)))),f310(x43431,f850(x43431),x43432,f317(f137(x43431,x43432),x43433)))),f317(f230(f857(f850(x43431),f850(x43431))),f317(f247(f850(x43431),f850(x43431),a842),f317(f317(f7(f850(x43431),f858(f850(x43431),a842),f858(f850(x43431),a842)),f317(f317(f8(f858(a842,a842),f858(f858(f850(x43431),a842),f858(f850(x43431),a842)),f850(x43431)),f8(a842,a842,f850(x43431))),f317(f317(f8(a842,f858(a842,a842),f850(x43431)),a315),f317(f317(f7(f850(x43431),a849,a842),f317(f317(f8(a849,f858(a849,a842),f850(x43431)),a314),f189(f850(x43431)))),f317(a124,x43433))))),f317(f317(f7(f850(x43431),a849,a842),f317(f317(f8(a849,f858(a849,a842),f850(x43431)),a314),f189(f850(x43431)))),f317(a124,x43433)))))),f317(f137(x43431,x43432),f317(a124,x43433))) % 168.19/168.05 [3828]E(f55(a849,f317(a124,f317(f317(f89(a849),f317(f317(f90(a849),x38281),x38282)),x38283)),x38282),f55(a849,f317(a124,x38283),x38282)) % 168.19/168.05 [4094]E(f317(f230(x40941),f317(f317(f18(x40941,a842,a842),f317(f317(f8(a842,f858(a842,a842),x40941),a315),x40942)),x40943)),f317(f317(f113(f858(x40941,a842)),f317(f230(x40941),x40942)),f317(f230(x40941),x40943))) % 168.19/168.05 [4095]E(f317(f230(x40951),f317(f317(f18(x40951,a842,a842),f317(f317(f8(a842,f858(a842,a842),x40951),a316),x40952)),x40953)),f317(f317(f122(f858(x40951,a842)),f317(f230(x40951),x40952)),f317(f230(x40951),x40953))) % 168.19/168.05 [4097]E(f317(f317(f127(x40971),f317(f317(f132(x40971),f55(a849,x40972,f317(f189(f850(x40971)),x40973))),x40973)),f317(f317(f167(x40971),f55(a849,x40972,f317(f189(f850(x40971)),x40973))),x40973)),f317(f317(f317(f182(f850(x40971),f850(x40971)),x40972),f162(x40971)),x40973)) % 168.19/168.05 [4102]E(f317(f230(x41021),f317(f317(f18(x41021,a842,a842),f317(f317(f8(a842,f858(a842,a842),x41021),a320),x41022)),x41023)),f317(f317(f122(f858(x41021,a842)),f317(f88(f858(x41021,a842)),f317(f230(x41021),x41022))),f317(f230(x41021),x41023))) % 168.19/168.05 [4116]E(f317(f317(f89(a849),f317(f189(f850(x41161)),f317(f130(x41161,x41162),x41163))),f317(f189(f850(x41161)),f317(f130(x41161,f317(f317(f8(a842,a842,x41161),a312),x41162)),x41163))),f317(f189(f850(x41161)),x41163)) % 168.19/168.05 [4140]P22(f317(f317(f225(f858(x41401,a842)),f317(f317(f122(f858(x41401,a842)),f50(f858(x41401,a842),x41402)),f50(f858(x41401,a842),x41403))),f50(f858(x41401,a842),f317(f317(f113(f858(f858(x41401,a842),a842)),x41402),x41403)))) % 168.19/168.05 [4156]E(f317(f166(x41561),f317(f130(x41561,f317(f317(f8(a842,a842,x41561),a312),f317(f317(f7(x41561,x41561,a842),a314),x41562))),x41563)),f317(f317(f21(f858(x41561,a842)),f317(f166(x41561),x41563)),f317(f317(f286(x41561),x41562),f188(f858(x41561,a842))))) % 168.19/168.05 [4165]P22(f317(f317(f225(f858(f857(x41651,x41651),a842)),f317(f317(f122(f858(f857(x41651,x41651),a842)),f284(x41651,x41652)),f284(x41651,x41653))),f284(x41651,f317(f317(f122(f858(f857(x41651,x41651),a842)),x41652),x41653)))) % 168.19/168.05 [4192]E(f317(f317(f90(a849),f317(a124,f317(a124,f2(a849)))),f317(f317(f6(a849,a849),f317(f317(f8(a849,a849,a849),f317(f89(a849),x41921)),f317(f317(f7(a849,a849,a849),f90(a849)),x41922))),f317(f231(a849),x41923))),f317(f317(f90(a849),x41923),f317(f317(f89(a849),x41921),f317(f317(f89(a849),x41921),f317(f317(f90(a849),f317(f317(f21(a849),x41923),f87(a849))),x41922))))) % 168.19/168.05 [4202]E(f317(f230(x42021),f317(f317(f18(x42021,a842,a842),f317(f317(f8(a842,f858(a842,a842),x42021),a315),f317(f317(f7(x42021,f858(x42021,a842),a842),f319(x42021)),f317(f166(x42021),x42022)))),x42023)),f317(f166(x42021),f317(f130(x42021,x42023),x42022))) % 168.19/168.05 [4342]E(f317(f230(x43421),f317(f317(f8(f858(a849,a842),a842,x43421),f96(a849)),f317(f317(f7(x43421,f858(a849,a842),f858(a849,a842)),f317(f317(f8(f858(a849,f858(a842,a842)),f858(f858(a849,a842),f858(a849,a842)),x43421),f18(a849,a842,a842)),f317(f317(f8(f858(a849,a842),f858(a849,f858(a842,a842)),x43421),f317(f8(a842,f858(a842,a842),a849),a315)),f317(f317(f7(x43421,f858(a849,x43421),f858(a849,a842)),f317(f317(f8(f858(x43421,a842),f858(f858(a849,x43421),f858(a849,a842)),x43421),f8(x43421,a842,a849)),a314)),f317(f159(x43421),x43422))))),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),f317(f317(f7(a849,a849,a842),f226(a849)),f317(f189(f850(x43421)),x43422)))),f317(f317(f7(a849,f858(a849,a842),a842),f319(a849)),x43423))))),f317(f166(x43421),f168(x43421,x43422,x43423))) % 168.19/168.05 [4241]E(f317(f230(x42411),f317(f317(f18(x42411,a842,a842),f317(f317(f8(a842,f858(a842,a842),x42411),a320),f317(f317(f8(a842,a842,x42411),a312),f317(f317(f7(x42411,x42411,a842),a314),x42412)))),x42413)),f317(f317(f286(x42411),x42412),f317(f230(x42411),x42413))) % 168.19/168.05 [4272]E(f317(f317(f148(f857(x42721,a849),x42721),f244(x42721,a849)),f317(f130(f857(x42721,a849),f317(f317(f7(f857(x42721,a849),f858(a849,a842),a842),f317(f317(f8(a849,f858(f858(a849,a842),a842),f857(x42721,a849)),f319(a849)),f246(x42721,a849))),x42722)),f317(f317(f175(x42721,a849),x42723),f133(a849,f317(f278(a849,f2(a849)),f317(f189(f850(x42721)),x42723)))))),f168(x42721,x42723,x42722)) % 168.19/168.05 [4301]E(f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f6(a849,a1),f317(f317(f8(a1,a1,a849),f317(f89(a1),x43011)),f317(f317(f7(a849,a1,a1),f317(f317(f8(a1,f858(a1,a1),a849),f90(a1)),f112(a1))),x43012))),f317(f231(a849),x43013))),f317(f317(f90(a1),f317(f112(a1),x43013)),f317(f317(f89(a1),x43011),f317(f317(f89(a1),x43011),f317(f317(f90(a1),f317(f112(a1),f317(f317(f21(a849),x43013),f87(a849)))),x43012))))) % 168.19/168.05 [4336]E(f317(f230(f857(x43361,x43362)),f317(f247(x43361,x43362,a842),f317(f317(f7(x43361,f858(f857(x43362,x43361),a842),f858(x43362,a842)),f317(f317(f8(f858(x43362,f858(f858(f857(x43362,x43361),a842),a842)),f858(f858(f857(x43362,x43361),a842),f858(x43362,a842)),x43361),f7(x43362,f858(f857(x43362,x43361),a842),a842)),f317(f317(f8(f858(x43362,f857(x43362,x43361)),f858(x43362,f858(f858(f857(x43362,x43361),a842),a842)),x43361),f317(f8(f857(x43362,x43361),f858(f858(f857(x43362,x43361),a842),a842),x43362),f319(f857(x43362,x43361)))),f317(f7(x43362,x43361,f857(x43362,x43361)),f237(x43362,x43361))))),x43363))),f317(f263(x43362,x43361),x43363)) % 168.19/168.05 [4370]E(f317(f230(f850(x43701)),f317(f317(f8(f858(x43701,a842),a842,f850(x43701)),f96(x43701)),f317(f317(f8(f858(x43701,f858(f850(x43701),a842)),f858(x43701,a842),f850(x43701)),f317(f8(f858(f850(x43701),a842),a842,x43701),f96(f850(x43701)))),f317(f317(f7(f850(x43701),f858(x43701,f858(f850(x43701),a842)),f858(x43701,f858(f850(x43701),a842))),f317(f317(f8(f858(x43701,f858(f858(f850(x43701),a842),f858(f850(x43701),a842))),f858(f858(x43701,f858(f850(x43701),a842)),f858(x43701,f858(f850(x43701),a842))),f850(x43701)),f18(x43701,f858(f850(x43701),a842),f858(f850(x43701),a842))),f317(f317(f8(f858(x43701,f858(f850(x43701),f858(a842,a842))),f858(x43701,f858(f858(f850(x43701),a842),f858(f850(x43701),a842))),f850(x43701)),f317(f8(f858(f850(x43701),f858(a842,a842)),f858(f858(f850(x43701),a842),f858(f850(x43701),a842)),x43701),f18(f850(x43701),a842,a842))),f317(f317(f8(f858(x43701,f858(f850(x43701),a842)),f858(x43701,f858(f850(x43701),f858(a842,a842))),f850(x43701)),f317(f8(f858(f850(x43701),a842),f858(f850(x43701),f858(a842,a842)),x43701),f317(f8(a842,f858(a842,a842),f850(x43701)),a315))),f317(f317(f7(f850(x43701),f858(x43701,f858(f850(x43701),f850(x43701))),f858(x43701,f858(f850(x43701),a842))),f317(f317(f8(f858(f858(f850(x43701),f850(x43701)),f858(f850(x43701),a842)),f858(f858(x43701,f858(f850(x43701),f850(x43701))),f858(x43701,f858(f850(x43701),a842))),f850(x43701)),f8(f858(f850(x43701),f850(x43701)),f858(f850(x43701),a842),x43701)),f317(f317(f8(f858(f850(x43701),a842),f858(f858(f850(x43701),f850(x43701)),f858(f850(x43701),a842)),f850(x43701)),f8(f850(x43701),a842,f850(x43701))),a314))),f145(x43701)))))),f317(f317(f7(x43701,f858(f850(x43701),a842),f858(f850(x43701),a842)),f317(f317(f8(f858(a842,a842),f858(f858(f850(x43701),a842),f858(f850(x43701),a842)),x43701),f8(a842,a842,f850(x43701))),f317(f317(f8(a842,f858(a842,a842),x43701),a315),f317(f317(f7(x43701,f858(x43701,a842),a842),f319(x43701)),x43702)))),f317(f317(f7(f850(x43701),f858(f850(x43701),a842),a842),f319(f850(x43701))),x43703)))))),f169(x43701,x43702,x43703)) % 168.19/168.05 [4356]E(f317(f317(f95(a1,f857(a1,a1)),f317(f317(f21(a1),x43561),x43562)),f317(f317(f7(a1,f857(a1,a1),f857(a1,a1)),f317(f317(f18(a1,f857(a1,a1),f858(f857(a1,a1),f857(a1,a1))),f317(f317(f8(a842,f858(f857(a1,a1),f858(f857(a1,a1),f857(a1,a1))),a1),f108(f857(a1,a1))),f317(f225(a1),f2(a1)))),f317(f237(a1,a1),f317(f317(f89(a1),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x43563)),f87(a1))))),f317(f317(f237(a1,a1),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x43563)),x43561))),f317(f53(x43562),f317(f317(f237(a1,a1),x43563),x43561))) % 168.19/168.05 [3758]P32(x37581,x37582,x37583,f178(x37581,x37582,x37584,x37583)) % 168.19/168.05 [4409]~E(f30(x44091,x44092),f36(x44093,x44094)) % 168.19/168.05 [4412]~E(f35(x44121,x44122),f36(x44123,x44124)) % 168.19/168.05 [4413]~E(f35(x44131,x44132),f30(x44133,x44134)) % 168.19/168.05 [4432]~E(f317(a29,x44321),f31(x44322,x44323,x44324)) % 168.19/168.05 [4433]~E(f317(a29,x44331),f33(x44332,x44333,x44334)) % 168.19/168.05 [4434]~E(f317(a29,x44341),f32(x44342,x44343,x44344)) % 168.19/168.05 [4435]~E(f31(x44351,x44352,x44353),f317(a29,x44354)) % 168.19/168.05 [4436]~E(f33(x44361,x44362,x44363),f317(a29,x44364)) % 168.19/168.05 [4437]~E(f32(x44371,x44372,x44373),f317(a29,x44374)) % 168.19/168.05 [3380]E(f317(f317(f317(f81(x33801,x33802),x33803),x33804),f317(x33803,x33804)),x33803) % 168.19/168.05 [3438]E(f317(f317(f239(x34381,x34382,x34383),x34384),f2(a849)),x34382) % 168.19/168.05 [3452]E(f43(x34521,x34522,x34523,f40(x34524)),f317(x34523,x34524)) % 168.19/168.05 [3453]E(f43(x34531,x34532,x34533,f41(x34534)),f317(x34532,x34534)) % 168.19/168.05 [3454]E(f44(x34541,x34542,x34543,f40(x34544)),f317(x34543,x34544)) % 168.19/168.05 [3455]E(f44(x34551,x34552,x34553,f41(x34554)),f317(x34552,x34554)) % 168.19/168.05 [3482]E(f184(x34821,x34822,x34823,f317(a124,x34824)),f317(x34823,x34824)) % 168.19/168.05 [3520]E(f164(x35201,x35202,f164(x35201,x35203,x35204)),f164(x35201,x35203,f164(x35201,x35202,x35204))) % 168.19/168.05 [3650]E(f317(f220(x36501,x36502,x36503,x36504),f191(x36502)),x36503) % 168.19/168.05 [3652]E(f317(f150(x36521,x36522,x36523,x36524),f125(x36522)),x36523) % 168.19/168.05 [3653]E(f317(f136(x36531,x36532,x36533,x36534),f125(x36532)),x36534) % 168.19/168.05 [3686]E(f317(f189(f854(x36861,x36862)),f208(x36861,x36862,x36863,x36864)),f2(a849)) % 168.19/168.05 [3759]P32(x37591,x37592,f317(f317(f317(f81(x37591,f853(x37592)),x37593),x37594),f191(x37592)),x37593) % 168.19/168.05 [3773]E(f317(f220(f853(x37731),x37732,f191(x37731),f317(f16(f853(x37731),x37732),f191(x37731))),f317(x37733,x37734)),f191(x37731)) % 168.19/168.05 [3816]E(f317(f317(f122(f858(x38161,a842)),f177(x38161,x38162,x38163)),f177(x38161,x38162,x38164)),f177(x38161,x38162,f178(x38161,x38162,x38164,x38163))) % 168.19/168.05 [3848]E(f317(f317(f249(x38481,x38482,x38483,f857(x38482,x38483)),x38484),f237(x38482,x38483)),x38484) % 168.19/168.05 [3857]E(f221(x38571,x38572,x38573,x38574,f191(x38572)),x38573) % 168.19/168.05 [3858]E(f180(x38581,x38582,x38583,x38584,f125(x38582)),x38583) % 168.19/168.05 [3859]E(f180(x38591,x38592,x38593,f125(x38591),x38594),x38593) % 168.19/168.05 [4147]P41(x41471,x41472,x41473,x41474,f188(f858(x41471,a842)),x41474) % 168.19/168.05 [4461]~E(f317(f297(x44611,x44612),x44613),f317(f288(x44612,x44611),x44614)) % 168.19/168.05 [3176]E(f317(f317(f16(x31761,x31762),x31763),x31764),x31763) % 168.19/168.05 [3297]E(f317(f317(f192(x32971,x32972),x32973),f317(f217(x32971),x32974)),f317(f217(x32972),f317(x32973,x32974))) % 168.19/168.05 [3473]E(f164(x34731,x34732,f317(f130(x34731,x34733),x34734)),f317(f130(x34731,x34733),f164(x34731,x34732,x34734))) % 168.19/168.05 [3505]E(f317(f317(f74(x35051,x35052,x35053),x35054),f188(f858(x35051,a842))),x35054) % 168.19/168.05 [3526]E(f317(f317(f159(x35261),f317(f317(f145(x35261),x35262),x35263)),f317(a124,x35264)),f317(f317(f159(x35261),x35263),x35264)) % 168.19/168.05 [3566]P30(x35661,f2(a849),f317(f317(f317(f100(x35661),x35662),f317(a29,x35663)),x35664)) % 168.19/168.05 [3593]E(f317(f317(x35931,x35932),f317(f183(x35933,x35934,x35931),x35932)),f317(f183(x35933,x35934,x35931),f317(a124,x35932))) % 168.19/168.05 [3684]E(f317(f317(f153(x36841,f317(f317(f145(x36841),x36842),x36843)),f2(a849)),x36844),f317(f317(f145(x36841),x36844),x36843)) % 168.19/168.05 [3696]E(f317(f317(f51(f858(x36961,a842),f858(x36962,a842)),x36963),f287(x36961,x36962,x36964)),f317(f287(x36961,x36962,x36964),f49(f858(x36961,a842),x36963))) % 168.19/168.05 [3697]E(f317(f317(f51(f858(x36971,a842),f858(x36972,a842)),x36973),f289(x36972,x36971,x36974)),f317(f289(x36972,x36971,x36974),f49(f858(x36971,a842),x36973))) % 168.19/168.05 [3800]E(f177(x38001,x38002,f181(x38001,x38002,x38003,x38004)),f317(f317(f113(f858(x38001,a842)),f177(x38001,x38002,x38003)),x38004)) % 168.19/168.05 [3822]E(f317(f136(x38221,x38222,f317(f7(x38222,x38221,x38221),x38223),x38224),f317(f163(x38222),f125(x38222))),x38224) % 168.19/168.05 [3862]P22(f317(f317(f317(f317(a197,f30(x38621,x38622)),x38623),x38624),f317(f317(f317(a200,x38623),x38621),f317(x38622,x38623)))) % 168.19/168.05 [3871]E(f85(x38711,x38712,x38713,x38714,f188(f858(x38711,a842))),x38713) % 168.19/168.05 [3916]E(f317(f317(f317(f317(f81(x39161,f853(x39162)),f317(f16(f853(x39162),x39161),f191(x39162))),x39163),f191(x39162)),x39164),f191(x39162)) % 168.19/168.05 [4068]E(f303(x40681,x40682,x40683,f317(f317(f8(f856(x40681,x40683),x40682,x40681),x40684),f288(x40681,x40683)),f317(f317(f8(f856(x40681,x40683),x40682,x40683),x40684),f297(x40683,x40681))),x40684) % 168.19/168.05 [4077]E(f317(f247(x40771,x40772,x40773),f317(f317(f8(f858(x40772,f857(x40771,x40772)),f858(x40772,x40773),x40771),f317(f8(f857(x40771,x40772),x40773,x40772),x40774)),f237(x40771,x40772))),x40774) % 168.19/168.05 [3305]E(f317(f317(f196(x33051,x33052),f317(f217(x33051),x33053)),x33054),f317(x33054,x33053)) % 168.19/168.05 [3378]E(f317(f246(x33781,x33782),f317(f317(f237(x33781,x33782),x33783),x33784)),x33784) % 168.19/168.05 [3379]E(f317(f244(x33791,x33792),f317(f317(f237(x33791,x33792),x33793),x33794)),x33793) % 168.19/168.05 [3412]E(f317(f189(f850(x34121)),f317(f317(f148(x34122,x34121),x34123),x34124)),f317(f189(f850(x34122)),x34124)) % 168.19/168.05 [3413]E(f317(f189(f850(x34131)),f317(f317(f153(x34131,x34132),x34133),x34134)),f317(f189(f850(x34131)),x34132)) % 168.19/168.05 [3433]E(f317(f317(f132(x34331),f317(a124,x34332)),f317(f317(f145(x34331),x34333),x34334)),f317(f317(f132(x34331),x34332),x34334)) % 168.19/168.05 [3508]E(f317(f317(f286(x35081),x35082),f317(f317(f286(x35081),x35083),x35084)),f317(f317(f286(x35081),x35083),f317(f317(f286(x35081),x35082),x35084))) % 168.19/168.05 [3510]E(f317(f317(f148(x35101,x35102),x35103),f126(x35101,x35104)),f126(x35102,f317(f317(f148(x35101,x35102),x35103),x35104))) % 168.19/168.05 [3524]E(f317(f163(x35241),f317(f317(f148(x35242,x35241),x35243),x35244)),f317(f317(f148(x35242,x35241),x35243),f317(f163(x35242),x35244))) % 168.19/168.05 [3525]E(f317(f317(f148(x35251,x35252),x35253),f317(f165(x35251),x35254)),f317(f165(x35252),f317(f317(f148(x35251,x35252),x35253),x35254))) % 168.19/168.05 [3538]E(f317(f317(f167(x35381),f317(a124,x35382)),f317(f317(f145(x35381),x35383),x35384)),f317(f317(f145(x35381),x35383),f317(f317(f167(x35381),x35382),x35384))) % 168.19/168.05 [3542]E(f317(f166(x35421),f317(f317(f148(x35422,x35421),x35423),x35424)),f317(f287(x35422,x35421,x35423),f317(f166(x35422),x35424))) % 168.19/168.05 [3592]E(f17(x35921,x35922,x35923,f317(a3,f317(a124,f317(a19,x35924)))),f317(x35923,x35924)) % 168.19/168.05 [3594]E(f317(f317(f127(x35941),f317(f130(x35941,x35942),x35943)),f317(f130(x35941,x35942),x35944)),f317(f130(x35941,x35942),f317(f317(f127(x35941),x35943),x35944))) % 168.19/168.05 [3607]E(f146(x36071,f317(f317(f148(x36072,x36071),x36073),f146(x36072,x36074))),f146(x36071,f317(f317(f148(x36072,x36071),x36073),x36074))) % 168.19/168.05 [3621]E(f317(f263(x36211,x36211),f317(f317(f264(x36212,x36211),x36213),x36214)),f317(f317(f264(x36212,x36211),f317(f263(x36212,x36212),x36213)),x36214)) % 168.19/168.05 [3632]E(f317(f317(f265(x36321,x36322,x36323),x36324),f188(f858(f857(x36322,x36323),a842))),f188(f858(f857(x36321,x36323),a842))) % 168.19/168.05 [3633]E(f317(f317(f167(x36331),f317(f317(f21(a849),x36332),x36333)),f317(f317(f132(x36331),x36333),x36334)),f317(f317(f132(x36331),x36333),f317(f317(f167(x36331),x36332),x36334))) % 168.19/168.05 [3676]E(f49(f858(x36761,a842),f317(f287(x36762,f858(x36761,a842),x36763),x36764)),f317(f317(f51(x36762,f858(x36761,a842)),x36764),x36763)) % 168.19/168.05 [3677]E(f50(f858(x36771,a842),f317(f287(x36772,f858(x36771,a842),x36773),x36774)),f317(f317(f52(x36772,f858(x36771,a842)),x36774),x36773)) % 168.19/168.05 [3678]E(f317(f189(f850(f857(x36781,x36782))),f317(f317(f175(x36781,x36782),x36783),x36784)),f317(f317(f223(a849),f317(f189(f850(x36781)),x36783)),f317(f189(f850(x36782)),x36784))) % 168.19/168.05 [3680]E(f317(f289(x36801,x36802,x36803),f317(f88(f858(x36802,a842)),x36804)),f317(f88(f858(x36801,a842)),f317(f289(x36801,x36802,x36803),x36804))) % 168.19/168.05 [3713]E(f317(f181(x37131,x37132,x37133,f188(f858(x37131,a842))),x37134),f191(x37132)) % 168.19/168.05 [3734]E(f317(f289(x37341,x37342,x37343),f317(f230(x37342),x37344)),f317(f230(x37341),f317(f317(f8(x37342,a842,x37341),x37344),x37343))) % 168.19/168.05 [3751]E(f317(f317(f159(x37511),f317(f317(f127(x37511),x37512),f317(f317(f145(x37511),x37513),x37514))),f317(f189(f850(x37511)),x37512)),x37513) % 168.19/168.05 [3757]E(f317(f181(x37571,x37572,f317(f16(f853(x37572),x37571),f191(x37572)),x37573),x37574),f191(x37572)) % 168.19/168.05 [3781]E(f317(f287(x37811,x37812,x37813),f317(f289(x37811,x37812,x37813),x37814)),f317(f317(f113(f858(x37812,a842)),x37814),f317(f287(x37811,x37812,x37813),f233(f858(x37811,a842))))) % 168.19/168.05 [3799]P22(f317(f317(f319(x37991),f317(x37992,x37993)),f317(f287(x37994,x37991,x37992),f233(f858(x37994,a842))))) % 168.19/168.05 [3811]E(f317(f317(f245(x38111,x38112),f317(f166(x38111),x38113)),f317(f16(f858(x38112,a842),x38111),f317(f166(x38112),x38114))),f317(f166(f857(x38111,x38112)),f69(x38111,x38112,x38113,x38114))) % 168.19/168.05 [3825]E(f149(x38251,x38252,f317(f317(f145(x38251),x38253),x38254)),f317(f317(f89(a849),f317(f317(f89(a849),f317(x38252,x38253)),f149(x38251,x38252,x38254))),f317(a124,f2(a849)))) % 168.19/168.05 [3839]E(f184(f850(x38391),f317(f317(f145(x38391),x38392),x38393),f317(f317(f7(a849,f850(x38391),f850(x38391)),f132(x38391)),x38393),x38394),f317(f317(f132(x38391),x38394),f317(f317(f145(x38391),x38392),x38393))) % 168.19/168.05 [3840]P19(x38401,f857(x38402,x38401),f321(x38403,x38404,x38402,x38401),f317(f317(f51(x38402,f858(x38401,a842)),x38404),x38403)) % 168.19/168.05 [3849]E(f317(f317(f21(f858(x38491,a842)),f317(f317(f21(f858(x38491,a842)),x38492),x38493)),f317(f317(f286(x38491),x38494),f188(f858(x38491,a842)))),f317(f317(f21(f858(x38491,a842)),x38492),f317(f317(f286(x38491),x38494),x38493))) % 168.19/168.05 [3860]E(f317(f317(f182(f858(x38601,x38602),f858(x38601,x38602)),x38603),f82(x38602,x38602,x38601,x38604)),f82(x38602,x38602,x38601,f317(f317(f182(x38602,x38602),x38603),x38604))) % 168.19/168.05 [3939]E(f317(f317(f317(f182(f850(x39391),f850(x39391)),x39392),f162(x39391)),f317(f317(f317(f182(f850(x39391),f850(x39391)),x39393),f162(x39391)),x39394)),f317(f317(f317(f182(f850(x39391),f850(x39391)),f317(f317(f89(a849),x39392),x39393)),f162(x39391)),x39394)) % 168.19/168.05 [3986]E(f317(f317(f122(f858(f856(x39861,x39862),a842)),f317(f287(x39861,f856(x39861,x39862),f288(x39861,x39862)),x39863)),f317(f287(x39862,f856(x39861,x39862),f297(x39862,x39861)),x39864)),f298(x39861,x39862,x39863,x39864)) % 168.19/168.05 [4027]P22(f317(f317(f225(f858(x40271,a842)),f317(f166(x40271),f317(f317(f153(x40271,x40272),x40273),x40274))),f317(f317(f286(x40271),x40274),f317(f166(x40271),x40272)))) % 168.19/168.05 [4066]E(f317(f317(f51(f858(x40661,a842),f858(f857(x40661,x40662),a842)),x40663),f317(f317(f7(f858(x40661,a842),f858(x40661,f858(x40662,a842)),f858(f857(x40661,x40662),a842)),f245(x40661,x40662)),x40664)),f317(f317(f245(x40661,x40662),f49(f858(x40661,a842),x40663)),x40664)) % 168.19/168.05 [4123]P22(f317(f76(x41231,x41232,x41233,x41234,f188(f858(x41231,a842))),x41234)) % 168.19/168.05 [4168]E(f317(f317(f51(x41681,f858(x41682,a842)),x41683),f317(f317(f7(x41681,f858(x41682,a842),f858(x41682,a842)),f317(f317(f8(x41682,f858(f858(x41682,a842),f858(x41682,a842)),x41681),f286(x41682)),x41684)),f188(f858(x41682,a842)))),f317(f287(x41681,x41682,x41684),x41683)) % 168.19/168.05 [4176]P22(f317(f317(f225(f858(x41761,a842)),f317(f234(x41762,x41761),f317(f317(f113(f858(f857(x41762,x41761),a842)),x41763),x41764))),f317(f317(f113(f858(x41761,a842)),f317(f234(x41762,x41761),x41763)),f317(f234(x41762,x41761),x41764)))) % 168.19/168.05 [4177]P22(f317(f317(f225(f858(x41771,a842)),f317(f236(x41771,x41772),f317(f317(f113(f858(f857(x41771,x41772),a842)),x41773),x41774))),f317(f317(f113(f858(x41771,a842)),f317(f236(x41771,x41772),x41773)),f317(f236(x41771,x41772),x41774)))) % 168.19/168.05 [4239]P22(f317(f317(f225(f858(f857(x42391,x42392),a842)),f317(f287(x42392,f857(x42391,x42392),f321(x42393,x42394,x42391,x42392)),f317(f317(f51(x42391,f858(x42392,a842)),x42394),x42393))),f317(f317(f245(x42391,x42392),x42394),x42393))) % 168.19/168.05 [4278]E(f94(f857(x42781,x42782),f317(f247(x42781,x42782,a842),f317(f317(f7(x42781,f858(x42782,a842),f858(x42782,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x42782,a842),f858(x42782,a842)),x42781),f8(a842,a842,x42782)),f317(f317(f8(a842,f858(a842,a842),x42781),a315),f317(a314,x42783)))),f317(a314,x42784)))),f317(f317(f237(x42781,x42782),x42783),x42784)) % 168.19/168.05 [4279]E(f99(f857(x42791,x42792),f317(f247(x42791,x42792,a842),f317(f317(f7(x42791,f858(x42792,a842),f858(x42792,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x42792,a842),f858(x42792,a842)),x42791),f8(a842,a842,x42792)),f317(f317(f8(a842,f858(a842,a842),x42791),a315),f317(a314,x42793)))),f317(a314,x42794)))),f317(f317(f237(x42791,x42792),x42793),x42794)) % 168.19/168.05 [4346]E(f317(f317(f247(f850(x43461),f850(x43461),f857(f850(x43461),f850(x43461))),f317(f317(f18(f850(x43461),f858(f850(x43461),f857(f850(x43461),f850(x43461))),f858(f850(x43461),f857(f850(x43461),f850(x43461)))),f317(f317(f8(f858(f850(x43461),f858(f857(f850(x43461),f850(x43461)),f857(f850(x43461),f850(x43461)))),f858(f858(f850(x43461),f857(f850(x43461),f850(x43461))),f858(f850(x43461),f857(f850(x43461),f850(x43461)))),f850(x43461)),f18(f850(x43461),f857(f850(x43461),f850(x43461)),f857(f850(x43461),f850(x43461)))),f317(f317(f8(f858(f850(x43461),f857(f850(x43461),f850(x43461))),f858(f850(x43461),f858(f857(f850(x43461),f850(x43461)),f857(f850(x43461),f850(x43461)))),f850(x43461)),f317(f8(f857(f850(x43461),f850(x43461)),f858(f857(f850(x43461),f850(x43461)),f857(f850(x43461),f850(x43461))),f850(x43461)),f317(f108(f857(f850(x43461),f850(x43461))),f317(x43462,x43463)))),f317(f317(f8(f850(x43461),f858(f850(x43461),f857(f850(x43461),f850(x43461))),f850(x43461)),f237(f850(x43461),f850(x43461))),f317(f145(x43461),x43463))))),f317(f317(f7(f850(x43461),f858(f850(x43461),f850(x43461)),f858(f850(x43461),f857(f850(x43461),f850(x43461)))),f317(f317(f8(f858(f850(x43461),f857(f850(x43461),f850(x43461))),f858(f858(f850(x43461),f850(x43461)),f858(f850(x43461),f857(f850(x43461),f850(x43461)))),f850(x43461)),f8(f850(x43461),f857(f850(x43461),f850(x43461)),f850(x43461))),f237(f850(x43461),f850(x43461)))),f317(f145(x43461),x43463)))),f161(x43461,x43462,x43464)),f161(x43461,x43462,f317(f317(f145(x43461),x43463),x43464))) % 168.19/168.05 [4352]E(f317(f136(f858(x43521,f853(x43522)),f857(x43521,x43522),f317(f7(f857(x43521,x43522),f858(x43521,f853(x43522)),f858(x43521,f853(x43522))),f317(f247(x43521,x43522,f858(f858(x43521,f853(x43522)),f858(x43521,f853(x43522)))),f317(f317(f7(x43521,f858(x43522,f853(x43522)),f858(x43522,f858(f858(x43521,f853(x43522)),f858(x43521,f853(x43522))))),f317(f317(f8(f858(f853(x43522),f858(f858(x43521,f853(x43522)),f858(x43521,f853(x43522)))),f858(f858(x43522,f853(x43522)),f858(x43522,f858(f858(x43521,f853(x43522)),f858(x43521,f853(x43522))))),x43521),f8(f853(x43522),f858(f858(x43521,f853(x43522)),f858(x43521,f853(x43522))),x43522)),f317(f317(f8(f858(f858(x43521,f853(x43522)),f858(f853(x43522),f858(x43521,f853(x43522)))),f858(f853(x43522),f858(f858(x43521,f853(x43522)),f858(x43521,f853(x43522)))),x43521),f7(f858(x43521,f853(x43522)),f853(x43522),f858(x43521,f853(x43522)))),f317(f7(f858(x43521,f853(x43522)),x43521,f858(f853(x43522),f858(x43521,f853(x43522)))),f81(x43521,f853(x43522)))))),f217(x43522)))),x43523),f317(f163(f857(x43521,x43522)),x43524)),f178(x43521,x43522,x43523,f317(f171(x43521,x43522),x43524))) % 168.19/168.05 [3450]E(f317(f189(f848(x34501)),f317(f317(f317(f100(x34501),x34502),x34503),x34504)),f2(a849)) % 168.19/168.05 [3570]E(f317(f317(f167(x35701),x35702),f317(f317(f167(x35701),x35703),x35704)),f317(f317(f167(x35701),f317(f317(f223(a849),x35702),x35703)),x35704)) % 168.19/168.05 [3571]E(f317(f317(f132(x35711),x35712),f317(f317(f132(x35711),x35713),x35714)),f317(f317(f132(x35711),f317(f317(f89(a849),x35712),x35713)),x35714)) % 168.19/168.05 [3584]E(f317(f317(f127(x35841),f317(f317(f145(x35841),x35842),x35843)),x35844),f317(f317(f145(x35841),x35842),f317(f317(f127(x35841),x35843),x35844))) % 168.19/168.05 [3585]E(f317(f317(f127(x35851),f317(f317(f127(x35851),x35852),x35853)),x35854),f317(f317(f127(x35851),x35852),f317(f317(f127(x35851),x35853),x35854))) % 168.19/168.05 [3662]E(f317(f317(f159(x36621),f317(f317(f145(x36621),x36622),x36623)),x36624),f184(x36621,x36622,f317(f159(x36621),x36623),x36624)) % 168.19/168.05 [3671]E(f317(f317(f182(x36711,x36711),x36712),f317(f317(f182(x36711,x36711),x36713),x36714)),f317(f317(f182(x36711,x36711),f317(f317(f90(a849),x36713),x36712)),x36714)) % 168.19/168.05 [3699]E(f317(f317(f122(f858(x36991,a842)),x36992),f317(f317(f286(x36991),x36993),x36994)),f317(f317(f286(x36991),x36993),f317(f317(f122(f858(x36991,a842)),x36992),x36994))) % 168.19/168.05 [3717]E(f317(f317(f317(f182(x37171,x37171),x37172),x37173),f317(x37173,x37174)),f317(x37173,f317(f317(f317(f182(x37171,x37171),x37172),x37173),x37174))) % 168.19/168.05 [3724]E(f317(f317(f265(x37241,x37242,x37243),f188(f858(f857(x37241,x37242),a842))),x37244),f188(f858(f857(x37241,x37243),a842))) % 168.19/168.05 [3740]E(f317(f317(f122(f858(x37401,a842)),f317(f317(f286(x37401),x37402),x37403)),x37404),f317(f317(f286(x37401),x37402),f317(f317(f122(f858(x37401,a842)),x37403),x37404))) % 168.19/168.05 [3761]E(f178(x37611,x37612,f317(f171(x37611,x37612),x37613),f317(f171(x37611,x37612),x37614)),f317(f171(x37611,x37612),f317(f317(f127(f857(x37611,x37612)),x37614),x37613))) % 168.19/168.05 [3762]E(f317(f54(f857(x37621,x37622)),f317(f317(f245(x37621,x37622),x37623),f317(f16(f858(x37622,a842),x37621),x37624))),f317(f317(f90(a849),f317(f54(x37621),x37623)),f317(f54(x37622),x37624))) % 168.19/168.05 [3770]E(f317(f317(f113(f858(x37701,a842)),f317(f317(f286(x37701),x37702),x37703)),f317(f317(f286(x37701),x37702),x37704)),f317(f317(f286(x37701),x37702),f317(f317(f113(f858(x37701,a842)),x37703),x37704))) % 168.19/168.05 [3786]E(f317(f317(f122(f858(x37861,a842)),x37862),f317(f317(f122(f858(x37861,a842)),x37863),x37864)),f317(f317(f122(f858(x37861,a842)),x37863),f317(f317(f122(f858(x37861,a842)),x37862),x37864))) % 168.19/168.05 [3787]E(f317(f317(f113(f858(x37871,a842)),x37872),f317(f317(f113(f858(x37871,a842)),x37873),x37874)),f317(f317(f113(f858(x37871,a842)),x37873),f317(f317(f113(f858(x37871,a842)),x37872),x37874))) % 168.19/168.05 [3796]E(f74(x37961,x37962,f317(f317(f8(x37962,f858(x37962,x37962),x37961),x37963),x37964)),f317(f75(x37962,x37961,x37963),x37964)) % 168.19/168.05 [3804]E(f173(x38041,f317(f317(f148(f850(x38042),f850(x38041)),f317(f148(x38042,x38041),x38043)),x38044)),f317(f317(f148(f850(x38042),f850(x38041)),f317(f148(x38042,x38041),x38043)),f173(x38042,x38044))) % 168.19/168.05 [3821]E(f317(f136(f850(x38211),f850(x38211),f127(x38211),f125(x38211)),f317(f317(f148(x38212,f850(x38211)),x38213),x38214)),f158(x38212,x38211,x38213,x38214)) % 168.19/168.05 [3824]E(f181(x38241,x38242,x38243,f317(f88(f858(x38241,a842)),f317(f317(f286(x38241),x38244),f188(f858(x38241,a842))))),f317(f317(f317(f81(x38241,f853(x38242)),x38243),x38244),f191(x38242))) % 168.19/168.05 [3867]E(f317(f317(f317(f81(x38671,f853(x38672)),f317(f171(x38671,x38672),x38673)),f317(f244(x38671,x38672),x38674)),f317(f217(x38672),f317(f246(x38671,x38672),x38674))),f317(f171(x38671,x38672),f317(f317(f145(f857(x38671,x38672)),x38674),x38673))) % 168.19/168.05 [3884]E(f317(f82(x38841,x38841,x38841,f317(f317(f182(x38841,x38841),x38842),x38843)),f317(f317(f182(x38841,x38841),x38844),x38843)),f317(f317(f182(x38841,x38841),f317(f317(f89(a849),x38842),x38844)),x38843)) % 168.19/168.05 [3908]E(f317(f317(f113(f858(x39081,a842)),f317(f317(f21(f858(x39081,a842)),x39082),x39083)),f317(f317(f21(f858(x39081,a842)),x39082),x39084)),f317(f317(f21(f858(x39081,a842)),x39082),f317(f317(f122(f858(x39081,a842)),x39083),x39084))) % 168.19/168.05 [3909]E(f317(f317(f122(f858(x39091,a842)),f317(f317(f21(f858(x39091,a842)),x39092),x39093)),f317(f317(f21(f858(x39091,a842)),x39092),x39094)),f317(f317(f21(f858(x39091,a842)),x39092),f317(f317(f113(f858(x39091,a842)),x39093),x39094))) % 168.19/168.05 [3910]E(f317(f317(f113(f858(x39101,a842)),f317(f317(f122(f858(x39101,a842)),x39102),x39103)),f317(f317(f122(f858(x39101,a842)),x39102),x39104)),f317(f317(f122(f858(x39101,a842)),x39102),f317(f317(f113(f858(x39101,a842)),x39103),x39104))) % 168.19/168.05 [3911]E(f317(f317(f21(f858(x39111,a842)),f317(f317(f113(f858(x39111,a842)),x39112),x39113)),f317(f317(f113(f858(x39111,a842)),x39112),x39114)),f317(f317(f113(f858(x39111,a842)),x39112),f317(f317(f21(f858(x39111,a842)),x39113),x39114))) % 168.19/168.05 [3912]E(f317(f317(f122(f858(x39121,a842)),f317(f317(f113(f858(x39121,a842)),x39122),x39123)),f317(f317(f113(f858(x39121,a842)),x39122),x39124)),f317(f317(f113(f858(x39121,a842)),x39122),f317(f317(f122(f858(x39121,a842)),x39123),x39124))) % 168.19/168.05 [3918]E(f317(f54(f857(x39181,x39182)),f317(f317(f245(x39181,x39182),f317(f317(f286(x39181),x39183),f188(f858(x39181,a842)))),f317(f16(f858(x39182,a842),x39181),x39184))),f317(f54(x39182),x39184)) % 168.19/168.05 [3953]E(f317(f317(f52(x39531,f858(x39532,a842)),x39533),f317(f317(f8(f858(x39532,a842),f858(x39532,a842),x39531),f88(f858(x39532,a842))),x39534)),f317(f88(f858(x39532,a842)),f317(f317(f51(x39531,f858(x39532,a842)),x39533),x39534))) % 168.19/168.05 [3954]E(f317(f317(f51(x39541,f858(x39542,a842)),x39543),f317(f317(f8(f858(x39542,a842),f858(x39542,a842),x39541),f88(f858(x39542,a842))),x39544)),f317(f88(f858(x39542,a842)),f317(f317(f52(x39541,f858(x39542,a842)),x39543),x39544))) % 168.19/168.05 [3970]E(f317(f317(f265(x39701,x39701,x39701),f317(f317(f182(f857(x39701,x39701),a842),x39702),x39703)),f317(f317(f182(f857(x39701,x39701),a842),x39704),x39703)),f317(f317(f182(f857(x39701,x39701),a842),f317(f317(f89(a849),x39702),x39704)),x39703)) % 168.19/168.05 [4004]E(f317(f317(f52(x40041,f858(f858(x40042,a842),a842)),x40043),f317(f317(f8(f858(x40042,a842),f858(f858(x40042,a842),a842),x40041),f285(x40042)),x40044)),f317(f285(x40042),f317(f317(f52(x40041,f858(x40042,a842)),x40043),x40044))) % 168.19/168.05 [4032]E(f317(f317(f51(f858(x40321,a842),f858(x40322,a842)),x40323),f317(f317(f7(f858(x40321,a842),f858(x40321,f858(x40322,a842)),f858(x40322,a842)),f51(x40321,f858(x40322,a842))),x40324)),f317(f317(f51(x40321,f858(x40322,a842)),f49(f858(x40321,a842),x40323)),x40324)) % 168.19/168.05 [4033]E(f317(f317(f52(f858(x40331,a842),f858(x40332,a842)),x40333),f317(f317(f7(f858(x40331,a842),f858(x40331,f858(x40332,a842)),f858(x40332,a842)),f52(x40331,f858(x40332,a842))),x40334)),f317(f317(f52(x40331,f858(x40332,a842)),f49(f858(x40331,a842),x40333)),x40334)) % 168.19/168.05 [4038]E(f317(f317(f148(x40381,x40382),x40383),f317(f136(f850(x40381),f850(x40381),f127(x40381),f125(x40381)),x40384)),f317(f136(f850(x40382),f850(x40382),f127(x40382),f125(x40382)),f317(f317(f148(f850(x40381),f850(x40382)),f317(f148(x40381,x40382),x40383)),x40384))) % 168.19/168.05 [4041]E(f184(f850(x40411),f125(x40411),f317(f317(f8(f850(x40411),f850(x40411),a849),f317(f145(x40411),x40412)),f317(f317(f7(a849,f850(x40411),f850(x40411)),f167(x40411)),x40413)),x40414),f317(f317(f167(x40411),x40414),f317(f317(f145(x40411),x40412),x40413))) % 168.19/168.05 [4087]P22(f317(f317(f225(f858(x40871,a842)),f317(f287(x40872,x40871,x40873),f317(f289(x40872,x40871,x40873),x40874))),x40874)) % 168.19/168.05 [4090]E(f317(f287(f857(x40901,x40902),f857(x40902,x40901),f317(f247(x40901,x40902,f857(x40902,x40901)),f317(f7(x40902,x40901,f857(x40902,x40901)),f237(x40902,x40901)))),f317(f317(f245(x40901,x40902),x40903),f317(f16(f858(x40902,a842),x40901),x40904))),f317(f317(f245(x40902,x40901),x40904),f317(f16(f858(x40901,a842),x40902),x40903))) % 168.19/168.05 [4099]E(f317(f317(f51(x40991,f858(x40992,a842)),x40993),f317(f317(f8(f858(x40991,a842),f858(x40992,a842),x40991),f289(x40992,x40991,x40994)),f317(f317(f7(x40991,f858(x40991,a842),f858(x40991,a842)),f286(x40991)),f188(f858(x40991,a842))))),f317(f289(x40992,x40991,x40994),x40993)) % 168.19/168.05 [4100]E(f317(f317(f51(x41001,f858(x41002,a842)),x41003),f317(f317(f8(f858(x41001,a842),f858(x41002,a842),x41001),f262(x41001,x41002,x41004)),f317(f317(f7(x41001,f858(x41001,a842),f858(x41001,a842)),f286(x41001)),f188(f858(x41001,a842))))),f317(f262(x41001,x41002,x41004),x41003)) % 168.19/168.05 [4191]E(f317(f317(f122(f858(x41911,a842)),f317(f317(f122(f858(x41911,a842)),f317(f317(f113(f858(x41911,a842)),x41912),x41913)),f317(f317(f113(f858(x41911,a842)),x41913),x41914))),f317(f317(f113(f858(x41911,a842)),x41914),x41912)),f317(f317(f113(f858(x41911,a842)),f317(f317(f113(f858(x41911,a842)),f317(f317(f122(f858(x41911,a842)),x41912),x41913)),f317(f317(f122(f858(x41911,a842)),x41913),x41914))),f317(f317(f122(f858(x41911,a842)),x41914),x41912))) % 168.19/168.05 [4252]E(f317(f136(f850(x42521),f850(x42521),f127(x42521),f125(x42521)),f317(f317(f148(x42522,f850(x42521)),f317(f317(f7(x42522,f850(x42521),f850(x42521)),f317(f317(f8(x42521,f858(f850(x42521),f850(x42521)),x42522),f145(x42521)),x42523)),f125(x42521))),x42524)),f317(f317(f148(x42522,x42521),x42523),x42524)) % 168.19/168.05 [4263]E(f317(f317(f95(a1,x42631),f317(f115(a1),f317(f317(f89(a1),x42632),a109))),f317(f317(f18(a1,x42631,x42631),f317(f317(f7(a1,x42631,f858(x42631,x42631)),f317(f317(f8(a842,f858(x42631,f858(x42631,x42631)),a1),f108(x42631)),a193)),x42633)),f317(f317(f8(a849,x42631,a1),x42634),a116))),f184(x42631,x42633,x42634,f317(f115(a849),x42632))) % 168.19/168.05 [4503]~P22(f317(f317(f188(f858(x45031,f858(x45032,a842))),x45033),x45034)) % 168.19/168.05 [3727]E(f317(f317(f159(x37271),f317(f317(f127(x37271),x37272),x37273)),f317(f317(f89(a849),f317(f189(f850(x37271)),x37272)),x37274)),f317(f317(f159(x37271),x37273),x37274)) % 168.19/168.05 [3733]E(f317(f317(f132(x37331),x37332),f317(f317(f167(x37331),f317(f317(f89(a849),x37333),x37332)),x37334)),f317(f317(f167(x37331),x37333),f317(f317(f132(x37331),x37332),x37334))) % 168.19/168.05 [3837]E(f317(f317(f122(f858(x38371,a842)),f317(f234(x38372,x38371),x38373)),f317(f234(x38372,x38371),x38374)),f317(f234(x38372,x38371),f317(f317(f122(f858(f857(x38372,x38371),a842)),x38373),x38374))) % 168.19/168.05 [3838]E(f317(f317(f122(f858(x38381,a842)),f317(f236(x38381,x38382),x38383)),f317(f236(x38381,x38382),x38384)),f317(f236(x38381,x38382),f317(f317(f122(f858(f857(x38381,x38382),a842)),x38383),x38384))) % 168.19/168.05 [3843]E(f317(f317(f21(f858(x38431,a842)),f317(f317(f113(f858(x38431,a842)),x38432),x38433)),x38434),f317(f317(f113(f858(x38431,a842)),x38432),f317(f317(f21(f858(x38431,a842)),x38433),x38434))) % 168.19/168.05 [3844]E(f317(f317(f122(f858(x38441,a842)),f317(f317(f122(f858(x38441,a842)),x38442),x38443)),x38444),f317(f317(f122(f858(x38441,a842)),x38442),f317(f317(f122(f858(x38441,a842)),x38443),x38444))) % 168.19/168.05 [3845]E(f317(f317(f113(f858(x38451,a842)),f317(f317(f113(f858(x38451,a842)),x38452),x38453)),x38454),f317(f317(f113(f858(x38451,a842)),x38452),f317(f317(f113(f858(x38451,a842)),x38453),x38454))) % 168.19/168.05 [3886]E(f317(f317(f122(f858(f857(x38861,x38862),a842)),f317(f263(x38862,x38861),x38863)),f317(f263(x38862,x38861),x38864)),f317(f263(x38862,x38861),f317(f317(f122(f858(f857(x38862,x38861),a842)),x38863),x38864))) % 168.19/168.05 [3887]E(f317(f317(f113(f858(f857(x38871,x38872),a842)),f317(f263(x38872,x38871),x38873)),f317(f263(x38872,x38871),x38874)),f317(f263(x38872,x38871),f317(f317(f113(f858(f857(x38872,x38871),a842)),x38873),x38874))) % 168.19/168.05 [3957]E(f317(f317(f122(f858(x39571,a842)),f317(f317(f21(f858(x39571,a842)),x39572),x39573)),f317(f317(f21(f858(x39571,a842)),x39574),x39573)),f317(f317(f21(f858(x39571,a842)),f317(f317(f122(f858(x39571,a842)),x39572),x39574)),x39573)) % 168.19/168.05 [3958]E(f317(f317(f113(f858(x39581,a842)),f317(f317(f122(f858(x39581,a842)),x39582),x39583)),f317(f317(f122(f858(x39581,a842)),x39584),x39583)),f317(f317(f122(f858(x39581,a842)),f317(f317(f113(f858(x39581,a842)),x39582),x39584)),x39583)) % 168.19/168.05 [3959]E(f317(f317(f21(f858(x39591,a842)),f317(f317(f113(f858(x39591,a842)),x39592),x39593)),f317(f317(f113(f858(x39591,a842)),x39594),x39593)),f317(f317(f113(f858(x39591,a842)),f317(f317(f21(f858(x39591,a842)),x39592),x39594)),x39593)) % 168.19/168.05 [3960]E(f317(f317(f122(f858(x39601,a842)),f317(f317(f113(f858(x39601,a842)),x39602),x39603)),f317(f317(f113(f858(x39601,a842)),x39604),x39603)),f317(f317(f113(f858(x39601,a842)),f317(f317(f122(f858(x39601,a842)),x39602),x39604)),x39603)) % 168.19/168.05 [3961]E(f317(f317(f21(f858(x39611,a842)),f317(f317(f113(f858(x39611,a842)),x39612),x39613)),f317(f317(f113(f858(x39611,a842)),x39614),x39613)),f317(f317(f21(f858(x39611,a842)),f317(f317(f113(f858(x39611,a842)),x39612),x39613)),x39614)) % 168.19/168.05 [3973]E(f317(f317(f21(f858(x39731,a842)),f317(f317(f21(f858(x39731,a842)),x39732),f317(f317(f286(x39731),x39733),f188(f858(x39731,a842))))),x39734),f317(f317(f21(f858(x39731,a842)),x39732),f317(f317(f286(x39731),x39733),x39734))) % 168.19/168.05 [4029]E(f317(f317(f122(f858(x40291,a842)),f317(f317(f286(x40291),x40292),f317(f317(f286(x40291),x40293),f188(f858(x40291,a842))))),f317(f261(x40291),x40294)),f317(f261(x40291),f317(f317(f286(f857(x40291,x40291)),f317(f317(f237(x40291,x40291),x40292),x40293)),x40294))) % 168.19/168.05 [4061]E(f317(f317(f51(a849,f858(x40611,a842)),f317(f277(a849),x40612)),f317(f317(f8(a849,f858(x40611,a842),a849),x40613),f317(f317(f7(a849,a849,a849),f89(a849)),x40614))),f317(f317(f51(a849,f858(x40611,a842)),f279(a849,x40614,f317(f317(f89(a849),x40612),x40614))),x40613)) % 168.19/168.05 [4062]E(f169(x40621,f317(f262(x40621,x40621,x40622),f317(f317(f286(x40621),x40623),f188(f858(x40621,a842)))),f317(f262(f850(x40621),f850(x40621),f152(x40621,x40622)),f317(f317(f286(f850(x40621)),x40624),f188(f858(f850(x40621),a842))))),f317(f262(f850(x40621),f850(x40621),f152(x40621,x40622)),f317(f317(f286(f850(x40621)),f317(f317(f145(x40621),x40623),x40624)),f188(f858(f850(x40621),a842))))) % 168.19/168.05 [4121]E(f317(f171(x41211,x41212),f317(f317(f148(x41211,f857(x41211,x41212)),f317(f317(f18(x41211,x41212,f857(x41211,x41212)),f237(x41211,x41212)),x41213)),x41214)),f181(x41211,x41212,f317(f82(x41212,f853(x41212),x41211,f217(x41212)),x41213),f317(f166(x41211),x41214))) % 168.19/168.05 [4126]E(f317(f230(x41261),f317(f317(f7(x41261,f858(x41262,a842),a842),f317(f317(f8(x41262,f858(f858(x41262,a842),a842),x41261),f319(x41262)),x41263)),x41264)),f317(f289(x41261,x41262,x41263),x41264)) % 168.19/168.05 [4224]E(f317(f230(x42241),f317(f317(f7(x42241,f858(f857(x42242,x42241),a842),a842),f317(f317(f8(f857(x42242,x42241),f858(f858(f857(x42242,x42241),a842),a842),x42241),f319(f857(x42242,x42241))),f317(f237(x42242,x42241),x42243))),x42244)),f317(f262(x42242,x42241,x42244),f317(f317(f286(x42242),x42243),f188(f858(x42242,a842))))) % 168.19/168.05 [4238]E(f317(f317(f148(f857(x42381,a849),x42381),f244(x42381,a849)),f317(f130(f857(x42381,a849),f317(f317(f8(a849,a842,f857(x42381,a849)),x42382),f317(f317(f8(a849,a849,f857(x42381,a849)),a124),f246(x42381,a849)))),f317(f317(f175(x42381,a849),x42383),x42384))),f317(f317(f148(f857(x42381,a849),x42381),f244(x42381,a849)),f317(f130(f857(x42381,a849),f317(f317(f8(a849,a842,f857(x42381,a849)),x42382),f246(x42381,a849))),f317(f317(f175(x42381,a849),x42383),f317(f317(f148(a849,a849),a124),x42384))))) % 168.19/168.05 [4245]P22(f317(f317(f225(f858(f858(x42451,a842),a842)),f317(f317(f51(x42452,f858(f858(x42451,a842),a842)),x42453),f317(f317(f8(f858(x42451,a842),f858(f858(x42451,a842),a842),x42452),f285(x42451)),x42454))),f317(f285(x42451),f317(f317(f51(x42452,f858(x42451,a842)),x42453),x42454)))) % 168.19/168.05 [4285]E(f317(f317(f95(a1,x42851),f317(f115(a1),f317(f317(f89(a1),x42852),a109))),f317(f317(f18(a1,x42851,x42851),f317(f317(f7(a1,x42851,f858(x42851,x42851)),f317(f317(f8(a842,f858(x42851,f858(x42851,x42851)),a1),f108(x42851)),a193)),x42853)),f317(f317(f18(a1,x42851,x42851),f317(f317(f8(a849,f858(x42851,x42851),a1),x42854),a116)),f317(f317(f8(a849,x42851,a1),f183(x42851,x42853,x42854)),a116)))),f317(f183(x42851,x42853,x42854),f317(f115(a849),x42852))) % 168.19/168.05 [4288]E(f317(f317(f148(x42881,x42882),f317(f82(f853(x42882),x42882,x42881,f222(x42882)),x42883)),f317(f130(x42881,f317(f317(f8(a842,a842,x42881),a312),f317(f317(f7(x42881,f853(x42882),a842),f317(f317(f8(f853(x42882),f858(f853(x42882),a842),x42881),a314),x42883)),f191(x42882)))),x42884)),f157(x42881,x42882,x42883,x42884)) % 168.19/168.05 [4310]E(f317(f230(f857(x43101,x43102)),f317(f247(x43101,x43102,a842),f317(f317(f7(x43101,f858(x43102,a842),f858(x43102,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x43102,a842),f858(x43102,a842)),x43101),f8(a842,a842,x43102)),f317(f317(f8(a842,f858(a842,a842),x43101),a315),f317(f317(f7(x43101,f858(x43101,a842),a842),f319(x43101)),x43103)))),f317(f317(f7(x43102,f858(x43102,a842),a842),f319(x43102)),x43104)))),f215(x43101,x43102,x43103,x43104)) % 168.19/168.05 [4339]E(f317(f317(f51(x43391,f858(f857(x43391,x43392),a842)),x43393),f317(f317(f18(x43391,f858(x43392,f858(f857(x43391,x43392),a842)),f858(f857(x43391,x43392),a842)),f317(f317(f8(f858(x43392,a842),f858(f858(x43392,f858(f857(x43391,x43392),a842)),f858(f857(x43391,x43392),a842)),x43391),f51(x43392,f858(f857(x43391,x43392),a842))),x43394)),f317(f317(f7(x43391,f858(f857(x43391,x43392),a842),f858(x43392,f858(f857(x43391,x43392),a842))),f317(f317(f8(f858(x43392,f858(f858(f857(x43391,x43392),a842),f858(f857(x43391,x43392),a842))),f858(f858(f857(x43391,x43392),a842),f858(x43392,f858(f857(x43391,x43392),a842))),x43391),f7(x43392,f858(f857(x43391,x43392),a842),f858(f857(x43391,x43392),a842))),f317(f317(f8(f858(x43392,f857(x43391,x43392)),f858(x43392,f858(f858(f857(x43391,x43392),a842),f858(f857(x43391,x43392),a842))),x43391),f317(f8(f857(x43391,x43392),f858(f858(f857(x43391,x43392),a842),f858(f857(x43391,x43392),a842)),x43392),f286(f857(x43391,x43392)))),f237(x43391,x43392)))),f188(f858(f857(x43391,x43392),a842))))),f317(f317(f245(x43391,x43392),x43393),x43394)) % 168.19/168.05 [3895]E(f317(f317(f127(x38951),f317(f317(f167(x38951),x38952),x38953)),f317(f317(f167(x38951),f317(f317(f21(a849),x38952),f317(f189(f850(x38951)),x38953))),x38954)),f317(f317(f167(x38951),x38952),f317(f317(f127(x38951),x38953),x38954))) % 168.19/168.05 [3896]E(f317(f317(f127(x38961),f317(f317(f132(x38961),x38962),x38963)),f317(f317(f132(x38961),f317(f317(f21(a849),x38962),f317(f189(f850(x38961)),x38963))),x38964)),f317(f317(f132(x38961),x38962),f317(f317(f127(x38961),x38963),x38964))) % 168.19/168.05 [3947]E(f317(f317(f89(a849),f317(f317(f90(a849),x39471),x39472)),f317(f317(f89(a849),f317(f317(f90(a849),x39473),x39472)),x39474)),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f89(a849),x39471),x39473)),x39472)),x39474)) % 168.19/168.05 [4153]P22(f317(f317(f225(f858(x41531,a842)),f317(f317(f21(f858(x41531,a842)),f317(f234(x41532,x41531),x41533)),f317(f234(x41532,x41531),x41534))),f317(f234(x41532,x41531),f317(f317(f21(f858(f857(x41532,x41531),a842)),x41533),x41534)))) % 168.19/168.05 [4154]P22(f317(f317(f225(f858(x41541,a842)),f317(f317(f21(f858(x41541,a842)),f317(f236(x41541,x41542),x41543)),f317(f236(x41541,x41542),x41544))),f317(f236(x41541,x41542),f317(f317(f21(f858(f857(x41541,x41542),a842)),x41543),x41544)))) % 168.19/168.05 [4265]E(f317(f317(f89(a1),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x42651),x42652)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x42653),x42654)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),f317(f317(f89(a849),x42651),x42653)),f317(f317(f89(a849),x42652),x42654))),f188(f858(f857(a849,a849),a842)))))) % 168.19/168.05 [4305]E(f317(f317(f90(a1),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x43051),x43052)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x43053),x43054)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),f317(f317(f89(a849),f317(f317(f90(a849),x43051),x43053)),f317(f317(f90(a849),x43052),x43054))),f317(f317(f89(a849),f317(f317(f90(a849),x43051),x43054)),f317(f317(f90(a849),x43052),x43053)))),f188(f858(f857(a849,a849),a842)))))) % 168.19/168.05 [4322]E(f317(f230(x43221),f317(f317(f8(f858(x43222,a842),a842,x43221),f97(x43222)),f317(f317(f8(f858(x43222,a842),f858(x43222,a842),x43221),f317(f18(x43222,a842,a842),f317(f317(f8(a842,f858(a842,a842),x43222),a320),f317(f317(f7(x43222,f858(x43222,a842),a842),f319(x43222)),x43223)))),f317(f317(f7(x43221,f858(x43222,f858(x43221,a842)),f858(x43222,a842)),f317(f317(f8(f858(f858(x43221,a842),a842),f858(f858(x43222,f858(x43221,a842)),f858(x43222,a842)),x43221),f8(f858(x43221,a842),a842,x43222)),f319(x43221))),x43224)))),f317(f317(f52(x43222,f858(x43221,a842)),x43223),x43224)) % 168.19/168.05 [4355]E(f317(f317(f265(x43551,x43551,x43551),f317(f317(f286(f857(x43551,x43551)),f317(f317(f237(x43551,x43551),x43552),x43553)),x43554)),f284(x43551,f317(f317(f286(f857(x43551,x43551)),f317(f317(f237(x43551,x43551),x43552),x43553)),x43554))),f317(f317(f122(f858(f857(x43551,x43551),a842)),f317(f317(f265(x43551,x43551,x43551),x43554),f284(x43551,x43554))),f317(f230(f857(x43551,x43551)),f317(f247(x43551,x43551,a842),f317(f317(f7(x43551,f858(x43551,a842),f858(x43551,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x43551,a842),f858(x43551,a842)),x43551),f8(a842,a842,x43551)),f317(f317(f8(a842,f858(a842,a842),x43551),a315),f317(f317(f7(x43551,f858(f857(x43551,x43551),a842),a842),f317(f317(f8(f857(x43551,x43551),f858(f858(f857(x43551,x43551),a842),a842),x43551),f319(f857(x43551,x43551))),f317(f317(f7(x43551,x43551,f857(x43551,x43551)),f237(x43551,x43551)),x43552))),f284(x43551,x43554))))),f317(f317(f7(x43551,f858(f857(x43551,x43551),a842),a842),f317(f317(f8(f857(x43551,x43551),f858(f858(f857(x43551,x43551),a842),a842),x43551),f319(f857(x43551,x43551))),f317(f237(x43551,x43551),x43553))),f284(x43551,x43554))))))) % 168.19/168.05 [4155]E(f317(f130(x41551,f317(f317(f18(x41551,a842,a842),f317(f317(f8(a842,f858(a842,a842),x41551),a315),x41552)),x41553)),x41554),f317(f130(x41551,x41553),f317(f130(x41551,x41552),x41554))) % 168.19/168.05 [4259]E(f317(f317(f127(x42591),f317(f317(f317(f108(f850(x42591)),f317(f317(f319(a849),f2(a849)),x42592)),f317(f317(f145(x42591),x42593),f125(x42591))),f125(x42591))),f168(x42591,x42594,f317(f230(a849),f317(f317(f7(a849,f858(a849,a842),a842),f317(f317(f8(a849,f858(f858(a849,a842),a842),a849),f319(a849)),a124)),x42592)))),f168(x42591,f317(f317(f145(x42591),x42593),x42594),x42592)) % 168.19/168.05 [4350]E(f317(f230(f857(x43501,x43502)),f317(f317(f8(f858(a849,a842),a842,f857(x43501,x43502)),f96(a849)),f317(f317(f7(f857(x43501,x43502),f858(a849,a842),f858(a849,a842)),f317(f317(f8(f858(a849,f858(a842,a842)),f858(f858(a849,a842),f858(a849,a842)),f857(x43501,x43502)),f18(a849,a842,a842)),f317(f317(f8(f858(a849,a842),f858(a849,f858(a842,a842)),f857(x43501,x43502)),f317(f8(a842,f858(a842,a842),a849),a315)),f317(f317(f7(f857(x43501,x43502),f858(a849,f857(x43501,x43502)),f858(a849,a842)),f317(f317(f8(f858(f857(x43501,x43502),a842),f858(f858(a849,f857(x43501,x43502)),f858(a849,a842)),f857(x43501,x43502)),f8(f857(x43501,x43502),a842,a849)),a314)),f317(f317(f18(a849,x43502,f857(x43501,x43502)),f317(f317(f8(x43501,f858(x43502,f857(x43501,x43502)),a849),f237(x43501,x43502)),f317(f159(x43501),x43503))),f317(f159(x43502),x43504)))))),f317(f317(f7(a849,a849,a842),f226(a849)),f317(f317(f223(a849),f317(f189(f850(x43501)),x43503)),f317(f189(f850(x43502)),x43504)))))),f317(f166(f857(x43501,x43502)),f317(f317(f175(x43501,x43502),x43503),x43504))) % 168.19/168.05 [4277]E(f317(f230(f857(x42771,x42772)),f317(f247(x42771,x42772,a842),f317(f317(f7(x42771,f858(x42772,a842),f858(x42772,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x42772,a842),f858(x42772,a842)),x42771),f8(a842,a842,x42772)),f317(f317(f8(a842,f858(a842,a842),x42771),a315),x42773))),x42774))),f317(f317(f245(x42771,x42772),f317(f230(x42771),x42773)),f317(f16(f858(x42772,a842),x42771),f317(f230(x42772),x42774)))) % 168.19/168.05 [4280]E(f317(f230(f857(x42801,x42802)),f317(f247(x42801,x42802,a842),f317(f317(f18(x42801,f858(x42802,a842),f858(x42802,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x42802,a842),f858(x42802,a842)),x42801),f8(a842,a842,x42802)),f317(f317(f8(a842,f858(a842,a842),x42801),a315),x42803))),x42804))),f317(f317(f245(x42801,x42802),f317(f230(x42801),x42803)),f317(f317(f8(f858(x42802,a842),f858(x42802,a842),x42801),f230(x42802)),x42804))) % 168.19/168.05 [4295]E(f317(f230(x42951),f317(f317(f8(f858(x42952,a842),a842,x42951),f97(x42952)),f317(f317(f8(f858(x42952,a842),f858(x42952,a842),x42951),f317(f18(x42952,a842,a842),f317(f317(f8(a842,f858(a842,a842),x42952),a320),f317(f317(f7(x42952,f858(x42952,a842),a842),f319(x42952)),x42953)))),x42954))),f317(f317(f52(x42952,f858(x42951,a842)),x42953),f317(f317(f8(f858(x42951,a842),f858(x42951,a842),x42952),f230(x42951)),f317(f7(x42951,x42952,a842),x42954)))) % 168.19/168.05 [4334]E(f317(f317(f148(f857(x43341,a849),x43341),f244(x43341,a849)),f317(f130(f857(x43341,a849),f317(f317(f7(f857(x43341,a849),f858(a849,a842),a842),f317(f317(f8(a849,f858(f858(a849,a842),a842),f857(x43341,a849)),f319(a849)),f246(x43341,a849))),x43342)),f317(f317(f175(x43341,a849),x43343),f133(a849,f317(f278(a849,x43344),f317(f317(f89(a849),x43344),f317(f189(f850(x43341)),x43343))))))),f317(f317(f148(f857(x43341,a849),x43341),f244(x43341,a849)),f317(f130(f857(x43341,a849),f317(f317(f7(f857(x43341,a849),f858(a849,a842),a842),f317(f317(f8(a849,f858(f858(a849,a842),a842),f857(x43341,a849)),f319(a849)),f317(f317(f7(f857(x43341,a849),a849,a849),f317(f317(f8(a849,f858(a849,a849),f857(x43341,a849)),f89(a849)),f246(x43341,a849))),x43344))),x43342)),f317(f317(f175(x43341,a849),x43343),f133(a849,f317(f278(a849,f2(a849)),f317(f189(f850(x43341)),x43343))))))) % 168.19/168.05 [4335]E(f317(a124,f317(f317(f224(a849),f317(f189(f850(x43351)),x43352)),f317(f136(a849,f850(x43353),f317(f7(f850(x43353),a849,a849),f317(f317(f8(a849,f858(a849,a849),f850(x43353)),f224(a849)),f317(f317(f7(f850(x43353),a849,a849),f317(f317(f8(a849,f858(a849,a849),f850(x43353)),f21(a849)),f189(f850(x43353)))),f317(a124,f2(a849))))),f2(a849)),f317(f163(f850(x43353)),f317(f130(f850(x43353),f317(f317(f8(a842,a842,f850(x43353)),a312),f317(f317(f7(f850(x43353),f850(x43353),a842),a314),f125(x43353)))),x43354))))),f317(f317(f224(a849),f317(a124,f317(f189(f850(x43351)),x43352))),f317(f136(a849,f850(x43353),f317(f7(f850(x43353),a849,a849),f317(f317(f8(a849,f858(a849,a849),f850(x43353)),f224(a849)),f189(f850(x43353)))),f2(a849)),f317(f163(f850(x43353)),x43354)))) % 168.19/168.05 [4294]E(f317(f317(f127(x42941),f168(x42941,x42942,x42943)),f168(x42941,x42944,f317(f230(a849),f317(f317(f7(a849,f858(a849,a842),a842),f317(f317(f8(a849,f858(f858(a849,a842),a842),a849),f319(a849)),f317(f317(f7(a849,a849,a849),f89(a849)),f317(f189(f850(x42941)),x42942)))),x42943)))),f168(x42941,f317(f317(f127(x42941),x42942),x42944),x42943)) % 168.19/168.05 [4341]E(f317(f317(f145(f850(x43411)),f317(f317(f145(x43411),x43412),f317(f136(f850(x43411),f850(x43411),f127(x43411),f125(x43411)),f317(f317(f148(f850(x43411),f850(x43411)),f150(f850(x43411),x43411,f125(x43411),f317(f317(f8(f850(x43411),f858(f850(x43411),f850(x43411)),x43411),f16(f850(x43411),f850(x43411))),f317(f317(f7(x43411,f850(x43411),f850(x43411)),f145(x43411)),f125(x43411))))),x43413)))),f173(x43411,f317(f317(f145(f850(x43411)),x43414),f317(f136(f850(f850(x43411)),f850(f850(x43411)),f127(f850(x43411)),f125(f850(x43411))),f317(f317(f148(f850(x43411),f850(f850(x43411))),f150(f850(f850(x43411)),x43411,f125(f850(x43411)),f317(f16(f858(f850(x43411),f850(f850(x43411))),x43411),f317(f317(f7(f850(x43411),f850(f850(x43411)),f850(f850(x43411))),f145(f850(x43411))),f125(f850(x43411)))))),x43413))))),f173(x43411,f317(f317(f145(f850(x43411)),f317(f317(f145(x43411),x43412),x43414)),x43413))) % 168.19/168.05 [4351]E(f317(f230(f857(x43511,x43511)),f317(f247(x43511,x43511,a842),f317(f317(f7(x43511,f858(f857(x43512,x43512),a842),f858(x43511,a842)),f317(f317(f8(f858(x43511,f858(f858(f857(x43512,x43512),a842),a842)),f858(f858(f857(x43512,x43512),a842),f858(x43511,a842)),x43511),f7(x43511,f858(f857(x43512,x43512),a842),a842)),f317(f317(f8(f858(x43511,f857(x43512,x43512)),f858(x43511,f858(f858(f857(x43512,x43512),a842),a842)),x43511),f317(f8(f857(x43512,x43512),f858(f858(f857(x43512,x43512),a842),a842),x43511),f319(f857(x43512,x43512)))),f317(f317(f7(x43511,f858(x43511,x43512),f858(x43511,f857(x43512,x43512))),f317(f317(f8(f858(x43512,f857(x43512,x43512)),f858(f858(x43511,x43512),f858(x43511,f857(x43512,x43512))),x43511),f8(x43512,f857(x43512,x43512),x43511)),f317(f317(f8(x43512,f858(x43512,f857(x43512,x43512)),x43511),f237(x43512,x43512)),x43513))),x43513)))),x43514))),f317(f317(f264(x43512,x43511),x43514),x43513)) % 168.19/168.05 [4438]~E(f36(x44381,x44382),f31(x44383,x44384,x44385)) % 168.19/168.05 [4439]~E(f36(x44391,x44392),f33(x44393,x44394,x44395)) % 168.19/168.05 [4440]~E(f36(x44401,x44402),f32(x44403,x44404,x44405)) % 168.19/168.05 [4441]~E(f30(x44411,x44412),f31(x44413,x44414,x44415)) % 168.19/168.05 [4442]~E(f30(x44421,x44422),f33(x44423,x44424,x44425)) % 168.19/168.05 [4443]~E(f30(x44431,x44432),f32(x44433,x44434,x44435)) % 168.19/168.05 [4444]~E(f35(x44441,x44442),f31(x44443,x44444,x44445)) % 168.19/168.05 [4445]~E(f35(x44451,x44452),f33(x44453,x44454,x44455)) % 168.19/168.05 [4446]~E(f35(x44461,x44462),f32(x44463,x44464,x44465)) % 168.19/168.05 [4447]~E(f31(x44471,x44472,x44473),f36(x44474,x44475)) % 168.19/168.05 [4448]~E(f31(x44481,x44482,x44483),f30(x44484,x44485)) % 168.19/168.05 [4449]~E(f31(x44491,x44492,x44493),f35(x44494,x44495)) % 168.19/168.05 [4450]~E(f33(x44501,x44502,x44503),f36(x44504,x44505)) % 168.19/168.05 [4451]~E(f33(x44511,x44512,x44513),f30(x44514,x44515)) % 168.19/168.05 [4452]~E(f33(x44521,x44522,x44523),f35(x44524,x44525)) % 168.19/168.05 [4453]~E(f32(x44531,x44532,x44533),f36(x44534,x44535)) % 168.19/168.05 [4454]~E(f32(x44541,x44542,x44543),f30(x44544,x44545)) % 168.19/168.05 [4455]~E(f32(x44551,x44552,x44553),f35(x44554,x44555)) % 168.19/168.05 [3835]E(f317(f178(x38351,x38352,x38353,x38354),x38355),f317(f220(f853(x38352),x38352,f317(x38353,x38355),f217(x38352)),f317(x38354,x38355))) % 168.19/168.05 [3924]E(f178(x39241,x39242,f178(x39241,x39242,x39243,x39244),x39245),f178(x39241,x39242,x39243,f178(x39241,x39242,x39244,x39245))) % 168.19/168.05 [4109]E(f317(f317(f122(f858(x41091,a842)),f317(f166(x41091),f317(f317(f167(x41091),f317(f189(f850(x41092)),x41093)),x41094))),f177(x41091,x41092,x41095)),f177(x41091,x41092,f180(x41091,x41092,x41095,x41094,x41093))) % 168.19/168.05 [3658]E(f317(f317(f247(x36581,x36582,x36583),x36584),x36585),f317(f317(x36584,f317(f244(x36581,x36582),x36585)),f317(f246(x36581,x36582),x36585))) % 168.19/168.05 [3681]E(f317(f220(x36811,x36812,x36813,x36814),f317(f217(x36812),x36815)),f317(x36814,x36815)) % 168.19/168.05 [3691]E(f317(f317(f317(f75(x36911,x36912,x36913),x36914),x36915),f188(f858(x36912,a842))),x36915) % 168.19/168.05 [3707]E(f317(f300(x37071,x37072,x37073,x37074),f317(f288(x37071,x37073),x37075)),f317(x37074,x37075)) % 168.19/168.05 [3708]E(f317(f301(x37081,x37082,x37083,x37084),f317(f297(x37081,x37083),x37085)),f317(x37084,x37085)) % 168.19/168.05 [3868]E(f221(x38681,x38682,x38683,x38684,f317(f217(x38682),x38685)),f317(x38684,x38685)) % 168.19/168.05 [3903]E(f302(x39031,x39032,x39033,x39034,f317(f288(x39031,x39032),x39035)),f317(f317(f89(a849),f317(x39033,x39035)),f317(a124,f2(a849)))) % 168.19/168.05 [3904]E(f302(x39041,x39042,x39043,x39044,f317(f297(x39042,x39041),x39045)),f317(f317(f89(a849),f317(x39044,x39045)),f317(a124,f2(a849)))) % 168.19/168.05 [3979]E(f317(f82(f853(x39791),f853(x39792),f853(x39793),f317(f192(x39791,x39792),x39794)),f317(f192(x39793,x39791),x39795)),f317(f192(x39793,x39792),f317(f82(x39791,x39792,x39793,x39794),x39795))) % 168.19/168.05 [3981]E(f317(f82(f850(x39811),f850(x39812),f850(x39813),f317(f148(x39811,x39812),x39814)),f317(f148(x39813,x39811),x39815)),f317(f148(x39813,x39812),f317(f82(x39811,x39812,x39813,x39814),x39815))) % 168.19/168.05 [4065]E(f94(x40651,f76(x40652,x40651,x40653,x40654,x40655)),f317(f317(f74(x40652,x40651,x40653),x40654),x40655)) % 168.19/168.05 [4101]E(f317(f317(f89(a849),f317(f317(f89(a849),f317(x41011,f317(f244(x41012,x41013),x41014))),f317(x41015,f317(f246(x41012,x41013),x41014)))),f317(a124,f2(a849))),f251(x41012,x41013,x41011,x41015,x41014)) % 168.19/168.05 [4290]E(f157(x42901,x42902,f317(f317(f7(x42901,f853(x42902),f853(x42902)),f317(f317(f18(x42901,f853(x42902),f858(f853(x42902),f853(x42902))),f317(f317(f8(a842,f858(f853(x42902),f858(f853(x42902),f853(x42902))),x42901),f108(f853(x42902))),x42903)),f317(f317(f8(x42902,f853(x42902),x42901),f217(x42902)),x42904))),f191(x42902)),x42905),f317(f317(f148(x42901,x42902),x42904),f317(f130(x42901,x42903),x42905))) % 168.19/168.05 [4496]~E(f317(f317(f317(f81(x44961,f853(x44962)),x44963),x44964),f317(f217(x44962),x44965)),f317(f16(f853(x44962),x44961),f191(x44962))) % 168.19/168.05 [3595]E(f317(f317(f167(x35951),x35952),f317(f317(f148(x35953,x35951),x35954),x35955)),f317(f317(f148(x35953,x35951),x35954),f317(f317(f167(x35953),x35952),x35955))) % 168.19/168.05 [3596]E(f317(f317(f132(x35961),x35962),f317(f317(f148(x35963,x35961),x35964),x35965)),f317(f317(f148(x35963,x35961),x35964),f317(f317(f132(x35963),x35962),x35965))) % 168.19/168.05 [3627]E(f317(f317(f148(x36271,x36272),x36273),f317(f317(f145(x36271),x36274),x36275)),f317(f317(f145(x36272),f317(x36273,x36274)),f317(f317(f148(x36271,x36272),x36273),x36275))) % 168.19/168.05 [3685]E(f317(f287(x36851,x36852,x36853),f317(f317(f286(x36851),x36854),x36855)),f317(f317(f286(x36852),f317(x36853,x36854)),f317(f287(x36851,x36852,x36853),x36855))) % 168.19/168.05 [3753]E(f317(f317(f175(x37531,x37532),f317(f317(f167(x37531),x37533),x37534)),f317(f317(f167(x37532),x37533),x37535)),f317(f317(f167(f857(x37531,x37532)),x37533),f317(f317(f175(x37531,x37532),x37534),x37535))) % 168.19/168.05 [3754]E(f317(f317(f175(x37541,x37542),f317(f317(f132(x37541),x37543),x37544)),f317(f317(f132(x37542),x37543),x37545)),f317(f317(f132(f857(x37541,x37542)),x37543),f317(f317(f175(x37541,x37542),x37544),x37545))) % 168.19/168.05 [3769]E(f317(f317(f153(x37691,f317(f317(f145(x37691),x37692),x37693)),f317(a124,x37694)),x37695),f317(f317(f145(x37691),x37692),f317(f317(f153(x37691,x37693),x37694),x37695))) % 168.19/168.05 [3772]E(f317(f220(f853(x37721),x37722,f191(x37721),x37723),f317(f317(f16(f853(x37722),x37724),f191(x37722)),x37725)),f191(x37721)) % 168.19/168.05 [3774]E(f317(f317(f127(x37741),f317(f317(f148(x37742,x37741),x37743),x37744)),f317(f317(f148(x37742,x37741),x37743),x37745)),f317(f317(f148(x37742,x37741),x37743),f317(f317(f127(x37742),x37744),x37745))) % 168.19/168.05 [3779]E(f317(f317(x37791,x37792),f317(f317(f239(x37793,x37794,x37791),x37792),x37795)),f317(f317(f239(x37793,x37794,x37791),x37792),f317(a124,x37795))) % 168.19/168.05 [3807]E(f158(x38071,x38072,x38073,f317(f317(f145(x38071),x38074),x38075)),f317(f317(f127(x38072),f317(x38073,x38074)),f158(x38071,x38072,x38073,x38075))) % 168.19/168.05 [3819]E(f317(f317(f265(x38191,x38192,x38193),f317(f263(x38192,x38191),x38194)),f317(f263(x38193,x38192),x38195)),f317(f263(x38193,x38191),f317(f317(f265(x38193,x38192,x38191),x38195),x38194))) % 168.19/168.05 [3853]E(f317(f317(f317(f182(f850(x38531),f850(x38531)),x38532),f162(x38531)),f317(f317(f148(x38533,x38531),x38534),x38535)),f317(f317(f148(x38533,x38531),x38534),f317(f317(f317(f182(f850(x38533),f850(x38533)),x38532),f162(x38533)),x38535))) % 168.19/168.05 [3854]E(f317(f317(f249(x38541,x38542,x38541,x38543),f317(f237(x38542,x38541),x38544)),x38545),f317(x38545,x38544)) % 168.19/168.05 [3882]E(f149(x38821,x38822,f317(f317(f148(x38823,x38821),x38824),x38825)),f149(x38823,f317(f82(x38821,a849,x38823,x38822),x38824),x38825)) % 168.19/168.05 [3945]E(f317(f317(f82(f853(x39451),f853(x39452),x39453,f317(f192(x39451,x39452),x39454)),f317(f16(f853(x39451),x39453),f191(x39451))),x39455),f191(x39452)) % 168.19/168.05 [3946]E(f170(f857(x39461,x39462),f317(f82(x39462,a842,f857(x39461,x39462),x39463),f246(x39461,x39462)),f317(f317(f175(x39461,x39462),x39464),x39465)),f317(f317(f175(x39461,x39462),x39464),f170(x39462,x39463,x39465))) % 168.19/168.05 [3951]E(f317(f287(x39511,x39512,f317(f317(f8(x39513,x39512,x39511),x39514),x39515)),f233(f858(x39511,a842))),f317(f287(x39513,x39512,x39514),f317(f287(x39511,x39513,x39515),f233(f858(x39511,a842))))) % 168.19/168.05 [3964]E(f170(f857(x39641,x39642),f317(f82(x39641,a842,f857(x39641,x39642),x39643),f244(x39641,x39642)),f317(f317(f175(x39641,x39642),x39644),x39645)),f317(f317(f175(x39641,x39642),f170(x39641,x39643,x39644)),x39645)) % 168.19/168.05 [3985]E(f317(f317(f122(f858(x39851,a842)),f317(f289(x39851,x39852,x39853),f317(f317(f286(x39852),x39854),f188(f858(x39852,a842))))),f317(f289(x39851,x39852,x39853),x39855)),f317(f289(x39851,x39852,x39853),f317(f317(f286(x39852),x39854),x39855))) % 168.19/168.05 [4046]E(f317(f317(f127(f857(x40461,x40462)),f317(f317(f148(x40462,f857(x40461,x40462)),f317(f237(x40461,x40462),x40463)),x40464)),f69(x40461,x40462,x40465,x40464)),f69(x40461,x40462,f317(f317(f145(x40461),x40463),x40465),x40464)) % 168.19/168.05 [4047]E(f317(f317(f148(x40471,x40472),x40473),f170(x40471,f317(f82(x40472,a842,x40471,x40474),x40473),x40475)),f170(x40472,x40474,f317(f317(f148(x40471,x40472),x40473),x40475))) % 168.19/168.05 [4056]E(f317(f136(x40561,x40562,f317(f7(x40562,x40561,x40561),f317(f7(x40561,x40562,x40561),x40563)),x40564),f317(f163(x40562),f317(f163(x40562),x40565))),f317(f136(x40561,x40562,x40563,x40564),x40565)) % 168.19/168.05 [4057]E(f317(f317(f317(f81(x40571,f853(x40572)),f181(x40571,x40572,x40573,x40574)),x40575),f317(x40573,x40575)),f181(x40571,x40572,x40573,f317(f317(f286(x40571),x40575),x40574))) % 168.19/168.05 [4067]E(f317(f303(x40671,x40672,x40673,f317(f16(x40672,x40671),x40674),f317(f16(x40672,x40673),x40674)),x40675),x40674) % 168.19/168.05 [4124]E(f317(f220(f850(x41241),x41241,f157(x41242,x41241,x41243,x41244),f317(f317(f7(x41241,f850(x41241),f850(x41241)),f145(x41241)),f157(x41242,x41241,x41243,x41244))),f317(x41243,x41245)),f157(x41242,x41241,x41243,f317(f317(f145(x41242),x41245),x41244))) % 168.19/168.05 [4163]P22(f317(f317(f225(f858(x41631,a842)),f317(f287(x41632,x41631,x41633),f317(f317(f113(f858(x41632,a842)),x41634),x41635))),f317(f317(f113(f858(x41631,a842)),f317(f287(x41632,x41631,x41633),x41634)),f317(f287(x41632,x41631,x41633),x41635)))) % 168.19/168.05 [4164]P22(f317(f317(f225(f858(x41641,a842)),f317(f262(x41642,x41641,x41643),f317(f317(f113(f858(x41642,a842)),x41644),x41645))),f317(f317(f113(f858(x41641,a842)),f317(f262(x41642,x41641,x41643),x41644)),f317(f262(x41642,x41641,x41643),x41645)))) % 168.19/168.05 [4266]E(f317(f246(x42661,x42662),f317(f248(x42663,x42661,x42662,x42662,x42664,f39(x42662)),x42665)),f317(f246(x42663,x42662),x42665)) % 168.19/168.05 [4267]E(f317(f244(x42671,x42672),f317(f248(x42671,x42671,x42673,x42672,f39(x42671),x42674),x42675)),f317(f244(x42671,x42673),x42675)) % 168.19/168.05 [4345]P18(x43451,x43452,f317(f317(f286(f848(x43451)),f317(f317(f317(f100(x43451),f317(f317(f7(x43451,f858(a845,a845),f858(a845,a842)),f317(f317(f8(f858(a845,a842),f858(f858(a845,a845),f858(a845,a842)),x43451),f8(a845,a842,a845)),x43453)),f317(f317(f18(a845,a849,a845),f317(f317(f7(a845,a844,f858(a849,a845)),a200),x43454)),x43455))),f30(x43454,x43455)),x43453)),f188(f858(f848(x43451),a842)))) % 168.19/168.05 [4347]E(f317(f136(f858(x43471,f853(x43472)),f857(x43471,x43472),f317(f317(f8(f858(x43471,f858(x43472,f858(x43471,f853(x43472)))),f858(f857(x43471,x43472),f858(x43471,f853(x43472))),f858(x43471,f853(x43472))),f247(x43471,x43472,f858(x43471,f853(x43472)))),f317(f317(f7(f858(x43471,f853(x43472)),f858(x43472,f853(x43472)),f858(x43471,f858(x43472,f858(x43471,f853(x43472))))),f317(f317(f8(f858(x43471,f858(f858(x43472,f853(x43472)),f858(x43472,f858(x43471,f853(x43472))))),f858(f858(x43472,f853(x43472)),f858(x43471,f858(x43472,f858(x43471,f853(x43472))))),f858(x43471,f853(x43472))),f7(x43471,f858(x43472,f853(x43472)),f858(x43472,f858(x43471,f853(x43472))))),f317(f317(f8(f858(x43471,f858(f853(x43472),f858(x43471,f853(x43472)))),f858(x43471,f858(f858(x43472,f853(x43472)),f858(x43472,f858(x43471,f853(x43472))))),f858(x43471,f853(x43472))),f317(f8(f858(f853(x43472),f858(x43471,f853(x43472))),f858(f858(x43472,f853(x43472)),f858(x43472,f858(x43471,f853(x43472)))),x43471),f8(f853(x43472),f858(x43471,f853(x43472)),x43472))),f81(x43471,f853(x43472))))),f217(x43472))),x43473),f317(f317(f175(x43471,x43472),x43474),x43475)),f180(x43471,x43472,x43473,x43474,x43475)) % 168.19/168.05 [4349]P18(x43491,x43492,f317(f317(f286(f848(x43491)),f317(f317(f317(f100(x43491),f317(f317(f7(x43491,f858(a845,a842),f858(a845,a842)),f317(f317(f8(f858(a845,f858(a842,a842)),f858(f858(a845,a842),f858(a845,a842)),x43491),f18(a845,a842,a842)),f317(f317(f8(f858(a845,a842),f858(a845,f858(a842,a842)),x43491),f317(f8(a842,f858(a842,a842),a845),a315)),x43493))),f317(f317(f8(a842,a842,a845),a312),x43494))),f35(x43494,x43495)),x43493)),f188(f858(f848(x43491),a842)))) % 168.19/168.05 [3486]E(f105(x34861,x34862,f317(f317(f317(f100(x34861),x34863),x34864),x34865)),f2(a849)) % 168.19/168.05 [3580]E(f317(f317(f317(f317(f81(x35801,x35802),x35803),x35804),x35805),x35804),x35805) % 168.19/168.05 [3808]E(f317(f317(f51(x38081,f858(x38082,a842)),f317(f317(f286(x38081),x38083),x38084)),x38085),f317(f317(f122(f858(x38082,a842)),f317(x38085,x38083)),f317(f317(f51(x38081,f858(x38082,a842)),x38084),x38085))) % 168.19/168.05 [3809]E(f317(f317(f52(x38091,f858(x38092,a842)),f317(f317(f286(x38091),x38093),x38094)),x38095),f317(f317(f113(f858(x38092,a842)),f317(x38095,x38093)),f317(f317(f52(x38091,f858(x38092,a842)),x38094),x38095))) % 168.19/168.05 [3875]E(f317(f317(f122(f858(x38751,a842)),f317(f287(x38752,x38751,x38753),x38754)),f317(f287(x38752,x38751,x38753),x38755)),f317(f287(x38752,x38751,x38753),f317(f317(f122(f858(x38752,a842)),x38754),x38755))) % 168.19/168.05 [3876]E(f317(f317(f21(f858(x38761,a842)),f317(f289(x38761,x38762,x38763),x38764)),f317(f289(x38761,x38762,x38763),x38765)),f317(f289(x38761,x38762,x38763),f317(f317(f21(f858(x38762,a842)),x38764),x38765))) % 168.19/168.05 [3877]E(f317(f317(f122(f858(x38771,a842)),f317(f289(x38771,x38772,x38773),x38774)),f317(f289(x38771,x38772,x38773),x38775)),f317(f289(x38771,x38772,x38773),f317(f317(f122(f858(x38772,a842)),x38774),x38775))) % 168.19/168.05 [3878]E(f317(f317(f113(f858(x38781,a842)),f317(f289(x38781,x38782,x38783),x38784)),f317(f289(x38781,x38782,x38783),x38785)),f317(f289(x38781,x38782,x38783),f317(f317(f113(f858(x38782,a842)),x38784),x38785))) % 168.19/168.05 [3879]E(f317(f317(f122(f858(x38791,a842)),f317(f262(x38792,x38791,x38793),x38794)),f317(f262(x38792,x38791,x38793),x38795)),f317(f262(x38792,x38791,x38793),f317(f317(f122(f858(x38792,a842)),x38794),x38795))) % 168.19/168.05 [3881]E(f181(x38811,x38812,f181(x38811,x38812,x38813,x38814),x38815),f181(x38811,x38812,x38813,f317(f317(f113(f858(x38811,a842)),x38814),x38815))) % 168.19/168.05 [3942]E(f317(f317(f153(x39421,f317(f317(f127(x39421),x39422),f317(f317(f145(x39421),x39423),x39424))),f317(f189(f850(x39421)),x39422)),x39425),f317(f317(f127(x39421),x39422),f317(f317(f145(x39421),x39425),x39424))) % 168.19/168.05 [3949]E(f317(f317(f52(x39491,f858(x39492,a842)),x39493),f317(f317(f8(f858(x39492,a842),f858(x39492,a842),x39491),f317(f286(x39492),x39494)),x39495)),f317(f317(f286(x39492),x39494),f317(f317(f52(x39491,f858(x39492,a842)),x39493),x39495))) % 168.19/168.05 [4020]E(f181(x40201,x40202,f317(f317(f317(f81(x40201,f853(x40202)),x40203),x40204),f317(f217(x40202),x40205)),f317(f88(f858(x40201,a842)),f317(f317(f286(x40201),x40204),f188(f858(x40201,a842))))),f181(x40201,x40202,x40203,f317(f88(f858(x40201,a842)),f317(f317(f286(x40201),x40204),f188(f858(x40201,a842)))))) % 168.19/168.05 [4114]E(f317(f317(f148(x41141,x41142),x41143),f317(f130(x41141,f317(f82(x41142,a842,x41141,x41144),x41143)),x41145)),f317(f130(x41142,x41144),f317(f317(f148(x41141,x41142),x41143),x41145))) % 168.19/168.05 [4118]E(f317(f189(f850(x41181)),f317(f130(x41181,x41182),f317(f317(f148(x41183,x41181),x41184),x41185))),f317(f189(f850(x41183)),f317(f130(x41183,f317(f82(x41181,a842,x41183,x41182),x41184)),x41185))) % 168.19/168.05 [4258]E(f317(f317(f122(f858(x42581,a842)),f317(f317(f21(f858(x42581,a842)),f177(x42581,x42582,x42583)),f317(f230(x42581),f317(f317(f7(x42581,f858(x42581,a842),a842),f319(x42581)),f317(f317(f21(f858(x42581,a842)),x42584),f177(x42581,x42582,x42585)))))),f317(f230(x42581),f317(f317(f7(x42581,f858(x42581,a842),a842),f319(x42581)),f317(f317(f113(f858(x42581,a842)),x42584),f177(x42581,x42582,x42585))))),f177(x42581,x42582,f85(x42581,f853(x42582),x42583,x42585,x42584))) % 168.19/168.05 [4326]E(f317(f150(f850(f857(x43261,x43262)),x43262,f125(f857(x43261,x43262)),f317(f317(f7(x43262,f858(f850(x43262),f850(f857(x43261,x43262))),f858(f850(x43262),f850(f857(x43261,x43262)))),f317(f317(f8(f858(f850(f857(x43261,x43262)),f850(f857(x43261,x43262))),f858(f858(f850(x43262),f850(f857(x43261,x43262))),f858(f850(x43262),f850(f857(x43261,x43262)))),x43262),f8(f850(f857(x43261,x43262)),f850(f857(x43261,x43262)),f850(x43262))),f317(f317(f8(f857(x43261,x43262),f858(f850(f857(x43261,x43262)),f850(f857(x43261,x43262))),x43262),f145(f857(x43261,x43262))),f317(f237(x43261,x43262),x43263)))),f317(f175(x43261,x43262),x43264))),x43265),f317(f317(f175(x43261,x43262),f317(f317(f145(x43261),x43263),x43264)),x43265)) % 168.19/168.05 [3803]E(f317(f317(f153(x38031,f317(f317(f153(x38031,x38032),x38033),x38034)),x38033),x38035),f317(f317(f153(x38031,x38032),x38033),x38035)) % 168.19/168.05 [3855]E(f317(f234(x38551,x38552),f317(f317(f286(f857(x38551,x38552)),f317(f317(f237(x38551,x38552),x38553),x38554)),x38555)),f317(f317(f286(x38552),x38554),f317(f234(x38551,x38552),x38555))) % 168.19/168.05 [3856]E(f317(f236(x38561,x38562),f317(f317(f286(f857(x38561,x38562)),f317(f317(f237(x38561,x38562),x38563),x38564)),x38565)),f317(f317(f286(x38561),x38563),f317(f236(x38561,x38562),x38565))) % 168.19/168.05 [3935]E(f317(f317(f21(f858(f857(x39351,x39352),a842)),f317(f317(f245(x39351,x39352),x39353),x39354)),f317(f317(f245(x39351,x39352),x39355),x39354)),f317(f317(f245(x39351,x39352),f317(f317(f21(f858(x39351,a842)),x39353),x39355)),x39354)) % 168.19/168.05 [3936]E(f317(f317(f122(f858(f857(x39361,x39362),a842)),f317(f317(f245(x39361,x39362),x39363),x39364)),f317(f317(f245(x39361,x39362),x39365),x39364)),f317(f317(f245(x39361,x39362),f317(f317(f122(f858(x39361,a842)),x39363),x39365)),x39364)) % 168.19/168.05 [3937]E(f317(f317(f113(f858(f857(x39371,x39372),a842)),f317(f317(f245(x39371,x39372),x39373),x39374)),f317(f317(f245(x39371,x39372),x39375),x39374)),f317(f317(f245(x39371,x39372),f317(f317(f113(f858(x39371,a842)),x39373),x39375)),x39374)) % 168.19/168.05 [4000]E(f317(f317(f122(f858(x40001,a842)),f317(f317(f51(x40002,f858(x40001,a842)),x40003),x40004)),f317(f317(f51(x40002,f858(x40001,a842)),x40005),x40004)),f317(f317(f51(x40002,f858(x40001,a842)),f317(f317(f122(f858(x40002,a842)),x40003),x40005)),x40004)) % 168.19/168.05 [4001]E(f317(f317(f113(f858(x40011,a842)),f317(f317(f52(x40012,f858(x40011,a842)),x40013),x40014)),f317(f317(f52(x40012,f858(x40011,a842)),x40015),x40014)),f317(f317(f52(x40012,f858(x40011,a842)),f317(f317(f122(f858(x40012,a842)),x40013),x40015)),x40014)) % 168.19/168.05 [4015]E(f317(f317(f51(x40151,f858(x40152,a842)),x40153),f317(f317(f8(f858(x40152,a842),f858(x40152,a842),x40151),f317(f21(f858(x40152,a842)),x40154)),x40155)),f317(f317(f21(f858(x40152,a842)),x40154),f317(f317(f52(x40151,f858(x40152,a842)),x40153),x40155))) % 168.19/168.05 [4016]E(f317(f317(f51(x40161,f858(x40162,a842)),x40163),f317(f317(f8(f858(x40162,a842),f858(x40162,a842),x40161),f317(f113(f858(x40162,a842)),x40164)),x40165)),f317(f317(f113(f858(x40162,a842)),x40164),f317(f317(f51(x40161,f858(x40162,a842)),x40163),x40165))) % 168.19/168.05 [4017]E(f317(f317(f52(x40171,f858(x40172,a842)),x40173),f317(f317(f8(f858(x40172,a842),f858(x40172,a842),x40171),f317(f122(f858(x40172,a842)),x40174)),x40175)),f317(f317(f122(f858(x40172,a842)),x40174),f317(f317(f52(x40171,f858(x40172,a842)),x40173),x40175))) % 168.19/168.05 [4054]E(f178(x40541,x40542,x40543,f317(f171(x40541,x40542),f317(f163(f857(x40541,x40542)),f317(f317(f175(x40541,x40542),x40544),x40545)))),f180(x40541,x40542,x40543,x40544,x40545)) % 168.19/168.05 [4078]E(f184(f850(x40781),f317(f317(f145(x40781),x40782),x40783),f317(f317(f8(f850(x40781),f850(x40781),a849),f317(f145(x40781),x40784)),f317(f317(f7(a849,x40781,f850(x40781)),f153(x40781,x40783)),x40782)),x40785),f317(f317(f153(x40781,f317(f317(f145(x40781),x40784),x40783)),x40785),x40782)) % 168.19/168.05 [4082]E(f317(f317(f51(x40821,f858(f857(x40822,x40823),a842)),x40824),f317(f317(f8(f858(f857(x40823,x40822),a842),f858(f857(x40822,x40823),a842),x40821),f263(x40823,x40822)),x40825)),f317(f263(x40823,x40822),f317(f317(f51(x40821,f858(f857(x40823,x40822),a842)),x40824),x40825))) % 168.19/168.05 [4083]E(f317(f317(f52(x40831,f858(f857(x40832,x40833),a842)),x40834),f317(f317(f8(f858(f857(x40833,x40832),a842),f858(f857(x40832,x40833),a842),x40831),f263(x40833,x40832)),x40835)),f317(f263(x40833,x40832),f317(f317(f52(x40831,f858(f857(x40833,x40832),a842)),x40834),x40835))) % 168.19/168.05 [4135]E(f177(x41351,x41352,f317(f317(f18(x41351,f853(x41353),f853(x41352)),f317(f317(f8(f858(x41353,x41352),f858(f853(x41353),f853(x41352)),x41351),f192(x41353,x41352)),x41354)),x41355)),f177(x41351,x41353,x41355)) % 168.19/168.05 [4190]P22(f317(f317(f225(f858(x41901,a842)),f317(f317(f21(f858(x41901,a842)),f317(f287(x41902,x41901,x41903),x41904)),f317(f287(x41902,x41901,x41903),x41905))),f317(f287(x41902,x41901,x41903),f317(f317(f21(f858(x41902,a842)),x41904),x41905)))) % 168.19/168.05 [4330]E(f317(f150(f850(f857(x43301,x43302)),x43301,f125(f857(x43301,x43302)),f317(f317(f7(x43301,f858(f850(x43301),f850(f857(x43301,x43302))),f858(f850(x43301),f850(f857(x43301,x43302)))),f317(f317(f8(f858(f850(f857(x43301,x43302)),f850(f857(x43301,x43302))),f858(f858(f850(x43301),f850(f857(x43301,x43302))),f858(f850(x43301),f850(f857(x43301,x43302)))),x43301),f8(f850(f857(x43301,x43302)),f850(f857(x43301,x43302)),f850(x43301))),f317(f317(f8(f857(x43301,x43302),f858(f850(f857(x43301,x43302)),f850(f857(x43301,x43302))),x43301),f145(f857(x43301,x43302))),f317(f317(f7(x43301,x43302,f857(x43301,x43302)),f237(x43301,x43302)),x43303)))),f317(f317(f7(f850(x43301),f850(x43302),f850(f857(x43301,x43302))),f175(x43301,x43302)),x43304))),x43305),f317(f317(f175(x43301,x43302),x43305),f317(f317(f145(x43302),x43303),x43304))) % 168.19/168.05 [4040]E(f317(f317(f122(f858(x40401,a842)),f317(f262(x40402,x40401,x40403),x40404)),f317(f262(x40402,x40401,x40405),x40404)),f317(f262(x40402,x40401,f317(f317(f122(f858(f857(x40402,x40401),a842)),x40403),x40405)),x40404)) % 168.19/168.05 [4085]E(f317(f317(f127(f857(x40851,x40852)),f317(f317(f175(x40851,x40852),x40853),f317(f317(f167(x40852),f317(f189(f850(x40851)),x40853)),x40854))),f317(f317(f175(x40851,x40852),x40855),f317(f317(f132(x40852),f317(f189(f850(x40851)),x40853)),x40854))),f317(f317(f175(x40851,x40852),f317(f317(f127(x40851),x40853),x40855)),x40854)) % 168.19/168.05 [4193]E(f317(f317(f245(x41931,x41932),x41933),f317(f317(f18(x41931,f858(x41932,a842),f858(x41932,a842)),f317(f317(f8(f858(x41932,a842),f858(f858(x41932,a842),f858(x41932,a842)),x41931),f21(f858(x41932,a842))),x41934)),x41935)),f317(f317(f21(f858(f857(x41931,x41932),a842)),f317(f317(f245(x41931,x41932),x41933),x41934)),f317(f317(f245(x41931,x41932),x41933),x41935))) % 168.19/168.05 [4194]E(f317(f317(f245(x41941,x41942),x41943),f317(f317(f18(x41941,f858(x41942,a842),f858(x41942,a842)),f317(f317(f8(f858(x41942,a842),f858(f858(x41942,a842),f858(x41942,a842)),x41941),f122(f858(x41942,a842))),x41944)),x41945)),f317(f317(f122(f858(f857(x41941,x41942),a842)),f317(f317(f245(x41941,x41942),x41943),x41944)),f317(f317(f245(x41941,x41942),x41943),x41945))) % 168.19/168.05 [4195]E(f317(f317(f245(x41951,x41952),x41953),f317(f317(f18(x41951,f858(x41952,a842),f858(x41952,a842)),f317(f317(f8(f858(x41952,a842),f858(f858(x41952,a842),f858(x41952,a842)),x41951),f113(f858(x41952,a842))),x41954)),x41955)),f317(f317(f113(f858(f857(x41951,x41952),a842)),f317(f317(f245(x41951,x41952),x41953),x41954)),f317(f317(f245(x41951,x41952),x41953),x41955))) % 168.19/168.05 [4199]E(f317(f317(f51(x41991,f858(x41992,a842)),x41993),f317(f317(f7(x41991,f858(x41992,a842),f858(x41992,a842)),f317(f317(f8(f858(x41992,a842),f858(f858(x41992,a842),f858(x41992,a842)),x41991),f21(f858(x41992,a842))),x41994)),x41995)),f317(f317(f21(f858(x41992,a842)),f317(f317(f51(x41991,f858(x41992,a842)),x41993),x41994)),x41995)) % 168.19/168.05 [4200]E(f317(f317(f51(x42001,f858(x42002,a842)),x42003),f317(f317(f7(x42001,f858(x42002,a842),f858(x42002,a842)),f317(f317(f8(f858(x42002,a842),f858(f858(x42002,a842),f858(x42002,a842)),x42001),f113(f858(x42002,a842))),x42004)),x42005)),f317(f317(f113(f858(x42002,a842)),f317(f317(f51(x42001,f858(x42002,a842)),x42003),x42004)),x42005)) % 168.19/168.05 [4201]E(f317(f317(f52(x42011,f858(x42012,a842)),x42013),f317(f317(f7(x42011,f858(x42012,a842),f858(x42012,a842)),f317(f317(f8(f858(x42012,a842),f858(f858(x42012,a842),f858(x42012,a842)),x42011),f122(f858(x42012,a842))),x42014)),x42015)),f317(f317(f122(f858(x42012,a842)),f317(f317(f52(x42011,f858(x42012,a842)),x42013),x42014)),x42015)) % 168.19/168.05 [4205]E(f317(f317(f51(x42051,f858(x42052,a842)),x42053),f317(f317(f18(x42051,f858(x42052,a842),f858(x42052,a842)),f317(f317(f8(f858(x42052,a842),f858(f858(x42052,a842),f858(x42052,a842)),x42051),f122(f858(x42052,a842))),x42054)),x42055)),f317(f317(f122(f858(x42052,a842)),f317(f317(f51(x42051,f858(x42052,a842)),x42053),x42054)),f317(f317(f51(x42051,f858(x42052,a842)),x42053),x42055))) % 168.19/168.05 [4206]E(f317(f317(f52(x42061,f858(x42062,a842)),x42063),f317(f317(f18(x42061,f858(x42062,a842),f858(x42062,a842)),f317(f317(f8(f858(x42062,a842),f858(f858(x42062,a842),f858(x42062,a842)),x42061),f113(f858(x42062,a842))),x42064)),x42065)),f317(f317(f113(f858(x42062,a842)),f317(f317(f52(x42061,f858(x42062,a842)),x42063),x42064)),f317(f317(f52(x42061,f858(x42062,a842)),x42063),x42065))) % 168.19/168.05 [4220]E(f317(f317(f51(x42201,f858(x42202,a842)),x42203),f317(f317(f18(x42201,f858(x42202,a842),f858(x42202,a842)),f317(f317(f8(f858(x42202,a842),f858(f858(x42202,a842),f858(x42202,a842)),x42201),f122(f858(x42202,a842))),x42204)),x42205)),f317(f317(f122(f858(x42202,a842)),f49(f858(x42202,a842),f317(f287(x42201,f858(x42202,a842),x42204),x42203))),f49(f858(x42202,a842),f317(f287(x42201,f858(x42202,a842),x42205),x42203)))) % 168.19/168.05 [4221]E(f317(f317(f52(x42211,f858(x42212,a842)),x42213),f317(f317(f18(x42211,f858(x42212,a842),f858(x42212,a842)),f317(f317(f8(f858(x42212,a842),f858(f858(x42212,a842),f858(x42212,a842)),x42211),f113(f858(x42212,a842))),x42214)),x42215)),f317(f317(f113(f858(x42212,a842)),f50(f858(x42212,a842),f317(f287(x42211,f858(x42212,a842),x42214),x42213))),f50(f858(x42212,a842),f317(f287(x42211,f858(x42212,a842),x42215),x42213)))) % 168.19/168.05 [4254]E(f317(f317(f132(x42541),f317(f189(f850(x42541)),f170(x42541,x42542,f317(f317(f148(x42543,x42541),x42544),x42545)))),f317(f317(f148(x42543,x42541),x42544),x42545)),f317(f317(f148(x42543,x42541),x42544),f317(f317(f132(x42543),f317(f189(f850(x42543)),f170(x42543,f317(f82(x42541,a842,x42543,x42542),x42544),x42545))),x42545))) % 168.19/168.05 [4125]E(f317(f317(f127(f857(x41251,x41252)),f317(f317(f175(x41251,x41252),f317(f317(f167(x41251),f317(f189(f850(x41252)),x41253)),x41254)),x41253)),f317(f317(f175(x41251,x41252),f317(f317(f132(x41251),f317(f189(f850(x41252)),x41253)),x41254)),x41255)),f317(f317(f175(x41251,x41252),x41254),f317(f317(f127(x41252),x41253),x41255))) % 168.19/168.05 [4246]E(f94(x42461,f317(f317(f18(x42461,a842,a842),f317(f317(f8(a842,f858(a842,a842),x42461),a315),f317(f317(f7(x42461,f858(x42461,a842),a842),f319(x42461)),x42462))),f317(f317(f7(x42461,x42463,a842),f317(f317(f8(x42463,f858(x42463,a842),x42461),a314),x42464)),x42465))),f317(f86(x42461,x42463,x42462,x42464),x42465)) % 168.19/168.05 [4296]E(f317(f317(f95(a1,x42961),f317(f115(a1),f317(f317(f89(a1),x42962),a109))),f317(f317(f18(a1,x42961,x42961),f317(f317(f7(a1,x42961,f858(x42961,x42961)),f317(f317(f8(a842,f858(x42961,f858(x42961,x42961)),a1),f108(x42961)),a193)),f184(x42961,x42963,x42964,x42965))),f317(f317(f8(a849,x42961,a1),x42964),f317(f317(f7(a1,a849,a849),f317(f317(f8(a849,f858(a849,a849),a1),f89(a849)),a116)),x42965)))),f184(x42961,x42963,x42964,f317(f317(f89(a849),f317(f115(a849),x42962)),x42965))) % 168.19/168.05 [4327]E(f317(f171(x43271,x43272),f317(f317(f148(f857(x43271,x43273),f857(x43271,x43272)),f317(f247(x43271,x43273,f857(x43271,x43272)),f317(f317(f7(x43271,f858(x43273,x43272),f858(x43273,f857(x43271,x43272))),f317(f317(f8(f858(x43272,f857(x43271,x43272)),f858(f858(x43273,x43272),f858(x43273,f857(x43271,x43272))),x43271),f8(x43272,f857(x43271,x43272),x43273)),f237(x43271,x43272))),x43274))),x43275)),f317(f82(f853(x43273),f853(x43272),x43271,f317(f192(x43273,x43272),x43274)),f317(f171(x43271,x43273),x43275))) % 168.19/168.05 [4289]E(f177(x42891,x42892,f317(f317(f18(x42891,f853(x42892),f853(x42892)),f317(f317(f18(x42891,f853(x42892),f858(f853(x42892),f853(x42892))),f317(f317(f8(a842,f858(f853(x42892),f858(f853(x42892),f853(x42892))),x42891),f108(f853(x42892))),x42893)),x42894)),x42895)),f317(f317(f122(f858(x42891,a842)),f317(f317(f113(f858(x42891,a842)),f177(x42891,x42892,x42894)),f317(f230(x42891),x42893))),f317(f317(f113(f858(x42891,a842)),f177(x42891,x42892,x42895)),f317(f230(x42891),f317(f317(f8(a842,a842,x42891),a312),x42893))))) % 168.19/168.05 [4325]E(f317(f317(f95(a1,x43251),f317(f115(a1),f317(f317(f89(a1),x43252),a109))),f317(f317(f18(a1,x43251,x43251),f317(f317(f7(a1,x43251,f858(x43251,x43251)),f317(f317(f8(a842,f858(x43251,f858(x43251,x43251)),a1),f108(x43251)),a193)),f317(f183(x43251,x43253,x43254),x43255))),f317(f317(f18(a1,x43251,x43251),f317(f317(f8(a849,f858(x43251,x43251),a1),x43254),f317(f317(f7(a1,a849,a849),f317(f317(f8(a849,f858(a849,a849),a1),f89(a849)),a116)),x43255))),f317(f317(f8(a849,x43251,a1),f183(x43251,x43253,x43254)),f317(f317(f7(a1,a849,a849),f317(f317(f8(a849,f858(a849,a849),a1),f89(a849)),a116)),x43255))))),f317(f183(x43251,x43253,x43254),f317(f317(f89(a849),f317(f115(a849),x43252)),x43255))) % 168.19/168.05 [4373]E(f317(f230(f857(x43731,x43732)),f317(f247(x43731,x43732,a842),f317(f317(f8(f858(x43732,f858(x43733,a842)),f858(x43732,a842),x43731),f317(f8(f858(x43733,a842),a842,x43732),f96(x43733))),f317(f317(f7(x43731,f858(x43732,f858(x43733,a842)),f858(x43732,f858(x43733,a842))),f317(f317(f8(f858(f858(x43733,a842),f858(x43733,a842)),f858(f858(x43732,f858(x43733,a842)),f858(x43732,f858(x43733,a842))),x43731),f8(f858(x43733,a842),f858(x43733,a842),x43732)),f317(f317(f8(f858(x43733,f858(a842,a842)),f858(f858(x43733,a842),f858(x43733,a842)),x43731),f18(x43733,a842,a842)),f317(f317(f8(f858(x43733,a842),f858(x43733,f858(a842,a842)),x43731),f317(f8(a842,f858(a842,a842),x43733),a315)),f317(f317(f7(x43731,f858(f857(x43731,x43733),a842),f858(x43733,a842)),f317(f317(f8(f858(x43733,f858(f858(f857(x43731,x43733),a842),a842)),f858(f858(f857(x43731,x43733),a842),f858(x43733,a842)),x43731),f7(x43733,f858(f857(x43731,x43733),a842),a842)),f317(f317(f8(f858(x43733,f857(x43731,x43733)),f858(x43733,f858(f858(f857(x43731,x43733),a842),a842)),x43731),f317(f8(f857(x43731,x43733),f858(f858(f857(x43731,x43733),a842),a842),x43733),f319(f857(x43731,x43733)))),f237(x43731,x43733)))),x43734))))),f317(f317(f7(x43732,f858(f857(x43733,x43732),a842),f858(x43733,a842)),f317(f317(f8(f858(x43733,f858(f858(f857(x43733,x43732),a842),a842)),f858(f858(f857(x43733,x43732),a842),f858(x43733,a842)),x43732),f7(x43733,f858(f857(x43733,x43732),a842),a842)),f317(f317(f8(f858(x43733,f857(x43733,x43732)),f858(x43733,f858(f858(f857(x43733,x43732),a842),a842)),x43732),f317(f8(f857(x43733,x43732),f858(f858(f857(x43733,x43732),a842),a842),x43733),f319(f857(x43733,x43732)))),f317(f7(x43733,x43732,f857(x43733,x43732)),f237(x43733,x43732))))),x43735))))),f317(f317(f265(x43731,x43733,x43732),x43734),x43735)) % 168.19/168.05 [4478]~E(f33(x44781,x44782,x44783),f31(x44784,x44785,x44786)) % 168.19/168.05 [4481]~E(f32(x44811,x44812,x44813),f31(x44814,x44815,x44816)) % 168.19/168.05 [4482]~E(f32(x44821,x44822,x44823),f33(x44824,x44825,x44826)) % 168.19/168.05 [3965]E(f212(x39651,x39652,x39653,x39654,f208(x39651,x39652,x39655,x39656)),f317(f317(x39654,x39655),x39656)) % 168.19/168.05 [3966]E(f213(x39661,x39662,x39663,x39664,f208(x39661,x39662,x39665,x39666)),f317(f317(x39664,x39665),x39666)) % 168.19/168.05 [4112]E(f180(x41121,x41122,f178(x41121,x41122,x41123,x41124),x41125,x41126),f178(x41121,x41122,x41123,f180(x41121,x41122,x41124,x41125,x41126))) % 168.19/168.05 [4236]E(f317(f82(f857(x42361,x42362),x42362,f857(x42363,x42364),f246(x42361,x42362)),f248(x42363,x42361,x42364,x42362,x42365,x42366)),f317(f82(x42364,x42362,f857(x42363,x42364),x42366),f246(x42363,x42364))) % 168.19/168.05 [4237]E(f317(f82(f857(x42371,x42372),x42371,f857(x42373,x42374),f244(x42371,x42372)),f248(x42373,x42371,x42374,x42372,x42375,x42376)),f317(f82(x42373,x42371,f857(x42373,x42374),x42375),f244(x42373,x42374))) % 168.19/168.05 [3830]E(f317(f317(f82(x38301,x38302,x38303,x38304),x38305),x38306),f317(x38304,f317(x38305,x38306))) % 168.19/168.05 [4028]E(f214(x40281,x40282,x40283,x40284,f208(x40281,x40282,x40285,x40286)),f317(f317(f89(a849),f317(f317(f89(a849),f317(x40283,x40285)),f317(x40284,x40286))),f317(a124,f2(a849)))) % 168.19/168.05 [4052]E(f317(f303(x40521,x40522,x40523,x40524,x40525),f317(f288(x40521,x40523),x40526)),f317(x40524,x40526)) % 168.19/168.05 [4053]E(f317(f303(x40531,x40532,x40533,x40534,x40535),f317(f297(x40533,x40531),x40536)),f317(x40535,x40536)) % 168.19/168.05 [4148]E(f304(x41481,x41482,x41483,x41484,x41485,f317(f288(x41481,x41483),x41486)),f317(x41484,x41486)) % 168.19/168.05 [4149]E(f304(x41491,x41492,x41493,x41494,x41495,f317(f297(x41493,x41491),x41496)),f317(x41495,x41496)) % 168.19/168.05 [3623]E(f317(f317(f247(x36231,x36232,x36233),x36234),f317(f317(f237(x36231,x36232),x36235),x36236)),f317(f317(x36234,x36235),x36236)) % 168.19/168.05 [3682]E(f317(f317(f317(f8(x36821,x36822,x36823),x36824),x36825),x36826),f317(x36824,f317(x36825,x36826))) % 168.19/168.05 [3683]E(f317(f317(f317(f7(x36831,x36832,x36833),x36834),x36835),x36836),f317(f317(x36834,x36836),x36835)) % 168.19/168.05 [3701]E(f317(f317(f317(f18(x37011,x37012,x37013),x37014),x37015),x37016),f317(f317(x37014,x37016),f317(x37015,x37016))) % 168.19/168.05 [3725]E(f317(f150(x37251,x37252,x37253,x37254),f317(f317(f145(x37252),x37255),x37256)),f317(f317(x37254,x37255),x37256)) % 168.19/168.05 [3834]E(f317(f317(f145(f857(x38341,x38342)),f317(f317(f237(x38341,x38342),x38343),x38344)),f317(f317(f175(x38341,x38342),x38345),x38346)),f317(f317(f175(x38341,x38342),f317(f317(f145(x38341),x38343),x38345)),f317(f317(f145(x38342),x38344),x38346))) % 168.19/168.05 [3836]E(f317(f317(f148(x38361,x38362),x38363),f317(f317(f153(x38361,x38364),x38365),x38366)),f317(f317(f153(x38362,f317(f317(f148(x38361,x38362),x38363),x38364)),x38365),f317(x38363,x38366))) % 168.19/168.05 [3880]E(f317(f136(x38801,x38802,x38803,x38804),f317(f317(f145(x38802),x38805),x38806)),f317(f136(x38801,x38802,x38803,f317(f317(x38803,x38804),x38805)),x38806)) % 168.19/168.05 [3906]E(f250(x39061,x39062,x39063,x39064,f317(f317(f237(x39061,x39062),x39065),x39066)),f317(f317(x39064,x39065),x39066)) % 168.19/168.05 [3991]E(f317(f317(f51(x39911,f858(x39912,a842)),x39913),f317(f82(x39914,f858(x39912,a842),x39911,x39915),x39916)),f317(f317(f51(x39914,f858(x39912,a842)),f317(f287(x39911,x39914,x39916),x39913)),x39915)) % 168.19/168.05 [4043]E(f317(f317(f192(x40431,x40432),x40433),f317(f317(f192(x40434,x40431),x40435),x40436)),f317(f317(f192(x40434,x40432),f317(f82(x40431,x40432,x40434,x40433),x40435)),x40436)) % 168.19/168.05 [4045]E(f317(f317(f148(x40451,x40452),x40453),f317(f317(f148(x40454,x40451),x40455),x40456)),f317(f317(f148(x40454,x40452),f317(f82(x40451,x40452,x40454,x40453),x40455)),x40456)) % 168.19/168.05 [4050]E(f317(f287(x40501,x40502,f317(f82(x40503,x40502,x40501,x40504),x40505)),x40506),f317(f287(x40503,x40502,x40504),f317(f287(x40501,x40503,x40505),x40506))) % 168.19/168.05 [4051]E(f317(f289(x40511,x40512,f317(f82(x40513,x40512,x40511,x40514),x40515)),x40516),f317(f289(x40511,x40513,x40515),f317(f289(x40513,x40512,x40514),x40516))) % 168.19/168.05 [4084]E(f178(x40841,x40842,x40843,f317(f317(f317(f81(x40841,f853(x40842)),x40844),x40845),f317(f217(x40842),x40846))),f317(f317(f317(f81(x40841,f853(x40842)),f178(x40841,x40842,x40843,x40844)),x40845),f317(f217(x40842),x40846))) % 168.19/168.05 [4086]E(f317(f136(x40861,x40862,x40863,f317(f136(x40861,x40862,x40863,x40864),x40865)),x40866),f317(f136(x40861,x40862,x40863,x40864),f317(f317(f127(x40862),x40865),x40866))) % 168.19/168.05 [4226]E(f317(f248(x42261,x42261,x42262,x42263,f39(x42261),x42264),f317(f317(f237(x42261,x42262),x42265),x42266)),f317(f317(f237(x42261,x42263),x42265),f317(x42264,x42266))) % 168.19/168.05 [4227]E(f317(f248(x42271,x42272,x42273,x42273,x42274,f39(x42273)),f317(f317(f237(x42271,x42273),x42275),x42276)),f317(f317(f237(x42272,x42273),f317(x42274,x42275)),x42276)) % 168.19/168.05 [4312]E(f317(f317(f148(f857(x43121,x43122),f857(x43121,x43123)),f317(f247(x43121,x43122,f857(x43121,x43123)),f317(f317(f7(x43121,f858(x43122,x43123),f858(x43122,f857(x43121,x43123))),f317(f317(f8(f858(x43123,f857(x43121,x43123)),f858(f858(x43122,x43123),f858(x43122,f857(x43121,x43123))),x43121),f8(x43123,f857(x43121,x43123),x43122)),f237(x43121,x43123))),x43124))),f317(f317(f175(x43121,x43122),x43125),x43126)),f317(f317(f175(x43121,x43123),x43125),f317(f317(f148(x43122,x43123),x43124),x43126))) % 168.19/168.05 [3688]E(f106(x36881,x36882,x36883,f317(f317(f317(f100(x36881),x36884),x36885),x36886)),f317(f317(f317(x36883,x36884),x36885),x36886)) % 168.19/168.05 [3689]E(f107(x36891,x36892,x36893,f317(f317(f317(f100(x36891),x36894),x36895),x36896)),f317(f317(f317(x36893,x36894),x36895),x36896)) % 168.19/168.05 [3890]E(f317(f317(f82(x38901,x38902,x38903,f317(f16(x38902,x38901),x38904)),x38905),x38906),x38904) % 168.19/168.05 [3926]E(f317(f287(x39261,x39262,x39263),f317(f287(x39264,x39261,x39265),x39266)),f317(f287(x39264,x39262,f317(f317(f8(x39261,x39262,x39264),x39263),x39265)),x39266)) % 168.19/168.05 [3931]E(f317(f317(f51(x39311,f858(x39312,a842)),f317(f287(x39313,x39311,x39314),x39315)),x39316),f317(f317(f51(x39313,f858(x39312,a842)),x39315),f317(f317(f8(x39311,f858(x39312,a842),x39313),x39316),x39314))) % 168.19/168.05 [3932]E(f317(f317(f52(x39321,f858(x39322,a842)),f317(f287(x39323,x39321,x39324),x39325)),x39326),f317(f317(f52(x39323,f858(x39322,a842)),x39325),f317(f317(f8(x39321,f858(x39322,a842),x39323),x39326),x39324))) % 168.19/168.05 [3933]E(f317(f317(f51(x39331,f858(x39332,a842)),x39333),f317(f317(f8(x39334,f858(x39332,a842),x39331),x39335),x39336)),f317(f317(f51(x39334,f858(x39332,a842)),f317(f287(x39331,x39334,x39336),x39333)),x39335)) % 168.19/168.05 [3934]E(f317(f317(f52(x39341,f858(x39342,a842)),x39343),f317(f317(f8(x39344,f858(x39342,a842),x39341),x39345),x39346)),f317(f317(f52(x39344,f858(x39342,a842)),f317(f287(x39341,x39344,x39346),x39343)),x39345)) % 168.19/168.05 [3993]E(f317(f317(f51(x39931,f858(x39932,a842)),x39933),f317(f317(f8(f858(x39934,a842),f858(x39932,a842),x39931),f287(x39934,x39932,x39935)),x39936)),f317(f287(x39934,x39932,x39935),f317(f317(f51(x39931,f858(x39934,a842)),x39933),x39936))) % 168.19/168.05 [3994]E(f317(f317(f51(x39941,f858(x39942,a842)),x39943),f317(f317(f8(f858(x39944,a842),f858(x39942,a842),x39941),f289(x39942,x39944,x39945)),x39946)),f317(f289(x39942,x39944,x39945),f317(f317(f51(x39941,f858(x39944,a842)),x39943),x39946))) % 168.19/168.05 [3995]E(f317(f317(f52(x39951,f858(x39952,a842)),x39953),f317(f317(f8(f858(x39954,a842),f858(x39952,a842),x39951),f289(x39952,x39954,x39955)),x39956)),f317(f289(x39952,x39954,x39955),f317(f317(f52(x39951,f858(x39954,a842)),x39953),x39956))) % 168.19/168.05 [3996]E(f317(f317(f51(x39961,f858(x39962,a842)),x39963),f317(f317(f8(f858(x39964,a842),f858(x39962,a842),x39961),f262(x39964,x39962,x39965)),x39966)),f317(f262(x39964,x39962,x39965),f317(f317(f51(x39961,f858(x39964,a842)),x39963),x39966))) % 168.19/168.05 [4093]E(f317(f136(x40931,x40932,f317(f7(x40932,x40931,x40931),x40933),x40934),f317(f163(x40932),f317(f317(f145(x40932),x40935),x40936))),f317(f317(x40933,x40935),f317(f136(x40931,x40932,f317(f7(x40932,x40931,x40931),x40933),x40934),f317(f163(x40932),x40936)))) % 168.19/168.05 [4150]E(f317(f317(f18(f857(x41501,x41502),x41502,x41503),f317(f317(f8(x41504,f858(x41502,x41503),f857(x41501,x41502)),x41505),f317(f317(f8(x41501,x41504,f857(x41501,x41502)),x41506),f244(x41501,x41502)))),f246(x41501,x41502)),f317(f247(x41501,x41502,x41503),f317(f317(f8(x41504,f858(x41502,x41503),x41501),x41505),x41506))) % 168.19/168.05 [4157]E(f317(f136(x41571,x41572,f317(f7(x41572,x41571,x41571),x41573),f317(f136(x41571,x41572,f317(f7(x41572,x41571,x41571),x41573),x41574),f317(f163(x41572),x41575))),f317(f163(x41572),x41576)),f317(f136(x41571,x41572,f317(f7(x41572,x41571,x41571),x41573),x41574),f317(f163(x41572),f317(f317(f127(x41572),x41576),x41575)))) % 168.19/168.05 [4159]E(f317(f317(f148(f857(x41591,x41592),f857(x41593,x41592)),f317(f247(x41591,x41592,f857(x41593,x41592)),f317(f317(f8(x41593,f858(x41592,f857(x41593,x41592)),x41591),f237(x41593,x41592)),x41594))),f317(f317(f175(x41591,x41592),x41595),x41596)),f317(f317(f175(x41593,x41592),f317(f317(f148(x41591,x41593),x41594),x41595)),x41596)) % 168.19/168.05 [4209]P22(f317(f317(f225(f858(x42091,a842)),f317(f262(x42092,x42091,x42093),f317(f317(f52(x42094,f858(x42092,a842)),x42095),x42096))),f317(f317(f52(x42094,f858(x42091,a842)),x42095),f317(f317(f8(f858(x42092,a842),f858(x42091,a842),x42094),f262(x42092,x42091,x42093)),x42096)))) % 168.19/168.05 [4008]E(f317(f317(f175(x40081,x40082),f317(f317(f153(x40081,x40083),x40084),f317(f244(x40081,x40082),x40085))),f317(f317(f153(x40082,x40086),x40084),f317(f246(x40081,x40082),x40085))),f317(f317(f153(f857(x40081,x40082),f317(f317(f175(x40081,x40082),x40083),x40086)),x40084),x40085)) % 168.19/168.05 [4074]E(f317(f317(f122(f858(f857(x40741,x40742),a842)),f317(f317(f265(x40741,x40743,x40742),x40744),x40745)),f317(f317(f265(x40741,x40743,x40742),x40744),x40746)),f317(f317(f265(x40741,x40743,x40742),x40744),f317(f317(f122(f858(f857(x40743,x40742),a842)),x40745),x40746))) % 168.19/168.05 [4171]E(f317(f317(f286(f857(x41711,x41712)),f317(f317(f237(x41711,x41712),x41713),x41714)),f317(f317(f122(f858(f857(x41711,x41712),a842)),f317(f317(f245(x41711,x41712),x41715),f317(f16(f858(x41712,a842),x41711),f317(f317(f286(x41712),x41714),x41716)))),f317(f317(f245(x41711,x41712),f317(f317(f286(x41711),x41713),x41715)),f317(f16(f858(x41712,a842),x41711),x41716)))),f317(f317(f245(x41711,x41712),f317(f317(f286(x41711),x41713),x41715)),f317(f16(f858(x41712,a842),x41711),f317(f317(f286(x41712),x41714),x41716)))) % 168.19/168.05 [4175]E(f317(f317(f196(x41751,x41752),x41753),f317(f317(f7(x41751,f858(x41754,f853(x41752)),f853(x41752)),f317(f317(f8(f853(x41754),f858(f858(x41754,f853(x41752)),f853(x41752)),x41751),f196(x41754,x41752)),x41755)),x41756)),f317(f317(f196(x41754,x41752),f317(f317(f196(x41751,x41754),x41753),x41755)),x41756)) % 168.19/168.05 [4249]E(f317(f317(f113(f858(x42491,a842)),f317(f289(x42491,x42492,f317(f82(f857(x42492,x42493),x42492,x42491,f244(x42492,x42493)),x42494)),x42495)),f317(f289(x42491,x42493,f317(f82(f857(x42492,x42493),x42493,x42491,f246(x42492,x42493)),x42494)),x42496)),f317(f289(x42491,f857(x42492,x42493),x42494),f317(f317(f245(x42492,x42493),x42495),f317(f16(f858(x42493,a842),x42492),x42496)))) % 168.19/168.05 [3990]E(f317(f317(f317(f81(x39901,x39902),f317(f317(f317(f81(x39901,x39902),x39903),x39904),x39905)),x39904),x39906),f317(f317(f317(f81(x39901,x39902),x39903),x39904),x39906)) % 168.19/168.05 [4098]E(f317(f317(f122(f858(f857(x40981,x40982),a842)),f317(f317(f265(x40981,x40983,x40982),x40984),x40985)),f317(f317(f265(x40981,x40983,x40982),x40986),x40985)),f317(f317(f265(x40981,x40983,x40982),f317(f317(f122(f858(f857(x40981,x40983),a842)),x40984),x40986)),x40985)) % 168.19/168.05 [4234]E(f317(f317(f51(x42341,f858(x42342,a842)),x42343),f317(f317(f7(x42341,f858(x42344,f858(x42342,a842)),f858(x42342,a842)),f317(f317(f8(f858(x42344,a842),f858(f858(x42344,f858(x42342,a842)),f858(x42342,a842)),x42341),f51(x42344,f858(x42342,a842))),x42345)),x42346)),f317(f317(f51(x42344,f858(x42342,a842)),f317(f317(f51(x42341,f858(x42344,a842)),x42343),x42345)),x42346)) % 168.19/168.05 [4235]E(f317(f317(f52(x42351,f858(x42352,a842)),x42353),f317(f317(f7(x42351,f858(x42354,f858(x42352,a842)),f858(x42352,a842)),f317(f317(f8(f858(x42354,a842),f858(f858(x42354,f858(x42352,a842)),f858(x42352,a842)),x42351),f52(x42354,f858(x42352,a842))),x42355)),x42356)),f317(f317(f52(x42354,f858(x42352,a842)),f317(f317(f51(x42351,f858(x42354,a842)),x42353),x42355)),x42356)) % 168.19/168.05 [4284]E(f317(f247(x42841,x42842,f857(x42843,x42844)),f317(f317(f7(x42841,f858(x42842,x42844),f858(x42842,f857(x42843,x42844))),f317(f317(f8(f858(x42844,f857(x42843,x42844)),f858(f858(x42842,x42844),f858(x42842,f857(x42843,x42844))),x42841),f8(x42844,f857(x42843,x42844),x42842)),f317(f317(f8(x42843,f858(x42844,f857(x42843,x42844)),x42841),f237(x42843,x42844)),x42845))),x42846)),f248(x42841,x42843,x42842,x42844,x42845,x42846)) % 168.19/168.05 [4208]E(f317(f317(f317(f81(x42081,f853(x42082)),f181(x42081,x42082,x42083,f317(f317(f21(f858(x42081,a842)),x42084),f317(f317(f286(x42081),x42085),f188(f858(x42081,a842)))))),x42085),x42086),f317(f317(f317(f81(x42081,f853(x42082)),f181(x42081,x42082,x42083,x42084)),x42085),x42086)) % 168.19/168.05 [4308]E(f317(f287(x43081,x43082,f317(f317(f18(x43081,x43082,x43082),f317(f317(f18(x43081,x43082,f858(x43082,x43082)),f317(f317(f8(a842,f858(x43082,f858(x43082,x43082)),x43081),f108(x43082)),x43083)),x43084)),x43085)),x43086),f317(f317(f122(f858(x43082,a842)),f317(f287(x43081,x43082,x43084),f317(f317(f113(f858(x43081,a842)),x43086),f317(f230(x43081),x43083)))),f317(f287(x43081,x43082,x43085),f317(f317(f113(f858(x43081,a842)),x43086),f317(f230(x43081),f317(f317(f8(a842,a842,x43081),a312),x43083)))))) % 168.19/168.05 [4317]E(f317(f287(x43171,f857(x43172,x43173),f317(f317(f18(x43171,x43173,f857(x43172,x43173)),f317(f317(f8(x43172,f858(x43173,f857(x43172,x43173)),x43171),f237(x43172,x43173)),x43174)),x43175)),x43176),f317(f317(f245(x43172,x43173),f317(f287(x43171,x43172,x43174),x43176)),f317(f317(f8(f858(x43171,a842),f858(x43173,a842),x43172),f287(x43171,x43173,x43175)),f317(f317(f7(x43172,f858(x43171,a842),f858(x43171,a842)),f317(f317(f8(f858(x43171,a842),f858(f858(x43171,a842),f858(x43171,a842)),x43172),f113(f858(x43171,a842))),f317(f317(f8(f858(x43172,a842),f858(x43171,a842),x43172),f289(x43171,x43172,x43174)),f317(f317(f7(x43172,f858(x43172,a842),f858(x43172,a842)),f286(x43172)),f188(f858(x43172,a842)))))),x43176)))) % 168.19/168.05 [4268]E(f317(f246(x42681,x42682),f317(f248(x42683,x42681,x42684,x42682,x42685,x42686),x42687)),f317(x42686,f317(f246(x42683,x42684),x42687))) % 168.19/168.05 [4269]E(f317(f244(x42691,x42692),f317(f248(x42693,x42691,x42694,x42692,x42695,x42696),x42697)),f317(x42695,f317(f244(x42693,x42694),x42697))) % 168.19/168.05 [3967]E(f317(f317(f175(x39671,x39672),f317(f317(f153(x39671,x39673),x39674),x39675)),f317(f317(f153(x39672,x39676),x39674),x39677)),f317(f317(f153(f857(x39671,x39672),f317(f317(f175(x39671,x39672),x39673),x39676)),x39674),f317(f317(f237(x39671,x39672),x39675),x39677))) % 168.19/168.05 [4037]E(f317(f317(f317(f249(x40371,x40372,x40373,x40374),x40375),x40376),x40377),f317(f317(f247(x40372,x40373,x40374),x40376),f317(x40375,x40377))) % 168.19/168.05 [4049]E(f317(f317(f317(f249(x40491,x40492,x40493,x40494),x40495),x40496),x40497),f317(f317(x40496,f317(f244(x40492,x40493),f317(x40495,x40497))),f317(f246(x40492,x40493),f317(x40495,x40497)))) % 168.19/168.05 [4088]E(f180(x40881,x40882,f317(f317(f317(f81(x40881,f853(x40882)),x40883),x40884),f317(f217(x40882),x40885)),x40886,x40887),f180(x40881,x40882,x40883,f317(f317(f145(x40881),x40884),x40886),f317(f317(f145(x40882),x40885),x40887))) % 168.19/168.05 [4105]E(f317(f82(x41051,x41052,x41053,x41054),f317(f82(x41055,x41051,x41053,x41056),x41057)),f317(f82(x41055,x41052,x41053,f317(f82(x41051,x41052,x41055,x41054),x41056)),x41057)) % 168.19/168.05 [4166]E(f317(f82(f853(x41661),f853(x41662),x41663,f317(f192(x41661,x41662),x41664)),f317(f317(f317(f81(x41663,f853(x41661)),x41665),x41666),f317(f217(x41661),x41667))),f317(f317(f317(f81(x41663,f853(x41662)),f317(f82(f853(x41661),f853(x41662),x41663,f317(f192(x41661,x41662),x41664)),x41665)),x41666),f317(f217(x41662),f317(x41664,x41667)))) % 168.19/168.05 [4291]E(f317(f248(x42911,x42912,x42913,x42913,x42914,f39(x42913)),f317(f248(x42911,x42911,x42915,x42913,f39(x42911),x42916),x42917)),f317(f317(f237(x42912,x42913),f317(x42914,f317(f244(x42911,x42915),x42917))),f317(x42916,f317(f246(x42911,x42915),x42917)))) % 168.19/168.05 [4292]E(f317(f248(x42921,x42921,x42922,x42923,f39(x42921),x42924),f317(f248(x42925,x42921,x42922,x42922,x42926,f39(x42922)),x42927)),f317(f317(f237(x42921,x42923),f317(x42926,f317(f244(x42925,x42922),x42927))),f317(x42924,f317(f246(x42925,x42922),x42927)))) % 168.19/168.05 [4306]E(f317(f248(x43061,x43062,x43063,x43063,x43064,f39(x43063)),f317(f248(x43065,x43061,x43063,x43063,x43066,f39(x43063)),x43067)),f317(f248(x43065,x43062,x43063,x43063,f317(f82(x43061,x43062,x43065,x43064),x43066),f39(x43063)),x43067)) % 168.19/168.05 [4307]E(f317(f248(x43071,x43071,x43072,x43073,f39(x43071),x43074),f317(f248(x43071,x43071,x43075,x43072,f39(x43071),x43076),x43077)),f317(f248(x43071,x43071,x43075,x43073,f39(x43071),f317(f82(x43072,x43073,x43075,x43074),x43076)),x43077)) % 168.19/168.05 [4314]E(f317(f248(x43141,x43142,x43143,x43143,x43144,f39(x43143)),f317(f248(x43141,x43141,x43145,x43143,f39(x43141),x43146),x43147)),f317(f248(x43142,x43142,x43145,x43143,f39(x43142),x43146),f317(f248(x43141,x43142,x43145,x43145,x43144,f39(x43145)),x43147))) % 168.19/168.05 [4005]E(f317(f317(f265(x40051,x40052,x40053),f317(f317(f265(x40051,x40054,x40052),x40055),x40056)),x40057),f317(f317(f265(x40051,x40054,x40053),x40055),f317(f317(f265(x40054,x40052,x40053),x40056),x40057))) % 168.19/168.05 [4079]E(f317(f317(f247(x40791,x40792,x40793),f317(f82(x40794,f858(x40792,x40793),x40791,x40795),x40796)),x40797),f317(f317(x40795,f317(x40796,f317(f244(x40791,x40792),x40797))),f317(f246(x40791,x40792),x40797))) % 168.19/168.05 [4128]E(f317(f82(x41281,x41282,x41283,x41284),f317(f317(f317(f81(x41283,x41281),x41285),x41286),x41287)),f317(f317(f317(f81(x41283,x41282),f317(f82(x41281,x41282,x41283,x41284),x41285)),x41286),f317(x41284,x41287))) % 168.19/168.05 [4162]E(f317(f136(x41621,x41622,f317(f7(x41622,x41621,x41621),x41623),x41624),f317(f163(x41622),f317(f317(f148(x41625,x41622),x41626),x41627))),f317(f136(x41621,x41625,f317(f7(x41625,x41621,x41621),f317(f82(x41622,f858(x41621,x41621),x41625,x41623),x41626)),x41624),f317(f163(x41625),x41627))) % 168.19/168.05 [4167]E(f303(x41671,f853(x41672),x41673,f317(f82(f853(x41674),f853(x41672),x41671,f317(f192(x41674,x41672),x41675)),x41676),f317(f82(f853(x41674),f853(x41672),x41673,f317(f192(x41674,x41672),x41675)),x41677)),f317(f82(f853(x41674),f853(x41672),f856(x41671,x41673),f317(f192(x41674,x41672),x41675)),f303(x41671,f853(x41674),x41673,x41676,x41677))) % 168.19/168.05 [4106]E(f317(f317(f51(x41061,f858(f857(x41062,x41063),a842)),x41064),f317(f317(f8(f858(f857(x41065,x41063),a842),f858(f857(x41062,x41063),a842),x41061),f317(f265(x41062,x41065,x41063),x41066)),x41067)),f317(f317(f265(x41062,x41065,x41063),x41066),f317(f317(f51(x41061,f858(f857(x41065,x41063),a842)),x41064),x41067))) % 168.19/168.05 [4255]E(f317(f317(f51(x42551,f858(f857(x42552,x42553),a842)),x42554),f317(f317(f7(x42551,f858(f857(x42555,x42553),a842),f858(f857(x42552,x42553),a842)),f317(f317(f8(f858(f857(x42552,x42555),a842),f858(f858(f857(x42555,x42553),a842),f858(f857(x42552,x42553),a842)),x42551),f265(x42552,x42555,x42553)),x42556)),x42557)),f317(f317(f265(x42552,x42555,x42553),f317(f317(f51(x42551,f858(f857(x42552,x42555),a842)),x42554),x42556)),x42557)) % 168.19/168.05 [4256]E(f317(f136(x42561,x42562,f317(f317(f7(x42561,f858(x42562,x42563),f858(x42562,x42561)),f317(f317(f8(f858(x42563,x42561),f858(f858(x42562,x42563),f858(x42562,x42561)),x42561),f8(x42563,x42561,x42562)),x42564)),x42565),x42566),x42567),f317(f136(x42561,x42563,x42564,x42566),f317(f317(f148(x42562,x42563),x42565),x42567))) % 168.19/168.05 [4315]E(f317(f317(f52(x43151,f858(x43152,a842)),x43153),f317(f317(f8(f858(x43154,f858(x43152,a842)),f858(x43152,a842),x43151),f317(f52(x43154,f858(x43152,a842)),x43155)),f317(f317(f7(x43151,f858(x43154,f858(x43152,a842)),f858(x43154,f858(x43152,a842))),f317(f317(f8(f858(f858(x43152,a842),f858(x43152,a842)),f858(f858(x43154,f858(x43152,a842)),f858(x43154,f858(x43152,a842))),x43151),f8(f858(x43152,a842),f858(x43152,a842),x43154)),f317(f317(f8(f858(x43152,a842),f858(f858(x43152,a842),f858(x43152,a842)),x43151),f122(f858(x43152,a842))),x43156))),x43157))),f317(f317(f122(f858(x43152,a842)),f317(f317(f52(x43151,f858(x43152,a842)),x43153),x43156)),f317(f317(f52(x43154,f858(x43152,a842)),x43155),x43157))) % 168.19/168.05 [4316]E(f317(f317(f51(x43161,f858(x43162,a842)),x43163),f317(f317(f8(f858(x43164,f858(x43162,a842)),f858(x43162,a842),x43161),f317(f51(x43164,f858(x43162,a842)),x43165)),f317(f317(f7(x43161,f858(x43164,f858(x43162,a842)),f858(x43164,f858(x43162,a842))),f317(f317(f8(f858(f858(x43162,a842),f858(x43162,a842)),f858(f858(x43164,f858(x43162,a842)),f858(x43164,f858(x43162,a842))),x43161),f8(f858(x43162,a842),f858(x43162,a842),x43164)),f317(f317(f8(f858(x43162,a842),f858(f858(x43162,a842),f858(x43162,a842)),x43161),f113(f858(x43162,a842))),x43166))),x43167))),f317(f317(f113(f858(x43162,a842)),f317(f317(f51(x43161,f858(x43162,a842)),x43163),x43166)),f317(f317(f51(x43164,f858(x43162,a842)),x43165),x43167))) % 168.19/168.05 [4228]E(f317(f248(x42281,x42282,x42283,x42284,x42285,x42286),f317(f317(f237(x42281,x42283),x42287),x42288)),f317(f317(f237(x42282,x42284),f317(x42285,x42287)),f317(x42286,x42288))) % 168.19/168.05 [4324]E(f317(f317(f148(f857(x43241,x43242),f857(x43243,x43244)),f317(f247(x43241,x43242,f857(x43243,x43244)),f317(f317(f7(x43241,f858(x43242,x43244),f858(x43242,f857(x43243,x43244))),f317(f317(f8(f858(x43244,f857(x43243,x43244)),f858(f858(x43242,x43244),f858(x43242,f857(x43243,x43244))),x43241),f8(x43244,f857(x43243,x43244),x43242)),f317(f317(f8(x43243,f858(x43244,f857(x43243,x43244)),x43241),f237(x43243,x43244)),x43245))),x43246))),f317(f317(f175(x43241,x43242),x43247),x43248)),f317(f317(f175(x43243,x43244),f317(f317(f148(x43241,x43243),x43245),x43247)),f317(f317(f148(x43242,x43244),x43246),x43248))) % 168.19/168.05 [4328]E(f317(f317(f148(f857(x43281,x43282),x43283),f317(f247(x43281,x43282,x43283),f317(f317(f8(f858(x43282,f857(x43281,x43284)),f858(x43282,x43283),x43281),f317(f8(f857(x43281,x43284),x43283,x43282),x43285)),f317(f317(f7(x43281,f858(x43282,x43284),f858(x43282,f857(x43281,x43284))),f317(f317(f8(f858(x43284,f857(x43281,x43284)),f858(f858(x43282,x43284),f858(x43282,f857(x43281,x43284))),x43281),f8(x43284,f857(x43281,x43284),x43282)),f237(x43281,x43284))),x43286)))),f317(f317(f175(x43281,x43282),x43287),x43288)),f317(f317(f148(f857(x43281,x43284),x43283),x43285),f317(f317(f175(x43281,x43284),x43287),f317(f317(f148(x43282,x43284),x43286),x43288)))) % 168.19/168.05 [4260]E(f317(f317(f148(f857(x42601,x42602),x42603),f317(f247(x42601,x42602,x42603),f317(f317(f8(f858(x42602,f857(x42604,x42602)),f858(x42602,x42603),x42601),f317(f8(f857(x42604,x42602),x42603,x42602),x42605)),f317(f317(f8(x42604,f858(x42602,f857(x42604,x42602)),x42601),f237(x42604,x42602)),x42606)))),f317(f317(f175(x42601,x42602),x42607),x42608)),f317(f317(f148(f857(x42604,x42602),x42603),x42605),f317(f317(f175(x42604,x42602),f317(f317(f148(x42601,x42604),x42606),x42607)),x42608))) % 168.19/168.05 [4219]E(f317(f317(f247(x42191,x42192,x42193),f317(f317(f8(f858(x42192,f857(x42194,x42195)),f858(x42192,x42193),x42191),f317(f8(f857(x42194,x42195),x42193,x42192),f317(f247(x42194,x42195,x42193),x42196))),x42197)),x42198),f317(f317(f247(x42194,x42195,x42193),x42196),f317(f317(f247(x42191,x42192,f857(x42194,x42195)),x42197),x42198))) % 168.19/168.05 [4329]E(f317(f317(f51(f857(x43291,x43292),f858(f857(x43293,x43294),a842)),f317(f317(f245(x43291,x43292),x43295),f317(f16(f858(x43292,a842),x43291),x43296))),f317(f247(x43291,x43292,f858(f857(x43293,x43294),a842)),f317(f317(f7(x43291,f858(x43292,f858(x43293,f858(x43294,a842))),f858(x43292,f858(f857(x43293,x43294),a842))),f317(f317(f8(f858(f858(x43293,f858(x43294,a842)),f858(f857(x43293,x43294),a842)),f858(f858(x43292,f858(x43293,f858(x43294,a842))),f858(x43292,f858(f857(x43293,x43294),a842))),x43291),f8(f858(x43293,f858(x43294,a842)),f858(f857(x43293,x43294),a842),x43292)),f317(f317(f8(f858(x43293,a842),f858(f858(x43293,f858(x43294,a842)),f858(f857(x43293,x43294),a842)),x43291),f245(x43293,x43294)),x43297))),f317(f317(f8(f858(x43294,a842),f858(x43293,f858(x43294,a842)),x43292),f16(f858(x43294,a842),x43293)),x43298)))),f317(f317(f245(x43293,x43294),f317(f317(f51(x43291,f858(x43293,a842)),x43295),x43297)),f317(f16(f858(x43294,a842),x43293),f317(f317(f51(x43292,f858(x43294,a842)),x43296),x43298)))) % 168.19/168.05 [4358]E(f37(x43581,x43582,x43583,x43584,x43585,x43586,x43587,x43588,x43589,a23),x43582) % 168.19/168.05 [4359]E(f38(x43591,x43592,x43593,x43594,x43595,x43596,x43597,x43598,x43599,a23),x43592) % 168.19/168.05 [4273]E(f317(f317(f249(x42731,x42732,x42733,x42734),f317(f317(f249(x42731,x42735,x42736,f857(x42732,x42733)),x42737),x42738)),x42739),f317(f317(f249(x42731,x42735,x42736,x42734),x42737),f317(f317(f7(x42735,f858(x42732,f858(x42733,x42734)),f858(x42736,x42734)),f317(f317(f8(f858(x42736,f857(x42732,x42733)),f858(f858(x42732,f858(x42733,x42734)),f858(x42736,x42734)),x42735),f249(x42736,x42732,x42733,x42734)),x42738)),x42739))) % 168.19/168.05 [4360]E(f37(x43601,x43602,x43603,x43604,x43605,x43606,x43607,x43608,x43609,f317(a29,x436010)),f317(x43608,x436010)) % 168.19/168.05 [4361]E(f38(x43611,x43612,x43613,x43614,x43615,x43616,x43617,x43618,x43619,f317(a29,x436110)),f317(x43618,x436110)) % 168.19/168.05 [4303]E(f317(f82(f857(x43031,x43032),f857(x43033,x43034),f857(x43035,x43036),f248(x43031,x43033,x43032,x43034,x43037,x43038)),f248(x43035,x43031,x43036,x43032,x43039,x430310)),f248(x43035,x43033,x43036,x43034,f317(f82(x43031,x43033,x43035,x43037),x43039),f317(f82(x43032,x43034,x43036,x43038),x430310))) % 168.19/168.05 [4362]E(f37(x43621,x43622,x43623,x43624,x43625,x43626,x43627,x43628,x43629,f36(x436210,x436211)),f317(f317(x43625,x436210),x436211)) % 168.19/168.05 [4363]E(f37(x43631,x43632,x43633,x43634,x43635,x43636,x43637,x43638,x43639,f30(x436310,x436311)),f317(f317(x43633,x436310),x436311)) % 168.19/168.05 [4364]E(f37(x43641,x43642,x43643,x43644,x43645,x43646,x43647,x43648,x43649,f35(x436410,x436411)),f317(f317(x43647,x436410),x436411)) % 168.19/168.05 [4365]E(f38(x43651,x43652,x43653,x43654,x43655,x43656,x43657,x43658,x43659,f30(x436510,x436511)),f317(f317(x43653,x436510),x436511)) % 168.19/168.05 [4371]E(f317(f317(f317(x43711,x43712),x43713),f38(x43714,x43715,x43716,x43717,x43718,x43719,x43711,x437110,x437111,x43713)),f38(x43714,x43715,x43716,x43717,x43718,x43719,x43711,x437110,x437111,f35(x43712,x43713))) % 168.19/168.05 [4375]E(f317(f317(f317(f317(x43751,x43752),x43753),f38(x43754,x43755,x43756,x43757,x43751,x43758,x43759,x437510,x437511,x43752)),f38(x43754,x43755,x43756,x43757,x43751,x43758,x43759,x437510,x437511,x43753)),f38(x43754,x43755,x43756,x43757,x43751,x43758,x43759,x437510,x437511,f36(x43752,x43753))) % 168.19/168.05 [4309]E(f317(f248(x43091,x43092,x43093,x43094,x43095,x43096),f317(f248(x43097,x43091,x43098,x43093,x43099,x430910),x430911)),f317(f248(x43097,x43092,x43098,x43094,f317(f82(x43091,x43092,x43097,x43095),x43099),f317(f82(x43093,x43094,x43098,x43096),x430910)),x430911)) % 168.19/168.05 [4372]E(f317(f317(f317(f317(x43721,x43722),x43723),x43724),f38(x43725,x43726,x43727,x43721,x43728,x43729,x437210,x437211,x437212,x43724)),f38(x43725,x43726,x43727,x43721,x43728,x43729,x437210,x437211,x437212,f32(x43722,x43723,x43724))) % 168.19/168.05 [4376]E(f317(f317(f317(f317(f317(x43761,x43762),x43763),x43764),f38(x43765,x43766,x43767,x43768,x43769,x43761,x437610,x437611,x437612,x43763)),f38(x43765,x43766,x43767,x43768,x43769,x43761,x437610,x437611,x437612,x43764)),f38(x43765,x43766,x43767,x43768,x43769,x43761,x437610,x437611,x437612,f33(x43762,x43763,x43764))) % 168.19/168.05 [4366]E(f37(x43661,x43662,x43663,x43664,x43665,x43666,x43667,x43668,x43669,f31(x436610,x436611,x436612)),f317(f317(f317(x43669,x436610),x436611),x436612)) % 168.19/168.05 [4367]E(f37(x43671,x43672,x43673,x43674,x43675,x43676,x43677,x43678,x43679,f33(x436710,x436711,x436712)),f317(f317(f317(x43676,x436710),x436711),x436712)) % 168.19/168.05 [4368]E(f37(x43681,x43682,x43683,x43684,x43685,x43686,x43687,x43688,x43689,f32(x436810,x436811,x436812)),f317(f317(f317(x43684,x436810),x436811),x436812)) % 168.19/168.05 [4369]E(f38(x43691,x43692,x43693,x43694,x43695,x43696,x43697,x43698,x43699,f31(x436910,x436911,x436912)),f317(f317(f317(x43699,x436910),x436911),x436912)) % 168.19/168.05 [4510]~E(a573,a653)+~P4(a5000) % 168.19/168.05 [4512]~E(f764(x45121),x45121)+~P4(a5000) % 168.19/168.05 [4515]~P56(x45151)+P56(f853(x45151)) % 168.19/168.05 [4516]~P57(x45161)+P57(f853(x45161)) % 168.19/168.05 [4519]~P136(x45191)+~E(f87(x45191),f2(x45191)) % 168.19/168.05 [4521]~E(x45211,f2(a111))+E(f317(a20,x45211),f2(a1)) % 168.19/168.05 [4522]~E(x45221,f2(a1))+E(f91(a1,x45221),f2(a1)) % 168.19/168.05 [4529]~P110(x45291)+P31(x45291,f2(x45291)) % 168.19/168.05 [4531]~P103(x45311)+P29(x45311,f125(x45311)) % 168.19/168.05 [4541]P22(x45411)+P22(f317(a312,x45411)) % 168.19/168.05 [4584]~P110(x45841)+~P31(x45841,f87(x45841)) % 168.19/168.05 [4634]~P22(x46341)+~P22(f317(a312,x46341)) % 168.19/168.05 [4659]E(f317(a116,x46591),f2(a849))+~P22(f317(a193,x46591)) % 168.19/168.05 [4723]~P92(x47231)+P11(x47231,x47231,f122(x47231)) % 168.19/168.05 [4724]~P91(x47241)+P11(x47241,x47241,f90(x47241)) % 168.19/168.05 [4725]~P98(x47251)+P11(x47251,x47251,f113(x47251)) % 168.19/168.05 [4726]~P103(x47261)+P11(x47261,x47261,f223(x47261)) % 168.19/168.05 [4727]~P103(x47271)+P11(x47271,x47271,f224(x47271)) % 168.19/168.05 [4526]~E(x45261,f2(a849))+E(f317(f112(a1),x45261),f2(a1)) % 168.19/168.05 [4534]~P90(x45341)+E(f317(f115(x45341),a92),f2(x45341)) % 168.19/168.05 [4537]~E(f574(x45371),f2(a849))+E(f317(f160(a849),x45371),f2(a849)) % 168.19/168.05 [4538]~P102(x45381)+E(f227(x45381,f225(x45381)),f223(x45381)) % 168.19/168.05 [4539]~P102(x45391)+E(f228(x45391,f225(x45391)),f224(x45391)) % 168.19/168.05 [4540]~P82(x45401)+E(f91(x45401,f2(x45401)),f2(x45401)) % 168.19/168.05 [4549]~P110(x45491)+E(f317(f112(x45491),f2(a849)),f2(x45491)) % 168.19/168.05 [4550]~P110(x45501)+E(f317(f112(x45501),f87(a849)),f87(x45501)) % 168.19/168.05 [4551]~P111(x45511)+E(f317(f114(x45511),f2(a1)),f2(x45511)) % 168.19/168.05 [4552]~P111(x45521)+E(f317(f114(x45521),f87(a1)),f87(x45521)) % 168.19/168.05 [4553]E(x45531,f2(a849))+~E(f317(f112(a1),x45531),f2(a1)) % 168.19/168.05 [4578]~P69(x45781)+E(f317(f88(x45781),f2(x45781)),f2(x45781)) % 168.19/168.05 [4579]~P86(x45791)+E(f317(f88(x45791),f188(x45791)),f233(x45791)) % 168.19/168.05 [4580]~P86(x45801)+E(f317(f88(x45801),f233(x45801)),f188(x45801)) % 168.19/168.05 [4581]~P79(x45811)+E(f317(f84(x45811),f2(x45811)),f2(x45811)) % 168.19/168.05 [4582]~P113(x45821)+E(f317(f84(x45821),f87(x45821)),f87(x45821)) % 168.19/168.05 [4583]~P66(x45831)+E(f317(f160(x45831),f125(x45831)),f2(x45831)) % 168.19/168.05 [4600]E(x46001,f2(a1))+E(f317(f48(a1,x46001),x46001),f87(a1)) % 168.19/168.05 [4605]~P36(x46051)+P39(f317(f166(a1),x46051)) % 168.19/168.05 [4639]~P90(x46391)+E(f317(f88(x46391),f87(x46391)),f317(f115(x46391),a109)) % 168.19/168.05 [4656]~P90(x46561)+P31(x46561,f317(f115(x46561),a92)) % 168.19/168.05 [4675]~P57(x46751)+E(f317(f166(x46751),f65(x46751)),f233(f858(x46751,a842))) % 168.19/168.05 [4685]P36(x46851)+~P39(f317(f166(a1),x46851)) % 168.19/168.05 [4686]~P57(x46861)+P22(f317(f131(x46861),f65(x46861))) % 168.19/168.05 [4728]E(f317(f112(a1),f317(a116,x47281)),x47281)+P22(f317(a193,x47281)) % 168.19/168.05 [4743]~P102(x47431)+E(f101(x47431,x47431,f5(x47431)),f102(x47431)) % 168.19/168.05 [4795]~P106(x47951)+E(f239(x47951,f87(x47951),f90(x47951)),f238(x47951)) % 168.19/168.05 [4825]~P90(x48251)+~P31(x48251,f317(f115(x48251),a109)) % 168.19/168.05 [4835]E(f317(a27,x48351),f191(a843))+P22(f317(a24,f317(a29,x48351))) % 168.19/168.05 [4959]E(f317(f84(a1),x49591),x49591)+P22(f317(f317(f226(a1),x49591),f2(a1))) % 168.19/168.05 [4980]~E(f317(a116,x49801),f2(a849))+P22(f317(f317(f225(a1),x49801),f2(a1))) % 168.19/168.05 [5043]~P22(f317(a193,x50431))+P22(f317(f317(f226(a1),x50431),f2(a1))) % 168.19/168.05 [5083]~P111(x50831)+P22(f317(f317(f319(x50831),f2(x50831)),f121(x50831))) % 168.19/168.05 [5084]~P110(x50841)+P22(f317(f317(f319(x50841),f2(x50841)),f185(x50841))) % 168.19/168.05 [5085]~P111(x50851)+P22(f317(f317(f319(x50851),f87(x50851)),f121(x50851))) % 168.19/168.05 [5086]~P110(x50861)+P22(f317(f317(f319(x50861),f87(x50861)),f185(x50861))) % 168.19/168.05 [5087]~P112(x50871)+P22(f317(f317(f225(x50871),f2(x50871)),f87(x50871))) % 168.19/168.05 [5088]~P112(x50881)+P22(f317(f317(f226(x50881),f2(x50881)),f87(x50881))) % 168.19/168.05 [5091]E(f317(f217(a843),f520(x50911)),f317(a27,x50911))+~P22(f317(a24,f317(a29,x50911))) % 168.19/168.05 [5092]E(f317(f217(a843),f801(x50921)),f317(a27,x50921))+~P22(f317(a24,f317(a29,x50921))) % 168.19/168.05 [5147]E(x51471,f2(a849))+~P22(f317(f317(f225(a849),x51471),f2(a849))) % 168.19/168.05 [5189]E(f317(a116,x51891),f2(a849))+~P22(f317(f317(f225(a1),x51891),f2(a1))) % 168.19/168.05 [5247]P22(f317(a193,x52471))+~P22(f317(f317(f226(a1),x52471),f2(a1))) % 168.19/168.05 [5269]P39(x52691)+~P22(f317(f317(f225(a1),f2(a1)),f799(x52691))) % 168.19/168.05 [5275]E(f317(f84(a1),x52751),f317(f88(a1),x52751))+~P22(f317(f317(f226(a1),x52751),f2(a1))) % 168.19/168.05 [5443]~P112(x54431)+~P22(f317(f317(f225(x54431),f87(x54431)),f2(x54431))) % 168.19/168.05 [5444]~P112(x54441)+~P22(f317(f317(f226(x54441),f87(x54441)),f2(x54441))) % 168.19/168.05 [5454]~E(x54541,f2(a849))+P22(f317(f317(f225(a1),f317(f112(a1),x54541)),f2(a1))) % 168.19/168.05 [5455]~E(x54551,f2(a1))+P22(f317(f317(f226(a1),f317(f84(a1),x54551)),f87(a1))) % 168.19/168.05 [5580]~P66(x55801)+E(f136(x55801,x55801,f89(x55801),f2(x55801)),f160(x55801)) % 168.19/168.05 [5737]~P99(x57371)+P19(a849,x57371,f112(x57371),f233(f858(a849,a842))) % 168.19/168.05 [5936]E(x59361,f2(a849))+~P22(f317(f317(f225(a1),f317(f112(a1),x59361)),f2(a1))) % 168.19/168.05 [5937]E(x59371,f2(a1))+~P22(f317(f317(f226(a1),f317(f84(a1),x59371)),f87(a1))) % 168.19/168.05 [6711]~P22(f317(f317(f226(a1),x67111),f2(a1)))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x67111),x67111)),f2(a1))) % 168.19/168.05 [7255]P22(f317(f317(f226(a1),x72551),f2(a1)))+~P22(f317(f317(f226(a1),f317(f317(f89(a1),x72551),x72551)),f2(a1))) % 168.19/168.05 [7802]E(x78021,f317(a3,f2(a849)))+P22(f317(f317(f226(a849),f317(f317(f21(a849),f317(a19,x78021)),f317(a124,f2(a849)))),f317(a19,x78021))) % 168.19/168.05 [8572]~P22(f317(f317(f226(a1),x85721),f2(a1)))+P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x85721),x85721)),a109)),f2(a1))) % 168.19/168.05 [8658]~P22(f317(f317(f226(a1),x86581),f2(a1)))+P22(f317(f317(f226(a1),f317(f317(f89(a1),f317(f317(f89(a1),f87(a1)),x86581)),x86581)),f2(a1))) % 168.19/168.05 [8976]P22(f317(f317(f226(a1),x89761),f2(a1)))+~P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x89761),x89761)),a109)),f2(a1))) % 168.19/168.05 [9038]P22(f317(f317(f226(a1),x90381),f2(a1)))+~P22(f317(f317(f226(a1),f317(f317(f89(a1),f317(f317(f89(a1),f87(a1)),x90381)),x90381)),f2(a1))) % 168.19/168.05 [4627]~E(a92,x46271)+E(f317(f317(f89(a1),x46271),x46271),a92) % 168.19/168.05 [4628]~E(x46281,a92)+E(f317(f317(f89(a1),x46281),x46281),a92) % 168.19/168.05 [4772]E(x47721,a92)+~E(f317(f317(f89(a1),x47721),x47721),a92) % 168.19/168.05 [4773]E(a92,x47731)+~E(f317(f317(f89(a1),x47731),x47731),a92) % 168.19/168.05 [4785]~P103(x47851)+E(f133(x47851,f188(f858(x47851,a842))),f125(x47851)) % 168.19/168.05 [4786]~P27(x47861)+E(f49(x47861,f188(f858(x47861,a842))),f188(x47861)) % 168.19/168.05 [4787]~P27(x47871)+E(f49(x47871,f233(f858(x47871,a842))),f233(x47871)) % 168.19/168.05 [4788]~P27(x47881)+E(f50(x47881,f188(f858(x47881,a842))),f233(x47881)) % 168.19/168.05 [4789]~P27(x47891)+E(f50(x47891,f233(f858(x47891,a842))),f188(x47891)) % 168.19/168.05 [4920]E(x49201,f2(a849))+P22(f317(f317(f226(a849),f2(a849)),x49201)) % 168.19/168.05 [4938]~P28(x49381)+P22(f317(f317(f225(a1),f2(a1)),x49381)) % 168.19/168.05 [4971]~E(f317(f115(a849),x49711),f2(a849))+P22(f317(f317(f225(a1),x49711),a92)) % 168.19/168.05 [4976]P39(x49761)+P22(f317(f317(f319(a1),f799(x49761)),x49761)) % 168.19/168.05 [4977]E(x49771,f317(a3,f2(a849)))+P22(f317(f317(f225(a111),f87(a111)),x49771)) % 168.19/168.05 [5018]P22(f317(a193,x50181))+P22(f317(f317(f225(a1),f2(a1)),x50181)) % 168.19/168.05 [5065]E(f317(f112(a1),f317(a116,x50651)),f2(a1))+P22(f317(f317(f225(a1),f2(a1)),x50651)) % 168.19/168.05 [5133]E(f317(f112(a1),f317(f115(a849),x51331)),f317(f115(a1),x51331))+P22(f317(a193,f317(f115(a1),x51331))) % 168.19/168.05 [5153]E(f317(f115(a849),x51531),f2(a849))+~P22(f317(a193,f317(f115(a1),x51531))) % 168.19/168.05 [5154]E(f317(f115(a849),x51541),f2(a849))+~P22(f317(f317(f225(a1),x51541),a92)) % 168.19/168.05 [5186]P28(x51861)+~P22(f317(f317(f225(a1),f2(a1)),x51861)) % 168.19/168.05 [5254]E(f317(a124,f802(x52541)),x52541)+~P22(f317(f317(f226(a849),f2(a849)),x52541)) % 168.19/168.05 [5263]E(f317(a124,f317(f115(a849),x52631)),f87(a849))+~P22(f317(a193,f317(f115(a1),x52631))) % 168.19/168.05 [5271]E(f317(f112(a1),f820(x52711)),x52711)+~P22(f317(f317(f226(a1),f2(a1)),x52711)) % 168.19/168.05 [5278]~E(x52781,f317(a3,f2(a849)))+~P22(f317(f317(f225(a111),f87(a111)),x52781)) % 168.19/168.05 [5285]E(f317(f112(a1),f317(f115(a849),x52851)),f2(a1))+~P22(f317(a193,f317(f115(a1),x52851))) % 168.19/168.05 [5308]E(f317(f160(a849),x53081),f2(a849))+P22(f317(f317(f319(a849),f574(x53081)),f317(f166(a849),x53081))) % 168.19/168.05 [5328]E(f317(f112(a1),f317(a116,x53281)),x53281)+~P22(f317(f317(f225(a1),f2(a1)),x53281)) % 168.19/168.05 [5337]~P22(f317(a193,x53371))+~P22(f317(f317(f225(a1),f2(a1)),x53371)) % 168.19/168.05 [5436]E(f317(f317(f89(a849),f87(a849)),f317(f115(a849),x54361)),f87(a849))+~P22(f317(f317(f226(a1),x54361),a92)) % 168.19/168.05 [5496]E(x54961,f2(a849))+~P22(f317(f317(f226(a849),x54961),f317(a124,f2(a849)))) % 168.19/168.05 [5538]E(f317(f317(f89(a849),f317(f115(a849),x55381)),f87(a849)),f87(a849))+~P22(f317(f317(f226(a1),x55381),a92)) % 168.19/168.05 [5539]E(f317(f317(f21(a849),f317(f115(a849),x55391)),f87(a849)),f2(a849))+~P22(f317(f317(f225(a1),x55391),a92)) % 168.19/168.05 [5551]~P39(x55511)+E(f317(f54(a849),f317(f287(a1,a849,a116),x55511)),f317(f54(a1),x55511)) % 168.19/168.05 [5581]~P103(x55811)+E(f227(x55811,f317(f7(x55811,x55811,a842),f225(x55811))),f224(x55811)) % 168.19/168.05 [5582]~P103(x55821)+E(f228(x55821,f317(f7(x55821,x55821,a842),f225(x55821))),f223(x55821)) % 168.19/168.05 [5592]E(f55(a849,f317(a124,f2(a849)),f317(f115(a849),x55921)),f317(a124,f2(a849)))+~P22(f317(a193,f317(f115(a1),x55921))) % 168.19/168.05 [5600]~P22(f317(f317(f226(a1),f2(a1)),x56001))+P22(f317(f317(f225(a1),f87(a1)),x56001)) % 168.19/168.05 [5601]P22(f317(f317(f226(a1),f2(a1)),x56011))+~P22(f317(f317(f225(a1),f87(a1)),x56011)) % 168.19/168.05 [5607]E(f317(a124,f317(f317(f21(a849),x56071),f87(a849))),x56071)+~P22(f317(f317(f226(a849),f2(a849)),x56071)) % 168.19/168.05 [5666]P22(f317(f317(f226(a849),f2(a849)),f820(x56661)))+~P22(f317(f317(f226(a1),f2(a1)),x56661)) % 168.19/168.05 [5719]E(f55(a1,f317(f115(a1),a109),x57191),f317(f317(f21(a1),x57191),f87(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x57191)) % 168.19/168.05 [5748]~P22(f317(f317(f226(a1),a92),x57481))+P22(f317(f317(f226(a849),f2(a849)),f317(f115(a849),x57481))) % 168.19/168.05 [5800]P22(f317(f317(f226(a849),f2(a849)),f317(a116,x58001)))+~P22(f317(f317(f226(a1),f2(a1)),x58001)) % 168.19/168.05 [5848]~P22(f317(f317(f226(a849),f2(a849)),x58481))+P22(f317(f317(f226(a1),f2(a1)),f317(f112(a1),x58481))) % 168.19/168.05 [5886]~P22(f317(f317(f226(a849),f2(a849)),f317(a116,x58861)))+P22(f317(f317(f226(a1),f2(a1)),x58861)) % 168.19/168.05 [5904]~P39(x59041)+E(f317(f287(a849,a1,f112(a1)),f317(f287(a1,a849,a116),x59041)),x59041) % 168.19/168.05 [5917]P22(f317(f317(f226(a1),a92),x59171))+~P22(f317(f317(f226(a849),f2(a849)),f317(f115(a849),x59171))) % 168.19/168.05 [5961]~P57(x59611)+E(f317(f317(f145(f853(x59611)),f191(x59611)),f317(f317(f148(x59611,f853(x59611)),f217(x59611)),f65(x59611))),f65(f853(x59611))) % 168.19/168.05 [5971]P22(f317(f317(f226(a849),f2(a849)),x59711))+~P22(f317(f317(f226(a1),f2(a1)),f317(f112(a1),x59711))) % 168.19/168.05 [6079]E(f317(f287(a849,a1,f112(a1)),f317(f231(a849),f317(a116,x60791))),f317(f278(a1,f2(a1)),x60791))+~P22(f317(f317(f225(a1),f2(a1)),x60791)) % 168.19/168.05 [6093]~P112(x60931)+P22(f317(f317(f226(x60931),f2(x60931)),f317(f317(f89(x60931),f87(x60931)),f87(x60931)))) % 168.19/168.05 [6146]P22(f317(f317(f226(a849),f317(a124,f2(a849))),f317(a116,x61461)))+~P22(f317(f317(f226(a1),f87(a1)),x61461)) % 168.19/168.05 [6237]E(x62371,f2(a1))+P22(f317(f58(f2(a1),x62371),f317(f317(f237(a1,a1),f2(a1)),f2(a1)))) % 168.19/168.05 [6404]~P22(f317(f317(f226(a849),f317(a124,f2(a849))),f317(a116,x64041)))+P22(f317(f317(f226(a1),f87(a1)),x64041)) % 168.19/168.05 [6817]~P107(x68171)+P37(x68171,f317(f230(f857(x68171,x68171)),f317(f247(x68171,x68171,a842),f226(x68171)))) % 168.19/168.05 [5483]E(f317(f115(a849),f317(f317(f21(a1),x54831),a109)),f317(a124,f317(f115(a849),x54831)))+P22(f317(a193,f317(f115(a1),x54831))) % 168.19/168.05 [5499]~P36(x54991)+E(f317(f317(f148(a849,a1),f112(a1)),f317(f317(f148(a1,a849),a116),x54991)),x54991) % 168.19/168.05 [5608]E(f317(f48(a1,f317(f115(a1),a109)),x56081),f317(f115(a1),a109))+~P22(f317(f317(f226(a1),f2(a1)),x56081)) % 168.19/168.05 [5614]E(f317(f88(a1),f317(f112(a1),f317(a124,f821(x56141)))),x56141)+~P22(f317(f317(f226(a1),x56141),f2(a1))) % 168.19/168.05 [5625]E(f317(f317(f89(a849),f87(a849)),f317(f115(a849),x56251)),f317(f115(a849),f317(f317(f21(a1),x56251),a109)))+P22(f317(f317(f226(a1),x56251),a92)) % 168.19/168.05 [5744]E(f317(f317(f89(a849),f317(f115(a849),x57441)),f87(a849)),f317(f115(a849),f317(f317(f21(a1),x57441),a109)))+P22(f317(f317(f226(a1),x57441),a92)) % 168.19/168.05 [5745]E(f317(f317(f21(a849),f317(f115(a849),x57451)),f87(a849)),f317(f115(a849),f317(f317(f89(a1),x57451),a109)))+P22(f317(f317(f225(a1),x57451),a92)) % 168.19/168.05 [5788]E(f317(a116,f317(f317(f89(a1),f87(a1)),x57881)),f317(a124,f317(a116,x57881)))+~P22(f317(f317(f225(a1),f2(a1)),x57881)) % 168.19/168.05 [5823]E(f317(a124,f317(f317(f21(a849),x58231),f317(a124,f2(a849)))),x58231)+~P22(f317(f317(f226(a849),f2(a849)),x58231)) % 168.19/168.05 [6028]E(f55(a849,f317(a124,f2(a849)),f317(f115(a849),x60281)),f317(a116,f55(a1,f87(a1),f317(f115(a1),x60281))))+P22(f317(a193,f317(f115(a1),x60281))) % 168.19/168.05 [6070]~P22(f317(f317(f225(a1),a92),x60701))+P22(f317(f317(f225(a1),a92),f317(f317(f89(a1),x60701),x60701))) % 168.19/168.05 [6071]~P22(f317(f317(f226(a1),a109),x60711))+P22(f317(f317(f225(a1),a109),f317(f317(f89(a1),x60711),x60711))) % 168.19/168.05 [6072]~P22(f317(f317(f226(a1),a92),x60721))+P22(f317(f317(f226(a1),a92),f317(f317(f89(a1),x60721),x60721))) % 168.19/168.05 [6073]~P22(f317(f317(f226(a1),a109),x60731))+P22(f317(f317(f226(a1),a109),f317(f317(f89(a1),x60731),x60731))) % 168.19/168.05 [6250]~P22(f317(f71(x62501),f233(f858(x62501,a842))))+P22(f317(f71(f853(x62501)),f233(f858(f853(x62501),a842)))) % 168.19/168.05 [6319]E(f317(f244(a1,a1),f56(f87(a1),f317(f115(a1),x63191))),f317(f48(a1,f87(a1)),f317(f115(a1),x63191)))+~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x63191))) % 168.19/168.05 [6337]~P22(f317(f317(f225(a1),f2(a1)),x63371))+P22(f317(f317(f226(a1),f2(a1)),f317(f317(f89(a1),f87(a1)),x63371))) % 168.19/168.05 [6363]E(f317(f246(a1,a1),f56(f87(a1),f317(f115(a1),x63631))),f55(a1,f87(a1),f317(f115(a1),x63631)))+~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x63631))) % 168.19/168.05 [6375]P22(f317(f71(x63751),f233(f858(x63751,a842))))+~P22(f317(f71(f853(x63751)),f233(f858(f853(x63751),a842)))) % 168.19/168.05 [6405]P22(f317(f317(f225(a1),a92),x64051))+~P22(f317(f317(f225(a1),a92),f317(f317(f89(a1),x64051),x64051))) % 168.19/168.05 [6406]P22(f317(f317(f226(a1),a92),x64061))+~P22(f317(f317(f226(a1),a92),f317(f317(f89(a1),x64061),x64061))) % 168.19/168.05 [6407]P22(f317(f317(f226(a1),a109),x64071))+~P22(f317(f317(f225(a1),a109),f317(f317(f89(a1),x64071),x64071))) % 168.19/168.05 [6408]P22(f317(f317(f226(a1),a109),x64081))+~P22(f317(f317(f226(a1),a109),f317(f317(f89(a1),x64081),x64081))) % 168.19/168.05 [6715]~P22(f317(f71(x67151),f233(f858(x67151,a842))))+P22(f317(f317(f226(a849),f2(a849)),f317(f54(x67151),f233(f858(x67151,a842))))) % 168.19/168.05 [7297]P22(f317(f71(a849),x72971))+~P22(f317(f71(a1),f317(f287(a849,a1,f112(a1)),x72971))) % 168.19/168.05 [5412]~E(a109,x54121)+E(f317(f317(f21(a1),f317(f317(f89(a1),x54121),x54121)),a109),a109) % 168.19/168.05 [5413]~E(x54131,a109)+E(f317(f317(f21(a1),f317(f317(f89(a1),x54131),x54131)),a109),a109) % 168.19/168.05 [5909]E(x59091,a109)+~E(f317(f317(f21(a1),f317(f317(f89(a1),x59091),x59091)),a109),a109) % 168.19/168.05 [5910]E(a109,x59101)+~E(f317(f317(f21(a1),f317(f317(f89(a1),x59101),x59101)),a109),a109) % 168.19/168.05 [6303]~E(f317(f115(a849),x63031),f2(a849))+P22(f317(a193,f317(f115(a1),f317(f317(f89(a1),x63031),a109)))) % 168.19/168.05 [6647]~P22(f317(a193,f317(f115(a1),x66471)))+P22(f317(a193,f317(f115(a1),f317(f317(f89(a1),x66471),x66471)))) % 168.19/168.05 [6648]~P22(f317(f317(f225(a1),x66481),a92))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x66481),x66481)),a92)) % 168.19/168.05 [6649]~P22(f317(f317(f225(a1),x66491),a109))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x66491),x66491)),a109)) % 168.19/168.05 [6650]~P22(f317(f317(f226(a1),x66501),a92))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x66501),x66501)),a92)) % 168.19/168.05 [6651]~P22(f317(f317(f225(a1),x66511),a109))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x66511),x66511)),a109)) % 168.19/168.05 [6969]E(f317(f115(a849),x69691),f2(a849))+~P22(f317(a193,f317(f115(a1),f317(f317(f89(a1),x69691),a109)))) % 168.19/168.05 [7204]~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x72041)))+P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),f317(f317(f89(a1),x72041),x72041)))) % 168.19/168.05 [7205]P22(f317(a193,f317(f115(a1),x72051)))+~P22(f317(a193,f317(f115(a1),f317(f317(f89(a1),x72051),x72051)))) % 168.19/168.05 [7206]P22(f317(f317(f225(a1),x72061),a92))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),x72061),x72061)),a92)) % 168.19/168.05 [7207]P22(f317(f317(f225(a1),x72071),a109))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),x72071),x72071)),a109)) % 168.19/168.05 [7208]P22(f317(f317(f225(a1),x72081),a109))+~P22(f317(f317(f226(a1),f317(f317(f89(a1),x72081),x72081)),a109)) % 168.19/168.05 [7209]P22(f317(f317(f226(a1),x72091),a92))+~P22(f317(f317(f226(a1),f317(f317(f89(a1),x72091),x72091)),a92)) % 168.19/168.05 [7573]E(f317(a118,f521(x75731)),x75731)+~P22(f317(f317(f319(f858(f857(a849,a849),a842)),x75731),a110)) % 168.19/168.05 [6223]~P90(x62231)+E(f317(f115(x62231),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f87(x62231)) % 168.19/168.05 [6695]~P22(f317(a193,f317(f115(a1),x66951)))+E(f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),x66951),x66951)),a109)),f2(a849)) % 168.19/168.05 [7722]~P22(f317(f317(f226(a1),f317(f115(a1),x77221)),f2(a1)))+E(f317(f244(a1,a1),f317(a60,f59(f317(f88(a1),f87(a1)),f317(f88(a1),f317(f115(a1),x77221))))),f317(f48(a1,f87(a1)),f317(f115(a1),x77221))) % 168.19/168.05 [7764]~P22(f317(f317(f226(a1),f317(f115(a1),x77641)),f2(a1)))+E(f317(f246(a1,a1),f317(a60,f59(f317(f88(a1),f87(a1)),f317(f88(a1),f317(f115(a1),x77641))))),f55(a1,f87(a1),f317(f115(a1),x77641))) % 168.19/168.05 [7806]~P22(f317(f317(f225(a1),a92),x78061))+P22(f317(f317(f225(a1),a92),f317(f317(f21(a1),f317(f317(f89(a1),x78061),x78061)),a109))) % 168.19/168.05 [7807]~P22(f317(f317(f225(a1),a109),x78071))+P22(f317(f317(f225(a1),a109),f317(f317(f21(a1),f317(f317(f89(a1),x78071),x78071)),a109))) % 168.19/168.05 [7808]~P22(f317(f317(f225(a1),a92),x78081))+P22(f317(f317(f226(a1),a92),f317(f317(f21(a1),f317(f317(f89(a1),x78081),x78081)),a109))) % 168.19/168.05 [7809]~P22(f317(f317(f226(a1),a109),x78091))+P22(f317(f317(f226(a1),a109),f317(f317(f21(a1),f317(f317(f89(a1),x78091),x78091)),a109))) % 168.19/168.05 [8115]~P90(x81151)+~P31(x81151,f317(f115(x81151),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))) % 168.19/168.05 [8299]P22(f317(f317(f225(a1),a92),x82991))+~P22(f317(f317(f225(a1),a92),f317(f317(f21(a1),f317(f317(f89(a1),x82991),x82991)),a109))) % 168.19/168.05 [8300]P22(f317(f317(f225(a1),a92),x83001))+~P22(f317(f317(f226(a1),a92),f317(f317(f21(a1),f317(f317(f89(a1),x83001),x83001)),a109))) % 168.19/168.05 [8301]P22(f317(f317(f225(a1),a109),x83011))+~P22(f317(f317(f225(a1),a109),f317(f317(f21(a1),f317(f317(f89(a1),x83011),x83011)),a109))) % 168.19/168.05 [8302]P22(f317(f317(f226(a1),a109),x83021))+~P22(f317(f317(f226(a1),a109),f317(f317(f21(a1),f317(f317(f89(a1),x83021),x83021)),a109))) % 168.19/168.05 [8616]E(f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),x86161),x86161)),a109)),f317(f317(f95(a849,a849),f317(f115(a849),x86161)),f317(f317(f8(a849,a849,a849),a124),f317(f317(f18(a849,a849,a849),f89(a849)),f5(a849)))))+P22(f317(a193,f317(f115(a1),x86161))) % 168.19/168.05 [9448]E(x94481,f188(f858(f857(a849,a849),a842)))+P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),x94481),f188(f858(f857(a849,a849),a842)))),a46)) % 168.19/168.05 [8549]~P22(f317(a193,f317(f115(a1),x85491)))+P22(f317(a193,f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),x85491),x85491)),a109)))) % 168.19/168.05 [8550]~P22(f317(f317(f226(a1),x85501),a92))+P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),x85501),x85501)),a109)),a92)) % 168.19/168.05 [8551]~P22(f317(f317(f225(a1),x85511),a109))+P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),x85511),x85511)),a109)),a109)) % 168.19/168.05 [8552]~P22(f317(f317(f226(a1),x85521),a92))+P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x85521),x85521)),a109)),a92)) % 168.19/168.05 [8553]~P22(f317(f317(f226(a1),x85531),a109))+P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x85531),x85531)),a109)),a109)) % 168.19/168.05 [8651]~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x86511)))+P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),x86511),x86511)),a109)))) % 168.19/168.05 [8805]~P90(x88051)+E(f317(f317(f89(x88051),f87(x88051)),f87(x88051)),f317(f115(x88051),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))) % 168.19/168.05 [8961]P22(f317(a193,f317(f115(a1),x89611)))+~P22(f317(a193,f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),x89611),x89611)),a109)))) % 168.19/168.05 [8962]P22(f317(f317(f225(a1),x89621),a109))+~P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),x89621),x89621)),a109)),a109)) % 168.19/168.05 [8963]P22(f317(f317(f226(a1),x89631),a92))+~P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),x89631),x89631)),a109)),a92)) % 168.19/168.05 [8964]P22(f317(f317(f226(a1),x89641),a92))+~P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x89641),x89641)),a109)),a92)) % 168.19/168.05 [8965]P22(f317(f317(f226(a1),x89651),a109))+~P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x89651),x89651)),a109)),a109)) % 168.19/168.05 [9496]~P22(f317(f71(f857(a849,a849)),x94961))+P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),f188(f858(f857(a849,a849),a842))),x94961)),a78)) % 168.19/168.05 [9281]~P110(x92811)+E(f317(f317(f238(x92811),f2(x92811)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f2(x92811)) % 168.19/168.05 [9282]~P110(x92821)+E(f317(f317(f238(x92821),f87(x92821)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f87(x92821)) % 168.19/168.05 [9713]~P22(f317(f317(f226(a849),f87(a849)),x97131))+P22(f317(f317(f226(a849),f2(a849)),f317(f48(a849,x97131),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.19/168.05 [9728]~P22(f317(f317(f226(a849),f2(a849)),x97281))+P22(f317(f317(f226(a849),f2(a849)),f317(f48(a849,f317(f317(f89(a849),x97281),f87(a849))),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.19/168.05 [9769]~E(f55(a849,x97691,f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f87(a849))+P22(f317(f317(f226(a849),f2(a849)),f55(a849,x97691,f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.19/168.05 [9793]E(f55(a849,x97931,f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f87(a849))+~P22(f317(f317(f226(a849),f2(a849)),f55(a849,x97931,f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.19/168.05 [4557]~P37(x45571,x45572)+P52(x45571,x45572) % 168.19/168.05 [4558]~P42(x45581,x45582)+P52(x45581,x45582) % 168.19/168.05 [4513]E(x45131,x45132)+~E(f40(x45131),f40(x45132)) % 168.19/168.05 [4514]E(x45141,x45142)+~E(f41(x45141),f41(x45142)) % 168.19/168.05 [4517]~E(x45171,x45172)+E(f255(x45171,x45172),f87(a111)) % 168.19/168.05 [4520]E(f198(x45201,x45202),x45201)+~E(x45202,f2(a849)) % 168.19/168.05 [4525]P38(x45251,x45252)+~E(x45252,f191(x45251)) % 168.19/168.05 [4528]~E(x45282,f125(x45281))+E(f146(x45281,x45282),f125(x45281)) % 168.19/168.05 [4532]~P38(x45322,x45321)+E(x45321,f191(x45322)) % 168.19/168.05 [4548]~E(f146(x45482,x45481),f125(x45482))+E(x45481,f125(x45482)) % 168.19/168.05 [4562]~P85(x45622)+P85(f858(x45621,x45622)) % 168.19/168.05 [4563]~P71(x45632)+P71(f858(x45631,x45632)) % 168.19/168.05 [4564]~P73(x45642)+P73(f858(x45641,x45642)) % 168.19/168.05 [4565]~P86(x45652)+P86(f858(x45651,x45652)) % 168.19/168.05 [4566]~P101(x45662)+P101(f858(x45661,x45662)) % 168.19/168.05 [4567]~P102(x45672)+P102(f858(x45671,x45672)) % 168.19/168.05 [4568]~P104(x45682)+P104(f858(x45681,x45682)) % 168.19/168.05 [4569]~P93(x45692)+P92(f858(x45691,x45692)) % 168.19/168.05 [4570]~P93(x45702)+P93(f858(x45701,x45702)) % 168.19/168.05 [4571]~P95(x45712)+P94(f858(x45711,x45712)) % 168.19/168.05 [4572]~P93(x45722)+P98(f858(x45721,x45722)) % 168.19/168.05 [4573]~P96(x45732)+P96(f858(x45731,x45732)) % 168.19/168.05 [4574]~P105(x45742)+P105(f858(x45741,x45742)) % 168.19/168.05 [4575]~P95(x45752)+P97(f858(x45751,x45752)) % 168.19/168.05 [4576]~P27(x45762)+P27(f858(x45761,x45762)) % 168.19/168.05 [4577]~P95(x45772)+P95(f858(x45771,x45772)) % 168.19/168.05 [4589]E(x45891,x45892)+~E(f317(a29,x45891),f317(a29,x45892)) % 168.19/168.05 [4591]E(x45911,x45912)+~E(f317(a124,x45911),f317(a124,x45912)) % 168.19/168.05 [4592]E(x45921,x45922)+~E(f317(a118,x45921),f317(a118,x45922)) % 168.19/168.05 [4593]E(x45931,x45932)+~E(f317(a3,x45931),f317(a3,x45932)) % 168.19/168.05 [4595]E(x45951,x45952)+~E(f317(a19,x45951),f317(a19,x45952)) % 168.19/168.05 [4703]~P55(x47031)+E(f55(x47031,x47032,x47032),f2(x47031)) % 168.19/168.05 [4734]~P37(x47341,x47342)+P37(f850(x47341),f140(x47341,x47342)) % 168.19/168.05 [4735]~P37(x47351,x47352)+P37(f850(x47351),f139(x47351,x47352)) % 168.19/168.05 [4830]~P37(x48301,x48302)+P37(f858(x48301,a842),f308(x48301,x48302)) % 168.19/168.05 [4831]~P37(x48311,x48312)+P37(f858(x48311,a842),f309(x48311,x48312)) % 168.19/168.05 [4944]~P28(x49441)+P39(f279(a1,x49441,x49442)) % 168.19/168.05 [5046]~P37(x50461,x50462)+P54(x50461,f77(x50461,x50461,x50462)) % 168.19/168.05 [5544]~P78(x55441)+P19(x55441,x55441,f88(x55441),x55442) % 168.19/168.05 [4543]~E(x45432,f125(x45431))+E(f317(f162(x45431),x45432),f125(x45431)) % 168.19/168.05 [4544]~E(x45442,f125(x45441))+E(f317(f163(x45441),x45442),f125(x45441)) % 168.19/168.05 [4599]E(x45991,f317(a116,x45992))+~E(f317(f112(a1),x45991),x45992) % 168.19/168.05 [4603]E(x46031,f125(x46032))+~E(f317(f162(x46032),x46031),f125(x46032)) % 168.19/168.05 [4604]E(x46041,f125(x46042))+~E(f317(f163(x46042),x46041),f125(x46042)) % 168.19/168.05 [4615]~E(x46152,f2(a1))+E(f317(f48(a1,x46151),x46152),f2(a1)) % 168.19/168.05 [4624]~P90(x46241)+E(f317(f115(x46241),x46242),f317(f114(x46241),x46242)) % 168.19/168.05 [4631]~E(x46312,f191(x46311))+E(f218(x46311,x46312),f188(f858(x46311,a842))) % 168.19/168.05 [4633]~P56(x46331)+P22(f317(f71(x46331),x46332)) % 168.19/168.05 [4640]E(x46401,f191(x46402))+E(f317(f217(x46402),f798(x46402,x46401)),x46401) % 168.19/168.05 [4641]E(x46411,f191(x46412))+E(f317(f217(x46412),f323(x46412,x46411)),x46411) % 168.19/168.05 [4642]E(x46421,f191(x46422))+E(f317(f217(x46422),f334(x46422,x46421)),x46421) % 168.19/168.05 [4643]~E(f608(x46432,x46431),f125(x46431))+E(f173(x46431,x46432),f125(f850(x46431))) % 168.19/168.05 [4645]~P55(x46451)+E(f317(f48(x46451,x46452),f87(x46451)),x46452) % 168.19/168.05 [4652]~E(x46522,f125(x46521))+E(f317(f166(x46521),x46522),f188(f858(x46521,a842))) % 168.19/168.05 [4653]~E(x46532,f125(x46531))+E(f188(f858(x46531,a842)),f317(f166(x46531),x46532)) % 168.19/168.05 [4655]E(x46551,x46552)+~E(f317(f112(a1),x46551),f317(f112(a1),x46552)) % 168.19/168.05 [4658]~P55(x46581)+E(f317(f48(x46581,x46582),f2(x46581)),f2(x46581)) % 168.19/168.05 [4660]E(f206(x46601,x46602),f2(a849))+P22(f317(f71(x46601),x46602)) % 168.19/168.05 [4680]~P113(x46801)+E(f91(x46801,f91(x46801,x46802)),f91(x46801,x46802)) % 168.19/168.05 [4694]~P84(x46941)+E(f317(f317(f238(x46941),x46942),f87(a849)),x46942) % 168.19/168.05 [4695]~P75(x46951)+E(f317(f317(f238(x46951),x46952),f87(a849)),x46952) % 168.19/168.05 [4697]E(x46971,x46972)+E(f255(x46971,x46972),f317(f317(f89(a111),x46972),f87(a111))) % 168.19/168.05 [4700]E(f317(f54(x47001),x47002),f2(a849))+P22(f317(f71(x47001),x47002)) % 168.19/168.05 [4704]~E(f146(x47041,x47042),x47042)+P22(f317(f131(x47041),x47042)) % 168.19/168.05 [4707]~P66(x47071)+E(f317(f317(f89(x47071),x47072),f2(x47071)),x47072) % 168.19/168.05 [4708]~P67(x47081)+E(f317(f317(f89(x47081),x47082),f2(x47081)),x47082) % 168.19/168.05 [4709]~P84(x47091)+E(f317(f317(f89(x47091),x47092),f2(x47091)),x47092) % 168.19/168.05 [4710]~P69(x47101)+E(f317(f317(f21(x47101),x47102),f2(x47101)),x47102) % 168.19/168.05 [4711]~P94(x47111)+E(f317(f317(f122(x47111),x47112),f188(x47111)),x47112) % 168.19/168.05 [4712]~P84(x47121)+E(f317(f317(f90(x47121),x47122),f87(x47121)),x47122) % 168.19/168.05 [4713]~P75(x47131)+E(f317(f317(f90(x47131),x47132),f87(x47131)),x47132) % 168.19/168.05 [4714]~P70(x47141)+E(f317(f317(f90(x47141),x47142),f87(x47141)),x47142) % 168.19/168.05 [4715]~P97(x47151)+E(f317(f317(f113(x47151),x47152),f233(x47151)),x47152) % 168.19/168.05 [4716]~P115(x47161)+E(f317(f317(f266(x47161),x47162),f87(x47161)),x47162) % 168.19/168.05 [4717]~P84(x47171)+E(f317(f317(f238(x47171),x47172),f2(a849)),f87(x47171)) % 168.19/168.05 [4718]~P106(x47181)+E(f317(f317(f238(x47181),x47182),f2(a849)),f87(x47181)) % 168.19/168.05 [4719]~E(x47192,f188(f858(x47191,a842)))+E(f317(f54(x47191),x47192),f2(a849)) % 168.19/168.05 [4729]~P55(x47291)+E(f55(x47291,x47292,f2(x47291)),x47292) % 168.19/168.05 [4736]~P97(x47361)+E(f317(f317(f122(x47361),x47362),f233(x47361)),f233(x47361)) % 168.19/168.05 [4737]~P84(x47371)+E(f317(f317(f90(x47371),x47372),f2(x47371)),f2(x47371)) % 168.19/168.05 [4738]~P123(x47381)+E(f317(f317(f90(x47381),x47382),f2(x47381)),f2(x47381)) % 168.19/168.05 [4739]~P94(x47391)+E(f317(f317(f113(x47391),x47392),f188(x47391)),f188(x47391)) % 168.19/168.05 [4740]~P116(x47401)+E(f317(f317(f266(x47401),x47402),f2(x47401)),f2(x47401)) % 168.19/168.05 [4741]E(x47411,f191(x47412))+~E(f218(x47412,x47411),f188(f858(x47412,a842))) % 168.19/168.05 [4744]~P55(x47441)+E(f55(x47441,x47442,f87(x47441)),f2(x47441)) % 168.19/168.05 [4745]~P55(x47451)+E(f55(x47451,f2(x47451),x47452),f2(x47451)) % 168.19/168.05 [4774]E(x47741,f2(a849))+E(f64(x47742,x47741,f125(x47742)),f125(f850(x47742))) % 168.19/168.05 [4797]P37(x47971,x47972)+~E(f684(x47972,x47971),f188(f858(x47971,a842))) % 168.19/168.05 [4798]E(x47981,f125(x47982))+~E(f317(f166(x47982),x47981),f188(f858(x47982,a842))) % 168.19/168.05 [4799]E(x47991,f125(x47992))+~E(f188(f858(x47992,a842)),f317(f166(x47992),x47991)) % 168.19/168.05 [4802]~E(x48021,x48022)+P22(f317(f317(a314,x48021),x48022)) % 168.19/168.05 [4812]P22(x48121)+P22(f317(f317(a320,x48121),x48122)) % 168.19/168.05 [4813]E(x48131,f125(x48132))+E(f317(f317(f159(x48132),x48131),f2(a849)),f317(f135(x48132),x48131)) % 168.19/168.05 [4816]E(f146(x48161,x48162),x48162)+~P22(f317(f131(x48161),x48162)) % 168.19/168.05 [4821]~P22(x48212)+P22(f317(f317(a320,x48211),x48212)) % 168.19/168.05 [4822]~P22(x48222)+P22(f317(f317(a316,x48221),x48222)) % 168.19/168.05 [4823]~P22(x48231)+P22(f317(f317(a316,x48231),x48232)) % 168.19/168.05 [4833]~E(f575(x48332,x48331),f596(x48332,x48331))+P22(f317(f131(x48331),x48332)) % 168.19/168.05 [4841]E(f317(f230(x48411),x48412),f188(f858(x48411,a842)))+P22(f317(x48412,f518(x48412))) % 168.19/168.05 [4842]E(f188(f858(x48421,a842)),f317(f230(x48421),x48422))+P22(f317(x48422,f519(x48422))) % 168.19/168.05 [4907]~P113(x49071)+E(f317(f317(f90(x49071),x49072),f91(x49071,x49072)),f317(f84(x49071),x49072)) % 168.19/168.05 [4943]~P52(x49431,x49432)+P52(x49431,f317(f263(x49431,x49431),x49432)) % 168.19/168.05 [4960]~E(f317(a27,x49601),f317(f217(a843),x49602))+P22(f317(a24,f317(a29,x49601))) % 168.19/168.05 [4965]E(x49651,x49652)+~P22(f317(f317(a314,x49651),x49652)) % 168.19/168.05 [4969]~P22(f317(a24,x49692))+P22(f317(a24,f35(x49691,x49692))) % 168.19/168.05 [4978]P22(x49781)+~P22(f317(f317(a315,x49782),x49781)) % 168.19/168.05 [4979]P22(x49791)+~P22(f317(f317(a315,x49791),x49792)) % 168.19/168.05 [4983]~P105(x49831)+P22(f317(f317(f225(x49831),x49832),f233(x49831))) % 168.19/168.05 [4987]E(x49871,x49872)+~E(f317(x49871,f359(x49872,x49871)),f317(x49872,f359(x49872,x49871))) % 168.19/168.05 [5020]E(x50201,f2(a849))+E(f198(x50201,f55(a849,x50202,x50201)),f198(x50202,x50201)) % 168.19/168.05 [5025]~P103(x50251)+P29(x50251,f317(f317(f145(x50251),x50252),f125(x50251))) % 168.19/168.05 [5044]~E(x50441,x50442)+P22(f317(f317(f226(a849),x50441),f317(a124,x50442))) % 168.19/168.05 [5054]~E(x50541,f2(a849))+P22(f317(f317(f226(a849),x50541),f317(a124,x50542))) % 168.19/168.05 [5064]P22(f317(x50641,x50642))+P22(f317(f317(f225(a1),f2(a1)),f836(x50641))) % 168.19/168.05 [5101]P22(f317(a24,x51011))+~P22(f317(a24,f35(x51012,x51011))) % 168.19/168.05 [5103]P22(f317(a24,x51031))+~P22(f317(a24,f36(x51032,x51031))) % 168.19/168.05 [5105]P22(f317(a24,x51051))+~P22(f317(a24,f36(x51051,x51052))) % 168.19/168.05 [5137]P52(x51371,x51372)+~P52(x51371,f317(f263(x51371,x51371),x51372)) % 168.19/168.05 [5140]~E(f55(a849,x51402,x51401),f2(a849))+E(f317(f317(f90(a849),x51401),f324(x51401,x51402)),x51402) % 168.19/168.05 [5141]~E(f55(a1,x51412,x51411),f2(a1))+E(f317(f317(f90(a1),x51411),f325(x51411,x51412)),x51412) % 168.19/168.05 [5166]~P22(f317(x51661,x51662))+P22(f317(f317(f225(a1),f2(a1)),f800(x51661))) % 168.19/168.05 [5178]E(f317(f317(f21(a849),f317(a116,x51781)),f317(a116,x51782)),f317(a116,x51781))+~P22(f317(a193,x51782)) % 168.19/168.05 [5207]E(f256(x52071,x52072),f87(a111))+~P22(f317(f317(f225(a111),x52071),f87(a111))) % 168.19/168.05 [5295]E(f317(f317(f159(x52951),x52952),f575(x52952,x52951)),f317(f317(f159(x52951),x52952),f596(x52952,x52951)))+P22(f317(f131(x52951),x52952)) % 168.19/168.05 [5338]~P22(f317(x53381,f99(x53382,x53381)))+P22(f317(x53381,f609(x53382,x53381))) % 168.19/168.05 [5402]P54(x54021,x54022)+~P22(f317(f305(x54021,x54022),f546(x54022,x54021))) % 168.19/168.05 [5552]~E(f317(a124,f55(a849,x55521,x55522)),x55522)+E(f55(a849,f317(a124,x55521),x55522),f2(a849)) % 168.19/168.05 [5610]~P111(x56101)+P22(f317(f317(f319(x56101),f317(f112(x56101),x56102)),f121(x56101))) % 168.19/168.05 [5611]~P110(x56111)+P22(f317(f317(f319(x56111),f317(f112(x56111),x56112)),f185(x56111))) % 168.19/168.05 [5612]~P90(x56121)+P22(f317(f317(f319(x56121),f317(f115(x56121),x56122)),f121(x56121))) % 168.19/168.05 [5613]~P111(x56131)+P22(f317(f317(f319(x56131),f317(f114(x56131),x56132)),f121(x56131))) % 168.19/168.05 [5747]E(f317(a124,f55(a849,x57471,x57472)),x57472)+E(f55(a849,f317(a124,x57471),x57472),f317(a124,f55(a849,x57471,x57472))) % 168.19/168.05 [6127]~E(x61271,f2(a1))+E(f317(f317(f237(a1,a1),f317(f48(a1,x61271),x61272)),f55(a1,x61271,x61272)),f317(f317(f237(a1,a1),f2(a1)),f2(a1))) % 168.19/168.05 [6158]P37(x61581,x61582)+~P22(f317(f317(f319(x61581),f547(x61582,x61581)),f306(x61581,x61582))) % 168.19/168.05 [6194]~P112(x61941)+~P22(f317(f317(f226(x61941),f317(f112(x61941),x61942)),f2(x61941))) % 168.19/168.05 [6195]~P79(x61951)+~P22(f317(f317(f226(x61951),f317(f84(x61951),x61952)),f2(x61951))) % 168.19/168.05 [6277]P22(f317(f317(f226(a1),x62771),f55(a1,x62772,x62771)))+~P22(f317(f317(f226(a1),x62771),f2(a1))) % 168.19/168.05 [6377]E(f317(f317(f286(a849),f317(a124,x63771)),f279(a849,x63772,x63771)),f279(a849,x63772,f317(a124,x63771)))+~P22(f317(f317(f225(a849),x63772),f317(a124,x63771))) % 168.19/168.05 [6465]~P103(x64651)+P29(x64651,f142(x64651,x64651,f5(x64651),x64652)) % 168.19/168.05 [6593]E(f317(f162(x65931),x65932),x65932)+~P22(f317(f317(f225(a849),f317(f189(f850(x65931)),x65932)),f87(a849))) % 168.19/168.05 [6608]~P79(x66081)+P22(f317(f317(f225(x66081),f317(f88(x66081),f317(f84(x66081),x66082))),f2(x66081))) % 168.19/168.05 [6644]~P37(x66441,x66442)+P37(x66441,f317(f317(f265(x66441,x66441,x66441),x66442),f284(x66441,x66442))) % 168.19/168.05 [6858]~P22(f317(f317(f226(a1),x68582),f2(a1)))+P22(f317(f317(f225(a1),f55(a1,x68581,x68582)),f2(a1))) % 168.19/168.05 [7252]~P110(x72521)+E(f190(x72521,f317(f317(f7(x72521,x72521,x72521),f89(x72521)),f87(x72521)),x72522,f2(x72521)),f317(f112(x72521),x72522)) % 168.19/168.05 [7278]~P119(x72781)+~P22(f317(f317(f226(x72781),f317(f317(f90(x72781),x72782),x72782)),f2(x72781))) % 168.19/168.05 [9889]~P113(x98891)+~P22(f317(f317(f226(x98891),f317(f317(f238(x98891),x98892),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f2(x98891))) % 168.19/168.05 [4601]~E(x46012,f125(x46011))+E(f317(f189(f850(x46011)),x46012),f2(a849)) % 168.19/168.05 [4644]~E(x46441,f2(a849))+E(f317(f317(f89(a849),x46441),x46442),x46442) % 168.19/168.05 [4646]~E(x46462,f2(a849))+E(f317(f317(f90(a849),x46461),x46462),f2(a849)) % 168.19/168.05 [4648]~E(x46481,f2(a849))+E(f317(f317(f90(a849),x46481),x46482),f2(a849)) % 168.19/168.05 [4649]~E(x46492,f2(a849))+E(f317(f317(f238(a849),x46491),x46492),f87(a849)) % 168.19/168.05 [4661]E(x46611,f125(x46612))+~E(f317(f189(f850(x46612)),x46611),f2(a849)) % 168.19/168.05 [4663]~P92(x46631)+E(f317(f317(f122(x46631),x46632),x46632),x46632) % 168.19/168.05 [4664]~P93(x46641)+E(f317(f317(f122(x46641),x46642),x46642),x46642) % 168.19/168.05 [4666]~P91(x46661)+E(f317(f317(f90(x46661),x46662),x46662),x46662) % 168.19/168.05 [4667]~P93(x46671)+E(f317(f317(f113(x46671),x46672),x46672),x46672) % 168.19/168.05 [4669]~P98(x46691)+E(f317(f317(f113(x46691),x46692),x46692),x46692) % 168.19/168.05 [4671]~P103(x46711)+E(f317(f317(f223(x46711),x46712),x46712),x46712) % 168.19/168.05 [4673]~P103(x46731)+E(f317(f317(f224(x46731),x46732),x46732),x46732) % 168.19/168.05 [4692]~P55(x46921)+E(f317(f48(x46921,f2(x46921)),x46922),f2(x46921)) % 168.19/168.05 [4693]~P69(x46931)+E(f317(f317(f21(x46931),x46932),x46932),f2(x46931)) % 168.19/168.05 [4705]~P69(x47051)+E(f317(f88(x47051),f317(f88(x47051),x47052)),x47052) % 168.19/168.05 [4706]~P86(x47061)+E(f317(f88(x47061),f317(f88(x47061),x47062)),x47062) % 168.19/168.05 [4722]~E(x47222,f2(a849))+E(f317(f317(f238(a849),x47221),x47222),f317(a124,f2(a849))) % 168.19/168.05 [4753]~P66(x47531)+E(f317(f317(f89(x47531),f2(x47531)),x47532),x47532) % 168.19/168.05 [4754]~P67(x47541)+E(f317(f317(f89(x47541),f2(x47541)),x47542),x47542) % 168.19/168.05 [4755]~P84(x47551)+E(f317(f317(f89(x47551),f2(x47551)),x47552),x47552) % 168.19/168.05 [4756]~P94(x47561)+E(f317(f317(f122(x47561),f188(x47561)),x47562),x47562) % 168.19/168.05 [4757]~P84(x47571)+E(f317(f317(f90(x47571),f87(x47571)),x47572),x47572) % 168.19/168.05 [4758]~P75(x47581)+E(f317(f317(f90(x47581),f87(x47581)),x47582),x47582) % 168.19/168.05 [4759]~P70(x47591)+E(f317(f317(f90(x47591),f87(x47591)),x47592),x47592) % 168.19/168.05 [4760]~P97(x47601)+E(f317(f317(f113(x47601),f233(x47601)),x47602),x47602) % 168.19/168.05 [4779]~P97(x47791)+E(f317(f317(f122(x47791),f233(x47791)),x47792),f233(x47791)) % 168.19/168.05 [4780]~P84(x47801)+E(f317(f317(f90(x47801),f2(x47801)),x47802),f2(x47801)) % 168.19/168.05 [4781]~P123(x47811)+E(f317(f317(f90(x47811),f2(x47811)),x47812),f2(x47811)) % 168.19/168.05 [4782]~P94(x47821)+E(f317(f317(f113(x47821),f188(x47821)),x47822),f188(x47821)) % 168.19/168.05 [4783]~P75(x47831)+E(f317(f317(f238(x47831),f87(x47831)),x47832),f87(x47831)) % 168.19/168.05 [4784]~P115(x47841)+E(f317(f317(f266(x47841),f2(x47841)),x47842),f2(x47841)) % 168.19/168.05 [4792]E(x47921,f125(x47922))+E(f138(x47922,f317(f163(x47922),x47921)),f317(f135(x47922),x47921)) % 168.19/168.05 [4793]E(x47931,f125(x47932))+E(f317(f135(x47932),f317(f163(x47932),x47931)),f138(x47932,x47931)) % 168.19/168.05 [4794]E(x47941,f2(a849))+~E(f317(f317(f89(a849),x47942),x47941),x47942) % 168.19/168.05 [4800]~P111(x48001)+E(f317(f114(x48001),f317(f112(a1),x48002)),f317(f112(x48001),x48002)) % 168.19/168.05 [4801]~P90(x48011)+E(f317(f114(x48011),f317(f115(a1),x48012)),f317(f115(x48011),x48012)) % 168.19/168.05 [4808]E(x48081,f2(a849))+~E(f317(f317(f89(a849),x48082),x48081),f2(a849)) % 168.19/168.05 [4809]E(x48091,f2(a849))+~E(f317(f317(f89(a849),x48091),x48092),f2(a849)) % 168.19/168.05 [4810]E(x48101,f87(a849))+~E(f317(f317(f90(a849),x48102),x48101),f87(a849)) % 168.19/168.05 [4811]E(x48111,f87(a849))+~E(f317(f317(f90(a849),x48111),x48112),f87(a849)) % 168.19/168.05 [4826]~P79(x48261)+E(f317(f84(x48261),f317(f88(x48261),x48262)),f317(f84(x48261),x48262)) % 168.19/168.05 [4827]~P113(x48271)+E(f317(f84(x48271),f317(f112(x48271),x48272)),f317(f112(x48271),x48272)) % 168.19/168.05 [4828]~P79(x48281)+E(f317(f84(x48281),f317(f84(x48281),x48282)),f317(f84(x48281),x48282)) % 168.19/168.05 [4829]~P67(x48291)+E(f317(f160(x48291),f317(f163(x48291),x48292)),f317(f160(x48291),x48292)) % 168.19/168.05 [4834]~E(x48341,f317(a124,f2(a849)))+E(f317(f317(f238(a849),x48341),x48342),f317(a124,f2(a849))) % 168.19/168.05 [4845]~P69(x48451)+E(f317(f317(f21(x48451),f2(x48451)),x48452),f317(f88(x48451),x48452)) % 168.19/168.05 [4846]~E(x48462,f2(a849))+E(f133(a849,f317(f278(a849,x48461),x48462)),f125(a849)) % 168.19/168.05 [4855]~P90(x48551)+E(f317(f317(f89(x48551),x48552),f317(f115(x48551),a92)),x48552) % 168.19/168.05 [4856]E(x48561,f2(a1))+E(f56(f317(f84(a1),x48562),f317(f84(a1),x48561)),f62(x48562,x48561)) % 168.19/168.05 [4870]~E(x48701,x48702)+P22(f317(f317(f225(a849),x48701),x48702)) % 168.19/168.05 [4877]~E(x48771,f2(a111))+E(f317(f317(f89(a849),f317(a19,x48771)),x48772),x48772) % 168.19/168.05 [4878]~E(f317(f115(a1),x48782),f317(f112(a1),x48781))+E(x48781,f317(a116,f317(f115(a1),x48782))) % 168.19/168.05 [4887]~P28(x48871)+P28(f317(f317(f238(a1),x48871),x48872)) % 168.19/168.05 [4888]~P69(x48881)+E(f317(f317(f89(x48881),x48882),f317(f88(x48881),x48882)),f2(x48881)) % 168.19/168.05 [4889]~P86(x48891)+E(f317(f317(f122(x48891),x48892),f317(f88(x48891),x48892)),f233(x48891)) % 168.19/168.05 [4890]~P86(x48901)+E(f317(f317(f113(x48901),x48902),f317(f88(x48901),x48902)),f188(x48901)) % 168.19/168.05 [4915]E(x49151,f2(a849))+~E(f317(f88(a1),f317(f112(a1),x49152)),f317(f112(a1),x49151)) % 168.19/168.05 [4916]E(x49161,f2(a849))+~E(f317(f88(a1),f317(f112(a1),x49161)),f317(f112(a1),x49162)) % 168.19/168.05 [4921]E(f195(x49211,x49212),f2(a1))+P22(f317(f317(f225(a1),x49212),x49211)) % 168.19/168.05 [4922]E(f172(x49221,x49222),f125(a1))+P22(f317(f317(f225(a1),x49221),x49222)) % 168.19/168.05 [4935]E(x49351,f317(a124,f2(a849)))+~E(f317(f317(f90(a849),x49352),x49351),f317(a124,f2(a849))) % 168.19/168.05 [4936]E(x49361,f317(a124,f2(a849)))+~E(f317(f317(f90(a849),x49361),x49362),f317(a124,f2(a849))) % 168.19/168.05 [4937]~P101(x49371)+P22(f317(f317(f225(x49371),x49372),x49372)) % 168.19/168.05 [4940]~P90(x49401)+E(f317(f317(f90(x49401),x49402),f317(f115(x49401),a109)),f317(f88(x49401),x49402)) % 168.19/168.05 [4957]~P90(x49571)+E(f317(f88(x49571),f317(f115(x49571),x49572)),f317(f115(x49571),f317(f88(a1),x49572))) % 168.19/168.05 [4958]~P111(x49581)+E(f317(f88(x49581),f317(f114(x49581),x49582)),f317(f114(x49581),f317(f88(a1),x49582))) % 168.19/168.05 [4992]~E(x49921,f317(a124,x49922))+P22(f317(f317(f226(a849),f2(a849)),x49921)) % 168.19/168.05 [5009]~P103(x50091)+E(f317(f88(f858(x50091,a842)),f317(f277(x50091),x50092)),f317(f280(x50091),x50092)) % 168.19/168.05 [5010]~P103(x50101)+E(f317(f88(f858(x50101,a842)),f317(f280(x50101),x50102)),f317(f277(x50101),x50102)) % 168.19/168.05 [5011]~P103(x50111)+E(f317(f88(f858(x50111,a842)),f317(f231(x50111),x50112)),f317(f232(x50111),x50112)) % 168.19/168.05 [5012]~P103(x50121)+E(f317(f88(f858(x50121,a842)),f317(f232(x50121),x50122)),f317(f231(x50121),x50122)) % 168.19/168.05 [5019]~E(f317(f112(a1),x50192),x50191)+P22(f317(f317(f225(a1),f2(a1)),x50191)) % 168.19/168.05 [5026]~E(x50262,f2(a1))+E(f62(x50261,x50262),f317(f317(f237(a1,a1),f2(a1)),f317(f84(a1),x50261))) % 168.19/168.05 [5027]~P85(x50271)+P22(f317(f317(f225(x50271),f188(x50271)),x50272)) % 168.19/168.05 [5059]E(x50591,x50592)+~E(f317(f317(f89(a1),x50591),x50591),f317(f317(f89(a1),x50592),x50592)) % 168.19/168.05 [5063]~P22(f317(x50631,x50632))+P22(f317(x50631,f317(a116,f800(x50631)))) % 168.19/168.05 [5089]~P113(x50891)+E(f317(f317(f90(x50891),f91(x50891,x50892)),f317(f84(x50891),x50892)),x50892) % 168.19/168.05 [5090]E(x50901,x50902)+~P22(f317(f317(f194(a23),x50901),x50902)) % 168.19/168.05 [5099]~E(x50992,f2(a849))+E(f94(f857(a849,a849),f57(x50991,x50992)),f317(f317(f237(a849,a849),f2(a849)),x50991)) % 168.19/168.05 [5110]~E(x51101,x51102)+~P22(f317(f317(f226(a849),x51101),x51102)) % 168.19/168.05 [5111]~E(x51111,x51112)+~P22(f317(f317(f226(a1),x51111),x51112)) % 168.19/168.05 [5114]~P110(x51141)+E(f317(f317(f89(x51141),f87(x51141)),f317(f112(x51141),x51142)),f317(f112(x51141),f317(a124,x51142))) % 168.19/168.05 [5118]~E(x51181,f2(a849))+~P22(f317(f317(f226(a849),x51182),x51181)) % 168.19/168.05 [5134]E(f146(x51341,x51342),x51342)+~E(f317(f189(f850(x51341)),f146(x51341,x51342)),f317(f189(f850(x51341)),x51342)) % 168.19/168.05 [5135]E(f317(f54(x51351),f317(f166(x51351),x51352)),f317(f189(f850(x51351)),x51352))+~P22(f317(f131(x51351),x51352)) % 168.19/168.05 [5145]~P22(f317(x51451,f812(x51451)))+P22(f317(x51451,f317(f112(a1),x51452))) % 168.19/168.05 [5156]E(f172(x51561,x51562),f125(a1))+~P22(f317(f317(f226(a1),x51562),x51561)) % 168.19/168.05 [5157]E(f256(x51571,x51572),f87(a111))+~P22(f317(f317(f226(a111),x51572),x51571)) % 168.19/168.05 [5160]~P104(x51601)+E(f279(x51601,x51602,x51602),f317(f317(f286(x51601),x51602),f188(f858(x51601,a842)))) % 168.19/168.05 [5181]~E(f317(f317(f21(a849),x51811),x51812),f2(a849))+P22(f317(f317(f225(a849),x51811),x51812)) % 168.19/168.05 [5204]~E(x52042,f2(a849))+E(f64(x52041,x52042,f125(x52041)),f317(f317(f145(f850(x52041)),f125(x52041)),f125(f850(x52041)))) % 168.19/168.05 [5208]~P101(x52081)+~P22(f317(f317(f226(x52081),x52082),x52082)) % 168.19/168.05 [5211]~E(f55(a1,x52111,x52112),f2(a1))+E(f55(a1,x52111,f317(f88(a1),x52112)),f2(a1)) % 168.19/168.05 [5213]~E(f55(a1,x52131,x52132),f2(a1))+E(f55(a1,f317(f88(a1),x52131),x52132),f2(a1)) % 168.19/168.05 [5220]E(f317(f278(a849,x52201),f317(a124,x52202)),f188(f858(a849,a842)))+P22(f317(f317(f225(a849),x52201),x52202)) % 168.19/168.05 [5239]E(f133(a849,f317(f278(a849,x52391),x52392)),f125(a849))+P22(f317(f317(f226(a849),x52391),x52392)) % 168.19/168.05 [5244]~E(f317(f54(x52441),f317(f166(x52441),x52442)),f317(f189(f850(x52441)),x52442))+P22(f317(f131(x52441),x52442)) % 168.19/168.05 [5248]~P22(f317(f131(x52481),x52482))+P22(f317(f131(x52481),f317(f162(x52481),x52482))) % 168.19/168.05 [5249]~P22(f317(f131(x52491),x52492))+P22(f317(f131(x52491),f317(f165(x52491),x52492))) % 168.19/168.05 [5250]~P22(f317(f131(x52501),x52502))+P22(f317(f131(x52501),f317(f163(x52501),x52502))) % 168.19/168.05 [5256]E(f317(f48(a849,x52561),x52562),f2(a849))+~P22(f317(f317(f226(a849),x52561),x52562)) % 168.19/168.05 [5257]P22(f317(x52571,x52572))+~P22(f317(x52571,f317(a116,f836(x52571)))) % 168.19/168.05 [5258]P22(f317(f317(f225(a849),x52582),x52581))+P22(f317(f317(f225(a849),x52581),x52582)) % 168.19/168.05 [5259]P22(f317(f317(f225(a1),x52592),x52591))+P22(f317(f317(f225(a1),x52591),x52592)) % 168.19/168.05 [5261]~P79(x52611)+P22(f317(f317(f225(x52611),x52612),f317(f84(x52611),x52612))) % 168.19/168.05 [5264]P22(f317(x52641,f817(x52641)))+~P22(f317(x52641,f317(f112(a1),x52642))) % 168.19/168.05 [5289]E(f317(f317(f21(a849),x52891),x52892),f2(a849))+~P22(f317(f317(f225(a849),x52891),x52892)) % 168.19/168.05 [5306]E(f55(a849,x53061,x53062),x53061)+~P22(f317(f317(f226(a849),x53061),x53062)) % 168.19/168.05 [5314]E(f55(a1,x53141,f317(f88(a1),x53142)),f267(x53141,x53142))+P22(f317(f317(f225(a1),f2(a1)),x53142)) % 168.19/168.05 [5326]E(f317(f317(f21(a1),x53261),x53262),f195(x53261,x53262))+~P22(f317(f317(f225(a1),x53262),x53261)) % 168.19/168.05 [5345]P22(f317(f317(f225(a1),f2(a1)),f812(x53451)))+P22(f317(x53451,f317(f112(a1),x53452))) % 168.19/168.05 [5357]~P57(x53571)+P22(f317(f317(f319(x53571),x53572),f317(f166(x53571),f65(x53571)))) % 168.19/168.05 [5359]~P112(x53591)+P22(f317(f317(f225(x53591),f2(x53591)),f317(f112(x53591),x53592))) % 168.19/168.05 [5360]~P79(x53601)+P22(f317(f317(f225(x53601),f2(x53601)),f317(f84(x53601),x53602))) % 168.19/168.05 [5368]E(f317(f48(a1,x53681),x53682),f268(x53681,x53682))+~P22(f317(f317(f225(a1),f2(a1)),x53682)) % 168.19/168.05 [5388]E(f317(f317(f89(a849),x53881),f803(x53882,x53881)),x53882)+~P22(f317(f317(f225(a849),x53881),x53882)) % 168.19/168.05 [5400]~E(f317(f115(a1),x54001),f317(f112(a1),x54002))+P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x54001))) % 168.19/168.05 [5403]E(f279(a1,x54031,x54032),f188(f858(a1,a842)))+~P22(f317(f317(f226(a1),x54032),x54031)) % 168.19/168.05 [5406]~P113(x54061)+E(f317(f317(f90(x54061),f317(f84(x54061),x54062)),f317(f84(x54061),x54062)),f317(f317(f90(x54061),x54062),x54062)) % 168.19/168.05 [5411]E(f133(a849,f317(f278(a849,x54111),f317(a124,x54112))),f125(a849))+P22(f317(f317(f225(a849),x54111),x54112)) % 168.19/168.05 [5434]P22(f317(f131(x54341),x54342))+~P22(f317(f131(x54341),f317(f162(x54341),x54342))) % 168.19/168.05 [5435]P22(f317(f131(x54351),x54352))+~P22(f317(f131(x54351),f317(f163(x54351),x54352))) % 168.22/168.05 [5456]P22(f317(f71(a849),x54561))+P22(f317(f317(f319(a849),f361(x54561,x54562)),x54561)) % 168.22/168.05 [5457]P22(f317(f71(a849),x54571))+P22(f317(f317(f319(a849),f363(x54571,x54572)),x54571)) % 168.22/168.05 [5458]P22(f317(f317(f226(a849),x54582),f317(a124,x54581)))+P22(f317(f317(f226(a849),x54581),x54582)) % 168.22/168.05 [5459]E(f55(a1,x54591,x54592),f267(x54591,x54592))+~P22(f317(f317(f225(a1),f2(a1)),x54592)) % 168.22/168.05 [5462]E(f133(a849,f317(f278(a849,x54621),x54622)),f125(a849))+~P22(f317(f317(f225(a849),x54622),x54621)) % 168.22/168.05 [5463]~P78(x54631)+E(f317(f287(x54631,x54631,f88(x54631)),f317(f277(x54631),x54632)),f317(f232(x54631),f317(f88(x54631),x54632))) % 168.22/168.05 [5464]~P78(x54641)+E(f317(f287(x54641,x54641,f88(x54641)),f317(f280(x54641),x54642)),f317(f231(x54641),f317(f88(x54641),x54642))) % 168.22/168.05 [5465]~P78(x54651)+E(f317(f287(x54651,x54651,f88(x54651)),f317(f231(x54651),x54652)),f317(f280(x54651),f317(f88(x54651),x54652))) % 168.22/168.05 [5466]~P78(x54661)+E(f317(f287(x54661,x54661,f88(x54661)),f317(f232(x54661),x54662)),f317(f277(x54661),f317(f88(x54661),x54662))) % 168.22/168.05 [5479]E(x54791,f188(f858(x54792,a842)))+P22(f317(f317(f319(x54792),f612(x54791,x54792)),x54791)) % 168.22/168.05 [5480]E(x54801,f188(f858(x54802,a842)))+P22(f317(f317(f319(x54802),f613(x54801,x54802)),x54801)) % 168.22/168.05 [5491]~P22(f317(f317(f226(a849),x54911),x54912))+P22(f317(f317(f225(a849),x54911),x54912)) % 168.22/168.05 [5492]~P22(f317(f317(f226(a1),x54921),x54922))+P22(f317(f317(f225(a1),x54921),x54922)) % 168.22/168.05 [5508]E(f56(x55081,x55082),f317(f317(f237(a1,a1),f2(a1)),x55081))+~P22(f317(f317(f226(a1),x55081),x55082)) % 168.22/168.05 [5510]E(f209(f317(f88(a1),x55101),f317(f88(a1),x55102)),f209(x55101,x55102))+~P22(f317(f317(f226(a1),x55102),f2(a1))) % 168.22/168.05 [5522]E(x55221,x55222)+~E(f317(a3,f317(a124,f317(a19,x55221))),f317(a3,f317(a124,f317(a19,x55222)))) % 168.22/168.05 [5527]E(f56(x55271,x55272),f317(f317(f237(a1,a1),f2(a1)),x55271))+~P22(f317(f317(f225(a1),x55272),f2(a1))) % 168.22/168.05 [5558]E(f55(a849,f317(f115(a849),x55581),f317(f115(a849),x55582)),f2(a849))+~P22(f317(a193,f317(f115(a1),x55581))) % 168.22/168.05 [5575]P22(f317(f317(f225(a1),f2(a1)),f817(x55751)))+~P22(f317(x55751,f317(f112(a1),x55752))) % 168.22/168.05 [5604]P39(f279(a1,x56041,x56042))+~P22(f317(f317(f225(a1),f2(a1)),x56041)) % 168.22/168.05 [5605]~P22(f317(f71(x56051),x56052))+P22(f317(f71(f858(x56051,a842)),f317(f285(x56051),x56052))) % 168.22/168.05 [5619]E(f317(f48(a849,f317(f115(a849),x56191)),f317(f115(a849),x56192)),f2(a849))+~P22(f317(a193,f317(f115(a1),x56191))) % 168.22/168.05 [5620]E(f317(f317(f89(a1),x56201),f317(f112(a1),f813(x56202,x56201))),x56202)+~P22(f317(f317(f225(a1),x56201),x56202)) % 168.22/168.05 [5628]P22(f317(f317(f225(a849),x56281),x56282))+P22(f317(f317(f225(a849),f317(a124,x56282)),x56281)) % 168.22/168.05 [5670]E(f317(f317(f90(a849),f317(f115(a849),x56701)),f317(f115(a849),x56702)),f2(a849))+~P22(f317(f317(f226(a1),x56701),a92)) % 168.22/168.05 [5672]P22(f317(f317(f225(a849),x56721),f317(a124,x56722)))+~P22(f317(f317(f225(a849),x56721),x56722)) % 168.22/168.05 [5674]P22(f317(f317(f226(a849),x56741),f317(a124,x56742)))+~P22(f317(f317(f225(a849),x56741),x56742)) % 168.22/168.05 [5676]P22(f317(f317(f226(a849),x56761),f317(a124,x56762)))+~P22(f317(f317(f226(a849),x56761),x56762)) % 168.22/168.05 [5679]~E(x56791,x56792)+P22(f317(f317(f226(a1),x56791),f317(f317(f89(a1),x56792),f87(a1)))) % 168.22/168.05 [5682]E(f55(a1,x56821,x56822),f2(a1))+E(f317(f317(f21(a1),x56822),f55(a1,x56821,x56822)),f55(a1,f317(f88(a1),x56821),x56822)) % 168.22/168.05 [5690]E(x56901,f125(x56902))+P22(f317(f317(f319(x56902),f138(x56902,x56901)),f317(f166(x56902),x56901))) % 168.22/168.05 [5701]E(f94(f857(a849,a849),f57(x57011,x57012)),f317(f317(f237(a849,a849),f2(a849)),x57011))+~P22(f317(f317(f226(a849),x57011),x57012)) % 168.22/168.05 [5729]E(f317(f317(f89(a849),f317(f115(a849),x57291)),f317(f115(a849),x57292)),f317(f115(a849),x57292))+~P22(f317(f317(f226(a1),x57291),a92)) % 168.22/168.05 [5730]E(f317(f317(f21(a849),f317(f115(a849),x57301)),f317(f115(a849),x57302)),f317(f115(a849),x57301))+~P22(f317(f317(f226(a1),x57302),a92)) % 168.22/168.05 [5735]E(f317(a124,f317(f317(f89(a849),x57351),f807(x57352,x57351))),x57352)+~P22(f317(f317(f226(a849),x57351),x57352)) % 168.22/168.05 [5757]P22(f317(x57571,x57572))+~P22(f317(x57571,f317(a98,f569(x57572,x57571)))) % 168.22/168.05 [5765]~P22(f317(f317(f226(a849),x57651),f317(a124,x57652)))+P22(f317(f317(f225(a849),x57651),x57652)) % 168.22/168.05 [5811]E(f317(f317(f286(a849),x58111),f317(f278(a849,x58112),x58111)),f317(f278(a849,x58112),f317(a124,x58111)))+~P22(f317(f317(f225(a849),x58112),x58111)) % 168.22/168.05 [5816]E(x58161,f125(x58162))+E(f317(f317(f127(x58162),f126(x58162,x58161)),f317(f317(f145(x58162),f138(x58162,x58161)),f125(x58162))),x58161) % 168.22/168.05 [5828]P22(f317(f71(x58281),x58282))+~P22(f317(f317(f226(a849),f2(a849)),f317(f54(x58281),x58282))) % 168.22/168.05 [5830]~E(x58301,f188(f858(x58302,a842)))+~P22(f317(f317(f226(a849),f2(a849)),f317(f54(x58302),x58301))) % 168.22/168.05 [5841]~P22(f317(f317(f226(a849),x58411),x58412))+P22(f317(f317(f225(a849),f317(a124,x58411)),x58412)) % 168.22/168.05 [5849]~P103(x58491)+E(f142(x58491,x58491,f5(x58491),f146(x58491,x58492)),f133(x58491,f317(f166(x58491),x58492))) % 168.22/168.05 [5852]E(x58521,f125(x58522))+P22(f317(f317(f319(x58522),f317(f135(x58522),x58521)),f317(f166(x58522),x58521))) % 168.22/168.05 [5858]~P112(x58581)+P22(f317(f317(f226(x58581),x58582),f317(f317(f89(x58581),x58582),f87(x58581)))) % 168.22/168.05 [5860]~P79(x58601)+P22(f317(f317(f225(x58601),f317(f88(x58601),x58602)),f317(f84(x58601),x58602))) % 168.22/168.05 [5896]P22(f317(f71(a849),x58961))+~P22(f317(f317(f225(a849),f361(x58961,x58962)),x58962)) % 168.22/168.05 [5897]P22(f317(f71(a849),x58971))+~P22(f317(f317(f226(a849),f363(x58971,x58972)),x58972)) % 168.22/168.05 [5901]~P22(f317(f71(f857(x59011,x59011)),x59012))+P22(f317(f71(x59011),f317(f261(x59011),x59012))) % 168.22/168.05 [5918]E(f317(f48(a849,f317(a116,x59181)),f317(a116,x59182)),f317(a116,f317(f48(a1,x59181),x59182)))+~P22(f317(f317(f225(a1),f2(a1)),x59181)) % 168.22/168.05 [5953]~P22(f317(f317(f226(a849),x59532),f317(a124,x59531)))+~P22(f317(f317(f226(a849),x59531),x59532)) % 168.22/168.05 [5954]~P104(x59541)+E(f317(f317(f113(f858(x59541,a842)),f317(f277(x59541),x59542)),f317(f232(x59541),x59542)),f317(f317(f286(x59541),x59542),f188(f858(x59541,a842)))) % 168.22/168.05 [5966]P22(f317(f71(x59661),x59662))+~P22(f317(f71(f858(x59661,a842)),f317(f285(x59661),x59662))) % 168.22/168.05 [5989]P22(f317(f317(f225(a849),f317(a124,x59891)),f317(a124,x59892)))+~P22(f317(f317(f225(a849),x59891),x59892)) % 168.22/168.05 [5990]P22(f317(f317(f225(a849),f317(a19,x59901)),f317(a19,x59902)))+~P22(f317(f317(f225(a111),x59901),x59902)) % 168.22/168.05 [5991]P22(f317(f317(f225(a111),f317(a3,x59911)),f317(a3,x59912)))+~P22(f317(f317(f225(a849),x59911),x59912)) % 168.22/168.05 [5993]P22(f317(f317(f226(a849),f317(a124,x59931)),f317(a124,x59932)))+~P22(f317(f317(f226(a849),x59931),x59932)) % 168.22/168.05 [5994]P22(f317(f317(f226(a849),f317(a19,x59941)),f317(a19,x59942)))+~P22(f317(f317(f226(a111),x59941),x59942)) % 168.22/168.05 [5995]P22(f317(f317(f226(a111),f317(a3,x59951)),f317(a3,x59952)))+~P22(f317(f317(f226(a849),x59951),x59952)) % 168.22/168.05 [5998]E(x59981,x59982)+~E(f317(f287(a849,a1,f112(a1)),x59981),f317(f287(a849,a1,f112(a1)),x59982)) % 168.22/168.05 [6013]P22(f317(f317(f225(a849),x60131),x60132))+~P22(f317(f317(f225(a849),f317(a124,x60131)),x60132)) % 168.22/168.05 [6016]P22(f317(f317(f226(a849),x60161),x60162))+~P22(f317(f317(f225(a849),f317(a124,x60161)),x60162)) % 168.22/168.05 [6017]P22(f317(f317(f226(a849),x60171),x60172))+~P22(f317(f317(f226(a849),f317(a124,x60171)),x60172)) % 168.22/168.05 [6031]E(f55(a1,x60311,x60312),f2(a1))+E(f317(f317(f21(a1),f55(a1,x60311,x60312)),x60312),f55(a1,x60311,f317(f88(a1),x60312))) % 168.22/168.05 [6096]E(f317(f54(f858(x60961,a842)),f317(f285(x60961),x60962)),f317(f317(f238(a849),f317(a124,f317(a124,f2(a849)))),f317(f54(x60961),x60962)))+~P22(f317(f71(x60961),x60962)) % 168.22/168.05 [6099]E(x60991,f125(x60992))+E(f317(f317(f159(x60992),x60991),f317(f317(f21(a849),f317(f189(f850(x60992)),x60991)),f87(a849))),f138(x60992,x60991)) % 168.22/168.05 [6124]E(x61241,f125(x61242))+E(f317(f317(f127(x61242),f317(f165(x61242),x61241)),f317(f317(f145(x61242),f317(f135(x61242),x61241)),f125(x61242))),f317(f162(x61242),x61241)) % 168.22/168.05 [6155]~P22(f317(f71(x61551),f49(f858(x61551,a842),x61552)))+P22(f317(f71(f858(x61551,a842)),x61552)) % 168.22/168.05 [6178]P22(f317(f317(f225(a849),f317(f115(a849),x61781)),f317(f115(a849),x61782)))+~P22(f317(f317(f225(a1),x61781),a92)) % 168.22/168.05 [6196]~P22(f317(f317(f226(a1),x61961),x61962))+P22(f317(f317(f225(a1),x61961),f317(f317(f21(a1),x61962),f87(a1)))) % 168.22/168.05 [6197]~P22(f317(f317(f225(a1),x61971),x61972))+P22(f317(f317(f226(a1),x61971),f317(f317(f89(a1),x61972),f87(a1)))) % 168.22/168.05 [6198]~P22(f317(f317(f226(a1),x61981),x61982))+P22(f317(f317(f226(a1),x61981),f317(f317(f89(a1),x61982),f87(a1)))) % 168.22/168.05 [6200]~P22(f317(f317(f225(a1),x62001),x62002))+P22(f317(f317(f225(a849),f317(f115(a849),x62001)),f317(f115(a849),x62002))) % 168.22/168.05 [6202]~P22(f317(f317(f225(a849),x62021),x62022))+P22(f317(f317(f225(a1),f317(f112(a1),x62021)),f317(f112(a1),x62022))) % 168.22/168.05 [6203]~P22(f317(f317(f225(a1),x62031),x62032))+P22(f317(f317(f225(a1),f317(f115(a1),x62031)),f317(f115(a1),x62032))) % 168.22/168.05 [6205]~P22(f317(f317(f226(a849),x62051),x62052))+P22(f317(f317(f226(a1),f317(f112(a1),x62051)),f317(f112(a1),x62052))) % 168.22/168.05 [6206]~P22(f317(f317(f226(a1),x62061),x62062))+P22(f317(f317(f226(a1),f317(f115(a1),x62061)),f317(f115(a1),x62062))) % 168.22/168.05 [6221]~P22(f317(f317(f225(a849),x62211),x62212))+~P22(f317(f317(f225(a849),f317(a124,x62212)),x62211)) % 168.22/168.05 [6264]~P22(f317(f317(f225(a849),f317(a124,x62641)),f317(a124,x62642)))+P22(f317(f317(f225(a849),x62641),x62642)) % 168.22/168.05 [6265]~P22(f317(f317(f225(a111),f317(a3,x62651)),f317(a3,x62652)))+P22(f317(f317(f225(a849),x62651),x62652)) % 168.22/168.05 [6266]~P22(f317(f317(f225(a849),f317(a19,x62661)),f317(a19,x62662)))+P22(f317(f317(f225(a111),x62661),x62662)) % 168.22/168.05 [6268]~P22(f317(f317(f226(a849),f317(a124,x62681)),f317(a124,x62682)))+P22(f317(f317(f226(a849),x62681),x62682)) % 168.22/168.05 [6269]~P22(f317(f317(f226(a111),f317(a3,x62691)),f317(a3,x62692)))+P22(f317(f317(f226(a849),x62691),x62692)) % 168.22/168.05 [6270]~P22(f317(f317(f226(a849),f317(a116,x62701)),f317(a116,x62702)))+P22(f317(f317(f226(a1),x62701),x62702)) % 168.22/168.05 [6271]~P22(f317(f317(f226(a849),f317(a19,x62711)),f317(a19,x62712)))+P22(f317(f317(f226(a111),x62711),x62712)) % 168.22/168.05 [6311]~P22(f317(f317(f226(a849),f317(a116,x63112)),f317(a116,x63111)))+P22(f317(f317(f226(a1),f2(a1)),x63111)) % 168.22/168.05 [6343]P22(f317(f317(f225(a1),f2(a1)),f55(a1,x63431,x63432)))+~P22(f317(f317(f226(a1),f2(a1)),x63432)) % 168.22/168.05 [6498]P37(x64981,x64982)+~E(f317(f317(f265(x64981,x64981,x64981),x64982),x64982),f188(f858(f857(x64981,x64981),a842))) % 168.22/168.05 [6510]~P37(x65101,x65102)+P37(x65101,f317(f317(f265(x65101,x65101,x65101),x65102),x65102)) % 168.22/168.05 [6522]P22(f317(f317(f225(a1),x65221),x65222))+~P22(f317(f317(f226(a1),x65221),f317(f317(f89(a1),x65222),f87(a1)))) % 168.22/168.05 [6523]P22(f317(f317(f226(a1),x65231),x65232))+~P22(f317(f317(f225(a1),x65231),f317(f317(f21(a1),x65232),f87(a1)))) % 168.22/168.05 [6526]P22(f317(f317(f225(a849),x65261),x65262))+~P22(f317(f317(f225(a1),f317(f112(a1),x65261)),f317(f112(a1),x65262))) % 168.22/168.05 [6527]P22(f317(f317(f225(a1),x65271),x65272))+~P22(f317(f317(f225(a1),f317(f115(a1),x65271)),f317(f115(a1),x65272))) % 168.22/168.05 [6529]P22(f317(f317(f226(a849),x65291),x65292))+~P22(f317(f317(f226(a1),f317(f112(a1),x65291)),f317(f112(a1),x65292))) % 168.22/168.05 [6530]P22(f317(f317(f226(a1),x65301),x65302))+~P22(f317(f317(f226(a849),f317(f115(a849),x65301)),f317(f115(a849),x65302))) % 168.22/168.05 [6531]P22(f317(f317(f226(a1),x65311),x65312))+~P22(f317(f317(f226(a1),f317(f115(a1),x65311)),f317(f115(a1),x65312))) % 168.22/168.05 [6623]~E(f649(x66232,x66231),f125(x66231))+E(f317(f136(f850(x66231),f850(x66231),f127(x66231),f125(x66231)),x66232),f125(x66231)) % 168.22/168.05 [6624]~E(f650(x66242,x66241),f125(x66241))+E(f317(f136(f850(x66241),f850(x66241),f127(x66241),f125(x66241)),x66242),f125(x66241)) % 168.22/168.05 [6631]~P27(x66311)+E(f317(f136(x66311,x66311,f122(x66311),f188(x66311)),x66312),f49(x66311,f317(f166(x66311),x66312))) % 168.22/168.05 [6632]~P27(x66321)+E(f317(f136(x66321,x66321,f113(x66321),f233(x66321)),x66322),f50(x66321,f317(f166(x66321),x66322))) % 168.22/168.05 [6645]E(x66451,f2(a111))+E(f317(f317(f89(a849),f317(a19,f317(f317(f21(a111),x66451),f87(a111)))),f317(a124,x66452)),f317(f317(f89(a849),f317(a19,x66451)),x66452)) % 168.22/168.05 [6691]P22(f317(f317(f226(a1),f317(f317(f21(a1),x66911),x66912)),f2(a1)))+~P22(f317(f317(f226(a1),x66911),x66912)) % 168.22/168.05 [6717]~P103(x67171)+E(f317(f317(f122(f858(x67171,a842)),f317(f317(f286(x67171),x67172),f188(f858(x67171,a842)))),f317(f280(x67171),x67172)),f317(f232(x67171),x67172)) % 168.22/168.05 [6786]~P54(x67861,x67862)+P37(x67861,f317(f230(f857(x67861,x67861)),f317(f247(x67861,x67861,a842),x67862))) % 168.22/168.05 [6787]~P54(x67871,x67872)+P52(x67871,f317(f230(f857(x67871,x67871)),f317(f247(x67871,x67871,a842),x67872))) % 168.22/168.05 [6788]E(x67881,f188(f858(x67882,a842)))+~P22(f317(f317(f225(f858(x67882,a842)),x67881),f188(f858(x67882,a842)))) % 168.22/168.05 [6875]~P22(f317(f317(f226(a849),f2(a849)),x68752))+P22(f317(f317(f225(a849),f55(a849,x68751,x68752)),x68752)) % 168.22/168.05 [6876]~P22(f317(f317(f225(a1),f2(a1)),x68761))+P22(f317(f317(f225(a1),f55(a1,x68761,x68762)),x68761)) % 168.22/168.05 [6877]~P22(f317(f317(f226(a849),f2(a849)),x68772))+P22(f317(f317(f226(a849),f55(a849,x68771,x68772)),x68772)) % 168.22/168.05 [6879]~P22(f317(f317(f226(a1),f2(a1)),x68792))+P22(f317(f317(f226(a1),f55(a1,x68791,x68792)),x68792)) % 168.22/168.05 [6958]~P104(x69581)+E(f317(f317(f21(f858(x69581,a842)),f317(f317(f286(x69581),x69582),f188(f858(x69581,a842)))),f317(f231(x69581),x69582)),f317(f317(f286(x69581),x69582),f188(f858(x69581,a842)))) % 168.22/168.05 [7031]~P47(x70311,x70312)+P45(x70311,f233(f858(x70311,a842)),f317(f230(f857(x70311,x70311)),f317(f247(x70311,x70311,a842),x70312))) % 168.22/168.05 [7032]P22(f317(x70321,x70322))+P22(f317(f317(f319(f858(f857(a849,a849),a842)),f569(x70322,x70321)),a110)) % 168.22/168.05 [7081]E(f317(f317(f127(a849),f133(a849,f317(f278(a849,x70811),x70812))),f317(f317(f145(a849),x70812),f125(a849))),f133(a849,f317(f278(a849,x70811),f317(a124,x70812))))+~P22(f317(f317(f225(a849),x70811),x70812)) % 168.22/168.05 [7213]E(x72131,f2(a849))+~E(f317(f136(a849,a849,f89(a849),x72131),x72132),f2(a849)) % 168.22/168.05 [7243]~P22(f317(f317(f226(a1),f317(f317(f21(a1),x72431),x72432)),f2(a1)))+P22(f317(f317(f226(a1),x72431),x72432)) % 168.22/168.05 [7270]P37(x72701,x72702)+~P37(x72701,f317(f317(f265(x72701,x72701,x72701),x72702),x72702)) % 168.22/168.05 [7300]~P22(f317(f317(f225(a849),f317(a124,x73001)),x73002))+P22(f184(a842,a187,f317(f225(a849),x73001),x73002)) % 168.22/168.05 [7454]P19(a849,a849,f317(f317(f7(a849,a849,a849),f21(a849)),x74541),x74542)+P22(f317(f317(f319(a849),f827(x74541,x74542)),x74542)) % 168.22/168.05 [7510]E(f317(f317(f317(f75(a849,x75101,f89(a849)),f317(f16(a849,x75101),f87(a849))),f2(a849)),x75102),f317(f54(x75101),x75102))+~P22(f317(f71(x75101),x75102)) % 168.22/168.05 [7550]P19(a849,a849,f317(f317(f7(a849,a849,a849),f21(a849)),x75501),x75502)+~P22(f317(f317(f225(a849),x75501),f827(x75501,x75502))) % 168.22/168.05 [7607]P37(x76071,x76072)+P22(f317(f317(f225(f858(x76071,a842)),f684(x76072,x76071)),f317(f262(x76071,x76071,x76072),f684(x76072,x76071)))) % 168.22/168.05 [7612]P54(x76121,x76122)+~P37(x76121,f317(f230(f857(x76121,x76121)),f317(f247(x76121,x76121,a842),x76122))) % 168.22/168.05 [7685]P22(f317(f317(f225(a849),f317(a124,x76851)),x76852))+~P22(f184(a842,a187,f317(f225(a849),x76851),x76852)) % 168.22/168.05 [7741]P22(f317(f317(f319(f857(a849,a849)),f317(f317(f237(a849,a849),x77411),x77412)),f284(a849,a307)))+~P22(f317(f317(f225(a849),x77411),x77412)) % 168.22/168.05 [7828]P47(x78281,x78282)+~P45(x78281,f233(f858(x78281,a842)),f317(f230(f857(x78281,x78281)),f317(f247(x78281,x78281,a842),x78282))) % 168.22/168.05 [7887]~P22(f317(f131(x78871),x78872))+P22(f317(f131(f858(x78871,a842)),f317(f317(f148(f850(x78871),f858(x78871,a842)),f166(x78871)),f63(x78871,x78872)))) % 168.22/168.05 [8092]~P37(x80921,f317(f263(x80921,x80921),x80922))+P37(x80921,f317(f263(x80921,x80921),f317(f317(f265(x80921,x80921,x80921),x80922),f284(x80921,x80922)))) % 168.22/168.05 [8129]E(x81291,f2(a1))+P22(f317(f58(x81292,x81291),f317(f317(f237(a1,a1),f317(f48(a1,x81292),x81291)),f55(a1,x81292,x81291)))) % 168.22/168.05 [8213]P22(f317(f71(f857(x82131,x82131)),f317(f317(f265(x82131,x82131,x82131),x82132),f284(x82131,x82132))))+~P22(f317(f71(f857(x82131,x82131)),x82132)) % 168.22/168.05 [8258]~P22(f317(f317(f319(f857(a849,a849)),f317(f317(f237(a849,a849),x82581),x82582)),f284(a849,a307)))+P22(f317(f317(f225(a849),x82581),x82582)) % 168.22/168.05 [8276]~P66(x82761)+E(f317(f136(x82761,x82761,f317(f7(x82761,x82761,x82761),f89(x82761)),f2(x82761)),f317(f163(x82761),x82762)),f317(f136(x82761,x82761,f89(x82761),f2(x82761)),x82762)) % 168.22/168.05 [8461]~P103(x84611)+E(f317(f136(f850(x84611),x84611,f317(f7(x84611,f850(x84611),f850(x84611)),f143(x84611,x84611,f5(x84611))),f125(x84611)),x84612),f142(x84611,x84611,f5(x84611),x84612)) % 168.22/168.05 [8571]P22(f317(f317(f319(f857(a849,a849)),f317(f317(f237(a849,a849),x85711),x85712)),f317(f317(f265(a849,a849,a849),a307),f284(a849,a307))))+~P22(f317(f317(f226(a849),x85711),x85712)) % 168.22/168.05 [8614]~P22(f317(f71(f857(x86141,x86141)),f317(f317(f265(x86141,x86141,x86141),x86142),f284(x86141,x86142))))+P22(f317(f71(f857(x86141,x86141)),x86142)) % 168.22/168.05 [8864]P52(x88641,x88642)+P22(f317(f317(f319(f857(x88641,x88641)),f317(f317(f237(x88641,x88641),f748(x88642,x88641)),f748(x88642,x88641))),f317(f317(f265(x88641,x88641,x88641),x88642),f284(x88641,x88642)))) % 168.22/168.05 [8865]P52(x88651,x88652)+P22(f317(f317(f319(f857(x88651,x88651)),f317(f317(f237(x88651,x88651),f757(x88652,x88651)),f757(x88652,x88651))),f317(f317(f265(x88651,x88651,x88651),x88652),f284(x88651,x88652)))) % 168.22/168.05 [8979]~P22(f317(f317(f319(f857(a849,a849)),f317(f317(f237(a849,a849),x89791),x89792)),f317(f317(f265(a849,a849,a849),a307),f284(a849,a307))))+P22(f317(f317(f226(a849),x89791),x89792)) % 168.22/168.05 [5005]~P90(x50051)+E(f317(f317(f89(x50051),f317(f115(x50051),a92)),x50052),x50052) % 168.22/168.05 [5032]~P25(x50321)+E(f317(f317(f89(x50321),f317(f88(x50321),x50322)),x50322),f2(x50321)) % 168.22/168.05 [5033]~P69(x50331)+E(f317(f317(f89(x50331),f317(f88(x50331),x50332)),x50332),f2(x50331)) % 168.22/168.05 [5034]~P86(x50341)+E(f317(f317(f122(x50341),f317(f88(x50341),x50342)),x50342),f233(x50341)) % 168.22/168.05 [5035]~P86(x50351)+E(f317(f317(f113(x50351),f317(f88(x50351),x50352)),x50352),f188(x50351)) % 168.22/168.05 [5067]~P90(x50671)+E(f317(f317(f90(x50671),f317(f115(x50671),a109)),x50672),f317(f88(x50671),x50672)) % 168.22/168.05 [5233]~P100(x52331)+E(f317(f317(f90(x52331),f317(f88(x52331),f87(x52331))),x52332),f317(f88(x52331),x52332)) % 168.22/168.05 [5274]E(f317(f84(a1),x52741),f87(a1))+~E(f317(f84(a1),f317(f317(f90(a1),x52741),x52742)),f87(a1)) % 168.22/168.05 [5362]~P90(x53621)+E(f317(f317(f89(x53621),f87(x53621)),f317(f115(x53621),x53622)),f317(f115(x53621),f317(f317(f21(a1),x53622),a109))) % 168.22/168.05 [5415]~P93(x54151)+E(f11(x54151,f317(f317(f286(x54151),x54152),f188(f858(x54151,a842)))),x54152) % 168.22/168.05 [5416]~P93(x54161)+E(f10(x54161,f317(f317(f286(x54161),x54162),f188(f858(x54161,a842)))),x54162) % 168.22/168.05 [5417]~P103(x54171)+E(f14(x54171,f317(f317(f286(x54171),x54172),f188(f858(x54171,a842)))),x54172) % 168.22/168.05 [5418]~P103(x54181)+E(f15(x54181,f317(f317(f286(x54181),x54182),f188(f858(x54181,a842)))),x54182) % 168.22/168.05 [5419]~P27(x54191)+E(f49(x54191,f317(f317(f286(x54191),x54192),f188(f858(x54191,a842)))),x54192) % 168.22/168.05 [5420]~P27(x54201)+E(f50(x54201,f317(f317(f286(x54201),x54202),f188(f858(x54201,a842)))),x54202) % 168.22/168.05 [5442]E(f317(f317(f89(a849),x54421),f317(f317(f21(a849),x54422),x54421)),x54422)+P22(f317(f317(f226(a849),x54422),x54421)) % 168.22/168.05 [5472]E(x54721,f125(x54722))+P22(f317(f317(f226(a849),f2(a849)),f317(f189(f850(x54722)),x54721))) % 168.22/168.05 [5594]E(f317(f88(a1),f317(f48(a1,x55941),f317(f88(a1),x55942))),f268(x55941,x55942))+P22(f317(f317(f225(a1),f2(a1)),x55942)) % 168.22/168.05 [5602]~P103(x56021)+E(f12(x56021,f224(x56021),f317(f317(f286(x56021),x56022),f188(f858(x56021,a842)))),x56022) % 168.22/168.05 [5603]~P103(x56031)+E(f13(x56031,f223(x56031),f317(f317(f286(x56031),x56032),f188(f858(x56031,a842)))),x56032) % 168.22/168.05 [5662]E(f317(f317(f89(a849),x56621),f317(f317(f21(a849),x56622),x56621)),x56622)+~P22(f317(f317(f225(a849),x56621),x56622)) % 168.22/168.05 [5663]E(f317(f317(f21(a849),x56631),f317(f317(f21(a849),x56631),x56632)),x56632)+~P22(f317(f317(f225(a849),x56632),x56631)) % 168.22/168.05 [5681]E(f55(a849,f317(f317(f21(a849),x56811),x56812),x56812),f55(a849,x56811,x56812))+P22(f317(f317(f226(a849),x56811),x56812)) % 168.22/168.05 [5692]~E(x56922,f2(a849))+P22(f317(f317(f226(a849),f2(a849)),f317(f317(f238(a849),x56921),x56922))) % 168.22/168.05 [5738]~P90(x57381)+E(f317(f317(f89(x57381),f317(f88(x57381),f87(x57381))),f317(f115(x57381),x57382)),f317(f115(x57381),f317(f317(f89(a1),x57382),a109))) % 168.22/168.05 [5739]E(f317(f317(f238(a849),f317(f115(a849),x57391)),x57392),f317(f317(f238(a849),f2(a849)),x57392))+~P22(f317(a193,f317(f115(a1),x57391))) % 168.22/168.05 [5833]E(f317(f135(a849),f133(a849,f317(f278(a849,x58331),x58332))),x58331)+~P22(f317(f317(f226(a849),x58331),x58332)) % 168.22/168.05 [5853]E(f317(f317(f90(a849),f317(f115(a849),x58531)),f317(f115(a849),x58532)),f317(f115(a849),f317(f317(f90(a1),x58531),x58532)))+P22(f317(f317(f226(a1),x58531),a92)) % 168.22/168.05 [5859]~P119(x58591)+P22(f317(f317(f225(x58591),f2(x58591)),f317(f317(f90(x58591),x58592),x58592))) % 168.22/168.05 [5871]E(f317(f317(f21(a849),f317(a124,x58711)),x58712),f317(a124,f317(f317(f21(a849),x58711),x58712)))+~P22(f317(f317(f225(a849),x58712),x58711)) % 168.22/168.05 [5874]E(f55(a849,f317(f317(f21(a849),x58741),x58742),x58742),f55(a849,x58741,x58742))+~P22(f317(f317(f225(a849),x58742),x58741)) % 168.22/168.05 [5932]E(f317(f317(f238(a849),f317(a116,x59321)),x59322),f317(a116,f317(f317(f238(a1),x59321),x59322)))+~P22(f317(f317(f225(a1),f2(a1)),x59321)) % 168.22/168.05 [5944]P22(f317(f131(x59441),x59442))+P22(f317(f317(f226(a849),f575(x59442,x59441)),f317(f189(f850(x59441)),x59442))) % 168.22/168.05 [5945]P22(f317(f131(x59451),x59452))+P22(f317(f317(f226(a849),f596(x59452,x59451)),f317(f189(f850(x59451)),x59452))) % 168.22/168.05 [5960]~E(x59601,f125(x59602))+~P22(f317(f317(f226(a849),f2(a849)),f317(f189(f850(x59602)),x59601))) % 168.22/168.05 [5973]E(f138(a849,f133(a849,f317(f278(a849,x59731),x59732))),f317(f317(f21(a849),x59732),f87(a849)))+~P22(f317(f317(f226(a849),x59731),x59732)) % 168.22/168.05 [5976]E(f317(f317(f89(a1),x59761),f317(f112(a1),f317(a124,f814(x59762,x59761)))),x59762)+~P22(f317(f317(f226(a1),x59761),x59762)) % 168.22/168.05 [5983]E(x59831,f2(a849))+E(f317(f317(f90(a849),x59832),f317(f317(f238(a849),x59832),f317(f317(f21(a849),x59831),f87(a849)))),f317(f317(f238(a849),x59832),x59831)) % 168.22/168.05 [6007]E(f317(f317(f90(a849),f317(a116,x60071)),f317(a116,x60072)),f317(a116,f317(f317(f90(a1),x60071),x60072)))+~P22(f317(f317(f225(a1),f2(a1)),x60071)) % 168.22/168.05 [6021]~P84(x60211)+E(f317(f317(f89(x60211),x60212),x60212),f317(f317(f90(x60211),f317(f317(f89(x60211),f87(x60211)),f87(x60211))),x60212)) % 168.22/168.05 [6035]E(f317(f317(f21(a1),f317(f112(a1),x60351)),f317(f112(a1),x60352)),f317(f112(a1),f317(f317(f21(a849),x60351),x60352)))+~P22(f317(f317(f225(a849),x60352),x60351)) % 168.22/168.05 [6040]E(f317(f317(f237(a1,a1),f317(f115(a1),a109)),f317(f317(f89(a1),x60401),x60402)),f59(x60401,x60402))+~P22(f317(f317(f225(a1),x60402),f2(a1))) % 168.22/168.05 [6076]E(f173(x60761,x60762),f125(f850(x60761)))+P22(f317(f317(f319(f850(x60761)),f608(x60762,x60761)),f317(f166(f850(x60761)),x60762))) % 168.22/168.05 [6161]E(f317(f317(f145(a1),x61611),f172(f317(f317(f89(a1),x61611),f87(a1)),x61612)),f172(x61611,x61612))+~P22(f317(f317(f225(a1),x61611),x61612)) % 168.22/168.05 [6199]~P22(f317(f317(f226(a849),x61992),x61991))+P22(f317(f317(f226(a849),f2(a849)),f317(f317(f21(a849),x61991),x61992))) % 168.22/168.05 [6225]~P22(f317(f317(f226(a849),x62251),f317(a116,x62252)))+P22(f317(f317(f226(a1),f317(f112(a1),x62251)),x62252)) % 168.22/168.05 [6256]~P103(x62561)+E(f317(f317(f122(f858(x62561,a842)),f317(f231(x62561),x62562)),f317(f317(f286(x62561),x62562),f188(f858(x62561,a842)))),f317(f277(x62561),x62562)) % 168.22/168.05 [6257]~P22(f317(f317(f225(a1),f2(a1)),x62571))+P22(f317(f317(f225(a1),f2(a1)),f317(f317(f238(a1),x62571),x62572))) % 168.22/168.05 [6260]~P22(f317(f317(f226(a849),f2(a849)),x62601))+P22(f317(f317(f226(a849),f2(a849)),f317(f317(f238(a849),x62601),x62602))) % 168.22/168.05 [6286]~E(f317(x62861,f2(a849)),f2(a849))+E(f317(f317(f6(a849,a849),x62861),f279(a849,f317(a124,f2(a849)),x62862)),f317(f317(f6(a849,a849),x62861),f279(a849,f2(a849),x62862))) % 168.22/168.05 [6350]~P90(x63501)+E(f317(f317(f90(x63501),f317(f317(f89(x63501),f87(x63501)),f87(x63501))),f317(f115(x63501),x63502)),f317(f115(x63501),f317(f317(f89(a1),x63502),x63502))) % 168.22/168.05 [6366]E(f317(f317(f286(a1),x63661),f279(a1,f317(f317(f89(a1),x63661),f87(a1)),x63662)),f279(a1,x63661,x63662))+P22(f317(f317(f226(a1),x63662),x63661)) % 168.22/168.05 [6367]P22(f317(f317(f226(a849),x63671),f317(a116,x63672)))+~P22(f317(f317(f226(a1),f317(f112(a1),x63671)),x63672)) % 168.22/168.05 [6397]E(f317(a116,f317(f48(a1,f317(f115(a1),x63971)),f317(f115(a1),x63972))),f317(f48(a849,f317(f115(a849),x63971)),f317(f115(a849),x63972)))+P22(f317(a193,f317(f115(a1),x63971))) % 168.22/168.05 [6524]P22(f317(f317(f226(a849),x65241),x65242))+~P22(f317(f317(f226(a849),f2(a849)),f317(f317(f21(a849),x65242),x65241))) % 168.22/168.05 [6566]P22(f317(f317(f226(a849),f2(a849)),x65661))+~P22(f317(f317(f226(a849),f2(a849)),f317(f317(f90(a849),x65662),x65661))) % 168.22/168.05 [6567]P22(f317(f317(f226(a849),f2(a849)),x65671))+~P22(f317(f317(f226(a849),f2(a849)),f317(f317(f90(a849),x65671),x65672))) % 168.22/168.05 [6587]~P22(f317(f317(f225(a1),x65871),f2(a1)))+E(f317(f317(f90(a849),f317(a116,f317(f88(a1),x65871))),f317(a116,f317(f88(a1),x65872))),f317(a116,f317(f317(f90(a1),x65871),x65872))) % 168.22/168.05 [6642]~E(x66422,f188(f858(x66421,a842)))+P22(f317(f317(f225(f858(x66421,a842)),x66422),f317(f88(f858(x66421,a842)),x66422))) % 168.22/168.05 [6700]~P90(x67001)+E(f317(f317(f89(x67001),f317(f317(f89(x67001),f2(x67001)),f317(f115(x67001),x67002))),f317(f115(x67001),x67002)),f317(f115(x67001),f317(f317(f89(a1),x67002),x67002))) % 168.22/168.05 [6754]~P22(f317(f317(f226(a1),x67541),x67542))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x67541),f87(a1))),x67542)) % 168.22/168.05 [6820]E(x68201,f2(a849))+~P22(f317(f317(f225(a1),f317(f112(a1),x68202)),f317(f88(a1),f317(f112(a1),x68201)))) % 168.22/168.05 [6821]E(x68211,f2(a849))+~P22(f317(f317(f225(a1),f317(f112(a1),x68211)),f317(f88(a1),f317(f112(a1),x68212)))) % 168.22/168.05 [6931]E(f317(f317(f237(a1,a1),f317(f115(a1),a109)),f317(f317(f89(a1),x69311),x69312)),f59(x69311,x69312))+~P22(f317(f317(f225(a1),f2(a1)),f317(f317(f89(a1),x69311),x69312))) % 168.22/168.05 [6971]~P20(x69711,x69712)+P37(x69711,f317(f244(f858(f857(x69711,x69711),a842),f858(f857(x69711,x69711),a842)),x69712)) % 168.22/168.05 [6993]~P22(f317(f317(f225(a849),f317(a124,f2(a849))),x69931))+P22(f317(f317(f225(a849),f317(a124,f2(a849))),f317(f317(f238(a849),x69931),x69932))) % 168.22/168.05 [7162]~P22(f317(f317(f225(a1),x71621),x71622))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x71621),x71621)),f317(f317(f89(a1),x71622),x71622))) % 168.22/168.05 [7167]~P22(f317(f317(f226(a1),x71671),x71672))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x71671),x71671)),f317(f317(f89(a1),x71672),x71672))) % 168.22/168.05 [7215]~P22(f317(f317(f226(a849),f2(a849)),x72151))+P22(f317(f317(f226(a849),f317(f317(f21(a849),x72151),f317(a124,x72152))),x72151)) % 168.22/168.05 [7253]P22(f317(f317(f225(a849),f317(a124,f2(a849))),x72531))+~P22(f317(f317(f225(a849),f317(a124,f2(a849))),f317(f317(f90(a849),x72532),x72531))) % 168.22/168.05 [7254]P22(f317(f317(f225(a849),f317(a124,f2(a849))),x72541))+~P22(f317(f317(f225(a849),f317(a124,f2(a849))),f317(f317(f90(a849),x72541),x72542))) % 168.22/168.05 [7257]P22(f317(f317(f225(a849),f317(f317(f159(a849),x72571),x72572)),f317(f160(a849),x72571)))+~P22(f317(f317(f226(a849),x72572),f317(f189(f850(a849)),x72571))) % 168.22/168.05 [7299]P22(f317(f317(f226(a1),x72991),x72992))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),x72991),f87(a1))),x72992)) % 168.22/168.05 [7341]P22(f317(f71(x73411),f233(f858(x73411,a842))))+~P22(f317(f71(f858(x73412,x73411)),f233(f858(f858(x73412,x73411),a842)))) % 168.22/168.05 [7342]P22(f317(f71(x73421),f233(f858(x73421,a842))))+~P22(f317(f71(f856(x73422,x73421)),f233(f858(f856(x73422,x73421),a842)))) % 168.22/168.05 [7343]P22(f317(f71(x73431),f233(f858(x73431,a842))))+~P22(f317(f71(f856(x73431,x73432)),f233(f858(f856(x73431,x73432),a842)))) % 168.22/168.05 [7384]E(x73841,f188(f858(x73842,a842)))+~P22(f317(f317(f225(f858(x73842,a842)),x73841),f317(f88(f858(x73842,a842)),x73841))) % 168.22/168.05 [7520]E(f317(f136(f850(x75201),f850(x75201),f127(x75201),f125(x75201)),x75202),f125(x75201))+P22(f317(f317(f319(f850(x75201)),f649(x75202,x75201)),f317(f166(f850(x75201)),x75202))) % 168.22/168.05 [7521]E(f317(f136(f850(x75211),f850(x75211),f127(x75211),f125(x75211)),x75212),f125(x75211))+P22(f317(f317(f319(f850(x75211)),f650(x75212,x75211)),f317(f166(f850(x75211)),x75212))) % 168.22/168.05 [7757]P22(f317(f317(f225(a1),x77571),x77572))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),x77571),x77571)),f317(f317(f89(a1),x77572),x77572))) % 168.22/168.05 [7762]P22(f317(f317(f226(a1),x77621),x77622))+~P22(f317(f317(f226(a1),f317(f317(f89(a1),x77621),x77621)),f317(f317(f89(a1),x77622),x77622))) % 168.22/168.05 [7848]~P84(x78481)+E(f317(f317(f90(x78481),f317(f317(f89(x78481),f87(x78481)),f87(x78481))),f317(f317(f6(a849,x78481),f112(x78481)),f279(a849,f87(a849),x78482))),f317(f317(f90(x78481),f317(f112(x78481),x78482)),f317(f317(f89(x78481),f317(f112(x78481),x78482)),f87(x78481)))) % 168.22/168.05 [7901]P22(f317(f317(f319(a849),x79011),x79012))+~P22(f317(f317(f319(a1),f317(f112(a1),x79011)),f317(f287(a849,a1,f112(a1)),x79012))) % 168.22/168.05 [8064]~P22(f317(f71(x80641),x80642))+E(f317(f287(a849,x80641,f549(x80642,x80641)),f317(f230(a849),f317(f317(f7(a849,a849,a842),f226(a849)),f550(x80642,x80641)))),x80642) % 168.22/168.05 [8355]P46(x83551,x83552)+P22(f317(f317(f319(f857(x83551,x83551)),f317(f317(f237(x83551,x83551),f356(x83552,x83551)),f356(x83552,x83551))),x83552)) % 168.22/168.05 [8503]~P90(x85031)+E(f317(f317(f21(x85031),f87(x85031)),f317(f115(x85031),x85032)),f317(f115(x85031),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f88(a1),x85032)))) % 168.22/168.05 [8611]~P22(f317(f317(f226(f858(a849,a842)),x86111),x86112))+P22(f317(f317(f226(f858(a1,a842)),f317(f287(a849,a1,f112(a1)),x86111)),f317(f287(a849,a1,f112(a1)),x86112))) % 168.22/168.05 [8639]~P22(f317(f317(f226(a1),x86391),x86392))+P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),x86391),x86391)),a109)),f317(f317(f89(a1),x86392),x86392))) % 168.22/168.05 [8641]~P22(f317(f317(f226(a1),x86411),x86412))+P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x86411),x86411)),a109)),f317(f317(f89(a1),x86412),x86412))) % 168.22/168.05 [8709]~P22(f317(f317(f319(a849),x87091),f317(f166(a849),x87092)))+P22(f317(f317(f225(a849),x87091),f317(f136(a849,a849,f89(a849),f2(a849)),x87092))) % 168.22/168.05 [8799]P44(x87991,x87992)+~P22(f317(f317(f319(f857(x87991,x87991)),f317(f317(f237(x87991,x87991),f338(x87992,x87991)),f338(x87992,x87991))),x87992)) % 168.22/168.05 [8947]~P22(f317(f317(f225(f858(a1,a842)),f317(f287(a849,a1,f112(a1)),x89471)),f317(f287(a849,a1,f112(a1)),x89472)))+P22(f317(f317(f225(f858(a849,a842)),x89471),x89472)) % 168.22/168.05 [8948]~P22(f317(f317(f226(f858(a1,a842)),f317(f287(a849,a1,f112(a1)),x89481)),f317(f287(a849,a1,f112(a1)),x89482)))+P22(f317(f317(f226(f858(a849,a842)),x89481),x89482)) % 168.22/168.05 [9025]P22(f317(f317(f226(a1),x90251),x90252))+~P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),x90251),x90251)),a109)),f317(f317(f89(a1),x90252),x90252))) % 168.22/168.05 [9027]P22(f317(f317(f226(a1),x90271),x90272))+~P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x90271),x90271)),a109)),f317(f317(f89(a1),x90272),x90272))) % 168.22/168.05 [9928]~P22(f317(f71(x99281),x99282))+E(f317(f189(f850(x99281)),f99(f850(x99281),f317(f317(f18(f850(x99281),a842,a842),f317(f317(f8(a842,f858(a842,a842),f850(x99281)),a315),f317(f317(f7(f850(x99281),f858(x99281,a842),a842),f317(f317(f8(f858(x99281,a842),f858(f858(x99281,a842),a842),f850(x99281)),a314),f166(x99281))),x99282))),f131(x99281)))),f206(x99281,x99282)) % 168.22/168.05 [10061]~P18(a845,x100611,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),x100612),f194(x100612))),f188(f858(f848(a845),a842))))+P18(a845,x100611,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),f317(f317(f8(f858(a845,f858(a845,a842)),f858(a845,a842),a845),f317(f8(f858(a845,a842),a842,a845),f97(a845))),f317(f317(f8(f858(a845,a842),f858(a845,f858(a845,a842)),a845),f317(f7(a845,f858(a845,a842),f858(a845,a842)),f317(f317(f8(f858(a845,f858(a842,a842)),f858(f858(a845,a842),f858(a845,a842)),a845),f18(a845,a842,a842)),f317(f317(f8(f858(a845,a842),f858(a845,f858(a842,a842)),a845),f317(f8(a842,f858(a842,a842),a845),a320)),f194(x100612))))),a314))),x100612),a314)),f188(f858(f848(a845),a842)))) % 168.22/168.05 [5972]E(f317(f317(f89(a849),f317(f317(f21(a849),x59721),x59722)),x59722),x59721)+~P22(f317(f317(f225(a849),x59722),x59721)) % 168.22/168.05 [6010]E(f317(f48(a849,f317(f317(f90(a849),x60101),x60102)),x60102),x60101)+~P22(f317(f317(f226(a849),f2(a849)),x60102)) % 168.22/168.05 [6011]E(f317(f48(a849,f317(f317(f90(a849),x60111),x60112)),x60111),x60112)+~P22(f317(f317(f226(a849),f2(a849)),x60111)) % 168.22/168.05 [6036]~P67(x60361)+E(f317(f317(f6(a849,x60361),f317(f159(x60361),x60362)),f317(f278(a849,f2(a849)),f317(f189(f850(x60361)),x60362))),f317(f160(x60361),x60362)) % 168.22/168.05 [6153]E(f55(a849,f317(a124,f317(f317(f90(a849),x61531),x61532)),x61531),f87(a849))+~P22(f317(f317(f226(a849),f87(a849)),x61531)) % 168.22/168.05 [6159]E(f317(a124,f317(f317(f89(a849),f317(f115(a849),x61591)),x61592)),f317(f317(f89(a849),f87(a849)),x61592))+~P22(f317(a193,f317(f115(a1),x61591))) % 168.22/168.05 [6187]E(f317(a116,f317(f317(f238(a1),f317(f115(a1),x61871)),x61872)),f317(f317(f238(a849),f317(f115(a849),x61871)),x61872))+P22(f317(a193,f317(f115(a1),x61871))) % 168.22/168.05 [6421]E(f317(f317(f21(a849),x64211),f317(f115(a849),f317(f317(f89(a1),x64212),a109))),f317(f317(f21(a849),f317(a124,x64211)),f317(f115(a849),x64212)))+~P22(f317(f317(f226(a1),a92),x64212)) % 168.22/168.05 [6497]E(x64971,f2(a849))+E(f317(a124,f317(f317(f89(a849),f317(f317(f21(a849),x64971),f87(a849))),x64972)),f317(f317(f89(a849),x64971),x64972)) % 168.22/168.05 [6537]E(x65371,f2(a1))+P22(f317(f317(f226(a1),f2(a1)),f317(f317(f238(a1),f317(f84(a1),x65371)),x65372))) % 168.22/168.05 [6552]~E(x65522,f2(a849))+P22(f317(f317(f226(a1),f2(a1)),f317(f317(f238(a1),f317(f84(a1),x65521)),x65522))) % 168.22/168.05 [6591]E(x65911,f2(a849))+E(f317(f317(f89(a849),x65912),f317(f317(f90(a849),f317(f317(f21(a849),x65911),f87(a849))),x65912)),f317(f317(f90(a849),x65911),x65912)) % 168.22/168.05 [6636]~P22(f317(f317(f225(a1),x66361),x66362))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x66361),a109)),x66362)) % 168.22/168.05 [6757]E(f317(f317(f145(a849),x67571),f133(a849,f317(f278(a849,f317(a124,x67571)),x67572))),f133(a849,f317(f278(a849,x67571),x67572)))+~P22(f317(f317(f226(a849),x67571),x67572)) % 168.22/168.05 [6963]E(x69631,x69632)+~E(f317(f317(f21(a1),f317(f317(f89(a1),x69631),x69631)),a109),f317(f317(f21(a1),f317(f317(f89(a1),x69632),x69632)),a109)) % 168.22/168.05 [6966]E(x69661,f125(x69662))+E(f252(x69662,f317(f317(f148(x69662,f857(a111,x69662)),f317(f237(a111,x69662),f87(a111))),x69661)),f259(x69662,x69661)) % 168.22/168.05 [7185]P22(f317(f317(f225(a1),x71851),x71852))+~P22(f317(f317(f226(a1),f317(f317(f89(a1),x71851),a109)),x71852)) % 168.22/168.05 [7661]~P22(f317(f317(f226(a849),x76611),x76612))+P22(f317(f317(f319(f857(a849,a849)),f317(f317(f237(a849,a849),x76611),x76612)),a229)) % 168.22/168.05 [7875]~P22(f317(f317(f226(a111),f2(a111)),x78751))+P22(f317(f317(f226(a111),f317(f244(a111,f857(a111,a111)),f317(f253(x78751),x78752))),x78751)) % 168.22/168.05 [8192]~P79(x81921)+P22(f317(f317(f225(x81921),f317(f84(x81921),f317(f160(x81921),x81922))),f317(f160(x81921),f317(f317(f148(x81921,x81921),f84(x81921)),x81922)))) % 168.22/168.05 [8215]P22(f317(f317(f226(a849),x82151),x82152))+~P22(f317(f317(f319(f857(a849,a849)),f317(f317(f237(a849,a849),x82151),x82152)),a229)) % 168.22/168.05 [8380]E(f317(f317(f237(x83801,x83801),f769(x83802,x83801)),f769(x83802,x83801)),x83802)+~P22(f317(f317(f319(f857(x83801,x83801)),x83802),f284(x83801,f188(f858(f857(x83801,x83801),a842))))) % 168.22/168.05 [8424]E(f317(f278(a849,x84241),f317(f317(f89(a849),x84241),f317(f54(a849),x84242))),x84242)+~P22(f317(f317(f225(f858(a849,a842)),x84242),f317(f278(a849,x84241),f317(f317(f89(a849),x84241),f317(f54(a849),x84242))))) % 168.22/168.05 [8738]E(f317(f48(a1,f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),x87381),x87381)),a109))),f317(f115(a1),f317(f317(f89(a1),x87382),x87382))),f317(f48(a1,f317(f115(a1),x87381)),f317(f115(a1),x87382)))+~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x87382))) % 168.22/168.05 [8863]E(f317(f48(a1,f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),x88631),x88631)),a109))),f317(f115(a1),f317(f317(f89(a1),x88632),x88632))),f317(f48(a1,f317(f317(f89(a1),f317(f115(a1),x88631)),f87(a1))),f317(f115(a1),x88632)))+P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x88632))) % 168.22/168.05 [8875]E(f170(f850(x88751),f317(f317(f8(a842,a842,f850(x88751)),a312),f317(f317(f7(f850(x88751),f850(x88751),a842),a314),f125(x88751))),x88752),f173(x88751,f173(x88751,x88752)))+~P29(a849,f317(f163(a849),f317(f317(f148(f850(x88751),a849),f189(f850(x88751))),x88752))) % 168.22/168.05 [9524]P18(a845,x95241,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),f317(a29,x95242)),f194(f317(a29,x95242)))),f188(f858(f848(a845),a842))))+~P18(a845,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),f317(a29,x95242)),f194(f317(a29,x95242)))),x95241),f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),f317(f222(a843),f317(a27,x95242))),f194(f317(f222(a843),f317(a27,x95242))))),f188(f858(f848(a845),a842)))) % 168.22/168.05 [9692]P22(f317(a193,x96922))+E(f317(f317(f95(a1,a849),f317(f317(f21(a1),x96921),x96922)),f317(f317(f18(a1,a849,a849),f317(f317(f7(a1,a849,f858(a849,a849)),f317(f317(f8(a842,f858(a849,f858(a849,a849)),a1),f108(a849)),a193)),f2(a849))),a116)),f317(f317(f21(a849),f317(a116,x96921)),f317(a116,x96922))) % 168.22/168.05 [9700]E(f317(f317(f95(a1,a849),f317(f115(a1),f317(f317(f89(a1),x97001),f317(f88(a1),x97002)))),f317(f317(f18(a1,a849,a849),f317(f317(f7(a1,a849,f858(a849,a849)),f317(f317(f8(a842,f858(a849,f858(a849,a849)),a1),f108(a849)),a193)),f2(a849))),a116)),f317(f317(f21(a849),f317(f115(a849),x97001)),f317(f115(a849),x97002)))+P22(f317(f317(f226(a1),x97002),a92)) % 168.22/168.05 [9701]~P20(x97011,x97012)+P22(f317(f317(f225(f858(f857(x97011,x97011),a842)),f317(f317(f265(x97011,x97011,x97011),f317(f244(f858(f857(x97011,x97011),a842),f858(f857(x97011,x97011),a842)),x97012)),f317(f246(f858(f857(x97011,x97011),a842),f858(f857(x97011,x97011),a842)),x97012))),f317(f244(f858(f857(x97011,x97011),a842),f858(f857(x97011,x97011),a842)),x97012))) % 168.22/168.05 [9770]~E(f317(f54(a849),f317(f230(a849),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),f317(f317(f7(a849,f858(a849,a842),a842),f319(a849)),x97701))),f317(f317(f7(a849,a849,a842),f226(a849)),f317(a124,x97702))))),f2(a849))+~P22(f317(f317(f319(a849),f2(a849)),x97701)) % 168.22/168.05 [9831]E(f55(a1,f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),x98311),x98311)),a109)),f317(f115(a1),f317(f317(f89(a1),x98312),x98312))),f317(f317(f89(a1),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f55(a1,f317(f115(a1),x98311),f317(f115(a1),x98312)))),f87(a1)))+~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x98312))) % 168.22/168.05 [9840]E(f55(a1,f317(f115(a1),f317(f317(f21(a1),f317(f317(f89(a1),x98401),x98401)),a109)),f317(f115(a1),f317(f317(f89(a1),x98402),x98402))),f317(f317(f21(a1),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f55(a1,f317(f317(f89(a1),f317(f115(a1),x98401)),f87(a1)),f317(f115(a1),x98402)))),f87(a1)))+P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x98402))) % 168.22/168.05 [9896]~P27(x98961)+E(f49(x98961,f317(f230(x98961),f317(f317(f8(f858(x98961,a842),a842,x98961),f97(x98961)),f317(f317(f8(f858(x98961,a842),f858(x98961,a842),x98961),f317(f18(x98961,a842,a842),f317(f317(f8(a842,f858(a842,a842),x98961),a320),f317(f317(f7(x98961,f858(x98961,a842),a842),f319(x98961)),x98962)))),f225(x98961))))),f50(x98961,x98962)) % 168.22/168.05 [9921]~P37(x99211,x99212)+P54(x99211,f317(f317(f7(x99211,f858(f857(x99211,x99211),a842),f858(x99211,a842)),f317(f317(f8(f858(x99211,f858(f858(f857(x99211,x99211),a842),a842)),f858(f858(f857(x99211,x99211),a842),f858(x99211,a842)),x99211),f7(x99211,f858(f857(x99211,x99211),a842),a842)),f317(f317(f8(f858(x99211,f857(x99211,x99211)),f858(x99211,f858(f858(f857(x99211,x99211),a842),a842)),x99211),f317(f8(f857(x99211,x99211),f858(f858(f857(x99211,x99211),a842),a842),x99211),f319(f857(x99211,x99211)))),f237(x99211,x99211)))),x99212)) % 168.22/168.05 [9922]~P6(x99221,f233(f858(x99221,a842)),x99222)+P5(x99221,f317(f317(f7(x99221,f858(f857(x99221,x99221),a842),f858(x99221,a842)),f317(f317(f8(f858(x99221,f858(f858(f857(x99221,x99221),a842),a842)),f858(f858(f857(x99221,x99221),a842),f858(x99221,a842)),x99221),f7(x99221,f858(f857(x99221,x99221),a842),a842)),f317(f317(f8(f858(x99221,f857(x99221,x99221)),f858(x99221,f858(f858(f857(x99221,x99221),a842),a842)),x99221),f317(f8(f857(x99221,x99221),f858(f858(f857(x99221,x99221),a842),a842),x99221),f319(f857(x99221,x99221)))),f237(x99221,x99221)))),x99222)) % 168.22/168.05 [9957]P37(x99571,x99572)+~P54(x99571,f317(f317(f7(x99571,f858(f857(x99571,x99571),a842),f858(x99571,a842)),f317(f317(f8(f858(x99571,f858(f858(f857(x99571,x99571),a842),a842)),f858(f858(f857(x99571,x99571),a842),f858(x99571,a842)),x99571),f7(x99571,f858(f857(x99571,x99571),a842),a842)),f317(f317(f8(f858(x99571,f857(x99571,x99571)),f858(x99571,f858(f858(f857(x99571,x99571),a842),a842)),x99571),f317(f8(f857(x99571,x99571),f858(f858(f857(x99571,x99571),a842),a842),x99571),f319(f857(x99571,x99571)))),f237(x99571,x99571)))),x99572)) % 168.22/168.05 [9958]P6(x99581,f233(f858(x99581,a842)),x99582)+~P5(x99581,f317(f317(f7(x99581,f858(f857(x99581,x99581),a842),f858(x99581,a842)),f317(f317(f8(f858(x99581,f858(f858(f857(x99581,x99581),a842),a842)),f858(f858(f857(x99581,x99581),a842),f858(x99581,a842)),x99581),f7(x99581,f858(f857(x99581,x99581),a842),a842)),f317(f317(f8(f858(x99581,f857(x99581,x99581)),f858(x99581,f858(f858(f857(x99581,x99581),a842),a842)),x99581),f317(f8(f857(x99581,x99581),f858(f858(f857(x99581,x99581),a842),a842),x99581),f319(f857(x99581,x99581)))),f237(x99581,x99581)))),x99582)) % 168.22/168.05 [7145]E(f317(f317(f89(a849),f317(f115(a849),f317(f317(f21(a1),x71451),a109))),x71452),f317(a124,f317(f317(f89(a849),f317(f115(a849),x71451)),x71452)))+P22(f317(a193,f317(f115(a1),x71451))) % 168.22/168.05 [7577]~P90(x75771)+E(f317(f317(f89(x75771),f317(f317(f89(x75771),f87(x75771)),f317(f115(x75771),x75772))),f317(f115(x75771),x75772)),f317(f115(x75771),f317(f317(f21(a1),f317(f317(f89(a1),x75772),x75772)),a109))) % 168.22/168.05 [8219]~P22(f317(f317(f225(a1),x82191),x82192))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x82191),x82191)),f317(f317(f21(a1),f317(f317(f89(a1),x82192),x82192)),a109))) % 168.22/168.05 [8221]~P22(f317(f317(f225(a1),x82211),x82212))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x82211),x82211)),f317(f317(f21(a1),f317(f317(f89(a1),x82212),x82212)),a109))) % 168.22/168.05 [8643]P22(f317(f317(f225(a1),x86431),x86432))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),x86431),x86431)),f317(f317(f21(a1),f317(f317(f89(a1),x86432),x86432)),a109))) % 168.22/168.05 [8645]P22(f317(f317(f225(a1),x86451),x86452))+~P22(f317(f317(f226(a1),f317(f317(f89(a1),x86451),x86451)),f317(f317(f21(a1),f317(f317(f89(a1),x86452),x86452)),a109))) % 168.22/168.05 [8936]~P22(f317(f317(f225(a1),x89361),x89362))+P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),x89361),x89361)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),x89362),x89362)),a109))) % 168.22/168.05 [8938]~P22(f317(f317(f226(a1),x89381),x89382))+P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x89381),x89381)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),x89382),x89382)),a109))) % 168.22/168.05 [9196]P22(f317(f317(f225(a1),x91961),x91962))+~P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),x91961),x91961)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),x91962),x91962)),a109))) % 168.22/168.05 [9198]P22(f317(f317(f226(a1),x91981),x91982))+~P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),x91981),x91981)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),x91982),x91982)),a109))) % 168.22/168.05 [9228]~P22(f317(f71(x92281),x92282))+P22(f317(f71(f858(x92281,a842)),f317(f230(f858(x92281,a842)),f317(f317(f7(f858(x92281,a842),f858(x92281,a842),a842),f225(f858(x92281,a842))),x92282)))) % 168.22/168.05 [9276]~E(f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),x92761),f188(f858(f857(a849,a849),a842)))),f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),x92762),f188(f858(f857(a849,a849),a842)))))+P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),x92761),x92762)),a120)) % 168.22/168.05 [9358]E(f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),x93581),f188(f858(f857(a849,a849),a842)))),f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),x93582),f188(f858(f857(a849,a849),a842)))))+~P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),x93581),x93582)),a120)) % 168.22/168.05 [9906]~P27(x99061)+E(f50(x99061,f317(f230(x99061),f317(f317(f8(f858(x99061,a842),a842,x99061),f97(x99061)),f317(f317(f8(f858(x99061,a842),f858(x99061,a842),x99061),f317(f18(x99061,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99061),a320),f317(f317(f7(x99061,f858(x99061,a842),a842),f319(x99061)),x99062)))),f317(f7(x99061,x99061,a842),f225(x99061)))))),f49(x99061,x99062)) % 168.22/168.05 [9927]P22(f317(f317(f319(a849),f2(a849)),x99271))+E(f317(f54(a849),f317(f230(a849),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),f317(f317(f7(a849,f858(a849,a842),a842),f317(f317(f8(a849,f858(f858(a849,a842),a842),a849),f319(a849)),a124)),x99271))),f317(f317(f7(a849,a849,a842),f226(a849)),x99272)))),f317(f54(a849),f317(f230(a849),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),f317(f317(f7(a849,f858(a849,a842),a842),f319(a849)),x99271))),f317(f317(f7(a849,a849,a842),f226(a849)),f317(a124,x99272)))))) % 168.22/168.05 [7447]~P90(x74471)+E(f317(f317(f90(x74471),x74472),f317(f115(x74471),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),x74472) % 168.22/168.05 [7710]~P90(x77101)+E(f317(f317(f89(x77101),f317(f115(x77101),x77102)),f87(x77101)),f317(f115(x77101),f317(f317(f89(a1),x77102),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))) % 168.22/168.05 [7846]P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x78462)))+E(f317(f317(f238(a1),x78461),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),x78462),x78462)),a109))),f87(a1)) % 168.22/168.05 [9253]~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x92532)))+E(f317(f317(f238(a1),x92531),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),x92532),x92532)),a109))),f317(f317(f95(a1,a1),f317(f317(f238(a1),x92531),f317(f115(a849),x92532))),f317(f317(f18(a1,a1,a1),f317(f317(f8(a1,f858(a1,a1),a1),f90(a1)),f317(f90(a1),x92531))),f5(a1)))) % 168.22/168.05 [9760]~P22(f317(f317(f225(a849),f317(f115(a849),x97601)),f317(a124,x97602)))+P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x97601),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f7(a1,a849,a842),f317(f317(f8(a849,f858(a849,a842),a1),f225(a849)),a116)),x97602)))) % 168.22/168.05 [9761]~P22(f317(f317(f226(a849),f317(f115(a849),x97611)),f317(a124,x97612)))+P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x97611),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f7(a1,a849,a842),f317(f317(f8(a849,f858(a849,a842),a1),f226(a849)),a116)),x97612)))) % 168.22/168.05 [9815]P22(f317(f317(f225(a849),f317(f115(a849),x98151)),f317(a124,x98152)))+~P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x98151),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f7(a1,a849,a842),f317(f317(f8(a849,f858(a849,a842),a1),f225(a849)),a116)),x98152)))) % 168.22/168.05 [9816]P22(f317(f317(f226(a849),f317(f115(a849),x98161)),f317(a124,x98162)))+~P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x98161),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f7(a1,a849,a842),f317(f317(f8(a849,f858(a849,a842),a1),f226(a849)),a116)),x98162)))) % 168.22/168.05 [9846]~P22(f317(f317(f225(a849),f317(a124,x98462)),f317(f115(a849),x98461)))+P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x98461),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f8(a849,a842,a1),f317(f225(a849),x98462)),a116))))) % 168.22/168.05 [9847]~P22(f317(f317(f226(a849),f317(a124,x98472)),f317(f115(a849),x98471)))+P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x98471),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f8(a849,a842,a1),f317(f226(a849),x98472)),a116))))) % 168.22/168.05 [9894]P22(f317(f317(f225(a849),f317(a124,x98941)),f317(f115(a849),x98942)))+~P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x98942),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f8(a849,a842,a1),f317(f225(a849),x98941)),a116))))) % 168.22/168.05 [9895]P22(f317(f317(f226(a849),f317(a124,x98951)),f317(f115(a849),x98952)))+~P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x98952),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f8(a849,a842,a1),f317(f226(a849),x98951)),a116))))) % 168.22/168.05 [9965]~P22(f317(f317(f319(a849),f2(a849)),x99651))+E(f317(a124,f317(f54(a849),f317(f230(a849),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),f317(f317(f7(a849,f858(a849,a842),a842),f317(f317(f8(a849,f858(f858(a849,a842),a842),a849),f319(a849)),a124)),x99651))),f317(f317(f7(a849,a849,a842),f226(a849)),x99652))))),f317(f54(a849),f317(f230(a849),f317(f317(f18(a849,a842,a842),f317(f317(f8(a842,f858(a842,a842),a849),a315),f317(f317(f7(a849,f858(a849,a842),a842),f319(a849)),x99651))),f317(f317(f7(a849,a849,a842),f226(a849)),f317(a124,x99652)))))) % 168.22/168.05 [8404]~P90(x84041)+E(f317(f317(f90(x84041),f317(f115(x84041),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),x84042),x84042) % 168.22/168.05 [8470]~P90(x84701)+E(f317(f317(f89(x84701),f87(x84701)),f317(f115(x84701),x84702)),f317(f115(x84701),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),x84702))) % 168.22/168.05 [8525]~P90(x85251)+E(f317(f317(f21(x85251),f317(f115(x85251),x85252)),f87(x85251)),f317(f115(x85251),f317(f317(f89(a1),x85252),f317(f88(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.05 [8661]~P22(f317(f317(f226(a849),f317(f115(a849),a92)),x86612))+E(f317(f317(f21(a849),x86611),f317(f317(f21(a849),x86612),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f21(a849),f317(a124,x86611)),x86612)) % 168.22/168.05 [9292]~P84(x92921)+E(f317(f317(f90(x92921),x92922),x92922),f317(f317(f238(x92921),x92922),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.05 [9293]~P75(x92931)+E(f317(f317(f238(x92931),x92932),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f90(x92931),x92932),x92932)) % 168.22/168.05 [9295]~P90(x92951)+E(f317(f317(f90(x92951),x92952),f317(f115(x92951),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f89(x92951),x92952),x92952)) % 168.22/168.05 [9532]~P111(x95321)+E(f317(f317(f238(x95321),f317(f88(x95321),x95322)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f238(x95321),x95322),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.05 [9533]~P113(x95331)+E(f317(f317(f238(x95331),f317(f84(x95331),x95332)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f238(x95331),x95332),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.05 [9529]~P90(x95291)+E(f317(f317(f90(x95291),f317(f115(x95291),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x95292),f317(f317(f89(x95291),x95292),x95292)) % 168.22/168.05 [9650]~P113(x96501)+E(f317(f84(x96501),f317(f317(f238(x96501),x96502),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x96501),x96502),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.05 [9710]~P113(x97101)+P22(f317(f317(f225(x97101),f2(x97101)),f317(f317(f238(x97101),x97102),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.22/168.05 [9887]~E(f317(a124,x98872),f317(f115(a849),x98871))+P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x98871),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f7(a1,a849,a842),f317(f317(f8(a849,f858(a849,a842),a1),a314),a116)),x98872))))) % 168.22/168.05 [9888]~E(f317(f115(a849),x98881),f317(a124,x98882))+P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x98881),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f7(a1,a849,a842),f317(f317(f8(a849,f858(a849,a842),a1),a314),a116)),x98882))))) % 168.22/168.05 [9930]E(f317(a124,x99301),f317(f115(a849),x99302))+~P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x99302),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f7(a1,a849,a842),f317(f317(f8(a849,f858(a849,a842),a1),a314),a116)),x99301))))) % 168.22/168.05 [9931]E(f317(f115(a849),x99311),f317(a124,x99312))+~P22(f317(f317(f95(a1,a842),f317(f115(a1),f317(f317(f89(a1),x99311),a109))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a315),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f18(a1,a842,a842),f317(f317(f8(a842,f858(a842,a842),a1),a320),f317(f317(f8(a842,a842,a1),a312),a193))),f317(f317(f7(a1,a849,a842),f317(f317(f8(a849,f858(a849,a842),a1),a314),a116)),x99312))))) % 168.22/168.05 [9706]~P90(x97061)+E(f317(f317(f238(x97061),f317(f115(x97061),a109)),f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x97062)),f87(x97061)) % 168.22/168.05 [9707]~P111(x97071)+E(f317(f317(f238(x97071),f317(f88(x97071),f87(x97071))),f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x97072)),f87(x97071)) % 168.22/168.05 [9712]~P75(x97121)+E(f317(f317(f238(x97121),x97122),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),a109))),f317(f317(f90(x97121),f317(f317(f90(x97121),x97122),x97122)),x97122)) % 168.22/168.05 [9909]~P22(f317(f317(f225(a1),f2(a1)),x99092))+E(f55(a1,f317(f317(f89(a1),f87(a1)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99091)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99092)),f317(f317(f89(a1),f87(a1)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f55(a1,x99091,x99092)))) % 168.22/168.05 [9933]~P22(f317(f317(f225(a1),f2(a1)),x99332))+E(f317(f48(a1,f317(f317(f89(a1),f87(a1)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99331))),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99332)),f317(f48(a1,x99331),x99332)) % 168.22/168.05 [9935]~P22(f317(f317(f225(a1),x99352),f2(a1)))+E(f317(f48(a1,f317(f317(f89(a1),f87(a1)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99351))),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99352)),f317(f48(a1,f317(f317(f89(a1),x99351),f87(a1))),x99352)) % 168.22/168.05 [9936]~P22(f317(f317(f225(a1),x99362),f2(a1)))+E(f55(a1,f317(f317(f89(a1),f87(a1)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99361)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99362)),f317(f317(f21(a1),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f55(a1,f317(f317(f89(a1),x99361),f87(a1)),x99362))),f87(a1))) % 168.22/168.05 [9806]~P90(x98061)+E(f317(f317(f238(x98061),f317(f115(x98061),a109)),f317(a124,f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98062))),f317(f115(x98061),a109)) % 168.22/168.05 [9808]~P111(x98081)+E(f317(f317(f238(x98081),f317(f88(x98081),f87(x98081))),f317(a124,f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98082))),f317(f88(x98081),f87(x98081))) % 168.22/168.05 [5040]~P18(x50401,x50402,x50403)+P21(x50401,x50402,x50403) % 168.22/168.05 [7916]~E(x79162,x79163)+P35(x79161,x79161,a314,x79162,x79163) % 168.22/168.05 [8485]E(x84851,x84852)+~P35(x84853,x84853,a314,x84851,x84852) % 168.22/168.05 [5045]~P37(x50451,x50453)+P37(x50451,f311(x50451,x50452,x50453)) % 168.22/168.05 [5216]P30(x52161,x52162,x52163)+~P30(x52161,f317(a124,x52162),x52163) % 168.22/168.05 [5296]~P6(x52961,x52962,x52963)+P6(f850(x52961),f155(x52961,x52962),f152(x52961,x52963)) % 168.22/168.05 [5297]~P45(x52971,x52972,x52973)+P45(f850(x52971),f155(x52971,x52972),f152(x52971,x52973)) % 168.22/168.05 [5408]P49(x54081,x54082,x54083)+~E(f719(x54083,x54082,x54081),f720(x54083,x54082,x54081)) % 168.22/168.05 [5409]P50(x54091,x54092,x54093)+~E(f752(x54093,x54092,x54091),f753(x54093,x54092,x54091)) % 168.22/168.05 [6327]P21(x63271,x63272,x63273)+~P30(x63271,f576(x63273,x63272,x63271),f580(x63273,x63272,x63271)) % 168.22/168.05 [4597]~E(x45971,f191(x45972))+~E(x45971,f317(f217(x45972),x45973)) % 168.22/168.05 [4650]~E(f317(f163(x46502),x46501),x46503)+E(x46501,f317(f163(x46502),x46503)) % 168.22/168.05 [4651]~E(x46512,f317(f163(x46511),x46513))+E(f317(f163(x46511),x46512),x46513) % 168.22/168.05 [4701]E(x47011,x47012)+~E(f317(f217(x47013),x47011),f317(f217(x47013),x47012)) % 168.22/168.05 [4702]E(x47021,x47022)+~E(f317(f163(x47023),x47021),f317(f163(x47023),x47022)) % 168.22/168.05 [4903]~P5(x49033,x49031)+P22(f317(f317(x49031,x49032),x49032)) % 168.22/168.05 [4904]~P47(x49043,x49041)+P22(f317(f317(x49041,x49042),x49042)) % 168.22/168.05 [4906]~P54(x49061,x49062)+P22(f317(f305(x49061,x49062),x49063)) % 168.22/168.05 [4961]~P37(x49611,x49612)+P37(f850(x49611),f317(f137(x49611,x49612),x49613)) % 168.22/168.05 [4966]~P22(f317(x49662,x49663))+~E(f317(f230(x49661),x49662),f188(f858(x49661,a842))) % 168.22/168.05 [4967]~P22(f317(x49672,x49673))+~E(f188(f858(x49671,a842)),f317(f230(x49671),x49672)) % 168.22/168.05 [5002]~P22(f317(x50021,x50023))+P22(f317(x50021,f99(x50022,x50021))) % 168.22/168.05 [5126]~E(x51262,x51263)+P22(f317(f317(f319(x51261),x51262),f317(a314,x51263))) % 168.22/168.05 [5138]P22(f317(x51381,x51382))+~P22(f317(x51381,f545(x51381,x51383))) % 168.22/168.05 [5182]E(f317(f163(x51821),x51822),f317(f317(f145(x51821),x51823),f125(x51821)))+~E(x51822,f317(f317(f145(x51821),x51823),f125(x51821))) % 168.22/168.05 [5183]~E(x51833,f317(f317(f145(x51831),x51832),f125(x51831)))+E(f317(f317(f145(x51831),x51832),f125(x51831)),f317(f163(x51831),x51833)) % 168.22/168.05 [5209]~E(x52093,f317(f16(f853(x52092),x52091),f191(x52092)))+E(f177(x52091,x52092,x52093),f188(f858(x52091,a842))) % 168.22/168.05 [5229]~P34(x52291,x52292,x52293)+P34(x52291,x52292,f317(f163(x52291),x52293)) % 168.22/168.05 [5232]E(f317(f54(x52321),f360(x52322,x52323,x52321)),x52322)+~E(f317(f54(x52321),x52323),f317(a124,x52322)) % 168.22/168.05 [5238]~P37(x52381,x52383)+P22(f317(f317(f319(x52381),x52382),f306(x52381,x52383))) % 168.22/168.05 [5241]~E(f317(f163(x52412),x52411),f317(f317(f145(x52412),x52413),f125(x52412)))+E(x52411,f317(f317(f145(x52412),x52413),f125(x52412))) % 168.22/168.05 [5242]~E(f317(f317(f145(x52422),x52423),f125(x52422)),f317(f163(x52422),x52421))+E(x52421,f317(f317(f145(x52422),x52423),f125(x52422))) % 168.22/168.05 [5255]E(x52551,f317(f16(f853(x52552),x52553),f191(x52552)))+~E(f177(x52553,x52552,x52551),f188(f858(x52553,a842))) % 168.22/168.05 [5262]E(f94(f857(a849,a849),f57(x52621,x52622)),x52623)+~P22(f317(f57(x52621,x52622),x52623)) % 168.22/168.05 [5270]~E(x52703,f317(f217(x52701),x52702))+P22(f317(f317(f319(x52701),x52702),f218(x52701,x52703))) % 168.22/168.05 [5300]P34(x53001,x53002,x53003)+~P34(x53001,x53002,f317(f163(x53001),x53003)) % 168.22/168.05 [5361]~E(x53612,f125(x53611))+P22(f317(f317(f319(f850(x53611)),x53612),f155(x53611,x53613))) % 168.22/168.05 [5369]~P45(x53691,x53692,x53693)+P45(x53691,x53692,f317(f263(x53691,x53691),x53693)) % 168.22/168.05 [5370]~P50(x53701,x53702,x53703)+P50(x53701,x53702,f317(f263(x53701,x53701),x53703)) % 168.22/168.05 [5389]~P55(x53891)+E(f55(x53891,f55(x53891,x53892,x53893),x53893),f55(x53891,x53892,x53893)) % 168.22/168.05 [5485]E(x54851,x54852)+~P22(f317(f317(f319(x54853),x54851),f317(a314,x54852))) % 168.22/168.05 [5534]~P110(x55341)+E(f190(x55341,x55342,f2(a849),x55343),x55343) % 168.22/168.05 [5556]P45(x55561,x55562,x55563)+~P45(x55561,x55562,f317(f263(x55561,x55561),x55563)) % 168.22/168.05 [5557]P50(x55571,x55572,x55573)+~P50(x55571,x55572,f317(f263(x55571,x55571),x55573)) % 168.22/168.05 [5561]~P103(x55612)+E(f142(x55611,x55612,x55613,f125(x55611)),f125(x55611)) % 168.22/168.05 [5576]E(f164(x55761,x55762,f146(x55761,x55763)),f146(x55761,f164(x55761,x55762,x55763)))+~P22(f317(f131(x55761),x55763)) % 168.22/168.05 [5579]E(x55791,f317(f217(x55792),x55793))+~P22(f317(f317(f319(x55792),x55793),f218(x55792,x55791))) % 168.22/168.05 [5660]~P22(f317(a24,x56603))+P22(f317(a24,f32(x56601,x56602,x56603))) % 168.22/168.05 [5669]E(f317(f130(x56691,x56692),x56693),f125(x56691))+P22(f317(x56692,f632(x56693,x56692,x56691))) % 168.22/168.05 [5804]~P22(f317(f131(x58041),x58043))+P22(f317(f131(x58041),f164(x58041,x58042,x58043))) % 168.22/168.05 [5805]~P22(f317(f131(x58051),x58052))+P22(f317(f131(x58051),f168(x58051,x58052,x58053))) % 168.22/168.05 [5806]~P22(f317(f131(x58061),x58063))+P22(f317(f131(x58061),f170(x58061,x58062,x58063))) % 168.22/168.05 [5807]~P22(f317(f131(x58071),x58073))+P22(f317(f131(x58071),f134(x58071,x58072,x58073))) % 168.22/168.05 [5808]~P138(x58081,x58082,x58083)+P22(f317(x58081,f55(a1,x58082,x58083))) % 168.22/168.05 [5826]~P34(x58263,x58261,x58262)+P22(f317(x58261,f734(x58262,x58261,x58263))) % 168.22/168.05 [5847]E(f317(f130(x58471,x58472),x58473),f170(x58471,x58472,x58473))+P22(f317(x58472,f669(x58473,x58472,x58471))) % 168.22/168.05 [5892]~P22(f317(f131(x58921),x58923))+P22(f317(f131(f850(x58921)),f64(x58921,x58922,x58923))) % 168.22/168.05 [5912]P22(f317(a24,f31(x59121,x59122,x59123)))+~P22(f317(a24,f317(a29,x59122))) % 168.22/168.05 [5927]~P104(x59271)+E(f317(f317(f113(f858(x59271,a842)),f317(f277(x59271),x59272)),f282(x59271,x59272,x59273)),f188(f858(x59271,a842))) % 168.22/168.05 [5928]~P104(x59281)+E(f317(f317(f113(f858(x59281,a842)),f317(f277(x59281),x59282)),f281(x59281,x59282,x59283)),f188(f858(x59281,a842))) % 168.22/168.05 [5929]~P104(x59291)+E(f317(f317(f113(f858(x59291,a842)),f317(f231(x59291),x59292)),f279(x59291,x59292,x59293)),f188(f858(x59291,a842))) % 168.22/168.05 [6065]P22(f317(a24,x60651))+~P22(f317(a24,f32(x60652,x60653,x60651))) % 168.22/168.05 [6067]P22(f317(a24,x60671))+~P22(f317(a24,f33(x60672,x60673,x60671))) % 168.22/168.05 [6069]P22(f317(a24,x60691))+~P22(f317(a24,f33(x60692,x60691,x60693))) % 168.22/168.05 [6149]E(f317(f130(x61491,x61492),x61493),x61493)+~P22(f317(x61492,f640(x61493,x61492,x61491))) % 168.22/168.05 [6151]E(f317(f317(f286(x61511),f365(x61512,x61513,x61511)),f360(x61512,x61513,x61511)),x61513)+~E(f317(f54(x61511),x61513),f317(a124,x61512)) % 168.22/168.05 [6167]P138(x61671,x61672,x61673)+~P22(f317(x61671,f55(a1,x61672,x61673))) % 168.22/168.05 [6215]E(f170(x62151,x62152,x62153),x62153)+~P22(f317(x62152,f658(x62153,x62152,x62151))) % 168.22/168.05 [6252]~P22(f317(a24,f31(x62522,x62521,x62523)))+P22(f317(a24,f317(a29,x62521))) % 168.22/168.05 [6293]~P22(f317(x62932,f571(x62933,x62932,x62931)))+P22(f317(f241(x62931,x62932),x62933)) % 168.22/168.05 [6294]~P22(f317(x62942,f641(x62943,x62942,x62941)))+P22(f317(f154(x62941,x62942),x62943)) % 168.22/168.05 [6538]~P22(f317(f305(x65381,x65382),f336(x65383,x65382,x65381)))+P22(f317(f305(x65381,x65382),x65383)) % 168.22/168.05 [6539]~P22(f317(f305(x65391,x65392),f341(x65393,x65392,x65391)))+P22(f317(f305(x65391,x65392),x65393)) % 168.22/168.05 [6893]~P55(x68931)+E(f317(f317(f89(x68931),f317(f317(f90(x68931),x68932),f317(f48(x68931,x68933),x68932))),f55(x68931,x68933,x68932)),x68933) % 168.22/168.05 [7600]E(f317(f317(f237(x76001,x76001),f489(x76002,x76003,x76001)),f489(x76002,x76003,x76001)),x76003)+~P22(f317(f317(f319(f857(x76001,x76001)),x76003),f235(x76001,x76002))) % 168.22/168.05 [7614]~P55(x76141)+E(f317(f317(f89(x76141),f317(f317(f90(x76141),f317(f48(x76141,x76142),x76143)),x76143)),f55(x76141,x76142,x76143)),x76142) % 168.22/168.05 [7718]~P22(f317(f317(f319(x77181),f345(x77183,x77182,x77181)),f306(x77181,x77183)))+P22(f317(f317(f319(x77181),x77182),f306(x77181,x77183))) % 168.22/168.05 [7719]~P22(f317(f317(f319(x77191),f722(x77193,x77192,x77191)),f306(x77191,x77193)))+P22(f317(f317(f319(x77191),x77192),f306(x77191,x77193))) % 168.22/168.05 [7720]~P22(f317(f317(f319(x77201),f731(x77203,x77202,x77201)),f306(x77201,x77203)))+P22(f317(f317(f319(x77201),x77202),f306(x77201,x77203))) % 168.22/168.05 [7942]~E(f317(f54(x79421),x79422),f317(a124,x79423))+~P22(f317(f317(f319(x79421),f365(x79423,x79422,x79421)),f360(x79423,x79422,x79421))) % 168.22/168.05 [8573]P22(f317(f317(f225(f858(f857(x85731,x85731),a842)),f284(x85731,x85732)),f284(x85731,x85733)))+~P22(f317(f317(f225(f858(f857(x85731,x85731),a842)),x85732),f284(x85731,x85733))) % 168.22/168.05 [8842]E(x88421,f125(x88422))+~P22(f317(f317(f319(f857(f850(x88422),f850(x88422))),f317(f317(f237(f850(x88422),f850(x88422)),x88421),f125(x88422))),f152(x88422,x88423))) % 168.22/168.05 [8869]E(x88691,f125(x88692))+~P22(f317(f317(f319(f857(f850(x88692),f850(x88692))),f317(f317(f237(f850(x88692),f850(x88692)),f125(x88692)),x88691)),f152(x88692,x88693))) % 168.22/168.05 [8990]E(f317(f317(f145(x89901),f628(x89902,x89903,x89901)),f629(x89902,x89903,x89901)),x89903)+~P22(f317(f317(f319(f857(f850(x89901),f850(x89901))),f317(f317(f237(f850(x89901),f850(x89901)),f125(x89901)),x89903)),f141(x89901,x89902))) % 168.22/168.05 [9221]~P119(x92211)+~P22(f317(f317(f226(x92211),f317(f317(f89(x92211),f317(f317(f90(x92211),x92212),x92212)),f317(f317(f90(x92211),x92213),x92213))),f2(x92211))) % 168.22/168.05 [9271]P22(f317(f71(x92711),x92712))+~P22(f317(f317(f319(f857(f858(x92711,a842),f858(x92711,a842))),f317(f317(f237(f858(x92711,a842),f858(x92711,a842)),x92713),x92712)),f283(x92711))) % 168.22/168.05 [10010]~P113(x100101)+~P22(f317(f317(f226(x100101),f317(f317(f89(x100101),f317(f317(f238(x100101),x100102),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x100101),x100103),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f2(x100101))) % 168.22/168.05 [4683]~E(x46833,f125(x46831))+E(f317(f317(f127(x46831),x46832),x46833),x46832) % 168.22/168.05 [4684]~E(x46842,f125(x46841))+E(f317(f317(f127(x46841),x46842),x46843),x46843) % 168.22/168.05 [4691]~E(x46912,f2(a849))+E(f317(f317(f167(x46911),x46912),x46913),f125(x46911)) % 168.22/168.05 [4696]~E(x46963,f125(x46961))+E(f317(f317(f167(x46961),x46962),x46963),f125(x46961)) % 168.22/168.05 [4733]~E(x47331,x47333)+E(x47331,f317(f317(f127(x47332),f125(x47332)),x47333)) % 168.22/168.05 [4819]~P85(x48192)+E(f317(f188(f858(x48191,x48192)),x48193),f188(x48192)) % 168.22/168.05 [4820]~P105(x48202)+E(f317(f233(f858(x48201,x48202)),x48203),f233(x48202)) % 168.22/168.05 [4839]E(x48391,f125(x48392))+~E(f317(f317(f127(x48392),x48393),x48391),x48393) % 168.22/168.05 [4840]E(x48401,f125(x48402))+~E(f317(f317(f127(x48402),x48401),x48403),x48403) % 168.22/168.05 [4849]E(x48491,f125(x48492))+~E(f317(f317(f127(x48492),x48493),x48491),f125(x48492)) % 168.22/168.05 [4850]E(x48501,f125(x48502))+~E(f317(f317(f127(x48502),x48501),x48503),f125(x48502)) % 168.22/168.05 [4873]~E(x48732,f2(a849))+E(f317(f317(f90(a849),x48731),x48732),f317(f317(f90(a849),x48733),x48732)) % 168.22/168.05 [4875]~E(x48751,f2(a849))+E(f317(f317(f90(a849),x48751),x48752),f317(f317(f90(a849),x48751),x48753)) % 168.22/168.05 [4923]~P84(x49231)+E(f317(f317(f89(x49231),x49232),x49233),f317(f317(f89(x49231),x49233),x49232)) % 168.22/168.05 [4925]~P92(x49251)+E(f317(f317(f122(x49251),x49252),x49253),f317(f317(f122(x49251),x49253),x49252)) % 168.22/168.05 [4926]~P93(x49261)+E(f317(f317(f122(x49261),x49262),x49263),f317(f317(f122(x49261),x49263),x49262)) % 168.22/168.05 [4927]~P84(x49271)+E(f317(f317(f90(x49271),x49272),x49273),f317(f317(f90(x49271),x49273),x49272)) % 168.22/168.05 [4928]~P93(x49281)+E(f317(f317(f113(x49281),x49282),x49283),f317(f317(f113(x49281),x49283),x49282)) % 168.22/168.05 [4930]~P98(x49301)+E(f317(f317(f113(x49301),x49302),x49303),f317(f317(f113(x49301),x49303),x49302)) % 168.22/168.05 [4932]~P103(x49321)+E(f317(f317(f223(x49321),x49322),x49323),f317(f317(f223(x49321),x49323),x49322)) % 168.22/168.05 [4934]~P103(x49341)+E(f317(f317(f224(x49341),x49342),x49343),f317(f317(f224(x49341),x49343),x49342)) % 168.22/168.05 [4997]E(f55(a849,x49971,x49972),f2(a849))+~E(x49971,f317(f317(f90(a849),x49972),x49973)) % 168.22/168.05 [4998]E(f55(a1,x49981,x49982),f2(a1))+~E(x49981,f317(f317(f90(a1),x49982),x49983)) % 168.22/168.05 [5057]E(x50571,x50572)+~E(f317(f317(f89(a849),x50573),x50571),f317(f317(f89(a849),x50573),x50572)) % 168.22/168.05 [5058]E(x50581,x50582)+~E(f317(f317(f89(a849),x50581),x50583),f317(f317(f89(a849),x50582),x50583)) % 168.22/168.05 [5068]~P25(x50681)+E(f317(f317(f89(x50681),x50682),f317(f88(x50681),x50683)),f317(f317(f21(x50681),x50682),x50683)) % 168.22/168.05 [5069]~P69(x50691)+E(f317(f317(f89(x50691),x50692),f317(f88(x50691),x50693)),f317(f317(f21(x50691),x50692),x50693)) % 168.22/168.05 [5070]~P100(x50701)+E(f317(f317(f89(x50701),x50702),f317(f88(x50701),x50703)),f317(f317(f21(x50701),x50702),x50703)) % 168.22/168.05 [5071]~P86(x50711)+E(f317(f317(f113(x50711),x50712),f317(f88(x50711),x50713)),f317(f317(f21(x50711),x50712),x50713)) % 168.22/168.05 [5072]~P69(x50721)+E(f317(f317(f21(x50721),x50722),f317(f88(x50721),x50723)),f317(f317(f89(x50721),x50722),x50723)) % 168.22/168.05 [5119]~P22(f317(x51193,x51192))+P22(f317(f317(f319(x51191),x51192),x51193)) % 168.22/168.05 [5121]~P70(x51212)+E(f317(f317(f9(x51211,x51212),x51213),f188(f858(x51211,a842))),f87(x51212)) % 168.22/168.05 [5123]~P67(x51232)+E(f317(f317(f6(x51231,x51232),x51233),f188(f858(x51231,a842))),f2(x51232)) % 168.22/168.05 [5171]~E(x51712,f317(f317(f89(a849),x51711),x51713))+P22(f317(f317(f225(a849),x51711),x51712)) % 168.22/168.05 [5174]~E(x51742,f188(f858(x51741,a842)))+E(f317(f317(f70(x51741),x51742),x51743),f188(f858(f858(x51741,a842),a842))) % 168.22/168.05 [5175]~E(x51752,f188(f858(x51751,a842)))+E(f188(f858(f858(x51751,a842),a842)),f317(f317(f70(x51751),x51752),x51753)) % 168.22/168.05 [5245]~E(f317(f234(x52452,x52453),x52451),f188(f858(x52453,a842)))+E(x52451,f188(f858(f857(x52452,x52453),a842))) % 168.22/168.05 [5246]~E(f317(f236(x52462,x52463),x52461),f188(f858(x52462,a842)))+E(x52461,f188(f858(f857(x52462,x52463),a842))) % 168.22/168.05 [5276]E(f317(f234(x52761,x52762),x52763),f188(f858(x52762,a842)))+~E(x52763,f188(f858(f857(x52761,x52762),a842))) % 168.22/168.05 [5277]E(f317(f236(x52771,x52772),x52773),f188(f858(x52771,a842)))+~E(x52773,f188(f858(f857(x52771,x52772),a842))) % 168.22/168.05 [5280]E(f258(x52801,x52802,x52803),f317(f317(f21(a111),x52802),x52803))+P22(f317(f317(f226(a111),x52802),x52803)) % 168.22/168.05 [5294]P22(f317(x52941,x52942))+~P22(f317(f317(f319(x52943),x52942),x52941)) % 168.22/168.05 [5331]E(x53311,x53312)+~E(f317(f88(f858(x53313,a842)),x53311),f317(f88(f858(x53313,a842)),x53312)) % 168.22/168.05 [5336]E(f291(x53361,x53362,x53363),f191(f850(a313)))+~P22(f317(f317(f226(a1),x53362),x53363)) % 168.22/168.05 [5341]~E(x53411,f188(f858(x53412,a842)))+~P22(f317(f317(f319(x53412),x53413),x53411)) % 168.22/168.05 [5371]~E(x53712,f317(f317(f89(a1),x53711),f317(f112(a1),x53713)))+P22(f317(f317(f225(a1),x53711),x53712)) % 168.22/168.05 [5387]E(f317(f317(f286(x53871),x53872),x53873),x53873)+~P22(f317(f317(f319(x53871),x53872),x53873)) % 168.22/168.05 [5398]E(x53981,f188(f858(x53982,a842)))+~E(f317(f317(f70(x53982),x53981),x53983),f188(f858(f858(x53982,a842),a842))) % 168.22/168.05 [5399]E(x53991,f188(f858(x53992,a842)))+~E(f188(f858(f858(x53992,a842),a842)),f317(f317(f70(x53992),x53991),x53993)) % 168.22/168.05 [5405]~P126(x54051)+E(f317(f317(f90(x54051),f317(f88(x54051),x54052)),f317(f88(x54051),x54053)),f317(f317(f90(x54051),x54052),x54053)) % 168.22/168.05 [5407]~P58(x54071)+E(f317(f317(f266(x54071),f317(f88(x54071),x54072)),f317(f88(x54071),x54073)),f317(f317(f266(x54071),x54072),x54073)) % 168.22/168.05 [5438]~P22(f317(x54383,x54382))+P22(f317(f317(f319(x54381),x54382),f317(f230(x54381),x54383))) % 168.22/168.05 [5478]E(f164(x54781,x54782,x54783),x54783)+P22(f317(f317(f319(x54781),x54782),f317(f166(x54781),x54783))) % 168.22/168.05 [5540]~P139(x55401,x55402,x55403)+P22(f317(x55401,f317(f48(a1,x55402),x55403))) % 168.22/168.05 [5562]~P55(x55621)+E(f317(f48(x55621,f55(x55621,x55622,x55623)),x55623),f2(x55621)) % 168.22/168.05 [5566]~P22(f317(f131(x55661),x55663))+P22(f317(f131(x55661),f317(f130(x55661,x55662),x55663))) % 168.22/168.05 [5624]E(f168(x56241,f317(f317(f145(x56241),x56242),f125(x56241)),x56243),f125(x56241))+P22(f317(f317(f319(a849),f2(a849)),x56243)) % 168.22/168.05 [5678]E(f317(f317(f145(x56781),x56782),x56783),f134(x56781,x56782,x56783))+P22(f317(f317(f319(x56781),x56782),f317(f166(x56781),x56783))) % 168.22/168.05 [5687]E(x56871,x56872)+~E(f317(f317(f90(a849),f317(a124,x56873)),x56871),f317(f317(f90(a849),f317(a124,x56873)),x56872)) % 168.22/168.05 [5688]~E(x56882,f317(f317(f89(a1),x56881),f317(f112(a1),f317(a124,x56883))))+P22(f317(f317(f226(a1),x56881),x56882)) % 168.22/168.05 [5787]~E(x57873,f125(x57871))+E(f317(f317(f317(f182(f850(x57871),f850(x57871)),x57872),f162(x57871)),x57873),f125(x57871)) % 168.22/168.05 [5791]P22(f317(x57911,x57912))+~P22(f317(f317(f319(x57913),x57912),f317(f230(x57913),x57911))) % 168.22/168.05 [5815]P139(x58151,x58152,x58153)+~P22(f317(x58151,f317(f48(a1,x58152),x58153))) % 168.22/168.05 [5822]E(x58221,x58222)+~E(f317(f317(f286(x58223),x58221),f188(f858(x58223,a842))),f317(f317(f286(x58223),x58222),f188(f858(x58223,a842)))) % 168.22/168.05 [5831]~P104(x58311)+E(f317(f317(f113(f858(x58311,a842)),f317(f231(x58311),x58312)),f317(f278(x58311,x58312),x58313)),f188(f858(x58311,a842))) % 168.22/168.05 [5873]E(f134(x58731,x58732,x58733),x58733)+~P22(f317(f317(f319(x58731),x58732),f317(f166(x58731),x58733))) % 168.22/168.05 [5900]~P78(x59001)+E(f317(f287(x59001,x59001,f88(x59001)),f317(f278(x59001,x59002),x59003)),f281(x59001,f317(f88(x59001),x59003),f317(f88(x59001),x59002))) % 168.22/168.05 [5908]E(f317(f189(f850(x59081)),f164(x59081,x59082,x59083)),f317(f189(f850(x59081)),x59083))+P22(f317(f317(f319(x59081),x59082),f317(f166(x59081),x59083))) % 168.22/168.05 [5959]~P104(x59591)+E(f317(f317(f113(f858(x59591,a842)),f317(f278(x59591,x59592),x59593)),f317(f232(x59591),x59593)),f188(f858(x59591,a842))) % 168.22/168.05 [5981]~P78(x59811)+E(f317(f287(x59811,x59811,f88(x59811)),f282(x59811,x59812,x59813)),f282(x59811,f317(f88(x59811),x59813),f317(f88(x59811),x59812))) % 168.22/168.05 [5982]~P78(x59821)+E(f317(f287(x59821,x59821,f88(x59821)),f279(x59821,x59822,x59823)),f279(x59821,f317(f88(x59821),x59823),f317(f88(x59821),x59822))) % 168.22/168.05 [6033]E(f168(x60331,f317(f317(f145(x60331),x60332),f125(x60331)),x60333),f317(f317(f145(x60331),x60332),f125(x60331)))+~P22(f317(f317(f319(a849),f2(a849)),x60333)) % 168.22/168.05 [6043]~P78(x60431)+E(f317(f287(x60431,x60431,f88(x60431)),f281(x60431,x60432,x60433)),f317(f278(x60431,f317(f88(x60431),x60433)),f317(f88(x60431),x60432))) % 168.22/168.05 [6060]~P26(x60601)+E(f55(x60601,f317(f88(x60601),f55(x60601,x60602,x60603)),x60603),f55(x60601,f317(f88(x60601),x60602),x60603)) % 168.22/168.05 [6164]~P22(f317(f71(f857(x61642,x61641)),x61643))+P22(f317(f71(x61641),f317(f234(x61642,x61641),x61643))) % 168.22/168.05 [6165]~P22(f317(f71(f857(x61651,x61652)),x61653))+P22(f317(f71(x61651),f317(f236(x61651,x61652),x61653))) % 168.22/168.05 [6171]~P104(x61711)+E(f317(f317(f113(f858(x61711,a842)),f282(x61711,x61712,x61713)),f317(f232(x61711),x61713)),f188(f858(x61711,a842))) % 168.22/168.05 [6172]~P104(x61721)+E(f317(f317(f113(f858(x61721,a842)),f281(x61721,x61722,x61723)),f317(f280(x61721),x61723)),f188(f858(x61721,a842))) % 168.22/168.05 [6173]~P104(x61731)+E(f317(f317(f113(f858(x61731,a842)),f279(x61731,x61732,x61733)),f317(f280(x61731),x61733)),f188(f858(x61731,a842))) % 168.22/168.05 [6235]E(f317(f317(f159(x62351),x62352),f597(x62352,x62353,x62351)),x62353)+~P22(f317(f317(f319(x62351),x62353),f317(f166(x62351),x62352))) % 168.22/168.05 [6376]E(x63761,f125(x63762))+~E(f317(f317(f317(f182(f850(x63762),f850(x63762)),x63763),f162(x63762)),x63761),f125(x63762)) % 168.22/168.05 [6476]~P22(f317(f71(f857(x64762,x64761)),x64763))+P22(f317(f71(f857(x64761,x64762)),f317(f263(x64762,x64761),x64763))) % 168.22/168.05 [6625]P50(x66251,x66252,x66253)+P22(f317(f317(f319(x66251),f753(x66253,x66252,x66251)),x66252)) % 168.22/168.05 [6626]P50(x66261,x66262,x66263)+P22(f317(f317(f319(x66261),f752(x66263,x66262,x66261)),x66262)) % 168.22/168.05 [6638]P22(f317(f305(x66381,x66382),x66383))+P22(f317(f317(x66382,f336(x66383,x66382,x66381)),x66383)) % 168.22/168.05 [6639]P22(f317(f305(x66391,x66392),x66393))+P22(f317(f317(x66392,f341(x66393,x66392,x66391)),x66393)) % 168.22/168.05 [6669]E(f317(f189(f850(x66691)),f164(x66691,x66692,x66693)),f317(f317(f21(a849),f317(f189(f850(x66691)),x66693)),f87(a849)))+~P22(f317(f317(f319(x66691),x66692),f317(f166(x66691),x66693))) % 168.22/168.05 [6706]P22(f317(f241(x67061,x67062),x67063))+P22(f317(f317(f319(x67061),f571(x67063,x67062,x67061)),x67063)) % 168.22/168.05 [6716]~P22(f317(f71(f857(x67162,x67161)),f317(f263(x67161,x67162),x67163)))+P22(f317(f71(f857(x67161,x67162)),x67163)) % 168.22/168.05 [6769]~P22(f317(f317(f319(x67691),x67692),f317(f166(x67691),f126(x67691,x67693))))+P22(f317(f317(f319(x67691),x67692),f317(f166(x67691),x67693))) % 168.22/168.05 [6774]P21(x67741,x67742,x67743)+P22(f317(f317(f319(f848(x67741)),f580(x67743,x67742,x67741)),x67743)) % 168.22/168.05 [6801]E(f317(f130(x68011,x68012),x68013),x68013)+P22(f317(f317(f319(x68011),f640(x68013,x68012,x68011)),f317(f166(x68011),x68013))) % 168.22/168.05 [6816]E(f317(f130(x68161,x68162),x68163),f125(x68161))+P22(f317(f317(f319(x68161),f632(x68163,x68162,x68161)),f317(f166(x68161),x68163))) % 168.22/168.05 [6845]E(f170(x68451,x68452,x68453),x68453)+P22(f317(f317(f319(x68451),f658(x68453,x68452,x68451)),f317(f166(x68451),x68453))) % 168.22/168.05 [6855]~P22(f317(f317(f225(a849),x68551),x68553))+P22(f317(f317(f225(a849),f317(f48(a849,x68551),x68552)),f317(f48(a849,x68553),x68552))) % 168.22/168.05 [6932]P22(f317(f154(x69321,x69322),x69323))+P22(f317(f317(f319(x69321),f641(x69323,x69322,x69321)),f317(f166(x69321),x69323))) % 168.22/168.05 [6942]~P34(x69421,x69423,x69422)+P22(f317(f317(f319(x69421),f734(x69422,x69423,x69421)),f317(f166(x69421),x69422))) % 168.22/168.05 [6977]~P67(x69771)+E(f317(f317(f89(x69771),f317(f317(f6(a849,x69771),x69772),f317(f231(a849),x69773))),f317(x69772,x69773)),f317(f317(f6(a849,x69771),x69772),f317(f231(a849),f317(a124,x69773)))) % 168.22/168.05 [7068]~P34(x70682,x70681,x70683)+P22(f317(x70681,f317(f317(f159(x70682),x70683),f740(x70683,x70681,x70682)))) % 168.22/168.05 [7082]~P22(f317(f317(f319(x70821),x70822),f741(x70822,x70823,x70821)))+P22(f317(f317(f319(x70821),x70822),f50(f858(x70821,a842),x70823))) % 168.22/168.05 [7111]~P67(x71111)+E(f317(f317(f89(x71111),f317(f317(f6(a849,x71111),x71112),f317(f277(a849),x71113))),f317(x71112,f317(a124,x71113))),f317(f317(f6(a849,x71111),x71112),f317(f277(a849),f317(a124,x71113)))) % 168.22/168.05 [7240]P22(f317(f317(f319(f850(x72401)),x72402),f155(x72401,x72403)))+P22(f317(f317(f319(x72401),f598(x72403,x72402,x72401)),f317(f166(x72401),x72402))) % 168.22/168.05 [7256]~P22(f317(f317(f319(f850(x72561)),x72562),f155(x72561,f306(x72561,x72563))))+P22(f317(f317(f319(f850(x72561)),x72562),f306(f850(x72561),f151(x72561,x72563)))) % 168.22/168.05 [7279]~P22(f317(f317(f319(f850(x72791)),x72792),f306(f850(x72791),f151(x72791,x72793))))+P22(f317(f317(f319(f850(x72791)),x72792),f155(x72791,f306(x72791,x72793)))) % 168.22/168.05 [7315]E(f317(f317(f317(f182(f850(x73151),f850(x73151)),x73152),f162(x73151)),x73153),x73153)+~P22(f317(f317(f225(a849),f317(f189(f850(x73151)),x73153)),f87(a849))) % 168.22/168.05 [7350]E(f317(f317(f127(x73501),f768(x73502,x73503,x73501)),f317(f317(f145(x73501),x73503),f778(x73502,x73503,x73501))),x73502)+~P22(f317(f317(f319(x73501),x73503),f317(f166(x73501),x73502))) % 168.22/168.05 [7351]E(f317(f317(f127(x73511),f780(x73512,x73513,x73511)),f317(f317(f145(x73511),x73513),f781(x73512,x73513,x73511))),x73512)+~P22(f317(f317(f319(x73511),x73513),f317(f166(x73511),x73512))) % 168.22/168.05 [7352]E(f317(f317(f127(x73521),f782(x73522,x73523,x73521)),f317(f317(f145(x73521),x73523),f783(x73522,x73523,x73521))),x73522)+~P22(f317(f317(f319(x73521),x73523),f317(f166(x73521),x73522))) % 168.22/168.05 [7375]~P19(x73751,x73752,x73753,f233(f858(x73751,a842)))+P19(f850(x73751),f850(x73752),f317(f148(x73751,x73752),x73753),f233(f858(f850(x73751),a842))) % 168.22/168.05 [7524]E(x75241,f317(f317(f89(a849),f317(f317(f90(a849),f317(f244(a849,a849),x75242)),x75243)),f317(f246(a849,a849),x75242)))+~P22(f317(f57(x75241,x75243),x75242)) % 168.22/168.05 [7532]P19(x75321,x75322,x75323,f233(f858(x75321,a842)))+~P19(f850(x75321),f850(x75322),f317(f148(x75321,x75322),x75323),f233(f858(f850(x75321),a842))) % 168.22/168.05 [7567]~P22(f317(f317(f194(x75671),x75672),x75673))+P22(f317(f317(f317(f317(a197,x75671),x75672),f391(x75673,x75672,x75671)),x75673)) % 168.22/168.05 [7568]~P22(f317(f317(f194(x75681),x75682),x75683))+P22(f317(f317(f317(f317(a197,x75681),x75682),f482(x75683,x75682,x75681)),x75683)) % 168.22/168.05 [7572]P22(f317(f317(f319(f858(x75721,a842)),f741(x75722,x75723,x75721)),x75723))+P22(f317(f317(f319(x75721),x75722),f50(f858(x75721,a842),x75723))) % 168.22/168.05 [7666]P22(f317(f317(f319(f850(x76661)),x76662),f155(x76661,x76663)))+~P22(f317(f317(f319(x76661),f598(x76663,x76662,x76661)),x76663)) % 168.22/168.05 [7790]E(x77901,x77902)+~E(f317(f317(f7(x77903,f858(x77903,a842),a842),f319(x77903)),x77901),f317(f317(f7(x77903,f858(x77903,a842),a842),f319(x77903)),x77902)) % 168.22/168.05 [7795]~P22(f317(f317(f319(f857(x77951,x77951)),x77953),f235(x77951,x77952)))+P22(f317(f317(f319(x77951),f489(x77952,x77953,x77951)),x77952)) % 168.22/168.05 [7970]~P22(f317(f317(f319(x79701),x79702),f317(f166(x79701),f780(x79703,x79702,x79701))))+~P22(f317(f317(f319(x79701),x79702),f317(f166(x79701),x79703))) % 168.22/168.05 [7971]~P22(f317(f317(f319(x79711),x79712),f317(f166(x79711),f783(x79713,x79712,x79711))))+~P22(f317(f317(f319(x79711),x79712),f317(f166(x79711),x79713))) % 168.22/168.05 [8063]E(f317(f220(f853(f850(a313)),f850(a313),f291(x80631,x80632,f317(f317(f89(a1),x80633),f87(a1))),f217(f850(a313))),f317(x80631,x80633)),f291(x80631,x80632,x80633))+P22(f317(f317(f226(a1),x80632),x80633)) % 168.22/168.05 [8165]E(x81651,f125(x81652))+P22(f317(f317(f319(x81652),f317(f244(x81652,f857(a111,a111)),f317(f259(x81652,x81651),x81653))),f317(f166(x81652),x81651))) % 168.22/168.05 [8263]~P24(x82631)+E(f317(f136(x82631,x82631,f317(f7(x82631,x82631,x82631),f89(x82631)),x82632),f317(f163(x82631),x82633)),f317(f136(x82631,x82631,f89(x82631),x82632),x82633)) % 168.22/168.05 [8752]~P103(x87521)+E(f317(f166(x87521),f144(x87521,x87521,f5(x87521),x87522,x87523)),f317(f317(f286(x87521),x87522),f317(f166(x87521),x87523))) % 168.22/168.05 [8763]P22(f317(f317(f226(a849),f2(a849)),f756(x87631,x87632,x87633)))+~P22(f317(f317(f319(f857(x87633,x87633)),x87632),f317(f317(f265(x87633,x87633,x87633),x87631),f284(x87633,x87631)))) % 168.22/168.05 [9049]~P52(x90491,x90492)+~P22(f317(f317(f319(f857(x90491,x90491)),f317(f317(f237(x90491,x90491),x90493),x90493)),f317(f317(f265(x90491,x90491,x90491),x90492),f284(x90491,x90492)))) % 168.22/168.05 [9179]~E(f317(f317(f113(f858(f857(x91791,x91791),a842)),f317(f263(x91791,x91791),x91792)),f284(x91791,x91792)),f188(f858(f857(x91791,x91791),a842)))+~P22(f317(f317(f319(f857(x91791,x91791)),f317(f317(f237(x91791,x91791),x91793),x91793)),f317(f317(f265(x91791,x91791,x91791),x91792),f284(x91791,x91792)))) % 168.22/168.05 [9354]~P22(f317(f71(x93541),x93542))+P22(f317(f317(f225(a849),f317(f54(x93541),f317(f317(f21(f858(x93541,a842)),x93542),f317(f317(f286(x93541),x93543),f188(f858(x93541,a842)))))),f317(f54(x93541),x93542))) % 168.22/168.05 [4982]~E(x49823,f125(x49821))+E(f138(x49821,f317(f317(f145(x49821),x49822),x49823)),x49822) % 168.22/168.05 [4994]~E(x49943,f125(x49941))+E(f126(x49941,f317(f317(f145(x49941),x49942),x49943)),f125(x49941)) % 168.22/168.05 [5022]E(x50221,f125(x50222))+E(f138(x50222,f317(f317(f145(x50222),x50223),x50221)),f138(x50222,x50221)) % 168.22/168.05 [5024]E(x50241,f125(x50242))+E(f138(x50242,f317(f317(f127(x50242),x50243),x50241)),f138(x50242,x50241)) % 168.22/168.05 [5028]~E(x50283,f125(x50281))+E(f126(x50281,f317(f317(f127(x50281),x50282),x50283)),f126(x50281,x50282)) % 168.22/168.05 [5030]~E(x50303,f125(x50301))+E(f138(x50301,f317(f317(f127(x50301),x50302),x50303)),f138(x50301,x50302)) % 168.22/168.05 [5062]E(x50621,f125(x50622))+E(f317(f135(x50622),f317(f317(f127(x50622),x50621),x50623)),f317(f135(x50622),x50621)) % 168.22/168.05 [5093]~E(x50932,f125(x50931))+E(f317(f135(x50931),f317(f317(f127(x50931),x50932),x50933)),f317(f135(x50931),x50933)) % 168.22/168.05 [5148]~P93(x51481)+E(f317(f317(f122(x51481),x51482),f317(f317(f113(x51481),x51482),x51483)),x51482) % 168.22/168.05 [5149]~P93(x51491)+E(f317(f317(f113(x51491),x51492),f317(f317(f122(x51491),x51492),x51493)),x51492) % 168.22/168.05 [5150]~P103(x51501)+E(f317(f317(f223(x51501),x51502),f317(f317(f224(x51501),x51502),x51503)),x51502) % 168.22/168.05 [5151]~P103(x51511)+E(f317(f317(f224(x51511),x51512),f317(f317(f223(x51511),x51512),x51513)),x51512) % 168.22/168.05 [5169]~P55(x51691)+E(f55(x51691,f317(f317(f90(x51691),x51692),x51693),x51693),f2(x51691)) % 168.22/168.05 [5170]~P55(x51701)+E(f55(x51701,f317(f317(f90(x51701),x51702),x51703),x51702),f2(x51701)) % 168.22/168.05 [5240]~P25(x52401)+E(f317(f88(x52401),f317(f317(f21(x52401),x52402),x52403)),f317(f317(f21(x52401),x52403),x52402)) % 168.22/168.05 [5298]E(x52981,f125(x52982))+E(f126(x52982,f317(f317(f145(x52982),x52983),x52981)),f317(f317(f145(x52982),x52983),f126(x52982,x52981))) % 168.22/168.05 [5299]E(x52991,f125(x52992))+E(f126(x52992,f317(f317(f127(x52992),x52993),x52991)),f317(f317(f127(x52992),x52993),f126(x52992,x52991))) % 168.22/168.05 [5301]~P27(x53011)+E(f49(x53011,f317(f317(f286(x53011),x53012),x53013)),f317(f317(f122(x53011),x53012),f49(x53011,x53013))) % 168.22/168.05 [5302]~P27(x53021)+E(f50(x53021,f317(f317(f286(x53021),x53022),x53023)),f317(f317(f113(x53021),x53022),f50(x53021,x53023))) % 168.22/168.05 [5347]~P92(x53471)+E(f317(f317(f122(x53471),x53472),f317(f317(f122(x53471),x53472),x53473)),f317(f317(f122(x53471),x53472),x53473)) % 168.22/168.05 [5348]~P93(x53481)+E(f317(f317(f122(x53481),x53482),f317(f317(f122(x53481),x53482),x53483)),f317(f317(f122(x53481),x53482),x53483)) % 168.22/168.05 [5349]~P91(x53491)+E(f317(f317(f90(x53491),x53492),f317(f317(f90(x53491),x53492),x53493)),f317(f317(f90(x53491),x53492),x53493)) % 168.22/168.05 [5350]~P93(x53501)+E(f317(f317(f113(x53501),x53502),f317(f317(f113(x53501),x53502),x53503)),f317(f317(f113(x53501),x53502),x53503)) % 168.22/168.05 [5352]~P98(x53521)+E(f317(f317(f113(x53521),x53522),f317(f317(f113(x53521),x53522),x53523)),f317(f317(f113(x53521),x53522),x53523)) % 168.22/168.05 [5354]~P103(x53541)+E(f317(f317(f223(x53541),x53542),f317(f317(f223(x53541),x53542),x53543)),f317(f317(f223(x53541),x53542),x53543)) % 168.22/168.05 [5356]~P103(x53561)+E(f317(f317(f224(x53561),x53562),f317(f317(f224(x53561),x53562),x53563)),f317(f317(f224(x53561),x53562),x53563)) % 168.22/168.05 [5364]~P55(x53641)+E(f55(x53641,f317(f317(f89(x53641),x53642),x53643),x53643),f55(x53641,x53642,x53643)) % 168.22/168.05 [5365]~P55(x53651)+E(f55(x53651,f317(f317(f89(x53651),x53652),x53653),x53652),f55(x53651,x53653,x53652)) % 168.22/168.05 [5372]~P126(x53721)+E(f317(f317(f90(x53721),x53722),f317(f88(x53721),x53723)),f317(f88(x53721),f317(f317(f90(x53721),x53722),x53723))) % 168.22/168.05 [5373]~P58(x53731)+E(f317(f317(f266(x53731),x53732),f317(f88(x53731),x53733)),f317(f88(x53731),f317(f317(f266(x53731),x53732),x53733))) % 168.22/168.05 [5374]~P66(x53741)+E(f317(f317(f89(x53741),x53742),f317(f160(x53741),x53743)),f317(f160(x53741),f317(f317(f145(x53741),x53742),x53743))) % 168.22/168.05 [5404]~P126(x54041)+E(f317(f317(f90(x54041),f317(f88(x54041),x54042)),x54043),f317(f317(f90(x54041),x54042),f317(f88(x54041),x54043))) % 168.22/168.05 [5410]~P6(x54101,x54102,x54103)+E(f49(f858(x54101,a842),f317(f317(f70(x54101),x54102),x54103)),x54102) % 168.22/168.05 [5468]~P106(x54681)+E(f317(f317(f90(x54681),x54682),f317(f317(f238(x54681),x54682),x54683)),f317(f317(f238(x54681),x54682),f317(a124,x54683))) % 168.22/168.05 [5469]~P84(x54691)+E(f317(f317(f90(x54691),x54692),f317(f317(f238(x54691),x54692),x54693)),f317(f317(f238(x54691),x54692),f317(a124,x54693))) % 168.22/168.05 [5481]~P69(x54811)+E(f317(f317(f89(x54811),f317(f88(x54811),x54812)),f317(f317(f89(x54811),x54812),x54813)),x54813) % 168.22/168.05 [5504]~P110(x55041)+E(f317(f317(f238(x55041),f317(f112(x55041),x55042)),x55043),f317(f112(x55041),f317(f317(f238(a849),x55042),x55043))) % 168.22/168.05 [5505]~P111(x55051)+E(f317(f317(f238(x55051),f317(f114(x55051),x55052)),x55053),f317(f114(x55051),f317(f317(f238(a1),x55052),x55053))) % 168.22/168.05 [5511]~P79(x55111)+E(f317(f84(x55111),f317(f317(f21(x55111),x55112),x55113)),f317(f84(x55111),f317(f317(f21(x55111),x55113),x55112))) % 168.22/168.05 [5513]~P113(x55131)+E(f317(f317(f90(x55131),f91(x55131,x55132)),f91(x55131,x55133)),f91(x55131,f317(f317(f90(x55131),x55132),x55133))) % 168.22/168.05 [5518]E(x55181,f125(x55182))+E(f317(f317(f127(x55182),f317(f165(x55182),x55181)),x55183),f317(f165(x55182),f317(f317(f127(x55182),x55181),x55183))) % 168.22/168.05 [5523]~E(x55232,f317(a124,f317(f317(f89(a849),x55231),x55233)))+P22(f317(f317(f226(a849),x55231),x55232)) % 168.22/168.05 [5524]~P126(x55241)+E(f317(f317(f90(x55241),f317(f88(x55241),x55242)),x55243),f317(f88(x55241),f317(f317(f90(x55241),x55242),x55243))) % 168.22/168.05 [5525]~P115(x55251)+E(f317(f317(f266(x55251),f317(f88(x55251),x55252)),x55253),f317(f88(x55251),f317(f317(f266(x55251),x55252),x55253))) % 168.22/168.05 [5526]~P113(x55261)+E(f317(f317(f238(x55261),f317(f84(x55261),x55262)),x55263),f317(f84(x55261),f317(f317(f238(x55261),x55262),x55263))) % 168.22/168.05 [5623]E(f826(x56231,x56232,x56233),f835(x56231,x56232,x56233))+E(f317(f317(f113(f858(x56233,a842)),x56232),x56231),f188(f858(x56233,a842))) % 168.22/168.05 [5637]~P70(x56372)+E(f317(f317(f9(x56371,x56372),f317(f16(x56372,x56371),f87(x56372))),x56373),f87(x56372)) % 168.22/168.05 [5638]~P67(x56382)+E(f317(f317(f6(x56381,x56382),f317(f16(x56382,x56381),f2(x56382))),x56383),f2(x56382)) % 168.22/168.05 [5640]~P110(x56401)+E(f317(f317(f89(x56401),f317(f112(x56401),x56402)),f317(f112(x56401),x56403)),f317(f112(x56401),f317(f317(f89(a849),x56402),x56403))) % 168.22/168.05 [5641]~P110(x56411)+E(f317(f317(f90(x56411),f317(f112(x56411),x56412)),f317(f112(x56411),x56413)),f317(f112(x56411),f317(f317(f90(a849),x56412),x56413))) % 168.22/168.05 [5643]~P90(x56431)+E(f317(f317(f21(x56431),f317(f115(x56431),x56432)),f317(f115(x56431),x56433)),f317(f115(x56431),f317(f317(f21(a1),x56432),x56433))) % 168.22/168.05 [5645]~P111(x56451)+E(f317(f317(f89(x56451),f317(f114(x56451),x56452)),f317(f114(x56451),x56453)),f317(f114(x56451),f317(f317(f89(a1),x56452),x56453))) % 168.22/168.05 [5646]~P111(x56461)+E(f317(f317(f21(x56461),f317(f114(x56461),x56462)),f317(f114(x56461),x56463)),f317(f114(x56461),f317(f317(f21(a1),x56462),x56463))) % 168.22/168.05 [5647]~P111(x56471)+E(f317(f317(f90(x56471),f317(f114(x56471),x56472)),f317(f114(x56471),x56473)),f317(f114(x56471),f317(f317(f90(a1),x56472),x56473))) % 168.22/168.05 [5648]~P90(x56481)+E(f317(f317(f89(x56481),f317(f115(x56481),x56482)),f317(f115(x56481),x56483)),f317(f115(x56481),f317(f317(f89(a1),x56482),x56483))) % 168.22/168.05 [5649]~P90(x56491)+E(f317(f317(f90(x56491),f317(f115(x56491),x56492)),f317(f115(x56491),x56493)),f317(f115(x56491),f317(f317(f90(a1),x56492),x56493))) % 168.22/168.05 [5693]~E(x56933,x56932)+P22(f317(f317(f225(f858(x56931,a842)),x56932),x56933)) % 168.22/168.05 [5699]~E(x56992,x56993)+P22(f317(f317(f225(f858(x56991,a842)),x56992),x56993)) % 168.22/168.05 [5704]~P69(x57041)+E(f317(f317(f89(x57041),f317(f88(x57041),x57042)),f317(f88(x57041),x57043)),f317(f88(x57041),f317(f317(f89(x57041),x57043),x57042))) % 168.22/168.05 [5705]~P25(x57051)+E(f317(f317(f89(x57051),f317(f88(x57051),x57052)),f317(f88(x57051),x57053)),f317(f88(x57051),f317(f317(f89(x57051),x57052),x57053))) % 168.22/168.05 [5706]~P86(x57061)+E(f317(f317(f113(x57061),f317(f88(x57061),x57062)),f317(f88(x57061),x57063)),f317(f88(x57061),f317(f317(f122(x57061),x57062),x57063))) % 168.22/168.05 [5707]~P86(x57071)+E(f317(f317(f122(x57071),f317(f88(x57071),x57072)),f317(f88(x57071),x57073)),f317(f88(x57071),f317(f317(f113(x57071),x57072),x57073))) % 168.22/168.05 [5708]~P68(x57081)+E(f317(f317(f224(x57081),f317(f88(x57081),x57082)),f317(f88(x57081),x57083)),f317(f88(x57081),f317(f317(f223(x57081),x57082),x57083))) % 168.22/168.05 [5709]~P68(x57091)+E(f317(f317(f223(x57091),f317(f88(x57091),x57092)),f317(f88(x57091),x57093)),f317(f88(x57091),f317(f317(f224(x57091),x57092),x57093))) % 168.22/168.05 [5710]~P113(x57101)+E(f317(f317(f90(x57101),f317(f84(x57101),x57102)),f317(f84(x57101),x57103)),f317(f84(x57101),f317(f317(f90(x57101),x57102),x57103))) % 168.22/168.05 [5711]~P60(x57111)+E(f317(f317(f266(x57111),f317(f84(x57111),x57112)),f317(f84(x57111),x57113)),f317(f84(x57111),f317(f317(f266(x57111),x57112),x57113))) % 168.22/168.05 [5712]~P66(x57121)+E(f317(f317(f89(x57121),f317(f160(x57121),x57122)),f317(f160(x57121),x57123)),f317(f160(x57121),f317(f317(f127(x57121),x57122),x57123))) % 168.22/168.05 [5713]E(x57131,f188(f858(x57132,a842)))+~E(f317(f317(f122(f858(x57132,a842)),x57133),x57131),f188(f858(x57132,a842))) % 168.22/168.05 [5714]E(x57141,f188(f858(x57142,a842)))+~E(f317(f317(f122(f858(x57142,a842)),x57141),x57143),f188(f858(x57142,a842))) % 168.22/168.05 [5759]~P22(f317(f71(x57591),x57593))+P22(f317(f71(x57591),f317(f317(f286(x57591),x57592),x57593))) % 168.22/168.05 [5760]~P22(f317(f131(x57601),x57603))+P22(f317(f131(x57601),f317(f317(f167(x57601),x57602),x57603))) % 168.22/168.05 [5761]~P22(f317(f131(x57611),x57613))+P22(f317(f131(x57611),f317(f317(f132(x57611),x57612),x57613))) % 168.22/168.05 [5768]~E(x57681,f2(a849))+E(f317(f48(a849,f317(f317(f90(a849),x57681),x57682)),f317(f317(f90(a849),x57681),x57683)),f2(a849)) % 168.22/168.05 [5792]~P92(x57921)+P22(f317(f317(f225(x57921),x57922),f317(f317(f122(x57921),x57923),x57922))) % 168.22/168.05 [5793]~P93(x57931)+P22(f317(f317(f225(x57931),x57932),f317(f317(f122(x57931),x57933),x57932))) % 168.22/168.05 [5794]~P92(x57941)+P22(f317(f317(f225(x57941),x57942),f317(f317(f122(x57941),x57942),x57943))) % 168.22/168.05 [5795]~P93(x57951)+P22(f317(f317(f225(x57951),x57952),f317(f317(f122(x57951),x57952),x57953))) % 168.22/168.05 [5796]~P103(x57961)+P22(f317(f317(f225(x57961),x57962),f317(f317(f224(x57961),x57963),x57962))) % 168.22/168.05 [5797]~P103(x57971)+P22(f317(f317(f225(x57971),x57972),f317(f317(f224(x57971),x57972),x57973))) % 168.22/168.05 [5876]P22(f317(x58761,x58762))+P22(f317(f317(f194(f35(x58761,x58763)),x58762),x58762)) % 168.22/168.05 [5891]E(x58911,f2(a849))+E(f317(f48(a849,f317(f317(f90(a849),x58911),x58912)),f317(f317(f90(a849),x58911),x58913)),f317(f48(a849,x58912),x58913)) % 168.22/168.05 [5894]~P90(x58941)+E(f317(f317(f21(x58941),f317(f115(x58941),x58942)),f317(f115(x58941),x58943)),f317(f115(x58941),f317(f317(f89(a1),x58942),f317(f88(a1),x58943)))) % 168.22/168.05 [5979]E(f146(x59791,f317(f317(f145(x59791),x59792),x59793)),f317(f317(f145(x59791),x59792),f146(x59791,x59793)))+P22(f317(f317(f319(x59791),x59792),f317(f166(x59791),x59793))) % 168.22/168.05 [6081]E(x60811,f125(x60812))+E(f317(f317(f145(x60812),f317(f135(x60812),x60811)),f317(f317(f167(x60812),x60813),f317(f165(x60812),x60811))),f317(f317(f167(x60812),f317(a124,x60813)),x60811)) % 168.22/168.05 [6087]E(f317(f317(f21(f858(x60871,a842)),x60872),x60873),x60872)+~E(f317(f317(f113(f858(x60871,a842)),x60872),x60873),f188(f858(x60871,a842))) % 168.22/168.05 [6100]E(f146(x61001,f317(f317(f145(x61001),x61002),x61003)),f146(x61001,x61003))+~P22(f317(f317(f319(x61001),x61002),f317(f166(x61001),x61003))) % 168.22/168.05 [6137]~P22(f317(f317(f225(a849),x61371),x61373))+P22(f317(f317(f225(a849),x61371),f317(f317(f89(a849),x61372),x61373))) % 168.22/168.05 [6139]~P22(f317(f317(f225(a849),x61391),x61392))+P22(f317(f317(f225(a849),x61391),f317(f317(f89(a849),x61392),x61393))) % 168.22/168.05 [6141]~P22(f317(f317(f226(a849),x61411),x61413))+P22(f317(f317(f226(a849),x61411),f317(f317(f89(a849),x61412),x61413))) % 168.22/168.05 [6143]~P22(f317(f317(f226(a849),x61431),x61432))+P22(f317(f317(f226(a849),x61431),f317(f317(f89(a849),x61432),x61433))) % 168.22/168.05 [6180]P22(f317(f71(x61801),x61802))+~P22(f317(f71(x61801),f317(f317(f286(x61801),x61803),x61802))) % 168.22/168.05 [6181]P22(f317(f131(x61811),x61812))+~P22(f317(f131(x61811),f317(f317(f145(x61811),x61813),x61812))) % 168.22/168.05 [6182]P22(f317(f131(x61821),x61822))+~P22(f317(f131(x61821),f317(f317(f127(x61821),x61823),x61822))) % 168.22/168.05 [6183]P22(f317(f131(x61831),x61832))+~P22(f317(f131(x61831),f317(f317(f127(x61831),x61832),x61833))) % 168.22/168.05 [6224]~P84(x62241)+E(f317(f317(f89(x62241),x62242),f317(f317(f90(x62241),x62243),x62242)),f317(f317(f90(x62241),f317(f317(f89(x62241),x62243),f87(x62241))),x62242)) % 168.22/168.05 [6272]~E(x62721,x62722)+~P22(f317(f317(f226(f858(x62723,a842)),x62721),x62722)) % 168.22/168.05 [6316]P22(f317(f317(f319(x63161),x63162),x63163))+P22(f317(f317(f319(x63161),x63162),f317(f88(f858(x63161,a842)),x63163))) % 168.22/168.05 [6323]E(f317(f48(a1,x63231),f317(f317(f90(a1),x63232),x63233)),f317(f48(a1,f317(f48(a1,x63231),x63232)),x63233))+~P22(f317(f317(f226(a1),f2(a1)),x63233)) % 168.22/168.05 [6324]E(f138(x63241,f317(f317(f132(x63241),x63242),x63243)),f138(x63241,x63243))+~P22(f317(f317(f226(a849),x63242),f317(f189(f850(x63241)),x63243))) % 168.22/168.05 [6325]E(f317(f317(f167(x63251),x63252),f126(x63251,x63253)),f317(f317(f167(x63251),x63252),x63253))+~P22(f317(f317(f226(a849),x63252),f317(f189(f850(x63251)),x63253))) % 168.22/168.05 [6378]E(f317(f317(f317(f182(f850(x63781),f850(x63781)),x63782),f162(x63781)),x63783),x63783)+~E(f55(a849,x63782,f317(f189(f850(x63781)),x63783)),f2(a849)) % 168.22/168.05 [6385]~P6(x63851,x63853,x63852)+E(f317(f317(f265(x63851,x63851,x63851),f317(f263(x63851,x63851),x63852)),x63852),x63852) % 168.22/168.05 [6417]E(f317(f48(a849,f317(f317(f90(a849),x64171),x64172)),f317(f317(f90(a849),x64171),x64173)),f317(f48(a849,x64172),x64173))+~P22(f317(f317(f226(a849),f2(a849)),x64171)) % 168.22/168.05 [6426]~E(f317(f317(f122(f858(x64261,a842)),x64262),x64263),x64263)+P22(f317(f317(f225(f858(x64261,a842)),x64262),x64263)) % 168.22/168.05 [6431]~P49(x64311,x64311,x64313)+P49(x64311,x64311,f317(f317(f182(f857(x64311,x64311),a842),x64312),x64313)) % 168.22/168.05 [6433]~P22(f317(f317(f319(x64331),x64333),f317(f166(x64331),x64332)))+P22(f317(f317(f226(a849),f2(a849)),f317(f189(f850(x64331)),x64332))) % 168.22/168.05 [6460]~P79(x64601)+E(f317(f84(x64601),f317(f317(f89(x64601),f317(f84(x64601),x64602)),f317(f84(x64601),x64603))),f317(f317(f89(x64601),f317(f84(x64601),x64602)),f317(f84(x64601),x64603))) % 168.22/168.05 [6517]E(x65171,x65172)+~P22(f317(f317(f317(f317(a197,a23),x65171),x65173),x65172)) % 168.22/168.05 [6602]~P22(f317(f71(x66021),x66023))+E(f317(f317(f74(x66021,f858(x66021,a842),f286(x66021)),x66022),x66023),f317(f317(f122(f858(x66021,a842)),x66023),x66022)) % 168.22/168.05 [6662]E(f317(f317(f122(f858(x66621,a842)),x66622),x66623),x66622)+~P22(f317(f317(f225(f858(x66621,a842)),x66623),x66622)) % 168.22/168.05 [6664]E(f317(f317(f122(f858(x66641,a842)),x66642),x66643),x66643)+~P22(f317(f317(f225(f858(x66641,a842)),x66642),x66643)) % 168.22/168.05 [6665]E(f317(f317(f113(f858(x66651,a842)),x66652),x66653),x66653)+~P22(f317(f317(f225(f858(x66651,a842)),x66653),x66652)) % 168.22/168.05 [6666]E(f317(f317(f113(f858(x66661,a842)),x66662),x66663),x66662)+~P22(f317(f317(f225(f858(x66661,a842)),x66662),x66663)) % 168.22/168.05 [6714]~P22(f317(f131(x67141),x67142))+E(f317(f317(f21(f858(x67141,a842)),f317(f166(x67141),x67142)),f317(f317(f286(x67141),x67143),f188(f858(x67141,a842)))),f317(f166(x67141),f164(x67141,x67143,x67142))) % 168.22/168.05 [6764]P37(x67641,x67642)+~P37(x67641,f317(f317(f182(f857(x67641,x67641),a842),x67643),x67642)) % 168.22/168.05 [6829]P22(f317(f58(x68291,x68292),f317(a60,x68293)))+~P22(f317(f58(f317(f88(a1),x68291),f317(f88(a1),x68292)),x68293)) % 168.22/168.05 [6835]E(f317(f317(f21(f858(x68351,a842)),f317(f317(f286(x68351),x68352),x68353)),f317(f317(f286(x68351),x68352),f188(f858(x68351,a842)))),x68353)+P22(f317(f317(f319(x68351),x68352),x68353)) % 168.22/168.05 [6856]E(f317(f317(f113(f858(x68561,a842)),f317(f166(x68561),x68562)),f317(f166(x68561),x68563)),f188(f858(x68561,a842)))+~P22(f317(f131(x68561),f317(f317(f127(x68561),x68562),x68563))) % 168.22/168.05 [6871]~P22(f317(f317(f319(x68711),x68712),f317(f166(x68711),x68713)))+~P22(f317(f131(x68711),f317(f317(f145(x68711),x68712),x68713))) % 168.22/168.05 [6956]E(f317(f317(f113(f858(x69561,a842)),x69562),x69563),f188(f858(x69561,a842)))+P22(f317(f317(f319(x69561),f826(x69563,x69562,x69561)),x69562)) % 168.22/168.05 [6957]E(f317(f317(f113(f858(x69571,a842)),x69572),x69573),f188(f858(x69571,a842)))+P22(f317(f317(f319(x69571),f835(x69573,x69572,x69571)),x69573)) % 168.22/168.05 [6961]E(f126(x69611,f317(f317(f167(x69611),x69612),x69613)),f317(f317(f167(x69611),f317(f317(f21(a849),x69612),f87(a849))),x69613))+~P22(f317(f317(f225(a849),x69612),f317(f189(f850(x69611)),x69613))) % 168.22/168.05 [7021]~P34(x70213,x70212,x70211)+P22(f317(f317(f226(a849),f740(x70211,x70212,x70213)),f317(f189(f850(x70213)),x70211))) % 168.22/168.05 [7038]P22(f317(f317(f226(a849),f2(a849)),x70381))+P22(f317(f317(f225(a849),f317(f317(f90(a849),x70382),x70381)),f317(f317(f90(a849),x70383),x70381))) % 168.22/168.05 [7039]P22(f317(f317(f226(a849),f2(a849)),x70391))+P22(f317(f317(f225(a849),f317(f317(f90(a849),x70391),x70392)),f317(f317(f90(a849),x70391),x70393))) % 168.22/168.05 [7042]~P22(f317(f317(f319(x70421),x70422),x70423))+~P22(f317(f317(f319(x70421),x70422),f317(f88(f858(x70421,a842)),x70423))) % 168.22/168.05 [7051]~P22(f317(f317(f226(f858(x70511,a842)),x70512),x70513))+P22(f317(f317(f225(f858(x70511,a842)),x70512),x70513)) % 168.22/168.05 [7152]~P22(f317(f317(f225(a849),x71522),x71523))+P22(f317(f317(f225(a849),f317(f317(f89(a849),x71521),x71522)),f317(f317(f89(a849),x71521),x71523))) % 168.22/168.05 [7153]~P22(f317(f317(f225(a849),x71531),x71533))+P22(f317(f317(f225(a849),f317(f317(f89(a849),x71531),x71532)),f317(f317(f89(a849),x71533),x71532))) % 168.22/168.05 [7154]~P22(f317(f317(f225(a849),x71543),x71542))+P22(f317(f317(f225(a849),f317(f317(f21(a849),x71541),x71542)),f317(f317(f21(a849),x71541),x71543))) % 168.22/168.05 [7155]~P22(f317(f317(f225(a849),x71551),x71553))+P22(f317(f317(f225(a849),f317(f317(f21(a849),x71551),x71552)),f317(f317(f21(a849),x71553),x71552))) % 168.22/168.05 [7157]~P22(f317(f317(f225(a849),x71572),x71573))+P22(f317(f317(f225(a849),f317(f317(f90(a849),x71571),x71572)),f317(f317(f90(a849),x71571),x71573))) % 168.22/168.05 [7159]~P22(f317(f317(f225(a849),x71591),x71593))+P22(f317(f317(f225(a849),f317(f317(f90(a849),x71591),x71592)),f317(f317(f90(a849),x71593),x71592))) % 168.22/168.05 [7160]~P22(f317(f317(f225(a1),x71602),x71603))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x71601),x71602)),f317(f317(f89(a1),x71601),x71603))) % 168.22/168.05 [7163]~P22(f317(f317(f226(a849),x71632),x71633))+P22(f317(f317(f226(a849),f317(f317(f89(a849),x71631),x71632)),f317(f317(f89(a849),x71631),x71633))) % 168.22/168.05 [7164]~P22(f317(f317(f226(a849),x71641),x71643))+P22(f317(f317(f226(a849),f317(f317(f89(a849),x71641),x71642)),f317(f317(f89(a849),x71643),x71642))) % 168.22/168.05 [7165]~P22(f317(f317(f226(a1),x71651),x71653))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x71651),x71652)),f317(f317(f89(a1),x71653),x71652))) % 168.22/168.05 [7239]E(x72391,x72392)+~P22(f317(f317(f319(x72393),x72391),f317(f317(f286(x72393),x72392),f188(f858(x72393,a842))))) % 168.22/168.05 [7241]~E(f317(f317(f113(f858(x72411,a842)),x72412),x72413),f188(f858(x72411,a842)))+P22(f317(f317(f225(f858(x72411,a842)),x72412),f317(f88(f858(x72411,a842)),x72413))) % 168.22/168.05 [7249]P22(f317(f317(f319(f858(x72491,a842)),x72492),f317(f285(x72491),x72493)))+~P22(f317(f317(f225(f858(x72491,a842)),x72492),x72493)) % 168.22/168.05 [7301]E(f317(f317(f145(x73011),f317(f317(f159(x73011),x73012),x73013)),f317(f317(f132(x73011),f317(a124,x73013)),x73012)),f317(f317(f132(x73011),x73013),x73012))+~P22(f317(f317(f226(a849),x73013),f317(f189(f850(x73011)),x73012))) % 168.22/168.05 [7326]P22(f317(f317(f319(f857(x73261,x73261)),x73262),f284(x73261,x73263)))+~P22(f317(f317(f319(f857(x73261,x73261)),x73262),x73263)) % 168.22/168.05 [7336]~P22(f317(f317(f319(f858(x73361,a842)),x73362),f317(f285(x73361),x73363)))+P22(f317(f317(f225(f858(x73361,a842)),x73362),x73363)) % 168.22/168.05 [7381]P22(f317(f317(f225(f858(x73811,a842)),x73812),f49(f858(x73811,a842),x73813)))+~P22(f317(f317(f319(f858(x73811,a842)),x73812),x73813)) % 168.22/168.05 [7405]~P111(x74051)+E(f317(f317(f90(x74051),f317(f317(f238(x74051),f317(f88(x74051),f87(x74051))),x74052)),f317(f317(f238(x74051),x74053),x74052)),f317(f317(f238(x74051),f317(f88(x74051),x74053)),x74052)) % 168.22/168.05 [7426]E(f317(f317(f159(x74261),x74262),f317(f317(f21(a849),f317(f189(f850(x74261)),x74262)),f317(a124,x74263))),f317(f317(f159(x74261),f317(f163(x74261),x74262)),x74263))+~P22(f317(f317(f226(a849),x74263),f317(f189(f850(x74261)),x74262))) % 168.22/168.05 [7443]~E(f317(f317(f113(f858(x74431,a842)),f675(x74433,x74432,x74431)),x74433),f188(f858(x74431,a842)))+E(f317(f317(f113(f858(x74431,a842)),f49(f858(x74431,a842),x74432)),x74433),f188(f858(x74431,a842))) % 168.22/168.05 [7505]~P22(f317(f317(f319(x75053),x75052),f317(f166(x75053),x75051)))+P22(f317(f317(f226(a849),f597(x75051,x75052,x75053)),f317(f189(f850(x75053)),x75051))) % 168.22/168.05 [7513]P22(f317(f317(f319(x75131),f317(f317(f159(x75131),x75132),x75133)),f317(f166(x75131),x75132)))+~P22(f317(f317(f226(a849),x75133),f317(f189(f850(x75131)),x75132))) % 168.22/168.05 [7610]~P22(f317(x76102,f661(x76103,x76102,x76101)))+E(f317(f317(f132(x76101),f317(f189(f850(x76101)),f170(x76101,x76102,x76103))),x76103),f125(x76101)) % 168.22/168.05 [7622]P22(f317(f317(f225(f858(f850(x76221),a842)),f155(x76221,x76222)),f155(x76221,x76223)))+~P22(f317(f317(f225(f858(x76221,a842)),x76222),x76223)) % 168.22/168.05 [7623]P22(f317(f317(f225(f858(f850(x76231),a842)),f154(x76231,x76232)),f154(x76231,x76233)))+~P22(f317(f317(f225(f858(x76231,a842)),x76232),x76233)) % 168.22/168.05 [7653]E(f317(f317(f113(f858(x76531,a842)),f49(f858(x76531,a842),x76532)),x76533),f188(f858(x76531,a842)))+P22(f317(f317(f319(f858(x76531,a842)),f675(x76533,x76532,x76531)),x76532)) % 168.22/168.05 [7655]~P22(f317(f317(f319(f858(x76551,a842)),x76553),x76552))+P22(f317(f317(f225(f858(x76551,a842)),f50(f858(x76551,a842),x76552)),x76553)) % 168.22/168.05 [7657]E(f317(f317(f113(f858(x76571,a842)),x76572),x76573),f188(f858(x76571,a842)))+~P22(f317(f317(f225(f858(x76571,a842)),x76572),f317(f88(f858(x76571,a842)),x76573))) % 168.22/168.05 [7706]E(f317(f317(f21(a849),f317(f317(f89(a849),f317(f160(a849),x77061)),x77062)),f317(f317(f159(a849),x77061),x77063)),f317(f160(a849),f317(f317(f153(a849,x77061),x77063),x77062)))+~P22(f317(f317(f226(a849),x77063),f317(f189(f850(a849)),x77061))) % 168.22/168.05 [7755]P22(f317(f317(f225(a849),x77551),x77552))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),x77553),x77551)),f317(f317(f89(a849),x77553),x77552))) % 168.22/168.05 [7758]P22(f317(f317(f226(a849),x77581),x77582))+~P22(f317(f317(f226(a849),f317(f317(f89(a849),x77583),x77581)),f317(f317(f89(a849),x77583),x77582))) % 168.22/168.05 [7759]P22(f317(f317(f226(a849),x77591),x77592))+~P22(f317(f317(f226(a849),f317(f317(f90(a849),x77593),x77591)),f317(f317(f90(a849),x77593),x77592))) % 168.22/168.05 [7760]P22(f317(f317(f226(a849),x77601),x77602))+~P22(f317(f317(f226(a849),f317(f317(f90(a849),x77601),x77603)),f317(f317(f90(a849),x77602),x77603))) % 168.22/168.05 [7788]P22(f317(f317(f226(a849),f2(a849)),x77881))+~P22(f317(f317(f226(a849),f317(f317(f90(a849),x77882),x77881)),f317(f317(f90(a849),x77883),x77881))) % 168.22/168.05 [7789]P22(f317(f317(f226(a849),f2(a849)),x77891))+~P22(f317(f317(f226(a849),f317(f317(f90(a849),x77891),x77892)),f317(f317(f90(a849),x77891),x77893))) % 168.22/168.05 [7855]E(f240(x78551,x78552,x78553),x78552)+~P22(f317(f317(f225(f858(x78551,a842)),x78553),f317(f317(f286(x78551),x78552),f188(f858(x78551,a842))))) % 168.22/168.05 [7910]~P22(f317(f131(x79101),x79103))+E(f317(f130(x79101,f317(f317(f8(a842,a842,x79101),a312),f317(a314,x79102))),x79103),f164(x79101,x79102,x79103)) % 168.22/168.05 [7933]E(f317(f317(f132(x79331),f317(f189(f850(x79331)),f170(x79331,x79332,x79333))),x79333),f125(x79331))+P22(f317(f317(f319(x79331),f661(x79333,x79332,x79331)),f317(f166(x79331),x79333))) % 168.22/168.05 [7937]E(f317(f317(f127(x79371),f317(f317(f167(x79371),x79372),x79373)),f317(f317(f145(x79371),f317(f317(f159(x79371),x79373),x79372)),f125(x79371))),f317(f317(f167(x79371),f317(a124,x79372)),x79373))+~P22(f317(f317(f226(a849),x79372),f317(f189(f850(x79371)),x79373))) % 168.22/168.05 [7999]E(f317(f130(x79991,f317(f317(f8(a842,a842,x79991),a312),f317(a314,x79992))),x79993),x79993)+P22(f317(f317(f319(x79991),x79992),f317(f166(x79991),x79993))) % 168.22/168.05 [8009]P22(f317(f317(f225(f858(f858(x80091,a842),a842)),f241(x80091,x80092)),f241(x80091,x80093)))+~P22(f317(f317(f225(f858(x80091,a842)),x80092),x80093)) % 168.22/168.05 [8054]~P22(f317(f131(x80541),x80543))+P22(f317(f131(x80541),f317(f317(f317(f182(f850(x80541),f850(x80541)),x80542),f162(x80541)),x80543))) % 168.22/168.05 [8060]~P22(f317(f317(f226(a849),x80602),x80603))+P22(f317(f317(f226(a849),f317(f317(f90(a849),f317(a124,x80601)),x80602)),f317(f317(f90(a849),f317(a124,x80601)),x80603))) % 168.22/168.05 [8080]P22(f317(f317(f225(f858(f858(x80801,a842),a842)),f317(f285(x80801),x80802)),f317(f285(x80801),x80803)))+~P22(f317(f317(f225(f858(x80801,a842)),x80802),x80803)) % 168.22/168.05 [8248]~P22(f317(f317(f225(f858(x82481,a842)),x82483),x82482))+P22(f317(f317(f225(f858(x82481,a842)),f317(f88(f858(x82481,a842)),x82482)),f317(f88(f858(x82481,a842)),x82483))) % 168.22/168.05 [8279]E(f317(f287(a849,a849,f317(f317(f7(a849,a849,a849),f21(a849)),x82791)),f317(f278(a849,x82792),x82793)),f317(f278(a849,f317(f317(f21(a849),x82792),x82791)),f317(f317(f21(a849),x82793),x82791)))+~P22(f317(f317(f226(a849),x82791),x82793)) % 168.22/168.05 [8298]E(f317(f317(f89(a1),f317(f317(f90(a1),x82981),f55(a1,f317(f48(a1,x82982),x82981),x82983))),f55(a1,x82982,x82981)),f55(a1,x82982,f317(f317(f90(a1),x82981),x82983)))+~P22(f317(f317(f226(a1),f2(a1)),x82983)) % 168.22/168.05 [8308]~P66(x83081)+E(f317(f317(f89(x83081),x83082),f317(f136(x83081,x83081,f89(x83081),f2(x83081)),x83083)),f317(f136(x83081,x83081,f89(x83081),x83082),x83083)) % 168.22/168.05 [8392]~P79(x83921)+P22(f317(f317(f225(x83921),f317(f84(x83921),f317(f317(f89(x83921),x83922),x83923))),f317(f317(f89(x83921),f317(f84(x83921),x83922)),f317(f84(x83921),x83923)))) % 168.22/168.05 [8393]~P79(x83931)+P22(f317(f317(f225(x83931),f317(f84(x83931),f317(f317(f21(x83931),x83932),x83933))),f317(f317(f89(x83931),f317(f84(x83931),x83932)),f317(f84(x83931),x83933)))) % 168.22/168.05 [8410]E(f317(f317(f127(x84101),f317(f317(f167(x84101),x84102),x84103)),f317(f317(f145(x84101),f317(f135(x84101),f317(f317(f132(x84101),x84102),x84103))),f125(x84101))),f317(f317(f167(x84101),f317(a124,x84102)),x84103))+~P22(f317(f317(f226(a849),x84102),f317(f189(f850(x84101)),x84103))) % 168.22/168.05 [8432]E(f317(f254(x84321,f317(f317(f148(x84321,f857(a111,x84321)),f317(f237(a111,x84321),f87(a111))),x84322)),f317(a3,x84323)),f317(f317(f159(x84321),x84322),x84323))+~P22(f317(f317(f226(a849),x84323),f317(f189(f850(x84321)),x84322))) % 168.22/168.05 [8500]P22(f317(f317(f319(f857(x85001,x85001)),x85002),f317(f317(f265(x85001,x85001,x85001),x85003),f284(x85001,x85003))))+~P22(f317(f317(f319(f857(x85001,x85001)),x85002),x85003)) % 168.22/168.05 [8515]P22(f317(f317(f225(a849),x85151),x85152))+~P22(f317(f317(f225(a849),f317(f317(f90(a849),f317(a124,x85153)),x85151)),f317(f317(f90(a849),f317(a124,x85153)),x85152))) % 168.22/168.05 [8530]P22(f317(f317(f225(f858(x85301,a842)),x85302),x85303))+~P22(f317(f317(f225(f858(x85301,a842)),f317(f88(f858(x85301,a842)),x85303)),f317(f88(f858(x85301,a842)),x85302))) % 168.22/168.05 [8548]P22(f317(f131(x85481),x85482))+~P22(f317(f131(x85481),f317(f317(f317(f182(f850(x85481),f850(x85481)),x85483),f162(x85481)),x85482))) % 168.22/168.05 [8606]E(f317(f287(f857(x86061,x86062),x86062,f246(x86061,x86062)),f317(f166(f857(x86061,x86062)),x86063)),f179(x86061,x86062,f317(f171(x86061,x86062),x86063)))+~P22(f317(f131(x86061),f317(f317(f148(f857(x86061,x86062),x86061),f244(x86061,x86062)),x86063))) % 168.22/168.05 [8615]E(f317(f262(x86151,x86151,f284(x86151,x86152)),x86153),x86153)+~P22(f317(f317(f225(f858(x86151,a842)),f317(f262(x86151,x86151,x86152),x86153)),x86153)) % 168.22/168.05 [8657]~P103(x86571)+P29(x86571,f317(f130(x86571,f317(f317(f7(x86571,x86571,a842),a314),f317(x86572,x86573))),x86573)) % 168.22/168.05 [8663]~P22(f317(f317(f225(a849),x86631),x86632))+P22(f317(f317(f225(a849),x86631),f317(f136(a849,a849,f89(a849),x86632),x86633))) % 168.22/168.05 [8737]~P22(f317(f317(f319(f857(x87371,x87371)),x87372),f284(x87371,x87373)))+P22(f317(f317(f319(f857(x87371,x87371)),x87372),f317(f317(f182(f857(x87371,x87371),a842),f754(x87373,x87372,x87371)),x87373))) % 168.22/168.05 [8828]~P66(x88281)+E(f317(f317(f89(x88281),x88282),f317(f136(x88281,x88281,f317(f7(x88281,x88281,x88281),f89(x88281)),f2(x88281)),f317(f163(x88281),x88283))),f317(f136(x88281,x88281,f89(x88281),x88282),x88283)) % 168.22/168.05 [9093]P49(x90931,x90932,x90933)+P22(f317(f317(f319(f857(x90931,x90932)),f317(f317(f237(x90931,x90932),f750(x90933,x90932,x90931)),f720(x90933,x90932,x90931))),x90933)) % 168.22/168.05 [9094]P49(x90941,x90942,x90943)+P22(f317(f317(f319(f857(x90941,x90942)),f317(f317(f237(x90941,x90942),f750(x90943,x90942,x90941)),f719(x90943,x90942,x90941))),x90943)) % 168.22/168.05 [9164]~P22(f317(f317(f319(f857(x91641,x91641)),x91642),f317(f317(f265(x91641,x91641,x91641),x91643),f284(x91641,x91643))))+P22(f317(f317(f319(f857(x91641,x91641)),x91642),f317(f317(f182(f857(x91641,x91641),a842),f756(x91643,x91642,x91641)),x91643))) % 168.22/168.05 [9165]~P22(f317(x91651,f317(f317(f159(x91652),x91653),f317(f189(f850(x91652)),f170(x91652,x91651,x91653)))))+~P22(f317(f317(f226(a849),f317(f189(f850(x91652)),f170(x91652,x91651,x91653))),f317(f189(f850(x91652)),x91653))) % 168.22/168.05 [9250]~P22(f317(f317(f225(f858(x92501,a842)),x92502),x92503))+P22(f317(f317(f225(f858(x92501,a842)),f317(f317(f7(x92501,f858(x92501,a842),a842),f319(x92501)),x92502)),f317(f317(f7(x92501,f858(x92501,a842),a842),f319(x92501)),x92503))) % 168.22/168.05 [9304]~P22(f317(f317(f319(f857(f858(x93041,a842),f858(x93041,a842))),f317(f317(f237(f858(x93041,a842),f858(x93041,a842)),x93042),x93043)),f283(x93041)))+P22(f317(f317(f226(f858(x93041,a842)),x93042),x93043)) % 168.22/168.05 [9330]P50(x93301,x93302,x93303)+~P22(f317(f317(f319(f857(x93301,x93301)),f317(f317(f237(x93301,x93301),f753(x93303,x93302,x93301)),f752(x93303,x93302,x93301))),x93303)) % 168.22/168.05 [9331]P50(x93311,x93312,x93313)+~P22(f317(f317(f319(f857(x93311,x93311)),f317(f317(f237(x93311,x93311),f752(x93313,x93312,x93311)),f753(x93313,x93312,x93311))),x93313)) % 168.22/168.05 [9364]~P22(f317(f317(f319(f857(f850(x93641),f850(x93641))),f317(f317(f237(f850(x93641),f850(x93641)),x93642),x93642)),f141(x93641,x93643)))+P22(f317(f317(f319(f857(x93641,x93641)),f317(f317(f237(x93641,x93641),f607(x93642,x93643,x93641)),f607(x93642,x93643,x93641))),x93643)) % 168.22/168.05 [9419]P22(f317(f317(f225(f858(x94191,a842)),x94192),x94193))+~P22(f317(f317(f225(f858(x94191,a842)),f317(f317(f7(x94191,f858(x94191,a842),a842),f319(x94191)),x94192)),f317(f317(f7(x94191,f858(x94191,a842),a842),f319(x94191)),x94193))) % 168.22/168.05 [9500]E(f317(f317(f21(a849),f317(f317(f6(a849,a849),x95001),f317(f231(a849),x95002))),f317(f317(f6(a849,a849),x95003),f317(f231(a849),x95002))),f317(f317(f6(a849,a849),f317(f317(f18(a849,a849,a849),f317(f317(f8(a849,f858(a849,a849),a849),f21(a849)),x95001)),x95003)),f317(f231(a849),x95002)))+~P22(f317(f317(f225(a849),f317(x95003,f471(x95002,x95001,x95003))),f317(x95001,f471(x95002,x95001,x95003)))) % 168.22/168.05 [9801]E(f317(f230(f857(x98011,x98012)),f317(f247(x98011,x98012,a842),f317(f317(f7(x98011,f858(x98012,f853(x98012)),f858(x98012,a842)),f317(f317(f8(f858(f853(x98012),a842),f858(f858(x98012,f853(x98012)),f858(x98012,a842)),x98011),f8(f853(x98012),a842,x98012)),f317(f317(f8(f853(x98012),f858(f853(x98012),a842),x98011),a314),f317(f171(x98011,x98012),x98013)))),f217(x98012)))),f317(f166(f857(x98011,x98012)),x98013))+~P22(f317(f131(x98011),f317(f317(f148(f857(x98011,x98012),x98011),f244(x98011,x98012)),x98013))) % 168.22/168.05 [5563]~P69(x55631)+E(f317(f317(f89(x55631),f317(f317(f21(x55631),x55632),x55633)),x55633),x55632) % 168.22/168.05 [5564]~P69(x55641)+E(f317(f317(f21(x55641),f317(f317(f89(x55641),x55642),x55643)),x55643),x55642) % 168.22/168.05 [5767]~P69(x57671)+E(f317(f317(f89(x57671),x57672),f317(f317(f89(x57671),f317(f88(x57671),x57672)),x57673)),x57673) % 168.22/168.05 [5850]~P75(x58501)+E(f317(f317(f90(x58501),f317(f317(f238(x58501),x58502),x58503)),x58502),f317(f317(f238(x58501),x58502),f317(a124,x58503))) % 168.22/168.05 [5851]~P84(x58511)+E(f317(f317(f90(x58511),f317(f317(f238(x58511),x58512),x58513)),x58512),f317(f317(f238(x58511),x58512),f317(a124,x58513))) % 168.22/168.05 [6057]~P113(x60571)+E(f317(f84(x60571),f317(f317(f238(x60571),f317(f88(x60571),x60572)),x60573)),f317(f84(x60571),f317(f317(f238(x60571),x60572),x60573))) % 168.22/168.05 [6111]~P75(x61111)+E(f317(f317(f90(x61111),f317(f317(f238(x61111),x61112),x61113)),x61112),f317(f317(f90(x61111),x61112),f317(f317(f238(x61111),x61112),x61113))) % 168.22/168.05 [6170]E(f317(f317(f21(a111),f317(f317(f89(a111),x61701),x61702)),x61703),f258(x61701,x61702,x61703))+~P22(f317(f317(f226(a111),x61702),x61703)) % 168.22/168.05 [6192]~E(f317(f317(f132(x61921),x61923),x61922),f125(x61921))+P22(f317(f317(f225(a849),f317(f189(f850(x61921)),x61922)),x61923)) % 168.22/168.05 [6322]E(f317(f317(f90(a849),f317(f115(a849),x63221)),f317(f317(f90(a849),f317(f115(a849),x63222)),x63223)),f2(a849))+~P22(f317(f317(f226(a1),x63221),a92)) % 168.22/168.05 [6338]~P58(x63381)+E(f317(f317(f238(x63381),f317(f317(f266(x63381),f87(x63381)),x63382)),x63383),f317(f317(f266(x63381),f87(x63381)),f317(f317(f238(x63381),x63382),x63383))) % 168.22/168.05 [6415]E(f317(f317(f21(a849),f317(f317(f89(a849),x64151),x64152)),x64153),f317(f317(f21(a849),x64151),f317(f317(f21(a849),x64153),x64152)))+~P22(f317(f317(f225(a849),x64152),x64153)) % 168.22/168.05 [6416]E(f317(f317(f21(a849),f317(f317(f89(a849),x64161),x64162)),x64163),f317(f317(f89(a849),x64161),f317(f317(f21(a849),x64162),x64163)))+~P22(f317(f317(f225(a849),x64163),x64162)) % 168.22/168.05 [6451]~P93(x64511)+P22(f317(f317(f225(x64511),f317(f317(f113(x64511),x64512),x64513)),x64513)) % 168.22/168.05 [6452]~P98(x64521)+P22(f317(f317(f225(x64521),f317(f317(f113(x64521),x64522),x64523)),x64523)) % 168.22/168.05 [6453]~P93(x64531)+P22(f317(f317(f225(x64531),f317(f317(f113(x64531),x64532),x64533)),x64532)) % 168.22/168.05 [6454]~P98(x64541)+P22(f317(f317(f225(x64541),f317(f317(f113(x64541),x64542),x64543)),x64542)) % 168.22/168.05 [6455]~P103(x64551)+P22(f317(f317(f225(x64551),f317(f317(f223(x64551),x64552),x64553)),x64553)) % 168.22/168.05 [6456]~P103(x64561)+P22(f317(f317(f225(x64561),f317(f317(f223(x64561),x64562),x64563)),x64562)) % 168.22/168.05 [6520]~P84(x65201)+E(f317(f317(f89(x65201),f317(f317(f90(x65201),x65202),x65203)),x65203),f317(f317(f90(x65201),f317(f317(f89(x65201),x65202),f87(x65201))),x65203)) % 168.22/168.05 [6521]~P90(x65211)+E(f317(f317(f90(x65211),f317(f88(x65211),f317(f115(x65211),x65212))),x65213),f317(f317(f90(x65211),f317(f115(x65211),f317(f88(a1),x65212))),x65213)) % 168.22/168.05 [6594]~P66(x65941)+E(f317(f160(x65941),f317(f317(f148(x65942,x65941),f317(f16(x65941,x65942),f2(x65941))),x65943)),f2(x65941)) % 168.22/168.05 [6605]E(f317(f317(f89(a849),f317(f115(a849),x66051)),f317(f317(f89(a849),f317(f115(a849),x66052)),x66053)),f317(f317(f89(a849),f317(f115(a849),x66052)),x66053))+~P22(f317(a193,f317(f115(a1),x66051))) % 168.22/168.05 [6621]~P27(x66211)+E(f49(x66211,f317(f317(f286(x66211),x66212),f317(f317(f286(x66211),x66213),f188(f858(x66211,a842))))),f317(f317(f122(x66211),x66212),x66213)) % 168.22/168.05 [6622]~P27(x66221)+E(f50(x66221,f317(f317(f286(x66221),x66222),f317(f317(f286(x66221),x66223),f188(f858(x66221,a842))))),f317(f317(f113(x66221),x66222),x66223)) % 168.22/168.05 [6646]E(f317(f317(f167(x66461),x66462),x66463),x66463)+~P22(f317(f317(f225(a849),f317(f189(f850(x66461)),x66463)),x66462)) % 168.22/168.05 [6657]E(f317(f317(f132(x66571),x66572),x66573),f125(x66571))+~P22(f317(f317(f225(a849),f317(f189(f850(x66571)),x66573)),x66572)) % 168.22/168.05 [6668]E(f317(f317(f21(a849),f317(f317(f89(a849),x66681),x66682)),x66683),f317(f317(f89(a849),f317(f317(f21(a849),x66681),x66683)),x66682))+~P22(f317(f317(f225(a849),x66683),x66681)) % 168.22/168.05 [6682]~P22(f317(f317(f226(a849),x66821),x66823))+P22(f317(f317(f226(a849),f317(f317(f21(a849),x66821),x66822)),x66823)) % 168.22/168.05 [6707]~P103(x67071)+E(f164(x67071,x67072,f317(f317(f143(x67071,x67071,f5(x67071)),x67072),x67073)),x67073) % 168.22/168.05 [6789]E(f317(f317(f21(a849),f317(f317(f89(a849),x67891),x67892)),f317(a124,x67893)),f317(f317(f21(a849),x67891),f317(a124,f317(f317(f21(a849),x67893),x67892))))+~P22(f317(f317(f225(a849),x67892),x67893)) % 168.22/168.05 [6790]~P113(x67901)+P22(f317(f317(f225(x67901),f2(x67901)),f317(f317(f238(x67901),f317(f84(x67901),x67902)),x67903))) % 168.22/168.05 [6840]P18(x68401,x68402,x68403)+~P22(f317(f317(f225(f858(f848(x68401),a842)),x68403),x68402)) % 168.22/168.05 [6884]~P22(f317(f71(x68841),x68842))+P22(f317(f71(x68841),f317(f317(f21(f858(x68841,a842)),x68842),x68843))) % 168.22/168.05 [6885]~P22(f317(f71(x68851),x68853))+P22(f317(f71(x68851),f317(f317(f113(f858(x68851,a842)),x68852),x68853))) % 168.22/168.05 [6886]~P22(f317(f71(x68861),x68862))+P22(f317(f71(x68861),f317(f317(f113(f858(x68861,a842)),x68862),x68863))) % 168.22/168.05 [6903]~P55(x69031)+E(f317(f317(f89(x69031),f55(x69031,x69032,x69033)),f317(f317(f90(x69031),f317(f48(x69031,x69032),x69033)),x69033)),x69032) % 168.22/168.05 [7028]~P37(x70281,x70283)+P37(x70281,f317(f317(f113(f858(f857(x70281,x70281),a842)),x70282),x70283)) % 168.22/168.05 [7029]~P37(x70291,x70292)+P37(x70291,f317(f317(f113(f858(f857(x70291,x70291),a842)),x70292),x70293)) % 168.22/168.05 [7148]~P93(x71481)+E(f11(x71481,f317(f166(x71481),f317(f317(f145(x71481),x71482),x71483))),f317(f136(x71481,x71481,f113(x71481),x71482),x71483)) % 168.22/168.05 [7149]~P93(x71491)+E(f10(x71491,f317(f166(x71491),f317(f317(f145(x71491),x71492),x71493))),f317(f136(x71491,x71491,f122(x71491),x71492),x71493)) % 168.22/168.05 [7150]~P103(x71501)+E(f14(x71501,f317(f166(x71501),f317(f317(f145(x71501),x71502),x71503))),f317(f136(x71501,x71501,f224(x71501),x71502),x71503)) % 168.22/168.05 [7151]~P103(x71511)+E(f15(x71511,f317(f166(x71511),f317(f317(f145(x71511),x71512),x71513))),f317(f136(x71511,x71511,f223(x71511),x71512),x71513)) % 168.22/168.05 [7203]~P22(f317(f71(x72031),x72032))+P22(f317(f317(f225(a849),f317(f54(x72031),x72032)),f317(f54(x72031),f317(f317(f286(x72031),x72033),x72032)))) % 168.22/168.05 [7210]E(f317(f317(f122(f858(a849,a842)),f317(f278(a849,x72101),x72102)),f317(f278(a849,x72102),f317(f317(f89(a849),x72102),x72103))),f317(f278(a849,x72101),f317(f317(f89(a849),x72102),x72103)))+~P22(f317(f317(f225(a849),x72101),x72102)) % 168.22/168.05 [7220]P22(f317(f317(f225(a849),x72201),x72202))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),x72203),x72201)),x72202)) % 168.22/168.05 [7221]P22(f317(f317(f225(a849),x72211),x72212))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),x72211),x72213)),x72212)) % 168.22/168.05 [7222]P22(f317(f317(f226(a849),x72221),x72222))+~P22(f317(f317(f226(a849),f317(f317(f89(a849),x72221),x72223)),x72222)) % 168.22/168.05 [7264]~P103(x72641)+E(f12(x72641,f224(x72641),f317(f166(x72641),f317(f317(f145(x72641),x72642),x72643))),f317(f136(x72641,x72641,f224(x72641),x72642),x72643)) % 168.22/168.05 [7265]~P103(x72651)+E(f13(x72651,f223(x72651),f317(f166(x72651),f317(f317(f145(x72651),x72652),x72653))),f317(f136(x72651,x72651,f223(x72651),x72652),x72653)) % 168.22/168.05 [7269]~E(x72692,f188(f858(f857(x72691,x72691),a842)))+P22(f317(f317(f225(f858(f857(x72691,x72691),a842)),x72692),x72693)) % 168.22/168.05 [7376]E(f317(f317(f122(f858(x73761,a842)),x73762),f317(f317(f21(f858(x73761,a842)),x73763),x73762)),x73763)+~P22(f317(f317(f225(f858(x73761,a842)),x73762),x73763)) % 168.22/168.05 [7377]~P22(f317(f317(f225(a849),x73771),f317(f317(f89(a849),x73773),x73772)))+P22(f317(f317(f225(a849),f317(f317(f21(a849),x73771),x73772)),x73773)) % 168.22/168.05 [7378]~P22(f317(f317(f226(a849),x73781),f317(f317(f21(a849),x73783),x73782)))+P22(f317(f317(f226(a849),f317(f317(f89(a849),x73781),x73782)),x73783)) % 168.22/168.05 [7433]E(x74331,f125(x74332))+E(f317(f135(x74332),f317(f317(f317(f182(f850(x74332),f850(x74332)),x74333),f162(x74332)),x74331)),f317(f317(f159(x74332),x74331),f55(a849,x74333,f317(f189(f850(x74332)),x74331)))) % 168.22/168.05 [7442]E(f317(f317(f286(x74421),x74422),f317(f317(f21(f858(x74421,a842)),x74423),f317(f317(f286(x74421),x74422),f188(f858(x74421,a842))))),x74423)+~P22(f317(f317(f319(x74421),x74422),x74423)) % 168.22/168.05 [7602]P22(f317(f317(f225(a849),x76021),f317(f317(f89(a849),x76022),x76023)))+~P22(f317(f317(f225(a849),f317(f317(f21(a849),x76021),x76023)),x76022)) % 168.22/168.05 [7603]P22(f317(f317(f226(a849),x76031),f317(f317(f21(a849),x76032),x76033)))+~P22(f317(f317(f226(a849),f317(f317(f89(a849),x76031),x76033)),x76032)) % 168.22/168.05 [7627]P22(f317(f71(x76271),x76272))+~P22(f317(f71(x76271),f317(f317(f122(f858(x76271,a842)),x76273),x76272))) % 168.22/168.05 [7628]P22(f317(f71(x76281),x76282))+~P22(f317(f71(x76281),f317(f317(f122(f858(x76281,a842)),x76282),x76283))) % 168.22/168.05 [7704]~P44(x77041,x77043)+P22(f317(f317(f319(f857(x77041,x77041)),f317(f317(f237(x77041,x77041),x77042),x77042)),x77043)) % 168.22/168.05 [7829]E(f317(f317(f159(a849),f133(a849,f317(f278(a849,x78291),x78292))),x78293),f317(f317(f89(a849),x78291),x78293))+~P22(f317(f317(f226(a849),f317(f317(f89(a849),x78291),x78293)),x78292)) % 168.22/168.05 [7896]~P22(f317(f317(f194(f317(a29,x78961)),x78962),x78963))+P22(f317(f317(f194(f317(f222(a843),f317(a27,x78961))),x78962),x78963)) % 168.22/168.05 [7899]E(f317(f317(f167(a849),x78991),f133(a849,f317(f278(a849,x78992),x78993))),f133(a849,f317(f278(a849,x78992),f317(f317(f89(a849),x78992),x78991))))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),x78992),x78991)),x78993)) % 168.22/168.05 [7952]~P90(x79521)+E(f317(f317(f238(x79521),x79522),f317(f115(a849),f317(f317(f89(a1),x79523),x79523))),f317(f317(f95(x79521,x79521),f317(f317(f238(x79521),x79522),f317(f115(a849),x79523))),f317(f317(f18(x79521,x79521,x79521),f90(x79521)),f5(x79521)))) % 168.22/168.05 [8164]P22(f317(f317(f194(f317(a29,x81641)),x81642),x81643))+~P22(f317(f317(f194(f317(f222(a843),f317(a27,x81641))),x81642),x81643)) % 168.22/168.05 [8226]E(f317(f317(f127(x82261),f317(f317(f167(x82261),x82262),x82263)),f317(f317(f145(x82261),f317(f317(f159(x82261),x82263),x82262)),f317(f317(f132(x82261),f317(a124,x82262)),x82263))),x82263)+~P22(f317(f317(f226(a849),x82262),f317(f189(f850(x82261)),x82263))) % 168.22/168.05 [8234]P22(f317(f317(f225(f858(x82341,a842)),f305(x82341,x82342)),f305(x82341,x82343)))+~P22(f317(f317(f225(f858(x82341,f858(x82341,a842))),x82343),x82342)) % 168.22/168.05 [8236]~P50(x82361,x82362,x82363)+P50(x82361,x82362,f317(f317(f21(f858(f857(x82361,x82361),a842)),x82363),f284(x82361,f188(f858(f857(x82361,x82361),a842))))) % 168.22/168.05 [8253]P22(f317(f317(f225(f858(x82531,a842)),f306(x82531,x82532)),f306(x82531,x82533)))+~P22(f317(f317(f225(f858(f857(x82531,x82531),a842)),x82533),x82532)) % 168.22/168.05 [8259]~P119(x82591)+P22(f317(f317(f225(x82591),f2(x82591)),f317(f317(f89(x82591),f317(f317(f90(x82591),x82592),x82592)),f317(f317(f90(x82591),x82593),x82593)))) % 168.22/168.05 [8295]P22(f317(f317(f225(f858(x82951,a842)),f317(f261(x82951),x82952)),f317(f261(x82951),x82953)))+~P22(f317(f317(f225(f858(f857(x82951,x82951),a842)),x82952),x82953)) % 168.22/168.05 [8328]~P46(x83281,x83282)+~P22(f317(f317(f319(f857(x83281,x83281)),f317(f317(f237(x83281,x83281),x83283),x83283)),x83282)) % 168.22/168.05 [8330]~P37(x83301,x83302)+~P22(f317(f317(f319(f857(x83301,x83301)),f317(f317(f237(x83301,x83301),x83303),x83303)),x83302)) % 168.22/168.05 [8394]P22(f317(f317(f225(f858(x83941,a842)),f49(f858(x83941,a842),x83942)),f49(f858(x83941,a842),x83943)))+~P22(f317(f317(f225(f858(f858(x83941,a842),a842)),x83942),x83943)) % 168.22/168.05 [8395]P22(f317(f317(f225(f858(x83951,a842)),f50(f858(x83951,a842),x83952)),f50(f858(x83951,a842),x83953)))+~P22(f317(f317(f225(f858(f858(x83951,a842),a842)),x83953),x83952)) % 168.22/168.05 [8452]~P6(x84521,x84523,x84522)+P22(f317(f317(f225(f858(f857(x84521,x84521),a842)),x84522),f317(f317(f245(x84521,x84521),x84523),f317(f16(f858(x84521,a842),x84521),x84523)))) % 168.22/168.05 [8453]~P45(x84531,x84533,x84532)+P22(f317(f317(f225(f858(f857(x84531,x84531),a842)),x84532),f317(f317(f245(x84531,x84531),x84533),f317(f16(f858(x84531,a842),x84531),x84533)))) % 168.22/168.05 [8501]~P79(x85011)+P22(f317(f317(f225(x85011),f317(f317(f21(x85011),f317(f84(x85011),x85012)),f317(f84(x85011),x85013))),f317(f84(x85011),f317(f317(f21(x85011),x85013),x85012)))) % 168.22/168.05 [8502]~P79(x85021)+P22(f317(f317(f225(x85021),f317(f317(f21(x85021),f317(f84(x85021),x85022)),f317(f84(x85021),x85023))),f317(f84(x85021),f317(f317(f21(x85021),x85022),x85023)))) % 168.22/168.05 [8528]P22(f317(f317(f225(f858(f857(x85281,x85281),a842)),f284(x85281,x85282)),f284(x85281,x85283)))+~P22(f317(f317(f225(f858(f857(x85281,x85281),a842)),x85282),x85283)) % 168.22/168.05 [8680]P50(x86801,x86802,x86803)+~P50(x86801,x86802,f317(f317(f21(f858(f857(x86801,x86801),a842)),x86803),f284(x86801,f188(f858(f857(x86801,x86801),a842))))) % 168.22/168.05 [8697]P22(f317(f317(f225(f858(f857(f850(x86971),f850(x86971)),a842)),f152(x86971,x86972)),f152(x86971,x86973)))+~P22(f317(f317(f225(f858(f857(x86971,x86971),a842)),x86972),x86973)) % 168.22/168.05 [8698]P22(f317(f317(f225(f858(f857(f850(x86981),f850(x86981)),a842)),f151(x86981,x86982)),f151(x86981,x86983)))+~P22(f317(f317(f225(f858(f857(x86981,x86981),a842)),x86982),x86983)) % 168.22/168.05 [8717]~P45(x87171,x87173,x87172)+P22(f317(f317(f225(f858(f857(x87171,x87171),a842)),x87172),f317(f317(f265(x87171,x87171,x87171),f317(f263(x87171,x87171),x87172)),x87172))) % 168.22/168.05 [8764]~P22(f317(f131(x87641),x87642))+E(f317(f130(x87641,f317(f317(f7(x87641,f858(x87641,a842),a842),f319(x87641)),f317(f166(x87641),f168(x87641,x87642,x87643)))),x87642),f168(x87641,x87642,x87643)) % 168.22/168.05 [8826]E(x88261,x88262)+~P22(f317(f317(f319(f857(x88263,x88263)),f317(f317(f237(x88263,x88263),x88261),x88262)),f284(x88263,f188(f858(f857(x88263,x88263),a842))))) % 168.22/168.05 [8914]P22(f317(f317(f319(x89141),x89142),f306(x89141,x89143)))+P22(f317(f317(f319(f857(x89141,x89141)),f317(f317(f237(x89141,x89141),f345(x89143,x89142,x89141)),x89142)),x89143)) % 168.22/168.05 [8915]P22(f317(f317(f319(x89151),x89152),f306(x89151,x89153)))+P22(f317(f317(f319(f857(x89151,x89151)),f317(f317(f237(x89151,x89151),f722(x89153,x89152,x89151)),x89152)),x89153)) % 168.22/168.05 [8916]P22(f317(f317(f319(x89161),x89162),f306(x89161,x89163)))+P22(f317(f317(f319(f857(x89161,x89161)),f317(f317(f237(x89161,x89161),f731(x89163,x89162,x89161)),x89162)),x89163)) % 168.22/168.05 [8998]~P22(f317(f317(f319(f850(x89981)),x89983),f155(x89981,x89982)))+P22(f317(f154(x89981,f317(f317(f7(x89981,f858(x89981,a842),a842),f319(x89981)),x89982)),x89983)) % 168.22/168.05 [9019]P22(f317(x90193,x90192))+E(f317(f230(x90191),f317(f317(f18(x90191,a842,a842),f317(f317(f8(a842,f858(a842,a842),x90191),a315),f317(a314,x90192))),x90193)),f188(f858(x90191,a842))) % 168.22/168.05 [9040]~P79(x90401)+P22(f317(f317(f225(x90401),f317(f84(x90401),f317(f317(f21(x90401),f317(f84(x90401),x90402)),f317(f84(x90401),x90403)))),f317(f84(x90401),f317(f317(f21(x90401),x90402),x90403)))) % 168.22/168.05 [9052]~P22(f317(x90523,x90522))+E(f317(f230(x90521),f317(f317(f18(x90521,a842,a842),f317(f317(f8(a842,f858(a842,a842),x90521),a315),f317(a314,x90522))),x90523)),f317(f317(f286(x90521),x90522),f188(f858(x90521,a842)))) % 168.22/168.05 [9059]~P22(f317(f317(f319(f858(x90591,a842)),x90593),f317(f285(x90591),x90592)))+P22(f317(f241(x90591,f317(f317(f7(x90591,f858(x90591,a842),a842),f319(x90591)),x90592)),x90593)) % 168.22/168.05 [9092]P37(x90921,x90922)+P22(f317(f317(f319(f857(x90921,x90921)),f317(f317(f237(x90921,x90921),f317(f558(x90922,x90921),f317(a124,x90923))),f317(f558(x90922,x90921),x90923))),x90922)) % 168.22/168.05 [9230]P22(f317(f317(f319(f850(x92301)),x92302),f155(x92301,x92303)))+~P22(f317(f154(x92301,f317(f317(f7(x92301,f858(x92301,a842),a842),f319(x92301)),x92303)),x92302)) % 168.22/168.05 [9242]P22(f317(f317(f319(f858(x92421,a842)),x92422),f317(f285(x92421),x92423)))+~P22(f317(f241(x92421,f317(f317(f7(x92421,f858(x92421,a842),a842),f319(x92421)),x92423)),x92422)) % 168.22/168.05 [9300]P22(f317(f317(f319(x93001),f317(f254(x93001,x93002),x93003)),f317(f166(x93001),f317(f317(f148(f857(a111,x93001),x93001),f246(a111,x93001)),x93002))))+~P22(f317(f317(f226(a111),x93003),f317(f160(a111),f317(f317(f148(f857(a111,x93001),a111),f244(a111,x93001)),x93002)))) % 168.22/168.05 [9347]P22(f317(f317(f225(f858(f857(f850(x93471),f850(x93471)),a842)),f152(x93471,x93472)),f317(f317(f245(f850(x93471),f850(x93471)),f155(x93471,x93473)),f317(f16(f858(f850(x93471),a842),f850(x93471)),f155(x93471,x93473)))))+~P22(f317(f317(f225(f858(f857(x93471,x93471),a842)),x93472),f317(f317(f245(x93471,x93471),x93473),f317(f16(f858(x93471,a842),x93471),x93473)))) % 168.22/168.05 [9368]P22(f317(f317(f319(x93681),f317(f244(x93681,f857(a111,a111)),f317(f252(x93681,x93682),x93683))),f317(f166(x93681),f317(f317(f148(f857(a111,x93681),x93681),f246(a111,x93681)),x93682))))+~P22(f317(f317(f226(a111),f2(a111)),f317(f160(a111),f317(f317(f148(f857(a111,x93681),a111),f244(a111,x93681)),x93682)))) % 168.22/168.05 [9389]~P22(f317(f317(f225(f858(f857(x93891,x93891),a842)),x93892),f317(f317(f245(x93891,x93891),x93893),f317(f16(f858(x93891,a842),x93891),x93893))))+P22(f317(f317(f225(f858(f857(x93891,x93891),a842)),f317(f317(f265(x93891,x93891,x93891),x93892),f284(x93891,x93892))),f317(f317(f245(x93891,x93891),x93893),f317(f16(f858(x93891,a842),x93891),x93893)))) % 168.22/168.05 [9679]~P37(x96791,x96792)+~P22(f317(f317(f319(f857(x96791,x96791)),f317(f317(f237(x96791,x96791),f317(x96793,f317(a124,f559(x96792,x96791,x96793)))),f317(x96793,f559(x96792,x96791,x96793)))),x96792)) % 168.22/168.05 [9680]~P37(x96801,x96802)+~P22(f317(f317(f319(f857(x96801,x96801)),f317(f317(f237(x96801,x96801),f317(x96803,f317(a124,f745(x96803,x96802,x96801)))),f317(x96803,f745(x96803,x96802,x96801)))),x96802)) % 168.22/168.05 [9944]P22(f317(f317(f225(f858(f857(f858(x99441,a842),f858(x99441,a842)),a842)),f317(f317(f265(f858(x99441,a842),f858(x99441,a842),f858(x99441,a842)),f308(x99441,x99442)),f317(f317(f122(f858(f857(f858(x99441,a842),f858(x99441,a842)),a842)),f308(x99441,x99443)),f317(f317(f286(f857(f858(x99441,a842),f858(x99441,a842))),f317(f317(f237(f858(x99441,a842),f858(x99441,a842)),f188(f858(x99441,a842))),f188(f858(x99441,a842)))),f188(f858(f857(f858(x99441,a842),f858(x99441,a842)),a842)))))),f308(x99441,x99442)))+~P22(f317(f317(f225(f858(f857(x99441,x99441),a842)),f317(f317(f265(x99441,x99441,x99441),x99442),x99443)),x99442)) % 168.22/168.05 [9945]P22(f317(f317(f225(f858(f857(f858(x99451,a842),f858(x99451,a842)),a842)),f317(f317(f265(f858(x99451,a842),f858(x99451,a842),f858(x99451,a842)),f309(x99451,x99452)),f317(f317(f122(f858(f857(f858(x99451,a842),f858(x99451,a842)),a842)),f309(x99451,x99453)),f317(f317(f286(f857(f858(x99451,a842),f858(x99451,a842))),f317(f317(f237(f858(x99451,a842),f858(x99451,a842)),f188(f858(x99451,a842))),f188(f858(x99451,a842)))),f188(f858(f857(f858(x99451,a842),f858(x99451,a842)),a842)))))),f309(x99451,x99452)))+~P22(f317(f317(f225(f858(f857(x99451,x99451),a842)),f317(f317(f265(x99451,x99451,x99451),x99452),x99453)),x99452)) % 168.22/168.05 [7147]~P22(f317(f317(f225(a849),x71472),x71471))+E(f317(f317(f21(a849),f317(a124,f317(f317(f21(a849),x71471),x71472))),x71473),f317(f317(f21(a849),f317(a124,x71471)),f317(f317(f89(a849),x71472),x71473))) % 168.22/168.05 [7382]E(f317(f317(f90(a849),f317(f115(a849),x73821)),f317(f317(f90(a849),f317(f115(a849),x73822)),x73823)),f317(f317(f90(a849),f317(f115(a849),f317(f317(f90(a1),x73821),x73822))),x73823))+P22(f317(f317(f226(a1),x73821),a92)) % 168.22/168.05 [7838]~P22(f317(f317(f225(a849),x78383),x78382))+P22(f317(f317(f225(a849),x78381),f317(f317(f21(a849),f317(f317(f89(a849),x78382),x78381)),x78383))) % 168.22/168.05 [8043]~P22(f317(f317(f225(a849),x80431),x80432))+E(f317(f317(f127(a849),f133(a849,f317(f278(a849,x80431),x80432))),f133(a849,f317(f278(a849,x80432),f317(f317(f89(a849),x80432),x80433)))),f133(a849,f317(f278(a849,x80431),f317(f317(f89(a849),x80432),x80433)))) % 168.22/168.05 [8305]~P22(f317(f71(x83051),x83052))+E(f317(a124,f317(f54(x83051),f317(f317(f21(f858(x83051,a842)),x83052),f317(f317(f286(x83051),x83053),f188(f858(x83051,a842)))))),f317(f54(x83051),f317(f317(f286(x83051),x83053),x83052))) % 168.22/168.05 [8353]~P22(f317(f71(x83531),x83532))+E(f317(f317(f89(a849),f87(a849)),f317(f54(x83531),f317(f317(f21(f858(x83531,a842)),x83532),f317(f317(f286(x83531),x83533),f188(f858(x83531,a842)))))),f317(f54(x83531),f317(f317(f286(x83531),x83533),x83532))) % 168.22/168.05 [8537]E(f317(f317(f21(a849),f317(f54(x85371),x85372)),f317(f54(x85371),f317(f317(f113(f858(x85371,a842)),x85372),x85373))),f317(f54(x85371),f317(f317(f21(f858(x85371,a842)),x85372),x85373)))+~P22(f317(f71(x85371),f317(f317(f113(f858(x85371,a842)),x85372),x85373))) % 168.22/168.05 [8760]~P28(f317(x87602,f394(x87602,x87603,x87601)))+E(f317(f112(a1),f317(f317(f9(x87601,a849),f317(f317(f8(a1,a849,x87601),a116),x87602)),x87603)),f317(f317(f9(x87601,a1),x87602),x87603)) % 168.22/168.05 [8761]~P28(f317(x87612,f463(x87612,x87613,x87611)))+E(f317(f112(a1),f317(f317(f6(x87611,a849),f317(f317(f8(a1,a849,x87611),a116),x87612)),x87613)),f317(f317(f6(x87611,a1),x87612),x87613)) % 168.22/168.05 [8808]~P22(f317(f71(x88081),x88083))+P22(f317(f317(f225(a849),f317(f317(f21(a849),f317(f54(x88081),x88082)),f317(f54(x88081),x88083))),f317(f54(x88081),f317(f317(f21(f858(x88081,a842)),x88082),x88083)))) % 168.22/168.05 [8834]P22(f317(f317(f319(x88341),f394(x88342,x88343,x88341)),x88343))+E(f317(f112(a1),f317(f317(f9(x88341,a849),f317(f317(f8(a1,a849,x88341),a116),x88342)),x88343)),f317(f317(f9(x88341,a1),x88342),x88343)) % 168.22/168.05 [8835]P22(f317(f317(f319(x88351),f463(x88352,x88353,x88351)),x88353))+E(f317(f112(a1),f317(f317(f6(x88351,a849),f317(f317(f8(a1,a849,x88351),a116),x88352)),x88353)),f317(f317(f6(x88351,a1),x88352),x88353)) % 168.22/168.05 [8906]E(f94(x89061,f317(f317(f7(x89061,f858(x89061,a842),a842),f319(x89061)),f317(f317(f21(f858(x89061,a842)),x89062),f317(f317(f286(x89061),x89063),f188(f858(x89061,a842)))))),f240(x89061,x89063,x89062))+P22(f317(f317(f225(f858(x89061,a842)),x89062),f317(f317(f286(x89061),x89063),f188(f858(x89061,a842))))) % 168.22/168.05 [9243]E(f317(f317(f148(f850(x92431),x92431),f317(f317(f7(f850(x92431),a849,x92431),f159(x92431)),x92432)),f317(f130(f850(x92431),f317(f317(f8(a849,a842,f850(x92431)),f317(f226(a849),x92432)),f189(f850(x92431)))),x92433)),f317(f317(f159(f850(x92431)),f173(x92431,x92433)),x92432))+~P22(f317(f317(f226(a849),x92432),f317(f189(f850(f850(x92431))),f173(x92431,x92433)))) % 168.22/168.05 [9318]E(f317(f130(x93181,x93182),x93183),f170(x93181,x93182,x93183))+P22(f317(f317(f319(x93181),f669(x93183,x93182,x93181)),f317(f166(x93181),f317(f317(f132(x93181),f317(f189(f850(x93181)),f170(x93181,x93182,x93183))),x93183)))) % 168.22/168.05 [9457]E(f317(f317(f132(x94571),f317(f189(f850(x94571)),f170(x94571,x94572,x94573))),x94573),f125(x94571))+~P22(f317(x94572,f317(f135(x94571),f317(f317(f132(x94571),f317(f189(f850(x94571)),f170(x94571,x94572,x94573))),x94573)))) % 168.22/168.05 [9546]~P22(f317(f317(f319(f857(x95461,x95461)),x95462),f284(x95461,x95463)))+P22(f317(f317(f319(f857(x95461,x95461)),x95462),f317(f317(f51(a849,f858(f857(x95461,x95461),a842)),f233(f858(a849,a842))),f317(f317(f7(a849,f858(f857(x95461,x95461),a842),f858(f857(x95461,x95461),a842)),f182(f857(x95461,x95461),a842)),x95463)))) % 168.22/168.05 [9601]~P22(f317(f317(f225(f858(x96011,a842)),f317(f317(f51(a849,f858(x96011,a842)),f317(f278(a849,f2(a849)),f501(x96013,x96012,x96011))),x96012)),x96013))+P22(f317(f317(f225(f858(x96011,a842)),f317(f317(f51(a849,f858(x96011,a842)),f233(f858(a849,a842))),x96012)),x96013)) % 168.22/168.05 [9658]~P22(f317(f317(f226(a1),f2(a1)),x96583))+P22(f317(f317(f226(a1),x96581),f317(f317(f89(a1),x96582),f317(f317(f90(a1),f317(f317(f89(a1),f317(f84(a1),f317(f317(f21(a1),x96582),x96581))),f87(a1))),x96583)))) % 168.22/168.05 [9668]~P37(x96681,f317(f317(f122(f858(f857(x96681,x96681),a842)),x96682),x96683))+P37(x96681,f317(f317(f122(f858(f857(x96681,x96681),a842)),f317(f317(f122(f858(f857(x96681,x96681),a842)),f317(f317(f265(x96681,x96681,x96681),x96682),x96682)),f317(f317(f265(x96681,x96681,x96681),x96683),x96682))),x96683)) % 168.22/168.05 [9751]P37(x97511,f317(f317(f122(f858(f857(x97511,x97511),a842)),x97512),x97513))+~P37(x97511,f317(f317(f122(f858(f857(x97511,x97511),a842)),f317(f317(f122(f858(f857(x97511,x97511),a842)),f317(f317(f265(x97511,x97511,x97511),x97512),x97512)),f317(f317(f265(x97511,x97511,x97511),x97513),x97512))),x97513)) % 168.22/168.05 [9323]~P111(x93231)+E(f317(f114(x93231),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x93232),x93233)),f188(f858(f857(a849,a849),a842)))))),f317(f317(f21(x93231),f317(f112(x93231),x93232)),f317(f112(x93231),x93233))) % 168.22/168.05 [9406]P22(f317(x94063,x94062))+E(f317(f230(x94061),f317(f317(f18(x94061,a842,a842),f317(f317(f8(a842,f858(a842,a842),x94061),a315),f317(f317(f7(x94061,x94061,a842),a314),x94062))),x94063)),f188(f858(x94061,a842))) % 168.22/168.05 [9408]~P22(f317(x94083,x94082))+E(f317(f230(x94081),f317(f317(f18(x94081,a842,a842),f317(f317(f8(a842,f858(a842,a842),x94081),a315),f317(f317(f7(x94081,x94081,a842),a314),x94082))),x94083)),f317(f317(f286(x94081),x94082),f188(f858(x94081,a842)))) % 168.22/168.05 [9743]~P22(f317(f71(x97431),x97433))+E(f317(f317(f74(x97431,f858(x97431,a842),f317(f317(f8(f858(x97431,a842),f858(f858(x97431,a842),f858(x97431,a842)),x97431),f317(f7(f858(x97431,a842),f858(x97431,a842),f858(x97431,a842)),f21(f858(x97431,a842)))),f317(f317(f7(x97431,f858(x97431,a842),f858(x97431,a842)),f286(x97431)),f188(f858(x97431,a842))))),x97432),x97433),f317(f317(f21(f858(x97431,a842)),x97432),x97433)) % 168.22/168.05 [9779]~P22(f317(f317(f226(a1),f2(a1)),x97793))+P22(f317(f317(f226(a1),f317(f317(f21(a1),x97791),f317(f317(f90(a1),f317(f317(f89(a1),f317(f84(a1),f317(f317(f21(a1),x97791),x97792))),f87(a1))),x97793))),x97792)) % 168.22/168.05 [10006]~P22(f317(f317(f319(x100061),x100063),f306(x100061,x100062)))+P22(f317(f305(x100061,f317(f317(f7(x100061,f858(f857(x100061,x100061),a842),f858(x100061,a842)),f317(f317(f8(f858(x100061,f858(f858(f857(x100061,x100061),a842),a842)),f858(f858(f857(x100061,x100061),a842),f858(x100061,a842)),x100061),f7(x100061,f858(f857(x100061,x100061),a842),a842)),f317(f317(f8(f858(x100061,f857(x100061,x100061)),f858(x100061,f858(f858(f857(x100061,x100061),a842),a842)),x100061),f317(f8(f857(x100061,x100061),f858(f858(f857(x100061,x100061),a842),a842),x100061),f319(f857(x100061,x100061)))),f237(x100061,x100061)))),x100062)),x100063)) % 168.22/168.05 [10018]P22(f317(f317(f319(x100181),x100182),f306(x100181,x100183)))+~P22(f317(f305(x100181,f317(f317(f7(x100181,f858(f857(x100181,x100181),a842),f858(x100181,a842)),f317(f317(f8(f858(x100181,f858(f858(f857(x100181,x100181),a842),a842)),f858(f858(f857(x100181,x100181),a842),f858(x100181,a842)),x100181),f7(x100181,f858(f857(x100181,x100181),a842),a842)),f317(f317(f8(f858(x100181,f857(x100181,x100181)),f858(x100181,f858(f858(f857(x100181,x100181),a842),a842)),x100181),f317(f8(f857(x100181,x100181),f858(f858(f857(x100181,x100181),a842),a842),x100181),f319(f857(x100181,x100181)))),f237(x100181,x100181)))),x100183)),x100182)) % 168.22/168.05 [9599]~P22(f317(f71(x95991),f317(f230(x95991),x95993)))+P22(f317(f71(x95991),f317(f230(x95991),f317(f317(f18(x95991,a842,a842),f317(f317(f8(a842,f858(a842,a842),x95991),a315),x95992)),x95993)))) % 168.22/168.05 [9600]~P22(f317(f71(x96001),f317(f230(x96001),x96002)))+P22(f317(f71(x96001),f317(f230(x96001),f317(f317(f18(x96001,a842,a842),f317(f317(f8(a842,f858(a842,a842),x96001),a315),x96002)),x96003)))) % 168.22/168.05 [9698]P22(f317(f71(x96981),f317(f230(x96981),x96982)))+~P22(f317(f71(x96981),f317(f230(x96981),f317(f317(f18(x96981,a842,a842),f317(f317(f8(a842,f858(a842,a842),x96981),a316),x96983)),x96982)))) % 168.22/168.05 [9699]P22(f317(f71(x96991),f317(f230(x96991),x96992)))+~P22(f317(f71(x96991),f317(f230(x96991),f317(f317(f18(x96991,a842,a842),f317(f317(f8(a842,f858(a842,a842),x96991),a316),x96992)),x96993)))) % 168.22/168.05 [9994]~P22(f317(f71(x99941),x99942))+P22(f317(f71(f850(x99941)),f317(f230(f850(x99941)),f317(f317(f18(f850(x99941),a842,a842),f317(f317(f8(a842,f858(a842,a842),f850(x99941)),a315),f317(f317(f7(f850(x99941),f858(x99941,a842),a842),f317(f317(f8(f858(x99941,a842),f858(f858(x99941,a842),a842),f850(x99941)),f225(f858(x99941,a842))),f166(x99941))),x99942))),f317(f317(f7(f850(x99941),a849,a842),f317(f317(f8(a849,f858(a849,a842),f850(x99941)),a314),f189(f850(x99941)))),x99943))))) % 168.22/168.05 [9995]~P22(f317(f71(x99951),x99952))+P22(f317(f71(f850(x99951)),f317(f230(f850(x99951)),f317(f317(f18(f850(x99951),a842,a842),f317(f317(f8(a842,f858(a842,a842),f850(x99951)),a315),f317(f317(f7(f850(x99951),f858(x99951,a842),a842),f317(f317(f8(f858(x99951,a842),f858(f858(x99951,a842),a842),f850(x99951)),f225(f858(x99951,a842))),f166(x99951))),x99952))),f317(f317(f7(f850(x99951),a849,a842),f317(f317(f8(a849,f858(a849,a842),f850(x99951)),f225(a849)),f189(f850(x99951)))),x99953))))) % 168.22/168.05 [9714]~P84(x97141)+E(f317(f317(f238(x97141),x97142),f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x97143)),f317(f317(f90(x97141),f317(f317(f238(x97141),x97142),x97143)),f317(f317(f238(x97141),x97142),x97143))) % 168.22/168.05 [9756]~P75(x97561)+E(f317(f317(f238(x97561),f317(f317(f238(x97561),x97562),x97563)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f238(x97561),x97562),f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x97563))) % 168.22/168.05 [9807]~P111(x98071)+E(f317(f317(f238(x98071),f317(f88(x98071),x98072)),f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98073)),f317(f317(f238(x98071),x98072),f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98073))) % 168.22/168.05 [9951]~P113(x99511)+P22(f317(f317(f225(x99511),f2(x99511)),f317(f317(f89(x99511),f317(f317(f238(x99511),x99512),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x99511),x99513),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))))) % 168.22/168.05 [9817]~P84(x98171)+E(f317(f317(f238(x98171),x98172),f317(a124,f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98173))),f317(f317(f90(x98171),x98172),f317(f317(f90(x98171),f317(f317(f238(x98171),x98172),x98173)),f317(f317(f238(x98171),x98172),x98173)))) % 168.22/168.05 [9870]~P75(x98701)+E(f317(f317(f90(x98701),x98702),f317(f317(f238(x98701),f317(f317(f238(x98701),x98702),x98703)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x98701),x98702),f317(a124,f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98703)))) % 168.22/168.05 [9908]~P113(x99081)+P22(f317(f317(f225(x99081),f2(x99081)),f317(f317(f238(x99081),x99082),f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99083)))) % 168.22/168.05 [9972]~P90(x99721)+E(f317(f317(f89(x99721),f317(f317(f89(x99721),f317(f317(f238(x99721),x99722),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x99721),x99723),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f317(f317(f90(x99721),f317(f317(f90(x99721),f317(f115(x99721),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99722)),x99723)),f317(f317(f238(x99721),f317(f317(f89(x99721),x99722),x99723)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.05 [9973]~P90(x99731)+E(f317(f317(f21(x99731),f317(f317(f89(x99731),f317(f317(f238(x99731),x99732),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x99731),x99733),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f317(f317(f90(x99731),f317(f317(f90(x99731),f317(f115(x99731),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99732)),x99733)),f317(f317(f238(x99731),f317(f317(f21(x99731),x99732),x99733)),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.05 [10071]~P30(x100711,x100712,x100713)+P22(f106(x100711,a842,f317(f317(f8(f858(a843,f858(f858(x100711,f858(a845,a842)),f858(x100711,a842))),f858(a843,f858(f858(x100711,f858(a845,a842)),a842)),f858(x100711,f858(a845,a842))),f317(f8(f858(f858(x100711,f858(a845,a842)),f858(x100711,a842)),f858(f858(x100711,f858(a845,a842)),a842),a843),f317(f8(f858(x100711,a842),a842,f858(x100711,f858(a845,a842))),f97(x100711)))),f317(f317(f8(f858(a843,f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842)))),f858(a843,f858(f858(x100711,f858(a845,a842)),f858(x100711,a842))),f858(x100711,f858(a845,a842))),f317(f8(f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),f858(f858(x100711,f858(a845,a842)),f858(x100711,a842)),a843),f317(f8(f858(x100711,f858(a845,a842)),f858(x100711,a842),f858(x100711,f858(a845,a842))),f317(f8(f858(a845,a842),a842,x100711),f97(a845))))),f317(f317(f7(f858(x100711,f858(a845,a842)),f858(a843,f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842)))),f858(a843,f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))))),f317(f317(f8(f858(f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842)))),f858(f858(a843,f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842)))),f858(a843,f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))))),f858(x100711,f858(a845,a842))),f8(f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),a843)),f317(f317(f8(f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),f858(f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842)))),f858(x100711,f858(a845,a842))),f8(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842)))),f317(f317(f8(f858(x100711,f858(f858(a845,a842),f858(a845,a842))),f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),f858(x100711,f858(a845,a842))),f18(x100711,f858(a845,a842),f858(a845,a842))),f317(f317(f8(f858(x100711,f858(a845,f858(a842,a842))),f858(x100711,f858(f858(a845,a842),f858(a845,a842))),f858(x100711,f858(a845,a842))),f317(f8(f858(a845,f858(a842,a842)),f858(f858(a845,a842),f858(a845,a842)),x100711),f18(a845,a842,a842))),f317(f8(f858(a845,a842),f858(a845,f858(a842,a842)),x100711),f317(f8(a842,f858(a842,a842),a845),a320))))))),f317(f317(f8(f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,f858(a845,a842)))),f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),a843),f317(f8(f858(x100711,f858(a845,f858(a845,a842))),f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,a842))),f317(f8(f858(a845,f858(a845,a842)),f858(a845,a842),x100711),f317(f8(f858(a845,a842),a842,a845),f97(a845))))),f317(f317(f8(f858(f858(a845,a842),f858(a845,f858(a845,a842))),f858(f858(x100711,f858(a845,a842)),f858(x100711,f858(a845,f858(a845,a842)))),a843),f8(f858(a845,a842),f858(a845,f858(a845,a842)),x100711)),f317(f317(f8(f858(a845,f858(f858(a845,a842),f858(a845,a842))),f858(f858(a845,a842),f858(a845,f858(a845,a842))),a843),f7(a845,f858(a845,a842),f858(a845,a842))),f317(f317(f8(f858(a845,f858(a845,f858(a842,a842))),f858(a845,f858(f858(a845,a842),f858(a845,a842))),a843),f317(f8(f858(a845,f858(a842,a842)),f858(f858(a845,a842),f858(a845,a842)),a845),f18(a845,a842,a842))),f317(f317(f8(f858(a845,f858(a845,a842)),f858(a845,f858(a845,f858(a842,a842))),a843),f317(f8(f858(a845,a842),f858(a845,f858(a842,a842)),a845),f317(f8(a842,f858(a842,a842),a845),a320))),f317(f317(f7(a843,a849,f858(a845,f858(a845,a842))),f317(f317(f8(f858(a845,f858(a849,f858(a845,a842))),f858(a849,f858(a845,f858(a845,a842))),a843),f7(a845,a849,f858(a845,a842))),a197)),x100712))))))))),x100713)) % 168.22/168.05 [10073]P30(x100731,x100732,x100733)+~P22(f106(x100731,a842,f317(f317(f8(f858(a843,f858(f858(x100731,f858(a845,a842)),f858(x100731,a842))),f858(a843,f858(f858(x100731,f858(a845,a842)),a842)),f858(x100731,f858(a845,a842))),f317(f8(f858(f858(x100731,f858(a845,a842)),f858(x100731,a842)),f858(f858(x100731,f858(a845,a842)),a842),a843),f317(f8(f858(x100731,a842),a842,f858(x100731,f858(a845,a842))),f97(x100731)))),f317(f317(f8(f858(a843,f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842)))),f858(a843,f858(f858(x100731,f858(a845,a842)),f858(x100731,a842))),f858(x100731,f858(a845,a842))),f317(f8(f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),f858(f858(x100731,f858(a845,a842)),f858(x100731,a842)),a843),f317(f8(f858(x100731,f858(a845,a842)),f858(x100731,a842),f858(x100731,f858(a845,a842))),f317(f8(f858(a845,a842),a842,x100731),f97(a845))))),f317(f317(f7(f858(x100731,f858(a845,a842)),f858(a843,f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842)))),f858(a843,f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))))),f317(f317(f8(f858(f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842)))),f858(f858(a843,f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842)))),f858(a843,f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))))),f858(x100731,f858(a845,a842))),f8(f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),a843)),f317(f317(f8(f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),f858(f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842)))),f858(x100731,f858(a845,a842))),f8(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842)))),f317(f317(f8(f858(x100731,f858(f858(a845,a842),f858(a845,a842))),f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),f858(x100731,f858(a845,a842))),f18(x100731,f858(a845,a842),f858(a845,a842))),f317(f317(f8(f858(x100731,f858(a845,f858(a842,a842))),f858(x100731,f858(f858(a845,a842),f858(a845,a842))),f858(x100731,f858(a845,a842))),f317(f8(f858(a845,f858(a842,a842)),f858(f858(a845,a842),f858(a845,a842)),x100731),f18(a845,a842,a842))),f317(f8(f858(a845,a842),f858(a845,f858(a842,a842)),x100731),f317(f8(a842,f858(a842,a842),a845),a320))))))),f317(f317(f8(f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,f858(a845,a842)))),f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),a843),f317(f8(f858(x100731,f858(a845,f858(a845,a842))),f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,a842))),f317(f8(f858(a845,f858(a845,a842)),f858(a845,a842),x100731),f317(f8(f858(a845,a842),a842,a845),f97(a845))))),f317(f317(f8(f858(f858(a845,a842),f858(a845,f858(a845,a842))),f858(f858(x100731,f858(a845,a842)),f858(x100731,f858(a845,f858(a845,a842)))),a843),f8(f858(a845,a842),f858(a845,f858(a845,a842)),x100731)),f317(f317(f8(f858(a845,f858(f858(a845,a842),f858(a845,a842))),f858(f858(a845,a842),f858(a845,f858(a845,a842))),a843),f7(a845,f858(a845,a842),f858(a845,a842))),f317(f317(f8(f858(a845,f858(a845,f858(a842,a842))),f858(a845,f858(f858(a845,a842),f858(a845,a842))),a843),f317(f8(f858(a845,f858(a842,a842)),f858(f858(a845,a842),f858(a845,a842)),a845),f18(a845,a842,a842))),f317(f317(f8(f858(a845,f858(a845,a842)),f858(a845,f858(a845,f858(a842,a842))),a843),f317(f8(f858(a845,a842),f858(a845,f858(a842,a842)),a845),f317(f8(a842,f858(a842,a842),a845),a320))),f317(f317(f7(a843,a849,f858(a845,f858(a845,a842))),f317(f317(f8(f858(a845,f858(a849,f858(a845,a842))),f858(a849,f858(a845,f858(a845,a842))),a843),f7(a845,a849,f858(a845,a842))),a197)),x100732))))))))),x100733)) % 168.22/168.05 [4618]E(x46181,x46182)+~E(f36(x46183,x46181),f36(x46184,x46182)) % 168.22/168.05 [4619]E(x46191,x46192)+~E(f36(x46191,x46193),f36(x46192,x46194)) % 168.22/168.05 [4620]E(x46201,x46202)+~E(f30(x46203,x46201),f30(x46204,x46202)) % 168.22/168.05 [4621]E(x46211,x46212)+~E(f30(x46211,x46213),f30(x46212,x46214)) % 168.22/168.05 [4622]E(x46221,x46222)+~E(f35(x46223,x46221),f35(x46224,x46222)) % 168.22/168.05 [4623]E(x46231,x46232)+~E(f35(x46231,x46233),f35(x46232,x46234)) % 168.22/168.05 [7647]P19(x76471,x76472,x76473,x76474)+~E(f810(x76474,x76473,x76472,x76471),f811(x76474,x76473,x76472,x76471)) % 168.22/168.05 [7931]P35(x79311,x79312,x79313,x79314,f125(x79312))+~E(x79314,f125(x79311)) % 168.22/168.05 [7932]P35(x79321,x79322,x79323,f125(x79321),x79324)+~E(x79324,f125(x79322)) % 168.22/168.05 [8149]~P19(x81491,f853(x81492),x81494,f177(x81491,x81492,x81494))+P19(x81491,f853(x81492),f178(x81491,x81492,x81493,x81494),f177(x81491,x81492,x81494)) % 168.22/168.05 [8237]P32(x82371,x82372,x82373,f178(x82371,x82372,x82373,x82374))+~E(f178(x82371,x82372,x82373,x82374),f178(x82371,x82372,x82374,x82373)) % 168.22/168.05 [8333]~P32(x83331,x83332,x83333,f178(x83331,x83332,x83333,x83334))+E(f178(x83331,x83332,x83333,x83334),f178(x83331,x83332,x83334,x83333)) % 168.22/168.05 [8367]~P19(x83671,f853(x83672),f178(x83671,x83672,x83674,x83673),f177(x83671,x83672,x83673))+P19(x83671,f853(x83672),x83673,f177(x83671,x83672,x83673)) % 168.22/168.05 [8492]~P35(x84922,x84923,x84924,x84921,f125(x84923))+E(x84921,f125(x84922)) % 168.22/168.05 [8493]~P35(x84933,x84932,x84934,f125(x84933),x84931)+E(x84931,f125(x84932)) % 168.22/168.05 [4986]~P12(x49863,x49861,x49864)+E(f317(f317(x49861,x49862),x49862),x49862) % 168.22/168.05 [4989]E(x49891,x49892)+~E(f317(f288(x49893,x49894),x49891),f317(f288(x49893,x49894),x49892)) % 168.22/168.05 [4991]E(x49911,x49912)+~E(f317(f297(x49913,x49914),x49911),f317(f297(x49913,x49914),x49912)) % 168.22/168.05 [5273]~E(x52734,f188(f858(x52731,a842)))+E(f317(f287(x52731,x52732,x52733),x52734),f188(f858(x52732,a842))) % 168.22/168.05 [5542]~E(f317(f287(x55422,x55423,x55424),x55421),f188(f858(x55423,a842)))+E(x55421,f188(f858(x55422,a842))) % 168.22/168.05 [5810]~P103(x58102)+E(f317(f317(f143(x58101,x58102,x58103),x58104),f125(x58101)),f317(f317(f145(x58101),x58104),f125(x58101))) % 168.22/168.05 [5846]E(f317(x58461,x58462),f191(x58463))+P22(f317(f317(f319(x58464),x58462),f177(x58464,x58463,x58461))) % 168.22/168.05 [6163]~E(x61631,f188(f858(x61632,a842)))+~P22(f317(f72(x61632,x61633,x61631),x61634)) % 168.22/168.05 [6185]~P53(x61851,x61853,x61854,x61852)+P22(f317(f71(x61851),x61852)) % 168.22/168.05 [6186]~P53(x61861,x61863,x61862,x61864)+P22(f317(f71(x61861),x61862)) % 168.22/168.05 [6193]~P53(x61932,x61933,x61934,x61931)+~E(x61931,f188(f858(x61932,a842))) % 168.22/168.05 [6220]~P104(x62201)+E(f317(f317(f113(f858(x62201,a842)),f317(f278(x62201,x62202),x62203)),f279(x62201,x62203,x62204)),f188(f858(x62201,a842))) % 168.22/168.05 [6246]~P22(f317(f317(x62463,x62464),x62462))+P22(f317(f317(f319(x62461),x62462),f269(x62461,x62463,x62464))) % 168.22/168.05 [6247]~P22(f317(f317(x62473,x62474),x62472))+P22(f317(f317(f319(x62471),x62472),f270(x62471,x62473,x62474))) % 168.22/168.05 [6248]~P22(f317(f317(x62483,x62482),x62484))+P22(f317(f317(f319(x62481),x62482),f271(x62481,x62483,x62484))) % 168.22/168.05 [6249]~P22(f317(f317(x62493,x62492),x62494))+P22(f317(f317(f319(x62491),x62492),f274(x62491,x62493,x62494))) % 168.22/168.05 [6389]~P104(x63891)+E(f317(f317(f113(f858(x63891,a842)),f282(x63891,x63892,x63893)),f279(x63891,x63893,x63894)),f188(f858(x63891,a842))) % 168.22/168.05 [6390]~P104(x63901)+E(f317(f317(f113(f858(x63901,a842)),f281(x63901,x63902,x63903)),f282(x63901,x63903,x63904)),f188(f858(x63901,a842))) % 168.22/168.05 [6391]~P104(x63911)+E(f317(f317(f113(f858(x63911,a842)),f281(x63911,x63912,x63913)),f281(x63911,x63913,x63914)),f188(f858(x63911,a842))) % 168.22/168.05 [6392]~P104(x63921)+E(f317(f317(f113(f858(x63921,a842)),f279(x63921,x63922,x63923)),f282(x63921,x63923,x63924)),f188(f858(x63921,a842))) % 168.22/168.05 [6393]~P104(x63931)+E(f317(f317(f113(f858(x63931,a842)),f279(x63931,x63932,x63933)),f281(x63931,x63933,x63934)),f188(f858(x63931,a842))) % 168.22/168.05 [6429]P22(f317(f317(x64291,x64292),f557(x64292,x64291)))+~P22(f317(f242(x64293,x64294,x64291),x64292)) % 168.22/168.05 [6477]~E(f317(x64771,x64772),f191(x64773))+~P22(f317(f317(f319(x64774),x64772),f177(x64774,x64773,x64771))) % 168.22/168.05 [6506]~P103(x65062)+E(f317(f166(x65061),f142(x65061,x65062,x65063,x65064)),f317(f166(x65061),x65064)) % 168.22/168.05 [6557]~P110(x65571)+E(f190(x65571,x65572,f317(a124,x65573),x65574),f190(x65571,x65572,x65573,f317(x65572,x65574))) % 168.22/168.05 [6614]~P22(f317(f317(f319(x66144),x66143),f269(x66144,x66141,x66142)))+P22(f317(f317(x66141,x66142),x66143)) % 168.22/168.05 [6615]~P22(f317(f317(f319(x66154),x66153),f270(x66154,x66151,x66152)))+P22(f317(f317(x66151,x66152),x66153)) % 168.22/168.05 [6616]~P22(f317(f317(f319(x66164),x66162),f271(x66164,x66161,x66163)))+P22(f317(f317(x66161,x66162),x66163)) % 168.22/168.05 [6617]~P22(f317(f317(f319(x66174),x66172),f274(x66174,x66171,x66173)))+P22(f317(f317(x66171,x66172),x66173)) % 168.22/168.05 [6693]E(f317(f54(f856(x66931,x66932)),f298(x66931,x66932,x66933,x66934)),f2(a849))+P22(f317(f71(x66932),x66934)) % 168.22/168.05 [6694]E(f317(f54(f856(x66941,x66942)),f298(x66941,x66942,x66943,x66944)),f2(a849))+P22(f317(f71(x66941),x66943)) % 168.22/168.05 [6895]~P11(x68954,x68951,x68952)+E(f317(f82(x68951,x68951,x68951,f317(x68952,x68953)),f317(x68952,x68953)),f317(x68952,x68953)) % 168.22/168.05 [7684]~P22(f317(x76841,x76844))+P22(f317(x76841,f104(x76842,a849,x76843,x76841))) % 168.22/168.05 [7766]~E(x77662,x77663)+P22(f317(f317(f319(f857(x77661,x77661)),f317(f317(f237(x77661,x77661),x77662),x77663)),f284(x77661,x77664))) % 168.22/168.05 [7794]~P19(x77941,x77942,x77943,f233(f858(x77941,a842)))+E(f317(f86(x77941,x77942,f233(f858(x77941,a842)),x77943),f317(x77943,x77944)),x77944) % 168.22/168.05 [7879]~P22(f317(f317(f319(f850(x78791)),f317(f317(f145(x78791),x78794),x78792)),f155(x78791,x78793)))+P22(f317(f317(f319(f850(x78791)),x78792),f155(x78791,x78793))) % 168.22/168.05 [7880]~P22(f317(f317(f319(f850(x78801)),f317(f317(f127(x78801),x78804),x78802)),f155(x78801,x78803)))+P22(f317(f317(f319(f850(x78801)),x78802),f155(x78801,x78803))) % 168.22/168.05 [7881]~P22(f317(f317(f319(f850(x78811)),f317(f317(f127(x78811),x78812),x78814)),f155(x78811,x78813)))+P22(f317(f317(f319(f850(x78811)),x78812),f155(x78811,x78813))) % 168.22/168.05 [7897]~P103(x78971)+P29(x78971,f317(f317(f148(x78972,x78971),x78973),f142(x78972,x78971,x78973,x78974))) % 168.22/168.05 [7992]P19(x79924,x79923,x79921,x79922)+E(f317(x79921,f810(x79922,x79921,x79923,x79924)),f317(x79921,f811(x79922,x79921,x79923,x79924))) % 168.22/168.05 [8008]E(f178(x80081,x80082,x80083,x80084),f178(x80081,x80082,x80084,x80083))+~E(f317(f317(f113(f858(x80081,a842)),f177(x80081,x80082,x80083)),f177(x80081,x80082,x80084)),f188(f858(x80081,a842))) % 168.22/168.05 [8045]~P32(x80451,x80452,x80453,x80454)+P22(f317(f317(f225(f858(x80451,a842)),f177(x80451,x80452,x80453)),f177(x80451,x80452,x80454))) % 168.22/168.06 [8111]~P19(x81112,x81111,x81114,x81113)+P19(x81111,x81112,f86(x81112,x81111,x81113,x81114),f317(f287(x81112,x81111,x81114),x81113)) % 168.22/168.06 [8251]P37(f857(x82512,x82514),f260(x82512,x82514,x82511,x82513))+P22(f317(x82511,f562(x82512,x82513,x82514,x82511))) % 168.22/168.06 [8375]E(x83751,x83752)+~P22(f317(f317(f319(f857(x83753,x83753)),f317(f317(f237(x83753,x83753),x83751),x83752)),f235(x83753,x83754))) % 168.22/168.06 [8443]~P22(f317(f71(f856(x84433,x84431)),f298(x84433,x84431,x84434,x84432)))+P22(f317(f71(x84431),x84432)) % 168.22/168.06 [8444]~P22(f317(f71(f856(x84441,x84443)),f298(x84441,x84443,x84442,x84444)))+P22(f317(f71(x84441),x84442)) % 168.22/168.06 [8454]P32(x84541,x84542,x84543,x84544)+~E(f317(x84543,f679(x84544,x84543,x84542,x84541)),f317(x84544,f679(x84544,x84543,x84542,x84541))) % 168.22/168.06 [8618]P37(f857(x86181,x86182),f260(x86181,x86182,x86183,x86184))+~P37(x86182,f317(x86184,f562(x86181,x86184,x86182,x86183))) % 168.22/168.06 [8758]P32(x87581,x87582,x87583,x87584)+P22(f317(f317(f319(x87581),f679(x87584,x87583,x87582,x87581)),f177(x87581,x87582,x87583))) % 168.22/168.06 [9169]E(f317(f317(f153(x91691,x91692),f605(x91693,x91694,x91692,x91691)),f606(x91693,x91694,x91692,x91691)),x91694)+~P22(f317(f317(f319(f857(f850(x91691),f850(x91691))),f317(f317(f237(f850(x91691),f850(x91691)),x91692),x91694)),f151(x91691,x91693))) % 168.22/168.06 [9170]~P22(f317(x91703,x91704))+P22(f317(f317(f225(a849),f317(x91701,f104(x91702,a849,x91701,x91703))),f317(x91701,x91704))) % 168.22/168.06 [9176]~P22(f317(f317(f319(f857(f850(x91761),f850(x91761))),f317(f317(f237(f850(x91761),f850(x91761)),x91762),x91763)),f139(x91761,x91764)))+P22(f317(f317(f319(f857(f850(x91761),f850(x91761))),f317(f317(f237(f850(x91761),f850(x91761)),x91762),x91763)),f141(x91761,x91764))) % 168.22/168.06 [9279]P22(f317(f71(x92791),x92792))+~P22(f317(f317(f319(f857(f858(x92791,a842),f858(x92791,a842))),f317(f317(f237(f858(x92791,a842),f858(x92791,a842)),x92793),x92792)),f309(x92791,x92794))) % 168.22/168.06 [9280]P22(f317(f71(x92801),x92802))+~P22(f317(f317(f319(f857(f858(x92801,a842),f858(x92801,a842))),f317(f317(f237(f858(x92801,a842),f858(x92801,a842)),x92802),x92803)),f309(x92801,x92804))) % 168.22/168.06 [9283]~E(x92831,f188(f858(x92832,a842)))+~P22(f317(f317(f319(f857(f858(x92832,a842),f858(x92832,a842))),f317(f317(f237(f858(x92832,a842),f858(x92832,a842)),x92833),x92831)),f309(x92832,x92834))) % 168.22/168.06 [9920]P9(x99201,x99202,x99203,x99204)+~P22(f317(f317(f247(x99201,x99201,a842),f317(f317(f7(x99201,f858(x99201,x99202),f858(x99201,a842)),f317(f317(f8(f858(x99202,a842),f858(f858(x99201,x99202),f858(x99201,a842)),x99201),f8(x99202,a842,x99201)),f317(f317(f8(x99202,f858(x99202,a842),x99201),a314),x99204))),x99204)),f572(x99204,x99203,x99202,x99201))) % 168.22/168.06 [4894]~E(x48944,f191(x48941))+E(f317(f317(f192(x48941,x48942),x48943),x48944),f191(x48942)) % 168.22/168.06 [4895]~E(x48954,f125(x48951))+E(f317(f317(f148(x48951,x48952),x48953),x48954),f125(x48952)) % 168.22/168.06 [4896]~E(x48962,f125(x48961))+E(f317(f317(f153(x48961,x48962),x48963),x48964),f125(x48961)) % 168.22/168.06 [5128]E(x51281,f191(x51282))+~E(f317(f317(f192(x51282,x51283),x51284),x51281),f191(x51283)) % 168.22/168.06 [5129]E(x51291,f125(x51292))+~E(f317(f317(f148(x51292,x51293),x51294),x51291),f125(x51293)) % 168.22/168.06 [5130]E(x51301,f125(x51302))+~E(f317(f317(f153(x51302,x51301),x51303),x51304),f125(x51302)) % 168.22/168.06 [5161]E(x51611,x51612)+~E(f317(f317(f127(x51613),x51614),x51611),f317(f317(f127(x51613),x51614),x51612)) % 168.22/168.06 [5162]E(x51621,x51622)+~E(f317(f317(f127(x51623),x51621),x51624),f317(f317(f127(x51623),x51622),x51624)) % 168.22/168.06 [5307]P22(f317(x53073,x53072))+E(f164(x53071,x53072,f317(f130(x53071,x53073),x53074)),f317(f130(x53071,x53073),x53074)) % 168.22/168.06 [5309]~P22(f317(x53092,x53093))+P34(x53091,x53092,f317(f317(f145(x53091),x53093),x53094)) % 168.22/168.06 [5318]E(x53181,x53182)+~E(f133(a849,f317(f278(a849,x53181),x53183)),f317(f317(f145(a849),x53182),x53184)) % 168.22/168.06 [5366]~P20(x53662,x53663)+P20(x53661,f317(f317(f83(x53662,x53661),x53663),x53664)) % 168.22/168.06 [5367]~P37(x53672,x53673)+P37(x53671,f317(f317(f264(x53672,x53671),x53673),x53674)) % 168.22/168.06 [5493]~P34(x54931,x54932,x54934)+P34(x54931,x54932,f317(f317(f145(x54931),x54933),x54934)) % 168.22/168.06 [5494]~P34(x54941,x54942,x54944)+P34(x54941,x54942,f317(f317(f127(x54941),x54943),x54944)) % 168.22/168.06 [5495]~P34(x54951,x54952,x54953)+P34(x54951,x54952,f317(f317(f127(x54951),x54953),x54954)) % 168.22/168.06 [5585]~E(x55851,f125(x55852))+~E(f317(f317(f127(x55852),x55853),f317(f317(f145(x55852),x55854),f125(x55852))),x55851) % 168.22/168.06 [5615]E(f126(x56151,x56152),x56153)+~E(f317(f317(f127(x56151),x56153),f317(f317(f145(x56151),x56154),f125(x56151))),x56152) % 168.22/168.06 [5616]E(f138(x56161,x56162),x56163)+~E(f317(f317(f127(x56161),x56164),f317(f317(f145(x56161),x56163),f125(x56161))),x56162) % 168.22/168.06 [5720]~E(f133(a849,f317(f278(a849,x57201),x57202)),f317(f317(f145(a849),x57203),x57204))+P22(f317(f317(f226(a849),x57201),x57202)) % 168.22/168.06 [5919]E(x59191,f317(f317(f127(x59192),f317(f163(x59192),x59193)),f317(f317(f145(x59192),x59194),f125(x59192))))+~E(f317(f163(x59192),x59191),f317(f317(f145(x59192),x59194),x59193)) % 168.22/168.06 [6083]~P104(x60831)+E(f317(f317(f113(f858(x60831,a842)),f317(f278(x60831,x60832),x60833)),f317(f278(x60831,x60833),x60834)),f188(f858(x60831,a842))) % 168.22/168.06 [6119]~P67(x61191)+E(f317(f160(x61191),f317(f317(f148(a1,x61191),x61192),f172(x61193,x61194))),f317(f317(f6(a1,x61191),x61192),f317(f166(a1),f172(x61193,x61194)))) % 168.22/168.06 [6120]~P67(x61201)+E(f317(f317(f6(a1,x61201),x61202),f317(f166(a1),f172(x61203,x61204))),f317(f160(x61201),f317(f317(f148(a1,x61201),x61202),f172(x61203,x61204)))) % 168.22/168.06 [6261]~E(x62612,f317(f317(f127(x62611),f317(f163(x62611),x62614)),f317(f317(f145(x62611),x62613),f125(x62611))))+E(f317(f163(x62611),x62612),f317(f317(f145(x62611),x62613),x62614)) % 168.22/168.06 [6275]~P14(x62752,x62753,x62754,x62751)+E(f317(x62751,f188(f858(x62752,a842))),f39(x62753)) % 168.22/168.06 [6300]~P104(x63001)+E(f317(f317(f113(f858(x63001,a842)),f282(x63001,x63002,x63003)),f317(f278(x63001,x63003),x63004)),f188(f858(x63001,a842))) % 168.22/168.06 [6507]E(x65071,f188(f858(x65072,a842)))+~E(f298(x65073,x65072,x65074,x65071),f188(f858(f856(x65073,x65072),a842))) % 168.22/168.06 [6508]E(x65081,f188(f858(x65082,a842)))+~E(f298(x65082,x65083,x65081,x65084),f188(f858(f856(x65082,x65083),a842))) % 168.22/168.06 [6577]~P103(x65772)+E(f317(f189(f850(x65771)),f142(x65771,x65772,x65773,x65774)),f317(f189(f850(x65771)),x65774)) % 168.22/168.06 [6590]~P22(f317(f243(x65903,x65904,x65901),x65902))+P22(f317(f317(x65901,f548(x65902,x65901)),x65902)) % 168.22/168.06 [6627]~P22(f317(f71(x66272),x66274))+P22(f317(f71(x66271),f317(f287(x66272,x66271,x66273),x66274))) % 168.22/168.06 [6852]~P19(x68522,x68521,x68523,x68524)+E(f317(f54(x68521),f317(f287(x68522,x68521,x68523),x68524)),f317(f54(x68522),x68524)) % 168.22/168.06 [6870]E(f317(f287(x68701,x68702,x68703),f317(f289(x68701,x68702,x68703),x68704)),x68704)+~E(f317(f287(x68701,x68702,x68703),f233(f858(x68701,a842))),f233(f858(x68702,a842))) % 168.22/168.06 [7277]~P19(x72771,x72772,x72773,f233(f858(x72771,a842)))+E(f317(f289(x72771,x72772,x72773),f317(f287(x72771,x72772,x72773),x72774)),x72774) % 168.22/168.06 [7604]P22(f317(x76041,x76042))+~P22(f317(f317(f319(x76043),x76042),f317(f166(x76043),f170(x76043,x76041,x76044)))) % 168.22/168.06 [7715]~P22(f317(f317(f319(f850(x77151)),f317(f317(f145(x77151),x77152),x77154)),f155(x77151,x77153)))+P22(f317(f317(f319(x77151),x77152),x77153)) % 168.22/168.06 [7834]~P22(f317(f317(f319(x78341),x78342),f317(f166(x78341),f164(x78341,x78344,x78343))))+P22(f317(f317(f319(x78341),x78342),f317(f166(x78341),x78343))) % 168.22/168.06 [7836]~P22(f317(f317(f319(x78361),x78362),f317(f166(x78361),f168(x78361,x78363,x78364))))+P22(f317(f317(f319(x78361),x78362),f317(f166(x78361),x78363))) % 168.22/168.06 [7837]~P22(f317(f317(f319(x78371),x78372),f317(f166(x78371),f170(x78371,x78374,x78373))))+P22(f317(f317(f319(x78371),x78372),f317(f166(x78371),x78373))) % 168.22/168.06 [7847]E(f317(f189(f850(x78471)),x78472),x78473)+~P22(f317(f317(f319(f850(x78471)),x78472),f317(f166(f850(x78471)),f64(x78471,x78473,x78474)))) % 168.22/168.06 [7943]P22(f317(x79433,x79432))+E(f317(f130(x79431,f317(f317(f8(a842,a842,x79431),a312),f317(a314,x79432))),f317(f130(x79431,x79433),x79434)),f317(f130(x79431,x79433),x79434)) % 168.22/168.06 [8061]E(f317(f317(f159(x80611),f170(x80611,x80612,x80613)),x80614),f317(f317(f159(x80611),x80613),x80614))+~P22(f317(f317(f226(a849),x80614),f317(f189(f850(x80611)),f170(x80611,x80612,x80613)))) % 168.22/168.06 [8147]~P67(x81471)+E(f317(f317(f6(a849,x81471),f317(f317(f8(a849,x81471,a849),x81472),a124)),f317(f278(a849,x81473),x81474)),f317(f317(f6(a849,x81471),x81472),f317(f278(a849,f317(a124,x81473)),f317(a124,x81474)))) % 168.22/168.06 [8156]~P67(x81561)+E(f317(f317(f6(a849,x81561),f317(f317(f8(a849,x81561,a849),x81562),a124)),f279(a849,x81563,x81564)),f317(f317(f6(a849,x81561),x81562),f279(a849,f317(a124,x81563),f317(a124,x81564)))) % 168.22/168.06 [8288]~P19(x82881,x82883,x82884,f233(f858(x82881,a842)))+P19(x82881,f858(x82882,x82883),f317(f317(f8(x82883,f858(x82882,x82883),x82881),f16(x82883,x82882)),x82884),f233(f858(x82881,a842))) % 168.22/168.06 [8383]~P19(x83832,x83831,x83834,x83833)+E(f317(f287(x83831,x83832,f86(x83832,x83831,x83833,x83834)),f317(f287(x83832,x83831,x83834),x83833)),x83833) % 168.22/168.06 [8445]~P22(f317(f317(f319(f857(x84451,x84451)),f317(f317(f237(x84451,x84451),x84452),x84454)),f235(x84451,x84453)))+P22(f317(f317(f319(x84451),x84452),x84453)) % 168.22/168.06 [8533]E(f317(f317(f317(f81(x85331,f853(x85332)),f317(f16(f853(x85332),x85331),f191(x85332))),x85333),f317(f217(x85332),f666(x85333,x85334,x85332,x85331))),x85334)+~E(f177(x85331,x85332,x85334),f317(f317(f286(x85331),x85333),f188(f858(x85331,a842)))) % 168.22/168.06 [8653]~E(f317(f317(f6(x86531,a849),x86534),x86533),f317(a124,x86532))+P22(f317(f317(f319(x86531),f716(x86532,x86533,x86534,x86531)),x86533)) % 168.22/168.06 [8672]~E(f317(f317(f6(x86724,a849),x86721),x86723),f317(a124,x86722))+P22(f317(f317(f226(a849),f2(a849)),f317(x86721,f716(x86722,x86723,x86721,x86724)))) % 168.22/168.06 [8683]~P22(f317(f71(x86832),x86834))+P22(f317(f317(f225(a849),f317(f54(x86831),f317(f287(x86832,x86831,x86833),x86834))),f317(f54(x86832),x86834))) % 168.22/168.06 [8691]P19(x86911,x86912,x86913,x86914)+P22(f317(f317(f319(x86911),f810(x86914,x86913,x86912,x86911)),x86914)) % 168.22/168.06 [8692]P19(x86921,x86922,x86923,x86924)+P22(f317(f317(f319(x86921),f811(x86924,x86923,x86922,x86921)),x86924)) % 168.22/168.06 [8751]P9(x87511,x87512,x87513,x87514)+P22(f317(f317(f319(f857(x87511,x87511)),f572(x87514,x87513,x87512,x87511)),x87513)) % 168.22/168.06 [8812]P22(f317(x88121,x88122))+~P22(f317(x88121,f317(f317(f237(x88123,x88124),f339(x88124,x88123,x88121)),f340(x88124,x88123,x88121)))) % 168.22/168.06 [8829]E(f317(f189(f850(x88291)),x88292),f317(f189(f850(x88291)),x88293))+~P22(f317(f317(f319(f857(f850(x88291),f850(x88291))),f317(f317(f237(f850(x88291),f850(x88291)),x88292),x88293)),f139(x88291,x88294))) % 168.22/168.06 [8832]E(f317(f189(f850(x88321)),x88322),f317(f189(f850(x88321)),x88323))+~P22(f317(f317(f319(f857(f850(x88321),f850(x88321))),f317(f317(f237(f850(x88321),f850(x88321)),x88322),x88323)),f152(x88321,x88324))) % 168.22/168.06 [8833]E(f317(f189(f850(x88331)),x88332),f317(f189(f850(x88331)),x88333))+~P22(f317(f317(f319(f857(f850(x88331),f850(x88331))),f317(f317(f237(f850(x88331),f850(x88331)),x88332),x88333)),f151(x88331,x88334))) % 168.22/168.06 [8910]P22(f317(f317(f225(a849),f149(x89101,x89102,x89103)),f149(x89101,x89104,x89103)))+P22(f317(f317(f319(x89101),f602(x89104,x89102,x89103,x89101)),f317(f166(x89101),x89103))) % 168.22/168.06 [8913]E(f317(f189(f850(x89131)),x89132),f317(f189(f850(x89131)),x89133))+~P22(f317(f317(f319(f857(f850(x89131),f850(x89131))),f317(f317(f237(f850(x89131),f850(x89131)),x89132),x89133)),f284(f850(x89131),f151(x89131,x89134)))) % 168.22/168.06 [9140]~P19(x91401,x91402,x91403,x91404)+~P22(f317(f317(f226(a849),f317(f54(x91402),f317(f287(x91401,x91402,x91403),x91404))),f317(f54(x91401),x91404))) % 168.22/168.06 [9187]~P22(f317(f317(f319(f857(f850(x91871),f850(x91871))),f317(f317(f237(f850(x91871),f850(x91871)),x91872),x91873)),f151(x91871,x91874)))+P22(f317(f317(f319(f857(f850(x91871),f850(x91871))),f317(f317(f237(f850(x91871),f850(x91871)),x91872),x91873)),f152(x91871,f284(x91871,x91874)))) % 168.22/168.06 [9191]~P22(f317(f317(f319(f857(f850(x91911),f850(x91911))),f317(f317(f237(f850(x91911),f850(x91911)),x91912),x91913)),f152(x91911,x91914)))+P22(f317(f317(f319(f857(f850(x91911),f850(x91911))),f317(f317(f237(f850(x91911),f850(x91911)),x91912),x91913)),f284(f850(x91911),f151(x91911,x91914)))) % 168.22/168.06 [9207]P22(f317(f317(f319(f857(x92071,x92071)),f317(f317(f237(x92071,x92071),x92072),x92073)),f284(x92071,x92074)))+~P22(f317(f317(f319(f857(x92071,x92071)),f317(f317(f237(x92071,x92071),x92072),x92073)),f317(f317(f265(x92071,x92071,x92071),x92074),f284(x92071,x92074)))) % 168.22/168.06 [9390]E(f317(f317(f127(x93901),f623(x93902,x93903,x93904,x93901)),f317(f317(f145(x93901),f621(x93902,x93903,x93904,x93901)),f625(x93902,x93903,x93904,x93901))),x93904)+~P22(f317(f317(f319(f857(f850(x93901),f850(x93901))),f317(f317(f237(f850(x93901),f850(x93901)),x93904),x93903)),f151(x93901,x93902))) % 168.22/168.06 [9391]E(f317(f317(f127(x93911),f623(x93912,x93913,x93914,x93911)),f317(f317(f145(x93911),f624(x93912,x93913,x93914,x93911)),f625(x93912,x93913,x93914,x93911))),x93913)+~P22(f317(f317(f319(f857(f850(x93911),f850(x93911))),f317(f317(f237(f850(x93911),f850(x93911)),x93914),x93913)),f151(x93911,x93912))) % 168.22/168.06 [9464]P22(f317(f317(f319(f857(x94641,x94641)),f317(f317(f237(x94641,x94641),x94642),f771(x94643,x94644,x94642,x94641))),f284(x94641,x94643)))+~P22(f317(f317(f319(f857(x94641,x94641)),f317(f317(f237(x94641,x94641),x94642),x94644)),f317(f317(f265(x94641,x94641,x94641),x94643),f284(x94641,x94643)))) % 168.22/168.06 [9530]P22(f317(f317(f225(a849),f149(x95301,x95302,x95303)),f149(x95301,x95304,x95303)))+~P22(f317(f317(f226(a849),f317(x95302,f602(x95304,x95302,x95303,x95301))),f317(x95304,f602(x95304,x95302,x95303,x95301)))) % 168.22/168.06 [9594]P22(f317(f317(f319(f857(x95941,x95941)),f317(f317(f237(x95941,x95941),f770(x95942,x95943,x95944,x95941)),x95943)),f284(x95941,x95942)))+~P22(f317(f317(f319(f857(x95941,x95941)),f317(f317(f237(x95941,x95941),x95944),x95943)),f317(f317(f265(x95941,x95941,x95941),x95942),f284(x95941,x95942)))) % 168.22/168.06 [5144]~E(x51442,x51443)+E(f164(x51441,x51442,f317(f317(f145(x51441),x51443),x51444)),x51444) % 168.22/168.06 [5265]P22(f317(x52652,x52653))+E(f170(x52651,x52652,f317(f317(f145(x52651),x52653),x52654)),f125(x52651)) % 168.22/168.06 [5330]~P73(x53302)+E(f317(f317(f88(f858(x53301,x53302)),x53303),x53304),f317(f88(x53302),f317(x53303,x53304))) % 168.22/168.06 [5342]~E(x53422,f2(a849))+E(f317(f317(f132(x53421),x53422),f317(f317(f145(x53421),x53423),x53424)),f317(f317(f145(x53421),x53423),x53424)) % 168.22/168.06 [5343]P22(f317(x53432,x53433))+E(f317(f130(x53431,x53432),f317(f317(f145(x53431),x53433),x53434)),f317(f130(x53431,x53432),x53434)) % 168.22/168.06 [5476]~E(x54762,x54764)+P22(f317(f317(f317(f286(x54761),x54762),x54763),x54764)) % 168.22/168.06 [5484]E(x54841,f125(x54842))+E(f138(x54843,f317(f317(f148(x54842,x54843),x54844),x54841)),f317(x54844,f138(x54842,x54841))) % 168.22/168.06 [5498]~E(x54981,f73(x54982,x54984))+E(f317(x54981,f317(f317(f286(x54982),x54983),f188(f858(x54982,a842)))),x54983) % 168.22/168.06 [5536]E(x55361,f125(x55362))+E(f317(f135(x55363),f317(f317(f148(x55362,x55363),x55364),x55361)),f317(x55364,f317(f135(x55362),x55361))) % 168.22/168.06 [5635]~P22(f317(x56353,x56354))+P22(f317(f317(f317(f286(x56351),x56352),x56353),x56354)) % 168.22/168.06 [5741]~P13(x57412,x57414,x57411)+E(f317(x57411,f317(f317(f286(x57412),x57413),f188(f858(x57412,a842)))),x57413) % 168.22/168.06 [5764]~E(x57642,x57643)+P22(f317(f317(f319(x57641),x57642),f317(f317(f286(x57641),x57643),x57644))) % 168.22/168.06 [5770]~P84(x57701)+E(f317(f317(f89(x57701),x57702),f317(f317(f89(x57701),x57703),x57704)),f317(f317(f89(x57701),x57703),f317(f317(f89(x57701),x57702),x57704))) % 168.22/168.06 [5772]~P92(x57721)+E(f317(f317(f122(x57721),x57722),f317(f317(f122(x57721),x57723),x57724)),f317(f317(f122(x57721),x57723),f317(f317(f122(x57721),x57722),x57724))) % 168.22/168.06 [5773]~P93(x57731)+E(f317(f317(f122(x57731),x57732),f317(f317(f122(x57731),x57733),x57734)),f317(f317(f122(x57731),x57733),f317(f317(f122(x57731),x57732),x57734))) % 168.22/168.06 [5774]~P84(x57741)+E(f317(f317(f90(x57741),x57742),f317(f317(f90(x57741),x57743),x57744)),f317(f317(f90(x57741),x57743),f317(f317(f90(x57741),x57742),x57744))) % 168.22/168.06 [5775]~P93(x57751)+E(f317(f317(f113(x57751),x57752),f317(f317(f113(x57751),x57753),x57754)),f317(f317(f113(x57751),x57753),f317(f317(f113(x57751),x57752),x57754))) % 168.22/168.06 [5777]~P98(x57771)+E(f317(f317(f113(x57771),x57772),f317(f317(f113(x57771),x57773),x57774)),f317(f317(f113(x57771),x57773),f317(f317(f113(x57771),x57772),x57774))) % 168.22/168.06 [5779]~P103(x57791)+E(f317(f317(f223(x57791),x57792),f317(f317(f223(x57791),x57793),x57794)),f317(f317(f223(x57791),x57793),f317(f317(f223(x57791),x57792),x57794))) % 168.22/168.06 [5781]~P103(x57811)+E(f317(f317(f224(x57811),x57812),f317(f317(f224(x57811),x57813),x57814)),f317(f317(f224(x57811),x57813),f317(f317(f224(x57811),x57812),x57814))) % 168.22/168.06 [5786]E(x57861,x57862)+E(f164(x57863,x57861,f317(f317(f145(x57863),x57862),x57864)),f317(f317(f145(x57863),x57862),f164(x57863,x57861,x57864))) % 168.22/168.06 [5799]~P22(f317(x57992,x57993))+E(f317(f130(x57991,x57992),f317(f317(f145(x57991),x57993),x57994)),f317(f317(f145(x57991),x57993),f317(f130(x57991,x57992),x57994))) % 168.22/168.06 [5938]~P22(f317(x59382,x59383))+E(f170(x59381,x59382,f317(f317(f145(x59381),x59383),x59384)),f317(f317(f145(x59381),x59383),f170(x59381,x59382,x59384))) % 168.22/168.06 [5984]P18(x59841,x59842,x59843)+~P18(x59841,x59842,f317(f317(f286(f848(x59841)),x59844),x59843)) % 168.22/168.06 [5996]E(x59961,f188(f858(x59962,a842)))+E(f317(f317(f51(x59962,f858(x59963,a842)),x59961),f317(f16(f858(x59963,a842),x59962),x59964)),x59964) % 168.22/168.06 [5997]E(x59971,f188(f858(x59972,a842)))+E(f317(f317(f52(x59972,f858(x59973,a842)),x59971),f317(f16(f858(x59973,a842),x59972),x59974)),x59974) % 168.22/168.06 [6005]~E(x60054,f188(f858(x60052,a842)))+E(f317(f317(f245(x60051,x60052),x60053),f317(f16(f858(x60052,a842),x60051),x60054)),f188(f858(f857(x60051,x60052),a842))) % 168.22/168.06 [6006]~E(x60063,f188(f858(x60061,a842)))+E(f317(f317(f245(x60061,x60062),x60063),f317(f16(f858(x60062,a842),x60061),x60064)),f188(f858(f857(x60061,x60062),a842))) % 168.22/168.06 [6051]E(x60511,f2(a849))+E(f317(f317(f132(x60512),x60511),f317(f317(f145(x60512),x60513),x60514)),f317(f317(f132(x60512),f317(f317(f21(a849),x60511),f87(a849))),x60514)) % 168.22/168.06 [6077]E(x60771,f188(f858(x60772,a842)))+E(f317(f287(x60772,x60773,f317(f16(x60773,x60772),x60774)),x60771),f317(f317(f286(x60773),x60774),f188(f858(x60773,a842)))) % 168.22/168.06 [6080]E(f317(f289(x60801,x60802,f317(f16(x60802,x60801),x60803)),x60804),f188(f858(x60801,a842)))+P22(f317(f317(f319(x60802),x60803),x60804)) % 168.22/168.06 [6147]~E(x61473,f188(f858(x61471,a842)))+E(f317(f317(f51(x61471,f858(x61472,a842)),x61473),f317(f16(f858(x61472,a842),x61471),x61474)),f188(f858(x61472,a842))) % 168.22/168.06 [6148]~E(x61483,f188(f858(x61481,a842)))+E(f317(f317(f52(x61481,f858(x61482,a842)),x61483),f317(f16(f858(x61482,a842),x61481),x61484)),f233(f858(x61482,a842))) % 168.22/168.06 [6150]~P55(x61501)+E(f55(x61501,f317(f317(f90(x61501),x61502),x61503),f317(f317(f90(x61501),x61502),x61504)),f317(f317(f90(x61501),x61502),f55(x61501,x61503,x61504))) % 168.22/168.06 [6312]E(f317(f289(x63121,x63122,f317(f16(x63122,x63121),x63123)),x63124),f233(f858(x63121,a842)))+~P22(f317(f317(f319(x63122),x63123),x63124)) % 168.22/168.06 [6336]~P22(f317(f317(f319(x63361),x63362),x63364))+P22(f317(f317(f319(x63361),x63362),f317(f317(f286(x63361),x63363),x63364))) % 168.22/168.06 [6341]P22(f317(x63411,x63412))+~P22(f317(f154(x63413,x63411),f317(f317(f145(x63413),x63412),x63414))) % 168.22/168.06 [6349]~E(x63493,f317(f317(f21(a849),f317(f189(f850(x63491)),x63492)),f87(a849)))+E(f126(x63491,f317(f317(f153(x63491,x63492),x63493),x63494)),f126(x63491,x63492)) % 168.22/168.06 [6368]~P103(x63681)+E(f317(f317(f113(f858(x63681,a842)),f317(f277(x63681),x63682)),f279(x63681,x63683,x63684)),f279(x63681,x63683,f317(f317(f223(x63681),x63682),x63684))) % 168.22/168.06 [6369]~P103(x63691)+E(f317(f317(f113(f858(x63691,a842)),f317(f232(x63691),x63692)),f279(x63691,x63693,x63694)),f279(x63691,f317(f317(f224(x63691),x63692),x63693),x63694)) % 168.22/168.06 [6384]E(f317(f317(f113(f858(x63841,a842)),x63842),f317(f317(f286(x63841),x63843),x63844)),f317(f317(f113(f858(x63841,a842)),x63842),x63844))+P22(f317(f317(f319(x63841),x63843),x63842)) % 168.22/168.06 [6396]E(f164(x63961,x63962,f317(f317(f127(x63961),x63963),x63964)),f317(f317(f127(x63961),x63963),f164(x63961,x63962,x63964)))+P22(f317(f317(f319(x63961),x63962),f317(f166(x63961),x63963))) % 168.22/168.06 [6401]~P75(x64011)+E(f317(f317(f90(x64011),f317(f317(f238(x64011),x64012),x64013)),f317(f317(f238(x64011),x64012),x64014)),f317(f317(f238(x64011),x64012),f317(f317(f89(a849),x64013),x64014))) % 168.22/168.06 [6402]~P84(x64021)+E(f317(f317(f90(x64021),f317(f317(f238(x64021),x64022),x64023)),f317(f317(f238(x64021),x64022),x64024)),f317(f317(f238(x64021),x64022),f317(f317(f89(a849),x64023),x64024))) % 168.22/168.06 [6436]~P96(x64361)+E(f317(f317(f113(x64361),f317(f317(f122(x64361),x64362),x64363)),f317(f317(f122(x64361),x64362),x64364)),f317(f317(f122(x64361),x64362),f317(f317(f113(x64361),x64363),x64364))) % 168.22/168.06 [6437]~P84(x64371)+E(f317(f317(f89(x64371),f317(f317(f90(x64371),x64372),x64373)),f317(f317(f90(x64371),x64372),x64374)),f317(f317(f90(x64371),x64372),f317(f317(f89(x64371),x64373),x64374))) % 168.22/168.06 [6438]~P96(x64381)+E(f317(f317(f122(x64381),f317(f317(f113(x64381),x64382),x64383)),f317(f317(f113(x64381),x64382),x64384)),f317(f317(f113(x64381),x64382),f317(f317(f122(x64381),x64383),x64384))) % 168.22/168.06 [6439]~P103(x64391)+E(f317(f317(f224(x64391),f317(f317(f223(x64391),x64392),x64393)),f317(f317(f223(x64391),x64392),x64394)),f317(f317(f223(x64391),x64392),f317(f317(f224(x64391),x64393),x64394))) % 168.22/168.06 [6440]~P103(x64401)+E(f317(f317(f223(x64401),f317(f317(f224(x64401),x64402),x64403)),f317(f317(f224(x64401),x64402),x64404)),f317(f317(f224(x64401),x64402),f317(f317(f223(x64401),x64403),x64404))) % 168.22/168.06 [6473]~P55(x64731)+E(f55(x64731,f317(f317(f90(x64731),x64732),x64733),f317(f317(f90(x64731),x64734),x64733)),f317(f317(f90(x64731),f55(x64731,x64732,x64734)),x64733)) % 168.22/168.06 [6474]~E(f317(f189(f850(x64741)),x64743),f317(f189(f850(x64742)),x64744))+E(f317(f317(f148(f857(x64741,x64742),x64742),f246(x64741,x64742)),f317(f317(f175(x64741,x64742),x64743),x64744)),x64744) % 168.22/168.06 [6475]~E(f317(f189(f850(x64751)),x64753),f317(f189(f850(x64752)),x64754))+E(f317(f317(f148(f857(x64751,x64752),x64751),f244(x64751,x64752)),f317(f317(f175(x64751,x64752),x64753),x64754)),x64753) % 168.22/168.06 [6481]P22(f317(f154(x64811,x64812),x64813))+~P22(f317(f154(x64811,x64812),f317(f317(f145(x64811),x64814),x64813))) % 168.22/168.06 [6482]P22(f317(f154(x64821,x64822),x64823))+~P22(f317(f154(x64821,x64822),f317(f317(f127(x64821),x64824),x64823))) % 168.22/168.06 [6483]P22(f317(f154(x64831,x64832),x64833))+~P22(f317(f154(x64831,x64832),f317(f317(f127(x64831),x64833),x64834))) % 168.22/168.06 [6489]~P26(x64891)+E(f55(x64891,f317(f317(f21(x64891),x64892),f55(x64891,x64893,x64894)),x64894),f55(x64891,f317(f317(f21(x64891),x64892),x64893),x64894)) % 168.22/168.06 [6490]~P55(x64901)+E(f55(x64901,f317(f317(f90(x64901),x64902),f55(x64901,x64903,x64904)),x64904),f55(x64901,f317(f317(f90(x64901),x64902),x64903),x64904)) % 168.22/168.06 [6491]~P55(x64911)+E(f55(x64911,f317(f317(f89(x64911),x64912),f55(x64911,x64913,x64914)),x64914),f55(x64911,f317(f317(f89(x64911),x64912),x64913),x64914)) % 168.22/168.06 [6569]~P103(x65691)+E(f317(f317(f113(f858(x65691,a842)),f279(x65691,x65692,x65693)),f317(f277(x65691),x65694)),f279(x65691,x65692,f317(f317(f223(x65691),x65693),x65694))) % 168.22/168.06 [6570]~P103(x65701)+E(f317(f317(f113(f858(x65701,a842)),f279(x65701,x65702,x65703)),f317(f232(x65701),x65704)),f279(x65701,f317(f317(f224(x65701),x65702),x65704),x65703)) % 168.22/168.06 [6575]~E(f317(f189(f850(x65751)),x65753),f317(f189(f850(x65752)),x65754))+E(f317(f317(f175(x65751,x65752),f317(f163(x65751),x65753)),f317(f163(x65752),x65754)),f317(f163(f857(x65751,x65752)),f317(f317(f175(x65751,x65752),x65753),x65754))) % 168.22/168.06 [6586]E(x65861,f317(f317(f21(a849),f317(f189(f850(x65862)),x65863)),f87(a849)))+E(f126(x65862,f317(f317(f153(x65862,x65863),x65861),x65864)),f317(f317(f153(x65862,f126(x65862,x65863)),x65861),x65864)) % 168.22/168.06 [6597]~P22(f317(f131(x65972),x65974))+P22(f317(f131(f857(x65971,x65972)),f317(f317(f175(x65971,x65972),x65973),x65974))) % 168.22/168.06 [6598]~P22(f317(f131(x65981),x65983))+P22(f317(f131(f857(x65981,x65982)),f317(f317(f175(x65981,x65982),x65983),x65984))) % 168.22/168.06 [6687]E(x66871,f317(f317(f317(a200,x66872),x66873),f317(x66874,x66872)))+~P22(f317(f317(f194(f30(x66873,x66874)),x66872),x66871)) % 168.22/168.06 [6834]E(f317(f48(a849,x68341),x68342),x68343)+~P22(f317(f57(x68341,x68342),f317(f317(f237(a849,a849),x68343),x68344))) % 168.22/168.06 [6880]E(f55(a849,x68801,x68802),x68803)+~P22(f317(f57(x68801,x68802),f317(f317(f237(a849,a849),x68804),x68803))) % 168.22/168.06 [6883]P22(f317(f131(x68831),x68832))+~P22(f317(f131(x68833),f317(f317(f148(x68831,x68833),x68834),x68832))) % 168.22/168.06 [6891]~P18(x68911,x68912,f317(f317(f286(f848(x68911)),x68913),x68914))+P18(x68911,x68912,f317(f317(f286(f848(x68911)),x68913),f188(f858(f848(x68911),a842)))) % 168.22/168.06 [6899]P22(f317(f317(f194(x68991),x68992),x68993))+~P22(f317(f317(f317(f317(a197,x68991),x68992),x68994),x68993)) % 168.22/168.06 [6970]E(f164(x69701,x69702,f317(f317(f127(x69701),x69703),x69704)),f317(f317(f127(x69701),f164(x69701,x69702,x69703)),x69704))+~P22(f317(f317(f319(x69701),x69702),f317(f166(x69701),x69703))) % 168.22/168.06 [7064]~P26(x70641)+E(f55(x70641,f317(f317(f21(x70641),f55(x70641,x70642,x70643)),x70644),x70643),f55(x70641,f317(f317(f21(x70641),x70642),x70644),x70643)) % 168.22/168.06 [7066]~P55(x70661)+E(f55(x70661,f317(f317(f89(x70661),f55(x70661,x70662,x70663)),x70664),x70663),f55(x70661,f317(f317(f89(x70661),x70662),x70664),x70663)) % 168.22/168.06 [7067]~P55(x70671)+E(f55(x70671,f317(f317(f90(x70671),f55(x70671,x70672,x70673)),x70674),x70673),f55(x70671,f317(f317(f90(x70671),x70672),x70674),x70673)) % 168.22/168.06 [7250]~E(x72501,f317(f317(f145(x72502),x72503),x72504))+~P22(f317(f317(f225(a849),f317(f189(f850(x72502)),x72501)),f317(f189(f850(x72502)),x72504))) % 168.22/168.06 [7323]~E(f317(f171(x73231,x73232),x73233),f317(f171(x73231,x73232),x73234))+E(f317(f287(f857(x73231,x73232),x73231,f244(x73231,x73232)),f317(f166(f857(x73231,x73232)),x73233)),f317(f287(f857(x73231,x73232),x73231,f244(x73231,x73232)),f317(f166(f857(x73231,x73232)),x73234))) % 168.22/168.06 [7455]P19(x74551,x74552,x74553,f317(f166(x74551),x74554))+~P22(f317(f131(x74552),f317(f317(f148(x74551,x74552),x74553),x74554))) % 168.22/168.06 [7530]~P22(f317(f317(f225(f858(x75301,a842)),x75302),x75304))+P22(f317(f317(f225(f858(x75301,a842)),x75302),f317(f317(f286(x75301),x75303),x75304))) % 168.22/168.06 [7560]~P55(x75601)+E(f55(x75601,f317(f317(f89(x75601),f55(x75601,x75602,x75603)),f55(x75601,x75604,x75603)),x75603),f55(x75601,f317(f317(f89(x75601),x75602),x75604),x75603)) % 168.22/168.06 [7561]~P26(x75611)+E(f55(x75611,f317(f317(f21(x75611),f55(x75611,x75612,x75613)),f55(x75611,x75614,x75613)),x75613),f55(x75611,f317(f317(f21(x75611),x75612),x75614),x75613)) % 168.22/168.06 [7562]~P55(x75621)+E(f55(x75621,f317(f317(f90(x75621),f55(x75621,x75622,x75623)),f55(x75621,x75624,x75623)),x75623),f55(x75621,f317(f317(f90(x75621),x75622),x75624),x75623)) % 168.22/168.06 [7662]P22(f317(f317(f317(f317(a197,x76621),x76622),f317(a124,x76623)),x76624))+~P22(f317(f317(f317(f317(a197,x76621),x76622),x76623),x76624)) % 168.22/168.06 [7670]~E(f317(x76704,f490(x76704,x76703,x76701,x76702)),f188(f858(x76702,a842)))+E(f317(f317(f51(x76701,f858(x76702,a842)),x76703),x76704),f188(f858(x76702,a842))) % 168.22/168.06 [7671]~E(f317(x76714,f633(x76714,x76713,x76711,x76712)),f233(f858(x76712,a842)))+E(f317(f317(f52(x76711,f858(x76712,a842)),x76713),x76714),f233(f858(x76712,a842))) % 168.22/168.06 [7672]~E(f317(x76724,f491(x76724,x76723,x76722,x76721)),f188(f858(x76722,a842)))+E(f317(f317(f51(x76721,f858(x76722,a842)),x76723),x76724),f188(f858(x76722,a842))) % 168.22/168.06 [7673]~E(f317(x76734,f634(x76734,x76733,x76732,x76731)),f233(f858(x76732,a842)))+E(f317(f317(f52(x76731,f858(x76732,a842)),x76733),x76734),f233(f858(x76732,a842))) % 168.22/168.06 [8062]P22(f317(x80621,x80622))+~P22(f317(f317(f319(x80623),x80622),f317(f317(f113(f858(x80623,a842)),x80624),f317(f230(x80623),x80621)))) % 168.22/168.06 [8100]~P22(f317(f317(f225(f858(x81001,a842)),x81003),x81004))+P22(f317(f317(f225(f858(x81001,a842)),f317(f317(f286(x81001),x81002),x81003)),f317(f317(f286(x81001),x81002),x81004))) % 168.22/168.06 [8270]P22(f317(f317(f194(x82701),x82702),f354(x82703,x82702,x82704,x82701)))+~P22(f317(f317(f194(f36(x82701,x82704)),x82702),x82703)) % 168.22/168.06 [8271]P22(f317(f317(f194(x82711),x82712),f367(x82713,x82712,x82714,x82711)))+~P22(f317(f317(f194(f36(x82711,x82714)),x82712),x82713)) % 168.22/168.06 [8280]P22(f317(x82802,x82803))+E(f317(f317(f132(x82801),f317(f189(f850(x82801)),f170(x82801,x82802,f317(f317(f145(x82801),x82803),x82804)))),f317(f317(f145(x82801),x82803),x82804)),f317(f317(f145(x82801),x82803),x82804)) % 168.22/168.06 [8397]~P22(f317(f317(f226(a849),f317(x83974,x83972)),f317(x83974,x83973)))+P22(f317(f317(f319(f857(x83971,x83971)),f317(f317(f237(x83971,x83971),x83972),x83973)),f317(f317(f264(a849,x83971),a229),x83974))) % 168.22/168.06 [8495]~P22(f317(x84952,f717(x84954,x84952,x84953,x84951)))+E(f170(x84951,x84952,f317(f317(f127(x84951),x84953),x84954)),f317(f317(f127(x84951),x84953),f170(x84951,x84952,x84954))) % 168.22/168.06 [8558]P19(f850(x85581),f850(x85582),f317(f148(x85581,x85582),x85583),x85584)+~P19(x85581,x85582,x85583,f49(f858(x85581,a842),f317(f287(f850(x85581),f858(x85581,a842),f166(x85581)),x85584))) % 168.22/168.06 [8625]~P22(f317(x86252,x86253))+E(f317(f317(f132(x86251),f317(f189(f850(x86251)),f170(x86251,x86252,f317(f317(f145(x86251),x86253),x86254)))),f317(f317(f145(x86251),x86253),x86254)),f317(f317(f132(x86251),f317(f189(f850(x86251)),f170(x86251,x86252,x86254))),x86254)) % 168.22/168.06 [8664]~E(x86642,x86643)+E(f317(f130(x86641,f317(f317(f8(a842,a842,x86641),a312),f317(a314,x86642))),f317(f317(f145(x86641),x86643),x86644)),f317(f130(x86641,f317(f317(f8(a842,a842,x86641),a312),f317(a314,x86642))),x86644)) % 168.22/168.06 [8673]E(f317(f317(f51(x86731,f858(x86732,a842)),x86733),x86734),f188(f858(x86732,a842)))+P22(f317(f317(f319(x86731),f490(x86734,x86733,x86731,x86732)),x86733)) % 168.22/168.06 [8674]E(f317(f317(f52(x86741,f858(x86742,a842)),x86743),x86744),f233(f858(x86742,a842)))+P22(f317(f317(f319(x86741),f633(x86744,x86743,x86741,x86742)),x86743)) % 168.22/168.06 [8675]E(f317(f317(f51(x86751,f858(x86752,a842)),x86753),x86754),f188(f858(x86752,a842)))+P22(f317(f317(f319(x86751),f491(x86754,x86753,x86752,x86751)),x86753)) % 168.22/168.06 [8676]E(f317(f317(f52(x86761,f858(x86762,a842)),x86763),x86764),f233(f858(x86762,a842)))+P22(f317(f317(f319(x86761),f634(x86764,x86763,x86762,x86761)),x86763)) % 168.22/168.06 [8711]P22(f317(f317(f226(a849),f317(x87111,x87112)),f317(x87111,x87113)))+~P22(f317(f317(f319(f857(x87114,x87114)),f317(f317(f237(x87114,x87114),x87112),x87113)),f317(f317(f264(a849,x87114),a229),x87111))) % 168.22/168.06 [8731]E(f170(x87311,x87312,f317(f317(f127(x87311),x87313),x87314)),f317(f317(f127(x87311),x87313),f170(x87311,x87312,x87314)))+P22(f317(f317(f319(x87311),f717(x87314,x87312,x87313,x87311)),f317(f166(x87311),x87313))) % 168.22/168.06 [8767]P22(f317(f317(f194(x87671),f354(x87672,x87673,x87671,x87674)),x87672))+~P22(f317(f317(f194(f36(x87674,x87671)),x87673),x87672)) % 168.22/168.06 [8768]P22(f317(f317(f194(x87681),f367(x87682,x87683,x87681,x87684)),x87682))+~P22(f317(f317(f194(f36(x87684,x87681)),x87683),x87682)) % 168.22/168.06 [8878]~P55(x88781)+E(f317(f317(f89(x88781),f317(f317(f89(x88781),f317(f317(f90(x88781),x88782),f317(f48(x88781,x88783),x88782))),f55(x88781,x88783,x88782))),x88784),f317(f317(f89(x88781),x88783),x88784)) % 168.22/168.06 [8899]P22(f317(f317(f319(x88991),f474(x88992,x88993,x88994,x88991)),x88993))+~P22(f317(f317(f319(f858(x88991,a842)),x88994),f317(f317(f70(x88991),x88993),x88992))) % 168.22/168.06 [8902]E(x89021,x89022)+~P22(f317(f317(f319(f857(x89023,x89023)),f317(f317(f237(x89023,x89023),x89021),x89022)),f317(f317(f182(f857(x89023,x89023),a842),f2(a849)),x89024))) % 168.22/168.06 [8978]E(f317(f262(x89781,x89781,x89782),f317(f317(f286(x89781),f474(x89782,x89783,x89784,x89781)),f188(f858(x89781,a842)))),x89784)+~P22(f317(f317(f319(f858(x89781,a842)),x89784),f317(f317(f70(x89781),x89783),x89782))) % 168.22/168.06 [8983]~P22(f317(f317(f319(f857(x89831,x89831)),f317(f317(f237(x89831,x89831),x89833),x89832)),f284(x89831,x89834)))+P22(f317(f317(f319(f857(x89831,x89831)),f317(f317(f237(x89831,x89831),x89832),x89833)),f284(x89831,f317(f263(x89831,x89831),x89834)))) % 168.22/168.06 [9004]~P22(f317(f317(f319(x90041),x90043),x90044))+P22(f317(f317(f319(f858(x90041,a842)),f317(f262(x90041,x90041,x90042),f317(f317(f286(x90041),x90043),f188(f858(x90041,a842))))),f317(f317(f70(x90041),x90044),x90042))) % 168.22/168.06 [9015]P22(f317(f317(f319(f857(x90151,x90151)),f317(f317(f237(x90151,x90151),x90152),x90153)),f284(x90151,x90154)))+~P22(f317(f317(f319(f857(x90151,x90151)),f317(f317(f237(x90151,x90151),x90153),x90152)),f284(x90151,f317(f263(x90151,x90151),x90154)))) % 168.22/168.06 [9105]E(f317(f317(f153(x91051,f317(f163(x91051),x91052)),f317(f317(f21(a849),f317(f317(f21(a849),f317(f189(f850(x91051)),x91052)),x91053)),f87(a849))),x91054),f317(f163(x91051),f317(f317(f153(x91051,x91052),x91053),x91054)))+~P22(f317(f317(f226(a849),x91053),f317(f189(f850(x91051)),x91052))) % 168.22/168.06 [9108]~P22(f317(x91082,f708(x91084,x91082,x91083,x91081)))+E(f317(f317(f132(x91081),f317(f189(f850(x91081)),f170(x91081,x91082,f317(f317(f127(x91081),x91083),x91084)))),f317(f317(f127(x91081),x91083),x91084)),f317(f317(f132(x91081),f317(f189(f850(x91081)),f170(x91081,x91082,x91084))),x91084)) % 168.22/168.06 [9146]~P19(x91462,x91461,x91463,f233(f858(x91462,a842)))+P22(f317(f317(f225(f858(x91461,a842)),f317(f287(x91462,x91461,x91463),f317(f88(f858(x91462,a842)),x91464))),f317(f88(f858(x91461,a842)),f317(f287(x91462,x91461,x91463),x91464)))) % 168.22/168.06 [9156]~P55(x91561)+E(f317(f317(f89(x91561),f317(f317(f89(x91561),f317(f317(f90(x91561),f317(f48(x91561,x91562),x91563)),x91563)),f55(x91561,x91562,x91563))),x91564),f317(f317(f89(x91561),x91562),x91564)) % 168.22/168.06 [9160]~P27(x91601)+E(f317(f136(x91601,x91602,f317(f7(x91602,x91601,x91601),f317(f317(f8(x91601,f858(x91601,x91601),x91602),f122(x91601)),x91603)),f188(x91601)),x91604),f317(f317(f51(x91602,x91601),f317(f166(x91602),x91604)),x91603)) % 168.22/168.06 [9161]~P27(x91611)+E(f317(f136(x91611,x91612,f317(f7(x91612,x91611,x91611),f317(f317(f8(x91611,f858(x91611,x91611),x91612),f113(x91611)),x91613)),f233(x91611)),x91614),f317(f317(f52(x91612,x91611),f317(f166(x91612),x91614)),x91613)) % 168.22/168.06 [9173]E(f317(f317(f132(x91731),f317(f189(f850(x91731)),f170(x91731,x91732,f317(f317(f127(x91731),x91733),x91734)))),f317(f317(f127(x91731),x91733),x91734)),f317(f317(f132(x91731),f317(f189(f850(x91731)),f170(x91731,x91732,x91734))),x91734))+P22(f317(f317(f319(x91731),f708(x91734,x91732,x91733,x91731)),f317(f166(x91731),x91733))) % 168.22/168.06 [9238]~P22(f317(f317(f319(f857(f850(x92384),f850(x92384))),f317(f317(f237(f850(x92384),f850(x92384)),x92383),x92382)),f151(x92384,x92381)))+P22(f317(f317(f226(a849),f605(x92381,x92382,x92383,x92384)),f317(f189(f850(x92384)),x92383))) % 168.22/168.06 [9267]~P22(f317(f317(f319(f857(f850(x92671),f850(x92671))),f317(f317(f237(f850(x92671),f850(x92671)),x92672),x92673)),f317(f263(f850(x92671),f850(x92671)),f151(x92671,x92674))))+P22(f317(f317(f319(f857(f850(x92671),f850(x92671))),f317(f317(f237(f850(x92671),f850(x92671)),x92672),x92673)),f151(x92671,f317(f263(x92671,x92671),x92674)))) % 168.22/168.06 [9268]P22(f317(f317(f319(f857(f850(x92681),f850(x92681))),f317(f317(f237(f850(x92681),f850(x92681)),x92682),x92683)),f317(f263(f850(x92681),f850(x92681)),f151(x92681,x92684))))+~P22(f317(f317(f319(f857(f850(x92681),f850(x92681))),f317(f317(f237(f850(x92681),f850(x92681)),x92682),x92683)),f151(x92681,f317(f263(x92681,x92681),x92684)))) % 168.22/168.06 [9302]~P22(f317(f317(f319(x93021),x93023),f317(f236(x93021,x93022),x93024)))+P22(f317(f317(f319(f857(x93021,x93022)),f317(f317(f237(x93021,x93022),x93023),f561(x93024,x93022,x93023,x93021))),x93024)) % 168.22/168.06 [9303]~P22(f317(f317(f319(x93031),x93033),f317(f236(x93031,x93032),x93034)))+P22(f317(f317(f319(f857(x93031,x93032)),f317(f317(f237(x93031,x93032),x93033),f563(x93034,x93032,x93033,x93031))),x93034)) % 168.22/168.06 [9415]~P22(f317(f71(f853(x94151)),f317(f287(x94152,f853(x94151),x94153),f233(f858(x94152,a842)))))+P22(f317(f71(f853(x94151)),f317(f287(x94152,f853(x94151),f178(x94152,x94151,x94153,f317(f171(x94152,x94151),x94154))),f233(f858(x94152,a842))))) % 168.22/168.06 [9459]~P22(f317(f317(f319(f857(x94591,x94591)),f317(f317(f237(x94591,x94591),x94592),x94594)),f317(f317(f265(x94591,x94591,x94591),x94593),f284(x94591,x94593))))+P22(f317(f317(f319(f857(x94591,x94591)),f317(f317(f237(x94591,x94591),x94592),f770(x94593,x94594,x94592,x94591))),x94593)) % 168.22/168.06 [9648]~P22(f317(f317(f319(f857(f850(x96481),f850(x96481))),f317(f317(f237(f850(x96481),f850(x96481)),x96484),x96483)),f151(x96481,x96482)))+P22(f317(f317(f319(f857(x96481,x96481)),f317(f317(f237(x96481,x96481),f621(x96482,x96483,x96484,x96481)),f624(x96482,x96483,x96484,x96481))),x96482)) % 168.22/168.06 [9745]~P22(f317(f317(f319(f857(f850(x97451),f850(x97451))),f317(f317(f237(f850(x97451),f850(x97451)),x97452),x97454)),f151(x97451,x97453)))+P22(f317(f317(f319(f857(x97451,x97451)),f317(f317(f237(x97451,x97451),f317(f317(f159(x97451),x97452),f605(x97453,x97454,x97452,x97451))),f606(x97453,x97454,x97452,x97451))),x97453)) % 168.22/168.06 [9767]~P22(f317(f71(x97672),x97674))+E(f317(f317(f317(f75(f858(x97671,a842),x97672,f122(f858(x97671,a842))),f317(f317(f7(x97672,f858(x97671,a842),f858(x97671,a842)),f317(f317(f8(x97671,f858(f858(x97671,a842),f858(x97671,a842)),x97672),f286(x97671)),x97673)),f188(f858(x97671,a842)))),f188(f858(x97671,a842))),x97674),f317(f287(x97672,x97671,x97673),x97674)) % 168.22/168.06 [9873]~P19(x98731,x98732,x98733,f233(f858(x98731,a842)))+P22(f317(f317(f225(f858(x98731,a842)),f317(f289(x98731,x98732,x98733),f317(f317(f286(x98732),x98734),f188(f858(x98732,a842))))),f317(f317(f286(x98731),f94(x98731,f317(f317(f7(x98731,x98732,a842),f317(f317(f8(x98732,f858(x98732,a842),x98731),a314),x98733)),x98734))),f188(f858(x98731,a842))))) % 168.22/168.06 [5547]~E(f317(f317(f127(x55471),x55472),x55474),x55473)+E(f317(f317(f167(x55471),f317(f189(f850(x55471)),x55472)),x55473),x55472) % 168.22/168.06 [5548]~E(f317(f317(f127(x55482),x55483),x55481),x55484)+E(x55481,f317(f317(f132(x55482),f317(f189(f850(x55482)),x55483)),x55484)) % 168.22/168.06 [5559]~E(x55594,f2(a849))+E(f317(f317(f159(x55591),f317(f317(f145(x55591),x55592),x55593)),x55594),x55592) % 168.22/168.06 [6061]~P84(x60611)+E(f317(f317(f238(x60611),f317(f317(f238(x60611),x60612),x60613)),x60614),f317(f317(f238(x60611),x60612),f317(f317(f90(a849),x60613),x60614))) % 168.22/168.06 [6062]~P75(x60621)+E(f317(f317(f238(x60621),f317(f317(f238(x60621),x60622),x60623)),x60624),f317(f317(f238(x60621),x60622),f317(f317(f90(a849),x60623),x60624))) % 168.22/168.06 [6078]E(x60781,f2(a849))+E(f317(f317(f159(x60782),f317(f317(f145(x60782),x60783),x60784)),x60781),f317(f317(f159(x60782),x60784),f317(f317(f21(a849),x60781),f87(a849)))) % 168.22/168.06 [6103]~P115(x61031)+E(f317(f317(f266(x61031),f317(f317(f90(x61031),x61032),x61033)),x61034),f317(f317(f90(x61031),x61032),f317(f317(f266(x61031),x61033),x61034))) % 168.22/168.06 [6104]~P24(x61041)+E(f317(f317(f89(x61041),f317(f317(f89(x61041),x61042),x61043)),x61044),f317(f317(f89(x61041),x61042),f317(f317(f89(x61041),x61043),x61044))) % 168.22/168.06 [6105]~P84(x61051)+E(f317(f317(f89(x61051),f317(f317(f89(x61051),x61052),x61053)),x61054),f317(f317(f89(x61051),x61052),f317(f317(f89(x61051),x61053),x61054))) % 168.22/168.06 [6107]~P92(x61071)+E(f317(f317(f122(x61071),f317(f317(f122(x61071),x61072),x61073)),x61074),f317(f317(f122(x61071),x61072),f317(f317(f122(x61071),x61073),x61074))) % 168.22/168.06 [6108]~P93(x61081)+E(f317(f317(f122(x61081),f317(f317(f122(x61081),x61082),x61083)),x61084),f317(f317(f122(x61081),x61082),f317(f317(f122(x61081),x61083),x61084))) % 168.22/168.06 [6109]~P84(x61091)+E(f317(f317(f90(x61091),f317(f317(f90(x61091),x61092),x61093)),x61094),f317(f317(f90(x61091),x61092),f317(f317(f90(x61091),x61093),x61094))) % 168.22/168.06 [6110]~P64(x61101)+E(f317(f317(f90(x61101),f317(f317(f90(x61101),x61102),x61103)),x61104),f317(f317(f90(x61101),x61102),f317(f317(f90(x61101),x61103),x61104))) % 168.22/168.06 [6112]~P93(x61121)+E(f317(f317(f113(x61121),f317(f317(f113(x61121),x61122),x61123)),x61124),f317(f317(f113(x61121),x61122),f317(f317(f113(x61121),x61123),x61124))) % 168.22/168.06 [6114]~P98(x61141)+E(f317(f317(f113(x61141),f317(f317(f113(x61141),x61142),x61143)),x61144),f317(f317(f113(x61141),x61142),f317(f317(f113(x61141),x61143),x61144))) % 168.22/168.06 [6116]~P103(x61161)+E(f317(f317(f223(x61161),f317(f317(f223(x61161),x61162),x61163)),x61164),f317(f317(f223(x61161),x61162),f317(f317(f223(x61161),x61163),x61164))) % 168.22/168.06 [6118]~P103(x61181)+E(f317(f317(f224(x61181),f317(f317(f224(x61181),x61182),x61183)),x61184),f317(f317(f224(x61181),x61182),f317(f317(f224(x61181),x61183),x61184))) % 168.22/168.06 [6133]~P55(x61331)+E(f55(x61331,f317(f317(f89(x61331),x61332),f317(f317(f90(x61331),x61333),x61334)),x61334),f55(x61331,x61332,x61334)) % 168.22/168.06 [6134]~P55(x61341)+E(f55(x61341,f317(f317(f89(x61341),x61342),f317(f317(f90(x61341),x61343),x61344)),x61343),f55(x61341,x61342,x61343)) % 168.22/168.06 [6262]E(f317(f317(f159(x62621),f317(f317(f167(x62621),x62622),x62623)),x62624),f317(f317(f159(x62621),x62623),x62624))+~P22(f317(f317(f226(a849),x62624),x62622)) % 168.22/168.06 [6434]~P84(x64341)+E(f317(f317(f89(x64341),f317(f317(f89(x64341),x64342),x64343)),x64344),f317(f317(f89(x64341),f317(f317(f89(x64341),x64342),x64344)),x64343)) % 168.22/168.06 [6435]~P84(x64351)+E(f317(f317(f90(x64351),f317(f317(f90(x64351),x64352),x64353)),x64354),f317(f317(f90(x64351),f317(f317(f90(x64351),x64352),x64354)),x64353)) % 168.22/168.06 [6494]~P110(x64942)+E(f317(f317(f6(x64941,x64942),f317(f16(x64942,x64941),x64943)),x64944),f317(f317(f90(x64942),f317(f112(x64942),f317(f54(x64941),x64944))),x64943)) % 168.22/168.06 [6660]E(f317(f317(f113(f858(x66601,a842)),f317(f317(f286(x66601),x66602),x66603)),x66604),f317(f317(f113(f858(x66601,a842)),x66603),x66604))+P22(f317(f317(f319(x66601),x66602),x66604)) % 168.22/168.06 [6723]~P76(x67231)+E(f317(f317(f223(x67231),f317(f317(f89(x67231),x67232),x67233)),f317(f317(f89(x67231),x67234),x67233)),f317(f317(f89(x67231),f317(f317(f223(x67231),x67232),x67234)),x67233)) % 168.22/168.06 [6724]~P76(x67241)+E(f317(f317(f224(x67241),f317(f317(f89(x67241),x67242),x67243)),f317(f317(f89(x67241),x67244),x67243)),f317(f317(f89(x67241),f317(f317(f224(x67241),x67242),x67244)),x67243)) % 168.22/168.06 [6725]~P78(x67251)+E(f317(f317(f223(x67251),f317(f317(f21(x67251),x67252),x67253)),f317(f317(f21(x67251),x67254),x67253)),f317(f317(f21(x67251),f317(f317(f223(x67251),x67252),x67254)),x67253)) % 168.22/168.06 [6726]~P78(x67261)+E(f317(f317(f224(x67261),f317(f317(f21(x67261),x67262),x67263)),f317(f317(f21(x67261),x67264),x67263)),f317(f317(f21(x67261),f317(f317(f224(x67261),x67262),x67264)),x67263)) % 168.22/168.06 [6727]~P96(x67271)+E(f317(f317(f113(x67271),f317(f317(f122(x67271),x67272),x67273)),f317(f317(f122(x67271),x67274),x67273)),f317(f317(f122(x67271),f317(f317(f113(x67271),x67272),x67274)),x67273)) % 168.22/168.06 [6729]~P108(x67291)+E(f317(f317(f89(x67291),f317(f317(f90(x67291),x67292),x67293)),f317(f317(f90(x67291),x67294),x67293)),f317(f317(f90(x67291),f317(f317(f89(x67291),x67292),x67294)),x67293)) % 168.22/168.06 [6730]~P96(x67301)+E(f317(f317(f122(x67301),f317(f317(f113(x67301),x67302),x67303)),f317(f317(f113(x67301),x67304),x67303)),f317(f317(f113(x67301),f317(f317(f122(x67301),x67302),x67304)),x67303)) % 168.22/168.06 [6731]~P103(x67311)+E(f317(f317(f224(x67311),f317(f317(f223(x67311),x67312),x67313)),f317(f317(f223(x67311),x67314),x67313)),f317(f317(f223(x67311),f317(f317(f224(x67311),x67312),x67314)),x67313)) % 168.22/168.06 [6732]~P103(x67321)+E(f317(f317(f223(x67321),f317(f317(f224(x67321),x67322),x67323)),f317(f317(f224(x67321),x67324),x67323)),f317(f317(f224(x67321),f317(f317(f223(x67321),x67322),x67324)),x67323)) % 168.22/168.06 [6733]~P84(x67331)+E(f317(f317(f90(x67331),f317(f317(f238(x67331),x67332),x67333)),f317(f317(f238(x67331),x67334),x67333)),f317(f317(f238(x67331),f317(f317(f90(x67331),x67332),x67334)),x67333)) % 168.22/168.06 [6734]~P70(x67341)+E(f317(f317(f90(x67341),f317(f317(f238(x67341),x67342),x67343)),f317(f317(f238(x67341),x67344),x67343)),f317(f317(f238(x67341),f317(f317(f90(x67341),x67342),x67344)),x67343)) % 168.22/168.06 [6735]~P58(x67351)+E(f317(f317(f266(x67351),f317(f317(f238(x67351),x67352),x67353)),f317(f317(f238(x67351),x67354),x67353)),f317(f317(f238(x67351),f317(f317(f266(x67351),x67352),x67354)),x67353)) % 168.22/168.06 [6736]~P115(x67361)+E(f317(f317(f89(x67361),f317(f317(f266(x67361),x67362),x67363)),f317(f317(f266(x67361),x67364),x67363)),f317(f317(f266(x67361),f317(f317(f89(x67361),x67362),x67364)),x67363)) % 168.22/168.06 [6737]~P115(x67371)+E(f317(f317(f21(x67371),f317(f317(f266(x67371),x67372),x67373)),f317(f317(f266(x67371),x67374),x67373)),f317(f317(f266(x67371),f317(f317(f21(x67371),x67372),x67374)),x67373)) % 168.22/168.06 [6738]~P84(x67381)+E(f317(f317(f89(x67381),f317(f317(f90(x67381),x67382),x67383)),f317(f317(f90(x67381),x67384),x67383)),f317(f317(f90(x67381),f317(f317(f89(x67381),x67382),x67384)),x67383)) % 168.22/168.06 [6770]E(f317(f317(f153(x67701,x67702),x67703),x67704),x67702)+~P22(f317(f317(f225(a849),f317(f189(f850(x67701)),x67702)),x67703)) % 168.22/168.06 [6792]~P22(f317(x67923,x67924))+P22(f317(f317(f317(f122(f858(x67921,a842)),x67922),x67923),x67924)) % 168.22/168.06 [6794]~P22(f317(x67942,x67944))+P22(f317(f317(f317(f122(f858(x67941,a842)),x67942),x67943),x67944)) % 168.22/168.06 [6815]E(f317(f317(f159(x68151),f317(f317(f127(x68151),x68152),x68153)),x68154),f317(f317(f159(x68151),x68152),x68154))+~P22(f317(f317(f226(a849),x68154),f317(f189(f850(x68151)),x68152))) % 168.22/168.06 [6827]E(f317(f317(f21(f858(x68271,a842)),f317(f317(f286(x68271),x68272),x68273)),x68274),f317(f317(f21(f858(x68271,a842)),x68273),x68274))+~P22(f317(f317(f319(x68271),x68272),x68274)) % 168.22/168.06 [6868]~E(f133(a849,f317(f278(a849,x68681),x68682)),f317(f317(f145(a849),x68684),x68683))+E(f133(a849,f317(f278(a849,f317(f317(f89(a849),x68681),f87(a849))),x68682)),x68683) % 168.22/168.06 [6945]E(x69451,f2(a849))+E(f317(f317(f145(x69452),x69453),f317(f317(f167(x69452),f317(f317(f21(a849),x69451),f87(a849))),x69454)),f317(f317(f167(x69452),x69451),f317(f317(f145(x69452),x69453),x69454))) % 168.22/168.06 [7044]E(f317(f317(f159(x70441),x70442),f317(f317(f21(a849),x70443),f317(f189(f850(x70441)),x70444))),f317(f317(f159(x70441),f317(f317(f127(x70441),x70444),x70442)),x70443))+P22(f317(f317(f226(a849),x70443),f317(f189(f850(x70441)),x70444))) % 168.22/168.06 [7077]E(f317(f317(f113(f858(x70771,a842)),x70772),f317(f317(f286(x70771),x70773),x70774)),f317(f317(f286(x70771),x70773),f317(f317(f113(f858(x70771,a842)),x70772),x70774)))+~P22(f317(f317(f319(x70771),x70773),x70772)) % 168.22/168.06 [7112]E(f317(f317(f159(x71121),f317(f317(f153(x71121,x71122),x71123),x71124)),x71123),x71124)+~P22(f317(f317(f226(a849),x71123),f317(f189(f850(x71121)),x71122))) % 168.22/168.06 [7131]E(x71311,f188(f858(x71312,a842)))+E(f317(f287(f857(x71313,x71312),x71313,f244(x71313,x71312)),f317(f317(f245(x71313,x71312),x71314),f317(f16(f858(x71312,a842),x71313),x71311))),x71314) % 168.22/168.06 [7132]E(x71321,f188(f858(x71322,a842)))+E(f317(f287(f857(x71322,x71323),x71323,f246(x71322,x71323)),f317(f317(f245(x71322,x71323),x71321),f317(f16(f858(x71323,a842),x71322),x71324))),x71324) % 168.22/168.06 [7191]E(f317(f317(f21(f858(x71911,a842)),f317(f317(f286(x71911),x71912),x71913)),x71914),f317(f317(f286(x71911),x71912),f317(f317(f21(f858(x71911,a842)),x71913),x71914)))+P22(f317(f317(f319(x71911),x71912),x71914)) % 168.22/168.06 [7227]P22(f317(x72271,x72272))+P22(f317(f317(f317(f317(a197,f35(x72271,x72273)),x72272),x72274),x72272)) % 168.22/168.06 [7234]~E(x72344,f188(f858(x72342,a842)))+E(f317(f287(f857(x72341,x72342),x72341,f244(x72341,x72342)),f317(f317(f245(x72341,x72342),x72343),f317(f16(f858(x72342,a842),x72341),x72344))),f188(f858(x72341,a842))) % 168.22/168.06 [7235]~E(x72353,f188(f858(x72351,a842)))+E(f317(f287(f857(x72351,x72352),x72352,f246(x72351,x72352)),f317(f317(f245(x72351,x72352),x72353),f317(f16(f858(x72352,a842),x72351),x72354))),f188(f858(x72352,a842))) % 168.22/168.06 [7290]~P22(f317(f317(f319(x72901),x72902),x72904))+P22(f317(f317(f319(x72901),x72902),f317(f317(f122(f858(x72901,a842)),x72903),x72904))) % 168.22/168.06 [7293]~P22(f317(f317(f319(x72931),x72932),x72933))+P22(f317(f317(f319(x72931),x72932),f317(f317(f122(f858(x72931,a842)),x72933),x72934))) % 168.22/168.06 [7311]E(f317(f317(f113(f858(x73111,a842)),f317(f317(f286(x73111),x73112),x73113)),x73114),f317(f317(f286(x73111),x73112),f317(f317(f113(f858(x73111,a842)),x73113),x73114)))+~P22(f317(f317(f319(x73111),x73112),x73114)) % 168.22/168.06 [7584]P22(f317(x75841,x75842))+~P22(f317(f317(f317(f113(f858(x75843,a842)),x75844),x75841),x75842)) % 168.22/168.06 [7585]P22(f317(x75851,x75852))+~P22(f317(f317(f317(f113(f858(x75853,a842)),x75851),x75854),x75852)) % 168.22/168.06 [7588]E(f317(f317(f6(x75881,a849),x75882),f317(f317(f21(f858(x75881,a842)),x75883),f317(f317(f286(x75881),x75884),f188(f858(x75881,a842))))),f317(f317(f6(x75881,a849),x75882),x75883))+P22(f317(f317(f319(x75881),x75884),x75883)) % 168.22/168.06 [7593]~P67(x75931)+E(f317(f160(x75931),f317(f317(f148(a849,x75931),x75932),f133(a849,f317(f278(a849,x75933),x75934)))),f317(f317(f6(a849,x75931),x75932),f317(f166(a849),f133(a849,f317(f278(a849,x75933),x75934))))) % 168.22/168.06 [7594]~P67(x75941)+E(f317(f317(f6(a849,x75941),x75942),f317(f166(a849),f133(a849,f317(f278(a849,x75943),x75944)))),f317(f160(x75941),f317(f317(f148(a849,x75941),x75942),f133(a849,f317(f278(a849,x75943),x75944))))) % 168.22/168.06 [7708]~E(x77083,x77084)+P22(f317(f72(x77081,x77082,f317(f317(f286(x77081),x77083),f188(f858(x77081,a842)))),x77084)) % 168.22/168.06 [7800]P22(f317(f317(f319(x78001),x78002),f317(f166(x78001),x78003)))+~P22(f317(f317(f319(x78001),x78002),f317(f166(x78001),f317(f317(f167(x78001),x78004),x78003)))) % 168.22/168.06 [7801]P22(f317(f317(f319(x78011),x78012),f317(f166(x78011),x78013)))+~P22(f317(f317(f319(x78011),x78012),f317(f166(x78011),f317(f317(f132(x78011),x78014),x78013)))) % 168.22/168.06 [7869]P22(f317(f317(f319(x78691),x78692),x78693))+~P22(f317(f317(f319(x78691),x78692),f317(f317(f21(f858(x78691,a842)),x78693),x78694))) % 168.22/168.06 [7871]P22(f317(f317(f319(x78711),x78712),x78713))+~P22(f317(f317(f319(x78711),x78712),f317(f317(f113(f858(x78711,a842)),x78714),x78713))) % 168.22/168.06 [7874]P22(f317(f317(f319(x78741),x78742),x78743))+~P22(f317(f317(f319(x78741),x78742),f317(f317(f113(f858(x78741,a842)),x78743),x78744))) % 168.22/168.06 [7892]E(f317(f317(f127(x78921),f317(f317(f167(x78921),x78922),x78923)),f317(f317(f145(x78921),x78924),f317(f317(f132(x78921),f317(a124,x78922)),x78923))),f317(f317(f153(x78921,x78923),x78922),x78924))+~P22(f317(f317(f226(a849),x78922),f317(f189(f850(x78921)),x78923))) % 168.22/168.06 [7915]P22(f317(f317(f319(x79151),x79152),x79153))+~P22(f317(f317(f225(f858(x79151,a842)),f317(f317(f286(x79151),x79152),x79154)),x79153)) % 168.22/168.06 [7948]~P22(f317(f317(f319(x79481),x79482),x79483))+~P22(f317(f317(f319(x79481),x79482),f317(f317(f21(f858(x79481,a842)),x79484),x79483))) % 168.22/168.06 [7981]~P22(f317(f317(f226(a849),x79814),f317(f189(f850(x79811)),x79813)))+P22(f317(f317(f319(x79811),x79812),f317(f166(x79811),f317(f317(f153(x79811,x79813),x79814),x79812)))) % 168.22/168.06 [8038]E(f317(f317(f159(x80381),f317(f317(f132(x80381),x80382),x80383)),x80384),f317(f317(f159(x80381),x80383),f317(f317(f89(a849),x80382),x80384)))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),x80382),x80384)),f317(f189(f850(x80381)),x80383))) % 168.22/168.06 [8049]~P110(x80492)+E(f317(f317(f6(x80491,x80492),f317(f317(f8(a849,x80492,x80491),f112(x80492)),x80493)),x80494),f317(f112(x80492),f317(f317(f6(x80491,a849),x80493),x80494))) % 168.22/168.06 [8050]~P111(x80502)+E(f317(f317(f6(x80501,x80502),f317(f317(f8(a1,x80502,x80501),f114(x80502)),x80503)),x80504),f317(f114(x80502),f317(f317(f6(x80501,a1),x80503),x80504))) % 168.22/168.06 [8102]~P61(x81022)+E(f317(f317(f9(x81021,x81022),f317(f317(f8(x81022,x81022,x81021),f84(x81022)),x81023)),x81024),f317(f84(x81022),f317(f317(f9(x81021,x81022),x81023),x81024))) % 168.22/168.06 [8103]~P25(x81032)+E(f317(f317(f6(x81031,x81032),f317(f317(f8(x81032,x81032,x81031),f88(x81032)),x81033)),x81034),f317(f88(x81032),f317(f317(f6(x81031,x81032),x81033),x81034))) % 168.22/168.06 [8105]E(f317(f317(f6(x81051,a849),x81052),f317(f317(f21(f858(x81051,a842)),x81053),f317(f317(f286(x81051),x81054),f188(f858(x81051,a842))))),f317(f317(f21(a849),f317(f317(f6(x81051,a849),x81052),x81053)),f317(x81052,x81054)))+~P22(f317(f317(f319(x81051),x81054),x81053)) % 168.22/168.06 [8125]P22(f317(f317(f225(f858(x81251,a842)),x81252),x81253))+~P22(f317(f317(f225(f858(x81251,a842)),f317(f317(f286(x81251),x81254),x81252)),x81253)) % 168.22/168.06 [8337]E(f317(a124,f445(x83371,x83372,x83373,x83374)),x83372)+~P22(f317(f317(f317(f317(a197,f317(a29,x83374)),x83373),x83372),x83371)) % 168.22/168.06 [8339]E(f317(f317(f171(x83391,x83392),x83393),x83394),f191(x83392))+P22(f317(f317(f319(x83391),x83394),f317(f287(f857(x83391,x83392),x83391,f244(x83391,x83392)),f317(f166(f857(x83391,x83392)),x83393)))) % 168.22/168.06 [8340]P37(x83401,x83402)+~P37(x83401,f317(f317(f286(f857(x83401,x83401)),f317(f317(f237(x83401,x83401),x83403),x83404)),x83402)) % 168.22/168.06 [8341]P52(x83411,x83412)+~P52(x83411,f317(f317(f286(f857(x83411,x83411)),f317(f317(f237(x83411,x83411),x83413),x83414)),x83412)) % 168.22/168.06 [8350]~P103(x83501)+E(f317(f317(f143(x83501,x83501,f5(x83501)),x83502),f317(f317(f143(x83501,x83501,f5(x83501)),x83503),x83504)),f317(f317(f143(x83501,x83501,f5(x83501)),x83503),f317(f317(f143(x83501,x83501,f5(x83501)),x83502),x83504))) % 168.22/168.06 [8359]E(x83591,x83592)+~P22(f317(f72(x83593,x83594,f317(f317(f286(x83593),x83591),f188(f858(x83593,a842)))),x83592)) % 168.22/168.06 [8370]E(f317(f317(f127(x83701),f317(f317(f167(x83701),x83702),x83703)),f317(f317(f167(x83701),x83704),f317(f317(f132(x83701),x83702),x83703))),f317(f317(f167(x83701),f317(f317(f89(a849),x83702),x83704)),x83703))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),x83702),x83704)),f317(f189(f850(x83701)),x83703))) % 168.22/168.06 [8412]P22(f317(f71(x84121),x84122))+~E(x84122,f317(f287(a849,x84121,x84123),f317(f230(a849),f317(f317(f7(a849,a849,a842),f226(a849)),x84124)))) % 168.22/168.06 [8435]~P83(x84351)+E(f317(f136(x84351,x84351,f89(x84351),f317(f317(f89(x84351),x84352),x84353)),x84354),f317(f317(f89(x84351),x84352),f317(f136(x84351,x84351,f89(x84351),x84353),x84354))) % 168.22/168.06 [8471]P22(f317(f317(f225(f858(x84711,a842)),f317(f236(x84711,x84712),x84713)),f317(f236(x84711,x84712),x84714)))+~P22(f317(f317(f225(f858(f857(x84711,x84712),a842)),x84713),x84714)) % 168.22/168.06 [8486]~P22(f317(f317(f225(a849),x84862),x84864))+P22(f317(f317(f225(f858(x84861,a842)),f317(f166(x84861),f317(f317(f167(x84861),x84862),x84863))),f317(f166(x84861),f317(f317(f167(x84861),x84864),x84863)))) % 168.22/168.06 [8487]~P22(f317(f317(f225(a849),x84874),x84872))+P22(f317(f317(f225(f858(x84871,a842)),f317(f166(x84871),f317(f317(f132(x84871),x84872),x84873))),f317(f166(x84871),f317(f317(f132(x84871),x84874),x84873)))) % 168.22/168.06 [8535]~P22(f317(f71(x85351),f317(f317(f21(f858(x85351,a842)),x85352),x85354)))+P22(f317(f71(x85351),f317(f317(f21(f858(x85351,a842)),x85352),f317(f317(f286(x85351),x85353),x85354)))) % 168.22/168.06 [8569]P22(f317(f317(f319(f857(x85691,x85691)),x85692),f284(x85691,x85693)))+~P22(f317(f317(f319(f857(x85691,x85691)),x85692),f317(f317(f182(f857(x85691,x85691),a842),x85694),x85693))) % 168.22/168.06 [8646]~P22(f317(f71(x86461),f317(f317(f21(f858(x86461,a842)),x86462),f317(f317(f286(x86461),x86464),x86463))))+P22(f317(f71(x86461),f317(f317(f21(f858(x86461,a842)),x86462),x86463))) % 168.22/168.06 [8789]~E(f317(f317(f171(x87891,x87892),x87893),x87894),f191(x87892))+~P22(f317(f317(f319(x87891),x87894),f317(f287(f857(x87891,x87892),x87891,f244(x87891,x87892)),f317(f166(f857(x87891,x87892)),x87893)))) % 168.22/168.06 [8855]~P93(x88551)+P22(f317(f317(f225(x88551),f317(f317(f122(x88551),x88552),f317(f317(f113(x88551),x88553),x88554))),f317(f317(f113(x88551),f317(f317(f122(x88551),x88552),x88553)),f317(f317(f122(x88551),x88552),x88554)))) % 168.22/168.06 [8856]~P103(x88561)+P22(f317(f317(f225(x88561),f317(f317(f224(x88561),x88562),f317(f317(f223(x88561),x88563),x88564))),f317(f317(f223(x88561),f317(f317(f224(x88561),x88562),x88563)),f317(f317(f224(x88561),x88562),x88564)))) % 168.22/168.06 [9000]E(x90001,x90002)+~P22(f317(f317(f319(f857(x90003,x90003)),f317(f317(f237(x90003,x90003),x90001),x90002)),f317(f166(f857(x90003,x90003)),f317(f317(f175(x90003,x90003),x90004),x90004)))) % 168.22/168.06 [9034]~P22(f317(f317(f319(f857(x90341,x90341)),f317(f317(f237(x90341,x90341),x90343),x90342)),f284(x90341,x90344)))+~P37(x90341,f317(f317(f286(f857(x90341,x90341)),f317(f317(f237(x90341,x90341),x90342),x90343)),x90344)) % 168.22/168.06 [9035]~P22(f317(f317(f319(f857(x90351,x90351)),f317(f317(f237(x90351,x90351),x90353),x90352)),f284(x90351,x90354)))+~P52(x90351,f317(f317(f286(f857(x90351,x90351)),f317(f317(f237(x90351,x90351),x90352),x90353)),x90354)) % 168.22/168.06 [9039]E(x90391,x90392)+E(f317(f130(x90393,f317(f317(f8(a842,a842,x90393),a312),f317(a314,x90391))),f317(f317(f145(x90393),x90392),x90394)),f317(f317(f145(x90393),x90392),f317(f130(x90393,f317(f317(f8(a842,a842,x90393),a312),f317(a314,x90391))),x90394))) % 168.22/168.06 [9081]~P93(x90811)+P22(f317(f317(f225(x90811),f317(f317(f122(x90811),f317(f317(f113(x90811),x90812),x90813)),f317(f317(f113(x90811),x90812),x90814))),f317(f317(f113(x90811),x90812),f317(f317(f122(x90811),x90813),x90814)))) % 168.22/168.06 [9082]~P103(x90821)+P22(f317(f317(f225(x90821),f317(f317(f224(x90821),f317(f317(f223(x90821),x90822),x90823)),f317(f317(f223(x90821),x90822),x90824))),f317(f317(f223(x90821),x90822),f317(f317(f224(x90821),x90823),x90824)))) % 168.22/168.06 [9155]~E(f317(f287(x91552,x91551,x91553),f233(f858(x91552,a842))),f233(f858(x91551,a842)))+P22(f317(f317(f225(f858(x91551,a842)),f317(f88(f858(x91551,a842)),f317(f287(x91552,x91551,x91553),x91554))),f317(f287(x91552,x91551,x91553),f317(f88(f858(x91552,a842)),x91554)))) % 168.22/168.06 [9231]P22(f317(f317(f317(f317(a197,f317(f222(a843),f317(a27,x92311))),x92312),f445(x92313,x92314,x92312,x92311)),x92313))+~P22(f317(f317(f317(f317(a197,f317(a29,x92311)),x92312),x92314),x92313)) % 168.22/168.06 [9474]P22(f317(f317(f319(f857(x94741,x94741)),f317(f317(f237(x94741,x94741),x94742),x94743)),f317(f263(x94741,x94741),f317(f317(f265(x94741,x94741,x94741),x94744),f284(x94741,x94744)))))+~P22(f317(f317(f319(f857(x94741,x94741)),f317(f317(f237(x94741,x94741),x94742),x94743)),f317(f317(f265(x94741,x94741,x94741),f317(f263(x94741,x94741),x94744)),f284(x94741,f317(f263(x94741,x94741),x94744))))) % 168.22/168.06 [9475]~P22(f317(f317(f319(f857(x94751,x94751)),f317(f317(f237(x94751,x94751),x94752),x94753)),f317(f263(x94751,x94751),f317(f317(f265(x94751,x94751,x94751),x94754),f284(x94751,x94754)))))+P22(f317(f317(f319(f857(x94751,x94751)),f317(f317(f237(x94751,x94751),x94752),x94753)),f317(f317(f265(x94751,x94751,x94751),f317(f263(x94751,x94751),x94754)),f284(x94751,f317(f263(x94751,x94751),x94754))))) % 168.22/168.06 [9497]~P22(f317(f317(f319(x94972),x94974),f317(f234(x94971,x94972),x94973)))+P22(f317(f317(f319(f857(x94971,x94972)),f317(f317(f237(x94971,x94972),f554(x94973,x94971,x94974,x94972)),x94974)),x94973)) % 168.22/168.06 [9498]~P22(f317(f317(f319(x94982),x94984),f317(f234(x94981,x94982),x94983)))+P22(f317(f317(f319(f857(x94981,x94982)),f317(f317(f237(x94981,x94982),f555(x94983,x94981,x94984,x94982)),x94984)),x94983)) % 168.22/168.06 [9517]~P22(f317(f317(f319(x95171),x95174),f317(f317(f122(f858(x95171,a842)),x95172),x95173)))+P22(f317(f317(f317(f122(f858(x95171,a842)),f317(f317(f7(x95171,f858(x95171,a842),a842),f319(x95171)),x95172)),f317(f317(f7(x95171,f858(x95171,a842),a842),f319(x95171)),x95173)),x95174)) % 168.22/168.06 [9518]~P22(f317(f317(f319(x95181),x95184),f317(f317(f113(f858(x95181,a842)),x95182),x95183)))+P22(f317(f317(f317(f113(f858(x95181,a842)),f317(f317(f7(x95181,f858(x95181,a842),a842),f319(x95181)),x95182)),f317(f317(f7(x95181,f858(x95181,a842),a842),f319(x95181)),x95183)),x95184)) % 168.22/168.06 [9592]~P22(f317(f317(f319(f857(x95921,x95921)),f317(f317(f237(x95921,x95921),x95924),x95923)),f317(f317(f265(x95921,x95921,x95921),x95922),f284(x95921,x95922))))+P22(f317(f317(f319(f857(x95921,x95921)),f317(f317(f237(x95921,x95921),f771(x95922,x95923,x95924,x95921)),x95923)),x95922)) % 168.22/168.06 [9636]P22(f317(f317(f319(x96361),x96362),f317(f317(f122(f858(x96361,a842)),x96363),x96364)))+~P22(f317(f317(f317(f122(f858(x96361,a842)),f317(f317(f7(x96361,f858(x96361,a842),a842),f319(x96361)),x96363)),f317(f317(f7(x96361,f858(x96361,a842),a842),f319(x96361)),x96364)),x96362)) % 168.22/168.06 [9637]P22(f317(f317(f319(x96371),x96372),f317(f317(f113(f858(x96371,a842)),x96373),x96374)))+~P22(f317(f317(f317(f113(f858(x96371,a842)),f317(f317(f7(x96371,f858(x96371,a842),a842),f319(x96371)),x96373)),f317(f317(f7(x96371,f858(x96371,a842),a842),f319(x96371)),x96374)),x96372)) % 168.22/168.06 [9925]P33(x99251,f317(f317(f7(x99251,f858(f857(x99251,x99251),a842),f858(x99251,a842)),f317(f317(f8(f858(x99251,f858(f858(f857(x99251,x99251),a842),a842)),f858(f858(f857(x99251,x99251),a842),f858(x99251,a842)),x99251),f7(x99251,f858(f857(x99251,x99251),a842),a842)),f317(f317(f8(f858(x99251,f857(x99251,x99251)),f858(x99251,f858(f858(f857(x99251,x99251),a842),a842)),x99251),f317(f8(f857(x99251,x99251),f858(f858(f857(x99251,x99251),a842),a842),x99251),f319(f857(x99251,x99251)))),f237(x99251,x99251)))),x99252),x99253,x99254)+~P22(f317(f317(f319(f857(f850(x99251),f850(x99251))),f317(f317(f237(f850(x99251),f850(x99251)),x99253),x99254)),f152(x99251,x99252))) % 168.22/168.06 [9929]P53(x99291,f317(f317(f7(x99291,f858(f857(x99291,x99291),a842),f858(x99291,a842)),f317(f317(f8(f858(x99291,f858(f858(f857(x99291,x99291),a842),a842)),f858(f858(f857(x99291,x99291),a842),f858(x99291,a842)),x99291),f7(x99291,f858(f857(x99291,x99291),a842),a842)),f317(f317(f8(f858(x99291,f857(x99291,x99291)),f858(x99291,f858(f858(f857(x99291,x99291),a842),a842)),x99291),f317(f8(f857(x99291,x99291),f858(f858(f857(x99291,x99291),a842),a842),x99291),f319(f857(x99291,x99291)))),f237(x99291,x99291)))),x99292),x99293,x99294)+~P22(f317(f317(f319(f857(f858(x99291,a842),f858(x99291,a842))),f317(f317(f237(f858(x99291,a842),f858(x99291,a842)),x99293),x99294)),f309(x99291,x99292))) % 168.22/168.06 [9956]E(x99561,x99562)+~E(f317(f317(f7(x99563,f858(f857(x99563,x99564),a842),f858(x99564,a842)),f317(f317(f8(f858(x99564,f858(f858(f857(x99563,x99564),a842),a842)),f858(f858(f857(x99563,x99564),a842),f858(x99564,a842)),x99563),f7(x99564,f858(f857(x99563,x99564),a842),a842)),f317(f317(f8(f858(x99564,f857(x99563,x99564)),f858(x99564,f858(f858(f857(x99563,x99564),a842),a842)),x99563),f317(f8(f857(x99563,x99564),f858(f858(f857(x99563,x99564),a842),a842),x99564),f319(f857(x99563,x99564)))),f237(x99563,x99564)))),x99561),f317(f317(f7(x99563,f858(f857(x99563,x99564),a842),f858(x99564,a842)),f317(f317(f8(f858(x99564,f858(f858(f857(x99563,x99564),a842),a842)),f858(f858(f857(x99563,x99564),a842),f858(x99564,a842)),x99563),f7(x99564,f858(f857(x99563,x99564),a842),a842)),f317(f317(f8(f858(x99564,f857(x99563,x99564)),f858(x99564,f858(f858(f857(x99563,x99564),a842),a842)),x99563),f317(f8(f857(x99563,x99564),f858(f858(f857(x99563,x99564),a842),a842),x99564),f319(f857(x99563,x99564)))),f237(x99563,x99564)))),x99562)) % 168.22/168.06 [9960]~P33(x99601,f317(f317(f7(x99601,f858(f857(x99601,x99601),a842),f858(x99601,a842)),f317(f317(f8(f858(x99601,f858(f858(f857(x99601,x99601),a842),a842)),f858(f858(f857(x99601,x99601),a842),f858(x99601,a842)),x99601),f7(x99601,f858(f857(x99601,x99601),a842),a842)),f317(f317(f8(f858(x99601,f857(x99601,x99601)),f858(x99601,f858(f858(f857(x99601,x99601),a842),a842)),x99601),f317(f8(f857(x99601,x99601),f858(f858(f857(x99601,x99601),a842),a842),x99601),f319(f857(x99601,x99601)))),f237(x99601,x99601)))),x99604),x99602,x99603)+P22(f317(f317(f319(f857(f850(x99601),f850(x99601))),f317(f317(f237(f850(x99601),f850(x99601)),x99602),x99603)),f152(x99601,x99604))) % 168.22/168.06 [9961]~P53(x99611,f317(f317(f7(x99611,f858(f857(x99611,x99611),a842),f858(x99611,a842)),f317(f317(f8(f858(x99611,f858(f858(f857(x99611,x99611),a842),a842)),f858(f858(f857(x99611,x99611),a842),f858(x99611,a842)),x99611),f7(x99611,f858(f857(x99611,x99611),a842),a842)),f317(f317(f8(f858(x99611,f857(x99611,x99611)),f858(x99611,f858(f858(f857(x99611,x99611),a842),a842)),x99611),f317(f8(f857(x99611,x99611),f858(f858(f857(x99611,x99611),a842),a842),x99611),f319(f857(x99611,x99611)))),f237(x99611,x99611)))),x99614),x99612,x99613)+P22(f317(f317(f319(f857(f858(x99611,a842),f858(x99611,a842))),f317(f317(f237(f858(x99611,a842),f858(x99611,a842)),x99612),x99613)),f309(x99611,x99614))) % 168.22/168.06 [7362]~P90(x73621)+E(f317(f317(f89(x73621),f317(f115(x73621),x73622)),f317(f317(f89(x73621),f317(f115(x73621),x73623)),x73624)),f317(f317(f89(x73621),f317(f115(x73621),f317(f317(f89(a1),x73622),x73623))),x73624)) % 168.22/168.06 [7363]~P90(x73631)+E(f317(f317(f89(x73631),f317(f115(x73631),x73632)),f317(f317(f21(x73631),f317(f115(x73631),x73633)),x73634)),f317(f317(f21(x73631),f317(f115(x73631),f317(f317(f89(a1),x73632),x73633))),x73634)) % 168.22/168.06 [7364]~P90(x73641)+E(f317(f317(f90(x73641),f317(f115(x73641),x73642)),f317(f317(f90(x73641),f317(f115(x73641),x73643)),x73644)),f317(f317(f90(x73641),f317(f115(x73641),f317(f317(f90(a1),x73642),x73643))),x73644)) % 168.22/168.06 [7406]~P110(x74061)+E(f317(f160(x74061),f317(f317(f148(x74062,x74061),f317(f16(x74061,x74062),x74063)),x74064)),f317(f317(f90(x74061),f317(f112(x74061),f317(f189(f850(x74062)),x74064))),x74063)) % 168.22/168.06 [7641]E(f317(f254(x76411,f317(f317(f145(f857(a111,x76411)),x76412),x76413)),x76414),f317(f246(a111,x76411),x76412))+~P22(f317(f317(f226(a111),x76414),f317(f244(a111,x76411),x76412))) % 168.22/168.06 [7686]~P90(x76861)+E(f317(f317(f89(x76861),f317(f115(x76861),x76862)),f317(f317(f21(x76861),x76863),f317(f115(x76861),x76864))),f317(f317(f89(x76861),f317(f115(x76861),f317(f317(f89(a1),x76862),f317(f88(a1),x76864)))),x76863)) % 168.22/168.06 [7810]E(f317(f254(x78101,x78102),f317(f317(f21(a111),x78103),f317(f244(a111,x78101),x78104))),f317(f254(x78101,f317(f317(f145(f857(a111,x78101)),x78104),x78102)),x78103))+P22(f317(f317(f226(a111),x78103),f317(f244(a111,x78101),x78104))) % 168.22/168.06 [8254]~P22(f317(f317(f319(x82541),x82542),f317(f166(x82541),f126(x82541,x82544))))+P22(f317(f317(f319(x82541),x82542),f317(f166(x82541),f126(x82541,f317(f317(f127(x82541),x82543),x82544))))) % 168.22/168.06 [8255]~P22(f317(f317(f319(x82551),x82552),f317(f166(x82551),f126(x82551,x82553))))+P22(f317(f317(f319(x82551),x82552),f317(f166(x82551),f126(x82551,f317(f317(f127(x82551),x82553),x82554))))) % 168.22/168.06 [8275]E(f317(f317(f122(f858(x82751,a842)),f317(f317(f113(f858(x82751,a842)),x82752),x82753)),x82754),f317(f317(f113(f858(x82751,a842)),x82752),f317(f317(f122(f858(x82751,a842)),x82753),x82754)))+~P22(f317(f317(f225(f858(x82751,a842)),x82754),x82752)) % 168.22/168.06 [8582]~E(f317(f317(f122(f858(x85821,a842)),f317(f317(f113(f858(x85821,a842)),x85823),x85824)),x85822),f317(f317(f113(f858(x85821,a842)),x85823),f317(f317(f122(f858(x85821,a842)),x85824),x85822)))+P22(f317(f317(f225(f858(x85821,a842)),x85822),x85823)) % 168.22/168.06 [8862]~P22(f317(f317(f225(f858(x88621,a842)),x88622),f317(f317(f122(f858(x88621,a842)),x88623),x88624)))+P22(f317(f317(f225(f858(x88621,a842)),f317(f317(f21(f858(x88621,a842)),x88622),x88623)),x88624)) % 168.22/168.06 [8923]~P22(f317(f317(f317(f317(a197,f317(a29,x89231)),x89232),f317(a124,x89233)),x89234))+P22(f317(f317(f317(f317(a197,f317(f222(a843),f317(a27,x89231))),x89232),x89233),x89234)) % 168.22/168.06 [8980]P22(f317(f317(f225(f858(x89801,a842)),x89802),f317(f317(f122(f858(x89801,a842)),x89803),x89804)))+~P22(f317(f317(f225(f858(x89801,a842)),f317(f317(f21(f858(x89801,a842)),x89802),x89803)),x89804)) % 168.22/168.06 [9033]P22(f317(f317(f317(f317(a197,f317(a29,x90331)),x90332),f317(a124,x90333)),x90334))+~P22(f317(f317(f317(f317(a197,f317(f222(a843),f317(a27,x90331))),x90332),x90333),x90334)) % 168.22/168.06 [9062]~P79(x90621)+E(f317(f84(x90621),f317(f317(f6(x90622,x90621),f317(f317(f8(x90621,x90621,x90622),f84(x90621)),x90623)),x90624)),f317(f317(f6(x90622,x90621),f317(f317(f8(x90621,x90621,x90622),f84(x90621)),x90623)),x90624)) % 168.22/168.06 [9229]~P79(x92291)+P22(f317(f317(f225(x92291),f2(x92291)),f317(f317(f6(x92292,x92291),f317(f317(f8(x92291,x92291,x92292),f84(x92291)),x92293)),x92294))) % 168.22/168.06 [9234]~P25(x92341)+E(f317(f160(x92341),f317(f317(f148(x92342,x92341),f317(f82(x92341,x92341,x92342,f88(x92341)),x92343)),x92344)),f317(f88(x92341),f317(f160(x92341),f317(f317(f148(x92342,x92341),x92343),x92344)))) % 168.22/168.06 [9367]~P79(x93671)+P22(f317(f317(f225(x93671),f317(f84(x93671),f317(f317(f6(x93672,x93671),x93673),x93674))),f317(f317(f6(x93672,x93671),f317(f317(f8(x93671,x93671,x93672),f84(x93671)),x93673)),x93674))) % 168.22/168.06 [9399]~E(f317(f317(f89(a849),x93991),x93994),f317(f317(f89(a849),x93993),x93992))+P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),f317(f317(f237(a849,a849),x93991),x93992)),f317(f317(f237(a849,a849),x93993),x93994))),a120)) % 168.22/168.06 [9400]~P22(f317(f317(f226(a849),x94001),x94003))+P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),f317(f317(f237(a849,a849),x94001),x94002)),f317(f317(f237(a849,a849),x94003),x94004))),a45)) % 168.22/168.06 [9401]~P22(f317(f317(f226(a849),x94011),x94013))+P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),f317(f317(f237(a849,a849),x94011),x94012)),f317(f317(f237(a849,a849),x94013),x94014))),a79)) % 168.22/168.06 [9542]E(f317(f317(f89(a849),x95421),x95422),f317(f317(f89(a849),x95423),x95424))+~P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),f317(f317(f237(a849,a849),x95421),x95424)),f317(f317(f237(a849,a849),x95423),x95422))),a120)) % 168.22/168.06 [9567]E(f317(f317(f159(x95671),f317(f317(f132(x95671),f317(f189(f850(x95671)),f170(x95671,x95672,x95673))),x95673)),x95674),f317(f317(f159(x95671),x95673),f317(f317(f89(a849),x95674),f317(f189(f850(x95671)),f170(x95671,x95672,x95673)))))+~P22(f317(f317(f226(a849),x95674),f317(f189(f850(x95671)),f317(f317(f132(x95671),f317(f189(f850(x95671)),f170(x95671,x95672,x95673))),x95673)))) % 168.22/168.06 [9583]~P22(f317(f317(f319(x95832),x95834),f317(f317(f51(x95831,f858(x95832,a842)),f233(f858(x95831,a842))),x95833)))+P22(f317(f317(f317(f51(x95831,f858(x95832,a842)),f233(f858(x95831,a842))),f317(f317(f8(f858(x95832,a842),f858(x95832,a842),x95831),f317(f7(x95832,f858(x95832,a842),a842),f319(x95832))),x95833)),x95834)) % 168.22/168.06 [9584]~P22(f317(f317(f319(x95842),x95844),f317(f317(f52(x95841,f858(x95842,a842)),f233(f858(x95841,a842))),x95843)))+P22(f317(f317(f317(f52(x95841,f858(x95842,a842)),f233(f858(x95841,a842))),f317(f317(f8(f858(x95842,a842),f858(x95842,a842),x95841),f317(f7(x95842,f858(x95842,a842),a842),f319(x95842))),x95843)),x95844)) % 168.22/168.06 [9664]~P22(f317(f58(x96641,x96642),f317(f317(f237(a1,a1),x96644),x96643)))+P22(f317(f58(f317(f88(a1),x96641),x96642),f317(f317(f237(a1,a1),f317(f317(f317(f108(a1),f317(f317(a314,x96643),f2(a1))),f317(f88(a1),x96644)),f317(f317(f21(a1),f317(f88(a1),x96644)),f87(a1)))),f317(f317(f317(f108(a1),f317(f317(a314,x96643),f2(a1))),f2(a1)),f317(f317(f21(a1),x96642),x96643))))) % 168.22/168.06 [9673]P22(f317(f317(f319(x96731),x96732),f317(f317(f51(x96733,f858(x96731,a842)),f233(f858(x96733,a842))),x96734)))+~P22(f317(f317(f317(f51(x96733,f858(x96731,a842)),f233(f858(x96733,a842))),f317(f317(f8(f858(x96731,a842),f858(x96731,a842),x96733),f317(f7(x96731,f858(x96731,a842),a842),f319(x96731))),x96734)),x96732)) % 168.22/168.06 [9674]P22(f317(f317(f319(x96741),x96742),f317(f317(f52(x96743,f858(x96741,a842)),f233(f858(x96743,a842))),x96744)))+~P22(f317(f317(f317(f52(x96743,f858(x96741,a842)),f233(f858(x96743,a842))),f317(f317(f8(f858(x96741,a842),f858(x96741,a842),x96743),f317(f7(x96741,f858(x96741,a842),a842),f319(x96741))),x96744)),x96742)) % 168.22/168.06 [9684]E(f317(f317(f51(a849,f858(x96841,a842)),f233(f858(a849,a842))),x96842),f317(f317(f51(a849,f858(x96841,a842)),f233(f858(a849,a842))),x96843))+~E(f317(f317(f51(a849,f858(x96841,a842)),f317(f278(a849,f2(a849)),f502(x96842,x96844,x96843,x96841))),x96843),f317(f317(f51(a849,f858(x96841,a842)),f317(f278(a849,f2(a849)),f317(f317(f89(a849),f502(x96842,x96844,x96843,x96841)),x96844))),x96842)) % 168.22/168.06 [10016]~P22(f317(f317(f225(f858(f857(x100161,x100162),a842)),x100163),x100164))+P22(f317(f317(f225(f858(x100161,f858(x100162,a842))),f317(f317(f7(x100161,f858(f857(x100161,x100162),a842),f858(x100162,a842)),f317(f317(f8(f858(x100162,f858(f858(f857(x100161,x100162),a842),a842)),f858(f858(f857(x100161,x100162),a842),f858(x100162,a842)),x100161),f7(x100162,f858(f857(x100161,x100162),a842),a842)),f317(f317(f8(f858(x100162,f857(x100161,x100162)),f858(x100162,f858(f858(f857(x100161,x100162),a842),a842)),x100161),f317(f8(f857(x100161,x100162),f858(f858(f857(x100161,x100162),a842),a842),x100162),f319(f857(x100161,x100162)))),f237(x100161,x100162)))),x100163)),f317(f317(f7(x100161,f858(f857(x100161,x100162),a842),f858(x100162,a842)),f317(f317(f8(f858(x100162,f858(f858(f857(x100161,x100162),a842),a842)),f858(f858(f857(x100161,x100162),a842),f858(x100162,a842)),x100161),f7(x100162,f858(f857(x100161,x100162),a842),a842)),f317(f317(f8(f858(x100162,f857(x100161,x100162)),f858(x100162,f858(f858(f857(x100161,x100162),a842),a842)),x100161),f317(f8(f857(x100161,x100162),f858(f858(f857(x100161,x100162),a842),a842),x100162),f319(f857(x100161,x100162)))),f237(x100161,x100162)))),x100164))) % 168.22/168.06 [10032]P22(f317(f317(f225(f858(f857(x100321,x100322),a842)),x100323),x100324))+~P22(f317(f317(f225(f858(x100321,f858(x100322,a842))),f317(f317(f7(x100321,f858(f857(x100321,x100322),a842),f858(x100322,a842)),f317(f317(f8(f858(x100322,f858(f858(f857(x100321,x100322),a842),a842)),f858(f858(f857(x100321,x100322),a842),f858(x100322,a842)),x100321),f7(x100322,f858(f857(x100321,x100322),a842),a842)),f317(f317(f8(f858(x100322,f857(x100321,x100322)),f858(x100322,f858(f858(f857(x100321,x100322),a842),a842)),x100321),f317(f8(f857(x100321,x100322),f858(f858(f857(x100321,x100322),a842),a842),x100322),f319(f857(x100321,x100322)))),f237(x100321,x100322)))),x100323)),f317(f317(f7(x100321,f858(f857(x100321,x100322),a842),f858(x100322,a842)),f317(f317(f8(f858(x100322,f858(f858(f857(x100321,x100322),a842),a842)),f858(f858(f857(x100321,x100322),a842),f858(x100322,a842)),x100321),f7(x100322,f858(f857(x100321,x100322),a842),a842)),f317(f317(f8(f858(x100322,f857(x100321,x100322)),f858(x100322,f858(f858(f857(x100321,x100322),a842),a842)),x100321),f317(f8(f857(x100321,x100322),f858(f858(f857(x100321,x100322),a842),a842),x100322),f319(f857(x100321,x100322)))),f237(x100321,x100322)))),x100324))) % 168.22/168.06 [9111]~P22(f317(f317(f319(f857(x91111,x91111)),x91112),f284(x91111,x91114)))+P22(f317(f317(f319(f857(x91111,x91111)),x91112),f284(x91111,f317(f317(f122(f858(f857(x91111,x91111),a842)),x91113),x91114)))) % 168.22/168.06 [9112]~P22(f317(f317(f319(f857(x91121,x91121)),x91122),f284(x91121,x91123)))+P22(f317(f317(f319(f857(x91121,x91121)),x91122),f284(x91121,f317(f317(f122(f858(f857(x91121,x91121),a842)),x91123),x91124)))) % 168.22/168.06 [9465]~E(f317(f166(x94651),x94654),f177(x94651,x94652,x94653))+E(f317(f171(x94651,x94652),f317(f317(f148(x94651,f857(x94651,x94652)),f317(f317(f18(x94651,x94652,f857(x94651,x94652)),f237(x94651,x94652)),f317(f317(f8(f853(x94652),x94652,x94651),f222(x94652)),x94653))),x94654)),x94653) % 168.22/168.06 [9785]~P22(f317(f317(f225(a849),f317(f317(f89(a849),x97851),x97854)),f317(f317(f89(a849),x97853),x97852)))+P22(f317(f317(f225(a1),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x97851),x97852)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x97853),x97854)),f188(f858(f857(a849,a849),a842))))))) % 168.22/168.06 [9786]~P22(f317(f317(f226(a849),f317(f317(f89(a849),x97861),x97864)),f317(f317(f89(a849),x97863),x97862)))+P22(f317(f317(f226(a1),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x97861),x97862)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x97863),x97864)),f188(f858(f857(a849,a849),a842))))))) % 168.22/168.06 [9868]P22(f317(f317(f225(a849),f317(f317(f89(a849),x98681),x98682)),f317(f317(f89(a849),x98683),x98684)))+~P22(f317(f317(f225(a1),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x98681),x98684)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x98683),x98682)),f188(f858(f857(a849,a849),a842))))))) % 168.22/168.06 [9869]P22(f317(f317(f226(a849),f317(f317(f89(a849),x98691),x98692)),f317(f317(f89(a849),x98693),x98694)))+~P22(f317(f317(f226(a1),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x98691),x98694)),f188(f858(f857(a849,a849),a842)))))),f317(a98,f317(f262(f857(a849,a849),f857(a849,a849),a120),f317(f317(f286(f857(a849,a849)),f317(f317(f237(a849,a849),x98693),x98692)),f188(f858(f857(a849,a849),a842))))))) % 168.22/168.06 [9910]P22(f317(f317(f225(f858(x99101,a842)),f317(f317(f51(a849,f858(x99101,a842)),f233(f858(a849,a842))),x99102)),f317(f317(f51(a849,f858(x99101,a842)),f233(f858(a849,a842))),x99103)))+~P22(f317(f317(f225(f858(x99101,a842)),f317(f317(f51(a849,f858(x99101,a842)),f317(f278(a849,f2(a849)),f503(x99103,x99104,x99102,x99101))),x99102)),f317(f317(f51(a849,f858(x99101,a842)),f317(f278(a849,f2(a849)),f317(f317(f89(a849),f503(x99103,x99104,x99102,x99101)),x99104))),x99103))) % 168.22/168.06 [10007]~P22(f317(f317(f319(x100072),x100074),f317(f234(x100071,x100072),x100073)))+P22(f317(f243(x100071,x100072,f317(f317(f7(x100071,f858(f857(x100071,x100072),a842),f858(x100072,a842)),f317(f317(f8(f858(x100072,f858(f858(f857(x100071,x100072),a842),a842)),f858(f858(f857(x100071,x100072),a842),f858(x100072,a842)),x100071),f7(x100072,f858(f857(x100071,x100072),a842),a842)),f317(f317(f8(f858(x100072,f857(x100071,x100072)),f858(x100072,f858(f858(f857(x100071,x100072),a842),a842)),x100071),f317(f8(f857(x100071,x100072),f858(f858(f857(x100071,x100072),a842),a842),x100072),f319(f857(x100071,x100072)))),f237(x100071,x100072)))),x100073)),x100074)) % 168.22/168.06 [10008]~P22(f317(f317(f319(x100081),x100084),f317(f236(x100081,x100082),x100083)))+P22(f317(f242(x100081,x100082,f317(f317(f7(x100081,f858(f857(x100081,x100082),a842),f858(x100082,a842)),f317(f317(f8(f858(x100082,f858(f858(f857(x100081,x100082),a842),a842)),f858(f858(f857(x100081,x100082),a842),f858(x100082,a842)),x100081),f7(x100082,f858(f857(x100081,x100082),a842),a842)),f317(f317(f8(f858(x100082,f857(x100081,x100082)),f858(x100082,f858(f858(f857(x100081,x100082),a842),a842)),x100081),f317(f8(f857(x100081,x100082),f858(f858(f857(x100081,x100082),a842),a842),x100082),f319(f857(x100081,x100082)))),f237(x100081,x100082)))),x100083)),x100084)) % 168.22/168.06 [10019]P22(f317(f317(f319(x100191),x100192),f317(f234(x100193,x100191),x100194)))+~P22(f317(f243(x100193,x100191,f317(f317(f7(x100193,f858(f857(x100193,x100191),a842),f858(x100191,a842)),f317(f317(f8(f858(x100191,f858(f858(f857(x100193,x100191),a842),a842)),f858(f858(f857(x100193,x100191),a842),f858(x100191,a842)),x100193),f7(x100191,f858(f857(x100193,x100191),a842),a842)),f317(f317(f8(f858(x100191,f857(x100193,x100191)),f858(x100191,f858(f858(f857(x100193,x100191),a842),a842)),x100193),f317(f8(f857(x100193,x100191),f858(f858(f857(x100193,x100191),a842),a842),x100191),f319(f857(x100193,x100191)))),f237(x100193,x100191)))),x100194)),x100192)) % 168.22/168.06 [10020]P22(f317(f317(f319(x100201),x100202),f317(f236(x100201,x100203),x100204)))+~P22(f317(f242(x100201,x100203,f317(f317(f7(x100201,f858(f857(x100201,x100203),a842),f858(x100203,a842)),f317(f317(f8(f858(x100203,f858(f858(f857(x100201,x100203),a842),a842)),f858(f858(f857(x100201,x100203),a842),f858(x100203,a842)),x100201),f7(x100203,f858(f857(x100201,x100203),a842),a842)),f317(f317(f8(f858(x100203,f857(x100201,x100203)),f858(x100203,f858(f858(f857(x100201,x100203),a842),a842)),x100201),f317(f8(f857(x100201,x100203),f858(f858(f857(x100201,x100203),a842),a842),x100203),f319(f857(x100201,x100203)))),f237(x100201,x100203)))),x100204)),x100202)) % 168.22/168.06 [9694]P22(f317(f154(x96941,x96942),x96943))+~P22(f317(f154(x96941,f317(f317(f18(x96941,a842,a842),f317(f317(f8(a842,f858(a842,a842),x96941),a315),x96944)),x96942)),x96943)) % 168.22/168.06 [9695]P22(f317(f154(x96951,x96952),x96953))+~P22(f317(f154(x96951,f317(f317(f18(x96951,a842,a842),f317(f317(f8(a842,f858(a842,a842),x96951),a315),x96952)),x96954)),x96953)) % 168.22/168.06 [9788]~P84(x97881)+E(f317(f317(f90(x97881),f317(f317(f89(x97881),f87(x97881)),f87(x97881))),f317(f317(f6(a849,x97881),f317(f317(f8(x97881,x97881,a849),f317(f89(x97881),x97882)),f317(f317(f7(a849,x97881,x97881),f317(f317(f8(x97881,f858(x97881,x97881),a849),f90(x97881)),f112(x97881))),x97883))),f317(f231(a849),x97884))),f317(f317(f90(x97881),f317(f112(x97881),x97884)),f317(f317(f89(x97881),x97882),f317(f317(f89(x97881),x97882),f317(f317(f90(x97881),f317(f112(x97881),f317(f317(f21(a849),x97884),f87(a849)))),x97883))))) % 168.22/168.06 [9932]P22(f317(x99321,f564(x99322,x99323,x99324,x99321)))+P37(x99322,f317(f230(f857(x99322,x99322)),f317(f247(x99322,x99322,a842),f317(f317(f8(f858(x99322,a842),f858(x99322,a842),x99322),f317(f18(x99322,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99322),a315),x99321))),f317(f317(f7(x99322,f858(x99322,x99322),f858(x99322,a842)),f317(f317(f8(f858(x99322,a842),f858(f858(x99322,x99322),f858(x99322,a842)),x99322),f8(x99322,a842,x99322)),a314)),x99323))))) % 168.22/168.06 [9946]~P22(f317(f317(f226(a849),f317(x99464,f317(x99463,f564(x99461,x99463,x99464,x99462)))),f317(x99464,f564(x99461,x99463,x99464,x99462))))+P37(x99461,f317(f230(f857(x99461,x99461)),f317(f247(x99461,x99461,a842),f317(f317(f8(f858(x99461,a842),f858(x99461,a842),x99461),f317(f18(x99461,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99461),a315),x99462))),f317(f317(f7(x99461,f858(x99461,x99461),f858(x99461,a842)),f317(f317(f8(f858(x99461,a842),f858(f858(x99461,x99461),f858(x99461,a842)),x99461),f8(x99461,a842,x99461)),a314)),x99463))))) % 168.22/168.06 [10045]~P22(f317(f317(f319(f857(x100451,x100451)),f317(f317(f237(x100451,x100451),x100453),x100454)),f317(f317(f122(f858(f857(x100451,x100451),a842)),x100452),f284(x100451,f188(f858(f857(x100451,x100451),a842))))))+P22(f317(f317(f317(f317(f122(f858(x100451,f858(x100451,a842))),f317(f317(f7(x100451,f858(f857(x100451,x100451),a842),f858(x100451,a842)),f317(f317(f8(f858(x100451,f858(f858(f857(x100451,x100451),a842),a842)),f858(f858(f857(x100451,x100451),a842),f858(x100451,a842)),x100451),f7(x100451,f858(f857(x100451,x100451),a842),a842)),f317(f317(f8(f858(x100451,f857(x100451,x100451)),f858(x100451,f858(f858(f857(x100451,x100451),a842),a842)),x100451),f317(f8(f857(x100451,x100451),f858(f858(f857(x100451,x100451),a842),a842),x100451),f319(f857(x100451,x100451)))),f237(x100451,x100451)))),x100452)),a314),x100453),x100454)) % 168.22/168.06 [10054]P22(f317(f317(f319(f857(x100541,x100541)),f317(f317(f237(x100541,x100541),x100542),x100543)),f317(f317(f122(f858(f857(x100541,x100541),a842)),x100544),f284(x100541,f188(f858(f857(x100541,x100541),a842))))))+~P22(f317(f317(f317(f317(f122(f858(x100541,f858(x100541,a842))),f317(f317(f7(x100541,f858(f857(x100541,x100541),a842),f858(x100541,a842)),f317(f317(f8(f858(x100541,f858(f858(f857(x100541,x100541),a842),a842)),f858(f858(f857(x100541,x100541),a842),f858(x100541,a842)),x100541),f7(x100541,f858(f857(x100541,x100541),a842),a842)),f317(f317(f8(f858(x100541,f857(x100541,x100541)),f858(x100541,f858(f858(f857(x100541,x100541),a842),a842)),x100541),f317(f8(f857(x100541,x100541),f858(f858(f857(x100541,x100541),a842),a842),x100541),f319(f857(x100541,x100541)))),f237(x100541,x100541)))),x100544)),a314),x100542),x100543)) % 168.22/168.06 [9918]~P102(x99183)+E(f99(x99181,f317(f317(f18(x99181,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99181),a315),x99182)),f317(f317(f8(f858(x99181,a842),a842,x99181),f97(x99181)),f317(f317(f8(f858(x99181,a842),f858(x99181,a842),x99181),f317(f18(x99181,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99181),a320),x99182))),f317(f317(f8(x99183,f858(x99181,a842),x99181),f317(f7(x99181,x99183,a842),f317(f317(f8(x99183,f858(x99183,a842),x99181),f225(x99183)),x99184))),x99184))))),f317(f101(x99181,x99183,x99184),x99182)) % 168.22/168.06 [9959]~P102(x99593)+E(f99(x99591,f317(f317(f18(x99591,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99591),a315),x99592)),f317(f317(f8(f858(x99591,a842),a842,x99591),f97(x99591)),f317(f317(f8(f858(x99591,a842),f858(x99591,a842),x99591),f317(f18(x99591,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99591),a320),x99592))),f317(f317(f7(x99591,f858(x99591,x99593),f858(x99591,a842)),f317(f317(f8(f858(x99593,a842),f858(f858(x99591,x99593),f858(x99591,a842)),x99591),f8(x99593,a842,x99591)),f317(f317(f8(x99593,f858(x99593,a842),x99591),f225(x99593)),x99594))),x99594))))),f104(x99591,x99593,x99594,x99592)) % 168.22/168.06 [10005]E(f317(f317(f145(f850(x100051)),f317(f317(f145(x100051),x100052),f317(f136(f850(x100051),f850(x100051),f127(x100051),f125(x100051)),f317(f317(f148(f850(x100051),f850(x100051)),f150(f850(x100051),x100051,f125(x100051),f317(f317(f8(f850(x100051),f858(f850(x100051),f850(x100051)),x100051),f16(f850(x100051),f850(x100051))),f317(f317(f7(x100051,f850(x100051),f850(x100051)),f145(x100051)),f125(x100051))))),x100053)))),f173(x100051,f317(f317(f145(f850(x100051)),x100054),f317(f136(f850(f850(x100051)),f850(f850(x100051)),f127(f850(x100051)),f125(f850(x100051))),f317(f317(f148(f850(x100051),f850(f850(x100051))),f150(f850(f850(x100051)),x100051,f125(f850(x100051)),f317(f16(f858(f850(x100051),f850(f850(x100051))),x100051),f317(f317(f7(f850(x100051),f850(f850(x100051)),f850(f850(x100051))),f145(f850(x100051))),f125(f850(x100051)))))),x100053))))),f173(x100051,f317(f317(f145(f850(x100051)),f317(f317(f145(x100051),x100052),x100054)),x100053)))+~P22(f317(f305(f850(f850(x100051)),f174(x100051)),f317(f317(f145(f850(x100051)),f317(f317(f145(x100051),x100052),x100054)),x100053))) % 168.22/168.06 [10044]~P22(f317(f71(x100442),f317(f230(x100442),x100444)))+P22(f317(f71(x100441),f317(f230(x100441),f317(f317(f8(f858(x100442,a842),a842,x100441),f96(x100442)),f317(f317(f7(x100441,f858(x100442,a842),f858(x100442,a842)),f317(f317(f8(f858(x100442,f858(a842,a842)),f858(f858(x100442,a842),f858(x100442,a842)),x100441),f18(x100442,a842,a842)),f317(f317(f8(f858(x100442,a842),f858(x100442,f858(a842,a842)),x100441),f317(f8(a842,f858(a842,a842),x100442),a315)),f317(f317(f7(x100441,f858(x100442,x100441),f858(x100442,a842)),f317(f317(f8(f858(x100441,a842),f858(f858(x100442,x100441),f858(x100442,a842)),x100441),f8(x100441,a842,x100442)),a314)),x100443)))),x100444))))) % 168.22/168.06 [7141]E(x71411,x71412)+~E(f300(x71413,x71414,x71415,x71411),f300(x71413,x71414,x71415,x71412)) % 168.22/168.06 [7142]E(x71421,x71422)+~E(f301(x71423,x71424,x71425,x71421),f301(x71423,x71424,x71425,x71422)) % 168.22/168.06 [8145]P32(x81451,x81452,x81453,x81454)+~P32(x81451,x81452,f178(x81451,x81452,x81455,x81453),x81454) % 168.22/168.06 [5573]E(f317(f317(f286(x55731),x55732),f177(x55731,x55733,x55734)),f177(x55731,x55733,x55734))+~E(f317(x55734,x55732),f317(f217(x55733),x55735)) % 168.22/168.06 [5963]P22(f317(f243(x59631,x59632,x59633),x59634))+~P22(f317(f317(x59633,x59635),x59634)) % 168.22/168.06 [5965]P22(f317(f242(x59651,x59652,x59653),x59654))+~P22(f317(f317(x59653,x59654),x59655)) % 168.22/168.06 [5968]~E(f317(x59684,x59682),f317(f217(x59683),x59685))+P22(f317(f317(f319(x59681),x59682),f177(x59681,x59683,x59684))) % 168.22/168.06 [5969]~E(f317(x59694,x59695),f317(f217(x59691),x59692))+P22(f317(f317(f319(x59691),x59692),f179(x59693,x59691,x59694))) % 168.22/168.06 [6558]~E(x65583,f2(a111))+E(f317(f257(x65581,x65582,x65583,x65584),x65585),f317(f237(x65581,x65582),x65585)) % 168.22/168.06 [6630]~E(f317(x66304,x66305),f191(x66302))+E(f317(f220(f853(x66301),x66302,f191(x66301),x66303),f317(x66304,x66305)),f191(x66301)) % 168.22/168.06 [7246]E(f317(x72461,x72462),f191(x72463))+~E(f317(f178(x72464,x72463,x72465,x72461),x72462),f191(x72463)) % 168.22/168.06 [7247]E(f317(x72471,x72472),f191(x72473))+~E(f317(f178(x72474,x72473,x72471,x72475),x72472),f191(x72473)) % 168.22/168.06 [7282]E(f317(f178(x72821,x72822,x72823,x72824),x72825),f317(x72823,x72825))+P22(f317(f317(f319(x72821),x72825),f177(x72821,x72822,x72824))) % 168.22/168.06 [7283]E(f317(f178(x72831,x72832,x72833,x72834),x72835),f317(x72834,x72835))+P22(f317(f317(f319(x72831),x72835),f177(x72831,x72832,x72833))) % 168.22/168.06 [7598]~P15(x75984,x75981,x75982,x75985)+E(f317(f82(x75981,x75981,x75981,f317(x75982,x75983)),f317(x75982,x75983)),f317(x75982,x75983)) % 168.22/168.06 [7646]E(f317(f178(x76461,x76462,x76463,x76464),x76465),f317(x76464,x76465))+~P22(f317(f317(f319(x76461),x76465),f177(x76461,x76462,x76464))) % 168.22/168.06 [8317]P22(f317(f317(f319(f857(x83171,x83171)),f317(f317(f237(x83171,x83171),x83172),x83173)),f311(x83171,x83174,x83175)))+~P22(f317(f317(f226(a849),f317(x83174,x83172)),f317(x83174,x83173))) % 168.22/168.06 [8420]~P22(f317(f317(f319(x84204),x84203),f275(x84204,x84201,x84202,x84205)))+P22(f317(f317(x84201,x84202),x84203)) % 168.22/168.06 [8421]~P22(f317(f317(f319(x84214),x84213),f272(x84214,x84211,x84212,x84215)))+P22(f317(f317(x84211,x84212),x84213)) % 168.22/168.06 [8422]~P22(f317(f317(f319(x84224),x84222),f275(x84224,x84221,x84225,x84223)))+P22(f317(f317(x84221,x84222),x84223)) % 168.22/168.06 [8423]~P22(f317(f317(f319(x84234),x84232),f272(x84234,x84231,x84235,x84233)))+P22(f317(f317(x84231,x84232),x84233)) % 168.22/168.06 [8559]~P51(x85592,x85591,x85595,x85593,x85594)+E(f317(f287(x85591,x85592,x85593),x85594),f233(f858(x85592,a842))) % 168.22/168.06 [8991]~P35(x89911,x89912,x89913,x89914,x89915)+P35(x89911,x89912,x89913,f317(f163(x89911),x89914),f317(f163(x89912),x89915)) % 168.22/168.06 [8993]~P35(x89931,x89932,x89933,f317(f163(x89931),x89934),x89935)+P35(x89931,x89932,x89933,x89934,f317(f163(x89932),x89935)) % 168.22/168.06 [8994]~P35(x89941,x89942,x89943,x89944,f317(f163(x89942),x89945))+P35(x89941,x89942,x89943,f317(f163(x89941),x89944),x89945) % 168.22/168.06 [8999]P35(x89991,x89992,x89993,x89994,x89995)+~P35(x89991,x89992,x89993,f317(f163(x89991),x89994),f317(f163(x89992),x89995)) % 168.22/168.06 [9392]P22(f317(f317(f319(f857(f850(x93921),f850(x93921))),f317(f317(f237(f850(x93921),f850(x93921)),f317(f317(f145(x93921),x93922),x93923)),f317(f317(f145(x93921),x93922),x93924))),f151(x93921,x93925)))+~P22(f317(f317(f319(f857(f850(x93921),f850(x93921))),f317(f317(f237(f850(x93921),f850(x93921)),x93923),x93924)),f151(x93921,x93925))) % 168.22/168.06 [9393]P22(f317(f317(f319(f857(f850(x93931),f850(x93931))),f317(f317(f237(f850(x93931),f850(x93931)),f317(f317(f127(x93931),x93932),x93933)),f317(f317(f127(x93931),x93932),x93934))),f141(x93931,x93935)))+~P22(f317(f317(f319(f857(f850(x93931),f850(x93931))),f317(f317(f237(f850(x93931),f850(x93931)),x93933),x93934)),f141(x93931,x93935))) % 168.22/168.06 [9572]E(f317(f317(f145(x95721),f589(x95722,x95723,x95724,x95725,x95721)),f593(x95722,x95723,x95724,x95725,x95721)),x95725)+~P22(f317(f317(f319(f857(f850(x95721),f850(x95721))),f317(f317(f237(f850(x95721),f850(x95721)),x95725),f317(f317(f145(x95721),x95724),x95723))),f152(x95721,x95722))) % 168.22/168.06 [9595]E(f317(f317(f145(x95951),f590(x95952,x95953,x95954,x95955,x95951)),f592(x95952,x95953,x95954,x95955,x95951)),x95953)+~P22(f317(f317(f319(f857(f850(x95951),f850(x95951))),f317(f317(f237(f850(x95951),f850(x95951)),f317(f317(f145(x95951),x95955),x95954)),x95953)),f152(x95951,x95952))) % 168.22/168.06 [9757]~P22(f317(f317(f319(f857(f850(x97571),f850(x97571))),f317(f317(f237(f850(x97571),f850(x97571)),f317(f317(f145(x97571),x97575),x97572)),x97574)),f152(x97571,x97573)))+P22(f317(f317(f319(f857(f850(x97571),f850(x97571))),f317(f317(f237(f850(x97571),f850(x97571)),x97572),f592(x97573,x97574,x97572,x97575,x97571))),f152(x97571,x97573))) % 168.22/168.06 [9832]~P22(f317(f317(f319(f857(f850(x98321),f850(x98321))),f317(f317(f237(f850(x98321),f850(x98321)),x98325),f317(f317(f145(x98321),x98324),x98323))),f152(x98321,x98322)))+P22(f317(f317(f319(f857(f850(x98321),f850(x98321))),f317(f317(f237(f850(x98321),f850(x98321)),f593(x98322,x98323,x98324,x98325,x98321)),x98323)),f152(x98321,x98322))) % 168.22/168.06 [9999]P22(f317(f317(f319(f857(x99991,x99991)),f317(f317(f237(x99991,x99991),f317(x99992,f317(f317(f89(a849),x99993),x99994))),f317(x99992,x99993))),f284(x99991,x99995)))+~P22(f317(f317(f319(f857(x99991,x99991)),f317(f317(f237(x99991,x99991),f317(x99992,f317(a124,f751(x99994,x99993,x99995,x99992,x99991)))),f317(x99992,f751(x99994,x99993,x99995,x99992,x99991)))),f284(x99991,x99995))) % 168.22/168.06 [10022]E(x100221,f2(a111))+E(f317(f220(f857(f850(x100222),x100223),f857(x100222,x100223),f317(f317(f237(f850(x100222),x100223),f125(x100222)),x100224),f317(f247(x100222,x100223,f857(f850(x100222),x100223)),f317(f317(f7(x100222,f858(x100223,f857(f850(x100222),x100223)),f858(x100223,f857(f850(x100222),x100223))),f317(f317(f8(f858(f857(f850(x100222),x100223),f857(f850(x100222),x100223)),f858(f858(x100223,f857(f850(x100222),x100223)),f858(x100223,f857(f850(x100222),x100223))),x100222),f8(f857(f850(x100222),x100223),f857(f850(x100222),x100223),x100223)),f317(f317(f8(f858(f850(x100222),f858(x100223,f857(f850(x100222),x100223))),f858(f857(f850(x100222),x100223),f857(f850(x100222),x100223)),x100222),f247(f850(x100222),x100223,f857(f850(x100222),x100223))),f317(f317(f8(f858(f850(x100222),f850(x100222)),f858(f850(x100222),f858(x100223,f857(f850(x100222),x100223))),x100222),f317(f8(f850(x100222),f858(x100223,f857(f850(x100222),x100223)),f850(x100222)),f237(f850(x100222),x100223))),f145(x100222))))),f129(x100223,x100222,x100225,f317(f317(f21(a111),x100221),f87(a111)))))),f317(x100225,x100224)),f317(f129(x100223,x100222,x100225,x100221),x100224)) % 168.22/168.06 [5163]E(x51631,x51632)+~E(f317(f317(f145(x51633),x51634),x51631),f317(f317(f145(x51633),x51635),x51632)) % 168.22/168.06 [5164]E(x51641,x51642)+~E(f317(f317(f145(x51643),x51641),x51644),f317(f317(f145(x51643),x51642),x51645)) % 168.22/168.06 [5214]P22(f317(x52141,x52142))+~E(f317(f130(x52143,x52141),x52144),f317(f317(f145(x52143),x52142),x52145)) % 168.22/168.06 [5215]P22(f317(x52151,x52152))+~E(f317(f317(f145(x52153),x52152),x52154),f317(f130(x52153,x52151),x52155)) % 168.22/168.06 [5363]~E(f317(f317(f132(x53631),x53633),x53632),f317(f317(f145(x53631),x53634),x53635))+E(f317(f317(f159(x53631),x53632),x53633),x53634) % 168.22/168.06 [5497]~P11(x54974,x54975,x54971)+E(f317(f317(x54971,x54972),f317(f317(x54971,x54972),x54973)),f317(f317(x54971,x54972),x54973)) % 168.22/168.06 [6086]~P103(x60862)+~E(f317(f317(f143(x60861,x60862,x60863),x60864),x60865),f125(x60861)) % 168.22/168.06 [6463]E(x64631,x64632)+~E(f317(f317(f127(x64633),x64634),f317(f317(f145(x64633),x64631),f125(x64633))),f317(f317(f127(x64633),x64635),f317(f317(f145(x64633),x64632),f125(x64633)))) % 168.22/168.06 [6464]E(x64641,x64642)+~E(f317(f317(f127(x64643),x64641),f317(f317(f145(x64643),x64644),f125(x64643))),f317(f317(f127(x64643),x64642),f317(f317(f145(x64643),x64645),f125(x64643)))) % 168.22/168.06 [6709]E(f317(f181(x67091,x67092,x67093,x67094),x67095),f191(x67092))+P22(f317(f317(f319(x67091),x67095),x67094)) % 168.22/168.06 [6768]E(f317(f317(f286(x67681),f317(x67682,x67683)),f317(f287(x67684,x67681,x67682),x67685)),f317(f287(x67684,x67681,x67682),x67685))+~P22(f317(f317(f319(x67684),x67683),x67685)) % 168.22/168.06 [6775]~P22(f317(x67754,f317(x67753,x67755)))+P22(f317(f317(f289(x67751,x67752,x67753),x67754),x67755)) % 168.22/168.06 [6779]~E(x67794,f2(a111))+E(f317(f129(x67791,x67792,x67793,x67794),x67795),f317(f317(f237(f850(x67792),x67791),f125(x67792)),x67795)) % 168.22/168.06 [6872]~E(f317(f287(x68721,x68722,x68723),x68724),x68725)+E(f317(f287(f858(x68721,a842),f858(x68722,a842),f287(x68721,x68722,x68723)),f317(f285(x68721),x68724)),f317(f285(x68722),x68725)) % 168.22/168.06 [6909]E(f317(f181(x69091,x69092,x69093,x69094),x69095),f317(x69093,x69095))+~P22(f317(f317(f319(x69091),x69095),x69094)) % 168.22/168.06 [7202]P19(x72021,x72022,x72023,x72024)+~P19(x72021,x72022,x72023,f317(f317(f286(x72021),x72025),x72024)) % 168.22/168.06 [7271]P22(f317(x72711,x72712))+~P22(f317(f317(f103(x72713,x72714,x72711),x72715),x72712)) % 168.22/168.06 [7314]~P22(f317(f317(f319(x73144),x73143),x73145))+P22(f317(f317(f319(x73141),f317(x73142,x73143)),f317(f287(x73144,x73141,x73142),x73145))) % 168.22/168.06 [7337]~P103(x73372)+E(f142(x73371,x73372,x73373,f317(f130(x73371,x73374),x73375)),f317(f130(x73371,x73374),f142(x73371,x73372,x73373,x73375))) % 168.22/168.06 [7371]P22(f317(x73711,f317(x73712,x73713)))+~P22(f317(f317(f289(x73714,x73715,x73712),x73711),x73713)) % 168.22/168.06 [7372]P22(f317(f317(x73721,x73722),x73723))+~P22(f317(f317(f103(x73724,x73721,x73725),x73722),x73723)) % 168.22/168.06 [7435]~P22(f317(f317(f319(x74353),f317(x74354,x74352)),x74355))+P22(f317(f317(f319(x74351),x74352),f317(f289(x74351,x74353,x74354),x74355))) % 168.22/168.06 [7824]~P22(f317(f317(f319(x78245),x78243),f317(f289(x78245,x78241,x78242),x78244)))+P22(f317(f317(f319(x78241),f317(x78242,x78243)),x78244)) % 168.22/168.06 [8051]~E(x80513,f317(f317(f317(f81(x80511,f853(x80512)),f317(f16(f853(x80512),x80511),f191(x80512))),x80514),f317(f217(x80512),x80515)))+E(f177(x80511,x80512,x80513),f317(f317(f286(x80511),x80514),f188(f858(x80511,a842)))) % 168.22/168.06 [8150]E(f317(x81501,f790(x81502,x81501,x81503,x81504)),x81504)+~P22(f317(f317(f319(x81505),x81504),f317(f287(x81503,x81505,x81501),x81502))) % 168.22/168.06 [8405]P22(f317(f317(f319(f856(x84051,x84052)),f317(f297(x84052,x84051),x84053)),f298(x84051,x84052,x84054,x84055)))+~P22(f317(f317(f319(x84052),x84053),x84055)) % 168.22/168.06 [8406]P22(f317(f317(f319(f856(x84061,x84062)),f317(f288(x84061,x84062),x84063)),f298(x84061,x84062,x84064,x84065)))+~P22(f317(f317(f319(x84061),x84063),x84064)) % 168.22/168.06 [8469]~E(x84692,f317(f317(f145(x84691),x84694),x84695))+P22(f317(f317(f319(f857(f850(x84691),f850(x84691))),f317(f317(f237(f850(x84691),f850(x84691)),f125(x84691)),x84692)),f141(x84691,x84693))) % 168.22/168.06 [8519]~P35(x85191,x85193,x85195,x85192,x85194)+E(f317(f189(f850(x85191)),x85192),f317(f189(f850(x85193)),x85194)) % 168.22/168.06 [8529]P22(f317(f317(f225(f858(x85291,a842)),f317(f317(f52(x85292,f858(x85291,a842)),x85293),x85294)),f317(x85294,x85295)))+~P22(f317(f317(f319(x85292),x85295),x85293)) % 168.22/168.06 [8575]~P51(x85751,x85752,x85753,x85755,x85754)+E(f317(f287(x85751,x85752,x85753),f233(f858(x85751,a842))),x85754) % 168.22/168.06 [8776]E(f317(f317(f317(f81(x87761,f853(x87762)),f181(x87761,x87762,x87763,x87764)),x87765),f191(x87762)),f181(x87761,x87762,x87763,x87764))+P22(f317(f317(f319(x87761),x87765),x87764)) % 168.22/168.06 [8778]E(f317(f130(x87781,x87782),f723(x87783,x87784,x87785,x87782,x87781)),x87783)+~E(f317(f130(x87781,x87782),x87785),f317(f317(f145(x87781),x87784),x87783)) % 168.22/168.06 [8779]E(f317(f130(x87791,x87792),f726(x87793,x87792,x87794,x87795,x87791)),x87794)+~E(f317(f317(f145(x87791),x87795),x87794),f317(f130(x87791,x87792),x87793)) % 168.22/168.06 [8782]E(f317(x87821,f779(x87822,x87823,x87821,x87824,x87825)),x87822)+~E(f317(f317(f192(x87825,x87824),x87821),x87823),f317(f217(x87824),x87822)) % 168.22/168.06 [8786]E(f317(f217(x87861),f779(x87862,x87863,x87864,x87865,x87861)),x87863)+~E(f317(f317(f192(x87861,x87865),x87864),x87863),f317(f217(x87865),x87862)) % 168.22/168.06 [8886]E(f317(f189(f850(x88861)),x88862),x88863)+~P22(f317(f317(f319(f857(f850(x88861),f850(x88861))),f317(f317(f237(f850(x88861),f850(x88861)),x88864),x88862)),f317(f137(x88861,x88865),x88863))) % 168.22/168.06 [8887]E(f317(f189(f850(x88871)),x88872),x88873)+~P22(f317(f317(f319(f857(f850(x88871),f850(x88871))),f317(f317(f237(f850(x88871),f850(x88871)),x88872),x88874)),f317(f137(x88871,x88875),x88873))) % 168.22/168.06 [8953]P22(f317(f317(f319(x89531),f790(x89532,x89533,x89531,x89534)),x89532))+~P22(f317(f317(f319(x89535),x89534),f317(f287(x89531,x89535,x89533),x89532))) % 168.22/168.06 [9109]E(f317(f287(x91091,x91092,x91093),f791(x91094,x91093,x91091,x91095,x91092)),x91095)+~P22(f317(f317(f225(f858(x91092,a842)),x91095),f317(f287(x91091,x91092,x91093),x91094))) % 168.22/168.06 [9357]E(f317(x93571,f701(x93572,x93571,x93573,x93574,x93575)),f317(f217(x93575),x93574))+~P22(f317(f317(f319(x93575),x93574),f179(x93573,x93575,f181(x93573,x93575,x93571,x93572)))) % 168.22/168.06 [9407]P22(f317(f317(f319(f857(f850(x94071),f850(x94071))),f317(f317(f237(f850(x94071),f850(x94071)),f317(f317(f145(x94071),x94072),x94073)),f317(f317(f145(x94071),x94072),x94074))),f284(f850(x94071),f151(x94071,x94075))))+~P22(f317(f317(f319(f857(f850(x94071),f850(x94071))),f317(f317(f237(f850(x94071),f850(x94071)),x94073),x94074)),f284(f850(x94071),f151(x94071,x94075)))) % 168.22/168.06 [9437]~E(f317(x94373,f583(x94375,x94374,x94373,x94372,x94371)),f317(x94375,f583(x94375,x94374,x94373,x94372,x94371)))+E(f317(f317(f148(x94371,x94372),x94373),x94374),f317(f317(f148(x94371,x94372),x94375),x94374)) % 168.22/168.06 [9512]~E(f317(f130(x95121,x95125),x95124),f317(f317(f145(x95121),x95123),x95122))+E(f317(f317(f127(x95121),f724(x95122,x95123,x95124,x95125,x95121)),f317(f317(f145(x95121),x95123),f723(x95122,x95123,x95124,x95125,x95121))),x95124) % 168.22/168.06 [9513]~E(f317(f317(f145(x95131),x95135),x95134),f317(f130(x95131,x95133),x95132))+E(f317(f317(f127(x95131),f727(x95132,x95133,x95134,x95135,x95131)),f317(f317(f145(x95131),x95135),f726(x95132,x95133,x95134,x95135,x95131))),x95132) % 168.22/168.06 [9514]E(f317(f317(f148(x95141,x95142),x95143),x95144),f317(f317(f148(x95141,x95142),x95145),x95144))+P22(f317(f317(f319(x95141),f583(x95143,x95144,x95145,x95142,x95141)),f317(f166(x95141),x95144))) % 168.22/168.06 [9543]~P22(f317(f317(f319(x95435),x95434),f317(f262(x95431,x95435,x95433),x95432)))+P22(f317(f317(f319(x95431),f355(x95432,x95433,x95431,x95434,x95435)),x95432)) % 168.22/168.06 [9544]~P22(f317(f317(f319(x95445),x95444),f317(f262(x95441,x95445,x95443),x95442)))+P22(f317(f317(f319(x95441),f411(x95442,x95443,x95441,x95444,x95445)),x95442)) % 168.22/168.06 [9568]~P22(f317(f317(f225(f858(x95685,a842)),x95684),f317(f287(x95681,x95685,x95683),x95682)))+P22(f317(f317(f225(f858(x95681,a842)),f791(x95682,x95683,x95681,x95684,x95685)),x95682)) % 168.22/168.06 [9618]~P22(f317(f317(f319(x96185),x96184),f179(x96181,x96185,f181(x96181,x96185,x96183,x96182))))+P22(f317(f317(f319(x96181),f701(x96182,x96183,x96181,x96184,x96185)),x96182)) % 168.22/168.06 [5377]~E(f317(x53773,x53774),x53775)+E(f317(f317(f317(f81(x53771,x53772),x53773),x53774),x53775),x53773) % 168.22/168.06 [5809]E(f317(x58091,x58092),x58093)+~E(f317(f317(f317(f81(x58094,x58095),x58091),x58092),x58093),x58091) % 168.22/168.06 [5905]E(x59051,x59052)+~E(f317(f246(x59053,x59054),f317(f317(f237(x59053,x59054),x59055),x59051)),x59052) % 168.22/168.06 [5906]E(x59061,x59062)+~E(f317(f244(x59063,x59064),f317(f317(f237(x59063,x59064),x59061),x59065)),x59062) % 168.22/168.06 [6162]~E(x61623,f317(f317(f127(x61621),x61624),f317(f317(f145(x61621),x61622),x61625)))+P22(f317(f317(f319(x61621),x61622),f317(f166(x61621),x61623))) % 168.22/168.06 [6546]E(f317(f287(x65461,x65462,f317(f16(x65462,x65461),x65463)),x65464),f317(f317(f286(x65462),x65463),f188(f858(x65462,a842))))+~P22(f317(f317(f319(x65461),x65465),x65464)) % 168.22/168.06 [6613]E(f317(f317(f122(f858(x66131,a842)),f317(f166(x66131),x66132)),f317(f166(x66131),x66133)),f317(f166(x66131),x66134))+~E(f161(x66131,x66135,x66134),f317(f317(f237(f850(x66131),f850(x66131)),x66132),x66133)) % 168.22/168.06 [6713]~P103(x67132)+E(f317(f189(f850(x67131)),f317(f317(f143(x67131,x67132,x67133),x67134),x67135)),f317(a124,f317(f189(f850(x67131)),x67135))) % 168.22/168.06 [6722]~P103(x67222)+E(f317(f166(x67221),f317(f317(f143(x67221,x67222,x67223),x67224),x67225)),f317(f317(f286(x67221),x67224),f317(f166(x67221),x67225))) % 168.22/168.06 [7001]~P84(x70011)+E(f317(f317(f89(x70011),f317(f317(f89(x70011),x70012),x70013)),f317(f317(f89(x70011),x70014),x70015)),f317(f317(f89(x70011),f317(f317(f89(x70011),x70012),x70014)),f317(f317(f89(x70011),x70013),x70015))) % 168.22/168.06 [7002]~P84(x70021)+E(f317(f317(f90(x70021),f317(f317(f90(x70021),x70022),x70023)),f317(f317(f90(x70021),x70024),x70025)),f317(f317(f90(x70021),f317(f317(f90(x70021),x70022),x70024)),f317(f317(f90(x70021),x70023),x70025))) % 168.22/168.06 [7003]~P58(x70031)+E(f317(f317(f266(x70031),f317(f317(f90(x70031),x70032),x70033)),f317(f317(f90(x70031),x70034),x70035)),f317(f317(f90(x70031),f317(f317(f266(x70031),x70032),x70034)),f317(f317(f266(x70031),x70033),x70035))) % 168.22/168.06 [7015]~P103(x70151)+E(f282(x70151,f317(f317(f224(x70151),x70152),x70153),f317(f317(f223(x70151),x70154),x70155)),f317(f317(f113(f858(x70151,a842)),f282(x70151,x70152,x70154)),f282(x70151,x70153,x70155))) % 168.22/168.06 [7016]~P103(x70161)+E(f281(x70161,f317(f317(f224(x70161),x70162),x70163),f317(f317(f223(x70161),x70164),x70165)),f317(f317(f113(f858(x70161,a842)),f281(x70161,x70162,x70164)),f281(x70161,x70163,x70165))) % 168.22/168.06 [7017]~P103(x70171)+E(f279(x70171,f317(f317(f224(x70171),x70172),x70173),f317(f317(f223(x70171),x70174),x70175)),f317(f317(f113(f858(x70171,a842)),f279(x70171,x70172,x70174)),f279(x70171,x70173,x70175))) % 168.22/168.06 [7018]~P103(x70181)+E(f317(f317(f113(f858(x70181,a842)),f317(f278(x70181,x70182),x70183)),f317(f278(x70181,x70184),x70185)),f317(f278(x70181,f317(f317(f224(x70181),x70182),x70184)),f317(f317(f223(x70181),x70183),x70185))) % 168.22/168.06 [7133]~P22(f317(x71331,f337(x71333,x71332,x71331)))+P22(f317(x71331,f317(f317(f237(x71332,x71333),x71334),x71335))) % 168.22/168.06 [7214]~E(f317(x72143,x72144),f191(x72142))+E(f179(x72141,x72142,f317(f317(f317(f81(x72141,f853(x72142)),x72143),x72144),f317(f217(x72142),x72145))),f317(f317(f286(x72142),x72145),f179(x72141,x72142,x72143))) % 168.22/168.06 [7237]~E(x72372,f317(x72374,x72375))+P22(f317(f317(f319(x72371),x72372),f317(f287(x72373,x72371,x72374),f233(f858(x72373,a842))))) % 168.22/168.06 [7294]~E(f317(x72943,x72944),f191(x72942))+E(f317(f317(f21(f858(x72941,a842)),f177(x72941,x72942,x72943)),f317(f317(f286(x72941),x72944),x72945)),f317(f317(f21(f858(x72941,a842)),f177(x72941,x72942,x72943)),x72945)) % 168.22/168.06 [7312]~P11(x73123,x73122,x73124)+P11(x73121,x73122,f317(f317(f8(x73123,f858(x73122,x73122),x73121),x73124),x73125)) % 168.22/168.06 [7452]~P19(x74521,x74522,x74523,x74524)+P19(x74521,x74522,x74523,f317(f317(f21(f858(x74521,a842)),x74524),x74525)) % 168.22/168.06 [7606]~P22(f317(f317(x76063,x76064),x76065))+P22(f317(f317(f247(x76061,x76062,a842),x76063),f317(f317(f237(x76061,x76062),x76064),x76065))) % 168.22/168.06 [7721]~P22(f317(x77212,x77214))+~E(f317(f317(f132(x77211),f317(f189(f850(x77211)),f170(x77211,x77212,x77213))),x77213),f317(f317(f145(x77211),x77214),x77215)) % 168.22/168.06 [7742]P19(x77421,x77422,x77423,x77424)+~P19(x77421,x77422,x77423,f317(f317(f122(f858(x77421,a842)),x77425),x77424)) % 168.22/168.06 [7743]P19(x77431,x77432,x77433,x77434)+~P19(x77431,x77432,x77433,f317(f317(f122(f858(x77431,a842)),x77434),x77435)) % 168.22/168.06 [7787]~P103(x77872)+E(f317(f317(f143(x77871,x77872,x77873),x77874),f142(x77871,x77872,x77873,x77875)),f142(x77871,x77872,x77873,f317(f317(f145(x77871),x77874),x77875))) % 168.22/168.06 [7941]~P30(x79411,f317(a124,x79412),f317(f317(f317(f100(x79411),x79413),f317(a29,x79414)),x79415))+P30(x79411,x79412,f317(f317(f317(f100(x79411),x79413),f317(f222(a843),f317(a27,x79414))),x79415)) % 168.22/168.06 [8077]P30(x80771,f317(a124,x80772),f317(f317(f317(f100(x80771),x80773),f317(a29,x80774)),x80775))+~P30(x80771,x80772,f317(f317(f317(f100(x80771),x80773),f317(f222(a843),f317(a27,x80774))),x80775)) % 168.22/168.06 [8106]~P11(x81062,x81061,x81063)+E(f317(f136(x81061,x81062,f317(f7(x81062,x81061,x81061),x81063),x81064),x81065),f317(f317(f74(x81062,x81061,x81063),x81064),f317(f166(x81062),x81065))) % 168.22/168.06 [8136]~E(f317(f317(f132(x81361),f317(f189(f850(x81361)),f170(x81361,x81362,x81363))),x81363),f317(f317(f145(x81361),x81364),x81365))+E(f317(f317(f127(x81361),f170(x81361,x81362,x81363)),f317(f317(f145(x81361),x81364),x81365)),x81363) % 168.22/168.06 [8160]P22(f317(f317(x81601,x81602),x81603))+~P22(f317(f317(f247(x81604,x81605,a842),x81601),f317(f317(f237(x81604,x81605),x81602),x81603))) % 168.22/168.06 [8225]~E(f317(f317(f171(x82251,x82252),x82255),x82253),f317(f217(x82252),x82254))+P22(f317(f317(f319(f857(x82251,x82252)),f317(f317(f237(x82251,x82252),x82253),x82254)),f317(f166(f857(x82251,x82252)),x82255))) % 168.22/168.06 [8630]P22(f317(f317(f225(f858(x86301,a842)),f317(f287(x86302,x86301,x86303),x86304)),f317(f287(x86302,x86301,x86303),x86305)))+~P22(f317(f317(f225(f858(x86302,a842)),x86304),x86305)) % 168.22/168.06 [8631]P22(f317(f317(f225(f858(x86311,a842)),f317(f289(x86311,x86312,x86313),x86314)),f317(f289(x86311,x86312,x86313),x86315)))+~P22(f317(f317(f225(f858(x86312,a842)),x86314),x86315)) % 168.22/168.06 [8704]E(x87041,f2(a111))+E(f317(f317(f249(x87042,x87043,x87042,f857(x87043,x87042)),f317(x87044,x87045)),f257(x87043,x87042,f317(f317(f21(a111),x87041),f87(a111)),x87044)),f317(f257(x87043,x87042,x87041,x87044),x87045)) % 168.22/168.06 [9020]P30(x90201,x90202,f317(f317(f317(f100(x90201),x90203),x90204),x90205))+P22(f317(f317(x90203,f495(x90205,x90204,x90203,x90202)),f508(x90205,x90204,x90203,x90202))) % 168.22/168.06 [9029]~P22(f317(f317(f194(x90293),f317(f317(f317(a200,x90294),f40(x90291)),f317(x90292,x90294))),x90295))+P22(f317(f317(f194(f32(x90291,x90292,x90293)),x90294),f317(f317(f317(a200,x90295),f40(x90291)),f317(f317(a201,x90294),x90291)))) % 168.22/168.06 [9217]E(f317(f217(x92171),f586(x92172,x92173,x92174,x92171,x92175)),f317(f317(f171(x92175,x92171),x92172),x92174))+~P22(f317(f317(f319(f857(x92175,x92171)),f317(f317(f237(x92175,x92171),x92174),x92173)),f317(f166(f857(x92175,x92171)),x92172))) % 168.22/168.06 [9260]P30(x92601,x92602,f317(f317(f317(f100(x92601),x92603),x92604),x92605))+~P22(f317(f317(x92605,f495(x92605,x92604,x92603,x92602)),f525(x92605,x92604,x92603,x92602))) % 168.22/168.06 [9321]P30(x93211,x93212,f317(f317(f317(f100(x93211),x93213),x93214),x93215))+P22(f317(f317(f317(f317(a197,x93214),f508(x93215,x93214,x93213,x93212)),x93212),f525(x93215,x93214,x93213,x93212))) % 168.22/168.06 [9324]~P18(x93241,x93242,f317(f317(f286(f848(x93241)),f317(f317(f317(f100(x93241),x93243),f317(f222(a843),f317(a27,x93244))),x93245)),f188(f858(f848(x93241),a842))))+P18(x93241,x93242,f317(f317(f286(f848(x93241)),f317(f317(f317(f100(x93241),x93243),f317(a29,x93244)),x93245)),f188(f858(f848(x93241),a842)))) % 168.22/168.06 [9349]~P22(f317(f71(x93493),f317(f287(x93492,x93493,x93495),f233(f858(x93492,a842)))))+P22(f317(f71(x93491),f317(f287(x93492,x93491,f317(f317(f8(x93493,x93491,x93492),x93494),x93495)),f233(f858(x93492,a842))))) % 168.22/168.06 [9370]P22(f317(f317(f225(f858(f858(x93701,a842),a842)),f317(f287(f858(x93702,a842),f858(x93701,a842),f287(x93702,x93701,x93703)),f317(f285(x93702),x93704))),f317(f285(x93701),x93705)))+~P22(f317(f317(f225(f858(x93701,a842)),f317(f287(x93702,x93701,x93703),x93704)),x93705)) % 168.22/168.06 [9387]~P22(f317(f71(f853(x93871)),f317(f287(x93872,f853(x93871),x93873),f233(f858(x93872,a842)))))+P22(f317(f71(f853(x93871)),f317(f287(x93872,f853(x93871),f317(f317(f317(f81(x93872,f853(x93871)),x93873),x93874),f317(f217(x93871),x93875))),f233(f858(x93872,a842))))) % 168.22/168.06 [9421]P22(f317(f317(f194(x94211),f317(f317(f317(a200,x94212),f40(x94213)),f317(x94214,x94212))),f556(x94215,x94212,x94211,x94214,x94213)))+~P22(f317(f317(f194(f32(x94213,x94214,x94211)),x94212),x94215)) % 168.22/168.06 [9446]E(x94461,x94462)+~P22(f317(f76(x94463,x94464,x94465,x94461,f188(f858(x94463,a842))),x94462)) % 168.22/168.06 [9460]E(f317(f317(f237(x94601,x94602),f534(x94603,x94604,x94605,x94602,x94601)),f535(x94603,x94604,x94605,x94602,x94601)),x94605)+~P22(f317(f317(f319(f857(x94601,x94602)),x94605),f317(f317(f245(x94601,x94602),x94604),x94603))) % 168.22/168.06 [9471]P22(f317(f317(f194(x94711),f317(f317(f317(a200,x94712),f40(x94713)),f317(x94714,x94712))),f543(x94715,x94712,x94711,x94714,x94713)))+~P22(f317(f317(f194(f32(x94713,x94714,x94711)),x94712),f317(f317(f317(a200,x94715),f40(x94713)),f317(f317(a201,x94712),x94713)))) % 168.22/168.06 [9477]~P22(f317(f317(f194(f317(a29,x94772)),f317(f317(f317(a200,f317(f317(a202,x94774),a203)),f40(a26)),f317(x94773,x94774))),x94775))+P22(f317(f317(f194(f31(x94771,x94772,x94773)),x94774),f317(f317(f317(a200,f317(f317(a202,x94775),f317(a201,x94774))),x94771),f317(f317(a201,x94775),a25)))) % 168.22/168.06 [9507]P22(f317(f317(f194(f317(a29,x95071)),f317(f317(f317(a200,f317(f317(a202,x95072),a203)),f40(a26)),f317(x95073,x95072))),f600(x95074,x95072,x95073,x95071,x95075)))+~P22(f317(f317(f194(f31(x95075,x95071,x95073)),x95072),x95074)) % 168.22/168.06 [9548]P22(f317(f317(f319(x95481),f534(x95482,x95483,x95484,x95485,x95481)),x95483))+~P22(f317(f317(f319(f857(x95481,x95485)),x95484),f317(f317(f245(x95481,x95485),x95483),x95482))) % 168.22/168.06 [9574]E(f317(f317(f317(a200,f556(x95741,x95742,x95743,x95744,x95745)),f40(x95745)),f317(f317(a201,x95742),x95745)),x95741)+~P22(f317(f317(f194(f32(x95745,x95744,x95743)),x95742),x95741)) % 168.22/168.06 [9596]E(f317(f317(f317(a200,f543(x95961,x95962,x95963,x95964,x95965)),f40(x95965)),f317(f317(a201,x95962),x95965)),f317(f317(f317(a200,x95961),f40(x95965)),f317(f317(a201,x95962),x95965)))+~P22(f317(f317(f194(f32(x95965,x95964,x95963)),x95962),f317(f317(f317(a200,x95961),f40(x95965)),f317(f317(a201,x95962),x95965)))) % 168.22/168.06 [9621]P22(f317(f317(f194(f317(a29,x96211)),f317(f317(f317(a200,f317(f317(a202,x96212),a203)),f40(a26)),f317(x96213,x96212))),f591(x96214,x96212,x96213,x96211,x96215)))+~P22(f317(f317(f194(f31(x96215,x96211,x96213)),x96212),f317(f317(f317(a200,f317(f317(a202,x96214),f317(a201,x96212))),x96215),f317(f317(a201,x96214),a25)))) % 168.22/168.06 [9654]P18(x96545,x96544,f317(f317(f286(f848(x96545)),f317(f317(f317(f100(x96545),x96541),x96543),x96542)),f188(f858(f848(x96545),a842))))+P22(f317(f317(x96541,f642(x96542,x96543,x96544,x96545,x96541)),f652(x96542,x96543,x96544,x96545,x96541))) % 168.22/168.06 [9702]P22(f317(f317(f319(x97021),f535(x97022,x97023,x97024,x97021,x97025)),f317(x97022,f534(x97022,x97023,x97024,x97021,x97025))))+~P22(f317(f317(f319(f857(x97025,x97021)),x97024),f317(f317(f245(x97025,x97021),x97023),x97022))) % 168.22/168.06 [9733]P22(f317(f317(f319(f857(x97331,x97331)),f317(f317(f237(x97331,x97331),x97332),f775(x97333,x97334,x97335,x97332,x97331))),x97333))+~P22(f317(f317(f319(f857(x97331,x97331)),f317(f317(f237(x97331,x97331),x97332),x97335)),f317(f317(f182(f857(x97331,x97331),a842),f317(a124,x97334)),x97333))) % 168.22/168.06 [9734]P22(f317(f317(f319(f857(x97341,x97341)),f317(f317(f237(x97341,x97341),x97342),f777(x97343,x97344,x97345,x97342,x97341))),x97343))+~P22(f317(f317(f319(f857(x97341,x97341)),f317(f317(f237(x97341,x97341),x97342),x97345)),f317(f317(f182(f857(x97341,x97341),a842),f317(a124,x97344)),x97343))) % 168.22/168.06 [9752]~P22(f317(f317(f319(f857(f850(x97521),f850(x97521))),f317(f317(f237(f850(x97521),f850(x97521)),f317(f317(f145(x97521),x97522),x97525)),x97524)),f152(x97521,x97523)))+P22(f317(f317(f319(f857(x97521,x97521)),f317(f317(f237(x97521,x97521),x97522),f590(x97523,x97524,x97525,x97522,x97521))),x97523)) % 168.22/168.06 [9754]~P18(x97541,x97542,f317(f317(f286(f848(x97541)),f317(f317(f317(f100(x97541),f103(x97541,x97543,x97544)),x97545),x97543)),f188(f858(f848(x97541),a842))))+P18(x97541,x97542,f317(f317(f286(f848(x97541)),f317(f317(f317(f100(x97541),x97543),f35(x97544,x97545)),f103(x97541,x97543,f317(f82(a842,a842,a845,a312),x97544)))),f188(f858(f848(x97541),a842)))) % 168.22/168.06 [9755]~P21(x97551,x97552,f317(f317(f286(f848(x97551)),f317(f317(f317(f100(x97551),f103(x97551,x97553,x97554)),x97555),x97553)),f188(f858(f848(x97551),a842))))+P21(x97551,x97552,f317(f317(f286(f848(x97551)),f317(f317(f317(f100(x97551),x97553),f35(x97554,x97555)),f103(x97551,x97553,f317(f82(a842,a842,a845,a312),x97554)))),f188(f858(f848(x97551),a842)))) % 168.22/168.06 [9863]E(f317(f317(f317(a200,f317(f317(a202,f600(x98631,x98632,x98633,x98634,x98635)),f317(a201,x98632))),x98635),f317(f317(a201,f600(x98631,x98632,x98633,x98634,x98635)),a25)),x98631)+~P22(f317(f317(f194(f31(x98635,x98634,x98633)),x98632),x98631)) % 168.22/168.06 [9872]E(f317(f317(f317(a200,f317(f317(a202,f591(x98721,x98722,x98723,x98724,x98725)),f317(a201,x98722))),x98725),f317(f317(a201,f591(x98721,x98722,x98723,x98724,x98725)),a25)),f317(f317(f317(a200,f317(f317(a202,x98721),f317(a201,x98722))),x98725),f317(f317(a201,x98721),a25)))+~P22(f317(f317(f194(f31(x98725,x98724,x98723)),x98722),f317(f317(f317(a200,f317(f317(a202,x98721),f317(a201,x98722))),x98725),f317(f317(a201,x98721),a25)))) % 168.22/168.06 [10023]P18(x100231,x100232,f317(f317(f286(f848(x100231)),f317(f317(f317(f100(x100231),x100233),x100234),x100235)),f188(f858(f848(x100231),a842))))+~P18(x100231,x100232,f317(f317(f286(f848(x100231)),f317(f317(f317(f100(x100231),f317(f16(f858(a845,a842),x100231),f317(f317(f7(a845,a845,a842),a314),f652(x100235,x100234,x100232,x100231,x100233)))),x100234),f317(f16(f858(a845,a842),x100231),f317(x100235,f642(x100235,x100234,x100232,x100231,x100233))))),f188(f858(f848(x100231),a842)))) % 168.22/168.06 [6232]P22(f317(x62322,x62324))+E(f170(x62321,x62322,f317(f317(f127(x62321),x62323),f317(f317(f145(x62321),x62324),x62325))),f170(x62321,x62322,x62323)) % 168.22/168.06 [6280]~P71(x62802)+E(f317(f317(f317(f21(f858(x62801,x62802)),x62803),x62804),x62805),f317(f317(f21(x62802),f317(x62803,x62805)),f317(x62804,x62805))) % 168.22/168.06 [6282]~P93(x62822)+E(f317(f317(f317(f122(f858(x62821,x62822)),x62823),x62824),x62825),f317(f317(f122(x62822),f317(x62823,x62825)),f317(x62824,x62825))) % 168.22/168.06 [6284]~P93(x62842)+E(f317(f317(f317(f113(f858(x62841,x62842)),x62843),x62844),x62845),f317(f317(f113(x62842),f317(x62843,x62845)),f317(x62844,x62845))) % 168.22/168.06 [6301]E(x63011,x63012)+E(f317(f317(f159(x63013),f317(f317(f153(x63013,x63014),x63011),x63015)),x63012),f317(f317(f159(x63013),x63014),x63012)) % 168.22/168.06 [6562]~E(x65624,f188(f858(x65623,a842)))+E(f317(f317(f21(f858(x65621,a842)),x65622),f317(f317(f51(x65623,f858(x65621,a842)),x65624),x65625)),x65622) % 168.22/168.06 [6563]~E(x65634,f188(f858(x65633,a842)))+E(f317(f317(f122(f858(x65631,a842)),x65632),f317(f317(f51(x65633,f858(x65631,a842)),x65634),x65635)),x65632) % 168.22/168.06 [6564]~E(x65644,f188(f858(x65643,a842)))+E(f317(f317(f113(f858(x65641,a842)),x65642),f317(f317(f52(x65643,f858(x65641,a842)),x65644),x65645)),x65642) % 168.22/168.06 [6580]~E(x65804,f188(f858(x65803,a842)))+E(f317(f317(f286(x65801),x65802),f317(f317(f51(x65803,f858(x65801,a842)),x65804),x65805)),f317(f317(f286(x65801),x65802),f188(f858(x65801,a842)))) % 168.22/168.06 [7359]E(f317(f317(f159(x73591),f317(f317(f148(x73592,x73591),x73593),x73594)),x73595),f317(x73593,f317(f317(f159(x73592),x73594),x73595)))+~P22(f317(f317(f226(a849),x73595),f317(f189(f850(x73592)),x73594))) % 168.22/168.06 [7423]E(f317(f317(f122(f858(x74231,a842)),f317(x74232,x74233)),f317(f317(f51(x74234,f858(x74231,a842)),x74235),x74232)),f317(f317(f51(x74234,f858(x74231,a842)),x74235),x74232))+~P22(f317(f317(f319(x74234),x74233),x74235)) % 168.22/168.06 [7424]E(f317(f317(f113(f858(x74241,a842)),f317(x74242,x74243)),f317(f317(f52(x74244,f858(x74241,a842)),x74245),x74242)),f317(f317(f52(x74244,f858(x74241,a842)),x74245),x74242))+~P22(f317(f317(f319(x74244),x74243),x74245)) % 168.22/168.06 [8022]~E(x80223,f188(f858(x80221,a842)))+E(f317(f317(f51(x80221,f858(x80222,a842)),x80223),f317(f317(f8(f858(x80222,a842),f858(x80222,a842),x80221),f317(f286(x80222),x80224)),x80225)),f188(f858(x80222,a842))) % 168.22/168.06 [8028]~P22(f317(f317(f319(x80284),x80283),x80285))+P22(f317(f317(f225(f858(x80281,a842)),f317(x80282,x80283)),f317(f317(f51(x80284,f858(x80281,a842)),x80285),x80282))) % 168.22/168.06 [8088]E(x80881,f317(f317(f317(a200,x80882),x80883),f317(x80884,x80882)))+~P22(f317(f317(f317(f317(a197,f30(x80883,x80884)),x80882),x80885),x80881)) % 168.22/168.06 [8159]~E(f317(x81594,x81592),x81595)+P22(f317(f317(f319(x81591),x81592),f317(f289(x81591,x81593,x81594),f317(f317(f286(x81593),x81595),f188(f858(x81593,a842)))))) % 168.22/168.06 [8205]~P49(x82051,x82052,f317(f263(x82052,x82051),x82053))+E(f317(f317(f113(f858(x82051,a842)),f317(f262(x82052,x82051,x82053),x82054)),f317(f262(x82052,x82051,x82053),x82055)),f317(f262(x82052,x82051,x82053),f317(f317(f113(f858(x82052,a842)),x82054),x82055))) % 168.22/168.06 [8327]E(x83271,f188(f858(x83272,a842)))+E(f317(f317(f51(x83272,f858(x83273,a842)),x83271),f317(f317(f8(f858(x83273,a842),f858(x83273,a842),x83272),f317(f286(x83273),x83274)),x83275)),f317(f317(f286(x83273),x83274),f317(f317(f51(x83272,f858(x83273,a842)),x83271),x83275))) % 168.22/168.06 [8384]~P19(x83842,x83841,x83843,f233(f858(x83842,a842)))+E(f317(f317(f21(f858(x83841,a842)),f317(f287(x83842,x83841,x83843),x83844)),f317(f287(x83842,x83841,x83843),x83845)),f317(f287(x83842,x83841,x83843),f317(f317(f21(f858(x83842,a842)),x83844),x83845))) % 168.22/168.06 [8385]~P19(x83852,x83851,x83853,f233(f858(x83852,a842)))+E(f317(f317(f113(f858(x83851,a842)),f317(f287(x83852,x83851,x83853),x83854)),f317(f287(x83852,x83851,x83853),x83855)),f317(f287(x83852,x83851,x83853),f317(f317(f113(f858(x83852,a842)),x83854),x83855))) % 168.22/168.06 [8455]~P22(f317(f317(f77(x84551,x84552,x84555),x84553),x84554))+P22(f317(f317(f319(f857(x84551,x84552)),f317(f317(f237(x84551,x84552),x84553),x84554)),x84555)) % 168.22/168.06 [8489]P22(f317(f317(f319(x84891),x84892),f317(f234(x84893,x84891),x84894)))+~P22(f317(f317(f319(f857(x84893,x84891)),f317(f317(f237(x84893,x84891),x84895),x84892)),x84894)) % 168.22/168.06 [8491]P22(f317(f317(f319(x84911),x84912),f317(f236(x84911,x84913),x84914)))+~P22(f317(f317(f319(f857(x84911,x84913)),f317(f317(f237(x84911,x84913),x84912),x84915)),x84914)) % 168.22/168.06 [8617]P22(f317(f317(f77(x86171,x86172,x86173),x86174),x86175))+~P22(f317(f317(f319(f857(x86171,x86172)),f317(f317(f237(x86171,x86172),x86174),x86175)),x86173)) % 168.22/168.06 [8652]E(f317(x86521,x86522),x86523)+~P22(f317(f317(f319(x86524),x86522),f317(f289(x86524,x86525,x86521),f317(f317(f286(x86525),x86523),f188(f858(x86525,a842)))))) % 168.22/168.06 [8883]P22(f317(f317(f319(f857(x88831,x88832)),f317(f317(f237(x88831,x88832),x88833),x88834)),f317(f263(x88832,x88831),x88835)))+~P22(f317(f317(f319(f857(x88832,x88831)),f317(f317(f237(x88832,x88831),x88834),x88833)),x88835)) % 168.22/168.06 [8901]~P22(f317(f317(x89011,x89015),x89014))+P22(f317(f317(x89011,f317(f246(x89012,x89013),f317(f317(f237(x89012,x89013),x89014),x89015))),f317(f244(x89012,x89013),f317(f317(f237(x89012,x89013),x89014),x89015)))) % 168.22/168.06 [8931]~P22(f317(f317(f319(f857(x89312,x89311)),f317(f317(f237(x89312,x89311),x89314),x89313)),f317(f263(x89311,x89312),x89315)))+P22(f317(f317(f319(f857(x89311,x89312)),f317(f317(f237(x89311,x89312),x89313),x89314)),x89315)) % 168.22/168.06 [8959]~P22(f317(f317(f319(f857(x89593,x89591)),f317(f317(f237(x89593,x89591),x89595),x89592)),x89594))+P22(f317(f317(f319(x89591),x89592),f317(f262(x89593,x89591,x89594),f317(f317(f286(x89593),x89595),f188(f858(x89593,a842)))))) % 168.22/168.06 [9002]P22(f317(f317(f319(f857(x90021,x90022)),f317(f317(f237(x90021,x90022),x90023),x90024)),x90025))+~P22(f317(f317(f319(x90022),x90024),f317(f262(x90021,x90022,x90025),f317(f317(f286(x90021),x90023),f188(f858(x90021,a842)))))) % 168.22/168.06 [9023]E(f317(f317(f317(f81(x90231,f853(x90232)),f181(x90231,x90232,x90233,x90234)),x90235),f191(x90232)),f181(x90231,x90232,x90233,f317(f317(f21(f858(x90231,a842)),x90234),f317(f317(f286(x90231),x90235),f188(f858(x90231,a842))))))+~P22(f317(f317(f319(x90231),x90235),x90234)) % 168.22/168.06 [9089]~P67(x90891)+E(f317(f317(f6(a849,x90891),x90892),f279(a849,f317(f317(f89(a849),x90893),x90894),f317(f317(f89(a849),x90895),x90894))),f317(f317(f6(a849,x90891),f317(f317(f8(a849,x90891,a849),x90892),f317(f317(f7(a849,a849,a849),f89(a849)),x90894))),f279(a849,x90893,x90895))) % 168.22/168.06 [9113]~P67(x91131)+E(f317(f317(f6(a849,x91131),x91132),f317(f278(a849,f317(f317(f89(a849),x91133),x91134)),f317(f317(f89(a849),x91135),x91134))),f317(f317(f6(a849,x91131),f317(f317(f8(a849,x91131,a849),x91132),f317(f317(f7(a849,a849,a849),f89(a849)),x91134))),f317(f278(a849,x91133),x91135))) % 168.22/168.06 [9166]~P19(x91661,x91662,x91663,f233(f858(x91661,a842)))+E(f317(f317(f148(x91661,x91662),x91663),f317(f130(x91661,f317(f317(f8(a842,a842,x91661),a312),f317(a314,x91664))),x91665)),f317(f130(x91662,f317(f317(f8(a842,a842,x91662),a312),f317(a314,f317(x91663,x91664)))),f317(f317(f148(x91661,x91662),x91663),x91665))) % 168.22/168.06 [9184]~P19(x91841,x91842,x91843,f317(f317(f286(x91841),x91844),f317(f166(x91841),x91845)))+E(f317(f317(f148(x91841,x91842),x91843),f317(f130(x91841,f317(f317(f8(a842,a842,x91841),a312),f317(a314,x91844))),x91845)),f317(f130(x91842,f317(f317(f8(a842,a842,x91842),a312),f317(a314,f317(x91843,x91844)))),f317(f317(f148(x91841,x91842),x91843),x91845))) % 168.22/168.06 [9338]P22(f317(f317(f319(f857(f850(x93381),f850(x93381))),f317(f317(f237(f850(x93381),f850(x93381)),f317(f317(f145(x93381),x93382),x93383)),f317(f317(f145(x93381),x93384),x93383))),f151(x93381,x93385)))+~P22(f317(f317(f319(f857(x93381,x93381)),f317(f317(f237(x93381,x93381),x93382),x93384)),x93385)) % 168.22/168.06 [9371]P22(f317(f317(f317(f317(a197,x93711),x93712),x93713),f413(x93714,x93713,x93712,x93715,x93711)))+~P22(f317(f317(f317(f317(a197,f36(x93711,x93715)),x93712),x93713),x93714)) % 168.22/168.06 [9372]P22(f317(f317(f317(f317(a197,x93721),x93722),x93723),f457(x93724,x93723,x93722,x93725,x93721)))+~P22(f317(f317(f317(f317(a197,f36(x93721,x93725)),x93722),x93723),x93724)) % 168.22/168.06 [9444]P18(x94441,x94442,f317(f317(f286(f848(x94441)),f317(f317(f317(f100(x94441),x94443),f317(a29,x94444)),x94445)),f188(f858(f848(x94441),a842))))+~P18(x94441,f317(f317(f286(f848(x94441)),f317(f317(f317(f100(x94441),x94443),f317(a29,x94444)),x94445)),x94442),f317(f317(f286(f848(x94441)),f317(f317(f317(f100(x94441),x94443),f317(f222(a843),f317(a27,x94444))),x94445)),f188(f858(f848(x94441),a842)))) % 168.22/168.06 [9455]E(f317(f317(f286(x94551),f510(x94552,x94553,x94554,x94555,x94551)),f511(x94552,x94553,x94554,x94555,x94551)),f317(f317(f286(x94551),x94554),x94553))+~P22(f317(f72(x94551,x94555,f317(f317(f286(x94551),x94554),x94553)),x94552)) % 168.22/168.06 [9456]E(f317(f317(f286(x94561),f512(x94562,x94563,x94564,x94565,x94561)),f513(x94562,x94563,x94564,x94565,x94561)),f317(f317(f286(x94561),x94564),x94563))+~P22(f317(f72(x94561,x94565,f317(f317(f286(x94561),x94564),x94563)),x94562)) % 168.22/168.06 [9535]P22(f317(f317(f319(x95351),f637(x95352,x95353,x95354,x95355,x95351)),x95354))+P22(f317(f317(f317(f52(x95351,f858(x95355,a842)),x95354),x95353),x95352)) % 168.22/168.06 [9539]P22(f317(f317(f319(x95391),f636(x95392,x95393,x95391,x95394,x95395)),x95393))+P22(f317(f317(f319(x95395),x95394),f317(f317(f52(x95391,f858(x95395,a842)),x95393),x95392))) % 168.22/168.06 [9547]P22(f317(f317(f319(x95471),f631(x95472,x95473,x95471,x95474,x95475)),x95473))+P22(f317(f317(f225(f858(x95475,a842)),x95474),f317(f317(f52(x95471,f858(x95475,a842)),x95473),x95472))) % 168.22/168.06 [9550]P22(f317(f317(x95501,f486(x95502,x95501,x95503,x95504,x95505)),x95502))+~P22(f317(f317(f317(f51(x95505,f858(x95504,a842)),x95503),x95501),x95502)) % 168.22/168.06 [9553]P22(f317(f317(f319(x95531),f486(x95532,x95533,x95534,x95535,x95531)),x95534))+~P22(f317(f317(f317(f51(x95531,f858(x95535,a842)),x95534),x95533),x95532)) % 168.22/168.06 [9561]P22(f317(f317(f319(x95611),f494(x95612,x95613,x95611,x95614,x95615)),x95613))+~P22(f317(f317(f319(x95615),x95614),f317(f317(f51(x95611,f858(x95615,a842)),x95613),x95612))) % 168.22/168.06 [9566]P22(f317(f317(f319(x95661),x95662),f317(x95663,f494(x95663,x95664,x95665,x95662,x95661))))+~P22(f317(f317(f319(x95661),x95662),f317(f317(f51(x95665,f858(x95661,a842)),x95664),x95663))) % 168.22/168.06 [9659]~P22(f317(f317(x96594,f637(x96595,x96594,x96593,x96592,x96591)),x96595))+P22(f317(f317(f317(f52(x96591,f858(x96592,a842)),x96593),x96594),x96595)) % 168.22/168.06 [9662]~P22(f317(f317(f319(x96621),x96622),f317(x96625,f636(x96625,x96624,x96623,x96622,x96621))))+P22(f317(f317(f319(x96621),x96622),f317(f317(f52(x96623,f858(x96621,a842)),x96624),x96625))) % 168.22/168.06 [9665]~P22(f317(f317(f225(f858(x96651,a842)),x96652),f317(x96655,f631(x96655,x96654,x96653,x96652,x96651))))+P22(f317(f317(f225(f858(x96651,a842)),x96652),f317(f317(f52(x96653,f858(x96651,a842)),x96654),x96655))) % 168.22/168.06 [9708]P22(f317(f317(f317(f317(a197,x97081),f413(x97082,x97083,x97084,x97081,x97085)),x97083),x97082))+~P22(f317(f317(f317(f317(a197,f36(x97085,x97081)),x97084),x97083),x97082)) % 168.22/168.06 [9709]P22(f317(f317(f317(f317(a197,x97091),f457(x97092,x97093,x97094,x97091,x97095)),x97093),x97092))+~P22(f317(f317(f317(f317(a197,f36(x97095,x97091)),x97094),x97093),x97092)) % 168.22/168.06 [9737]~P22(f317(f317(f319(x97371),f510(x97375,x97374,x97373,x97372,x97371)),f511(x97375,x97374,x97373,x97372,x97371)))+~P22(f317(f72(x97371,x97372,f317(f317(f286(x97371),x97373),x97374)),x97375)) % 168.22/168.06 [9738]~P22(f317(f317(f319(x97381),f512(x97385,x97384,x97383,x97382,x97381)),f513(x97385,x97384,x97383,x97382,x97381)))+~P22(f317(f72(x97381,x97382,f317(f317(f286(x97381),x97383),x97384)),x97385)) % 168.22/168.06 [9739]~P22(f317(f317(f319(f857(x97391,x97391)),f317(f317(f237(x97391,x97391),x97392),x97395)),f317(f317(f182(f857(x97391,x97391),a842),f317(a124,x97394)),x97393)))+P22(f317(f317(f319(f857(x97391,x97391)),f317(f317(f237(x97391,x97391),x97392),f776(x97393,x97394,x97395,x97392,x97391))),f317(f317(f182(f857(x97391,x97391),a842),x97394),x97393))) % 168.22/168.06 [9746]P22(f317(f76(x97461,x97461,x97462,f510(x97463,x97464,x97465,x97462,x97461),f511(x97463,x97464,x97465,x97462,x97461)),x97463))+~P22(f317(f72(x97461,x97462,f317(f317(f286(x97461),x97465),x97464)),x97463)) % 168.22/168.06 [9747]P22(f317(f76(x97471,x97471,x97472,f512(x97473,x97474,x97475,x97472,x97471),f513(x97473,x97474,x97475,x97472,x97471)),x97473))+~P22(f317(f72(x97471,x97472,f317(f317(f286(x97471),x97475),x97474)),x97473)) % 168.22/168.06 [9759]~P103(x97591)+P29(x97591,f317(f317(f148(x97592,x97591),x97593),f317(f130(x97592,f317(f317(f7(x97592,x97591,a842),f317(f317(f8(x97591,f858(x97591,a842),x97592),a314),x97593)),f317(x97594,x97595))),x97595))) % 168.22/168.06 [9804]~P22(f317(f317(f319(x98042),x98045),f317(f262(x98041,x98042,x98044),x98043)))+P22(f317(f317(f319(f857(x98041,x98042)),f317(f317(f237(x98041,x98042),f355(x98043,x98044,x98041,x98045,x98042)),x98045)),x98044)) % 168.22/168.06 [9805]~P22(f317(f317(f319(x98052),x98055),f317(f262(x98051,x98052,x98054),x98053)))+P22(f317(f317(f319(f857(x98051,x98052)),f317(f317(f237(x98051,x98052),f411(x98053,x98054,x98051,x98055,x98052)),x98055)),x98054)) % 168.22/168.06 [9825]~P22(f317(f317(f319(f857(x98251,x98251)),f317(f317(f237(x98251,x98251),x98255),x98254)),f317(f317(f182(f857(x98251,x98251),a842),f317(a124,x98253)),x98252)))+P22(f317(f317(f319(f857(x98251,x98251)),f317(f317(f237(x98251,x98251),f776(x98252,x98253,x98254,x98255,x98251)),x98254)),x98252)) % 168.22/168.06 [9828]~P22(f317(f317(f319(f857(x98281,x98281)),f317(f317(f237(x98281,x98281),x98285),x98284)),f317(f317(f182(f857(x98281,x98281),a842),f317(a124,x98283)),x98282)))+P22(f317(f317(f319(f857(x98281,x98281)),f317(f317(f237(x98281,x98281),f775(x98282,x98283,x98284,x98285,x98281)),x98284)),f317(f317(f182(f857(x98281,x98281),a842),x98283),x98282))) % 168.22/168.06 [9829]~P22(f317(f317(f319(f857(x98291,x98291)),f317(f317(f237(x98291,x98291),x98295),x98294)),f317(f317(f182(f857(x98291,x98291),a842),f317(a124,x98293)),x98292)))+P22(f317(f317(f319(f857(x98291,x98291)),f317(f317(f237(x98291,x98291),f777(x98292,x98293,x98294,x98295,x98291)),x98294)),f317(f317(f182(f857(x98291,x98291),a842),x98293),x98292))) % 168.22/168.06 [9830]~P22(f317(f317(f319(f857(f850(x98301),f850(x98301))),f317(f317(f237(f850(x98301),f850(x98301)),x98305),f317(f317(f145(x98301),x98304),x98303))),f152(x98301,x98302)))+P22(f317(f317(f319(f857(x98301,x98301)),f317(f317(f237(x98301,x98301),f589(x98302,x98303,x98304,x98305,x98301)),x98304)),x98302)) % 168.22/168.06 [6960]E(x69601,f191(x69602))+E(f177(x69603,x69602,f317(f317(f317(f81(x69603,f853(x69602)),x69604),x69605),x69601)),f317(f317(f286(x69603),x69605),f177(x69603,x69602,x69604))) % 168.22/168.06 [7444]~E(x74443,f188(f858(x74442,a842)))+E(f317(f317(f122(f858(x74441,a842)),f317(f317(f51(x74442,f858(x74441,a842)),x74443),x74444)),x74445),x74445) % 168.22/168.06 [7445]~E(x74453,f188(f858(x74452,a842)))+E(f317(f317(f113(f858(x74451,a842)),f317(f317(f52(x74452,f858(x74451,a842)),x74453),x74454)),x74455),x74455) % 168.22/168.06 [7799]~E(x77995,f191(x77992))+E(f177(x77991,x77992,f317(f317(f317(f81(x77991,f853(x77992)),x77993),x77994),x77995)),f317(f317(f21(f858(x77991,a842)),f177(x77991,x77992,x77993)),f317(f317(f286(x77991),x77994),f188(f858(x77991,a842))))) % 168.22/168.06 [7863]~E(x78633,f188(f858(x78632,a842)))+E(f317(f317(f21(f858(x78631,a842)),f317(f317(f52(x78632,f858(x78631,a842)),x78633),x78634)),x78635),f317(f317(f21(f858(x78631,a842)),f233(f858(x78631,a842))),x78635)) % 168.22/168.06 [7991]E(f317(f317(f153(x79911,f317(f317(f127(x79911),x79912),x79913)),x79914),x79915),f317(f317(f127(x79911),f317(f317(f153(x79911,x79912),x79914),x79915)),x79913))+~P22(f317(f317(f226(a849),x79914),f317(f189(f850(x79911)),x79912))) % 168.22/168.06 [8110]P22(f317(f317(f319(x81101),x81105),f317(f166(x81101),x81103)))+E(f317(f317(f171(x81101,x81102),f317(f317(f175(x81101,x81102),x81103),f317(f317(f148(x81101,x81102),x81104),x81103))),x81105),f191(x81102)) % 168.22/168.06 [8235]~P22(f317(f317(f319(x82351),x82355),f317(f166(x82351),x82353)))+E(f317(f317(f171(x82351,x82352),f317(f317(f175(x82351,x82352),x82353),f317(f317(f148(x82351,x82352),x82354),x82353))),x82355),f317(f217(x82352),f317(x82354,x82355))) % 168.22/168.06 [8274]E(f317(f317(f159(x82741),f317(f317(f148(a849,x82741),x82742),f133(a849,f317(f278(a849,x82743),x82744)))),x82745),f317(x82742,f317(f317(f89(a849),x82743),x82745)))+~P22(f317(f317(f226(a849),x82745),f317(f317(f21(a849),x82744),x82743))) % 168.22/168.06 [8314]~E(x83143,f188(f858(x83141,a842)))+E(f317(f317(f51(x83141,f858(x83142,a842)),x83143),f317(f317(f8(f858(x83142,a842),f858(x83142,a842),x83141),f317(f122(f858(x83142,a842)),x83144)),x83145)),f188(f858(x83142,a842))) % 168.22/168.06 [8315]~E(x83153,f188(f858(x83151,a842)))+E(f317(f317(f52(x83151,f858(x83152,a842)),x83153),f317(f317(f8(f858(x83152,a842),f858(x83152,a842),x83151),f317(f21(f858(x83152,a842)),x83154)),x83155)),f233(f858(x83152,a842))) % 168.22/168.06 [8316]~E(x83163,f188(f858(x83161,a842)))+E(f317(f317(f52(x83161,f858(x83162,a842)),x83163),f317(f317(f8(f858(x83162,a842),f858(x83162,a842),x83161),f317(f113(f858(x83162,a842)),x83164)),x83165)),f233(f858(x83162,a842))) % 168.22/168.06 [8321]~P135(x83212)+E(f317(f317(f6(x83211,x83212),f317(f317(f8(x83212,x83212,x83211),f317(f90(x83212),x83213)),x83214)),x83215),f317(f317(f90(x83212),x83213),f317(f317(f6(x83211,x83212),x83214),x83215))) % 168.22/168.06 [8602]E(x86021,f188(f858(x86022,a842)))+E(f317(f317(f51(x86022,f858(x86023,a842)),x86021),f317(f317(f8(f858(x86023,a842),f858(x86023,a842),x86022),f317(f122(f858(x86023,a842)),x86024)),x86025)),f317(f317(f122(f858(x86023,a842)),x86024),f317(f317(f51(x86022,f858(x86023,a842)),x86021),x86025))) % 168.22/168.06 [8603]E(x86031,f188(f858(x86032,a842)))+E(f317(f317(f52(x86032,f858(x86033,a842)),x86031),f317(f317(f8(f858(x86033,a842),f858(x86033,a842),x86032),f317(f21(f858(x86033,a842)),x86034)),x86035)),f317(f317(f21(f858(x86033,a842)),x86034),f317(f317(f51(x86032,f858(x86033,a842)),x86031),x86035))) % 168.22/168.06 [8604]E(x86041,f188(f858(x86042,a842)))+E(f317(f317(f52(x86042,f858(x86043,a842)),x86041),f317(f317(f8(f858(x86043,a842),f858(x86043,a842),x86042),f317(f113(f858(x86043,a842)),x86044)),x86045)),f317(f317(f113(f858(x86043,a842)),x86044),f317(f317(f52(x86042,f858(x86043,a842)),x86041),x86045))) % 168.22/168.06 [8794]~P22(f317(f317(f226(a849),f317(x87944,x87942)),f317(x87944,x87943)))+P22(f317(f317(f319(f857(x87941,x87941)),f317(f317(f237(x87941,x87941),x87942),x87943)),f147(x87941,f317(f317(f145(f858(x87941,a849)),x87944),x87945)))) % 168.22/168.06 [9056]~P19(x90562,x90561,x90563,f317(f317(f122(f858(x90562,a842)),x90564),x90565))+E(f317(f317(f113(f858(x90561,a842)),f317(f287(x90562,x90561,x90563),f317(f317(f21(f858(x90562,a842)),x90564),x90565))),f317(f287(x90562,x90561,x90563),f317(f317(f21(f858(x90562,a842)),x90565),x90564))),f188(f858(x90561,a842))) % 168.22/168.06 [9334]~P22(f317(f317(f225(f858(x93343,a842)),f317(f262(x93341,x93343,x93344),x93342)),x93345))+P22(f317(f317(f225(f858(x93341,a842)),x93342),f317(f88(f858(x93341,a842)),f317(f262(x93343,x93341,f317(f263(x93341,x93343),x93344)),f317(f88(f858(x93343,a842)),x93345))))) % 168.22/168.06 [9356]~P19(x93561,x93562,x93563,f317(f317(f286(x93561),x93564),x93565))+~P22(f317(f317(f319(x93562),f317(x93563,x93564)),f317(f287(x93561,x93562,x93563),f317(f317(f21(f858(x93561,a842)),x93565),f317(f317(f286(x93561),x93564),f188(f858(x93561,a842))))))) % 168.22/168.06 [9411]P22(f317(f317(f225(f858(x94111,a842)),f317(f262(x94112,x94111,x94113),x94114)),x94115))+~P22(f317(f317(f225(f858(x94112,a842)),x94114),f317(f88(f858(x94112,a842)),f317(f262(x94111,x94112,f317(f263(x94112,x94111),x94113)),f317(f88(f858(x94111,a842)),x94115))))) % 168.22/168.06 [9485]~P79(x94851)+P22(f317(f317(f225(x94851),f317(f84(x94851),f317(f317(f21(x94851),f317(f317(f89(x94851),x94852),x94853)),f317(f317(f89(x94851),x94854),x94855)))),f317(f317(f89(x94851),f317(f84(x94851),f317(f317(f21(x94851),x94852),x94854))),f317(f84(x94851),f317(f317(f21(x94851),x94853),x94855))))) % 168.22/168.06 [9580]P22(f317(f317(f319(x95801),f496(x95802,x95803,x95804,x95801,x95805)),x95804))+P22(f317(f317(f225(f858(x95805,a842)),f317(f317(f51(x95801,f858(x95805,a842)),x95804),x95803)),x95802)) % 168.22/168.06 [9781]~P22(f317(f317(f225(f858(x97811,a842)),f317(x97814,f496(x97815,x97814,x97813,x97812,x97811))),x97815))+P22(f317(f317(f225(f858(x97811,a842)),f317(f317(f51(x97812,f858(x97811,a842)),x97813),x97814)),x97815)) % 168.22/168.06 [8434]E(f317(f317(f127(x84341),x84342),f317(f317(f153(x84341,x84343),f317(f317(f21(a849),x84344),f317(f189(f850(x84341)),x84342))),x84345)),f317(f317(f153(x84341,f317(f317(f127(x84341),x84342),x84343)),x84344),x84345))+P22(f317(f317(f226(a849),x84344),f317(f189(f850(x84341)),x84342))) % 168.22/168.06 [8463]~P134(x84631)+E(f317(f317(f89(x84631),f317(f317(f90(x84631),x84632),x84633)),f317(f317(f89(x84631),f317(f317(f90(x84631),x84634),x84633)),x84635)),f317(f317(f89(x84631),f317(f317(f90(x84631),f317(f317(f89(x84631),x84632),x84634)),x84633)),x84635)) % 168.22/168.06 [9012]~P135(x90121)+E(f317(f160(x90121),f317(f317(f148(x90122,x90121),f317(f317(f8(x90121,x90121,x90122),f317(f90(x90121),x90123)),x90124)),x90125)),f317(f317(f90(x90121),x90123),f317(f160(x90121),f317(f317(f148(x90122,x90121),x90124),x90125)))) % 168.22/168.06 [9183]E(f317(f189(f850(x91831)),f317(f317(f167(x91831),f317(f317(f223(a849),f317(f189(f850(x91831)),x91832)),f317(f189(f850(x91833)),x91834))),x91832)),f317(f189(f850(x91833)),f317(f317(f167(x91833),f317(f317(f223(a849),f317(f189(f850(x91831)),x91832)),f317(f189(f850(x91833)),x91834))),x91834)))+P22(f317(x91835,f317(f317(f175(x91831,x91833),x91832),x91834))) % 168.22/168.06 [9423]~P135(x94232)+E(f317(f317(f6(x94231,x94232),f317(f317(f7(x94231,x94232,x94232),f317(f317(f8(x94232,f858(x94232,x94232),x94231),f90(x94232)),x94233)),x94234)),x94235),f317(f317(f90(x94232),f317(f317(f6(x94231,x94232),x94233),x94235)),x94234)) % 168.22/168.06 [9424]~P59(x94242)+E(f317(f317(f6(x94241,x94242),f317(f317(f7(x94241,x94242,x94242),f317(f317(f8(x94242,f858(x94242,x94242),x94241),f266(x94242)),x94243)),x94244)),x94245),f317(f317(f266(x94242),f317(f317(f6(x94241,x94242),x94243),x94245)),x94244)) % 168.22/168.06 [9430]~P70(x94302)+E(f317(f317(f9(x94301,x94302),f317(f317(f18(x94301,x94302,x94302),f317(f317(f8(x94302,f858(x94302,x94302),x94301),f90(x94302)),x94303)),x94304)),x94305),f317(f317(f90(x94302),f317(f317(f9(x94301,x94302),x94303),x94305)),f317(f317(f9(x94301,x94302),x94304),x94305))) % 168.22/168.06 [9431]~P67(x94312)+E(f317(f317(f6(x94311,x94312),f317(f317(f18(x94311,x94312,x94312),f317(f317(f8(x94312,f858(x94312,x94312),x94311),f89(x94312)),x94313)),x94314)),x94315),f317(f317(f89(x94312),f317(f317(f6(x94311,x94312),x94313),x94315)),f317(f317(f6(x94311,x94312),x94314),x94315))) % 168.22/168.06 [9432]~P25(x94322)+E(f317(f317(f6(x94321,x94322),f317(f317(f18(x94321,x94322,x94322),f317(f317(f8(x94322,f858(x94322,x94322),x94321),f21(x94322)),x94323)),x94324)),x94325),f317(f317(f21(x94322),f317(f317(f6(x94321,x94322),x94323),x94325)),f317(f317(f6(x94321,x94322),x94324),x94325))) % 168.22/168.06 [9468]~E(x94683,f188(f858(x94681,a842)))+E(f317(f317(f51(x94681,f858(x94682,a842)),x94683),f317(f317(f7(x94681,f858(x94682,a842),f858(x94682,a842)),f317(f317(f8(f858(x94682,a842),f858(f858(x94682,a842),f858(x94682,a842)),x94681),f122(f858(x94682,a842))),x94684)),x94685)),f188(f858(x94682,a842))) % 168.22/168.06 [9469]~E(x94693,f188(f858(x94691,a842)))+E(f317(f317(f52(x94691,f858(x94692,a842)),x94693),f317(f317(f7(x94691,f858(x94692,a842),f858(x94692,a842)),f317(f317(f8(f858(x94692,a842),f858(f858(x94692,a842),f858(x94692,a842)),x94691),f21(f858(x94692,a842))),x94694)),x94695)),f233(f858(x94692,a842))) % 168.22/168.06 [9470]~E(x94703,f188(f858(x94701,a842)))+E(f317(f317(f52(x94701,f858(x94702,a842)),x94703),f317(f317(f7(x94701,f858(x94702,a842),f858(x94702,a842)),f317(f317(f8(f858(x94702,a842),f858(f858(x94702,a842),f858(x94702,a842)),x94701),f113(f858(x94702,a842))),x94704)),x94705)),f233(f858(x94702,a842))) % 168.22/168.06 [9493]E(x94931,f188(f858(x94932,a842)))+E(f317(f317(f51(x94932,f858(x94933,a842)),x94931),f317(f317(f7(x94932,f858(x94933,a842),f858(x94933,a842)),f317(f317(f8(f858(x94933,a842),f858(f858(x94933,a842),f858(x94933,a842)),x94932),f122(f858(x94933,a842))),x94934)),x94935)),f317(f317(f122(f858(x94933,a842)),f317(f317(f51(x94932,f858(x94933,a842)),x94931),x94934)),x94935)) % 168.22/168.06 [9494]E(x94941,f188(f858(x94942,a842)))+E(f317(f317(f52(x94942,f858(x94943,a842)),x94941),f317(f317(f7(x94942,f858(x94943,a842),f858(x94943,a842)),f317(f317(f8(f858(x94943,a842),f858(f858(x94943,a842),f858(x94943,a842)),x94942),f21(f858(x94943,a842))),x94944)),x94945)),f317(f317(f21(f858(x94943,a842)),f317(f317(f52(x94942,f858(x94943,a842)),x94941),x94944)),x94945)) % 168.22/168.06 [9495]E(x94951,f188(f858(x94952,a842)))+E(f317(f317(f52(x94952,f858(x94953,a842)),x94951),f317(f317(f7(x94952,f858(x94953,a842),f858(x94953,a842)),f317(f317(f8(f858(x94953,a842),f858(f858(x94953,a842),f858(x94953,a842)),x94952),f113(f858(x94953,a842))),x94954)),x94955)),f317(f317(f113(f858(x94953,a842)),f317(f317(f52(x94952,f858(x94953,a842)),x94951),x94954)),x94955)) % 168.22/168.06 [9063]~P22(f317(f317(f225(a849),x90631),x90634))+E(f317(f317(f21(a849),f317(f317(f89(a849),f317(f317(f90(a849),x90631),x90632)),x90633)),f317(f317(f89(a849),f317(f317(f90(a849),x90634),x90632)),x90635)),f317(f317(f21(a849),x90633),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x90634),x90631)),x90632)),x90635))) % 168.22/168.06 [9639]~P135(x96391)+E(f317(f160(x96391),f317(f317(f148(x96392,x96391),f317(f317(f7(x96392,x96391,x96391),f317(f317(f8(x96391,f858(x96391,x96391),x96392),f90(x96391)),x96393)),x96394)),x96395)),f317(f317(f90(x96391),f317(f160(x96391),f317(f317(f148(x96392,x96391),x96393),x96395))),x96394)) % 168.22/168.06 [9645]~P67(x96451)+E(f317(f160(x96451),f317(f317(f148(x96452,x96451),f317(f317(f18(x96452,x96451,x96451),f317(f317(f8(x96451,f858(x96451,x96451),x96452),f89(x96451)),x96453)),x96454)),x96455)),f317(f317(f89(x96451),f317(f160(x96451),f317(f317(f148(x96452,x96451),x96453),x96455))),f317(f160(x96451),f317(f317(f148(x96452,x96451),x96454),x96455)))) % 168.22/168.06 [9646]~P25(x96461)+E(f317(f160(x96461),f317(f317(f148(x96462,x96461),f317(f317(f18(x96462,x96461,x96461),f317(f317(f8(x96461,f858(x96461,x96461),x96462),f21(x96461)),x96463)),x96464)),x96465)),f317(f317(f21(x96461),f317(f160(x96461),f317(f317(f148(x96462,x96461),x96463),x96465))),f317(f160(x96461),f317(f317(f148(x96462,x96461),x96464),x96465)))) % 168.22/168.06 [9794]P22(f317(x97941,f317(f317(f175(x97942,x97943),x97944),x97945)))+~P22(f317(x97941,f317(f317(f175(x97942,x97943),f317(f317(f167(x97942),f317(f317(f223(a849),f317(f189(f850(x97942)),x97944)),f317(f189(f850(x97943)),x97945))),x97944)),f317(f317(f167(x97943),f317(f317(f223(a849),f317(f189(f850(x97942)),x97944)),f317(f189(f850(x97943)),x97945))),x97945)))) % 168.22/168.06 [9301]~P22(f317(f317(f225(a849),x93014),x93011))+E(f317(f317(f21(a849),f317(f317(f89(a849),f317(f317(f90(a849),x93011),x93012)),x93013)),f317(f317(f89(a849),f317(f317(f90(a849),x93014),x93012)),x93015)),f317(f317(f21(a849),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x93011),x93014)),x93012)),x93013)),x93015)) % 168.22/168.06 [10048]P18(x100481,x100482,f317(f287(a846,f848(x100481),f317(f317(f18(a846,f858(x100481,f858(a845,a842)),f848(x100481)),f317(f317(f18(a846,a843,f858(f858(x100481,f858(a845,a842)),f848(x100481))),f317(f317(f8(f858(x100481,f858(a845,a842)),f858(a843,f858(f858(x100481,f858(a845,a842)),f848(x100481))),a846),f100(x100481)),x100483)),a29)),x100484)),x100485))+~P18(x100481,f317(f317(f122(f858(f848(x100481),a842)),x100482),f317(f287(a846,f848(x100481),f317(f317(f18(a846,f858(x100481,f858(a845,a842)),f848(x100481)),f317(f317(f18(a846,a843,f858(f858(x100481,f858(a845,a842)),f848(x100481))),f317(f317(f8(f858(x100481,f858(a845,a842)),f858(a843,f858(f858(x100481,f858(a845,a842)),f848(x100481))),a846),f100(x100481)),x100483)),a29)),x100484)),x100485)),f317(f287(a846,f848(x100481),f317(f317(f18(a846,f858(x100481,f858(a845,a842)),f848(x100481)),f317(f317(f18(a846,a843,f858(f858(x100481,f858(a845,a842)),f848(x100481))),f317(f317(f8(f858(x100481,f858(a845,a842)),f858(a843,f858(f858(x100481,f858(a845,a842)),f848(x100481))),a846),f100(x100481)),x100483)),f317(f317(f8(f853(a843),a843,a846),f222(a843)),a27))),x100484)),x100485)) % 168.22/168.06 [10049]P21(x100491,x100492,f317(f287(a846,f848(x100491),f317(f317(f18(a846,f858(x100491,f858(a845,a842)),f848(x100491)),f317(f317(f18(a846,a843,f858(f858(x100491,f858(a845,a842)),f848(x100491))),f317(f317(f8(f858(x100491,f858(a845,a842)),f858(a843,f858(f858(x100491,f858(a845,a842)),f848(x100491))),a846),f100(x100491)),x100493)),a29)),x100494)),x100495))+~P21(x100491,f317(f317(f122(f858(f848(x100491),a842)),x100492),f317(f287(a846,f848(x100491),f317(f317(f18(a846,f858(x100491,f858(a845,a842)),f848(x100491)),f317(f317(f18(a846,a843,f858(f858(x100491,f858(a845,a842)),f848(x100491))),f317(f317(f8(f858(x100491,f858(a845,a842)),f858(a843,f858(f858(x100491,f858(a845,a842)),f848(x100491))),a846),f100(x100491)),x100493)),a29)),x100494)),x100495)),f317(f287(a846,f848(x100491),f317(f317(f18(a846,f858(x100491,f858(a845,a842)),f848(x100491)),f317(f317(f18(a846,a843,f858(f858(x100491,f858(a845,a842)),f848(x100491))),f317(f317(f8(f858(x100491,f858(a845,a842)),f858(a843,f858(f858(x100491,f858(a845,a842)),f848(x100491))),a846),f100(x100491)),x100493)),f317(f317(f8(f853(a843),a843,a846),f222(a843)),a27))),x100494)),x100495)) % 168.22/168.06 [5190]E(x51901,x51902)+~E(f31(x51903,x51904,x51901),f31(x51905,x51906,x51902)) % 168.22/168.06 [5191]E(x51911,x51912)+~E(f31(x51913,x51911,x51914),f31(x51915,x51912,x51916)) % 168.22/168.06 [5192]E(x51921,x51922)+~E(f31(x51921,x51923,x51924),f31(x51922,x51925,x51926)) % 168.22/168.06 [5193]E(x51931,x51932)+~E(f33(x51933,x51934,x51931),f33(x51935,x51936,x51932)) % 168.22/168.06 [5194]E(x51941,x51942)+~E(f33(x51943,x51941,x51944),f33(x51945,x51942,x51946)) % 168.22/168.06 [5195]E(x51951,x51952)+~E(f33(x51951,x51953,x51954),f33(x51952,x51955,x51956)) % 168.22/168.06 [5196]E(x51961,x51962)+~E(f32(x51963,x51964,x51961),f32(x51965,x51966,x51962)) % 168.22/168.06 [5197]E(x51971,x51972)+~E(f32(x51973,x51971,x51974),f32(x51975,x51972,x51976)) % 168.22/168.06 [5198]E(x51981,x51982)+~E(f32(x51981,x51983,x51984),f32(x51982,x51985,x51986)) % 168.22/168.06 [7143]E(x71431,x71432)+~E(f208(x71433,x71434,x71435,x71431),f208(x71433,x71434,x71436,x71432)) % 168.22/168.06 [7144]E(x71441,x71442)+~E(f208(x71443,x71444,x71441,x71445),f208(x71443,x71444,x71442,x71446)) % 168.22/168.06 [9307]~P32(x93071,x93072,x93073,x93076)+P32(x93071,x93072,f180(x93071,x93072,x93073,x93074,x93075),f180(x93071,x93072,x93076,x93074,x93075)) % 168.22/168.06 [6604]E(f317(f178(x66041,x66042,x66043,x66044),x66045),f317(f217(x66042),x66046))+~E(f317(x66044,x66045),f317(f217(x66042),x66046)) % 168.22/168.06 [6742]E(f317(f220(f853(x67421),x67422,f191(x67421),x67423),f317(x67424,x67425)),f317(x67423,x67426))+~E(f317(x67424,x67425),f317(f217(x67422),x67426)) % 168.22/168.06 [8257]~P14(x82575,x82571,x82572,x82576)+E(f317(f82(x82571,x82571,x82571,f317(x82572,x82573)),f317(x82572,x82574)),f317(f82(x82571,x82571,x82571,f317(x82572,x82574)),f317(x82572,x82573))) % 168.22/168.06 [8504]~P51(x85044,x85045,x85042,x85041,x85046)+E(f317(x85041,f317(x85042,x85043)),x85043) % 168.22/168.06 [8650]P19(x86501,x86502,x86503,x86504)+~P19(x86501,x86505,f317(f82(x86502,x86505,x86501,x86506),x86503),x86504) % 168.22/168.06 [8730]~P19(x87304,x87302,f317(f82(x87301,x87302,x87304,x87303),x87305),x87306)+P19(x87301,x87302,x87303,f317(f287(x87304,x87301,x87305),x87306)) % 168.22/168.06 [9433]P22(f317(f71(x94331),x94332))+~P22(f317(f76(x94331,x94333,x94334,x94335,x94332),x94336)) % 168.22/168.06 [9440]~P22(f317(f317(f319(x94404),x94403),f276(x94404,x94405,x94401,x94402,x94406)))+P22(f317(f317(x94401,x94402),x94403)) % 168.22/168.06 [9441]~P22(f317(f317(f319(x94414),x94413),f273(x94414,x94411,x94415,x94412,x94416)))+P22(f317(f317(x94411,x94412),x94413)) % 168.22/168.06 [9442]~P22(f317(f317(f319(x94424),x94422),f276(x94424,x94421,x94425,x94426,x94423)))+P22(f317(f317(x94421,x94422),x94423)) % 168.22/168.06 [9443]~P22(f317(f317(f319(x94434),x94432),f273(x94434,x94435,x94431,x94436,x94433)))+P22(f317(f317(x94431,x94432),x94433)) % 168.22/168.06 [5684]E(x56841,x56842)+~E(f317(f317(f237(x56843,x56844),x56845),x56841),f317(f317(f237(x56843,x56844),x56846),x56842)) % 168.22/168.06 [5686]E(x56861,x56862)+~E(f317(f317(f237(x56863,x56864),x56861),x56865),f317(f317(f237(x56863,x56864),x56862),x56866)) % 168.22/168.06 [7193]~P33(x71934,x71931,f317(f317(f145(x71934),x71932),x71935),f317(f317(f145(x71934),x71933),x71936))+P22(f317(f317(x71931,x71932),x71933)) % 168.22/168.06 [7557]P33(x75571,x75572,x75573,x75574)+~P33(x75571,x75572,f317(f317(f145(x75571),x75575),x75573),f317(f317(f145(x75571),x75576),x75574)) % 168.22/168.06 [8365]~P32(x83651,x83652,x83653,x83655)+P32(x83651,x83652,f317(f317(f317(f81(x83651,f853(x83652)),x83653),x83654),f191(x83652)),f317(f317(f317(f81(x83651,f853(x83652)),x83655),x83654),f317(f217(x83652),x83656))) % 168.22/168.06 [8593]~P51(x85935,x85931,x85932,x85936,x85934)+P22(f317(f317(f319(x85931),f317(x85932,x85933)),x85934)) % 168.22/168.06 [8757]E(f317(f85(x87571,x87572,x87573,x87574,x87575),x87576),f317(x87573,x87576))+P22(f317(f317(f319(x87571),x87576),x87575)) % 168.22/168.06 [8777]~E(x87773,f317(f317(f145(x87771),x87775),x87776))+P22(f317(f317(f319(f857(f850(x87771),f850(x87771))),f317(f317(f237(f850(x87771),f850(x87771)),x87772),f317(f317(f127(x87771),x87772),x87773))),f141(x87771,x87774))) % 168.22/168.06 [8785]E(f317(f85(x87851,x87852,x87853,x87854,x87855),x87856),f317(x87854,x87856))+~P22(f317(f317(f319(x87851),x87856),x87855)) % 168.22/168.06 [8790]E(f317(f180(x87901,x87902,x87903,x87904,x87905),x87906),f317(x87903,x87906))+P22(f317(f317(f319(x87901),x87906),f317(f166(x87901),x87904))) % 168.22/168.06 [9016]~P35(x90161,x90162,x90163,x90165,x90166)+P35(x90161,x90162,x90163,f317(f317(f167(x90161),x90164),x90165),f317(f317(f167(x90162),x90164),x90166)) % 168.22/168.06 [9017]~P35(x90171,x90172,x90173,x90175,x90176)+P35(x90171,x90172,x90173,f317(f317(f132(x90171),x90174),x90175),f317(f317(f132(x90172),x90174),x90176)) % 168.22/168.06 [9504]~P17(x95044,x95042,x95045,x95043,x95046,x95041)+E(f317(x95041,f188(f858(x95042,a842))),x95043) % 168.22/168.06 [9740]~E(f317(x97404,f317(f244(x97401,x97403),x97405)),f317(x97406,f317(f244(x97401,x97403),x97405)))+E(f317(f248(x97401,x97402,x97403,x97403,x97404,f39(x97403)),x97405),f317(f248(x97401,x97402,x97403,x97403,x97406,f39(x97403)),x97405)) % 168.22/168.06 [9741]~E(f317(x97414,f317(f246(x97411,x97412),x97415)),f317(x97416,f317(f246(x97411,x97412),x97415)))+E(f317(f248(x97411,x97411,x97412,x97413,f39(x97411),x97414),x97415),f317(f248(x97411,x97411,x97412,x97413,f39(x97411),x97416),x97415)) % 168.22/168.06 [9791]~E(f317(f248(x97912,x97916,x97913,x97913,x97911,f39(x97913)),x97914),f317(f248(x97912,x97916,x97913,x97913,x97915,f39(x97913)),x97914))+E(f317(x97911,f317(f244(x97912,x97913),x97914)),f317(x97915,f317(f244(x97912,x97913),x97914))) % 168.22/168.06 [9792]~E(f317(f248(x97922,x97922,x97923,x97926,f39(x97922),x97921),x97924),f317(f248(x97922,x97922,x97923,x97926,f39(x97922),x97925),x97924))+E(f317(x97921,f317(f246(x97922,x97923),x97924)),f317(x97925,f317(f246(x97922,x97923),x97924))) % 168.22/168.06 [8687]P22(f317(f317(f319(x86871),x86872),x86873))+~P22(f317(f317(f319(f857(x86871,x86874)),f317(f317(f237(x86871,x86874),x86872),x86875)),f317(f317(f245(x86871,x86874),x86873),x86876))) % 168.22/168.06 [8701]P22(f317(f317(f319(x87011),x87012),f317(x87013,x87014)))+~P22(f317(f317(f319(f857(x87015,x87011)),f317(f317(f237(x87015,x87011),x87014),x87012)),f317(f317(f245(x87015,x87011),x87016),x87013))) % 168.22/168.06 [8787]~E(f317(f189(f850(x87871)),x87874),f317(f189(f850(x87872)),x87875))+E(f180(x87871,x87872,x87873,x87874,f317(f317(f127(x87872),x87875),x87876)),f180(x87871,x87872,x87873,x87874,x87875)) % 168.22/168.06 [8788]~E(f317(f189(f850(x87881)),x87884),f317(f189(f850(x87882)),x87886))+E(f180(x87881,x87882,x87883,f317(f317(f127(x87881),x87884),x87885),x87886),f180(x87881,x87882,x87883,x87884,x87886)) % 168.22/168.06 [9037]P22(f317(f317(f319(x90371),x90374),f177(x90371,x90372,x90376)))+E(f178(x90371,x90372,f317(f317(f317(f81(x90371,f853(x90372)),x90373),x90374),f317(f217(x90372),x90375)),x90376),f317(f317(f317(f81(x90371,f853(x90372)),f178(x90371,x90372,x90373,x90376)),x90374),f317(f217(x90372),x90375))) % 168.22/168.06 [9134]P22(f317(f317(f319(f857(x91341,x91341)),f317(f317(f237(x91341,x91341),f317(x91342,x91343)),f317(x91342,x91344))),x91345))+~P22(f317(f317(f319(f857(x91346,x91346)),f317(f317(f237(x91346,x91346),x91343),x91344)),f317(f317(f264(x91341,x91346),x91345),x91342))) % 168.22/168.06 [9153]~P22(f317(f317(f319(f857(x91534,x91534)),f317(f317(f237(x91534,x91534),f317(x91536,x91532)),f317(x91536,x91533))),x91535))+P22(f317(f317(f319(f857(x91531,x91531)),f317(f317(f237(x91531,x91531),x91532),x91533)),f317(f317(f264(x91534,x91531),x91535),x91536))) % 168.22/168.06 [9776]P22(f317(f317(f317(f317(a197,x97761),f317(f317(f317(a200,x97762),f40(x97763)),f317(x97764,x97762))),x97765),f536(x97766,x97765,x97762,x97761,x97764,x97763)))+~P22(f317(f317(f317(f317(a197,f32(x97763,x97764,x97761)),x97762),x97765),f317(f317(f317(a200,x97766),f40(x97763)),f317(f317(a201,x97762),x97763)))) % 168.22/168.06 [9795]P22(f317(f317(f317(f317(a197,f317(a29,x97951)),f317(f317(f317(a200,f317(f317(a202,x97952),a203)),f40(a26)),f317(x97953,x97952))),x97954),f579(x97955,x97954,x97952,x97953,x97951,x97956)))+~P22(f317(f317(f317(f317(a197,f31(x97956,x97951,x97953)),x97952),x97954),f317(f317(f317(a200,f317(f317(a202,x97955),f317(a201,x97952))),x97956),f317(f317(a201,x97955),a25)))) % 168.22/168.06 [9871]E(f317(f317(f317(a200,f536(x98711,x98712,x98713,x98714,x98715,x98716)),f40(x98716)),f317(f317(a201,x98713),x98716)),f317(f317(f317(a200,x98711),f40(x98716)),f317(f317(a201,x98713),x98716)))+~P22(f317(f317(f317(f317(a197,f32(x98716,x98715,x98714)),x98713),x98712),f317(f317(f317(a200,x98711),f40(x98716)),f317(f317(a201,x98713),x98716)))) % 168.22/168.06 [9989]E(f317(f317(f317(a200,f317(f317(a202,f579(x99891,x99892,x99893,x99894,x99895,x99896)),f317(a201,x99893))),x99896),f317(f317(a201,f579(x99891,x99892,x99893,x99894,x99895,x99896)),a25)),f317(f317(f317(a200,f317(f317(a202,x99891),f317(a201,x99893))),x99896),f317(f317(a201,x99891),a25)))+~P22(f317(f317(f317(f317(a197,f31(x99896,x99895,x99894)),x99893),x99892),f317(f317(f317(a200,f317(f317(a202,x99891),f317(a201,x99893))),x99896),f317(f317(a201,x99891),a25)))) % 168.22/168.06 [6075]~E(x60756,x60754)+E(f317(f317(f317(f317(f81(x60751,x60752),x60753),x60754),x60755),x60756),x60755) % 168.22/168.06 [6123]E(x61231,x61232)+E(f317(f317(f317(f317(f81(x61233,x61234),x61235),x61232),x61236),x61231),f317(x61235,x61231)) % 168.22/168.06 [7629]~P27(x76292)+E(f317(f317(f51(x76291,x76292),x76293),f317(f317(f7(x76291,x76294,x76292),x76295),x76296)),f317(f317(f317(f51(x76291,f858(x76294,x76292)),x76293),x76295),x76296)) % 168.22/168.06 [7630]~P27(x76302)+E(f317(f317(f52(x76301,x76302),x76303),f317(f317(f7(x76301,x76304,x76302),x76305),x76306)),f317(f317(f317(f52(x76301,f858(x76304,x76302)),x76303),x76305),x76306)) % 168.22/168.06 [8286]~P32(x82861,x82862,x82863,x82866)+P32(x82861,x82862,f317(f317(f317(f81(x82861,f853(x82862)),x82863),x82864),x82865),f317(f317(f317(f81(x82861,f853(x82862)),x82866),x82864),x82865)) % 168.22/168.06 [8415]E(f317(f317(f51(x84151,f858(x84152,a842)),x84153),f317(f317(f8(f858(x84152,a842),f858(x84152,a842),x84151),f317(f286(x84152),x84154)),x84155)),f317(f317(f286(x84152),x84154),f317(f317(f51(x84151,f858(x84152,a842)),x84153),x84155)))+~P22(f317(f317(f319(x84151),x84156),x84153)) % 168.22/168.06 [8840]~P27(x88402)+E(f317(f317(f51(x88401,x88402),x88403),f317(f317(f8(f858(x88404,x88402),x88402,x88401),f317(f51(x88404,x88402),x88405)),f317(f7(x88404,x88401,x88402),x88406))),f317(f317(f51(x88404,x88402),x88405),f317(f317(f8(f858(x88401,x88402),x88402,x88404),f317(f51(x88401,x88402),x88403)),x88406))) % 168.22/168.06 [8841]~P27(x88412)+E(f317(f317(f52(x88411,x88412),x88413),f317(f317(f8(f858(x88414,x88412),x88412,x88411),f317(f52(x88414,x88412),x88415)),f317(f7(x88414,x88411,x88412),x88416))),f317(f317(f52(x88414,x88412),x88415),f317(f317(f8(f858(x88411,x88412),x88412,x88414),f317(f52(x88411,x88412),x88413)),x88416))) % 168.22/168.06 [9046]P22(f317(f317(f319(x90461),x90462),f317(f166(x90461),x90463)))+~P22(f317(f317(f319(f857(x90464,x90461)),f317(f317(f237(x90464,x90461),x90465),x90462)),f317(f166(f857(x90464,x90461)),f317(f317(f175(x90464,x90461),x90466),x90463)))) % 168.22/168.06 [9047]P22(f317(f317(f319(x90471),x90472),f317(f166(x90471),x90473)))+~P22(f317(f317(f319(f857(x90471,x90474)),f317(f317(f237(x90471,x90474),x90472),x90475)),f317(f166(f857(x90471,x90474)),f317(f317(f175(x90471,x90474),x90473),x90476)))) % 168.22/168.06 [9147]P22(f317(f317(f225(f858(x91471,a842)),f317(f262(x91472,x91471,x91473),x91474)),x91475))+~P22(f317(f317(f225(f858(f857(x91472,x91471),a842)),x91473),f317(f317(f245(x91472,x91471),x91476),f317(f16(f858(x91471,a842),x91472),x91475)))) % 168.22/168.06 [9337]P22(f317(f317(f319(f857(f850(x93371),f850(x93371))),f317(f317(f237(f850(x93371),f850(x93371)),f317(f317(f145(x93371),x93372),x93373)),f317(f317(f145(x93371),x93374),x93375))),f141(x93371,x93376)))+~P22(f317(f317(f319(f857(x93371,x93371)),f317(f317(f237(x93371,x93371),x93372),x93374)),x93376)) % 168.22/168.06 [9375]P22(f317(f317(f317(f317(a197,f32(x93751,x93752,x93753)),x93754),x93755),f317(f317(f317(a200,x93756),f40(x93751)),f317(f317(a201,x93754),x93751))))+~P22(f317(f317(f317(f317(a197,x93753),f317(f317(f317(a200,x93754),f40(x93751)),f317(x93752,x93754))),x93755),x93756)) % 168.22/168.06 [9649]P22(f317(f317(f317(f317(a197,f31(x96491,x96492,x96493)),x96494),x96495),f317(f317(f317(a200,f317(f317(a202,x96496),f317(a201,x96494))),x96491),f317(f317(a201,x96496),a25))))+~P22(f317(f317(f317(f317(a197,f317(a29,x96492)),f317(f317(f317(a200,f317(f317(a202,x96494),a203)),f40(a26)),f317(x96493,x96494))),x96495),x96496)) % 168.22/168.06 [9771]P22(f317(f317(f317(f317(a197,x97711),f317(f317(f317(a200,x97712),f40(x97713)),f317(x97714,x97712))),x97715),f568(x97716,x97715,x97712,x97711,x97714,x97713)))+~P22(f317(f317(f317(f317(a197,f32(x97713,x97714,x97711)),x97712),x97715),x97716)) % 168.22/168.06 [9787]P22(f317(f317(f317(f317(a197,f317(a29,x97871)),f317(f317(f317(a200,f317(f317(a202,x97872),a203)),f40(a26)),f317(x97873,x97872))),x97874),f611(x97875,x97874,x97872,x97873,x97871,x97876)))+~P22(f317(f317(f317(f317(a197,f31(x97876,x97871,x97873)),x97872),x97874),x97875)) % 168.22/168.06 [9790]E(f317(f317(f237(x97901,x97902),f710(x97903,x97904,x97905,x97902,x97901,x97906)),f714(x97903,x97904,x97905,x97902,x97901,x97906)),x97906)+P22(f317(f317(f319(x97905),x97904),f317(f317(f247(x97901,x97902,f858(x97905,a842)),x97903),x97906))) % 168.22/168.06 [9796]E(f317(f317(f237(x97961,x97962),f711(x97963,x97964,x97962,x97961,x97965,x97966)),f713(x97963,x97964,x97962,x97961,x97965,x97966)),x97963)+~P22(f317(f317(f319(x97966),x97965),f317(f317(f247(x97961,x97962,f858(x97966,a842)),x97964),x97963))) % 168.22/168.06 [9867]E(f317(f317(f317(a200,f568(x98671,x98672,x98673,x98674,x98675,x98676)),f40(x98676)),f317(f317(a201,x98673),x98676)),x98671)+~P22(f317(f317(f317(f317(a197,f32(x98676,x98675,x98674)),x98673),x98672),x98671)) % 168.22/168.06 [9955]P22(f317(f317(f319(x99551),x99552),f317(f317(x99553,f711(x99554,x99553,x99555,x99556,x99552,x99551)),f713(x99554,x99553,x99555,x99556,x99552,x99551))))+~P22(f317(f317(f319(x99551),x99552),f317(f317(f247(x99556,x99555,f858(x99551,a842)),x99553),x99554))) % 168.22/168.06 [9975]~P22(f317(f317(f319(x99751),x99752),f317(f317(x99755,f710(x99755,x99752,x99751,x99754,x99753,x99756)),f714(x99755,x99752,x99751,x99754,x99753,x99756))))+P22(f317(f317(f319(x99751),x99752),f317(f317(f247(x99753,x99754,f858(x99751,a842)),x99755),x99756))) % 168.22/168.06 [9987]E(f317(f317(f317(a200,f317(f317(a202,f611(x99871,x99872,x99873,x99874,x99875,x99876)),f317(a201,x99873))),x99876),f317(f317(a201,f611(x99871,x99872,x99873,x99874,x99875,x99876)),a25)),x99871)+~P22(f317(f317(f317(f317(a197,f31(x99876,x99875,x99874)),x99873),x99872),x99871)) % 168.22/168.06 [7751]P22(f317(f317(f319(x77511),x77514),x77516))+E(f181(x77511,x77512,f317(f317(f317(f81(x77511,f853(x77512)),x77513),x77514),x77515),x77516),f181(x77511,x77512,x77513,x77516)) % 168.22/168.06 [7819]P22(f317(f317(f319(x78191),x78194),x78196))+E(f317(f287(x78191,x78192,f317(f317(f317(f81(x78191,x78192),x78193),x78194),x78195)),x78196),f317(f287(x78191,x78192,x78193),x78196)) % 168.22/168.06 [7845]P22(f317(f317(f319(x78451),x78454),f317(f166(x78451),x78456)))+E(f317(f317(f148(x78451,x78452),f317(f317(f317(f81(x78451,x78452),x78453),x78454),x78455)),x78456),f317(f317(f148(x78451,x78452),x78453),x78456)) % 168.22/168.06 [8307]E(x83071,x83072)+E(f317(f317(f153(x83073,f317(f317(f153(x83073,x83074),x83071),x83075)),x83072),x83076),f317(f317(f153(x83073,f317(f317(f153(x83073,x83074),x83072),x83076)),x83071),x83075)) % 168.22/168.06 [8846]~P22(f317(f317(f319(x88463),x88466),x88465))+E(f317(f317(f286(x88461),x88462),f317(f287(x88463,x88461,x88464),f317(f317(f21(f858(x88463,a842)),x88465),f317(f317(f286(x88463),x88466),f188(f858(x88463,a842)))))),f317(f287(x88463,x88461,f317(f317(f317(f81(x88463,x88461),x88464),x88466),x88462)),x88465)) % 168.22/168.06 [9603]E(f180(x96031,x96032,x96033,f317(f317(f127(x96031),x96034),f317(f317(f145(x96031),x96035),f125(x96031))),x96036),f317(f317(f317(f81(x96031,f853(x96032)),f180(x96031,x96032,x96033,x96034,x96036)),x96035),f317(f217(x96032),f317(f317(f159(x96032),x96036),f317(f189(f850(x96031)),x96034)))))+~P22(f317(f317(f226(a849),f317(f189(f850(x96031)),x96034)),f317(f189(f850(x96032)),x96036))) % 168.22/168.06 [8632]~E(x86323,x86326)+E(f317(f317(f171(x86321,x86322),f317(f317(f145(f857(x86321,x86322)),f317(f317(f237(x86321,x86322),x86323),x86324)),x86325)),x86326),f317(f217(x86322),x86324)) % 168.22/168.06 [8659]E(x86591,x86592)+E(f317(f317(f171(x86593,x86594),f317(f317(f145(f857(x86593,x86594)),f317(f317(f237(x86593,x86594),x86591),x86595)),x86596)),x86592),f317(f317(f171(x86593,x86594),x86596),x86592)) % 168.22/168.06 [8925]~P22(f317(f317(x89254,x89255),x89256))+P22(f317(f317(f317(f317(f122(f858(x89251,f858(x89252,a842))),x89253),x89254),x89255),x89256)) % 168.22/168.06 [8927]~P22(f317(f317(x89273,x89275),x89276))+P22(f317(f317(f317(f317(f122(f858(x89271,f858(x89272,a842))),x89273),x89274),x89275),x89276)) % 168.22/168.06 [9204]P22(f317(f317(x92041,x92042),x92043))+~P22(f317(f317(f317(f317(f113(f858(x92044,f858(x92045,a842))),x92046),x92041),x92042),x92043)) % 168.22/168.06 [9205]P22(f317(f317(x92051,x92052),x92053))+~P22(f317(f317(f317(f317(f113(f858(x92054,f858(x92055,a842))),x92051),x92056),x92052),x92053)) % 168.22/168.06 [9624]~P70(x96242)+E(f317(f317(f9(x96241,x96242),f317(f317(f7(x96241,f858(x96243,a842),x96242),f317(f317(f8(f858(x96243,x96242),f858(f858(x96243,a842),x96242),x96241),f9(x96243,x96242)),x96244)),x96245)),x96246),f317(f317(f9(f857(x96241,x96243),x96242),f317(f247(x96241,x96243,x96242),x96244)),f317(f317(f245(x96241,x96243),x96246),f317(f16(f858(x96243,a842),x96241),x96245)))) % 168.22/168.06 [9625]~P67(x96252)+E(f317(f317(f6(x96251,x96252),f317(f317(f7(x96251,f858(x96253,a842),x96252),f317(f317(f8(f858(x96253,x96252),f858(f858(x96253,a842),x96252),x96251),f6(x96253,x96252)),x96254)),x96255)),x96256),f317(f317(f6(f857(x96251,x96253),x96252),f317(f247(x96251,x96253,x96252),x96254)),f317(f317(f245(x96251,x96253),x96256),f317(f16(f858(x96253,a842),x96251),x96255)))) % 168.22/168.06 [9768]~P67(x97682)+E(f317(f317(f6(x97681,x97682),f317(f317(f7(x97681,f858(x97683,a842),x97682),f317(f317(f8(f858(x97683,x97682),f858(f858(x97683,a842),x97682),x97681),f6(x97683,x97682)),f317(f7(x97683,x97681,x97682),x97684))),x97685)),x97686),f317(f317(f6(x97683,x97682),f317(f317(f7(x97683,f858(x97681,a842),x97682),f317(f317(f8(f858(x97681,x97682),f858(f858(x97681,a842),x97682),x97683),f6(x97681,x97682)),x97684)),x97686)),x97685)) % 168.22/168.06 [9473]~P22(f317(f317(f319(x94731),x94735),x94734))+E(f317(f317(f317(f81(x94731,f853(x94732)),f181(x94731,x94732,x94733,f317(f317(f21(f858(x94731,a842)),x94734),f317(f317(f286(x94731),x94735),f188(f858(x94731,a842)))))),x94735),x94736),f181(x94731,x94732,f317(f317(f317(f81(x94731,f853(x94732)),x94733),x94735),x94736),x94734)) % 168.22/168.06 [10052]~P22(f317(f317(f319(f857(x100521,x100522)),f317(f317(f237(x100521,x100522),x100525),x100526)),f317(f317(f122(f858(f857(x100521,x100522),a842)),x100523),x100524)))+P22(f317(f317(f317(f317(f122(f858(x100521,f858(x100522,a842))),f317(f317(f7(x100521,f858(f857(x100521,x100522),a842),f858(x100522,a842)),f317(f317(f8(f858(x100522,f858(f858(f857(x100521,x100522),a842),a842)),f858(f858(f857(x100521,x100522),a842),f858(x100522,a842)),x100521),f7(x100522,f858(f857(x100521,x100522),a842),a842)),f317(f317(f8(f858(x100522,f857(x100521,x100522)),f858(x100522,f858(f858(f857(x100521,x100522),a842),a842)),x100521),f317(f8(f857(x100521,x100522),f858(f858(f857(x100521,x100522),a842),a842),x100522),f319(f857(x100521,x100522)))),f237(x100521,x100522)))),x100523)),f317(f317(f7(x100521,f858(f857(x100521,x100522),a842),f858(x100522,a842)),f317(f317(f8(f858(x100522,f858(f858(f857(x100521,x100522),a842),a842)),f858(f858(f857(x100521,x100522),a842),f858(x100522,a842)),x100521),f7(x100522,f858(f857(x100521,x100522),a842),a842)),f317(f317(f8(f858(x100522,f857(x100521,x100522)),f858(x100522,f858(f858(f857(x100521,x100522),a842),a842)),x100521),f317(f8(f857(x100521,x100522),f858(f858(f857(x100521,x100522),a842),a842),x100522),f319(f857(x100521,x100522)))),f237(x100521,x100522)))),x100524)),x100525),x100526)) % 168.22/168.06 [10053]~P22(f317(f317(f319(f857(x100531,x100532)),f317(f317(f237(x100531,x100532),x100535),x100536)),f317(f317(f113(f858(f857(x100531,x100532),a842)),x100533),x100534)))+P22(f317(f317(f317(f317(f113(f858(x100531,f858(x100532,a842))),f317(f317(f7(x100531,f858(f857(x100531,x100532),a842),f858(x100532,a842)),f317(f317(f8(f858(x100532,f858(f858(f857(x100531,x100532),a842),a842)),f858(f858(f857(x100531,x100532),a842),f858(x100532,a842)),x100531),f7(x100532,f858(f857(x100531,x100532),a842),a842)),f317(f317(f8(f858(x100532,f857(x100531,x100532)),f858(x100532,f858(f858(f857(x100531,x100532),a842),a842)),x100531),f317(f8(f857(x100531,x100532),f858(f858(f857(x100531,x100532),a842),a842),x100532),f319(f857(x100531,x100532)))),f237(x100531,x100532)))),x100533)),f317(f317(f7(x100531,f858(f857(x100531,x100532),a842),f858(x100532,a842)),f317(f317(f8(f858(x100532,f858(f858(f857(x100531,x100532),a842),a842)),f858(f858(f857(x100531,x100532),a842),f858(x100532,a842)),x100531),f7(x100532,f858(f857(x100531,x100532),a842),a842)),f317(f317(f8(f858(x100532,f857(x100531,x100532)),f858(x100532,f858(f858(f857(x100531,x100532),a842),a842)),x100531),f317(f8(f857(x100531,x100532),f858(f858(f857(x100531,x100532),a842),a842),x100532),f319(f857(x100531,x100532)))),f237(x100531,x100532)))),x100534)),x100535),x100536)) % 168.22/168.06 [10058]P22(f317(f317(f319(f857(x100581,x100582)),f317(f317(f237(x100581,x100582),x100583),x100584)),f317(f317(f122(f858(f857(x100581,x100582),a842)),x100585),x100586)))+~P22(f317(f317(f317(f317(f122(f858(x100581,f858(x100582,a842))),f317(f317(f7(x100581,f858(f857(x100581,x100582),a842),f858(x100582,a842)),f317(f317(f8(f858(x100582,f858(f858(f857(x100581,x100582),a842),a842)),f858(f858(f857(x100581,x100582),a842),f858(x100582,a842)),x100581),f7(x100582,f858(f857(x100581,x100582),a842),a842)),f317(f317(f8(f858(x100582,f857(x100581,x100582)),f858(x100582,f858(f858(f857(x100581,x100582),a842),a842)),x100581),f317(f8(f857(x100581,x100582),f858(f858(f857(x100581,x100582),a842),a842),x100582),f319(f857(x100581,x100582)))),f237(x100581,x100582)))),x100585)),f317(f317(f7(x100581,f858(f857(x100581,x100582),a842),f858(x100582,a842)),f317(f317(f8(f858(x100582,f858(f858(f857(x100581,x100582),a842),a842)),f858(f858(f857(x100581,x100582),a842),f858(x100582,a842)),x100581),f7(x100582,f858(f857(x100581,x100582),a842),a842)),f317(f317(f8(f858(x100582,f857(x100581,x100582)),f858(x100582,f858(f858(f857(x100581,x100582),a842),a842)),x100581),f317(f8(f857(x100581,x100582),f858(f858(f857(x100581,x100582),a842),a842),x100582),f319(f857(x100581,x100582)))),f237(x100581,x100582)))),x100586)),x100583),x100584)) % 168.22/168.06 [10059]P22(f317(f317(f319(f857(x100591,x100592)),f317(f317(f237(x100591,x100592),x100593),x100594)),f317(f317(f113(f858(f857(x100591,x100592),a842)),x100595),x100596)))+~P22(f317(f317(f317(f317(f113(f858(x100591,f858(x100592,a842))),f317(f317(f7(x100591,f858(f857(x100591,x100592),a842),f858(x100592,a842)),f317(f317(f8(f858(x100592,f858(f858(f857(x100591,x100592),a842),a842)),f858(f858(f857(x100591,x100592),a842),f858(x100592,a842)),x100591),f7(x100592,f858(f857(x100591,x100592),a842),a842)),f317(f317(f8(f858(x100592,f857(x100591,x100592)),f858(x100592,f858(f858(f857(x100591,x100592),a842),a842)),x100591),f317(f8(f857(x100591,x100592),f858(f858(f857(x100591,x100592),a842),a842),x100592),f319(f857(x100591,x100592)))),f237(x100591,x100592)))),x100595)),f317(f317(f7(x100591,f858(f857(x100591,x100592),a842),f858(x100592,a842)),f317(f317(f8(f858(x100592,f858(f858(f857(x100591,x100592),a842),a842)),f858(f858(f857(x100591,x100592),a842),f858(x100592,a842)),x100591),f7(x100592,f858(f857(x100591,x100592),a842),a842)),f317(f317(f8(f858(x100592,f857(x100591,x100592)),f858(x100592,f858(f858(f857(x100591,x100592),a842),a842)),x100591),f317(f8(f857(x100591,x100592),f858(f858(f857(x100591,x100592),a842),a842),x100592),f319(f857(x100591,x100592)))),f237(x100591,x100592)))),x100596)),x100593),x100594)) % 168.22/168.06 [10046]~P22(f317(f317(f319(f857(x100462,x100463)),f317(f317(f237(x100462,x100463),x100465),x100466)),f317(f317(f51(x100461,f858(f857(x100462,x100463),a842)),f233(f858(x100461,a842))),x100464)))+P22(f317(f317(f317(f317(f51(x100461,f858(x100462,f858(x100463,a842))),f233(f858(x100461,a842))),f317(f317(f8(f858(f857(x100462,x100463),a842),f858(x100462,f858(x100463,a842)),x100461),f317(f7(x100462,f858(f857(x100462,x100463),a842),f858(x100463,a842)),f317(f317(f8(f858(x100463,f858(f858(f857(x100462,x100463),a842),a842)),f858(f858(f857(x100462,x100463),a842),f858(x100463,a842)),x100462),f7(x100463,f858(f857(x100462,x100463),a842),a842)),f317(f317(f8(f858(x100463,f857(x100462,x100463)),f858(x100463,f858(f858(f857(x100462,x100463),a842),a842)),x100462),f317(f8(f857(x100462,x100463),f858(f858(f857(x100462,x100463),a842),a842),x100463),f319(f857(x100462,x100463)))),f237(x100462,x100463))))),x100464)),x100465),x100466)) % 168.22/168.06 [10047]~P22(f317(f317(f319(f857(x100472,x100473)),f317(f317(f237(x100472,x100473),x100475),x100476)),f317(f317(f52(x100471,f858(f857(x100472,x100473),a842)),f233(f858(x100471,a842))),x100474)))+P22(f317(f317(f317(f317(f52(x100471,f858(x100472,f858(x100473,a842))),f233(f858(x100471,a842))),f317(f317(f8(f858(f857(x100472,x100473),a842),f858(x100472,f858(x100473,a842)),x100471),f317(f7(x100472,f858(f857(x100472,x100473),a842),f858(x100473,a842)),f317(f317(f8(f858(x100473,f858(f858(f857(x100472,x100473),a842),a842)),f858(f858(f857(x100472,x100473),a842),f858(x100473,a842)),x100472),f7(x100473,f858(f857(x100472,x100473),a842),a842)),f317(f317(f8(f858(x100473,f857(x100472,x100473)),f858(x100473,f858(f858(f857(x100472,x100473),a842),a842)),x100472),f317(f8(f857(x100472,x100473),f858(f858(f857(x100472,x100473),a842),a842),x100473),f319(f857(x100472,x100473)))),f237(x100472,x100473))))),x100474)),x100475),x100476)) % 168.22/168.06 [10055]P22(f317(f317(f319(f857(x100551,x100552)),f317(f317(f237(x100551,x100552),x100553),x100554)),f317(f317(f51(x100555,f858(f857(x100551,x100552),a842)),f233(f858(x100555,a842))),x100556)))+~P22(f317(f317(f317(f317(f51(x100555,f858(x100551,f858(x100552,a842))),f233(f858(x100555,a842))),f317(f317(f8(f858(f857(x100551,x100552),a842),f858(x100551,f858(x100552,a842)),x100555),f317(f7(x100551,f858(f857(x100551,x100552),a842),f858(x100552,a842)),f317(f317(f8(f858(x100552,f858(f858(f857(x100551,x100552),a842),a842)),f858(f858(f857(x100551,x100552),a842),f858(x100552,a842)),x100551),f7(x100552,f858(f857(x100551,x100552),a842),a842)),f317(f317(f8(f858(x100552,f857(x100551,x100552)),f858(x100552,f858(f858(f857(x100551,x100552),a842),a842)),x100551),f317(f8(f857(x100551,x100552),f858(f858(f857(x100551,x100552),a842),a842),x100552),f319(f857(x100551,x100552)))),f237(x100551,x100552))))),x100556)),x100553),x100554)) % 168.22/168.06 [10056]P22(f317(f317(f319(f857(x100561,x100562)),f317(f317(f237(x100561,x100562),x100563),x100564)),f317(f317(f52(x100565,f858(f857(x100561,x100562),a842)),f233(f858(x100565,a842))),x100566)))+~P22(f317(f317(f317(f317(f52(x100565,f858(x100561,f858(x100562,a842))),f233(f858(x100565,a842))),f317(f317(f8(f858(f857(x100561,x100562),a842),f858(x100561,f858(x100562,a842)),x100565),f317(f7(x100561,f858(f857(x100561,x100562),a842),f858(x100562,a842)),f317(f317(f8(f858(x100562,f858(f858(f857(x100561,x100562),a842),a842)),f858(f858(f857(x100561,x100562),a842),f858(x100562,a842)),x100561),f7(x100562,f858(f857(x100561,x100562),a842),a842)),f317(f317(f8(f858(x100562,f857(x100561,x100562)),f858(x100562,f858(f858(f857(x100561,x100562),a842),a842)),x100561),f317(f8(f857(x100561,x100562),f858(f858(f857(x100561,x100562),a842),a842),x100562),f319(f857(x100561,x100562)))),f237(x100561,x100562))))),x100566)),x100563),x100564)) % 168.22/168.06 [9115]E(x91151,x91152)+~E(f303(x91153,x91154,x91155,x91156,x91151),f303(x91153,x91154,x91155,x91157,x91152)) % 168.22/168.06 [9116]E(x91161,x91162)+~E(f303(x91163,x91164,x91165,x91161,x91166),f303(x91163,x91164,x91165,x91162,x91167)) % 168.22/168.06 [7308]E(f317(x73081,f317(x73082,x73083)),f317(x73084,x73083))+~E(f317(f82(x73085,x73086,x73087,x73081),x73082),x73084) % 168.22/168.06 [9853]~P48(x98535,x98536,x98537,x98531,x98534,x98532,x98533)+P22(f317(f317(x98531,x98532),f560(x98533,x98532,x98534,x98531))) % 168.22/168.06 [9876]~E(f317(f220(f853(x98767),x98761,f191(x98767),x98765),f317(x98764,x98763)),f317(f217(x98767),x98762))+E(f317(f217(x98761),f825(x98762,x98763,x98764,x98765,x98766,x98767,x98761)),f317(x98764,x98763)) % 168.22/168.06 [9877]~E(f317(f220(f853(x98776),x98777,f191(x98776),x98771),f317(x98774,x98773)),f317(f217(x98776),x98772))+E(f317(x98771,f825(x98772,x98773,x98774,x98771,x98775,x98776,x98777)),f317(f217(x98776),x98772)) % 168.22/168.06 [5907]~E(f317(f317(f148(x59071,x59075),x59076),x59072),f317(f317(f148(x59073,x59075),x59077),x59074))+E(f317(f189(f850(x59071)),x59072),f317(f189(f850(x59073)),x59074)) % 168.22/168.06 [7383]E(x73831,x73832)+~E(f317(f317(f317(f81(x73833,f853(x73834)),x73835),x73836),f317(f217(x73834),x73831)),f317(f317(f317(f81(x73833,f853(x73834)),x73837),x73836),f317(f217(x73834),x73832))) % 168.22/168.06 [8346]E(f317(x83461,f317(x83462,x83463)),f317(x83464,x83463))+~E(f317(f82(x83465,x83466,x83467,x83461),x83462),f317(f82(x83466,x83466,x83467,f39(x83466)),x83464)) % 168.22/168.06 [8677]~P35(x86774,x86775,x86771,f317(f317(f145(x86774),x86772),x86776),f317(f317(f145(x86775),x86773),x86777))+P22(f317(f317(x86771,x86772),x86773)) % 168.22/168.06 [9051]P35(x90511,x90512,x90513,x90514,x90515)+~P35(x90511,x90512,x90513,f317(f317(f145(x90511),x90516),x90514),f317(f317(f145(x90512),x90517),x90515)) % 168.22/168.06 [9858]~P48(x98585,x98586,x98587,x98584,x98581,x98583,x98582)+P22(f317(f317(x98581,f560(x98582,x98583,x98581,x98584)),x98582)) % 168.22/168.06 [5949]E(x59491,x59492)+~E(f317(f317(f317(f100(x59493),x59494),x59495),x59491),f317(f317(f317(f100(x59493),x59496),x59497),x59492)) % 168.22/168.06 [5950]E(x59501,x59502)+~E(f317(f317(f317(f100(x59503),x59504),x59501),x59505),f317(f317(f317(f100(x59503),x59506),x59502),x59507)) % 168.22/168.06 [5951]E(x59511,x59512)+~E(f317(f317(f317(f100(x59513),x59511),x59514),x59515),f317(f317(f317(f100(x59513),x59512),x59516),x59517)) % 168.22/168.06 [8792]~P15(x87926,x87921,x87923,x87927)+E(f317(f82(x87921,x87921,x87922,f317(x87923,x87924)),f317(f82(x87921,x87921,x87922,f317(x87923,x87924)),x87925)),f317(f82(x87921,x87921,x87922,f317(x87923,x87924)),x87925)) % 168.22/168.06 [9157]~P35(x91573,x91572,x91574,f317(f317(f148(x91571,x91573),x91575),x91576),x91577)+P35(x91571,x91572,f317(f317(f8(x91573,f858(x91572,a842),x91571),x91574),x91575),x91576,x91577) % 168.22/168.06 [9180]P35(x91801,x91802,x91803,f317(f317(f148(x91804,x91801),x91805),x91806),x91807)+~P35(x91804,x91802,f317(f317(f8(x91801,f858(x91802,a842),x91804),x91803),x91805),x91806,x91807) % 168.22/168.06 [9582]E(f180(x95821,x95822,f317(f317(f317(f81(x95821,f853(x95822)),x95823),x95824),f317(f217(x95822),x95825)),x95826,x95827),f317(f317(f317(f81(x95821,f853(x95822)),f180(x95821,x95822,x95823,x95826,x95827)),x95824),f317(f217(x95822),x95825)))+P22(f317(f317(f319(x95821),x95824),f317(f166(x95821),x95826))) % 168.22/168.06 [8791]~P22(f317(f317(f319(x87911),x87912),f317(f317(x87915,x87916),x87917)))+P22(f317(f317(f319(x87911),x87912),f317(f317(f247(x87913,x87914,f858(x87911,a842)),x87915),f317(f317(f237(x87913,x87914),x87916),x87917)))) % 168.22/168.06 [9077]P22(f317(f317(f317(x90771,x90772),x90773),x90774))+~P22(f317(f317(f317(f247(x90775,x90776,f858(x90777,a842)),x90771),f317(f317(f237(x90775,x90776),x90772),x90773)),x90774)) % 168.22/168.06 [9218]P22(f317(f317(f319(x92181),f317(f317(x92182,x92183),x92184)),f317(f287(f857(x92185,x92186),x92181,f317(f247(x92185,x92186,x92181),x92182)),x92187)))+~P22(f317(f317(f319(f857(x92185,x92186)),f317(f317(f237(x92185,x92186),x92183),x92184)),x92187)) % 168.22/168.06 [9545]P22(f317(f317(f319(f857(f850(x95451),f850(x95451))),f317(f317(f237(f850(x95451),f850(x95451)),f317(f317(f127(x95451),x95452),f317(f317(f145(x95451),x95453),x95454))),f317(f317(f127(x95451),x95452),f317(f317(f145(x95451),x95455),x95456)))),f141(x95451,x95457)))+~P22(f317(f317(f319(f857(x95451,x95451)),f317(f317(f237(x95451,x95451),x95453),x95455)),x95457)) % 168.22/168.06 [9604]~P35(x96041,x96043,x96044,x96046,f317(f317(f148(x96042,x96043),x96045),x96047))+P35(x96041,x96042,f317(f317(f7(x96041,f858(x96042,x96043),f858(x96042,a842)),f317(f317(f8(f858(x96043,a842),f858(f858(x96042,x96043),f858(x96042,a842)),x96041),f8(x96043,a842,x96042)),x96044)),x96045),x96046,x96047) % 168.22/168.06 [9685]P35(x96851,x96852,x96853,x96854,f317(f317(f148(x96855,x96852),x96856),x96857))+~P35(x96851,x96855,f317(f317(f7(x96851,f858(x96855,x96852),f858(x96855,a842)),f317(f317(f8(f858(x96852,a842),f858(f858(x96855,x96852),f858(x96855,a842)),x96851),f8(x96852,a842,x96855)),x96853)),x96856),x96854,x96857) % 168.22/168.06 [9974]P48(x99741,x99742,x99743,f317(f317(f7(x99741,f858(f857(x99741,x99742),a842),f858(x99742,a842)),f317(f317(f8(f858(x99742,f858(f858(f857(x99741,x99742),a842),a842)),f858(f858(f857(x99741,x99742),a842),f858(x99742,a842)),x99741),f7(x99742,f858(f857(x99741,x99742),a842),a842)),f317(f317(f8(f858(x99742,f857(x99741,x99742)),f858(x99742,f858(f858(f857(x99741,x99742),a842),a842)),x99741),f317(f8(f857(x99741,x99742),f858(f858(f857(x99741,x99742),a842),a842),x99742),f319(f857(x99741,x99742)))),f237(x99741,x99742)))),x99744),f317(f317(f7(x99742,f858(f857(x99742,x99743),a842),f858(x99743,a842)),f317(f317(f8(f858(x99743,f858(f858(f857(x99742,x99743),a842),a842)),f858(f858(f857(x99742,x99743),a842),f858(x99743,a842)),x99742),f7(x99743,f858(f857(x99742,x99743),a842),a842)),f317(f317(f8(f858(x99743,f857(x99742,x99743)),f858(x99743,f858(f858(f857(x99742,x99743),a842),a842)),x99742),f317(f8(f857(x99742,x99743),f858(f858(f857(x99742,x99743),a842),a842),x99743),f319(f857(x99742,x99743)))),f237(x99742,x99743)))),x99745),x99746,x99747)+~P22(f317(f317(f319(f857(x99741,x99743)),f317(f317(f237(x99741,x99743),x99746),x99747)),f317(f317(f265(x99741,x99742,x99743),x99744),x99745))) % 168.22/168.06 [10004]~P48(x100041,x100045,x100042,f317(f317(f7(x100041,f858(f857(x100041,x100045),a842),f858(x100045,a842)),f317(f317(f8(f858(x100045,f858(f858(f857(x100041,x100045),a842),a842)),f858(f858(f857(x100041,x100045),a842),f858(x100045,a842)),x100041),f7(x100045,f858(f857(x100041,x100045),a842),a842)),f317(f317(f8(f858(x100045,f857(x100041,x100045)),f858(x100045,f858(f858(f857(x100041,x100045),a842),a842)),x100041),f317(f8(f857(x100041,x100045),f858(f858(f857(x100041,x100045),a842),a842),x100045),f319(f857(x100041,x100045)))),f237(x100041,x100045)))),x100046),f317(f317(f7(x100045,f858(f857(x100045,x100042),a842),f858(x100042,a842)),f317(f317(f8(f858(x100042,f858(f858(f857(x100045,x100042),a842),a842)),f858(f858(f857(x100045,x100042),a842),f858(x100042,a842)),x100045),f7(x100042,f858(f857(x100045,x100042),a842),a842)),f317(f317(f8(f858(x100042,f857(x100045,x100042)),f858(x100042,f858(f858(f857(x100045,x100042),a842),a842)),x100045),f317(f8(f857(x100045,x100042),f858(f858(f857(x100045,x100042),a842),a842),x100042),f319(f857(x100045,x100042)))),f237(x100045,x100042)))),x100047),x100043,x100044)+P22(f317(f317(f319(f857(x100041,x100042)),f317(f317(f237(x100041,x100042),x100043),x100044)),f317(f317(f265(x100041,x100045,x100042),x100046),x100047))) % 168.22/168.06 [9069]E(x90691,x90692)+E(f317(f317(f317(f81(x90693,x90694),f317(f317(f317(f81(x90693,x90694),x90695),x90691),x90696)),x90692),x90697),f317(f317(f317(f81(x90693,x90694),f317(f317(f317(f81(x90693,x90694),x90695),x90692),x90697)),x90691),x90696)) % 168.22/168.06 [9311]E(f180(x93111,x93112,f317(f317(f317(f81(x93111,f853(x93112)),x93113),x93114),f317(f217(x93112),x93115)),x93116,x93117),f180(x93111,x93112,x93113,x93116,x93117))+~P22(f317(f317(f319(x93111),x93114),f317(f166(x93111),f317(f317(f167(x93111),f317(f189(f850(x93112)),x93117)),x93116)))) % 168.22/168.06 [9616]E(f180(x96161,x96162,f317(f317(f317(f81(x96161,f853(x96162)),x96163),x96164),f317(f217(x96162),x96165)),x96166,x96167),f317(f317(f317(f81(x96161,f853(x96162)),f180(x96161,x96162,x96163,x96166,x96167)),x96164),f317(f217(x96162),x96165)))+P22(f317(f317(f319(x96161),x96164),f317(f166(x96161),f317(f317(f167(x96161),f317(f189(f850(x96162)),x96167)),x96166)))) % 168.22/168.06 [9986]P22(f317(f317(f319(x99861),f639(x99862,x99863,x99864,x99865,x99866,x99867,x99861)),x99865))+P22(f317(f317(f317(f317(f52(x99861,f858(x99867,f858(x99866,a842))),x99865),x99864),x99863),x99862)) % 168.22/168.06 [9988]P22(f317(f317(f319(x99881),f505(x99882,x99883,x99884,x99885,x99886,x99887,x99881)),x99885))+~P22(f317(f317(f317(f317(f51(x99881,f858(x99887,f858(x99886,a842))),x99885),x99884),x99883),x99882)) % 168.22/168.06 [10013]P22(f317(f317(f317(x100131,f505(x100132,x100133,x100131,x100134,x100135,x100136,x100137)),x100133),x100132))+~P22(f317(f317(f317(f317(f51(x100137,f858(x100136,f858(x100135,a842))),x100134),x100131),x100133),x100132)) % 168.22/168.06 [10030]~P22(f317(f317(f317(x100305,f639(x100307,x100306,x100305,x100304,x100303,x100302,x100301)),x100306),x100307))+P22(f317(f317(f317(f317(f52(x100301,f858(x100302,f858(x100303,a842))),x100304),x100305),x100306),x100307)) % 168.22/168.06 [9998]~P135(x99982)+E(f317(f317(f6(x99981,x99982),f317(f317(f7(x99981,f858(x99983,a842),x99982),f317(f317(f8(f858(x99983,x99982),f858(f858(x99983,a842),x99982),x99981),f6(x99983,x99982)),f317(f317(f7(x99981,f858(x99983,x99982),f858(x99983,x99982)),f317(f317(f8(f858(x99982,x99982),f858(f858(x99983,x99982),f858(x99983,x99982)),x99981),f8(x99982,x99982,x99983)),f317(f317(f8(x99982,f858(x99982,x99982),x99981),f90(x99982)),x99984))),x99985))),x99986)),x99987),f317(f317(f90(x99982),f317(f317(f6(x99981,x99982),x99984),x99987)),f317(f317(f6(x99983,x99982),x99985),x99986))) % 168.22/168.06 [9110]~P14(x91107,x91101,x91103,x91108)+E(f317(f82(x91101,x91101,x91102,f317(x91103,x91104)),f317(f82(x91101,x91101,x91102,f317(x91103,x91105)),x91106)),f317(f82(x91101,x91101,x91102,f317(x91103,x91105)),f317(f82(x91101,x91101,x91102,f317(x91103,x91104)),x91106))) % 168.22/168.06 [10041]P18(x100411,x100412,f317(f317(f286(f848(x100411)),f317(f317(f317(f100(x100411),f317(f317(f8(f858(a845,a842),f858(a845,a842),x100411),f317(f18(a845,a842,a842),f317(f317(f8(a842,f858(a842,a842),a845),a315),f317(a314,x100413)))),f317(f317(f7(x100411,f858(a845,a845),f858(a845,a842)),f317(f317(f8(f858(a845,a842),f858(f858(a845,a845),f858(a845,a842)),x100411),f8(a845,a842,a845)),x100414)),f317(f317(f18(a845,a849,a845),f317(f317(f7(a845,a844,f858(a849,a845)),a200),f40(x100415))),x100416)))),f32(x100415,x100416,x100417)),x100418)),f188(f858(f848(x100411),a842))))+~P18(x100411,x100412,f317(f317(f286(f848(x100411)),f317(f317(f317(f100(x100411),x100414),x100417),f317(f317(f7(x100411,f858(a845,a845),f858(a845,a842)),f317(f317(f8(f858(a845,a842),f858(f858(a845,a845),f858(a845,a842)),x100411),f8(a845,a842,a845)),x100418)),f317(f317(f7(a845,a849,a845),f317(f317(f7(a845,a844,f858(a849,a845)),a200),f40(x100415))),f317(f317(a201,x100413),x100415))))),f188(f858(f848(x100411),a842)))) % 168.22/168.06 [10050]E(f317(f317(f237(x100501,x100502),f317(x100503,f537(x100504,x100505,x100503,x100506,x100507,x100508,x100502,x100501))),f317(x100505,f538(x100504,x100505,x100503,x100506,x100507,x100508,x100502,x100501))),x100508)+~P22(f317(f317(f319(f857(x100501,x100502)),x100508),f317(f287(f857(x100507,x100506),f857(x100501,x100502),f248(x100507,x100501,x100506,x100502,x100503,x100505)),x100504))) % 168.22/168.06 [10065]P18(x100651,x100652,f317(f317(f286(f848(x100651)),f317(f317(f317(f100(x100651),f317(f317(f8(f858(a845,a842),f858(a845,a842),x100651),f317(f18(a845,a842,a842),f317(f317(f8(a842,f858(a842,a842),a845),a315),f317(a314,x100653)))),f317(f317(f7(x100651,f858(a845,a845),f858(a845,a842)),f317(f317(f8(f858(a845,a842),f858(f858(a845,a845),f858(a845,a842)),x100651),f8(a845,a842,a845)),x100654)),f317(f317(f18(a845,a849,a845),f317(f317(f7(a845,a844,f858(a849,a845)),f317(f317(f8(a845,f858(a844,f858(a849,a845)),a845),a200),f317(f317(f7(a845,f858(a847,a849),a845),a202),a203))),f40(a26))),x100655)))),f31(x100656,x100657,x100655)),x100658)),f188(f858(f848(x100651),a842))))+~P18(x100651,x100652,f317(f317(f286(f848(x100651)),f317(f317(f317(f100(x100651),x100654),f317(a29,x100657)),f317(f317(f7(x100651,f858(a845,a845),f858(a845,a842)),f317(f317(f8(f858(a845,a842),f858(f858(a845,a845),f858(a845,a842)),x100651),f8(a845,a842,a845)),x100658)),f317(f317(f18(a845,a849,a845),f317(f317(f7(a845,a844,f858(a849,a845)),f317(f317(f8(a845,f858(a844,f858(a849,a845)),a845),a200),f317(f317(f7(a845,f858(a847,a849),a845),a202),f317(a201,x100653)))),x100656)),f317(f317(f7(a845,a847,a849),a201),a25))))),f188(f858(f848(x100651),a842)))) % 168.22/168.06 [10066]~P22(f317(f317(f319(f857(x100668,x100667)),x100666),f317(f287(f857(x100661,x100662),f857(x100668,x100667),f248(x100661,x100668,x100662,x100667,x100665,x100664)),x100663)))+P22(f317(f317(f319(f857(x100661,x100662)),f317(f317(f237(x100661,x100662),f537(x100663,x100664,x100665,x100662,x100661,x100666,x100667,x100668)),f538(x100663,x100664,x100665,x100662,x100661,x100666,x100667,x100668))),x100663)) % 168.22/168.06 [9536]P22(f317(f317(f319(f857(f857(x95361,x95362),f857(x95361,x95362))),f317(f317(f237(f857(x95361,x95362),f857(x95361,x95362)),f317(f317(f237(x95361,x95362),x95363),x95364)),f317(f317(f237(x95361,x95362),x95365),x95366))),f310(x95361,x95362,x95367,x95368)))+~P22(f317(f317(f319(f857(x95361,x95361)),f317(f317(f237(x95361,x95361),x95363),x95365)),x95367)) % 168.22/168.06 [10039]E(f317(f136(x100391,x100392,f317(f7(x100392,x100391,x100391),x100393),f317(x100394,x100395)),x100396),f317(x100394,f317(f136(x100397,x100392,f317(f7(x100392,x100397,x100397),x100398),x100395),x100396)))+P22(f317(f317(f319(x100392),f706(x100395,x100398,x100394,x100393,x100397,x100391,x100396,x100392)),f317(f166(x100392),x100396))) % 168.22/168.06 [10057]~E(f317(f82(x100571,x100571,x100577,f317(x100573,f706(x100575,x100578,x100574,x100573,x100577,x100571,x100576,x100572))),x100574),f317(f82(x100577,x100571,x100577,x100574),f317(x100578,f706(x100575,x100578,x100574,x100573,x100577,x100571,x100576,x100572))))+E(f317(f136(x100571,x100572,f317(f7(x100572,x100571,x100571),x100573),f317(x100574,x100575)),x100576),f317(x100574,f317(f136(x100577,x100572,f317(f7(x100572,x100577,x100577),x100578),x100575),x100576))) % 168.22/168.06 [8352]E(f317(x83521,f317(x83522,x83523)),f317(x83524,f317(x83525,x83523)))+~E(f317(f82(x83526,x83527,x83528,x83521),x83522),f317(f82(x83529,x83527,x83528,x83524),x83525)) % 168.22/168.06 [9926]P22(f317(f317(f319(f857(x99261,x99262)),f317(f317(f237(x99261,x99262),f317(x99263,x99264)),f317(x99265,x99266))),f317(f287(f857(x99267,x99268),f857(x99261,x99262),f248(x99267,x99261,x99268,x99262,x99263,x99265)),x99269)))+~P22(f317(f317(f319(f857(x99267,x99268)),f317(f317(f237(x99267,x99268),x99264),x99266)),x99269)) % 168.22/168.06 [8626]~E(f317(x86264,f317(x86265,x86266)),f317(x86269,f317(x862610,x862611)))+E(f317(f317(f82(x86261,x86262,x86263,x86264),x86265),x86266),f317(f317(f82(x86267,x86262,x86268,x86269),x862610),x862611)) % 168.22/168.06 [4523]~P103(x45231)+~P98(x45231)+E(f113(x45231),f223(x45231)) % 168.22/168.06 [4524]~P103(x45241)+~P92(x45241)+E(f122(x45241),f224(x45241)) % 168.22/168.06 [4771]~P113(x47711)+~P90(x47711)+E(f317(f84(x47711),f317(f115(x47711),a109)),f87(x47711)) % 168.22/168.06 [5042]E(x50421,f2(a1))+E(f91(a1,x50421),f317(f88(a1),f87(a1)))+P22(f317(f317(f226(a1),f2(a1)),x50421)) % 168.22/168.06 [5251]E(x52511,f2(a1))+E(f91(a1,x52511),f87(a1))+~P22(f317(f317(f226(a1),f2(a1)),x52511)) % 168.22/168.06 [7199]~P39(x71991)+P22(f317(f71(a1),x71991))+~P22(f317(f71(a849),f317(f287(a1,a849,a116),x71991))) % 168.22/168.06 [8460]~P1(a5000)+~P22(f317(f317(f319(f857(a846,a843)),x84601),f317(f166(f857(a846,a843)),a28)))+P22(f317(f317(f247(a846,a843,a842),f317(f16(f858(a843,a842),a846),a24)),x84601)) % 168.22/168.06 [9503]E(x95031,f188(f858(f857(a849,a849),a842)))+~P22(f317(f71(f857(a849,a849)),x95031))+P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),f188(f858(f857(a849,a849),a842))),x95031)),a47)) % 168.22/168.06 [9663]E(x96631,f2(a849))+E(x96631,f317(a124,f2(a849)))+~P22(f317(f317(f226(a849),x96631),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.06 [9954]E(x99541,f2(a111))+E(f317(f317(f89(a1),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(a20,f317(f48(a111,x99541),f317(f115(a111),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))))),f87(a1)),f317(a20,x99541))+E(f55(a111,x99541,f317(f115(a111),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f2(a111)) % 168.22/168.06 [9800]E(x98001,f2(a111))+~E(f55(a111,x98001,f317(f115(a111),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f2(a111))+E(f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(a20,f317(f48(a111,x98001),f317(f115(a111),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f317(a20,x98001)) % 168.22/168.06 [4598]~P52(x45981,x45982)+P42(x45981,x45982)+~P43(a842) % 168.22/168.06 [4535]~P110(x45351)+P31(x45351,x45352)+~E(x45352,f2(x45351)) % 168.22/168.06 [4536]~P103(x45361)+P29(x45361,x45362)+~E(x45362,f125(x45361)) % 168.22/168.06 [4545]~P113(x45451)+~E(x45452,f2(x45451))+E(f91(x45451,x45452),f2(x45451)) % 168.22/168.06 [4546]~P82(x45461)+~E(x45462,f2(x45461))+E(f91(x45461,x45462),f2(x45461)) % 168.22/168.06 [4554]~P110(x45542)+~P31(x45542,x45541)+E(x45541,f2(x45542)) % 168.22/168.06 [4588]~P113(x45882)+~E(f91(x45882,x45881),f2(x45882))+E(x45881,f2(x45882)) % 168.22/168.06 [4606]~P28(x46062)+~P28(x46061)+P28(f195(x46061,x46062)) % 168.22/168.06 [4607]~P137(x46072)+~P137(x46071)+P137(f857(x46071,x46072)) % 168.22/168.06 [4608]~P56(x46082)+~P56(x46081)+P56(f858(x46081,x46082)) % 168.22/168.06 [4609]~P56(x46092)+~P56(x46091)+P56(f856(x46091,x46092)) % 168.22/168.06 [4610]~P56(x46102)+~P56(x46101)+P56(f857(x46101,x46102)) % 168.22/168.06 [4611]~P57(x46112)+~P57(x46111)+P57(f858(x46111,x46112)) % 168.22/168.06 [4612]~P57(x46122)+~P57(x46121)+P57(f856(x46121,x46122)) % 168.22/168.06 [4613]~P57(x46132)+~P57(x46131)+P57(f857(x46131,x46132)) % 168.22/168.06 [4614]~P57(x46141)+~P89(x46142)+P89(f858(x46141,x46142)) % 168.22/168.06 [4742]~P103(x47421)+~P29(x47421,x47422)+P29(x47421,f146(x47421,x47422)) % 168.22/168.06 [4972]~P28(x49722)+~P28(x49721)+P28(f55(a1,x49721,x49722)) % 168.22/168.06 [4556]~P68(x45561)+~E(x45562,f2(x45561))+E(f317(f88(x45561),x45562),x45562) % 168.22/168.06 [4560]~P87(x45601)+~E(x45602,f2(a1))+E(f317(f114(x45601),x45602),f2(x45601)) % 168.22/168.06 [4561]~P111(x45611)+~E(x45612,f2(a1))+E(f317(f114(x45611),x45612),f2(x45611)) % 168.22/168.06 [4585]~P69(x45851)+~E(f2(x45851),x45852)+E(f317(f88(x45851),x45852),f2(x45851)) % 168.22/168.06 [4586]~P69(x45861)+~E(x45862,f2(x45861))+E(f317(f88(x45861),x45862),f2(x45861)) % 168.22/168.06 [4587]~P79(x45871)+~E(x45872,f2(x45871))+E(f317(f84(x45871),x45872),f2(x45871)) % 168.22/168.06 [4617]~P68(x46172)+E(x46171,f2(x46172))+~E(f317(f88(x46172),x46171),x46171) % 168.22/168.06 [4625]E(x46251,f317(a116,x46252))+~E(x46251,f2(a849))+~E(x46252,f317(f112(a1),x46251)) % 168.22/168.06 [4626]E(f317(a116,x46261),x46262)+~E(x46262,f2(a849))+~E(x46261,f317(f112(a1),x46262)) % 168.22/168.06 [4630]~P87(x46302)+E(x46301,f2(a1))+~E(f317(f114(x46302),x46301),f2(x46302)) % 168.22/168.06 [4635]~P69(x46352)+E(x46351,f2(x46352))+~E(f317(f88(x46352),x46351),f2(x46352)) % 168.22/168.06 [4636]~P79(x46362)+E(x46361,f2(x46362))+~E(f317(f84(x46362),x46361),f2(x46362)) % 168.22/168.06 [4637]~P69(x46371)+E(f2(x46371),x46372)+~E(f317(f88(x46371),x46372),f2(x46371)) % 168.22/168.06 [4657]~P55(x46572)+E(x46571,f2(x46572))+E(f317(f48(x46572,x46571),x46571),f87(x46572)) % 168.22/168.06 [4776]~P1(a5000)+~E(f317(a27,x47762),f317(f217(a843),x47761))+P22(f317(a24,x47761)) % 168.22/168.06 [4817]~P103(x48171)+~P29(x48171,x48172)+P29(x48171,f317(f165(x48171),x48172)) % 168.22/168.06 [4843]~P22(x48432)+~P22(x48431)+P22(f317(f317(a315,x48431),x48432)) % 168.22/168.06 [4844]~P28(x48442)+~P28(x48441)+P28(f317(f48(a1,x48441),x48442)) % 168.22/168.06 [4876]~E(f87(a849),f2(a849))+E(f317(f54(x48761),x48762),f2(a849))+~P22(f317(f71(x48761),x48762)) % 168.22/168.06 [4909]~P106(x49091)+~P135(x49091)+E(f317(f317(f238(x49091),f2(x49091)),f317(a124,x49092)),f2(x49091)) % 168.22/168.06 [4941]~P103(x49411)+P29(x49411,f133(x49411,x49412))+~P22(f317(f71(x49411),x49412)) % 168.22/168.06 [4942]~P103(x49421)+P29(x49421,f685(x49422,x49421))+~P22(f317(f71(x49421),x49422)) % 168.22/168.06 [4962]~P103(x49621)+E(f317(f166(x49621),f133(x49621,x49622)),x49622)+~P22(f317(f71(x49621),x49622)) % 168.22/168.06 [4963]~P103(x49631)+E(f317(f166(x49631),f685(x49632,x49631)),x49632)+~P22(f317(f71(x49631),x49632)) % 168.22/168.06 [4996]P22(x49961)+P22(x49962)+~P22(f317(f317(a316,x49962),x49961)) % 168.22/168.06 [5008]E(x50081,f188(f858(x50082,a842)))+~E(f317(f54(x50082),x50081),f2(a849))+~P22(f317(f71(x50082),x50081)) % 168.22/168.06 [5013]P22(x50131)+~P22(x50132)+~P22(f317(f317(a320,x50132),x50131)) % 168.22/168.06 [5060]~P65(x50601)+E(f317(f84(x50601),x50602),x50602)+P22(f317(f317(f226(x50601),x50602),f2(x50601))) % 168.22/168.06 [5131]~P57(x51312)+~P22(f317(f67(x51312),x51311))+P22(f317(x51311,f655(x51311,x51312))) % 168.22/168.06 [5132]~P57(x51322)+~P22(f317(f67(x51322),x51321))+P22(f317(x51321,f667(x51321,x51322))) % 168.22/168.06 [5159]~P22(f317(a24,x51592))+~P22(f317(a24,x51591))+P22(f317(a24,f36(x51591,x51592))) % 168.22/168.06 [5167]E(x51671,f125(x51672))+P22(f317(f131(x51672),f126(x51672,x51671)))+~P22(f317(f131(x51672),x51671)) % 168.22/168.06 [5172]~P103(x51721)+~P22(f317(f71(x51721),x51722))+P22(f317(f131(x51721),f133(x51721,x51722))) % 168.22/168.06 [5173]~P103(x51731)+~P22(f317(f71(x51731),x51732))+P22(f317(f131(x51731),f685(x51732,x51731))) % 168.22/168.06 [5179]~P111(x51791)+E(f317(f112(x51791),f317(a116,x51792)),f317(f114(x51791),x51792))+P22(f317(f317(f226(a1),x51792),f2(a1))) % 168.22/168.06 [5206]P5(x52062,x52061)+E(f317(x52061,f433(x52061)),f317(x52061,f480(x52061)))+P22(f317(f317(x52061,f433(x52061)),f480(x52061))) % 168.22/168.06 [5219]E(f317(f112(a1),f839(x52191,x52192)),x52191)+P22(f317(x52192,f317(a116,x52191)))+~P22(f317(x52192,f2(a849))) % 168.22/168.06 [5230]~P57(x52301)+~P22(f317(x52302,f656(x52302,x52301)))+P22(f317(f68(x52301),x52302)) % 168.22/168.06 [5231]~P57(x52311)+~P22(f317(x52312,f668(x52312,x52311)))+P22(f317(f68(x52311),x52312)) % 168.22/168.06 [5260]~P113(x52601)+~E(f91(x52601,x52602),f317(f88(x52601),f87(x52601)))+P22(f317(f317(f226(x52601),x52602),f2(x52601))) % 168.22/168.06 [5332]~E(x53322,f2(a1))+E(f209(x53321,x53322),f317(f317(f237(a1,a1),f2(a1)),f87(a1)))+P22(f317(f317(f226(a1),x53322),f2(a1))) % 168.22/168.06 [5333]~E(x53331,f2(a1))+E(f209(x53331,x53332),f317(f317(f237(a1,a1),f2(a1)),f87(a1)))+P22(f317(f317(f226(a1),x53332),f2(a1))) % 168.22/168.06 [5386]E(f317(f112(a1),f839(x53861,x53862)),x53861)+P22(f317(x53862,f317(a116,x53861)))+P22(f317(f317(f226(a1),x53861),f2(a1))) % 168.22/168.06 [5448]~P113(x54481)+E(f91(x54481,x54482),f317(f88(x54481),f87(x54481)))+~P22(f317(f317(f226(x54481),x54482),f2(x54481))) % 168.22/168.06 [5449]~P79(x54491)+E(f317(f84(x54491),x54492),f317(f88(x54491),x54492))+~P22(f317(f317(f225(x54491),x54492),f2(x54491))) % 168.22/168.06 [5450]~P79(x54501)+E(f317(f84(x54501),x54502),f317(f88(x54501),x54502))+~P22(f317(f317(f226(x54501),x54502),f2(x54501))) % 168.22/168.06 [5451]~P65(x54511)+E(f317(f84(x54511),x54512),f317(f88(x54511),x54512))+~P22(f317(f317(f226(x54511),x54512),f2(x54511))) % 168.22/168.06 [5553]~P22(f317(x55531,f839(x55532,x55531)))+P22(f317(x55531,f317(a116,x55532)))+~P22(f317(x55531,f2(a849))) % 168.22/168.06 [5560]E(x55601,f2(a849))+E(f317(a124,f806(x55602,x55601)),x55601)+~P22(f317(f317(f226(a849),x55601),f317(a124,x55602))) % 168.22/168.06 [5565]P5(x55651,x55652)+~E(f317(x55652,f433(x55652)),f317(x55652,f480(x55652)))+~P22(f317(f317(x55652,f433(x55652)),f480(x55652))) % 168.22/168.06 [5583]~P103(x55831)+P29(x55831,x55832)+P22(f317(f317(f225(a849),f643(x55832,x55831)),f644(x55832,x55831))) % 168.22/168.06 [5584]~P103(x55841)+P29(x55841,x55842)+P22(f317(f317(f225(a849),f657(x55842,x55841)),f663(x55842,x55841))) % 168.22/168.06 [5667]~P79(x56671)+~E(x56672,f2(x56671))+P22(f317(f317(f225(x56671),f317(f84(x56671),x56672)),f2(x56671))) % 168.22/168.06 [5736]~P57(x57362)+~P57(x57361)+E(f69(x57361,x57362,f65(x57361),f65(x57362)),f65(f857(x57361,x57362))) % 168.22/168.06 [5740]~P22(f317(x57401,f839(x57402,x57401)))+P22(f317(x57401,f317(a116,x57402)))+P22(f317(f317(f226(a1),x57402),f2(a1))) % 168.22/168.06 [5762]~P22(f317(x57621,f317(a116,x57622)))+P22(f317(x57621,f2(a849)))+~P22(f317(f317(f226(a1),x57622),f2(a1))) % 168.22/168.06 [6095]~P113(x60951)+~P22(f317(f317(f226(x60951),x60952),f2(x60951)))+P22(f317(f317(f226(x60951),f91(x60951,x60952)),f2(x60951))) % 168.22/168.06 [6211]~P113(x62111)+P22(f317(f317(f225(x62111),f317(f114(x62111),x62112)),f2(x62111)))+~P22(f317(f317(f225(a1),x62112),f2(a1))) % 168.22/168.06 [6212]~P113(x62121)+P22(f317(f317(f226(x62121),f317(f114(x62121),x62122)),f2(x62121)))+~P22(f317(f317(f226(a1),x62122),f2(a1))) % 168.22/168.06 [6216]~P79(x62162)+E(x62161,f2(x62162))+~P22(f317(f317(f225(x62162),f317(f84(x62162),x62161)),f2(x62162))) % 168.22/168.06 [6291]~P111(x62911)+~P22(f317(f317(f319(x62911),x62912),f121(x62911)))+P22(f317(f317(f319(x62911),f317(f88(x62911),x62912)),f121(x62911))) % 168.22/168.06 [6326]~P113(x63261)+~P22(f317(f317(f226(x63261),f91(x63261,x63262)),f2(x63261)))+P22(f317(f317(f226(x63261),x63262),f2(x63261))) % 168.22/168.06 [6492]~P113(x64922)+~P22(f317(f317(f225(x64922),f317(f114(x64922),x64921)),f2(x64922)))+P22(f317(f317(f225(a1),x64921),f2(a1))) % 168.22/168.06 [6493]~P113(x64932)+~P22(f317(f317(f226(x64932),f317(f114(x64932),x64931)),f2(x64932)))+P22(f317(f317(f226(a1),x64931),f2(a1))) % 168.22/168.06 [6995]~P68(x69951)+~P22(f317(f317(f225(x69951),x69952),f2(x69951)))+P22(f317(f317(f225(x69951),f317(f317(f89(x69951),x69952),x69952)),f2(x69951))) % 168.22/168.06 [6996]~P68(x69961)+~P22(f317(f317(f226(x69961),x69962),f2(x69961)))+P22(f317(f317(f226(x69961),f317(f317(f89(x69961),x69962),x69962)),f2(x69961))) % 168.22/168.06 [6997]~P113(x69971)+~P22(f317(f317(f226(x69971),x69972),f2(x69971)))+P22(f317(f317(f226(x69971),f317(f317(f89(x69971),x69972),x69972)),f2(x69971))) % 168.22/168.06 [7551]~P68(x75511)+~P22(f317(f317(f225(x75511),f317(f317(f89(x75511),x75512),x75512)),f2(x75511)))+P22(f317(f317(f225(x75511),x75512),f2(x75511))) % 168.22/168.06 [7552]~P68(x75521)+~P22(f317(f317(f226(x75521),f317(f317(f89(x75521),x75522),x75522)),f2(x75521)))+P22(f317(f317(f226(x75521),x75522),f2(x75521))) % 168.22/168.06 [7553]~P113(x75531)+~P22(f317(f317(f226(x75531),f317(f317(f89(x75531),x75532),x75532)),f2(x75531)))+P22(f317(f317(f226(x75531),x75532),f2(x75531))) % 168.22/168.06 [4677]~E(x46772,f2(a849))+~E(x46771,f2(a849))+E(f317(f317(f89(a849),x46771),x46772),f2(a849)) % 168.22/168.06 [4678]~E(x46782,f87(a849))+~E(x46781,f87(a849))+E(f317(f317(f90(a849),x46781),x46782),f87(a849)) % 168.22/168.06 [4679]~E(x46792,f87(a1))+~E(x46791,f87(a1))+E(f317(f317(f90(a1),x46791),x46792),f87(a1)) % 168.22/168.06 [4730]~P115(x47302)+E(x47301,f2(x47302))+E(f317(f317(f266(x47302),x47301),x47301),f87(x47302)) % 168.22/168.06 [4731]~P116(x47312)+E(x47311,f2(x47312))+E(f317(f317(f266(x47312),x47311),x47311),f87(x47312)) % 168.22/168.06 [4747]~P68(x47471)+~E(x47472,f2(x47471))+E(f317(f317(f89(x47471),x47472),x47472),f2(x47471)) % 168.22/168.06 [4750]~P133(x47501)+~E(x47502,f87(x47501))+E(f317(f317(f90(x47501),x47502),x47502),f87(x47501)) % 168.22/168.06 [4751]~P116(x47511)+~E(x47512,f2(x47511))+E(f317(f317(f266(x47511),x47512),x47512),f2(x47511)) % 168.22/168.06 [4796]~E(x47962,f2(a849))+~E(x47961,f2(a849))+E(f317(f88(a1),f317(f112(a1),x47961)),f317(f112(a1),x47962)) % 168.22/168.06 [4814]E(x48141,f87(a849))+E(x48142,f2(a849))+~E(f317(f317(f90(a849),x48142),x48141),x48142) % 168.22/168.06 [4824]E(x48241,f2(a849))+E(x48242,f2(a849))+~E(f317(f317(f90(a849),x48242),x48241),f2(a849)) % 168.22/168.06 [4853]~E(x48532,f2(a849))+~E(x48531,f317(a124,f2(a849)))+E(f317(f317(f89(a849),x48531),x48532),f317(a124,f2(a849))) % 168.22/168.06 [4854]~E(x48541,f2(a849))+~E(x48542,f317(a124,f2(a849)))+E(f317(f317(f89(a849),x48541),x48542),f317(a124,f2(a849))) % 168.22/168.06 [4859]E(x48591,f87(a1))+E(x48592,f317(f115(a1),a109))+~E(f317(f317(f90(a1),x48591),x48592),f87(a1)) % 168.22/168.06 [4860]E(x48601,f87(a1))+E(x48602,f317(f115(a1),a109))+~E(f317(f317(f90(a1),x48602),x48601),f87(a1)) % 168.22/168.06 [4861]E(x48611,f87(a1))+E(x48611,f317(f115(a1),a109))+~E(f317(f317(f90(a1),x48612),x48611),f87(a1)) % 168.22/168.06 [4863]E(x48631,f87(a1))+E(x48631,f317(f115(a1),a109))+~E(f317(f317(f90(a1),x48631),x48632),f87(a1)) % 168.22/168.06 [4880]~P68(x48802)+E(x48801,f2(x48802))+~E(f317(f317(f89(x48802),x48801),x48801),f2(x48802)) % 168.22/168.06 [4886]~E(x48861,f317(f115(a1),a109))+~E(x48862,f317(f115(a1),a109))+E(f317(f317(f90(a1),x48861),x48862),f87(a1)) % 168.22/168.06 [4898]E(x48981,f2(a849))+E(x48982,f2(a849))+~E(f317(f317(f89(a849),x48982),x48981),f317(a124,f2(a849))) % 168.22/168.06 [4908]~P90(x49081)+~P58(x49081)+E(f317(f317(f266(x49081),x49082),f317(f115(x49081),a92)),f2(x49081)) % 168.22/168.06 [4914]~P133(x49141)+~E(x49142,f317(f88(x49141),f87(x49141)))+E(f317(f317(f90(x49141),x49142),x49142),f87(x49141)) % 168.22/168.06 [4917]~P28(x49172)+~P28(x49171)+P28(f317(f317(f89(a1),x49171),x49172)) % 168.22/168.06 [4918]~P28(x49182)+~P28(x49181)+P28(f317(f317(f90(a1),x49181),x49182)) % 168.22/168.06 [4939]~E(x49392,f317(a124,f2(a849)))+~E(x49391,f317(a124,f2(a849)))+E(f317(f317(f90(a849),x49391),x49392),f317(a124,f2(a849))) % 168.22/168.06 [4953]E(x49531,f2(a849))+E(x49532,f317(a124,f2(a849)))+~E(f317(f317(f238(a849),x49532),x49531),f317(a124,f2(a849))) % 168.22/168.06 [4954]E(x49541,f2(a849))+E(x49541,f317(a124,f2(a849)))+~E(f317(f317(f89(a849),x49542),x49541),f317(a124,f2(a849))) % 168.22/168.06 [4955]E(x49551,f2(a849))+E(x49551,f317(a124,f2(a849)))+~E(f317(f317(f89(a849),x49551),x49552),f317(a124,f2(a849))) % 168.22/168.06 [4964]~P90(x49641)+~P58(x49641)+E(f317(f317(f266(x49641),x49642),f317(f115(x49641),a109)),f317(f88(x49641),x49642)) % 168.22/168.06 [4984]E(x49841,f317(a116,x49842))+~E(x49841,f2(a849))+P22(f317(f317(f225(a1),f2(a1)),x49842)) % 168.22/168.06 [4985]E(f317(a116,x49851),x49852)+~E(x49852,f2(a849))+P22(f317(f317(f225(a1),f2(a1)),x49851)) % 168.22/168.06 [5004]E(x50041,f317(a124,f2(a849)))+E(x50042,f317(a124,f2(a849)))+~E(f317(f317(f89(a849),x50041),x50042),f317(a124,f2(a849))) % 168.22/168.06 [5014]~E(x50141,f317(a116,x50142))+E(x50141,f2(a849))+P22(f317(f317(f225(a1),f2(a1)),x50142)) % 168.22/168.06 [5015]~E(f317(a116,x50152),x50151)+E(x50151,f2(a849))+P22(f317(f317(f225(a1),f2(a1)),x50152)) % 168.22/168.06 [5036]~P93(x50361)+E(f317(f73(x50361,f113(x50361)),x50362),f11(x50361,x50362))+~P22(f317(f71(x50361),x50362)) % 168.22/168.06 [5037]~P93(x50371)+E(f317(f73(x50371,f122(x50371)),x50372),f10(x50371,x50372))+~P22(f317(f71(x50371),x50372)) % 168.22/168.06 [5038]~P103(x50381)+E(f317(f73(x50381,f224(x50381)),x50382),f14(x50381,x50382))+~P22(f317(f71(x50381),x50382)) % 168.22/168.06 [5039]~P103(x50391)+E(f317(f73(x50391,f223(x50391)),x50392),f15(x50391,x50392))+~P22(f317(f71(x50391),x50392)) % 168.22/168.06 [5041]~P57(x50411)+~P22(f317(x50412,f191(x50411)))+P22(f317(f67(f853(x50411)),x50412)) % 168.22/168.06 [5124]~P57(x51242)+P22(f317(x51241,f191(x51242)))+~P22(f317(f68(f853(x51242)),x51241)) % 168.22/168.06 [5125]E(x51251,x51252)+~E(f317(f317(f21(a849),x51252),x51251),f2(a849))+~E(f317(f317(f21(a849),x51251),x51252),f2(a849)) % 168.22/168.06 [5139]P28(x51391)+~P39(x51392)+~P22(f317(f317(f319(a1),x51391),x51392)) % 168.22/168.06 [5168]~P113(x51681)+~E(f91(x51681,x51682),f87(x51681))+P22(f317(f317(f226(x51681),f2(x51681)),x51682)) % 168.22/168.06 [5180]~P90(x51801)+E(f317(f112(x51801),f317(f115(a849),x51802)),f317(f115(x51801),x51802))+P22(f317(a193,f317(f115(a1),x51802))) % 168.22/168.06 [5185]~P42(x51851,x51852)+P43(a842)+P22(f317(f71(f857(x51851,x51851)),x51852)) % 168.22/168.06 [5252]~P103(x52521)+E(f317(f73(x52521,f224(x52521)),x52522),f12(x52521,f224(x52521),x52522))+~P22(f317(f71(x52521),x52522)) % 168.22/168.06 [5253]~P103(x52531)+E(f317(f73(x52531,f223(x52531)),x52532),f13(x52531,f223(x52531),x52532))+~P22(f317(f71(x52531),x52532)) % 168.22/168.06 [5267]E(x52671,x52672)+P22(f317(f317(f226(a849),x52672),x52671))+P22(f317(f317(f226(a849),x52671),x52672)) % 168.22/168.06 [5268]E(x52681,x52682)+P22(f317(f317(f226(a1),x52682),x52681))+P22(f317(f317(f226(a1),x52681),x52682)) % 168.22/168.06 [5319]~P90(x53191)+E(f317(f112(x53191),f317(f115(a849),x53192)),f2(x53191))+~P22(f317(a193,f317(f115(a1),x53192))) % 168.22/168.06 [5322]~E(x53222,f317(a116,x53221))+E(x53221,f317(f112(a1),x53222))+~P22(f317(f317(f225(a1),f2(a1)),x53221)) % 168.22/168.06 [5323]~E(f317(a116,x53231),x53232)+E(x53231,f317(f112(a1),x53232))+~P22(f317(f317(f225(a1),f2(a1)),x53231)) % 168.22/168.06 [5324]~E(x53241,f317(a116,x53242))+E(f317(f112(a1),x53241),x53242)+~P22(f317(f317(f225(a1),f2(a1)),x53242)) % 168.22/168.06 [5334]E(x53341,f317(a116,x53342))+~E(x53342,f317(f112(a1),x53341))+~P22(f317(f317(f225(a1),f2(a1)),x53342)) % 168.22/168.06 [5335]E(f317(a116,x53351),x53352)+~E(x53351,f317(f112(a1),x53352))+~P22(f317(f317(f225(a1),f2(a1)),x53351)) % 168.22/168.06 [5375]~P79(x53752)+E(x53751,f2(x53752))+P22(f317(f317(f226(x53752),f2(x53752)),f317(f84(x53752),x53751))) % 168.22/168.06 [5441]~P113(x54411)+E(f91(x54411,x54412),f87(x54411))+~P22(f317(f317(f226(x54411),f2(x54411)),x54412)) % 168.22/168.06 [5445]~P90(x54451)+E(f317(f112(x54451),f317(f115(a849),x54452)),f2(x54451))+P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x54452))) % 168.22/168.06 [5452]~P79(x54521)+E(f317(f84(x54521),x54522),x54522)+~P22(f317(f317(f225(x54521),f2(x54521)),x54522)) % 168.22/168.06 [5453]~P79(x54531)+E(f317(f84(x54531),x54532),x54532)+~P22(f317(f317(f226(x54531),f2(x54531)),x54532)) % 168.22/168.06 [5460]E(x54601,f2(a849))+~E(f133(a849,f317(f278(a849,x54602),x54601)),f125(a849))+P22(f317(f317(f225(a849),x54601),x54602)) % 168.22/168.06 [5470]~P67(x54701)+E(f317(f317(f6(x54701,x54701),f5(x54701)),f317(f166(x54701),x54702)),f317(f160(x54701),x54702))+~P22(f317(f131(x54701),x54702)) % 168.22/168.06 [5475]~P111(x54751)+E(f317(f112(x54751),f317(a116,x54752)),f317(f114(x54751),x54752))+~P22(f317(f317(f225(a1),f2(a1)),x54752)) % 168.22/168.06 [5502]E(x55021,x55022)+P22(f317(f317(f226(a849),x55021),x55022))+~P22(f317(f317(f225(a849),x55021),x55022)) % 168.22/168.06 [5503]E(x55031,x55032)+P22(f317(f317(f226(a1),x55031),x55032))+~P22(f317(f317(f225(a1),x55031),x55032)) % 168.22/168.06 [5506]E(x55061,f87(a1))+~E(f317(f317(f90(a1),x55062),x55061),f87(a1))+~P22(f317(f317(f226(a1),f2(a1)),x55062)) % 168.22/168.06 [5507]E(x55071,f87(a1))+~E(f317(f317(f90(a1),x55071),x55072),f87(a1))+~P22(f317(f317(f226(a1),f2(a1)),x55071)) % 168.22/168.06 [5509]E(x55091,f2(a1))+~E(f55(a1,x55092,x55091),f2(a1))+E(f317(f48(a1,x55092),f317(f88(a1),x55091)),f317(f88(a1),f317(f48(a1,x55092),x55091))) % 168.22/168.06 [5550]~P39(x55502)+P22(f317(f317(f225(a1),f2(a1)),x55501))+~P22(f317(f317(f319(a1),x55501),x55502)) % 168.22/168.06 [5570]~P52(x55701,x55702)+P37(x55701,x55702)+~P22(f317(f71(f857(x55701,x55701)),x55702)) % 168.22/168.06 [5572]~P52(x55721,x55722)+P42(x55721,x55722)+~P22(f317(f71(f857(x55721,x55721)),x55722)) % 168.22/168.06 [5609]E(x56091,f188(f858(x56092,a842)))+~P22(f317(f71(x56092),x56091))+P22(f317(f317(f226(a849),f2(a849)),f317(f54(x56092),x56091))) % 168.22/168.06 [5636]~P22(f317(x56361,x56362))+P22(f317(x56361,f2(a849)))+P22(f317(f317(f226(a849),f823(x56362,x56361)),x56362)) % 168.22/168.06 [5661]E(x56611,f2(a849))+~E(f317(f160(a849),x56612),f2(a849))+~P22(f317(f317(f319(a849),x56611),f317(f166(a849),x56612))) % 168.22/168.06 [5721]E(x57211,x57212)+~P22(f317(f317(f225(a849),x57212),x57211))+~P22(f317(f317(f225(a849),x57211),x57212)) % 168.22/168.06 [5722]E(x57221,x57222)+~P22(f317(f317(f225(a1),x57222),x57221))+~P22(f317(f317(f225(a1),x57221),x57222)) % 168.22/168.06 [5723]E(f317(f54(x57231),x57232),f2(a849))+~P22(f317(f71(x57231),x57232))+P22(f317(f317(f319(x57231),f721(x57232,x57231)),x57232)) % 168.22/168.06 [5751]~P22(f317(x57511,f837(x57511)))+P22(f317(x57511,f317(a116,x57512)))+~P22(f317(f317(f225(a1),f2(a1)),x57512)) % 168.22/168.06 [5753]P22(f317(f317(f225(a849),x57531),f362(x57532)))+~P22(f317(f71(a849),x57532))+~P22(f317(f317(f319(a849),x57531),x57532)) % 168.22/168.06 [5754]P22(f317(f317(f226(a849),x57541),f364(x57542)))+~P22(f317(f71(a849),x57542))+~P22(f317(f317(f319(a849),x57541),x57542)) % 168.22/168.06 [5785]E(x57851,x57852)+~P22(f317(f317(f226(a849),x57851),f317(a124,x57852)))+P22(f317(f317(f226(a849),x57851),x57852)) % 168.22/168.06 [5818]E(x58181,f317(a124,x58182))+~P22(f317(f317(f225(a849),x58181),f317(a124,x58182)))+P22(f317(f317(f225(a849),x58181),x58182)) % 168.22/168.06 [5829]P22(f317(x58291,f838(x58291)))+~P22(f317(x58291,f317(a116,x58292)))+~P22(f317(f317(f225(a1),f2(a1)),x58292)) % 168.22/168.06 [5842]~P22(f317(x58421,x58422))+~P22(f317(f317(f225(a1),f2(a1)),x58422))+P22(f317(x58421,f317(f112(a1),f818(x58421)))) % 168.22/168.06 [5857]~P79(x58572)+~E(x58571,f2(x58572))+~P22(f317(f317(f226(x58572),f2(x58572)),f317(f84(x58572),x58571))) % 168.22/168.06 [5884]~P52(x58841,x58842)+P37(x58841,f317(f263(x58841,x58841),x58842))+~P22(f317(f71(f857(x58841,x58841)),x58842)) % 168.22/168.06 [5888]E(f317(f48(a1,x58881),x58882),f2(a1))+~P22(f317(f317(f225(a1),x58881),f2(a1)))+~P22(f317(f317(f226(a1),x58882),x58881)) % 168.22/168.06 [5895]~P90(x58951)+E(f317(f112(x58951),f317(f115(a849),x58952)),f317(f115(x58951),x58952))+~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x58952))) % 168.22/168.06 [5899]E(f317(a124,x58991),x58992)+~P22(f317(f317(f226(a849),x58991),x58992))+P22(f317(f317(f226(a849),f317(a124,x58991)),x58992)) % 168.22/168.06 [5915]E(f317(f48(a1,x59151),x59152),f2(a1))+~P22(f317(f317(f225(a1),f2(a1)),x59151))+~P22(f317(f317(f226(a1),x59151),x59152)) % 168.22/168.06 [5926]E(f55(a1,x59261,x59262),x59261)+~P22(f317(f317(f225(a1),x59261),f2(a1)))+~P22(f317(f317(f226(a1),x59262),x59261)) % 168.22/168.06 [5955]E(f55(a849,f317(f115(a849),x59551),f317(f115(a849),x59552)),f317(f115(a849),x59551))+P22(f317(a193,f317(f115(a1),x59551)))+~P22(f317(a193,f317(f115(a1),x59552))) % 168.22/168.06 [5957]E(f55(a1,x59571,x59572),x59571)+~P22(f317(f317(f225(a1),f2(a1)),x59571))+~P22(f317(f317(f226(a1),x59571),x59572)) % 168.22/168.06 [5958]E(x59581,x59582)+~P22(f317(f317(f226(a849),x59581),f317(a124,x59582)))+~P22(f317(f317(f225(a849),x59582),x59581)) % 168.22/168.06 [5974]~P68(x59741)+~P22(f317(f317(f225(x59741),x59742),f2(x59741)))+P22(f317(f317(f225(x59741),x59742),f317(f88(x59741),x59742))) % 168.22/168.06 [5975]~P113(x59751)+~P22(f317(f317(f226(x59751),x59752),f2(x59751)))+P22(f317(f317(f226(x59751),x59752),f317(f88(x59751),x59752))) % 168.22/168.06 [5985]~P27(x59851)+E(f317(f317(f74(x59851,x59851,f122(x59851)),f188(x59851)),x59852),f49(x59851,x59852))+~P22(f317(f71(x59851),x59852)) % 168.22/168.06 [5986]~P27(x59861)+E(f317(f317(f74(x59861,x59861,f113(x59861)),f233(x59861)),x59862),f50(x59861,x59862))+~P22(f317(f71(x59861),x59862)) % 168.22/168.06 [5999]~P113(x59991)+~P22(f317(f317(f225(a1),f2(a1)),x59992))+P22(f317(f317(f225(x59991),f2(x59991)),f317(f114(x59991),x59992))) % 168.22/168.06 [6000]~P112(x60001)+~P22(f317(f317(f226(a849),f2(a849)),x60002))+P22(f317(f317(f226(x60001),f2(x60001)),f317(f112(x60001),x60002))) % 168.22/168.06 [6001]~P113(x60011)+~P22(f317(f317(f226(a1),f2(a1)),x60012))+P22(f317(f317(f226(x60011),f2(x60011)),f317(f114(x60011),x60012))) % 168.22/168.06 [6004]~P28(x60042)+~P28(x60041)+E(f317(f287(a849,a1,f112(a1)),f279(a849,f317(a116,x60041),f317(a116,x60042))),f279(a1,x60041,x60042)) % 168.22/168.06 [6008]P22(f317(x60081,x60082))+~P22(f317(f317(f225(a1),f2(a1)),x60082))+~P22(f317(x60081,f317(f112(a1),f819(x60081)))) % 168.22/168.06 [6032]E(f317(f317(f89(a849),f317(f115(a849),x60321)),f317(f115(a849),x60322)),f317(f115(a849),x60321))+P22(f317(f317(f226(a1),x60321),a92))+~P22(f317(f317(f226(a1),x60322),a92)) % 168.22/168.06 [6034]~P113(x60341)+P22(f317(f317(f226(x60341),f2(x60341)),f91(x60341,x60342)))+~P22(f317(f317(f226(x60341),f2(x60341)),x60342)) % 168.22/168.06 [6048]~P78(x60481)+~P22(f317(f317(f225(x60481),x60482),f2(x60481)))+P22(f317(f317(f225(x60481),f2(x60481)),f317(f88(x60481),x60482))) % 168.22/168.06 [6049]~P78(x60491)+~P22(f317(f317(f226(x60491),x60492),f2(x60491)))+P22(f317(f317(f226(x60491),f2(x60491)),f317(f88(x60491),x60492))) % 168.22/168.06 [6052]E(x60521,f233(f858(x60522,a842)))+~E(f317(f54(x60522),x60521),f317(f54(x60522),f233(f858(x60522,a842))))+~P22(f317(f71(x60522),f233(f858(x60522,a842)))) % 168.22/168.06 [6088]~P68(x60881)+P22(f317(f317(f225(x60881),x60882),f2(x60881)))+~P22(f317(f317(f225(x60881),x60882),f317(f88(x60881),x60882))) % 168.22/168.06 [6089]~P113(x60891)+P22(f317(f317(f226(x60891),x60892),f2(x60891)))+~P22(f317(f317(f226(x60891),x60892),f317(f88(x60891),x60892))) % 168.22/168.06 [6097]~P90(x60971)+P22(f317(f317(f319(x60971),f317(f115(x60971),x60972)),f185(x60971)))+~P22(f317(f317(f225(a1),a92),x60972)) % 168.22/168.06 [6131]~E(x61312,f2(a1))+E(x61311,f2(a1))+E(f317(f317(f237(a1,a1),f317(f48(a1,x61311),x61312)),f55(a1,x61311,x61312)),f317(f317(f237(a1,a1),f2(a1)),x61311)) % 168.22/168.06 [6132]E(x61321,f2(a849))+~P22(f317(f317(f226(a849),x61321),f317(a124,x61322)))+P22(f317(f317(f226(a849),f806(x61322,x61321)),x61322)) % 168.22/168.06 [6135]E(f317(f244(a1,a1),f59(x61351,x61352)),f317(f48(a1,x61351),x61352))+~P22(f317(f317(f226(a1),x61351),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x61352)) % 168.22/168.06 [6152]~P113(x61521)+~P22(f317(f317(f226(x61521),f2(x61521)),f91(x61521,x61522)))+P22(f317(f317(f226(x61521),f2(x61521)),x61522)) % 168.22/168.06 [6154]~E(f317(f115(a849),x61542),f317(f115(a849),x61541))+P22(f317(f317(f225(a1),f317(f115(a1),x61541)),f2(a1)))+~P22(f317(a193,f317(f115(a1),x61542))) % 168.22/168.06 [6189]E(f317(f244(a1,a1),f56(x61891,x61892)),f317(f48(a1,x61891),x61892))+~P22(f317(f317(f225(a1),f2(a1)),x61892))+~P22(f317(f317(f226(a1),f2(a1)),x61891)) % 168.22/168.06 [6214]E(f317(f246(a1,a1),f59(x62141,x62142)),f55(a1,x62141,x62142))+~P22(f317(f317(f226(a1),x62141),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x62142)) % 168.22/168.06 [6217]~P113(x62172)+~P22(f317(f317(f225(x62172),f2(x62172)),f317(f114(x62172),x62171)))+P22(f317(f317(f225(a1),f2(a1)),x62171)) % 168.22/168.06 [6218]~P112(x62182)+~P22(f317(f317(f226(x62182),f2(x62182)),f317(f112(x62182),x62181)))+P22(f317(f317(f226(a849),f2(a849)),x62181)) % 168.22/168.06 [6219]~P113(x62192)+~P22(f317(f317(f226(x62192),f2(x62192)),f317(f114(x62192),x62191)))+P22(f317(f317(f226(a1),f2(a1)),x62191)) % 168.22/168.06 [6236]E(f317(f246(a1,a1),f56(x62361,x62362)),f55(a1,x62361,x62362))+~P22(f317(f317(f225(a1),f2(a1)),x62362))+~P22(f317(f317(f226(a1),f2(a1)),x62361)) % 168.22/168.06 [6253]~P78(x62531)+P22(f317(f317(f225(x62531),x62532),f2(x62531)))+~P22(f317(f317(f225(x62531),f2(x62531)),f317(f88(x62531),x62532))) % 168.22/168.06 [6254]~P78(x62541)+P22(f317(f317(f226(x62541),x62542),f2(x62541)))+~P22(f317(f317(f226(x62541),f2(x62541)),f317(f88(x62541),x62542))) % 168.22/168.06 [6278]P22(f317(f58(x62781,x62782),f59(x62781,x62782)))+~P22(f317(f317(f226(a1),x62781),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x62782)) % 168.22/168.06 [6302]P22(f317(f58(x63021,x63022),f56(x63021,x63022)))+~P22(f317(f317(f225(a1),f2(a1)),x63021))+~P22(f317(f317(f226(a1),f2(a1)),x63022)) % 168.22/168.06 [6347]~P78(x63471)+P22(f317(f317(f225(x63471),f317(f88(x63471),x63472)),f2(x63471)))+~P22(f317(f317(f225(x63471),f2(x63471)),x63472)) % 168.22/168.06 [6348]~P78(x63481)+P22(f317(f317(f226(x63481),f317(f88(x63481),x63482)),f2(x63481)))+~P22(f317(f317(f226(x63481),f2(x63481)),x63482)) % 168.22/168.06 [6365]E(f317(f317(f21(a849),f317(a116,x63651)),f317(a116,x63652)),f317(a116,f195(x63651,x63652)))+~P22(f317(f317(f225(a1),f2(a1)),x63652))+~P22(f317(f317(f225(a1),f2(a1)),x63651)) % 168.22/168.06 [6382]P22(f317(f317(f225(a1),f2(a1)),f195(x63821,x63822)))+~P22(f317(f317(f225(a1),f2(a1)),x63822))+~P22(f317(f317(f225(a1),f2(a1)),x63821)) % 168.22/168.06 [6420]~P22(f317(x64201,x64202))+P22(f317(x64201,f2(a849)))+P22(f317(x64201,f317(f317(f89(a849),f823(x64202,x64201)),f87(a849)))) % 168.22/168.06 [6470]E(x64701,f2(a1))+E(f55(a1,x64702,x64701),f2(a1))+E(f317(f317(f21(a1),f317(f88(a1),f317(f48(a1,x64702),x64701))),f87(a1)),f317(f48(a1,x64702),f317(f88(a1),x64701))) % 168.22/168.06 [6499]E(f317(f115(a849),x64991),f317(f115(a849),x64992))+~P22(f317(f317(f225(a1),f317(f115(a1),x64992)),f2(a1)))+~P22(f317(a193,f317(f115(a1),x64991))) % 168.22/168.06 [6509]~E(x65091,f2(a849))+~E(f622(x65092,x65091),f2(a849))+E(f317(f136(a849,a849,f89(a849),x65091),x65092),f2(a849)) % 168.22/168.06 [6534]~P22(f317(f71(x65341),f672(x65342,x65341)))+~P22(f317(f71(f858(x65341,a842)),x65342))+P22(f317(f71(x65341),f49(f858(x65341,a842),x65342))) % 168.22/168.06 [6540]E(x65401,x65402)+P22(f317(f317(f226(a1),x65401),x65402))+~P22(f317(f317(f226(a1),x65401),f317(f317(f89(a1),x65402),f87(a1)))) % 168.22/168.06 [6541]P22(f317(f317(f225(a849),f317(a116,x65411)),f317(a116,x65412)))+~P22(f317(f317(f225(a1),f2(a1)),x65412))+~P22(f317(f317(f225(a1),x65411),x65412)) % 168.22/168.06 [6542]P22(f317(f317(f225(a849),f317(a116,x65421)),f317(a116,x65422)))+~P22(f317(f317(f226(a1),f2(a1)),x65421))+~P22(f317(f317(f225(a1),x65421),x65422)) % 168.22/168.06 [6544]P22(f317(f317(f226(a849),f317(a116,x65441)),f317(a116,x65442)))+~P22(f317(f317(f225(a1),f2(a1)),x65441))+~P22(f317(f317(f226(a1),x65441),x65442)) % 168.22/168.06 [6545]P22(f317(f317(f226(a849),f317(a116,x65451)),f317(a116,x65452)))+~P22(f317(f317(f226(a1),f2(a1)),x65452))+~P22(f317(f317(f226(a1),x65451),x65452)) % 168.22/168.06 [6556]E(f55(a849,f317(a116,x65561),f317(a116,x65562)),f317(a116,f55(a1,x65561,x65562)))+~P22(f317(f317(f225(a1),f2(a1)),x65562))+~P22(f317(f317(f225(a1),f2(a1)),x65561)) % 168.22/168.06 [6578]~P78(x65781)+~P22(f317(f317(f225(x65781),f317(f88(x65781),x65782)),f2(x65781)))+P22(f317(f317(f225(x65781),f2(x65781)),x65782)) % 168.22/168.06 [6579]~P78(x65791)+~P22(f317(f317(f226(x65791),f317(f88(x65791),x65792)),f2(x65791)))+P22(f317(f317(f226(x65791),f2(x65791)),x65792)) % 168.22/168.06 [6584]~P22(f317(f317(f226(a1),f2(a1)),x65842))+P22(f317(f317(f226(a1),f2(a1)),f317(f48(a1,x65841),x65842)))+~P22(f317(f317(f225(a1),x65842),x65841)) % 168.22/168.06 [6585]~P22(f317(f317(f225(a1),x65851),f2(a1)))+~P22(f317(f317(f226(a1),x65852),f2(a1)))+P22(f317(f317(f225(a1),f2(a1)),f317(f48(a1,x65851),x65852))) % 168.22/168.06 [6596]~P22(f317(f317(f226(a1),a92),x65962))+~P22(f317(f317(f226(a1),x65961),x65962))+P22(f317(f317(f226(a849),f317(f115(a849),x65961)),f317(f115(a849),x65962))) % 168.22/168.06 [6618]~P22(f317(f317(f225(a1),f2(a1)),x66182))+~P22(f317(f317(f225(a1),f2(a1)),x66181))+P22(f317(f317(f225(a1),f2(a1)),f317(f48(a1,x66181),x66182))) % 168.22/168.06 [6619]~P22(f317(f317(f225(a1),f2(a1)),x66191))+~P22(f317(f317(f226(a1),f2(a1)),x66192))+P22(f317(f317(f225(a1),f2(a1)),f317(f48(a1,x66191),x66192))) % 168.22/168.06 [6683]~P22(f317(f317(f225(a1),f2(a1)),x66831))+P22(f317(f317(f226(a849),f317(a116,x66831)),x66832))+~P22(f317(f317(f226(a1),x66831),f317(f112(a1),x66832))) % 168.22/168.06 [6705]E(f317(f317(f237(a1,a1),f317(f48(a1,x67051),x67052)),f55(a1,x67051,x67052)),f59(x67051,x67052))+P22(f317(f317(f225(a1),f2(a1)),x67051))+~P22(f317(f317(f226(a1),f2(a1)),x67052)) % 168.22/168.06 [6712]~P22(f317(f317(f225(a1),f2(a1)),x67121))+~P22(f317(f317(f226(a849),f317(a116,x67121)),x67122))+P22(f317(f317(f226(a1),x67121),f317(f112(a1),x67122))) % 168.22/168.06 [6744]~P22(f317(f317(f225(a849),f317(a116,x67441)),f317(a116,x67442)))+~P22(f317(f317(f225(a1),f2(a1)),x67442))+P22(f317(f317(f225(a1),x67441),x67442)) % 168.22/168.06 [6745]~P22(f317(f317(f225(a849),f317(a116,x67451)),f317(a116,x67452)))+~P22(f317(f317(f226(a1),f2(a1)),x67451))+P22(f317(f317(f225(a1),x67451),x67452)) % 168.22/168.06 [6773]P22(f317(f317(f225(a1),x67731),x67732))+~P22(f317(f317(f225(a849),f317(f115(a849),x67731)),f317(f115(a849),x67732)))+P22(f317(f317(f225(a1),x67731),a92)) % 168.22/168.06 [6797]P22(f317(f317(f225(a1),f2(a1)),f55(a1,x67971,x67972)))+~P22(f317(f317(f225(a1),f2(a1)),x67972))+~P22(f317(f317(f225(a1),f2(a1)),x67971)) % 168.22/168.06 [6804]P22(f317(f317(f225(a1),x68041),f2(a1)))+~P22(f317(f317(f226(a1),x68042),f2(a1)))+~P22(f317(f317(f225(a1),f2(a1)),f317(f48(a1,x68041),x68042))) % 168.22/168.06 [6818]~P22(f317(f317(f226(a1),f2(a1)),x68181))+~P22(f317(f317(f226(a1),f2(a1)),f317(f48(a1,x68182),x68181)))+P22(f317(f317(f225(a1),x68181),x68182)) % 168.22/168.06 [6819]~P22(f317(f317(f225(a1),f2(a1)),x68192))+~P22(f317(f317(f226(a1),f2(a1)),f317(f48(a1,x68192),x68191)))+P22(f317(f317(f225(a1),x68191),x68192)) % 168.22/168.06 [6848]E(f317(f317(f237(a1,a1),f317(f48(a1,x68481),x68482)),f55(a1,x68481,x68482)),f59(x68481,x68482))+~P22(f317(f317(f226(a1),x68481),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x68482)) % 168.22/168.06 [6849]P22(f317(f317(f225(a1),f2(a1)),x68491))+~P22(f317(f317(f226(a1),f2(a1)),x68492))+~P22(f317(f317(f225(a1),f2(a1)),f317(f48(a1,x68491),x68492))) % 168.22/168.06 [6850]P22(f317(f317(f226(a1),f2(a1)),x68501))+~P22(f317(f317(f225(a1),f2(a1)),x68502))+~P22(f317(f317(f226(a1),f2(a1)),f317(f48(a1,x68502),x68501))) % 168.22/168.06 [6874]E(f317(f317(f237(a1,a1),f317(f48(a1,x68741),x68742)),f55(a1,x68741,x68742)),f56(x68741,x68742))+~P22(f317(f317(f225(a1),f2(a1)),x68742))+~P22(f317(f317(f225(a1),f2(a1)),x68741)) % 168.22/168.06 [6904]P22(f317(f317(f226(a1),a92),x69041))+~P22(f317(f317(f226(a1),x69042),x69041))+~P22(f317(f317(f226(a849),f317(f115(a849),x69042)),f317(f115(a849),x69041))) % 168.22/168.06 [6972]~P22(f317(f317(f225(a1),x69721),f2(a1)))+P22(f317(f317(f225(a1),f317(f48(a1,x69721),x69722)),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x69722)) % 168.22/168.06 [6973]~P22(f317(f317(f226(a1),x69732),f2(a1)))+P22(f317(f317(f225(a1),f317(f48(a1,x69731),x69732)),f2(a1)))+~P22(f317(f317(f225(a1),f2(a1)),x69731)) % 168.22/168.06 [6974]~P22(f317(f317(f226(a1),x69742),f2(a1)))+P22(f317(f317(f226(a1),f317(f48(a1,x69741),x69742)),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x69741)) % 168.22/168.06 [6976]~P22(f317(f317(f226(a1),x69761),f2(a1)))+P22(f317(f317(f226(a1),f317(f48(a1,x69761),x69762)),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x69762)) % 168.22/168.06 [7026]~P91(x70262)+E(x70261,f125(x70262))+E(f317(f136(x70262,x70262,f90(x70262),f317(f135(x70262),x70261)),f317(f165(x70262),x70261)),f317(f73(x70262,f90(x70262)),f317(f166(x70262),x70261))) % 168.22/168.06 [7138]~E(x71381,f2(a849))+E(f317(f136(a849,a849,f89(a849),x71381),x71382),f2(a849))+P22(f317(f317(f319(a849),f622(x71382,x71381)),f317(f166(a849),x71382))) % 168.22/168.06 [7187]P22(f317(f317(f319(f858(x71871,a842)),f672(x71872,x71871)),x71872))+~P22(f317(f71(f858(x71871,a842)),x71872))+P22(f317(f71(x71871),f49(f858(x71871,a842),x71872))) % 168.22/168.06 [7287]P19(x72871,x72871,x72872,f233(f858(x72871,a842)))+~E(f317(f287(x72871,x72871,x72872),f233(f858(x72871,a842))),f233(f858(x72871,a842)))+~P22(f317(f71(x72871),f233(f858(x72871,a842)))) % 168.22/168.06 [7357]~P22(f317(f317(f226(a1),x73572),f2(a1)))+~P22(f317(f317(f226(a1),f317(f48(a1,x73571),x73572)),f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x73571)) % 168.22/168.06 [7360]P22(f317(f317(f226(a1),x73601),f2(a1)))+~P22(f317(f317(f226(a1),f317(f48(a1,x73601),x73602)),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x73602)) % 168.22/168.06 [7410]~P19(x74101,x74101,x74102,f233(f858(x74101,a842)))+E(f317(f287(x74101,x74101,x74102),f233(f858(x74101,a842))),f233(f858(x74101,a842)))+~P22(f317(f71(x74101),f233(f858(x74101,a842)))) % 168.22/168.06 [7523]E(f317(f48(a1,x75231),x75232),f317(f115(a1),a109))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),x75231),x75232)),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x75231)) % 168.22/168.06 [7608]E(f317(f317(f89(a1),x76081),x76082),f55(a1,x76081,x76082))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),x76081),x76082)),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x76081)) % 168.22/168.06 [7995]~P57(x79951)+~P22(f317(f68(f853(x79951)),x79952))+P22(f317(f68(x79951),f317(f317(f8(f853(x79951),a842,x79951),x79952),f217(x79951)))) % 168.22/168.06 [8312]~P103(x83121)+P29(x83121,x83122)+~P22(f317(f317(f225(x83121),f317(f317(f159(x83121),x83122),f643(x83122,x83121))),f317(f317(f159(x83121),x83122),f644(x83122,x83121)))) % 168.22/168.06 [8313]~P103(x83131)+P29(x83131,x83132)+~P22(f317(f317(f225(x83131),f317(f317(f159(x83131),x83132),f657(x83132,x83131))),f317(f317(f159(x83131),x83132),f663(x83132,x83131)))) % 168.22/168.06 [8373]~P57(x83732)+~P57(x83731)+E(f317(f317(f127(f856(x83731,x83732)),f317(f317(f148(x83731,f856(x83731,x83732)),f288(x83731,x83732)),f65(x83731))),f317(f317(f148(x83732,f856(x83731,x83732)),f297(x83732,x83731)),f65(x83732))),f65(f856(x83731,x83732))) % 168.22/168.06 [8476]~P57(x84761)+P22(f317(f67(f853(x84761)),x84762))+~P22(f317(f67(x84761),f317(f317(f8(f853(x84761),a842,x84761),x84762),f217(x84761)))) % 168.22/168.06 [9613]~P57(x96131)+~P57(x96132)+E(f317(f317(f148(f850(x96131),f858(x96132,x96131)),f317(f317(f8(f858(x96132,f853(x96131)),f858(x96132,x96131),f850(x96131)),f82(f853(x96131),x96131,x96132,f222(x96131))),f317(f317(f8(f850(f857(x96132,x96131)),f858(x96132,f853(x96131)),f850(x96131)),f171(x96132,x96131)),f317(f175(x96132,x96131),f65(x96132))))),f64(x96131,f317(f189(f850(x96132)),f65(x96132)),f65(x96131))),f65(f858(x96132,x96131))) % 168.22/168.06 [5621]~P39(x56212)+~P39(x56211)+P39(f317(f317(f122(f858(a1,a842)),x56211),x56212)) % 168.22/168.06 [5622]~P39(x56222)+~P39(x56221)+P39(f317(f317(f113(f858(a1,a842)),x56221),x56222)) % 168.22/168.06 [5629]E(x56291,f2(a1))+~E(f55(a1,x56292,x56291),f2(a1))+E(f317(f48(a1,f317(f88(a1),x56292)),x56291),f317(f88(a1),f317(f48(a1,x56292),x56291))) % 168.22/168.06 [5639]~P90(x56391)+~P58(x56391)+E(f317(f88(x56391),f317(f317(f266(x56391),f87(x56391)),x56392)),f317(f317(f266(x56391),f317(f115(x56391),a109)),x56392)) % 168.22/168.06 [5878]~P103(x58781)+P29(x58781,x58782)+P22(f317(f317(f226(a849),f644(x58782,x58781)),f317(f189(f850(x58781)),x58782))) % 168.22/168.06 [5879]~P103(x58791)+P29(x58791,x58792)+P22(f317(f317(f226(a849),f663(x58792,x58791)),f317(f189(f850(x58791)),x58792))) % 168.22/168.06 [6029]~P90(x60291)+~E(f317(f115(x60291),x60292),f2(x60291))+P31(x60291,f317(f115(x60291),f317(f317(f89(a1),x60292),f317(f88(a1),a92)))) % 168.22/168.06 [6030]~P90(x60301)+~E(f317(f115(x60301),x60302),f2(x60301))+P31(x60301,f317(f115(x60301),f317(f317(f89(a1),a92),f317(f88(a1),x60302)))) % 168.22/168.06 [6160]~E(x61602,f2(a849))+~E(x61601,f2(a849))+P22(f317(f317(f225(a1),f317(f112(a1),x61601)),f317(f88(a1),f317(f112(a1),x61602)))) % 168.22/168.06 [6179]E(f317(f317(f89(a111),f87(a111)),f256(x61791,f317(f48(a111,x61792),x61791))),f256(x61791,x61792))+P22(f317(f317(f225(a111),x61791),f87(a111)))+P22(f317(f317(f226(a111),x61792),x61791)) % 168.22/168.06 [6188]E(f317(f317(f89(a849),f317(f115(a849),x61881)),f317(f115(a849),x61882)),f317(f115(a849),f317(f317(f89(a1),x61881),x61882)))+P22(f317(f317(f226(a1),x61881),a92))+P22(f317(f317(f226(a1),x61882),a92)) % 168.22/168.06 [6313]~P68(x63131)+~P22(f317(f317(f225(x63131),f2(x63131)),x63132))+P22(f317(f317(f225(x63131),f317(f88(x63131),x63132)),x63132)) % 168.22/168.06 [6314]~P68(x63141)+~P22(f317(f317(f226(x63141),f2(x63141)),x63142))+P22(f317(f317(f226(x63141),f317(f88(x63141),x63142)),x63142)) % 168.22/168.06 [6485]E(f317(f317(f21(a849),f317(a116,x64851)),f317(a116,x64852)),f317(a116,f317(f317(f21(a1),x64851),x64852)))+~P22(f317(f317(f225(a1),f2(a1)),x64852))+~P22(f317(f317(f225(a1),x64852),x64851)) % 168.22/168.06 [6518]E(f317(a116,f55(a1,f317(f115(a1),x65181),f317(f115(a1),x65182))),f55(a849,f317(f115(a849),x65181),f317(f115(a849),x65182)))+P22(f317(a193,f317(f115(a1),x65181)))+P22(f317(a193,f317(f115(a1),x65182))) % 168.22/168.06 [6535]~P68(x65351)+P22(f317(f317(f225(x65351),f2(x65351)),x65352))+~P22(f317(f317(f225(x65351),f317(f88(x65351),x65352)),x65352)) % 168.22/168.06 [6536]~P68(x65361)+P22(f317(f317(f226(x65361),f2(x65361)),x65362))+~P22(f317(f317(f226(x65361),f317(f88(x65361),x65362)),x65362)) % 168.22/168.06 [6547]~P68(x65471)+~P22(f317(f317(f225(x65471),f2(x65471)),x65472))+P22(f317(f317(f225(x65471),f2(x65471)),f317(f317(f89(x65471),x65472),x65472))) % 168.22/168.06 [6550]~P68(x65501)+~P22(f317(f317(f226(x65501),f2(x65501)),x65502))+P22(f317(f317(f226(x65501),f2(x65501)),f317(f317(f89(x65501),x65502),x65502))) % 168.22/168.06 [6560]E(f317(f317(f89(a849),f317(a116,x65601)),f317(a116,x65602)),f317(a116,f317(f317(f89(a1),x65601),x65602)))+~P22(f317(f317(f225(a1),f2(a1)),x65602))+~P22(f317(f317(f225(a1),f2(a1)),x65601)) % 168.22/168.06 [6572]E(x65721,f2(a1))+E(f55(a1,x65722,x65721),f2(a1))+E(f317(f317(f21(a1),f317(f88(a1),f317(f48(a1,x65722),x65721))),f87(a1)),f317(f48(a1,f317(f88(a1),x65722)),x65721)) % 168.22/168.06 [6574]E(x65741,f2(a849))+P22(f317(f317(f226(a849),f2(a849)),x65742))+~P22(f317(f317(f226(a849),f2(a849)),f317(f317(f238(a849),x65742),x65741))) % 168.22/168.06 [6600]~P90(x66001)+E(f317(f115(x66001),x66002),f2(x66001))+~P31(x66001,f317(f115(x66001),f317(f317(f89(a1),a92),f317(f88(a1),x66002)))) % 168.22/168.06 [6601]~P90(x66011)+E(f317(f115(x66011),x66012),f2(x66011))+~P31(x66011,f317(f115(x66011),f317(f317(f89(a1),x66012),f317(f88(a1),a92)))) % 168.22/168.06 [6661]~P22(f317(f71(x66611),x66612))+~P22(f317(f71(x66611),f233(f858(x66611,a842))))+P22(f317(f71(x66611),f317(f88(f858(x66611,a842)),x66612))) % 168.22/168.06 [6719]~P22(f317(f317(f225(a1),f2(a1)),x67192))+~P22(f317(f317(f225(a1),f2(a1)),x67191))+P22(f317(f317(f225(a1),f2(a1)),f317(f317(f89(a1),x67191),x67192))) % 168.22/168.06 [6720]~P22(f317(f317(f225(a1),f2(a1)),x67202))+~P22(f317(f317(f225(a1),f2(a1)),x67201))+P22(f317(f317(f225(a1),f2(a1)),f317(f317(f90(a1),x67201),x67202))) % 168.22/168.06 [6721]~P22(f317(f317(f226(a849),f2(a849)),x67212))+~P22(f317(f317(f226(a849),f2(a849)),x67211))+P22(f317(f317(f226(a849),f2(a849)),f317(f317(f90(a849),x67211),x67212))) % 168.22/168.06 [6841]P22(f317(f317(f226(a849),f2(a849)),x68411))+P22(f317(f317(f226(a849),f2(a849)),x68412))+~P22(f317(f317(f226(a849),f2(a849)),f317(f317(f89(a849),x68412),x68411))) % 168.22/168.06 [6843]~P68(x68431)+P22(f317(f317(f225(x68431),f2(x68431)),x68432))+~P22(f317(f317(f225(x68431),f2(x68431)),f317(f317(f89(x68431),x68432),x68432))) % 168.22/168.06 [6844]~P68(x68441)+P22(f317(f317(f226(x68441),f2(x68441)),x68442))+~P22(f317(f317(f226(x68441),f2(x68441)),f317(f317(f89(x68441),x68442),x68442))) % 168.22/168.06 [6905]~P22(f317(f71(x69051),x69052))+P22(f317(f71(x69051),f233(f858(x69051,a842))))+~P22(f317(f71(x69051),f317(f88(f858(x69051,a842)),x69052))) % 168.22/168.06 [6962]E(f317(f317(f237(a1,a1),f317(f48(a1,x69621),x69622)),f55(a1,x69621,x69622)),f317(a60,f56(f317(f88(a1),x69621),f317(f88(a1),x69622))))+P22(f317(f317(f225(a1),f2(a1)),x69621))+P22(f317(f317(f226(a1),f2(a1)),x69622)) % 168.22/168.06 [6989]~P22(f317(f317(f226(a849),f2(a849)),x69891))+~P22(f317(f317(f226(a849),f87(a849)),x69892))+P22(f317(f317(f226(a849),f317(f48(a849,x69891),x69892)),x69891)) % 168.22/168.06 [6990]~P22(f317(f317(f226(a1),f2(a1)),x69901))+~P22(f317(f317(f226(a1),f87(a1)),x69902))+P22(f317(f317(f226(a1),f317(f48(a1,x69901),x69902)),x69901)) % 168.22/168.06 [7440]~P22(f317(f71(x74402),f233(f858(x74402,a842))))+~P22(f317(f71(x74401),f233(f858(x74401,a842))))+P22(f317(f71(f856(x74401,x74402)),f233(f858(f856(x74401,x74402),a842)))) % 168.22/168.06 [7441]~P22(f317(f71(x74412),f233(f858(x74412,a842))))+~P22(f317(f71(x74411),f233(f858(x74411,a842))))+P22(f317(f71(f857(x74411,x74412)),f233(f858(f857(x74411,x74412),a842)))) % 168.22/168.06 [7511]~P22(f317(f317(f226(a849),f317(a124,f2(a849))),x75111))+~P22(f317(f317(f226(a849),f317(a124,f2(a849))),x75112))+P22(f317(f317(f226(a849),x75111),f317(f317(f90(a849),x75112),x75111))) % 168.22/168.06 [7512]~P22(f317(f317(f226(a849),f317(a124,f2(a849))),x75121))+~P22(f317(f317(f226(a849),f317(a124,f2(a849))),x75122))+P22(f317(f317(f226(a849),x75121),f317(f317(f90(a849),x75121),x75122))) % 168.22/168.06 [7545]E(f317(f54(x75451),f233(f858(x75451,a842))),f317(a124,f2(a849)))+P22(f317(f71(x75452),f233(f858(x75452,a842))))+~P22(f317(f71(f858(x75452,x75451)),f233(f858(f858(x75452,x75451),a842)))) % 168.22/168.06 [7674]~P22(f317(f317(f225(a849),f317(a124,f2(a849))),x76741))+~P22(f317(f317(f225(a849),f317(a124,f2(a849))),x76742))+P22(f317(f317(f225(a849),f317(a124,f2(a849))),f317(f317(f90(a849),x76741),x76742))) % 168.22/168.06 [7675]~P22(f317(f317(f226(a849),f317(a124,f2(a849))),x76752))+~P22(f317(f317(f226(a849),f317(a124,f2(a849))),x76751))+P22(f317(f317(f226(a849),f317(a124,f2(a849))),f317(f317(f90(a849),x76751),x76752))) % 168.22/168.06 [8362]E(x83621,f125(x83622))+~P22(f317(f131(x83622),x83621))+E(f170(x83622,f317(f317(f8(a842,a842,x83622),a312),f317(f317(f7(x83622,x83622,a842),a314),f138(x83622,x83621))),x83621),f126(x83622,x83621)) % 168.22/168.06 [8465]~P39(x84652)+~P39(x84651)+E(f317(f287(a849,a1,f112(a1)),f317(f317(f122(f858(a849,a842)),f317(f287(a1,a849,a116),x84651)),f317(f287(a1,a849,a116),x84652))),f317(f317(f122(f858(a1,a842)),x84651),x84652)) % 168.22/168.06 [8466]~P39(x84662)+~P39(x84661)+E(f317(f287(a849,a1,f112(a1)),f317(f317(f113(f858(a849,a842)),f317(f287(a1,a849,a116),x84661)),f317(f287(a1,a849,a116),x84662))),f317(f317(f113(f858(a1,a842)),x84661),x84662)) % 168.22/168.06 [9104]~P90(x91041)+~E(f317(f115(x91041),x91042),f87(x91041))+P31(x91041,f317(f115(x91041),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f88(a1),x91042)))) % 168.22/168.06 [9335]~P90(x93351)+E(f317(f115(x93351),x93352),f87(x93351))+~P31(x93351,f317(f115(x93351),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f88(a1),x93352)))) % 168.22/168.06 [10062]E(x100621,f2(a1))+E(x100622,f2(a1))+E(f317(f248(a1,a1,a1,a1,f39(a1),f317(f90(a1),f91(a1,x100622))),f317(f317(f317(f108(f857(a1,a1)),f317(f317(a314,f91(a1,x100621)),f91(a1,x100622))),f62(x100621,x100622)),f317(f317(f247(a1,a1,f857(a1,a1)),f317(f317(f18(a1,f858(a1,f857(a1,a1)),f858(a1,f857(a1,a1))),f317(f317(f8(f858(a1,f858(f857(a1,a1),f857(a1,a1))),f858(f858(a1,f857(a1,a1)),f858(a1,f857(a1,a1))),a1),f18(a1,f857(a1,a1),f857(a1,a1))),f317(f317(f8(f857(a1,a1),f858(a1,f858(f857(a1,a1),f857(a1,a1))),a1),f317(f7(a1,f857(a1,a1),f858(f857(a1,a1),f857(a1,a1))),f317(f317(f8(a842,f858(f857(a1,a1),f858(f857(a1,a1),f857(a1,a1))),a1),f108(f857(a1,a1))),f317(f317(f7(a1,a1,a842),a314),f2(a1))))),f317(f317(f7(a1,a1,f857(a1,a1)),f317(f317(f8(a1,f858(a1,f857(a1,a1)),a1),f237(a1,a1)),f88(a1))),f2(a1))))),f317(f317(f7(a1,f858(a1,a1),f858(a1,f857(a1,a1))),f317(f317(f8(f858(a1,f857(a1,a1)),f858(f858(a1,a1),f858(a1,f857(a1,a1))),a1),f8(a1,f857(a1,a1),a1)),f317(f317(f8(a1,f858(a1,f857(a1,a1)),a1),f237(a1,a1)),f317(f317(f7(a1,a1,a1),f317(f317(f8(a1,f858(a1,a1),a1),f21(a1)),f88(a1))),f87(a1))))),f317(f21(a1),f317(f84(a1),x100622))))),f62(x100621,x100622)))),f317(f317(f237(a1,a1),f317(f48(a1,x100621),x100622)),f55(a1,x100621,x100622))) % 168.22/168.06 [10063]E(x100631,f2(a1))+E(x100632,f2(a1))+E(f317(f248(a1,a1,a1,a1,f39(a1),f317(f90(a1),f91(a1,x100632))),f317(f317(f317(f108(f857(a1,a1)),f317(f317(a316,f317(f317(a315,f317(f317(f226(a1),f2(a1)),x100632)),f317(f317(f225(a1),f2(a1)),x100631))),f317(f317(a315,f317(f317(f226(a1),x100632),f2(a1))),f317(f317(f226(a1),x100631),f2(a1))))),f62(x100631,x100632)),f317(f317(f247(a1,a1,f857(a1,a1)),f317(f317(f18(a1,f858(a1,f857(a1,a1)),f858(a1,f857(a1,a1))),f317(f317(f8(f858(a1,f858(f857(a1,a1),f857(a1,a1))),f858(f858(a1,f857(a1,a1)),f858(a1,f857(a1,a1))),a1),f18(a1,f857(a1,a1),f857(a1,a1))),f317(f317(f8(f857(a1,a1),f858(a1,f858(f857(a1,a1),f857(a1,a1))),a1),f317(f7(a1,f857(a1,a1),f858(f857(a1,a1),f857(a1,a1))),f317(f317(f8(a842,f858(f857(a1,a1),f858(f857(a1,a1),f857(a1,a1))),a1),f108(f857(a1,a1))),f317(f317(f7(a1,a1,a842),a314),f2(a1))))),f317(f317(f7(a1,a1,f857(a1,a1)),f317(f317(f8(a1,f858(a1,f857(a1,a1)),a1),f237(a1,a1)),f88(a1))),f2(a1))))),f317(f317(f7(a1,f858(a1,a1),f858(a1,f857(a1,a1))),f317(f317(f8(f858(a1,f857(a1,a1)),f858(f858(a1,a1),f858(a1,f857(a1,a1))),a1),f8(a1,f857(a1,a1),a1)),f317(f317(f8(a1,f858(a1,f857(a1,a1)),a1),f237(a1,a1)),f317(f317(f7(a1,a1,a1),f317(f317(f8(a1,f858(a1,a1),a1),f21(a1)),f88(a1))),f87(a1))))),f317(f21(a1),f317(f84(a1),x100632))))),f62(x100631,x100632)))),f317(f317(f237(a1,a1),f317(f48(a1,x100631),x100632)),f55(a1,x100631,x100632))) % 168.22/168.06 [10064]~P4(a5000)+P18(a845,x100641,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),x100642),f194(x100642))),f188(f858(f848(a845),a842))))+~P18(a845,x100641,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),f317(f317(f8(f858(a845,f858(a845,a842)),f858(a845,a842),a845),f317(f8(f858(a845,a842),a842,a845),f97(a845))),f317(f317(f8(f858(a845,a842),f858(a845,f858(a845,a842)),a845),f317(f7(a845,f858(a845,a842),f858(a845,a842)),f317(f317(f8(f858(a845,f858(a842,a842)),f858(f858(a845,a842),f858(a845,a842)),a845),f18(a845,a842,a842)),f317(f317(f8(f858(a845,a842),f858(a845,f858(a842,a842)),a845),f317(f8(a842,f858(a842,a842),a845),a320)),f194(x100642))))),a314))),x100642),a314)),f188(f858(f848(a845),a842)))) % 168.22/168.06 [5630]~P113(x56301)+~P90(x56301)+E(f317(f84(x56301),f317(f317(f238(x56301),f317(f115(x56301),a109)),x56302)),f87(x56301)) % 168.22/168.06 [6098]~P111(x60981)+~P22(f317(f317(f226(a1),x60982),f2(a1)))+E(f317(f88(x60981),f317(f112(x60981),f317(a116,f317(f88(a1),x60982)))),f317(f114(x60981),x60982)) % 168.22/168.06 [6887]~P87(x68871)+~P22(f317(f317(f319(x68871),x68872),f121(x68871)))+~E(f317(f317(f89(x68871),f317(f317(f89(x68871),f87(x68871)),x68872)),x68872),f2(x68871)) % 168.22/168.06 [6991]~P22(f317(f317(f225(a1),x69912),f2(a1)))+~P22(f317(f317(f226(a1),x69911),f2(a1)))+E(f317(f244(a1,a1),f317(a60,f56(f317(f88(a1),x69911),f317(f88(a1),x69912)))),f317(f48(a1,x69911),x69912)) % 168.22/168.06 [7005]~P22(f317(f317(f226(a1),x70052),f2(a1)))+E(f317(f244(a1,a1),f317(a60,f59(f317(f88(a1),x70051),f317(f88(a1),x70052)))),f317(f48(a1,x70051),x70052))+~P22(f317(f317(f226(a1),f2(a1)),x70051)) % 168.22/168.06 [7022]~P22(f317(f317(f225(a1),x70222),f2(a1)))+~P22(f317(f317(f226(a1),x70221),f2(a1)))+E(f317(f246(a1,a1),f317(a60,f56(f317(f88(a1),x70221),f317(f88(a1),x70222)))),f55(a1,x70221,x70222)) % 168.22/168.06 [7047]~P22(f317(f317(f226(a1),x70472),f2(a1)))+E(f317(f246(a1,a1),f317(a60,f59(f317(f88(a1),x70471),f317(f88(a1),x70472)))),f55(a1,x70471,x70472))+~P22(f317(f317(f226(a1),f2(a1)),x70471)) % 168.22/168.06 [7056]E(f317(f48(a1,f317(f317(f238(a1),x70561),x70562)),x70561),f317(f317(f238(a1),x70561),f317(f317(f21(a849),x70562),f317(a124,f2(a849)))))+~P22(f317(f317(f226(a849),f2(a849)),x70562))+~P22(f317(f317(f226(a1),f2(a1)),x70561)) % 168.22/168.06 [7186]~P22(f317(f317(f226(a849),f2(a849)),x71861))+~P22(f317(f317(f226(a849),f2(a849)),x71862))+P22(f317(f317(f226(a849),f317(f317(f21(a849),x71861),x71862)),x71861)) % 168.22/168.06 [7334]E(x73341,f2(a849))+~E(x73342,f2(a1))+~P22(f317(f317(f226(a1),f2(a1)),f317(f317(f238(a1),f317(f84(a1),x73342)),x73341))) % 168.22/168.06 [7753]~E(x77532,f125(f850(x77531)))+E(f317(f189(f850(f850(x77531))),f173(x77531,x77532)),f2(a849))+~P29(a849,f317(f163(a849),f317(f317(f148(f850(x77531),a849),f189(f850(x77531))),x77532))) % 168.22/168.06 [7994]P22(f317(x79941,x79942))+~P22(f317(x79941,f317(a118,f542(x79941,x79942))))+~P22(f317(f317(f319(f858(f857(a849,a849),a842)),x79942),a110)) % 168.22/168.06 [8015]E(x80151,f125(f850(x80152)))+E(f317(f189(f850(x80152)),f317(f317(f159(f850(x80152)),x80151),f2(a849))),f317(f189(f850(f850(x80152))),f173(x80152,x80151)))+~P29(a849,f317(f163(a849),f317(f317(f148(f850(x80152),a849),f189(f850(x80152))),x80151))) % 168.22/168.06 [8719]~P22(f317(f71(x87191),f317(f230(x87191),x87192)))+~P22(f317(f71(x87191),f233(f858(x87191,a842))))+P22(f317(f71(x87191),f317(f230(x87191),f317(f317(f8(a842,a842,x87191),a312),x87192)))) % 168.22/168.06 [8743]E(f317(f317(f237(a849,a849),f317(a124,f317(f48(a849,f317(f317(f21(a849),x87431),x87432)),x87432))),f55(a849,f317(f317(f21(a849),x87431),x87432),x87432)),f94(f857(a849,a849),f57(x87431,x87432)))+~P22(f317(f317(f226(a849),f2(a849)),x87432))+~P22(f317(f317(f225(a849),x87432),x87431)) % 168.22/168.06 [9067]~P22(f317(f71(x90671),f317(f230(x90671),x90672)))+P22(f317(f71(x90671),f233(f858(x90671,a842))))+~P22(f317(f71(x90671),f317(f230(x90671),f317(f317(f8(a842,a842,x90671),a312),x90672)))) % 168.22/168.06 [9783]P20(x97831,x97832)+~P37(x97831,f317(f244(f858(f857(x97831,x97831),a842),f858(f857(x97831,x97831),a842)),x97832))+~P22(f317(f317(f225(f858(f857(x97831,x97831),a842)),f317(f317(f265(x97831,x97831,x97831),f317(f244(f858(f857(x97831,x97831),a842),f858(f857(x97831,x97831),a842)),x97832)),f317(f246(f858(f857(x97831,x97831),a842),f858(f857(x97831,x97831),a842)),x97832))),f317(f244(f858(f857(x97831,x97831),a842),f858(f857(x97831,x97831),a842)),x97832))) % 168.22/168.06 [7046]~P22(f317(f317(f226(a849),f2(a849)),x70462))+P22(f317(f317(f226(a849),x70461),x70462))+E(f317(a124,f317(f48(a849,f317(f317(f21(a849),x70461),x70462)),x70462)),f317(f48(a849,x70461),x70462)) % 168.22/168.06 [7201]~P22(f317(f317(f226(a849),f2(a849)),x72012))+~P22(f317(f317(f225(a849),x72012),x72011))+E(f317(a124,f317(f48(a849,f317(f317(f21(a849),x72011),x72012)),x72012)),f317(f48(a849,x72011),x72012)) % 168.22/168.06 [8227]~P90(x82271)+~P87(x82271)+~P31(x82271,f317(f115(x82271),f317(f317(f21(a1),f317(f317(f89(a1),x82272),x82272)),a109))) % 168.22/168.06 [8977]E(x89771,f2(a849))+E(f317(f317(f247(a849,a849,f857(a849,a849)),f317(f317(f8(a849,f858(a849,f857(a849,a849)),a849),f237(a849,a849)),a124)),f94(f857(a849,a849),f57(f317(f317(f21(a849),x89772),x89771),x89771))),f94(f857(a849,a849),f57(x89772,x89771)))+P22(f317(f317(f226(a849),x89772),x89771)) % 168.22/168.06 [7469]~P90(x74691)+~P59(x74691)+E(f317(f317(f266(x74691),x74692),f317(f115(x74691),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))),x74692) % 168.22/168.06 [9103]~P90(x91031)+~E(f317(f115(x91031),x91032),f87(x91031))+P31(x91031,f317(f115(x91031),f317(f317(f89(a1),x91032),f317(f88(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.06 [9277]~P133(x92771)+~E(x92772,f2(x92771))+E(f317(f317(f238(x92771),x92772),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f2(x92771)) % 168.22/168.06 [9278]~P133(x92781)+~E(x92782,f87(x92781))+E(f317(f317(f238(x92781),x92782),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f87(x92781)) % 168.22/168.06 [9291]~P133(x92911)+~E(x92912,f317(f88(x92911),f87(x92911)))+E(f317(f317(f238(x92911),x92912),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f87(x92911)) % 168.22/168.06 [9336]~P90(x93361)+E(f317(f115(x93361),x93362),f87(x93361))+~P31(x93361,f317(f115(x93361),f317(f317(f89(a1),x93362),f317(f88(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.06 [9711]~P113(x97112)+E(x97111,f2(x97112))+P22(f317(f317(f226(x97112),f2(x97112)),f317(f317(f238(x97112),x97111),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.22/168.06 [9782]~P113(x97822)+~E(x97821,f2(x97822))+~P22(f317(f317(f226(x97822),f2(x97822)),f317(f317(f238(x97822),x97821),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.22/168.06 [9809]P22(f317(f317(f225(a1),x98091),f2(a1)))+P22(f317(f317(f226(a1),x98092),x98091))+E(f317(f53(x98091),f56(x98092,f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98091))),f56(x98092,x98091)) % 168.22/168.06 [9810]~P22(f317(f317(f226(a1),f2(a1)),x98101))+P22(f317(f317(f226(a1),x98102),x98101))+E(f317(f53(x98101),f56(x98102,f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98101))),f56(x98102,x98101)) % 168.22/168.06 [9811]P22(f317(f317(f225(a1),x98111),f2(a1)))+P22(f317(f317(f225(a1),f2(a1)),f317(f317(f89(a1),x98112),x98111)))+E(f317(f53(x98111),f59(x98112,f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98111))),f59(x98112,x98111)) % 168.22/168.06 [9812]~P22(f317(f317(f226(a1),f2(a1)),x98121))+P22(f317(f317(f225(a1),f2(a1)),f317(f317(f89(a1),x98122),x98121)))+E(f317(f53(x98121),f59(x98122,f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98121))),f59(x98122,x98121)) % 168.22/168.06 [9813]~P110(x98131)+~P22(f317(f317(f225(a1),f2(a1)),x98132))+E(f317(f112(x98131),f317(a116,f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x98132))),f317(f317(f89(x98131),f317(f112(x98131),f317(a116,x98132))),f317(f112(x98131),f317(a116,x98132)))) % 168.22/168.06 [4973]~P138(x49731,x49732,x49733)+~E(x49733,f2(a1))+P22(f317(x49731,x49732)) % 168.22/168.06 [5097]~P103(x50971)+~P29(x50971,x50973)+P29(x50971,f164(x50971,x50972,x50973)) % 168.22/168.06 [5098]~P103(x50981)+~P29(x50981,x50983)+P29(x50981,f170(x50981,x50982,x50983)) % 168.22/168.06 [4688]~P69(x46882)+~E(x46883,f317(f88(x46882),x46881))+E(x46881,f317(f88(x46882),x46883)) % 168.22/168.06 [4690]~P69(x46901)+~E(f317(f88(x46901),x46903),x46902)+E(f317(f88(x46901),x46902),x46903) % 168.22/168.06 [4761]~P69(x47613)+E(x47611,x47612)+~E(f317(f88(x47613),x47611),f317(f88(x47613),x47612)) % 168.22/168.06 [4762]~P86(x47623)+E(x47621,x47622)+~E(f317(f88(x47623),x47621),f317(f88(x47623),x47622)) % 168.22/168.06 [4763]~P99(x47633)+E(x47631,x47632)+~E(f317(f112(x47633),x47631),f317(f112(x47633),x47632)) % 168.22/168.06 [4764]~P87(x47643)+E(x47641,x47642)+~E(f317(f114(x47643),x47641),f317(f114(x47643),x47642)) % 168.22/168.06 [4765]~P103(x47653)+E(x47651,x47652)+~E(f317(f277(x47653),x47651),f317(f277(x47653),x47652)) % 168.22/168.06 [4766]~P103(x47663)+E(x47661,x47662)+~E(f317(f280(x47663),x47661),f317(f280(x47663),x47662)) % 168.22/168.06 [4767]~P103(x47673)+E(x47671,x47672)+~E(f317(f231(x47673),x47671),f317(f231(x47673),x47672)) % 168.22/168.06 [4768]~P103(x47683)+E(x47681,x47682)+~E(f317(f232(x47683),x47681),f317(f232(x47683),x47682)) % 168.22/168.06 [4867]~P57(x48671)+~P22(f317(x48672,x48673))+P22(f317(f67(x48671),x48672)) % 168.22/168.06 [4900]~P57(x49003)+P22(f317(x49001,x49002))+~P22(f317(f68(x49003),x49001)) % 168.22/168.06 [4995]~P139(x49951,x49953,x49952)+~E(x49952,f2(a1))+P22(f317(x49951,f2(a1))) % 168.22/168.06 [5031]~E(x50311,f2(a849))+E(f360(x50311,x50312,x50313),f188(f858(x50313,a842)))+~E(f317(f54(x50313),x50312),f317(a124,x50311)) % 168.22/168.06 [5184]~E(x51842,f2(a849))+E(f317(f244(a849,a849),x51841),f2(a849))+~P22(f317(f57(x51843,x51842),x51841)) % 168.22/168.06 [5228]P22(f317(x52281,x52282))+~E(x52283,f317(f112(a1),x52282))+~P22(f317(x52281,f317(a116,x52283))) % 168.22/168.06 [5689]~E(x56893,f2(a849))+~P22(f317(x56891,x56892))+P22(f317(x56891,f55(a849,x56892,x56893))) % 168.22/168.06 [5813]~P22(f317(a24,x58133))+~P22(f317(a24,x58132))+P22(f317(a24,f33(x58131,x58132,x58133))) % 168.22/168.06 [5843]~P57(x58433)+~P7(x58433,x58431,x58432)+P22(f317(x58431,f664(x58432,x58431,x58433))) % 168.22/168.06 [6082]~E(x60823,f2(a849))+P22(f317(x60821,x60822))+~P22(f317(x60821,f55(a849,x60822,x60823))) % 168.22/168.06 [6227]~P57(x62271)+P8(x62271,x62272,x62273)+~P22(f317(x62272,f665(x62273,x62272,x62271))) % 168.22/168.06 [6743]E(x67431,f2(a849))+~P22(f317(x67432,f331(x67431,x67433,x67432)))+P22(f317(x67432,f55(a849,x67433,x67431))) % 168.22/168.06 [6851]~P27(x68511)+~P22(f317(f317(f225(x68511),x68512),f676(x68513,x68512,x68511)))+P22(f317(f317(f225(x68511),x68512),f50(x68511,x68513))) % 168.22/168.06 [6853]~P22(f317(x68531,x68532))+~P22(f317(x68531,f331(x68533,x68532,x68531)))+P22(f317(x68531,f55(a849,x68532,x68533))) % 168.22/168.06 [6959]E(x69591,f125(x69592))+E(f317(f317(f145(x69592),f627(x69593,x69591,x69592)),f630(x69593,x69591,x69592)),x69591)+~P22(f317(f317(f319(f850(x69592)),x69591),f155(x69592,x69593))) % 168.22/168.06 [6994]~P111(x69941)+~P22(f317(f317(f319(x69941),x69942),f121(x69941)))+P22(f317(f317(f319(x69941),f317(f317(f238(x69941),x69942),x69943)),f121(x69941))) % 168.22/168.06 [7571]E(x75711,f125(x75712))+~P22(f317(f317(f319(f850(x75712)),x75711),f155(x75712,x75713)))+P22(f317(f317(f319(f850(x75712)),f630(x75713,x75711,x75712)),f155(x75712,x75713))) % 168.22/168.06 [7625]E(x76251,f2(a849))+E(f317(f317(f89(a849),f317(f317(f90(a849),x76251),f333(x76251,x76252,x76253))),f331(x76251,x76252,x76253)),x76252)+P22(f317(x76253,f55(a849,x76252,x76251))) % 168.22/168.06 [7663]P22(f317(f317(f226(a1),x76631),f326(x76632,x76633,x76631)))+P22(f317(f317(x76633,f317(f48(a1,x76632),x76631)),f55(a1,x76632,x76631)))+~P22(f317(f317(f226(a1),x76631),f2(a1))) % 168.22/168.06 [7669]~P22(f317(x76693,x76692))+E(f317(f317(f89(a849),f317(f317(f90(a849),x76691),f333(x76691,x76692,x76693))),f331(x76691,x76692,x76693)),x76692)+P22(f317(x76693,f55(a849,x76692,x76691))) % 168.22/168.06 [7993]P22(f317(f317(x79932,f317(f48(a1,x79931),x79933)),f55(a1,x79931,x79933)))+~P22(f317(f317(f226(a1),x79933),f2(a1)))+P22(f317(f317(f225(a1),f326(x79931,x79932,x79933)),f2(a1))) % 168.22/168.06 [8217]E(f317(f317(f89(a1),f317(f317(f90(a1),x82171),f327(x82172,x82173,x82171))),f326(x82172,x82173,x82171)),x82172)+P22(f317(f317(x82173,f317(f48(a1,x82172),x82171)),f55(a1,x82172,x82171)))+~P22(f317(f317(f226(a1),x82171),f2(a1))) % 168.22/168.06 [8474]~P22(f317(f317(x84741,f327(x84742,x84741,x84743)),f326(x84742,x84741,x84743)))+P22(f317(f317(x84741,f317(f48(a1,x84742),x84743)),f55(a1,x84742,x84743)))+~P22(f317(f317(f226(a1),x84743),f2(a1))) % 168.22/168.06 [8728]~P103(x87281)+~P29(x87281,x87283)+P29(x87281,f144(x87281,x87281,f5(x87281),x87282,x87283)) % 168.22/168.06 [9226]~P118(x92262)+E(x92261,f2(x92262))+~P22(f317(f317(f225(x92262),f317(f317(f89(x92262),f317(f317(f90(x92262),x92263),x92263)),f317(f317(f90(x92262),x92261),x92261))),f2(x92262))) % 168.22/168.06 [9227]~P118(x92272)+E(x92271,f2(x92272))+~P22(f317(f317(f225(x92272),f317(f317(f89(x92272),f317(f317(f90(x92272),x92271),x92271)),f317(f317(f90(x92272),x92273),x92273))),f2(x92272))) % 168.22/168.06 [10002]~P113(x100021)+~P22(f317(f317(f226(x100021),x100022),f2(x100021)))+P22(f317(f317(f226(x100021),f317(f317(f238(x100021),x100022),f317(a124,f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x100023)))),f2(x100021))) % 168.22/168.06 [10011]~P113(x100112)+E(x100111,f2(x100112))+~P22(f317(f317(f225(x100112),f317(f317(f89(x100112),f317(f317(f238(x100112),x100113),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x100112),x100111),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f2(x100112))) % 168.22/168.06 [10012]~P113(x100122)+E(x100121,f2(x100122))+~P22(f317(f317(f225(x100122),f317(f317(f89(x100122),f317(f317(f238(x100122),x100121),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x100122),x100123),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f2(x100122))) % 168.22/168.06 [4720]~E(x47202,x47203)+~P25(x47201)+E(f317(f317(f21(x47201),x47202),x47203),f2(x47201)) % 168.22/168.06 [4721]~E(x47212,x47213)+~P69(x47211)+E(f317(f317(f21(x47211),x47212),x47213),f2(x47211)) % 168.22/168.06 [4732]~P109(x47321)+~E(x47323,f2(x47321))+E(f317(f317(f89(x47321),x47322),x47323),x47322) % 168.22/168.06 [4748]~P132(x47481)+~E(x47483,f2(x47481))+E(f317(f317(f90(x47481),x47482),x47483),f2(x47481)) % 168.22/168.06 [4749]~P132(x47491)+~E(x47492,f2(x47491))+E(f317(f317(f90(x47491),x47492),x47493),f2(x47491)) % 168.22/168.06 [4770]~E(x47703,f125(x47701))+~E(x47702,f125(x47701))+E(f317(f317(f127(x47701),x47702),x47703),f125(x47701)) % 168.22/168.06 [4857]~P109(x48572)+E(x48571,f2(x48572))+~E(f317(f317(f89(x48572),x48573),x48571),x48573) % 168.22/168.06 [4858]~P69(x48581)+~E(x48582,f317(f88(x48581),x48583))+E(f317(f317(f89(x48581),x48582),x48583),f2(x48581)) % 168.22/168.06 [4865]E(x48651,f125(x48652))+E(x48653,f2(a849))+~E(f317(f317(f167(x48652),x48653),x48651),f125(x48652)) % 168.22/168.06 [4871]~P25(x48713)+E(x48711,x48712)+~E(f317(f317(f21(x48713),x48711),x48712),f2(x48713)) % 168.22/168.06 [4872]~P69(x48723)+E(x48721,x48722)+~E(f317(f317(f21(x48723),x48721),x48722),f2(x48723)) % 168.22/168.06 [4881]~P133(x48812)+E(x48811,f2(x48812))+~E(f317(f317(f238(x48812),x48811),x48813),f2(x48812)) % 168.22/168.06 [4882]~P94(x48822)+E(x48821,f188(x48822))+~E(f317(f317(f122(x48822),x48823),x48821),f188(x48822)) % 168.22/168.06 [4883]~P94(x48832)+E(x48831,f188(x48832))+~E(f317(f317(f122(x48832),x48831),x48833),f188(x48832)) % 168.22/168.06 [4884]~P97(x48842)+E(x48841,f233(x48842))+~E(f317(f317(f113(x48842),x48843),x48841),f233(x48842)) % 168.22/168.06 [4885]~P97(x48852)+E(x48851,f233(x48852))+~E(f317(f317(f113(x48852),x48851),x48853),f233(x48852)) % 168.22/168.06 [4945]~P69(x49452)+E(x49451,f317(f88(x49452),x49453))+~E(f317(f317(f89(x49452),x49451),x49453),f2(x49452)) % 168.22/168.06 [4946]~P69(x49461)+E(f317(f88(x49461),x49462),x49463)+~E(f317(f317(f89(x49461),x49462),x49463),f2(x49461)) % 168.22/168.06 [4948]~E(x49482,x49483)+~P101(x49481)+P22(f317(f317(f225(x49481),x49482),x49483)) % 168.22/168.06 [4950]~E(x49502,x49503)+~P104(x49501)+P22(f317(f317(f225(x49501),x49502),x49503)) % 168.22/168.06 [5047]~P114(x50471)+~E(x50472,f317(f88(x50471),x50473))+E(f317(f317(f90(x50471),x50472),x50472),f317(f317(f90(x50471),x50473),x50473)) % 168.22/168.06 [5055]~P103(x50551)+~P29(x50551,x50553)+P29(x50551,f317(f317(f167(x50551),x50552),x50553)) % 168.22/168.06 [5056]~P103(x50561)+~P29(x50561,x50563)+P29(x50561,f317(f317(f132(x50561),x50562),x50563)) % 168.22/168.06 [5095]E(x50951,x50952)+E(x50953,f2(a849))+~E(f317(f317(f90(a849),x50953),x50951),f317(f317(f90(a849),x50953),x50952)) % 168.22/168.06 [5096]E(x50961,x50962)+E(x50963,f2(a849))+~E(f317(f317(f90(a849),x50961),x50963),f317(f317(f90(a849),x50962),x50963)) % 168.22/168.06 [5176]~E(x51762,x51763)+~P104(x51761)+E(f279(x51761,x51762,x51763),f317(f317(f286(x51761),x51762),f188(f858(x51761,a842)))) % 168.22/168.06 [5226]~E(x52261,x52262)+~P103(x52263)+~P22(f317(f317(f226(x52263),x52261),x52262)) % 168.22/168.06 [5227]~E(x52271,x52272)+~P104(x52273)+~P22(f317(f317(f226(x52273),x52271),x52272)) % 168.22/168.06 [5236]~P104(x52361)+E(f317(f278(x52361,x52362),x52363),f188(f858(x52361,a842)))+P22(f317(f317(f226(x52361),x52362),x52363)) % 168.22/168.06 [5281]~P104(x52811)+E(f281(x52811,x52812,x52813),f188(f858(x52811,a842)))+P22(f317(f317(f226(x52811),x52812),x52813)) % 168.22/168.06 [5282]~P104(x52821)+E(f279(x52821,x52822,x52823),f188(f858(x52821,a842)))+P22(f317(f317(f225(x52821),x52822),x52823)) % 168.22/168.06 [5283]~P104(x52831)+E(f188(f858(x52831,a842)),f281(x52831,x52832,x52833))+P22(f317(f317(f226(x52831),x52832),x52833)) % 168.22/168.06 [5284]~P104(x52841)+E(f188(f858(x52841,a842)),f279(x52841,x52842,x52843))+P22(f317(f317(f225(x52841),x52842),x52843)) % 168.22/168.06 [5290]~P92(x52901)+~E(f317(f317(f122(x52901),x52902),x52903),x52903)+P22(f317(f317(f225(x52901),x52902),x52903)) % 168.22/168.06 [5291]~P98(x52911)+~E(f317(f317(f113(x52911),x52912),x52913),x52912)+P22(f317(f317(f225(x52911),x52912),x52913)) % 168.22/168.06 [5292]~P103(x52921)+~E(f317(f317(f223(x52921),x52922),x52923),x52922)+P22(f317(f317(f225(x52921),x52922),x52923)) % 168.22/168.06 [5293]~P103(x52931)+~E(f317(f317(f224(x52931),x52932),x52933),x52933)+P22(f317(f317(f225(x52931),x52932),x52933)) % 168.22/168.06 [5311]~P103(x53111)+P29(x53111,x53112)+~P29(x53111,f317(f317(f145(x53111),x53113),x53112)) % 168.22/168.06 [5312]~P103(x53121)+P29(x53121,x53122)+~P29(x53121,f317(f317(f127(x53121),x53123),x53122)) % 168.22/168.06 [5313]~P103(x53131)+P29(x53131,x53132)+~P29(x53131,f317(f317(f127(x53131),x53132),x53133)) % 168.22/168.06 [5379]~P103(x53791)+P22(f317(f317(f225(x53791),x53793),x53792))+P22(f317(f317(f225(x53791),x53792),x53793)) % 168.22/168.06 [5384]~P103(x53841)+P22(f317(f317(f226(x53841),x53843),x53842))+P22(f317(f317(f225(x53841),x53842),x53843)) % 168.22/168.06 [5421]~P92(x54211)+E(f317(f317(f122(x54211),x54212),x54213),x54212)+~P22(f317(f317(f225(x54211),x54213),x54212)) % 168.22/168.06 [5423]~P92(x54231)+E(f317(f317(f122(x54231),x54232),x54233),x54233)+~P22(f317(f317(f225(x54231),x54232),x54233)) % 168.22/168.06 [5424]~P98(x54241)+E(f317(f317(f113(x54241),x54242),x54243),x54243)+~P22(f317(f317(f225(x54241),x54243),x54242)) % 168.22/168.06 [5426]~P98(x54261)+E(f317(f317(f113(x54261),x54262),x54263),x54262)+~P22(f317(f317(f225(x54261),x54262),x54263)) % 168.22/168.06 [5427]~P103(x54271)+E(f317(f317(f223(x54271),x54272),x54273),x54273)+~P22(f317(f317(f225(x54271),x54273),x54272)) % 168.22/168.06 [5429]~P103(x54291)+E(f317(f317(f223(x54291),x54292),x54293),x54292)+~P22(f317(f317(f225(x54291),x54292),x54293)) % 168.22/168.06 [5430]~P103(x54301)+E(f317(f317(f224(x54301),x54302),x54303),x54302)+~P22(f317(f317(f225(x54301),x54303),x54302)) % 168.22/168.06 [5432]~P103(x54321)+E(f317(f317(f224(x54321),x54322),x54323),x54323)+~P22(f317(f317(f225(x54321),x54322),x54323)) % 168.22/168.06 [5439]~P115(x54392)+E(x54391,f2(x54392))+E(f317(f317(f266(x54392),f317(f88(x54392),x54393)),f317(f88(x54392),x54391)),f317(f317(f266(x54392),x54393),x54391)) % 168.22/168.06 [5474]~E(x54743,f2(a849))+~P22(f317(x54741,f2(a849)))+P22(f317(x54741,f317(f48(a849,x54742),x54743))) % 168.22/168.06 [5486]~P104(x54861)+E(f317(f278(x54861,x54862),x54863),f188(f858(x54861,a842)))+~P22(f317(f317(f225(x54861),x54863),x54862)) % 168.22/168.06 [5519]~P104(x55191)+E(f282(x55191,x55192,x55193),f188(f858(x55191,a842)))+~P22(f317(f317(f225(x55191),x55193),x55192)) % 168.22/168.06 [5520]~P104(x55201)+E(f281(x55201,x55202,x55203),f188(f858(x55201,a842)))+~P22(f317(f317(f225(x55201),x55203),x55202)) % 168.22/168.06 [5521]~P104(x55211)+E(f279(x55211,x55212,x55213),f188(f858(x55211,a842)))+~P22(f317(f317(f226(x55211),x55213),x55212)) % 168.22/168.06 [5577]~E(f317(f317(f21(a849),x55771),x55773),x55772)+E(x55771,f317(f317(f89(a849),x55772),x55773))+~P22(f317(f317(f225(a849),x55773),x55771)) % 168.22/168.06 [5578]~E(x55781,f317(f317(f89(a849),x55783),x55782))+E(f317(f317(f21(a849),x55781),x55782),x55783)+~P22(f317(f317(f225(a849),x55782),x55781)) % 168.22/168.06 [5617]~P22(f317(x56171,x56173))+P22(f317(x56171,f384(x56171,x56172)))+~P22(f317(f317(f225(a849),x56173),x56172)) % 168.22/168.06 [5618]~P22(f317(x56181,x56183))+P22(f317(x56181,f434(x56181,x56182)))+~P22(f317(f317(f226(a849),x56183),x56182)) % 168.22/168.06 [5627]~P104(x56271)+~E(f317(f278(x56271,x56272),x56273),f188(f858(x56271,a842)))+~P22(f317(f317(f226(x56271),x56272),x56273)) % 168.22/168.06 [5632]~P101(x56321)+~P22(f317(f317(f226(x56321),x56322),x56323))+P22(f317(f317(f225(x56321),x56322),x56323)) % 168.22/168.06 [5634]~P104(x56341)+~P22(f317(f317(f226(x56341),x56342),x56343))+P22(f317(f317(f225(x56341),x56342),x56343)) % 168.22/168.06 [5731]~P104(x57311)+~E(f281(x57311,x57312,x57313),f188(f858(x57311,a842)))+~P22(f317(f317(f226(x57311),x57312),x57313)) % 168.22/168.06 [5732]~P104(x57321)+~E(f279(x57321,x57322,x57323),f188(f858(x57321,a842)))+~P22(f317(f317(f225(x57321),x57322),x57323)) % 168.22/168.06 [5733]~P104(x57331)+~E(f188(f858(x57331,a842)),f281(x57331,x57332,x57333))+~P22(f317(f317(f226(x57331),x57332),x57333)) % 168.22/168.06 [5734]~P104(x57341)+~E(f188(f858(x57341,a842)),f279(x57341,x57342,x57343))+~P22(f317(f317(f225(x57341),x57342),x57343)) % 168.22/168.06 [5742]P22(f317(x57421,x57422))+~P22(f317(x57421,f385(x57421,x57423)))+~P22(f317(f317(f225(a849),x57422),x57423)) % 168.22/168.06 [5743]P22(f317(x57431,x57432))+~P22(f317(x57431,f435(x57431,x57433)))+~P22(f317(f317(f226(a849),x57432),x57433)) % 168.22/168.06 [5750]~E(x57501,f317(a124,x57503))+P22(f317(f317(f226(a849),x57501),f317(a124,x57502)))+~P22(f317(f317(f226(a849),x57503),x57502)) % 168.22/168.06 [5766]E(x57661,x57662)+~E(f317(f317(f90(a849),x57663),x57661),f317(f317(f90(a849),x57663),x57662))+~P22(f317(f317(f226(a849),f2(a849)),x57663)) % 168.22/168.06 [5769]~E(x57692,f2(a849))+P22(f317(x57691,f2(a849)))+~P22(f317(x57691,f317(f48(a849,x57693),x57692))) % 168.22/168.06 [5824]E(f317(x58241,f451(x58241,x58242,x58243)),f87(a849))+~E(f317(f317(f6(x58243,a849),x58241),x58242),f87(a849))+~P22(f317(f71(x58243),x58242)) % 168.22/168.06 [5834]~P27(x58341)+P22(f317(f317(f225(x58341),x58342),f49(x58341,x58343)))+~P22(f317(f317(f319(x58341),x58342),x58343)) % 168.22/168.06 [5861]~P101(x58611)+~P22(f317(f317(f226(x58611),x58613),x58612))+~P22(f317(f317(f225(x58611),x58612),x58613)) % 168.22/168.06 [5865]~P101(x58651)+~P22(f317(f317(f226(x58651),x58653),x58652))+~P22(f317(f317(f226(x58651),x58652),x58653)) % 168.22/168.06 [5868]~P103(x58681)+~P22(f317(f317(f226(x58681),x58683),x58682))+~P22(f317(f317(f225(x58681),x58682),x58683)) % 168.22/168.06 [5869]~P103(x58691)+~P22(f317(f317(f226(x58691),x58693),x58692))+~P22(f317(f317(f226(x58691),x58692),x58693)) % 168.22/168.06 [5870]~P104(x58701)+~P22(f317(f317(f226(x58701),x58703),x58702))+~P22(f317(f317(f226(x58701),x58702),x58703)) % 168.22/168.06 [5902]~E(f317(x59022,f386(x59022,x59023,x59021)),f87(a849))+E(f317(f317(f9(x59021,a849),x59022),x59023),f87(a849))+~P22(f317(f71(x59021),x59023)) % 168.22/168.06 [5903]~E(f317(x59032,f452(x59032,x59033,x59031)),f2(a849))+E(f317(f317(f6(x59031,a849),x59032),x59033),f2(a849))+~P22(f317(f71(x59031),x59033)) % 168.22/168.06 [5920]~P102(x59201)+~P22(f317(f317(f226(x59201),x59203),x59202))+P22(f317(f317(f319(x59201),x59202),f317(f280(x59201),x59203))) % 168.22/168.06 [5921]~P102(x59211)+~P22(f317(f317(f225(x59211),x59213),x59212))+P22(f317(f317(f319(x59211),x59212),f317(f232(x59211),x59213))) % 168.22/168.06 [5922]~P102(x59221)+~P22(f317(f317(f225(x59221),x59222),x59223))+P22(f317(f317(f319(x59221),x59222),f317(f277(x59221),x59223))) % 168.22/168.06 [5923]~P102(x59231)+~P22(f317(f317(f226(x59231),x59232),x59233))+P22(f317(f317(f319(x59231),x59232),f317(f231(x59231),x59233))) % 168.22/168.06 [5934]E(f317(x59341,f458(x59341,x59342,x59343)),f317(a124,f2(a849)))+~E(f317(f317(f6(x59343,a849),x59341),x59342),f317(a124,f2(a849)))+~P22(f317(f71(x59343),x59342)) % 168.22/168.06 [6009]~P27(x60091)+~P22(f317(f317(f319(x60091),x60093),x60092))+P22(f317(f317(f225(x60091),f50(x60091,x60092)),x60093)) % 168.22/168.06 [6026]~P22(f317(f317(f225(a849),x60261),x60263))+P22(f317(f317(f225(a849),x60261),x60262))+~P22(f317(f317(f225(a849),x60263),x60262)) % 168.22/168.06 [6027]~P22(f317(f317(f225(a1),x60271),x60273))+P22(f317(f317(f225(a1),x60271),x60272))+~P22(f317(f317(f225(a1),x60273),x60272)) % 168.22/168.06 [6044]~P102(x60441)+~P22(f317(f317(f319(x60441),x60443),f317(f232(x60441),x60442)))+P22(f317(f317(f225(x60441),x60442),x60443)) % 168.22/168.06 [6045]~P102(x60451)+~P22(f317(f317(f319(x60451),x60452),f317(f277(x60451),x60453)))+P22(f317(f317(f225(x60451),x60452),x60453)) % 168.22/168.06 [6046]~P102(x60461)+~P22(f317(f317(f319(x60461),x60463),f317(f280(x60461),x60462)))+P22(f317(f317(f226(x60461),x60462),x60463)) % 168.22/168.06 [6047]~P102(x60471)+~P22(f317(f317(f319(x60471),x60472),f317(f231(x60471),x60473)))+P22(f317(f317(f226(x60471),x60472),x60473)) % 168.22/168.06 [6166]P22(f317(x61661,x61662))+~P22(f317(x61661,f570(x61661)))+~P22(f317(f317(f319(x61663),x61662),f233(f858(x61663,a842)))) % 168.22/168.06 [6263]~P60(x62631)+P22(f317(f317(f226(x62631),f2(x62631)),f460(x62633,x62632,x62631)))+P22(f317(f317(f225(x62631),x62632),x62633)) % 168.22/168.06 [6331]~P78(x63311)+~P22(f317(f317(f225(x63311),x63313),f317(f88(x63311),x63312)))+P22(f317(f317(f225(x63311),x63312),f317(f88(x63311),x63313))) % 168.22/168.06 [6333]~P78(x63331)+~P22(f317(f317(f226(x63331),x63333),f317(f88(x63331),x63332)))+P22(f317(f317(f226(x63331),x63332),f317(f88(x63331),x63333))) % 168.22/168.06 [6344]~P22(f317(f317(f226(a849),x63441),x63443))+~P22(f317(f317(f226(a849),x63443),x63442))+P22(f317(f317(f226(a849),f317(a124,x63441)),x63442)) % 168.22/168.06 [6370]~P112(x63701)+P22(f317(f317(f225(x63701),f317(f112(x63701),x63702)),f317(f112(x63701),x63703)))+~P22(f317(f317(f225(a849),x63702),x63703)) % 168.22/168.06 [6371]~P113(x63711)+P22(f317(f317(f225(x63711),f317(f114(x63711),x63712)),f317(f114(x63711),x63713)))+~P22(f317(f317(f225(a1),x63712),x63713)) % 168.22/168.06 [6373]~P113(x63731)+P22(f317(f317(f226(x63731),f317(f114(x63731),x63732)),f317(f114(x63731),x63733)))+~P22(f317(f317(f226(a1),x63732),x63733)) % 168.22/168.06 [6374]~P112(x63741)+P22(f317(f317(f226(x63741),f317(f112(x63741),x63742)),f317(f112(x63741),x63743)))+~P22(f317(f317(f226(a849),x63742),x63743)) % 168.22/168.06 [6380]~P103(x63801)+E(f317(f317(f122(f858(x63801,a842)),f317(f231(x63801),x63802)),f317(f278(x63801,x63802),x63803)),f317(f231(x63801),x63803))+~P22(f317(f317(f225(x63801),x63802),x63803)) % 168.22/168.06 [6410]~P86(x64101)+~P22(f317(f317(f225(x64101),x64103),x64102))+P22(f317(f317(f225(x64101),f317(f88(x64101),x64102)),f317(f88(x64101),x64103))) % 168.22/168.06 [6412]~P78(x64121)+~P22(f317(f317(f225(x64121),x64123),x64122))+P22(f317(f317(f225(x64121),f317(f88(x64121),x64122)),f317(f88(x64121),x64123))) % 168.22/168.06 [6413]~P78(x64131)+~P22(f317(f317(f226(x64131),x64133),x64132))+P22(f317(f317(f226(x64131),f317(f88(x64131),x64132)),f317(f88(x64131),x64133))) % 168.22/168.06 [6441]E(x64411,f2(a849))+P22(f317(x64412,f335(x64411,x64413,x64412)))+~P22(f317(x64412,f317(f48(a849,x64413),x64411))) % 168.22/168.06 [6445]~P103(x64451)+E(f317(f317(f122(f858(x64451,a842)),f317(f277(x64451),x64452)),f282(x64451,x64452,x64453)),f317(f231(x64451),x64453))+~P22(f317(f317(f226(x64451),x64452),x64453)) % 168.22/168.06 [6446]~P103(x64461)+E(f317(f317(f122(f858(x64461,a842)),f317(f277(x64461),x64462)),f281(x64461,x64462,x64463)),f317(f277(x64461),x64463))+~P22(f317(f317(f225(x64461),x64462),x64463)) % 168.22/168.06 [6447]~P103(x64471)+E(f317(f317(f122(f858(x64471,a842)),f317(f231(x64471),x64472)),f279(x64471,x64472,x64473)),f317(f277(x64471),x64473))+~P22(f317(f317(f225(x64471),x64472),x64473)) % 168.22/168.06 [6480]~P103(x64801)+E(f317(f317(f122(f858(x64801,a842)),f317(f278(x64801,x64802),x64803)),f317(f232(x64801),x64803)),f317(f232(x64801),x64802))+~P22(f317(f317(f225(x64801),x64802),x64803)) % 168.22/168.06 [6565]P22(f317(x65651,f335(x65652,x65653,x65651)))+P22(f317(x65651,f2(a849)))+~P22(f317(x65651,f317(f48(a849,x65653),x65652))) % 168.22/168.06 [6573]E(x65731,f2(a849))+~P22(f317(x65732,f330(x65731,x65733,x65732)))+P22(f317(x65732,f317(f48(a849,x65733),x65731))) % 168.22/168.06 [6633]~P103(x66331)+E(f317(f317(f122(f858(x66331,a842)),f282(x66331,x66332,x66333)),f317(f232(x66331),x66333)),f317(f280(x66331),x66332))+~P22(f317(f317(f226(x66331),x66332),x66333)) % 168.22/168.06 [6634]~P103(x66341)+E(f317(f317(f122(f858(x66341,a842)),f281(x66341,x66342,x66343)),f317(f280(x66341),x66343)),f317(f280(x66341),x66342))+~P22(f317(f317(f225(x66341),x66342),x66343)) % 168.22/168.06 [6635]~P103(x66351)+E(f317(f317(f122(f858(x66351,a842)),f279(x66351,x66352,x66353)),f317(f280(x66351),x66353)),f317(f232(x66351),x66352))+~P22(f317(f317(f225(x66351),x66352),x66353)) % 168.22/168.06 [6643]~E(x66433,f317(f48(a849,x66431),x66432))+~P22(f317(f317(f226(a849),f2(a849)),x66432))+P22(f317(f317(f226(a849),x66431),f317(f317(f90(a849),x66432),f317(a124,x66433)))) % 168.22/168.06 [6653]P22(f317(x66531,x66532))+~P22(f317(f317(f225(a849),x66532),x66533))+P22(f317(f317(f319(a849),f385(x66531,x66533)),f279(a849,f2(a849),x66533))) % 168.22/168.06 [6684]E(x66841,x66842)+~E(f317(f317(f159(x66843),x66841),f584(x66843,x66842,x66841)),f317(f317(f159(x66843),x66842),f584(x66843,x66842,x66841)))+~E(f317(f189(f850(x66843)),x66841),f317(f189(f850(x66843)),x66842)) % 168.22/168.06 [6703]~P22(f317(x67031,x67033))+~P22(f317(f317(f225(a849),x67033),x67032))+P22(f317(f317(f319(a849),f384(x67031,x67032)),f279(a849,f2(a849),x67032))) % 168.22/168.06 [6704]~P22(f317(x67041,f330(x67043,x67042,x67041)))+~P22(f317(x67041,f2(a849)))+P22(f317(x67041,f317(f48(a849,x67042),x67043))) % 168.22/168.06 [6740]~P22(f317(x67401,x67403))+P22(f317(x67401,f421(x67401,x67402)))+~P22(f317(f317(f319(a849),x67403),f279(a849,f2(a849),x67402))) % 168.22/168.06 [6759]~P112(x67593)+~P22(f317(f317(f225(x67593),f317(f112(x67593),x67591)),f317(f112(x67593),x67592)))+P22(f317(f317(f225(a849),x67591),x67592)) % 168.22/168.06 [6760]~P113(x67603)+~P22(f317(f317(f225(x67603),f317(f114(x67603),x67601)),f317(f114(x67603),x67602)))+P22(f317(f317(f225(a1),x67601),x67602)) % 168.22/168.06 [6762]~P112(x67623)+~P22(f317(f317(f226(x67623),f317(f112(x67623),x67621)),f317(f112(x67623),x67622)))+P22(f317(f317(f226(a849),x67621),x67622)) % 168.22/168.06 [6763]~P113(x67633)+~P22(f317(f317(f226(x67633),f317(f114(x67633),x67631)),f317(f114(x67633),x67632)))+P22(f317(f317(f226(a1),x67631),x67632)) % 168.22/168.06 [6777]~P112(x67771)+~P22(f317(f317(f226(x67771),f87(x67771)),x67772))+P22(f317(f317(f226(x67771),f87(x67771)),f317(f317(f238(x67771),x67772),f317(a124,x67773)))) % 168.22/168.06 [6780]~P86(x67801)+~P22(f317(f317(f225(x67801),f317(f88(x67801),x67803)),f317(f88(x67801),x67802)))+P22(f317(f317(f225(x67801),x67802),x67803)) % 168.22/168.06 [6781]~P78(x67811)+~P22(f317(f317(f225(x67811),f317(f88(x67811),x67813)),f317(f88(x67811),x67812)))+P22(f317(f317(f225(x67811),x67812),x67813)) % 168.22/168.06 [6782]~P78(x67821)+~P22(f317(f317(f226(x67821),f317(f88(x67821),x67823)),f317(f88(x67821),x67822)))+P22(f317(f317(f226(x67821),x67822),x67823)) % 168.22/168.06 [6807]P22(f317(x68071,x68072))+~P22(f317(x68071,f414(x68071,x68073)))+~P22(f317(f317(f319(a849),x68072),f279(a849,f2(a849),x68073))) % 168.22/168.06 [6828]~P60(x68281)+P22(f317(f317(f226(x68281),f460(x68283,x68282,x68281)),f87(x68281)))+P22(f317(f317(f225(x68281),x68282),x68283)) % 168.22/168.06 [6846]~E(f55(a849,x68463,x68462),f55(a849,x68461,x68462))+E(f317(f317(f89(a849),x68461),f317(f317(f90(a849),x68462),f715(x68461,x68462,x68463))),x68463)+~P22(f317(f317(f225(a849),x68461),x68463)) % 168.22/168.06 [6867]E(f317(x68671,f687(x68671,x68672,x68673)),f191(x68672))+~P22(f317(f71(x68673),f177(x68673,x68672,x68671)))+P22(f317(f71(x68673),f233(f858(x68673,a842)))) % 168.22/168.06 [6912]E(f317(f317(f9(x69121,a849),x69122),x69123),f87(a849))+~P22(f317(f71(x69121),x69123))+P22(f317(f317(f319(x69121),f386(x69122,x69123,x69121)),x69123)) % 168.22/168.06 [6913]E(f317(f317(f6(x69131,a849),x69132),x69133),f2(a849))+~P22(f317(f71(x69131),x69133))+P22(f317(f317(f319(x69131),f452(x69132,x69133,x69131)),x69133)) % 168.22/168.06 [6935]~P104(x69351)+~P22(f317(f317(f225(x69351),x69352),x69353))+P22(f317(f317(f225(f858(x69351,a842)),f317(f277(x69351),x69352)),f317(f277(x69351),x69353))) % 168.22/168.06 [6936]~P103(x69361)+~P22(f317(f317(f225(x69361),x69363),x69362))+P22(f317(f317(f225(f858(x69361,a842)),f317(f280(x69361),x69362)),f317(f280(x69361),x69363))) % 168.22/168.06 [6937]~P103(x69371)+~P22(f317(f317(f225(x69371),x69372),x69373))+P22(f317(f317(f225(f858(x69371,a842)),f317(f231(x69371),x69372)),f317(f231(x69371),x69373))) % 168.22/168.06 [6938]~P104(x69381)+~P22(f317(f317(f225(x69381),x69383),x69382))+P22(f317(f317(f225(f858(x69381,a842)),f317(f232(x69381),x69382)),f317(f232(x69381),x69383))) % 168.22/168.06 [6939]~P103(x69391)+~P22(f317(f317(f226(x69391),x69392),x69393))+P22(f317(f317(f226(f858(x69391,a842)),f317(f231(x69391),x69392)),f317(f231(x69391),x69393))) % 168.22/168.06 [6946]E(x69461,f2(a849))+P22(f317(x69462,f317(f48(a849,x69463),x69461)))+P22(f317(f317(f226(a849),f332(x69461,x69463,x69462)),x69461)) % 168.22/168.06 [6947]~P27(x69471)+P22(f317(f317(f225(x69471),x69472),f50(x69471,x69473)))+P22(f317(f317(f319(x69471),f676(x69473,x69472,x69471)),x69473)) % 168.22/168.06 [6952]~P78(x69521)+P22(f317(f317(f225(x69521),f317(f317(f21(x69521),x69522),x69523)),f2(x69521)))+~P22(f317(f317(f225(x69521),x69522),x69523)) % 168.22/168.06 [6953]~P78(x69531)+P22(f317(f317(f226(x69531),f317(f317(f21(x69531),x69532),x69533)),f2(x69531)))+~P22(f317(f317(f226(x69531),x69532),x69533)) % 168.22/168.06 [6998]P22(f317(x69981,x69982))+P22(f317(f317(f225(a849),f414(x69981,x69983)),x69983))+~P22(f317(f317(f319(a849),x69982),f279(a849,f2(a849),x69983))) % 168.22/168.06 [7034]~E(f317(f317(f6(x70341,a849),x70342),x70343),f87(a849))+~P22(f317(f71(x70341),x70343))+P22(f317(f317(f319(x70341),f451(x70342,x70343,x70341)),x70343)) % 168.22/168.06 [7035]~P22(f317(x70351,x70353))+P22(f317(f317(f225(a849),f421(x70351,x70352)),x70352))+~P22(f317(f317(f319(a849),x70353),f279(a849,f2(a849),x70352))) % 168.22/168.06 [7078]~P27(x70781)+P22(f317(f317(f319(x70781),f674(x70783,x70782,x70781)),x70782))+P22(f317(f317(f225(x70781),f49(x70781,x70782)),x70783)) % 168.22/168.06 [7079]~P22(f317(x70791,f2(a849)))+P22(f317(x70791,f317(f48(a849,x70792),x70793)))+P22(f317(f317(f226(a849),f332(x70793,x70792,x70791)),x70793)) % 168.22/168.06 [7109]~E(f317(f317(f6(x71091,a849),x71092),x71093),f317(a124,f2(a849)))+~P22(f317(f71(x71091),x71093))+P22(f317(f317(f319(x71091),f458(x71092,x71093,x71091)),x71093)) % 168.22/168.06 [7120]E(x71201,f2(a849))+P22(f317(x71202,f55(a849,x71203,x71201)))+P22(f317(f317(f226(a849),f331(x71201,x71203,x71202)),x71201)) % 168.22/168.06 [7217]~P22(f317(x72171,x72172))+P22(f317(x72171,f55(a849,x72172,x72173)))+P22(f317(f317(f226(a849),f331(x72173,x72172,x72171)),x72173)) % 168.22/168.06 [7272]~P22(f317(f317(f226(a1),x72722),f2(a1)))+~P22(f317(f317(f225(a1),x72723),x72721))+P22(f317(f317(f225(a1),f317(f48(a1,x72721),x72722)),f317(f48(a1,x72723),x72722))) % 168.22/168.06 [7280]~P22(f317(f317(f226(a849),f2(a849)),x72803))+~P22(f317(f317(f225(a849),x72803),x72802))+P22(f317(f317(f225(a849),f317(f48(a849,x72801),x72802)),f317(f48(a849,x72801),x72803))) % 168.22/168.06 [7281]~P22(f317(f317(f226(a1),f2(a1)),x72812))+~P22(f317(f317(f225(a1),x72811),x72813))+P22(f317(f317(f225(a1),f317(f48(a1,x72811),x72812)),f317(f48(a1,x72813),x72812))) % 168.22/168.06 [7338]E(x73381,f125(x73382))+~P22(f317(f317(f319(f850(x73382)),x73381),f155(x73382,x73383)))+P22(f317(f317(f319(x73382),f627(x73383,x73381,x73382)),x73383)) % 168.22/168.06 [7361]~P103(x73611)+E(f317(f317(f122(f858(x73611,a842)),f317(f317(f286(x73611),x73612),f188(f858(x73611,a842)))),f282(x73611,x73612,x73613)),f317(f278(x73611,x73612),x73613))+~P22(f317(f317(f226(x73611),x73612),x73613)) % 168.22/168.06 [7385]~P103(x73851)+E(f317(f317(f122(f858(x73851,a842)),f317(f317(f286(x73851),x73852),f188(f858(x73851,a842)))),f281(x73851,x73852,x73853)),f279(x73851,x73852,x73853))+~P22(f317(f317(f225(x73851),x73852),x73853)) % 168.22/168.06 [7491]~P103(x74911)+P22(f317(f317(f225(x74911),x74912),x74913))+~P22(f317(f317(f225(f858(x74911,a842)),f317(f280(x74911),x74913)),f317(f280(x74911),x74912))) % 168.22/168.06 [7492]~P104(x74921)+P22(f317(f317(f225(x74921),x74922),x74923))+~P22(f317(f317(f225(f858(x74921,a842)),f317(f232(x74921),x74923)),f317(f232(x74921),x74922))) % 168.22/168.06 [7493]~P103(x74931)+P22(f317(f317(f225(x74931),x74932),x74933))+~P22(f317(f317(f225(f858(x74931,a842)),f317(f231(x74931),x74932)),f317(f231(x74931),x74933))) % 168.22/168.06 [7494]~P104(x74941)+P22(f317(f317(f225(x74941),x74942),x74943))+~P22(f317(f317(f225(f858(x74941,a842)),f317(f277(x74941),x74942)),f317(f277(x74941),x74943))) % 168.22/168.06 [7495]~P103(x74951)+P22(f317(f317(f226(x74951),x74952),x74953))+~P22(f317(f317(f226(f858(x74951,a842)),f317(f231(x74951),x74952)),f317(f231(x74951),x74953))) % 168.22/168.06 [7514]E(x75141,f2(a849))+E(f317(f317(f89(a849),f317(f317(f90(a849),x75141),f330(x75141,x75142,x75143))),f332(x75141,x75142,x75143)),x75142)+P22(f317(x75143,f317(f48(a849,x75142),x75141))) % 168.22/168.06 [7518]~P78(x75181)+~P22(f317(f317(f225(x75181),f317(f317(f21(x75181),x75182),x75183)),f2(x75181)))+P22(f317(f317(f225(x75181),x75182),x75183)) % 168.22/168.06 [7519]~P78(x75191)+~P22(f317(f317(f226(x75191),f317(f317(f21(x75191),x75192),x75193)),f2(x75191)))+P22(f317(f317(f226(x75191),x75192),x75193)) % 168.22/168.06 [7611]E(f317(f317(f89(a849),f317(f317(f90(a849),x76111),f330(x76111,x76112,x76113))),f332(x76111,x76112,x76113)),x76112)+~P22(f317(x76113,f2(a849)))+P22(f317(x76113,f317(f48(a849,x76112),x76111))) % 168.22/168.06 [7676]E(x76761,f2(a849))+~E(f317(f136(a849,a849,f89(a849),x76762),x76763),f2(a849))+~P22(f317(f317(f319(a849),x76761),f317(f166(a849),x76763))) % 168.22/168.06 [7680]~P27(x76801)+~P22(f317(f317(f225(x76801),f674(x76803,x76802,x76801)),x76803))+P22(f317(f317(f225(x76801),f49(x76801,x76802)),x76803)) % 168.22/168.06 [7705]P22(f317(f317(f225(a1),f2(a1)),f328(x77051,x77052,x77053)))+P22(f317(f317(x77052,f317(f48(a1,x77051),x77053)),f55(a1,x77051,x77053)))+~P22(f317(f317(f226(a1),f2(a1)),x77053)) % 168.22/168.06 [7917]E(x79171,x79172)+~E(f317(f189(f850(x79173)),x79171),f317(f189(f850(x79173)),x79172))+~P22(f317(f317(f247(x79173,x79173,a842),a314),f585(x79173,x79171,x79172))) % 168.22/168.06 [7984]~P37(x79842,x79843)+E(x79841,f188(f858(x79842,a842)))+~P22(f317(f317(f225(f858(x79842,a842)),x79841),f317(f262(x79842,x79842,x79843),x79841))) % 168.22/168.06 [8004]P22(f317(f317(x80042,f317(f48(a1,x80041),x80043)),f55(a1,x80041,x80043)))+~P22(f317(f317(f226(a1),f2(a1)),x80043))+P22(f317(f317(f226(a1),f328(x80041,x80042,x80043)),x80043)) % 168.22/168.06 [8058]P45(x80581,x80582,x80583)+P22(f317(f317(f319(x80581),f565(x80583,x80582,x80581)),x80582))+P22(f317(f317(f319(f857(x80581,x80581)),f566(x80583,x80582,x80581)),x80583)) % 168.22/168.06 [8104]E(f317(f287(a849,a849,f317(f317(f7(a849,a849,a849),f21(a849)),x81041)),f317(f278(a849,x81042),x81043)),f188(f858(a849,a842)))+P22(f317(f317(f226(a849),x81041),x81043))+P22(f317(f317(f226(a849),x81042),x81043)) % 168.22/168.06 [8210]E(f317(f287(a849,a849,f317(f317(f7(a849,a849,a849),f21(a849)),x82101)),f317(f278(a849,x82102),x82103)),f317(f317(f286(a849),f2(a849)),f188(f858(a849,a842))))+P22(f317(f317(f226(a849),x82101),x82103))+~P22(f317(f317(f226(a849),x82102),x82103)) % 168.22/168.06 [8229]~P103(x82291)+E(f144(x82291,x82291,f5(x82291),x82292,x82293),x82293)+~P22(f317(f317(f319(x82291),x82292),f317(f166(x82291),x82293))) % 168.22/168.06 [8230]E(f317(f317(f89(a1),f317(f317(f90(a1),x82301),f329(x82302,x82303,x82301))),f328(x82302,x82303,x82301)),x82302)+P22(f317(f317(x82303,f317(f48(a1,x82302),x82301)),f55(a1,x82302,x82301)))+~P22(f317(f317(f226(a1),f2(a1)),x82301)) % 168.22/168.06 [8246]P19(x82461,x82461,x82462,x82463)+~P22(f317(f71(x82461),x82463))+~P22(f317(f317(f225(f858(x82461,a842)),x82463),f317(f287(x82461,x82461,x82462),x82463))) % 168.22/168.06 [8475]~P22(f317(f317(x84751,f329(x84752,x84751,x84753)),f328(x84752,x84751,x84753)))+P22(f317(f317(x84751,f317(f48(a1,x84752),x84753)),f55(a1,x84752,x84753)))+~P22(f317(f317(f226(a1),f2(a1)),x84753)) % 168.22/168.06 [9362]~P22(f317(f71(x93621),x93622))+~P22(f317(f317(f319(x93621),x93623),x93622))+P22(f317(f317(f226(a849),f317(f54(x93621),f317(f317(f21(f858(x93621,a842)),x93622),f317(f317(f286(x93621),x93623),f188(f858(x93621,a842)))))),f317(f54(x93621),x93622))) % 168.22/168.06 [9962]P45(x99621,x99622,x99623)+~P22(f317(f317(f247(x99621,x99621,a842),f317(f317(f7(x99621,f858(x99621,a842),f858(x99621,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x99621,a842),f858(x99621,a842)),x99621),f8(a842,a842,x99621)),f317(f317(f8(a842,f858(a842,a842),x99621),a315),f317(f317(f7(x99621,f858(x99621,a842),a842),f319(x99621)),x99622)))),f317(f317(f7(x99621,f858(x99621,a842),a842),f319(x99621)),x99622))),f566(x99623,x99622,x99621)))+P22(f317(f317(f319(x99621),f565(x99623,x99622,x99621)),x99622)) % 168.22/168.06 [5401]~P115(x54012)+E(x54011,f2(x54012))+E(f317(f317(f266(x54012),x54013),f317(f88(x54012),x54011)),f317(f88(x54012),f317(f317(f266(x54012),x54013),x54011))) % 168.22/168.06 [5537]~E(x55373,f188(f858(x55371,a842)))+~E(x55372,f188(f858(x55371,a842)))+E(f317(f317(f122(f858(x55371,a842)),x55372),x55373),f188(f858(x55371,a842))) % 168.22/168.06 [5727]~P61(x57272)+E(x57271,f2(x57272))+E(f317(f317(f266(x57272),f317(f84(x57272),x57273)),f317(f84(x57272),x57271)),f317(f84(x57272),f317(f317(f266(x57272),x57273),x57271))) % 168.22/168.06 [5890]~P22(f317(f71(x58901),x58903))+E(f317(f54(x58901),f317(f317(f286(x58901),x58902),x58903)),f317(a124,f317(f54(x58901),x58903)))+P22(f317(f317(f319(x58901),x58902),x58903)) % 168.22/168.06 [5980]~P22(f317(f71(x59801),x59803))+E(f317(f54(x59801),f317(f317(f286(x59801),x59802),x59803)),f317(f54(x59801),x59803))+~P22(f317(f317(f319(x59801),x59802),x59803)) % 168.22/168.06 [6012]~P22(f317(f71(x60121),x60123))+E(f317(f54(x60121),f317(f317(f286(x60121),x60122),x60123)),f317(f317(f89(a849),f87(a849)),f317(f54(x60121),x60123)))+P22(f317(f317(f319(x60121),x60122),x60123)) % 168.22/168.06 [6128]E(f317(f317(f89(a849),x61281),f808(x61281,x61282,x61283)),x61282)+~P22(f317(x61283,f2(a849)))+P22(f317(x61283,f317(f317(f21(a849),x61282),x61281))) % 168.22/168.06 [6129]E(f317(f317(f89(a849),x61291),f809(x61291,x61292,x61293)),x61292)+~P22(f317(x61293,f2(a849)))+P22(f317(x61293,f317(f317(f21(a849),x61292),x61291))) % 168.22/168.06 [6176]~P27(x61761)+~P22(f317(f71(x61761),x61763))+E(f317(f317(f74(x61761,x61761,f122(x61761)),x61762),x61763),f317(f317(f122(x61761),x61762),f49(x61761,x61763))) % 168.22/168.06 [6177]~P27(x61771)+~P22(f317(f71(x61771),x61773))+E(f317(f317(f74(x61771,x61771,f113(x61771)),x61772),x61773),f317(f317(f113(x61771),x61772),f50(x61771,x61773))) % 168.22/168.06 [6184]~P90(x61841)+~E(f317(f115(x61841),x61842),f317(f115(x61841),x61843))+P31(x61841,f317(f115(x61841),f317(f317(f89(a1),x61842),f317(f88(a1),x61843)))) % 168.22/168.06 [6191]~P111(x61911)+E(f317(f317(f21(x61911),f317(f112(x61911),x61912)),f317(f112(x61911),x61913)),f317(f112(x61911),f317(f317(f21(a849),x61912),x61913)))+~P22(f317(f317(f225(a849),x61913),x61912)) % 168.22/168.06 [6273]E(f317(f317(f89(a849),x62731),f808(x62731,x62732,x62733)),x62732)+P22(f317(f317(f226(a849),x62732),x62731))+P22(f317(x62733,f317(f317(f21(a849),x62732),x62731))) % 168.22/168.06 [6274]E(f317(f317(f89(a849),x62741),f809(x62741,x62742,x62743)),x62742)+P22(f317(f317(f226(a849),x62742),x62741))+P22(f317(x62743,f317(f317(f21(a849),x62742),x62741))) % 168.22/168.06 [6288]~P113(x62881)+E(f317(f317(f90(x62881),f317(f84(x62881),x62882)),x62883),f317(f84(x62881),f317(f317(f90(x62881),x62882),x62883)))+~P22(f317(f317(f225(x62881),f2(x62881)),x62883)) % 168.22/168.06 [6289]~P60(x62891)+E(f317(f317(f266(x62891),f317(f84(x62891),x62892)),x62893),f317(f84(x62891),f317(f317(f266(x62891),x62892),x62893)))+~P22(f317(f317(f226(x62891),f2(x62891)),x62893)) % 168.22/168.06 [6296]~P93(x62961)+~P22(f317(f71(x62961),x62963))+E(f317(f317(f74(x62961,x62961,f113(x62961)),x62962),x62963),f11(x62961,f317(f317(f286(x62961),x62962),x62963))) % 168.22/168.06 [6297]~P93(x62971)+~P22(f317(f71(x62971),x62973))+E(f317(f317(f74(x62971,x62971,f122(x62971)),x62972),x62973),f10(x62971,f317(f317(f286(x62971),x62972),x62973))) % 168.22/168.06 [6298]~P103(x62981)+~P22(f317(f71(x62981),x62983))+E(f317(f317(f74(x62981,x62981,f224(x62981)),x62982),x62983),f14(x62981,f317(f317(f286(x62981),x62982),x62983))) % 168.22/168.06 [6299]~P103(x62991)+~P22(f317(f71(x62991),x62993))+E(f317(f317(f74(x62991,x62991,f223(x62991)),x62992),x62993),f15(x62991,f317(f317(f286(x62991),x62992),x62993))) % 168.22/168.06 [6346]E(x63461,f125(x63462))+~E(f173(x63462,x63463),f125(f850(x63462)))+~P22(f317(f317(f319(f850(x63462)),x63461),f317(f166(f850(x63462)),x63463))) % 168.22/168.06 [6388]~P22(f317(f131(x63881),x63883))+P22(f317(f317(f319(x63881),x63882),f317(f166(x63881),x63883)))+P22(f317(f131(x63881),f317(f317(f145(x63881),x63882),x63883))) % 168.22/168.06 [6400]~P91(x64001)+~P22(f317(f71(x64001),x64003))+E(f317(f73(x64001,f90(x64001)),f317(f317(f286(x64001),x64002),x64003)),f317(f317(f74(x64001,x64001,f90(x64001)),x64002),x64003)) % 168.22/168.06 [6422]~P103(x64221)+~P22(f317(f71(x64221),x64223))+E(f12(x64221,f224(x64221),f317(f317(f286(x64221),x64222),x64223)),f317(f317(f74(x64221,x64221,f224(x64221)),x64222),x64223)) % 168.22/168.06 [6423]~P103(x64231)+~P22(f317(f71(x64231),x64233))+E(f13(x64231,f223(x64231),f317(f317(f286(x64231),x64232),x64233)),f317(f317(f74(x64231,x64231,f223(x64231)),x64232),x64233)) % 168.22/168.06 [6425]P22(f317(x64251,f2(a849)))+~P22(f317(f317(f226(a849),x64252),x64253))+~P22(f317(x64251,f317(f317(f21(a849),x64252),x64253))) % 168.22/168.06 [6443]~P79(x64431)+P22(f317(f317(f225(x64431),x64432),x64433))+~P22(f317(f317(f225(x64431),f317(f84(x64431),x64432)),x64433)) % 168.22/168.06 [6444]~P113(x64441)+P22(f317(f317(f226(x64441),x64442),x64443))+~P22(f317(f317(f226(x64441),f317(f84(x64441),x64442)),x64443)) % 168.22/168.06 [6461]E(x64611,f125(x64612))+E(f317(f135(x64612),f317(f317(f132(x64612),x64613),x64611)),f317(f317(f159(x64612),x64611),x64613))+~P22(f317(f317(f226(a849),x64613),f317(f189(f850(x64612)),x64611))) % 168.22/168.06 [6511]~P22(f317(x65111,x65113))+P22(f317(x65111,f453(x65111,x65112)))+~P22(f317(f317(f319(a849),x65113),f317(f278(a849,f2(a849)),x65112))) % 168.22/168.06 [6532]P22(f317(x65321,x65322))+~P22(f317(f317(f226(a849),x65322),x65323))+P22(f317(f317(f319(a849),f435(x65321,x65323)),f317(f278(a849,f2(a849)),x65323))) % 168.22/168.06 [6548]~P112(x65481)+~P22(f317(f317(f225(x65481),f2(x65481)),x65482))+P22(f317(f317(f225(x65481),f2(x65481)),f317(f317(f238(x65481),x65482),x65483))) % 168.22/168.06 [6549]~P112(x65491)+~P22(f317(f317(f225(x65491),f87(x65491)),x65492))+P22(f317(f317(f225(x65491),f87(x65491)),f317(f317(f238(x65491),x65492),x65493))) % 168.22/168.06 [6551]~P112(x65511)+~P22(f317(f317(f226(x65511),f2(x65511)),x65512))+P22(f317(f317(f226(x65511),f2(x65511)),f317(f317(f238(x65511),x65512),x65513))) % 168.22/168.06 [6576]~P22(f317(x65761,x65763))+~P22(f317(f317(f226(a849),x65763),x65762))+P22(f317(f317(f319(a849),f434(x65761,x65762)),f317(f278(a849,f2(a849)),x65762))) % 168.22/168.06 [6582]P22(f317(f71(x65821),x65822))+~P22(f317(f71(x65821),x65823))+~P22(f317(f317(f225(f858(x65821,a842)),x65822),x65823)) % 168.22/168.06 [6592]P22(f317(x65921,x65922))+~P22(f317(x65921,f436(x65921,x65923)))+~P22(f317(f317(f319(a849),x65922),f317(f278(a849,f2(a849)),x65923))) % 168.22/168.06 [6606]~P118(x66062)+E(x66061,f2(x66062))+~E(f317(f317(f89(x66062),f317(f317(f90(x66062),x66063),x66063)),f317(f317(f90(x66062),x66061),x66061)),f2(x66062)) % 168.22/168.06 [6607]~P118(x66072)+E(x66071,f2(x66072))+~E(f317(f317(f89(x66072),f317(f317(f90(x66072),x66071),x66071)),f317(f317(f90(x66072),x66073),x66073)),f2(x66072)) % 168.22/168.06 [6658]~P103(x66581)+~P29(x66581,x66583)+P29(x66581,f317(f317(f143(x66581,x66581,f5(x66581)),x66582),x66583)) % 168.22/168.06 [6702]~P90(x67021)+E(f317(f115(x67021),x67022),f317(f115(x67021),x67023))+~P31(x67021,f317(f115(x67021),f317(f317(f89(a1),x67022),f317(f88(a1),x67023)))) % 168.22/168.06 [6766]E(x67661,f2(a1))+E(x67662,f2(a1))+~P22(f317(f58(x67662,x67662),f317(f317(f237(a1,a1),x67663),x67661))) % 168.22/168.06 [6767]E(x67671,f87(a1))+E(x67672,f2(a1))+~P22(f317(f58(x67672,x67672),f317(f317(f237(a1,a1),x67671),x67673))) % 168.22/168.06 [6778]P22(f317(x67781,x67782))+P22(f317(f317(f226(a849),f436(x67781,x67783)),x67783))+~P22(f317(f317(f319(a849),x67782),f317(f278(a849,f2(a849)),x67783))) % 168.22/168.06 [6802]~P22(f317(x68021,f808(x68023,x68022,x68021)))+~P22(f317(x68021,f2(a849)))+P22(f317(x68021,f317(f317(f21(a849),x68022),x68023))) % 168.22/168.06 [6803]~P22(f317(x68031,f809(x68033,x68032,x68031)))+~P22(f317(x68031,f2(a849)))+P22(f317(x68031,f317(f317(f21(a849),x68032),x68033))) % 168.22/168.06 [6824]~P22(f317(x68241,x68243))+P22(f317(f317(f226(a849),f453(x68241,x68242)),x68242))+~P22(f317(f317(f319(a849),x68243),f317(f278(a849,f2(a849)),x68242))) % 168.22/168.06 [6825]E(f317(f317(f21(a849),f317(f317(f21(a849),x68251),x68252)),f317(f317(f21(a849),x68253),x68252)),f317(f317(f21(a849),x68251),x68253))+~P22(f317(f317(f225(a849),x68252),x68251))+~P22(f317(f317(f225(a849),x68252),x68253)) % 168.22/168.06 [6861]~P78(x68611)+~P22(f317(f317(f225(x68611),f317(f88(x68611),x68613)),x68612))+P22(f317(f317(f225(x68611),f317(f88(x68611),x68612)),x68613)) % 168.22/168.06 [6863]~P79(x68631)+~P22(f317(f317(f225(x68631),f317(f84(x68631),x68632)),x68633))+P22(f317(f317(f225(x68631),f317(f88(x68631),x68632)),x68633)) % 168.22/168.06 [6865]~P78(x68651)+~P22(f317(f317(f226(x68651),f317(f88(x68651),x68653)),x68652))+P22(f317(f317(f226(x68651),f317(f88(x68651),x68652)),x68653)) % 168.22/168.06 [6866]~P113(x68661)+~P22(f317(f317(f226(x68661),f317(f84(x68661),x68662)),x68663))+P22(f317(f317(f226(x68661),f317(f88(x68661),x68662)),x68663)) % 168.22/168.06 [6906]~P22(f317(x69063,f808(x69062,x69061,x69063)))+P22(f317(f317(f226(a849),x69061),x69062))+P22(f317(x69063,f317(f317(f21(a849),x69061),x69062))) % 168.22/168.06 [6907]~P22(f317(x69073,f809(x69072,x69071,x69073)))+P22(f317(f317(f226(a849),x69071),x69072))+P22(f317(x69073,f317(f317(f21(a849),x69071),x69072))) % 168.22/168.06 [6955]~E(f677(x69553,x69552,x69551),f678(x69553,x69552,x69551))+E(f317(f317(f113(f858(x69551,a842)),x69552),f49(f858(x69551,a842),x69553)),f188(f858(x69551,a842)))+P22(f317(f317(f319(f858(x69551,a842)),x69552),x69553)) % 168.22/168.06 [6965]~P22(f317(f71(x69651),x69653))+P22(f317(f71(x69651),f50(f858(x69651,a842),x69652)))+~P22(f317(f317(f319(f858(x69651,a842)),x69653),x69652)) % 168.22/168.06 [7025]~P103(x70251)+E(f317(f317(f122(f858(x70251,a842)),f317(f278(x70251,x70252),x70253)),f317(f317(f286(x70251),x70253),f188(f858(x70251,a842)))),f279(x70251,x70252,x70253))+~P22(f317(f317(f225(x70251),x70252),x70253)) % 168.22/168.06 [7062]E(x70621,x70622)+~P22(f317(f317(f225(f858(x70623,a842)),x70621),x70622))+P22(f317(f317(f226(f858(x70623,a842)),x70621),x70622)) % 168.22/168.06 [7075]E(x70751,x70752)+~E(f317(f189(f850(x70753)),x70751),f317(f189(f850(x70753)),x70752))+P22(f317(f317(f226(a849),f584(x70753,x70751,x70752)),f317(f189(f850(x70753)),x70752))) % 168.22/168.06 [7121]P6(x71211,x71212,x71213)+~E(f317(f236(x71211,x71211),x71213),x71212)+~E(f317(f317(f265(x71211,x71211,x71211),f317(f263(x71211,x71211),x71213)),x71213),x71213) % 168.22/168.06 [7192]~P103(x71921)+E(f317(f317(f122(f858(x71921,a842)),f282(x71921,x71922,x71923)),f317(f317(f286(x71921),x71923),f188(f858(x71921,a842)))),f281(x71921,x71922,x71923))+~P22(f317(f317(f226(x71921),x71922),x71923)) % 168.22/168.06 [7295]~P22(f317(f71(x72951),x72953))+P22(f317(f317(f225(a849),f317(f54(x72951),x72952)),f317(f54(x72951),x72953)))+~P22(f317(f317(f225(f858(x72951,a842)),x72952),x72953)) % 168.22/168.06 [7296]~P22(f317(f71(x72961),x72963))+P22(f317(f317(f226(a849),f317(f54(x72961),x72962)),f317(f54(x72961),x72963)))+~P22(f317(f317(f226(f858(x72961,a842)),x72962),x72963)) % 168.22/168.06 [7332]~P22(f317(x73323,x73322))+P22(f317(f317(f194(x73321),x73322),f423(x73322,x73321,x73323)))+~P22(f317(f317(f194(f35(x73323,x73321)),x73322),x73322)) % 168.22/168.06 [7428]E(x74281,x74282)+~P22(f317(f317(f225(f858(x74283,a842)),x74282),x74281))+~P22(f317(f317(f225(f858(x74283,a842)),x74281),x74282)) % 168.22/168.06 [7431]~P103(x74311)+P29(x74311,x74312)+~P29(x74311,f317(f317(f143(x74311,x74311,f5(x74311)),x74313),x74312)) % 168.22/168.06 [7501]~P22(f317(f317(f226(a849),x75013),x75012))+~P22(f317(f317(f226(a849),x75013),x75011))+P22(f317(f317(f226(a849),f317(f317(f21(a849),x75011),x75012)),f317(f317(f21(a849),x75011),x75013))) % 168.22/168.06 [7502]~P22(f317(f317(f225(a849),x75022),x75021))+~P22(f317(f317(f226(a849),x75021),x75023))+P22(f317(f317(f226(a849),f317(f317(f21(a849),x75021),x75022)),f317(f317(f21(a849),x75023),x75022))) % 168.22/168.06 [7538]~P22(f317(f317(f226(a849),f2(a849)),x75382))+~P22(f317(f317(f226(a849),x75381),x75383))+P22(f317(f317(f226(a849),f317(f317(f90(a849),x75381),x75382)),f317(f317(f90(a849),x75383),x75382))) % 168.22/168.06 [7539]~P22(f317(f317(f226(a849),f2(a849)),x75391))+~P22(f317(f317(f226(a849),x75392),x75393))+P22(f317(f317(f226(a849),f317(f317(f90(a849),x75391),x75392)),f317(f317(f90(a849),x75391),x75393))) % 168.22/168.06 [7540]~P22(f317(f317(f226(a1),f2(a1)),x75401))+~P22(f317(f317(f226(a1),x75402),x75403))+P22(f317(f317(f226(a1),f317(f317(f90(a1),x75401),x75402)),f317(f317(f90(a1),x75401),x75403))) % 168.22/168.06 [7667]~P22(f317(f71(x76671),x76673))+P22(f317(f317(f319(x76671),f392(x76672,x76673,x76671)),x76673))+P22(f317(f317(f226(a849),f2(a849)),f317(f317(f9(x76671,a849),x76672),x76673))) % 168.22/168.06 [7668]~P22(f317(f71(x76681),x76683))+P22(f317(f317(f319(x76681),f522(x76682,x76683,x76681)),x76683))+P22(f317(f317(f226(a849),f2(a849)),f317(f317(f9(x76681,a849),x76682),x76683))) % 168.22/168.06 [7950]E(x79501,f188(f858(x79502,a842)))+E(x79501,f317(f317(f286(x79502),x79503),f188(f858(x79502,a842))))+~P22(f317(f317(f225(f858(x79502,a842)),x79501),f317(f317(f286(x79502),x79503),f188(f858(x79502,a842))))) % 168.22/168.06 [7968]~P57(x79681)+P8(x79681,x79682,x79683)+P22(f317(f317(f319(f850(x79681)),f665(x79683,x79682,x79681)),f317(f166(f850(x79681)),f64(x79681,x79683,f65(x79681))))) % 168.22/168.06 [7986]~P22(f317(f317(f226(a849),f2(a849)),x79863))+P22(f317(f317(f225(a849),x79861),x79862))+~P22(f317(f317(f225(a849),f317(f317(f90(a849),x79863),x79861)),f317(f317(f90(a849),x79863),x79862))) % 168.22/168.06 [7987]~P22(f317(f317(f226(a849),f2(a849)),x79873))+P22(f317(f317(f225(a849),x79871),x79872))+~P22(f317(f317(f225(a849),f317(f317(f90(a849),x79871),x79873)),f317(f317(f90(a849),x79872),x79873))) % 168.22/168.06 [7989]~P22(f317(f317(f226(a849),f2(a849)),x79893))+P22(f317(f317(f226(a849),x79891),x79892))+~P22(f317(f317(f226(a849),f317(f317(f238(a849),x79893),x79891)),f317(f317(f238(a849),x79893),x79892))) % 168.22/168.06 [8018]~P57(x80181)+~P7(x80181,x80183,x80182)+P22(f317(f317(f319(f850(x80181)),f664(x80182,x80183,x80181)),f317(f166(f850(x80181)),f64(x80181,x80182,f65(x80181))))) % 168.22/168.06 [8026]~P22(f317(x80261,x80263))+P22(f317(f317(f194(f35(x80261,x80262)),f423(x80263,x80262,x80261)),x80263))+~P22(f317(f317(f194(f35(x80261,x80262)),x80263),x80263)) % 168.22/168.06 [8035]~E(f317(f317(f113(f858(x80351,a842)),f678(x80353,x80352,x80351)),f677(x80353,x80352,x80351)),f188(f858(x80351,a842)))+E(f317(f317(f113(f858(x80351,a842)),x80352),f49(f858(x80351,a842),x80353)),f188(f858(x80351,a842)))+P22(f317(f317(f319(f858(x80351,a842)),x80352),x80353)) % 168.22/168.06 [8053]E(x80531,f125(x80532))+~E(f317(f136(f850(x80532),f850(x80532),f127(x80532),f125(x80532)),x80533),f125(x80532))+~P22(f317(f317(f319(f850(x80532)),x80531),f317(f166(f850(x80532)),x80533))) % 168.22/168.06 [8109]E(x81091,f188(f858(f858(x81092,a842),a842)))+P22(f317(f317(f319(f858(x81092,a842)),f695(x81093,x81091,x81092)),x81091))+P22(f317(f317(f225(f858(x81092,a842)),f50(f858(x81092,a842),x81091)),x81093)) % 168.22/168.06 [8116]~P67(x81161)+~P70(x81161)+E(f317(f317(f9(a1,x81161),f317(f317(f8(a849,x81161,a1),x81162),a116)),f317(f287(a849,a1,f112(a1)),x81163)),f317(f317(f9(a849,x81161),x81162),x81163)) % 168.22/168.06 [8117]~P67(x81171)+~P70(x81171)+E(f317(f317(f6(a1,x81171),f317(f317(f8(a849,x81171,a1),x81172),a116)),f317(f287(a849,a1,f112(a1)),x81173)),f317(f317(f6(a849,x81171),x81172),x81173)) % 168.22/168.06 [8157]~P22(f317(f71(x81571),x81573))+~P22(f317(f317(f226(a849),f2(a849)),f317(x81572,f392(x81572,x81573,x81571))))+P22(f317(f317(f226(a849),f2(a849)),f317(f317(f9(x81571,a849),x81572),x81573))) % 168.22/168.06 [8158]~P22(f317(f71(x81581),x81583))+~P22(f317(f317(f226(a849),f2(a849)),f317(x81582,f522(x81582,x81583,x81581))))+P22(f317(f317(f226(a849),f2(a849)),f317(f317(f9(x81581,a849),x81582),x81583))) % 168.22/168.06 [8193]~P59(x81932)+E(x81931,f87(x81932))+E(f317(f317(f266(x81932),f317(f317(f21(x81932),f317(f317(f238(x81932),x81931),x81933)),f87(x81932))),f317(f317(f21(x81932),x81931),f87(x81932))),f317(f317(f6(a849,x81932),f317(f238(x81932),x81931)),f317(f278(a849,f2(a849)),x81933))) % 168.22/168.06 [8222]E(x82221,f2(a849))+~P22(f317(x82223,f317(f48(a849,x82222),x82221)))+P22(f317(f317(f226(a849),x82222),f317(f317(f90(a849),x82221),f317(a124,f335(x82221,x82222,x82223))))) % 168.22/168.06 [8249]P22(f317(x82491,f2(a849)))+~P22(f317(x82491,f317(f48(a849,x82492),x82493)))+P22(f317(f317(f226(a849),x82492),f317(f317(f90(a849),x82493),f317(a124,f335(x82493,x82492,x82491))))) % 168.22/168.06 [8269]E(x82691,f2(a849))+~P22(f317(x82693,f317(f48(a849,x82692),x82691)))+P22(f317(f317(f225(a849),f317(f317(f90(a849),x82691),f335(x82691,x82692,x82693))),x82692)) % 168.22/168.06 [8289]P22(f317(x82891,f2(a849)))+~P22(f317(x82891,f317(f48(a849,x82893),x82892)))+P22(f317(f317(f225(a849),f317(f317(f90(a849),x82892),f335(x82892,x82893,x82891))),x82893)) % 168.22/168.06 [8356]~P103(x83561)+E(f317(f317(f143(x83561,x83561,f5(x83561)),x83562),x83563),f144(x83561,x83561,f5(x83561),x83562,x83563))+P22(f317(f317(f319(x83561),x83562),f317(f166(x83561),x83563))) % 168.22/168.06 [8396]~E(f317(x83963,f702(x83962,x83963,x83961)),f317(x83963,f707(x83962,x83963,x83961)))+~P54(x83961,f317(x83963,f703(x83962,x83963,x83961)))+P54(x83961,f317(f317(f51(x83962,f858(x83961,f858(x83961,a842))),f233(f858(x83962,a842))),x83963)) % 168.22/168.06 [8403]E(x84031,f188(f858(f858(x84032,a842),a842)))+~P22(f317(f317(f225(f858(x84032,a842)),f695(x84033,x84031,x84032)),x84033))+P22(f317(f317(f225(f858(x84032,a842)),f50(f858(x84032,a842),x84031)),x84033)) % 168.22/168.06 [8468]~P61(x84681)+~P22(f317(f317(f226(x84681),x84682),x84683))+P22(f317(f317(f226(x84681),x84682),f317(f317(f266(x84681),f317(f317(f89(x84681),x84682),x84683)),f317(f317(f89(x84681),f87(x84681)),f87(x84681))))) % 168.22/168.06 [8520]~P22(f317(f317(x85201,f342(x85201,x85203,x85202)),f343(x85201,x85203,x85202)))+P22(f317(f317(x85201,x85202),x85203))+~P22(f317(f305(f857(a1,a1),a61),f317(f317(f237(a1,a1),x85202),x85203))) % 168.22/168.06 [8521]~P22(f317(f317(x85211,f346(x85211,x85213,x85212)),f349(x85211,x85213,x85212)))+P22(f317(f317(x85211,x85212),x85213))+~P22(f317(f305(f857(a1,a1),a66),f317(f317(f237(a1,a1),x85212),x85213))) % 168.22/168.06 [8522]~P22(f317(f317(x85221,f350(x85221,x85223,x85222)),f351(x85221,x85223,x85222)))+P22(f317(f317(x85221,x85222),x85223))+~P22(f317(f305(f857(a1,a1),a211),f317(f317(f237(a1,a1),x85222),x85223))) % 168.22/168.06 [8523]~P22(f317(f317(x85231,f352(x85231,x85233,x85232)),f353(x85231,x85233,x85232)))+P22(f317(f317(x85231,x85232),x85233))+~P22(f317(f305(f857(a849,a849),a210),f317(f317(f237(a849,a849),x85232),x85233))) % 168.22/168.06 [8524]~P22(f317(f317(x85241,f614(x85241,x85243,x85242)),f616(x85241,x85243,x85242)))+P22(f317(f317(x85241,x85242),x85243))+~P22(f317(f305(f857(a1,a1),a176),f317(f317(f237(a1,a1),x85242),x85243))) % 168.22/168.06 [8770]P22(f317(f317(x87701,x87702),x87703))+P22(f317(f305(f857(a849,a849),a210),f317(f317(f237(a849,a849),f352(x87701,x87703,x87702)),f353(x87701,x87703,x87702))))+~P22(f317(f305(f857(a849,a849),a210),f317(f317(f237(a849,a849),x87702),x87703))) % 168.22/168.06 [8771]P22(f317(f317(x87711,x87712),x87713))+P22(f317(f305(f857(a1,a1),a61),f317(f317(f237(a1,a1),f342(x87711,x87713,x87712)),f343(x87711,x87713,x87712))))+~P22(f317(f305(f857(a1,a1),a61),f317(f317(f237(a1,a1),x87712),x87713))) % 168.22/168.06 [8772]P22(f317(f317(x87721,x87722),x87723))+P22(f317(f305(f857(a1,a1),a66),f317(f317(f237(a1,a1),f346(x87721,x87723,x87722)),f349(x87721,x87723,x87722))))+~P22(f317(f305(f857(a1,a1),a66),f317(f317(f237(a1,a1),x87722),x87723))) % 168.22/168.06 [8773]P22(f317(f317(x87731,x87732),x87733))+P22(f317(f305(f857(a1,a1),a211),f317(f317(f237(a1,a1),f350(x87731,x87733,x87732)),f351(x87731,x87733,x87732))))+~P22(f317(f305(f857(a1,a1),a211),f317(f317(f237(a1,a1),x87732),x87733))) % 168.22/168.06 [8774]P22(f317(f317(x87741,x87742),x87743))+P22(f317(f305(f857(a1,a1),a176),f317(f317(f237(a1,a1),f614(x87741,x87743,x87742)),f616(x87741,x87743,x87742))))+~P22(f317(f305(f857(a1,a1),a176),f317(f317(f237(a1,a1),x87742),x87743))) % 168.22/168.06 [9114]~P22(f317(f71(x91141),x91143))+P22(f317(f317(f319(f857(f858(x91141,a842),f858(x91141,a842))),f317(f317(f237(f858(x91141,a842),f858(x91141,a842)),x91142),x91143)),f283(x91141)))+~P22(f317(f317(f226(f858(x91141,a842)),x91142),x91143)) % 168.22/168.06 [9185]~P54(x91851,f317(x91853,f703(x91852,x91853,x91851)))+P54(x91851,f317(f317(f51(x91852,f858(x91851,f858(x91851,a842))),f233(f858(x91852,a842))),x91853))+~E(f317(f317(f113(f858(x91851,a842)),f242(x91851,x91851,f317(x91853,f702(x91852,x91853,x91851)))),f243(x91851,x91851,f317(x91853,f707(x91852,x91853,x91851)))),f188(f858(x91851,a842))) % 168.22/168.06 [9252]~P21(a845,f188(f858(f848(a845),a842)),f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),x92521),x92522),x92523)),f188(f858(f848(a845),a842))))+P18(a845,f188(f858(f848(a845),a842)),f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),x92521),x92522),x92523)),f188(f858(f848(a845),a842))))+~P18(a845,f188(f858(f848(a845),a842)),f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),x92522),f194(x92522))),f188(f858(f848(a845),a842)))) % 168.22/168.06 [9381]P45(x93811,x93812,x93813)+P22(f317(f317(f319(f857(x93811,x93811)),f566(x93813,x93812,x93811)),x93813))+~P22(f317(f317(f319(f857(x93811,x93811)),f317(f317(f237(x93811,x93811),f565(x93813,x93812,x93811)),f565(x93813,x93812,x93811))),x93813)) % 168.22/168.06 [9963]P45(x99631,x99632,x99633)+~P22(f317(f317(f247(x99631,x99631,a842),f317(f317(f7(x99631,f858(x99631,a842),f858(x99631,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x99631,a842),f858(x99631,a842)),x99631),f8(a842,a842,x99631)),f317(f317(f8(a842,f858(a842,a842),x99631),a315),f317(f317(f7(x99631,f858(x99631,a842),a842),f319(x99631)),x99632)))),f317(f317(f7(x99631,f858(x99631,a842),a842),f319(x99631)),x99632))),f566(x99633,x99632,x99631)))+~P22(f317(f317(f319(f857(x99631,x99631)),f317(f317(f237(x99631,x99631),f565(x99633,x99632,x99631)),f565(x99633,x99632,x99631))),x99633)) % 168.22/168.06 [5528]~P55(x55282)+E(x55281,f2(x55282))+E(f317(f48(x55282,f317(f317(f90(x55282),x55283),x55281)),x55281),x55283) % 168.22/168.06 [5529]~P55(x55292)+E(x55291,f2(x55292))+E(f317(f48(x55292,f317(f317(f90(x55292),x55291),x55293)),x55291),x55293) % 168.22/168.06 [6305]~P55(x63052)+E(x63051,f2(x63052))+E(f317(f48(x63052,f317(f317(f89(x63052),x63053),x63051)),x63051),f317(f317(f89(x63052),f317(f48(x63052,x63053),x63051)),f87(x63052))) % 168.22/168.06 [6306]~P55(x63062)+E(x63061,f2(x63062))+E(f317(f48(x63062,f317(f317(f89(x63062),x63061),x63063)),x63061),f317(f317(f89(x63062),f317(f48(x63062,x63063),x63061)),f87(x63062))) % 168.22/168.06 [6345]~P67(x63451)+~E(f317(x63452,f2(a849)),f2(x63451))+E(f317(f317(f6(a849,x63451),x63452),f317(f278(a849,f317(a124,f2(a849))),x63453)),f317(f317(f6(a849,x63451),x63452),f317(f278(a849,f2(a849)),x63453))) % 168.22/168.06 [6688]~P22(f317(x66883,f2(a1)))+P22(f317(f317(f225(a849),x66881),x66882))+P22(f317(x66883,f317(f112(a1),f317(f317(f21(a849),x66882),x66881)))) % 168.22/168.06 [6784]P22(f317(f317(f226(a849),x67842),x67841))+P22(f317(f317(f225(a849),x67841),x67842))+P22(f317(x67843,f317(f112(a1),f317(f317(f21(a849),x67842),x67841)))) % 168.22/168.06 [6859]E(f317(f317(f89(a849),f317(f115(a849),x68591)),f317(f317(f89(a849),f317(f115(a849),x68592)),x68593)),f317(f317(f89(a849),f317(f115(a849),x68591)),x68593))+P22(f317(a193,f317(f115(a1),x68591)))+~P22(f317(a193,f317(f115(a1),x68592))) % 168.22/168.06 [6892]~E(x68922,f317(f48(a849,x68923),x68921))+~P22(f317(f317(f226(a849),f2(a849)),x68921))+P22(f317(f317(f225(a849),f317(f317(f90(a849),x68921),x68922)),x68923)) % 168.22/168.06 [7060]~P22(f317(f71(x70601),x70603))+~P22(f317(f71(x70601),x70602))+P22(f317(f71(x70601),f317(f317(f122(f858(x70601,a842)),x70602),x70603))) % 168.22/168.06 [7344]~P103(x73441)+~P22(f317(f71(x73441),x73442))+E(f133(x73441,f317(f317(f21(f858(x73441,a842)),x73442),f317(f317(f286(x73441),x73443),f188(f858(x73441,a842))))),f164(x73441,x73443,f133(x73441,x73442))) % 168.22/168.06 [7408]P22(f317(x74081,f2(a1)))+~P22(f317(f317(f226(a849),x74082),x74083))+~P22(f317(x74081,f317(f112(a1),f317(f317(f21(a849),x74082),x74083)))) % 168.22/168.06 [7425]~P22(f317(f71(x74251),x74252))+E(f317(f54(x74251),f317(f317(f21(f858(x74251,a842)),x74252),f317(f317(f286(x74251),x74253),f188(f858(x74251,a842))))),f317(f54(x74251),x74252))+P22(f317(f317(f319(x74251),x74253),x74252)) % 168.22/168.06 [7554]~P112(x75541)+~P22(f317(f317(f226(x75541),f87(x75541)),x75542))+P22(f317(f317(f226(x75541),f87(x75541)),f317(f317(f90(x75541),x75542),f317(f317(f238(x75541),x75542),x75543)))) % 168.22/168.06 [7599]~P22(f317(f71(x75991),x75993))+E(f317(f317(f21(a849),f317(f54(x75991),x75992)),f317(f54(x75991),x75993)),f317(f54(x75991),f317(f317(f21(f858(x75991,a842)),x75992),x75993)))+~P22(f317(f317(f225(f858(x75991,a842)),x75993),x75992)) % 168.22/168.06 [7658]~P22(f317(f317(f225(a849),x76582),x76583))+~P22(f317(f317(f225(a849),x76581),f317(f317(f21(a849),x76583),x76582)))+P22(f317(f317(f225(a849),f317(f317(f89(a849),x76581),x76582)),x76583)) % 168.22/168.06 [7711]P22(f317(f71(x77111),x77112))+~P22(f317(f71(x77111),x77113))+~P22(f317(f71(x77111),f317(f317(f21(f858(x77111,a842)),x77112),x77113))) % 168.22/168.06 [7717]~P22(f317(f71(x77171),x77172))+E(f317(f54(x77171),f317(f317(f21(f858(x77171,a842)),x77172),f317(f317(f286(x77171),x77173),f188(f858(x77171,a842))))),f317(f317(f21(a849),f317(f54(x77171),x77172)),f87(a849)))+~P22(f317(f317(f319(x77171),x77173),x77172)) % 168.22/168.06 [7791]P54(x77911,x77912)+~P54(x77911,x77913)+~P22(f317(f317(f225(f858(x77911,f858(x77911,a842))),x77912),x77913)) % 168.22/168.06 [7826]~P22(f317(f317(f225(a849),x78263),x78262))+P22(f317(f317(f225(a849),x78261),f317(f317(f21(a849),x78262),x78263)))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),x78261),x78263)),x78262)) % 168.22/168.06 [7843]P37(x78431,x78432)+~P37(x78431,x78433)+~P22(f317(f317(f225(f858(f857(x78431,x78431),a842)),x78432),x78433)) % 168.22/168.06 [7844]P52(x78441,x78442)+~P52(x78441,x78443)+~P22(f317(f317(f225(f858(f857(x78441,x78441),a842)),x78442),x78443)) % 168.22/168.06 [8086]~P112(x80861)+~P22(f317(f317(f226(x80861),f87(x80861)),x80862))+P22(f317(f317(f226(x80861),f317(f317(f238(x80861),x80862),x80863)),f317(f317(f90(x80861),x80862),f317(f317(f238(x80861),x80862),x80863)))) % 168.22/168.06 [8177]~P22(f317(x81771,f2(a1)))+~P22(f317(x81771,f317(f317(f21(a1),f317(f112(a1),x81772)),f317(f112(a1),x81773))))+P22(f317(x81771,f317(f112(a1),f317(f317(f21(a849),x81772),x81773)))) % 168.22/168.06 [8190]~P22(f317(f317(f225(a849),x81903),x81902))+P22(f317(x81901,f317(f317(f21(a1),f317(f112(a1),x81902)),f317(f112(a1),x81903))))+~P22(f317(x81901,f317(f112(a1),f317(f317(f21(a849),x81902),x81903)))) % 168.22/168.06 [8207]P22(f317(f317(f226(a849),x82071),x82072))+~P22(f317(x82073,f317(f317(f21(a1),f317(f112(a1),x82071)),f317(f112(a1),x82072))))+P22(f317(x82073,f317(f112(a1),f317(f317(f21(a849),x82071),x82072)))) % 168.22/168.06 [8264]~P118(x82642)+E(x82641,f2(x82642))+P22(f317(f317(f226(x82642),f2(x82642)),f317(f317(f89(x82642),f317(f317(f90(x82642),x82643),x82643)),f317(f317(f90(x82642),x82641),x82641)))) % 168.22/168.06 [8265]~P118(x82652)+E(x82651,f2(x82652))+P22(f317(f317(f226(x82652),f2(x82652)),f317(f317(f89(x82652),f317(f317(f90(x82652),x82651),x82651)),f317(f317(f90(x82652),x82653),x82653)))) % 168.22/168.06 [8376]~P22(f317(f317(f226(a849),f2(a849)),x83761))+~P22(f317(f317(f226(a1),x83762),x83763))+P22(f317(f317(f226(a1),f317(f317(f90(a1),f317(f112(a1),x83761)),x83762)),f317(f317(f90(a1),f317(f112(a1),x83761)),x83763))) % 168.22/168.06 [8436]E(f317(f317(f113(f858(x84361,a842)),x84362),f49(f858(x84361,a842),x84363)),f188(f858(x84361,a842)))+P22(f317(f317(f319(f858(x84361,a842)),x84362),x84363))+P22(f317(f317(f319(f858(x84361,a842)),f678(x84363,x84362,x84361)),f317(f317(f286(f858(x84361,a842)),x84362),x84363))) % 168.22/168.06 [8437]E(f317(f317(f113(f858(x84371,a842)),x84372),f49(f858(x84371,a842),x84373)),f188(f858(x84371,a842)))+P22(f317(f317(f319(f858(x84371,a842)),x84372),x84373))+P22(f317(f317(f319(f858(x84371,a842)),f677(x84373,x84372,x84371)),f317(f317(f286(f858(x84371,a842)),x84372),x84373))) % 168.22/168.06 [8467]E(x84671,x84672)+~E(f317(f189(f850(x84673)),x84671),f317(f189(f850(x84673)),x84672))+P22(f317(f317(f319(f857(x84673,x84673)),f585(x84673,x84671,x84672)),f317(f166(f857(x84673,x84673)),f317(f317(f175(x84673,x84673),x84672),x84671)))) % 168.22/168.06 [8690]E(f284(x86901,x86902),f284(x86901,x86903))+~P22(f317(f317(f225(f858(f857(x86901,x86901),a842)),x86903),f284(x86901,x86902)))+~P22(f317(f317(f225(f858(f857(x86901,x86901),a842)),x86902),x86903)) % 168.22/168.06 [8748]~P45(x87481,f233(f858(x87481,a842)),x87483)+P22(f317(f317(f225(f858(f857(f850(x87481),f850(x87481)),a842)),f151(x87481,x87482)),f152(x87481,x87483)))+~P22(f317(f317(f225(f858(f857(x87481,x87481),a842)),x87482),x87483)) % 168.22/168.06 [8987]~P22(f317(f71(x89871),x89872))+P22(f317(f71(f858(x89871,a842)),f317(f317(f70(x89871),x89872),x89873)))+~P22(f317(f317(f225(f858(f857(x89871,x89871),a842)),x89873),f317(f317(f245(x89871,x89871),x89872),f317(f16(f858(x89871,a842),x89871),x89872)))) % 168.22/168.06 [9021]P45(x90211,x90212,x90213)+P22(f317(f317(f319(x90211),f533(x90213,x90212,x90211)),x90212))+~P22(f317(f317(f225(f858(f857(x90211,x90211),a842)),x90213),f317(f317(f245(x90211,x90211),x90212),f317(f16(f858(x90211,a842),x90211),x90212)))) % 168.22/168.06 [9022]P45(x90221,x90222,x90223)+P22(f317(f317(f319(x90221),f539(x90222,x90223,x90221)),x90222))+~P22(f317(f317(f225(f858(f857(x90221,x90221),a842)),x90223),f317(f317(f245(x90221,x90221),x90222),f317(f16(f858(x90221,a842),x90221),x90222)))) % 168.22/168.06 [9055]~P61(x90551)+~P22(f317(f317(f226(x90551),x90552),x90553))+P22(f317(f317(f226(x90551),f317(f317(f266(x90551),f317(f317(f89(x90551),x90552),x90553)),f317(f317(f89(x90551),f87(x90551)),f87(x90551)))),x90553)) % 168.22/168.06 [9084]~P60(x90841)+P22(f317(f317(f225(x90841),x90842),x90843))+~P22(f317(f317(f225(x90841),f317(f317(f90(x90841),f460(x90843,x90842,x90841)),x90842)),x90843)) % 168.22/168.06 [9219]E(f317(f189(f850(f850(x92191))),f317(f130(f850(x92191),f317(f317(f8(a849,a842,f850(x92191)),f317(f226(a849),x92192)),f189(f850(x92191)))),f173(x92191,x92193))),f317(f189(f850(x92191)),f317(f317(f159(f850(x92191)),x92193),x92192)))+~P29(a849,f317(f163(a849),f317(f317(f148(f850(x92191),a849),f189(f850(x92191))),x92193)))+~P22(f317(f317(f226(a849),x92192),f317(f189(f850(f850(x92191))),x92193))) % 168.22/168.06 [9326]~P37(x93261,x93262)+P20(x93261,f317(f317(f237(f858(f857(x93261,x93261),a842),f858(f857(x93261,x93261),a842)),x93262),x93263))+~P22(f317(f317(f225(f858(f857(x93261,x93261),a842)),f317(f317(f265(x93261,x93261,x93261),x93262),x93263)),x93262)) % 168.22/168.06 [9333]E(f317(f317(f148(f850(x93331),x93331),f317(f317(f7(f850(x93331),a849,x93331),f159(x93331)),x93332)),f317(f130(f850(x93331),f317(f317(f8(a849,a842,f850(x93331)),f317(f226(a849),x93332)),f189(f850(x93331)))),f173(x93331,x93333))),f317(f317(f159(f850(x93331)),x93333),x93332))+~P29(a849,f317(f163(a849),f317(f317(f148(f850(x93331),a849),f189(f850(x93331))),x93333)))+~P22(f317(f317(f226(a849),x93332),f317(f189(f850(f850(x93331))),x93333))) % 168.22/168.06 [9466]P45(x94661,x94662,x94663)+~P22(f317(f317(f319(f857(x94661,x94661)),f317(f317(f237(x94661,x94661),f533(x94663,x94662,x94661)),f533(x94663,x94662,x94661))),x94663))+~P22(f317(f317(f225(f858(f857(x94661,x94661),a842)),x94663),f317(f317(f245(x94661,x94661),x94662),f317(f16(f858(x94661,a842),x94661),x94662)))) % 168.22/168.06 [9467]P45(x94671,x94672,x94673)+~P22(f317(f317(f319(f857(x94671,x94671)),f317(f317(f237(x94671,x94671),f539(x94672,x94673,x94671)),f539(x94672,x94673,x94671))),x94673))+~P22(f317(f317(f225(f858(f857(x94671,x94671),a842)),x94673),f317(f317(f245(x94671,x94671),x94672),f317(f16(f858(x94671,a842),x94671),x94672)))) % 168.22/168.06 [9841]~E(x98413,f2(a849))+~E(f317(f189(f850(x98411)),f317(f317(f159(f850(x98411)),x98412),f651(x98413,x98411,x98412))),x98413)+E(f317(f317(f148(a849,f850(x98411)),f317(f317(f7(a849,f850(a849),f850(x98411)),f317(f317(f8(f858(a849,x98411),f858(f850(a849),f850(x98411)),a849),f148(a849,x98411)),f317(f7(a849,a849,x98411),f317(f317(f8(f850(x98411),f858(a849,x98411),a849),f159(x98411)),f317(f159(f850(x98411)),x98412))))),f133(a849,f317(f278(a849,f2(a849)),f317(f189(f850(f850(x98411))),x98412))))),f133(a849,f317(f278(a849,f2(a849)),x98413))),f173(x98411,x98412)) % 168.22/168.06 [9842]E(x98421,f125(f850(x98422)))+~E(f317(f189(f850(x98422)),f317(f317(f159(f850(x98422)),x98421),f651(x98423,x98422,x98421))),x98423)+E(f317(f317(f148(a849,f850(x98422)),f317(f317(f7(a849,f850(a849),f850(x98422)),f317(f317(f8(f858(a849,x98422),f858(f850(a849),f850(x98422)),a849),f148(a849,x98422)),f317(f7(a849,a849,x98422),f317(f317(f8(f850(x98422),f858(a849,x98422),a849),f159(x98422)),f317(f159(f850(x98422)),x98421))))),f133(a849,f317(f278(a849,f2(a849)),f317(f189(f850(f850(x98422))),x98421))))),f133(a849,f317(f278(a849,f2(a849)),x98423))),f173(x98422,x98421)) % 168.22/168.06 [9843]~E(x98433,f2(a849))+E(f317(f317(f148(a849,f850(x98431)),f317(f317(f7(a849,f850(a849),f850(x98431)),f317(f317(f8(f858(a849,x98431),f858(f850(a849),f850(x98431)),a849),f148(a849,x98431)),f317(f7(a849,a849,x98431),f317(f317(f8(f850(x98431),f858(a849,x98431),a849),f159(x98431)),f317(f159(f850(x98431)),x98432))))),f133(a849,f317(f278(a849,f2(a849)),f317(f189(f850(f850(x98431))),x98432))))),f133(a849,f317(f278(a849,f2(a849)),x98433))),f173(x98431,x98432))+P22(f317(f317(f226(a849),f651(x98433,x98431,x98432)),f317(f189(f850(f850(x98431))),x98432))) % 168.22/168.06 [9844]E(x98441,f125(f850(x98442)))+E(f317(f317(f148(a849,f850(x98442)),f317(f317(f7(a849,f850(a849),f850(x98442)),f317(f317(f8(f858(a849,x98442),f858(f850(a849),f850(x98442)),a849),f148(a849,x98442)),f317(f7(a849,a849,x98442),f317(f317(f8(f850(x98442),f858(a849,x98442),a849),f159(x98442)),f317(f159(f850(x98442)),x98441))))),f133(a849,f317(f278(a849,f2(a849)),f317(f189(f850(f850(x98442))),x98441))))),f133(a849,f317(f278(a849,f2(a849)),x98443))),f173(x98442,x98441))+P22(f317(f317(f226(a849),f651(x98443,x98442,x98441)),f317(f189(f850(f850(x98442))),x98441))) % 168.22/168.06 [7596]E(f317(f317(f89(a849),f317(f115(a849),x75961)),f317(f317(f89(a849),f317(f115(a849),x75962)),x75963)),f317(f317(f89(a849),f317(f115(a849),f317(f317(f89(a1),x75961),x75962))),x75963))+P22(f317(a193,f317(f115(a1),x75961)))+P22(f317(a193,f317(f115(a1),x75962))) % 168.22/168.06 [8366]~P22(f317(f71(x83661),x83662))+~P22(f317(f317(f319(x83661),x83663),x83662))+E(f317(a124,f317(f54(x83661),f317(f317(f21(f858(x83661,a842)),x83662),f317(f317(f286(x83661),x83663),f188(f858(x83661,a842)))))),f317(f54(x83661),x83662)) % 168.22/168.06 [8386]~P22(f317(f71(x83861),x83862))+~P22(f317(f317(f319(x83861),x83863),x83862))+E(f317(f317(f89(a849),f87(a849)),f317(f54(x83861),f317(f317(f21(f858(x83861,a842)),x83862),f317(f317(f286(x83861),x83863),f188(f858(x83861,a842)))))),f317(f54(x83861),x83862)) % 168.22/168.06 [8478]~P103(x84781)+~P22(f317(f71(x84781),x84783))+E(f317(f317(f143(x84781,x84781,f5(x84781)),x84782),f133(x84781,f317(f317(f21(f858(x84781,a842)),x84783),f317(f317(f286(x84781),x84782),f188(f858(x84781,a842)))))),f133(x84781,f317(f317(f286(x84781),x84782),x84783))) % 168.22/168.06 [8622]~P22(f317(f71(x86221),x86223))+~P22(f317(f71(x86221),x86222))+E(f317(f317(f89(a849),f317(f54(x86221),f317(f317(f122(f858(x86221,a842)),x86222),x86223))),f317(f54(x86221),f317(f317(f113(f858(x86221,a842)),x86222),x86223))),f317(f317(f89(a849),f317(f54(x86221),x86222)),f317(f54(x86221),x86223))) % 168.22/168.06 [9789]~P19(x97891,f858(f858(x97891,a842),a842),f317(f317(f7(x97891,f858(f857(x97891,x97891),a842),f858(f858(x97891,a842),a842)),f317(f317(f8(f858(x97891,a842),f858(f858(f857(x97891,x97891),a842),f858(f858(x97891,a842),a842)),x97891),f70(x97891)),f317(f317(f7(x97891,f858(x97891,a842),f858(x97891,a842)),f286(x97891)),f188(f858(x97891,a842))))),x97893),x97892)+~P22(f317(f71(x97891),x97892))+E(f317(f54(f858(x97891,a842)),f317(f317(f70(x97891),x97892),x97893)),f317(f54(x97891),x97892)) % 168.22/168.06 [7859]~P90(x78591)+P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x78593)))+E(f317(f317(f238(x78591),x78592),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),x78593),x78593)),a109))),f87(x78591)) % 168.22/168.06 [9309]~P90(x93091)+~P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),x93093)))+E(f317(f317(f238(x93091),x93092),f317(f115(a849),f317(f317(f21(a1),f317(f317(f89(a1),x93093),x93093)),a109))),f317(f317(f95(x93091,x93091),f317(f317(f238(x93091),x93092),f317(f115(a849),x93093))),f317(f317(f18(x93091,x93091,x93091),f317(f317(f8(x93091,f858(x93091,x93091),x93091),f90(x93091)),f317(f90(x93091),x93092))),f5(x93091)))) % 168.22/168.06 [9691]~P22(f317(f131(x96911),x96913))+~P22(f317(f317(f319(x96911),x96912),f317(f166(x96911),x96913)))+E(f317(f317(f132(x96911),f317(f189(f850(x96911)),f170(x96911,f317(f317(f8(a842,a842,x96911),a312),f317(f317(f7(x96911,x96911,a842),a314),x96912)),f317(f163(x96911),x96913)))),f317(f163(x96911),x96913)),f317(f317(f145(x96911),x96912),f317(f163(x96911),f170(x96911,f317(f317(f8(a842,a842,x96911),a312),f317(f317(f7(x96911,x96911,a842),a314),x96912)),x96913)))) % 168.22/168.06 [9765]P22(f317(f317(f225(f858(f857(x97651,x97651),a842)),f284(x97651,x97652)),x97653))+~P22(f317(f317(f225(f858(f857(x97651,x97651),a842)),f284(x97651,f188(f858(f857(x97651,x97651),a842)))),x97653))+~P22(f317(f317(f225(f858(f857(x97651,x97651),a842)),f317(f317(f265(x97651,x97651,x97651),f317(f317(f113(f858(f857(x97651,x97651),a842)),f284(x97651,x97652)),x97653)),x97652)),x97653)) % 168.22/168.06 [9606]~P22(f317(f71(x96061),f317(f230(x96061),x96063)))+~P22(f317(f71(x96061),f317(f230(x96061),x96062)))+P22(f317(f71(x96061),f317(f230(x96061),f317(f317(f18(x96061,a842,a842),f317(f317(f8(a842,f858(a842,a842),x96061),a316),x96062)),x96063)))) % 168.22/168.06 [9907]P22(f317(f317(f225(f858(f857(x99071,x99071),a842)),f317(f317(f265(x99071,x99071,x99071),x99072),f284(x99071,x99072))),x99073))+~P22(f317(f317(f225(f858(f857(x99071,x99071),a842)),x99072),x99073))+~P22(f317(f317(f225(f858(f857(x99071,x99071),a842)),f317(f317(f265(x99071,x99071,x99071),f317(f317(f113(f858(f857(x99071,x99071),a842)),f317(f317(f265(x99071,x99071,x99071),x99072),f284(x99071,x99072))),x99073)),x99072)),x99073)) % 168.22/168.06 [9859]~P113(x98592)+E(x98591,f2(x98592))+~E(f317(f317(f89(x98592),f317(f317(f238(x98592),x98593),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x98592),x98591),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f2(x98592)) % 168.22/168.06 [9860]~P113(x98602)+E(x98601,f2(x98602))+~E(f317(f317(f89(x98602),f317(f317(f238(x98602),x98601),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x98602),x98603),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f2(x98602)) % 168.22/168.06 [9866]~P22(f317(f131(x98661),x98663))+~P22(f317(f317(f319(x98661),x98662),f317(f166(x98661),x98663)))+E(f317(f163(x98661),f317(f165(x98661),f317(f317(f132(x98661),f317(f189(f850(x98661)),f170(x98661,f317(f317(f8(a842,a842,x98661),a312),f317(f317(f7(x98661,x98661,a842),a314),x98662)),x98663))),x98663))),f170(x98661,f317(f317(f8(a842,a842,x98661),a312),f317(f317(f7(x98661,x98661,a842),a314),x98662)),f317(f163(x98661),x98663))) % 168.22/168.06 [9952]~P113(x99522)+E(x99521,f2(x99522))+P22(f317(f317(f226(x99522),f2(x99522)),f317(f317(f89(x99522),f317(f317(f238(x99522),x99523),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x99522),x99521),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))))) % 168.22/168.06 [9953]~P113(x99532)+E(x99531,f2(x99532))+P22(f317(f317(f226(x99532),f2(x99532)),f317(f317(f89(x99532),f317(f317(f238(x99532),x99531),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x99532),x99533),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))))) % 168.22/168.06 [9996]~P113(x99961)+P22(f317(f317(f225(x99961),f2(x99961)),x99962))+~P22(f317(f317(f225(x99961),f2(x99961)),f317(f317(f238(x99961),x99962),f317(a124,f317(f317(f90(a849),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),x99963))))) % 168.22/168.06 [5414]~P18(x54141,x54144,x54143)+P18(x54141,x54142,x54143)+~P18(x54141,x54142,x54144) % 168.22/168.06 [7146]~P32(x71463,x71464,x71461,x71462)+E(x71461,x71462)+~P32(x71463,x71464,x71462,x71461) % 168.22/168.06 [4891]~E(x48912,f99(x48913,x48911))+P22(f317(x48911,x48912))+~P22(f317(x48911,x48914)) % 168.22/168.06 [6599]~P37(x65992,x65994)+~P37(x65991,x65993)+P37(f857(x65991,x65992),f310(x65991,x65992,x65993,x65994)) % 168.22/168.06 [5066]~P5(x50664,x50661)+~E(f317(x50661,x50662),f317(x50661,x50663))+P22(f317(f317(x50661,x50662),x50663)) % 168.22/168.06 [5234]~P5(x52344,x52341)+E(f317(x52341,x52342),f317(x52341,x52343))+~P22(f317(f317(x52341,x52342),x52343)) % 168.22/168.06 [5320]~P13(x53203,x53204,x53201)+E(f317(x53201,x53202),f317(f73(x53203,x53204),x53202))+~P22(f317(f71(x53203),x53202)) % 168.22/168.06 [5321]~P2(x53213,x53214,x53211)+E(f317(x53211,x53212),f317(f73(x53213,x53214),x53212))+~P22(f317(f71(x53213),x53212)) % 168.22/168.06 [5446]~P5(x54464,x54461)+~P22(f317(f317(x54461,x54463),x54462))+P22(f317(f317(x54461,x54462),x54463)) % 168.22/168.06 [5516]E(x55161,x55162)+~E(f317(f244(x55163,x55164),x55161),f317(f244(x55163,x55164),x55162))+~E(f317(f246(x55163,x55164),x55161),f317(f246(x55163,x55164),x55162)) % 168.22/168.06 [5545]E(x55451,x55452)+~P22(f317(f57(x55453,x55454),x55452))+~P22(f317(f57(x55453,x55454),x55451)) % 168.22/168.06 [5726]~P67(x57262)+E(f216(x57261,x57262,x57263,x57264),f2(x57262))+P22(f317(f71(x57261),x57264)) % 168.22/168.06 [5856]~P22(f317(f305(x58561,x58562),x58564))+P22(f317(f305(x58561,x58562),x58563))+~P22(f317(f317(x58562,x58563),x58564)) % 168.22/168.06 [7786]~P103(x77862)+~P22(f317(f131(x77861),x77864))+P22(f317(f131(x77861),f142(x77861,x77862,x77863,x77864))) % 168.22/168.06 [8006]~P22(f317(f71(x80062),x80064))+~P22(f317(f71(x80061),x80063))+P22(f317(f71(f856(x80061,x80062)),f298(x80061,x80062,x80063,x80064))) % 168.22/168.06 [8007]~P22(f317(f131(x80072),x80074))+~P22(f317(f131(x80071),x80073))+P22(f317(f131(f857(x80071,x80072)),f69(x80071,x80072,x80073,x80074))) % 168.22/168.06 [8011]P22(f317(f317(f319(f850(x80111)),f317(f317(f127(x80111),x80112),x80113)),f155(x80111,x80114)))+~P22(f317(f317(f319(f850(x80111)),x80113),f155(x80111,x80114)))+~P22(f317(f317(f319(f850(x80111)),x80112),f155(x80111,x80114))) % 168.22/168.06 [8345]~P103(x83453)+~P22(f317(f131(x83451),f142(x83451,x83453,x83454,x83452)))+P22(f317(f131(x83451),x83452)) % 168.22/168.06 [8613]~P22(f317(f317(f319(f857(x86131,x86131)),f317(f317(f237(x86131,x86131),x86132),x86134)),f284(x86131,x86133)))+P22(f317(f317(f319(x86131),x86132),f306(x86131,x86133)))+~P22(f317(f317(f319(x86131),x86134),f306(x86131,x86133))) % 168.22/168.06 [5050]~P70(x50502)+E(f317(f317(f9(x50501,x50502),x50503),x50504),f87(x50502))+P22(f317(f71(x50501),x50504)) % 168.22/168.06 [5053]~P67(x50532)+E(f317(f317(f6(x50531,x50532),x50533),x50534),f2(x50532))+P22(f317(f71(x50531),x50534)) % 168.22/168.06 [5200]~P62(x52003)+E(x52001,x52002)+~E(f317(f317(f89(x52003),x52004),x52001),f317(f317(f89(x52003),x52004),x52002)) % 168.22/168.06 [5201]~P63(x52013)+E(x52011,x52012)+~E(f317(f317(f89(x52013),x52014),x52011),f317(f317(f89(x52013),x52014),x52012)) % 168.22/168.06 [5203]~P62(x52033)+E(x52031,x52032)+~E(f317(f317(f89(x52033),x52031),x52034),f317(f317(f89(x52033),x52032),x52034)) % 168.22/168.06 [5316]~P27(x53163)+E(x53161,f188(f858(x53162,a842)))+E(f317(f317(f51(x53162,x53163),x53161),f317(f16(x53163,x53162),x53164)),x53164) % 168.22/168.06 [5317]~P27(x53173)+E(x53171,f188(f858(x53172,a842)))+E(f317(f317(f52(x53172,x53173),x53171),f317(f16(x53173,x53172),x53174)),x53174) % 168.22/168.06 [5532]~P104(x55323)+E(x55321,x55322)+~E(f279(x55323,x55324,x55321),f317(f317(f286(x55323),x55322),f188(f858(x55323,a842)))) % 168.22/168.06 [5533]~P104(x55333)+E(x55331,x55332)+~E(f279(x55333,x55331,x55332),f317(f317(f286(x55333),x55334),f188(f858(x55333,a842)))) % 168.22/168.06 [5814]P22(f317(x58141,x58142))+~P22(f317(f241(x58143,x58141),x58144))+~P22(f317(f317(f319(x58143),x58142),x58144)) % 168.22/168.06 [5832]P34(x58321,x58322,x58323)+~P34(x58321,x58322,f317(f317(f145(x58321),x58324),x58323))+P22(f317(x58322,x58324)) % 168.22/168.06 [5845]E(x58451,x58452)+~P22(f317(f317(f194(x58453),x58454),x58452))+~P22(f317(f317(f194(x58453),x58454),x58451)) % 168.22/168.06 [5916]P34(x59161,x59162,x59163)+P34(x59161,x59162,x59164)+~P34(x59161,x59162,f317(f317(f127(x59161),x59164),x59163)) % 168.22/168.06 [5935]~P67(x59351)+E(f317(f317(f6(a849,x59351),x59352),f317(f278(a849,x59353),f317(a124,x59354))),f2(x59351))+~P22(f317(f317(f226(a849),x59354),x59353)) % 168.22/168.06 [5939]~P26(x59391)+~E(f55(x59391,x59392,x59393),f55(x59391,x59394,x59393))+E(f55(x59391,f317(f88(x59391),x59392),x59393),f55(x59391,f317(f88(x59391),x59394),x59393)) % 168.22/168.06 [6002]P22(f317(x60021,x60022))+~E(f317(f130(x60023,x60021),x60024),x60024)+~P22(f317(f317(f319(x60023),x60022),f317(f166(x60023),x60024))) % 168.22/168.06 [6019]~E(f317(f317(f89(a849),x60193),x60192),f317(f317(f89(a849),x60191),x60194))+~P22(f317(f317(f226(a849),x60193),x60194))+P22(f317(f317(f226(a849),x60191),x60192)) % 168.22/168.06 [6023]P34(x60231,x60232,x60233)+~P22(f317(x60232,x60234))+~P22(f317(f317(f319(x60231),x60234),f317(f166(x60231),x60233))) % 168.22/168.06 [6058]~E(f317(f130(x60581,x60582),x60583),f125(x60581))+~P22(f317(x60582,x60584))+~P22(f317(f317(f319(x60581),x60584),f317(f166(x60581),x60583))) % 168.22/168.06 [6059]~E(f170(x60593,x60591,x60594),x60594)+P22(f317(x60591,x60592))+~P22(f317(f317(f319(x60593),x60592),f317(f166(x60593),x60594))) % 168.22/168.06 [6092]~E(x60924,f188(f858(x60922,a842)))+~E(x60923,f188(f858(x60921,a842)))+E(f298(x60921,x60922,x60923,x60924),f188(f858(f856(x60921,x60922),a842))) % 168.22/168.06 [6234]P22(f317(x62341,x62342))+~P22(f317(f154(x62343,x62341),x62344))+~P22(f317(f317(f319(x62343),x62342),f317(f166(x62343),x62344))) % 168.22/168.06 [6501]~P67(x65011)+E(f317(f317(f6(a849,x65011),x65012),f279(a849,x65013,f317(a124,x65014))),f2(x65011))+~P22(f317(f317(f226(a849),f317(a124,x65014)),x65013)) % 168.22/168.06 [6640]~P103(x66401)+E(f317(f317(f21(f858(x66401,a842)),f317(f278(x66401,x66402),x66403)),f317(f278(x66401,x66402),x66404)),f317(f278(x66401,x66404),x66403))+~P22(f317(f317(f225(x66401),x66402),x66404)) % 168.22/168.06 [6992]~P22(f317(f317(f319(f850(x69921)),x69924),f155(x69921,x69923)))+P22(f317(f317(f319(x69921),x69922),x69923))+~P22(f317(f317(f319(x69921),x69922),f317(f166(x69921),x69924))) % 168.22/168.06 [7053]~P70(x70531)+E(f317(f317(f317(f75(x70531,x70532,f90(x70531)),x70533),f87(x70531)),x70534),f317(f317(f9(x70532,x70531),x70533),x70534))+~P22(f317(f71(x70532),x70534)) % 168.22/168.06 [7055]~P67(x70551)+E(f317(f317(f317(f75(x70551,x70552,f89(x70551)),x70553),f2(x70551)),x70554),f317(f317(f6(x70552,x70551),x70553),x70554))+~P22(f317(f71(x70552),x70554)) % 168.22/168.06 [7085]P19(x70851,x70852,x70853,x70854)+~E(f317(f54(x70852),f317(f287(x70851,x70852,x70853),x70854)),f317(f54(x70851),x70854))+~P22(f317(f71(x70851),x70854)) % 168.22/168.06 [7262]~P67(x72621)+E(f317(f317(f89(x72621),f317(x72622,x72623)),f317(f317(f6(a849,x72621),x72622),f281(a849,x72623,x72624))),f317(f317(f6(a849,x72621),x72622),f279(a849,x72623,x72624)))+~P22(f317(f317(f225(a849),x72623),x72624)) % 168.22/168.06 [7273]~P70(x72731)+~P19(x72732,x72731,x72733,x72734)+E(f317(f317(f9(x72731,x72731),f39(x72731)),f317(f287(x72732,x72731,x72733),x72734)),f317(f317(f9(x72732,x72731),x72733),x72734)) % 168.22/168.06 [7274]~P67(x72741)+~P19(x72742,x72741,x72743,x72744)+E(f317(f317(f6(x72741,x72741),f39(x72741)),f317(f287(x72742,x72741,x72743),x72744)),f317(f317(f6(x72742,x72741),x72743),x72744)) % 168.22/168.06 [7325]E(f317(f54(f856(x73251,x73252)),f298(x73251,x73252,x73253,x73254)),f317(f317(f89(a849),f317(f54(x73251),x73253)),f317(f54(x73252),x73254)))+~P22(f317(f71(x73252),x73254))+~P22(f317(f71(x73251),x73253)) % 168.22/168.06 [7409]E(x74091,x74092)+P22(f317(f317(f319(x74093),x74091),f317(f166(x74093),f164(x74093,x74092,x74094))))+~P22(f317(f317(f319(x74093),x74091),f317(f166(x74093),x74094))) % 168.22/168.06 [7634]~P67(x76341)+E(f317(f317(f89(x76341),f317(f317(f6(a849,x76341),x76342),f317(f278(a849,x76343),x76344))),f317(x76342,x76344)),f317(f317(f6(a849,x76341),x76342),f317(f278(a849,x76343),f317(a124,x76344))))+P22(f317(f317(f226(a849),x76344),x76343)) % 168.22/168.06 [7688]~P19(x76881,x76882,x76883,f233(f858(x76881,a842)))+~P22(f317(f71(x76882),x76884))+P22(f317(f71(x76881),f317(f289(x76881,x76882,x76883),x76884))) % 168.22/168.06 [7796]P22(f317(f317(f319(f850(x77961)),f317(f317(f145(x77961),x77962),x77963)),f155(x77961,x77964)))+~P22(f317(f317(f319(f850(x77961)),x77963),f155(x77961,x77964)))+~P22(f317(f317(f319(x77961),x77962),x77964)) % 168.22/168.06 [7882]~E(f317(f287(x78823,x78821,x78824),f233(f858(x78823,a842))),f233(f858(x78821,a842)))+P22(f317(f71(x78821),x78822))+~P22(f317(f71(x78823),f317(f289(x78823,x78821,x78824),x78822))) % 168.22/168.06 [7976]~P19(x79761,x79763,x79764,x79762)+P22(f317(f71(x79761),x79762))+~P22(f317(f71(x79763),f317(f287(x79761,x79763,x79764),x79762))) % 168.22/168.06 [7997]~E(x79972,x79973)+P22(f317(f317(f319(f857(x79971,x79971)),f317(f317(f237(x79971,x79971),x79972),x79973)),f235(x79971,x79974)))+~P22(f317(f317(f319(x79971),x79972),x79974)) % 168.22/168.06 [8037]~P67(x80371)+E(f317(f317(f89(x80371),f317(f317(f6(a849,x80371),x80372),f279(a849,x80373,x80374))),f317(x80372,f317(a124,x80374))),f317(f317(f6(a849,x80371),x80372),f279(a849,x80373,f317(a124,x80374))))+P22(f317(f317(f226(a849),f317(a124,x80374)),x80373)) % 168.22/168.06 [8101]P22(f317(x81011,x81012))+~P22(f317(x81011,f317(f317(f159(x81013),x81014),f595(x81011,x81014,x81013))))+~P22(f317(f317(f319(x81013),x81012),f317(f166(x81013),x81014))) % 168.22/168.06 [8245]~P22(f317(f317(f319(x82451),x82452),f306(x82451,x82454)))+P22(f317(f317(f319(f850(x82451)),f317(f317(f145(x82451),x82452),x82453)),f306(f850(x82451),f151(x82451,x82454))))+~P22(f317(f317(f319(f850(x82451)),x82453),f306(f850(x82451),f151(x82451,x82454)))) % 168.22/168.06 [8256]~P19(x82562,x82563,x82564,f696(x82564,x82563,x82562,x82561))+P19(x82562,x82563,x82564,f50(f858(x82562,a842),x82561))+E(x82561,f188(f858(f858(x82562,a842),a842))) % 168.22/168.06 [8534]E(x85341,x85342)+~P22(f317(f317(f319(f857(x85343,x85343)),f317(f317(f237(x85343,x85343),x85341),x85342)),f284(x85343,x85344)))+P22(f317(f317(f319(x85343),x85341),f317(f236(x85343,x85343),x85344))) % 168.22/168.06 [8807]P19(x88072,x88073,x88074,f50(f858(x88072,a842),x88071))+E(x88071,f188(f858(f858(x88072,a842),a842)))+P22(f317(f317(f319(f858(x88072,a842)),f696(x88074,x88073,x88072,x88071)),x88071)) % 168.22/168.06 [8946]P22(f317(f71(x89461),x89462))+~P22(f317(f71(x89464),f317(f287(x89461,x89464,x89463),x89462)))+P22(f317(f317(f319(x89461),f567(x89463,x89464,x89462,x89461)),x89462)) % 168.22/168.06 [9036]~P27(x90362)+E(f317(f317(f74(x90361,x90362,f317(f317(f8(x90362,f858(x90362,x90362),x90361),f122(x90362)),x90363)),f188(x90362)),x90364),f317(f317(f51(x90361,x90362),x90364),x90363))+~P22(f317(f71(x90361),x90364)) % 168.22/168.06 [9117]P22(f317(x91171,x91172))+~P22(f317(x91171,f317(f317(f159(x91173),x91174),f697(x91172,x91171,x91174,x91173))))+~P22(f317(f317(f319(x91173),x91172),f317(f166(x91173),x91174))) % 168.22/168.06 [9137]E(x91371,x91372)+~P22(f317(f317(f319(f857(x91373,x91373)),f317(f317(f237(x91373,x91373),x91371),x91372)),f284(x91373,x91374)))+P22(f317(f317(f319(f857(x91373,x91373)),f317(f317(f237(x91373,x91373),x91371),x91372)),f317(f317(f265(x91373,x91373,x91373),x91374),f284(x91373,x91374)))) % 168.22/168.06 [9186]~E(f317(f189(f850(x91861)),x91862),f317(f189(f850(x91861)),x91863))+~P22(f317(f317(f319(f857(f850(x91861),f850(x91861))),f317(f317(f237(f850(x91861),f850(x91861)),x91862),x91863)),f141(x91861,x91864)))+P22(f317(f317(f319(f857(f850(x91861),f850(x91861))),f317(f317(f237(f850(x91861),f850(x91861)),x91862),x91863)),f139(x91861,x91864))) % 168.22/168.06 [9609]~P25(x96091)+E(f317(f317(f6(a849,x96091),f317(f317(f18(a849,x96091,x96091),f317(f317(f8(x96091,f858(x96091,x96091),a849),f21(x96091)),x96092)),f317(f317(f8(a849,x96091,a849),x96092),f317(f317(f7(a849,a849,a849),f89(a849)),f87(a849))))),f279(a849,x96093,x96094)),f2(x96091))+P22(f317(f317(f225(a849),x96093),x96094)) % 168.22/168.06 [9857]~P37(x98572,x98574)+~P19(x98572,x98571,x98573,f233(f858(x98572,a842)))+P37(x98571,f317(f287(f857(x98572,x98572),f857(x98571,x98571),f248(x98572,x98571,x98572,x98571,x98573,x98573)),x98574)) % 168.22/168.06 [10021]~E(f317(f189(f850(x100211)),x100213),f317(f189(f850(x100211)),x100212))+P22(f317(f317(f319(f857(f850(x100211),f850(x100211))),f317(f317(f237(f850(x100211),f850(x100211)),x100212),x100213)),f152(x100211,x100214)))+~P22(f317(f317(f247(x100211,x100211,a842),f317(f317(f7(x100211,f858(f857(x100211,x100211),a842),f858(x100211,a842)),f317(f317(f8(f858(x100211,f858(f858(f857(x100211,x100211),a842),a842)),f858(f858(f857(x100211,x100211),a842),f858(x100211,a842)),x100211),f7(x100211,f858(f857(x100211,x100211),a842),a842)),f317(f317(f8(f858(x100211,f857(x100211,x100211)),f858(x100211,f858(f858(f857(x100211,x100211),a842),a842)),x100211),f317(f8(f857(x100211,x100211),f858(f858(f857(x100211,x100211),a842),a842),x100211),f319(f857(x100211,x100211)))),f237(x100211,x100211)))),x100214)),f588(x100214,x100213,x100212,x100211))) % 168.22/168.06 [5898]~E(x58984,x58982)+P22(f317(x58981,x58982))+P22(f317(f317(f194(f35(x58981,x58983)),x58982),x58984)) % 168.22/168.06 [5946]~P55(x59461)+~E(x59462,f2(x59461))+E(f317(f48(x59461,f317(f317(f90(x59461),x59462),x59463)),f317(f317(f90(x59461),x59462),x59464)),f2(x59461)) % 168.22/168.06 [6022]E(x60221,f125(x60222))+E(x60223,f317(f317(f21(a849),f317(f189(f850(x60222)),x60221)),f87(a849)))+E(f138(x60222,f317(f317(f153(x60222,x60221),x60223),x60224)),f138(x60222,x60221)) % 168.22/168.06 [6037]~P55(x60372)+E(x60371,f2(x60372))+E(f317(f48(x60372,f317(f317(f90(x60372),x60373),x60371)),f317(f317(f90(x60372),x60374),x60371)),f317(f48(x60372,x60373),x60374)) % 168.22/168.06 [6039]~P55(x60392)+E(x60391,f2(x60392))+E(f317(f48(x60392,f317(f317(f90(x60392),x60391),x60393)),f317(f317(f90(x60392),x60391),x60394)),f317(f48(x60392,x60393),x60394)) % 168.22/168.06 [6050]E(x60501,x60502)+P22(f317(x60503,x60502))+~P22(f317(f317(f317(f286(x60504),x60501),x60503),x60502)) % 168.22/168.06 [6063]~P67(x60631)+~P22(f317(f131(x60632),x60634))+E(f317(f160(x60631),f317(f317(f148(x60632,x60631),x60633),x60634)),f317(f317(f6(x60632,x60631),x60633),f317(f166(x60632),x60634))) % 168.22/168.06 [6085]~P70(x60852)+~P22(f317(f71(x60851),x60854))+E(f317(f317(f9(x60851,x60852),f317(f16(x60852,x60851),x60853)),x60854),f317(f317(f238(x60852),x60853),f317(f54(x60851),x60854))) % 168.22/168.06 [6144]~P58(x61442)+E(x61441,f2(x61442))+E(f317(f317(f266(x61442),f317(f317(f90(x61442),x61443),x61441)),f317(f317(f90(x61442),x61444),x61441)),f317(f317(f266(x61442),x61443),x61444)) % 168.22/168.06 [6145]~P58(x61452)+E(x61451,f2(x61452))+E(f317(f317(f266(x61452),f317(f317(f90(x61452),x61451),x61453)),f317(f317(f90(x61452),x61451),x61454)),f317(f317(f266(x61452),x61453),x61454)) % 168.22/168.06 [6208]P22(f317(x62081,x62082))+~E(x62083,f317(f317(f89(a849),x62084),x62082))+~P22(f317(x62081,f317(f317(f21(a849),x62083),x62084))) % 168.22/168.06 [6285]P21(x62851,x62852,x62853)+P30(x62851,f576(x62853,x62852,x62851),x62854)+~P22(f317(f317(f319(f848(x62851)),x62854),x62852)) % 168.22/168.06 [6287]~P22(f317(x62872,x62873))+~P22(f317(f154(x62871,x62872),x62874))+P22(f317(f154(x62871,x62872),f317(f317(f145(x62871),x62873),x62874))) % 168.22/168.06 [6329]E(x63291,f125(x63292))+~E(x63293,f317(f317(f21(a849),f317(f189(f850(x63292)),x63291)),f87(a849)))+E(f138(x63292,f317(f317(f153(x63292,x63291),x63293),x63294)),x63294) % 168.22/168.06 [6351]~P92(x63511)+~P22(f317(f317(f225(x63511),x63512),x63514))+P22(f317(f317(f225(x63511),x63512),f317(f317(f122(x63511),x63513),x63514))) % 168.22/168.06 [6352]~P92(x63521)+~P22(f317(f317(f225(x63521),x63522),x63523))+P22(f317(f317(f225(x63521),x63522),f317(f317(f122(x63521),x63523),x63524))) % 168.22/168.06 [6354]~P103(x63541)+~P22(f317(f317(f225(x63541),x63542),x63544))+P22(f317(f317(f225(x63541),x63542),f317(f317(f224(x63541),x63543),x63544))) % 168.22/168.06 [6356]~P103(x63561)+~P22(f317(f317(f225(x63561),x63562),x63563))+P22(f317(f317(f225(x63561),x63562),f317(f317(f224(x63561),x63563),x63564))) % 168.22/168.06 [6357]~P92(x63571)+~P22(f317(f317(f226(x63571),x63572),x63574))+P22(f317(f317(f226(x63571),x63572),f317(f317(f122(x63571),x63573),x63574))) % 168.22/168.06 [6358]~P92(x63581)+~P22(f317(f317(f226(x63581),x63582),x63583))+P22(f317(f317(f226(x63581),x63582),f317(f317(f122(x63581),x63583),x63584))) % 168.22/168.06 [6360]~P103(x63601)+~P22(f317(f317(f226(x63601),x63602),x63604))+P22(f317(f317(f226(x63601),x63602),f317(f317(f224(x63601),x63603),x63604))) % 168.22/168.06 [6362]~P103(x63621)+~P22(f317(f317(f226(x63621),x63622),x63623))+P22(f317(f317(f226(x63621),x63622),f317(f317(f224(x63621),x63623),x63624))) % 168.22/168.06 [6448]~E(f317(f317(f159(x64481),x64482),x64483),x64484)+E(f317(f317(f153(x64481,x64482),x64483),x64484),x64482)+~P22(f317(f317(f226(a849),x64483),f317(f189(f850(x64481)),x64482))) % 168.22/168.06 [6467]E(x64671,x64672)+P22(f317(x64673,x64671))+~P22(f317(f317(f194(f35(x64673,x64674)),x64671),x64672)) % 168.22/168.06 [6487]P22(f317(x64871,x64872))+~P22(f317(x64873,x64872))+~P22(f317(f317(f225(f858(x64874,a842)),x64873),x64871)) % 168.22/168.06 [6519]~E(f317(f317(f153(x65191,x65192),x65193),x65194),x65192)+E(f317(f317(f159(x65191),x65192),x65193),x65194)+~P22(f317(f317(f226(a849),x65193),f317(f189(f850(x65191)),x65192))) % 168.22/168.06 [6533]~P22(f317(f154(x65331,x65332),x65334))+~P22(f317(f154(x65331,x65332),x65333))+P22(f317(f154(x65331,x65332),f317(f317(f127(x65331),x65333),x65334))) % 168.22/168.06 [6628]P30(x66281,x66282,x66283)+~P30(x66281,f317(a124,x66282),f577(x66282,x66284,x66281))+~P22(f317(f317(f319(f848(x66281)),x66283),x66284)) % 168.22/168.06 [6637]E(x66371,f188(f858(x66372,a842)))+E(x66373,f188(f858(x66374,a842)))+~E(f317(f317(f245(x66374,x66372),x66373),f317(f16(f858(x66372,a842),x66374),x66371)),f188(f858(f857(x66374,x66372),a842))) % 168.22/168.06 [6655]E(x66551,x66552)+P22(f317(f317(f319(x66553),x66551),x66554))+~P22(f317(f317(f319(x66553),x66551),f317(f317(f286(x66553),x66552),x66554))) % 168.22/168.06 [6672]~P103(x66721)+P22(f317(f317(f225(x66721),x66722),x66723))+~P22(f317(f317(f225(x66721),x66722),f317(f317(f223(x66721),x66724),x66723))) % 168.22/168.06 [6674]~P103(x66741)+P22(f317(f317(f225(x66741),x66742),x66743))+~P22(f317(f317(f225(x66741),x66742),f317(f317(f223(x66741),x66743),x66744))) % 168.22/168.06 [6676]~P98(x66761)+P22(f317(f317(f225(x66761),x66762),x66763))+~P22(f317(f317(f225(x66761),x66762),f317(f317(f113(x66761),x66764),x66763))) % 168.22/168.06 [6678]~P98(x66781)+P22(f317(f317(f225(x66781),x66782),x66783))+~P22(f317(f317(f225(x66781),x66782),f317(f317(f113(x66781),x66783),x66784))) % 168.22/168.06 [6679]~P103(x66791)+P22(f317(f317(f226(x66791),x66792),x66793))+~P22(f317(f317(f226(x66791),x66792),f317(f317(f223(x66791),x66794),x66793))) % 168.22/168.06 [6680]~P103(x66801)+P22(f317(f317(f226(x66801),x66802),x66803))+~P22(f317(f317(f226(x66801),x66802),f317(f317(f223(x66801),x66803),x66804))) % 168.22/168.06 [6698]~E(f317(f317(f159(x66981),x66983),x66984),x66982)+P22(f317(f317(f319(x66981),x66982),f317(f166(x66981),x66983)))+~P22(f317(f317(f226(a849),x66984),f317(f189(f850(x66981)),x66983))) % 168.22/168.06 [6710]~P103(x67101)+~P29(x67101,f317(f317(f145(x67101),x67102),f317(f317(f145(x67101),x67103),x67104)))+P22(f317(f317(f225(x67101),x67102),x67103)) % 168.22/168.06 [6842]E(x68421,f2(a1))+E(f317(f48(a1,x68422),x68421),x68423)+~P22(f317(f58(x68422,x68421),f317(f317(f237(a1,a1),x68423),x68424))) % 168.22/168.06 [6890]E(f55(a1,x68902,x68901),x68903)+E(x68901,f2(a1))+~P22(f317(f58(x68902,x68901),f317(f317(f237(a1,a1),x68904),x68903))) % 168.22/168.06 [7013]P22(f317(f317(f319(x70131),x70132),x70133))+~P22(f317(f317(f319(x70131),x70132),x70134))+~P22(f317(f317(f226(f858(x70131,a842)),x70134),x70133)) % 168.22/168.06 [7014]P22(f317(f317(f319(x70141),x70142),x70143))+~P22(f317(f317(f319(x70141),x70142),x70144))+~P22(f317(f317(f225(f858(x70141,a842)),x70144),x70143)) % 168.22/168.06 [7124]P34(x71241,x71242,x71243)+~P22(f317(x71242,f317(f317(f159(x71241),x71243),x71244)))+~P22(f317(f317(f226(a849),x71244),f317(f189(f850(x71241)),x71243))) % 168.22/168.06 [7229]~P102(x72292)+~P22(f317(f317(f226(f858(x72291,x72292)),x72293),x72294))+P22(f317(f317(f225(f858(x72291,x72292)),x72293),x72294)) % 168.22/168.06 [7313]~P18(x73131,x73132,x73134)+P18(x73131,x73132,f317(f317(f286(f848(x73131)),x73133),x73134))+~P18(x73131,x73132,f317(f317(f286(f848(x73131)),x73133),f188(f858(f848(x73131),a842)))) % 168.22/168.06 [7356]~P22(f317(f317(f319(x73561),x73562),x73564))+P22(f317(f317(f319(x73561),x73562),f49(f858(x73561,a842),x73563)))+~P22(f317(f317(f319(f858(x73561,a842)),x73564),x73563)) % 168.22/168.06 [7370]P30(x73701,x73702,x73703)+P22(f317(f317(f319(f848(x73701)),f577(x73702,x73704,x73701)),x73704))+~P22(f317(f317(f319(f848(x73701)),x73703),x73704)) % 168.22/168.06 [7387]~P76(x73871)+~P22(f317(f317(f225(x73871),x73873),x73874))+P22(f317(f317(f225(x73871),f317(f317(f89(x73871),x73872),x73873)),f317(f317(f89(x73871),x73872),x73874))) % 168.22/168.06 [7388]~P77(x73881)+~P22(f317(f317(f225(x73881),x73883),x73884))+P22(f317(f317(f225(x73881),f317(f317(f89(x73881),x73882),x73883)),f317(f317(f89(x73881),x73882),x73884))) % 168.22/168.06 [7389]~P76(x73891)+~P22(f317(f317(f225(x73891),x73892),x73894))+P22(f317(f317(f225(x73891),f317(f317(f89(x73891),x73892),x73893)),f317(f317(f89(x73891),x73894),x73893))) % 168.22/168.06 [7390]~P77(x73901)+~P22(f317(f317(f225(x73901),x73902),x73904))+P22(f317(f317(f225(x73901),f317(f317(f89(x73901),x73902),x73903)),f317(f317(f89(x73901),x73904),x73903))) % 168.22/168.06 [7391]~P76(x73911)+~P22(f317(f317(f226(x73911),x73913),x73914))+P22(f317(f317(f226(x73911),f317(f317(f89(x73911),x73912),x73913)),f317(f317(f89(x73911),x73912),x73914))) % 168.22/168.06 [7392]~P81(x73921)+~P22(f317(f317(f226(x73921),x73923),x73924))+P22(f317(f317(f226(x73921),f317(f317(f89(x73921),x73922),x73923)),f317(f317(f89(x73921),x73922),x73924))) % 168.22/168.06 [7393]~P76(x73931)+~P22(f317(f317(f226(x73931),x73932),x73934))+P22(f317(f317(f226(x73931),f317(f317(f89(x73931),x73932),x73933)),f317(f317(f89(x73931),x73934),x73933))) % 168.22/168.06 [7394]~P81(x73941)+~P22(f317(f317(f226(x73941),x73942),x73944))+P22(f317(f317(f226(x73941),f317(f317(f89(x73941),x73942),x73943)),f317(f317(f89(x73941),x73944),x73943))) % 168.22/168.06 [7403]~P134(x74031)+~P88(x74031)+E(f317(f317(f89(x74031),f317(f317(f90(x74031),x74032),f317(f115(x74031),x74033))),f317(f317(f90(x74031),x74034),f317(f115(x74031),x74033))),f317(f317(f90(x74031),f317(f317(f89(x74031),x74032),x74034)),f317(f115(x74031),x74033))) % 168.22/168.06 [7404]~P126(x74041)+~P88(x74041)+E(f317(f317(f21(x74041),f317(f317(f90(x74041),x74042),f317(f115(x74041),x74043))),f317(f317(f90(x74041),x74044),f317(f115(x74041),x74043))),f317(f317(f90(x74041),f317(f317(f21(x74041),x74042),x74044)),f317(f115(x74041),x74043))) % 168.22/168.06 [7439]~P67(x74391)+E(f317(f317(f89(x74391),f317(x74392,x74393)),f317(f317(f6(a849,x74391),x74392),f279(a849,f317(a124,x74393),x74394))),f317(f317(f6(a849,x74391),x74392),f279(a849,x74393,x74394)))+~P22(f317(f317(f225(a849),x74393),x74394)) % 168.22/168.06 [7451]~P19(x74512,x74511,x74513,f317(f166(x74512),x74514))+~P22(f317(f131(x74512),x74514))+P22(f317(f131(x74511),f317(f317(f148(x74512,x74511),x74513),x74514))) % 168.22/168.06 [7498]~P22(f317(f317(f225(a849),x74982),x74984))+~P22(f317(f317(f225(a849),x74981),x74983))+P22(f317(f317(f225(a849),f317(f317(f89(a849),x74981),x74982)),f317(f317(f89(a849),x74983),x74984))) % 168.22/168.06 [7499]~P22(f317(f317(f225(a849),x74992),x74994))+~P22(f317(f317(f225(a849),x74991),x74993))+P22(f317(f317(f225(a849),f317(f317(f90(a849),x74991),x74992)),f317(f317(f90(a849),x74993),x74994))) % 168.22/168.06 [7500]~P22(f317(f317(f226(a849),x75002),x75004))+~P22(f317(f317(f226(a849),x75001),x75003))+P22(f317(f317(f226(a849),f317(f317(f89(a849),x75001),x75002)),f317(f317(f89(a849),x75003),x75004))) % 168.22/168.06 [7503]~P22(f317(f317(f225(a1),x75032),x75034))+~P22(f317(f317(f226(a1),x75031),x75033))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x75031),x75032)),f317(f317(f89(a1),x75033),x75034))) % 168.22/168.06 [7549]P22(f317(f317(f319(x75491),x75492),x75493))+~P22(f317(f317(f319(x75491),x75492),f50(f858(x75491,a842),x75494)))+~P22(f317(f317(f319(f858(x75491,a842)),x75493),x75494)) % 168.22/168.06 [7564]~P22(f317(x75641,f594(x75641,x75643,x75642)))+P22(f317(x75641,f317(f317(f159(x75642),x75643),x75644)))+~P22(f317(f317(f226(a849),x75644),f317(f189(f850(x75642)),x75643))) % 168.22/168.06 [7570]P22(f317(x75701,x75702))+~P22(f317(f317(f319(x75704),x75702),f317(f166(x75704),x75703)))+P22(f317(f317(f226(a849),f595(x75701,x75703,x75704)),f317(f189(f850(x75704)),x75703))) % 168.22/168.06 [7589]~P22(f317(f317(f194(x75892),x75893),x75894))+~P22(f317(f317(f194(f35(x75891,x75892)),x75894),x75893))+P22(f317(f317(f194(f35(x75891,x75892)),x75893),x75893)) % 168.22/168.06 [7619]~P102(x76191)+~P22(f317(f317(f226(f858(x76192,x76191)),x76194),x76193))+~P22(f317(f317(f225(f858(x76192,x76191)),x76193),x76194)) % 168.22/168.06 [7665]~P22(f317(x76654,x76652))+~P22(f317(f317(f319(x76651),x76652),x76653))+P22(f317(f317(f319(x76651),x76652),f317(f317(f113(f858(x76651,a842)),x76653),f317(f230(x76651),x76654)))) % 168.22/168.06 [7804]~P22(f317(f317(f319(x78041),x78043),x78044))+~P22(f317(f317(f226(f858(x78041,a842)),x78042),x78044))+P22(f317(f317(f226(f858(x78041,a842)),x78042),f317(f317(f286(x78041),x78043),x78044))) % 168.22/168.06 [7805]E(f317(f317(f113(f858(x78051,a842)),x78052),x78053),f188(f858(x78051,a842)))+~E(f317(f317(f113(f858(x78051,a842)),f49(f858(x78051,a842),x78054)),x78053),f188(f858(x78051,a842)))+~P22(f317(f317(f319(f858(x78051,a842)),x78052),x78054)) % 168.22/168.06 [7878]P22(f317(f317(f319(x78781),x78782),x78783))+~P22(f317(f317(f225(f858(x78781,a842)),x78783),f317(f317(f286(x78781),x78782),x78784)))+P22(f317(f317(f225(f858(x78781,a842)),x78783),x78784)) % 168.22/168.06 [7898]P22(f317(f317(f319(x78982),f594(x78981,x78983,x78982)),f317(f166(x78982),x78983)))+P22(f317(x78981,f317(f317(f159(x78982),x78983),x78984)))+~P22(f317(f317(f226(a849),x78984),f317(f189(f850(x78982)),x78983))) % 168.22/168.06 [7906]~P22(f317(f317(f225(f858(x79061,a842)),x79062),x79064))+P22(f317(f317(f225(f858(x79061,a842)),x79062),x79063))+~P22(f317(f317(f225(f858(x79061,a842)),x79064),x79063)) % 168.22/168.06 [7907]~P22(f317(f317(f226(f858(x79071,a842)),x79072),x79074))+~P22(f317(f317(f225(f858(x79071,a842)),x79074),x79073))+P22(f317(f317(f226(f858(x79071,a842)),x79072),x79073)) % 168.22/168.06 [7908]~P22(f317(f317(f225(f858(x79081,a842)),x79082),x79084))+~P22(f317(f317(f226(f858(x79081,a842)),x79084),x79083))+P22(f317(f317(f226(f858(x79081,a842)),x79082),x79083)) % 168.22/168.06 [7909]~P22(f317(f317(f226(f858(x79091,a842)),x79092),x79094))+P22(f317(f317(f226(f858(x79091,a842)),x79092),x79093))+~P22(f317(f317(f226(f858(x79091,a842)),x79094),x79093)) % 168.22/168.06 [7949]~P22(f317(f317(f319(x79491),x79494),x79493))+~P22(f317(f317(f226(f858(x79491,a842)),x79492),f317(f317(f286(x79491),x79494),x79493)))+P22(f317(f317(f226(f858(x79491,a842)),x79492),x79493)) % 168.22/168.06 [7961]~P76(x79611)+P22(f317(f317(f225(x79611),x79612),x79613))+~P22(f317(f317(f225(x79611),f317(f317(f89(x79611),x79614),x79612)),f317(f317(f89(x79611),x79614),x79613))) % 168.22/168.06 [7963]~P76(x79631)+P22(f317(f317(f225(x79631),x79632),x79633))+~P22(f317(f317(f225(x79631),f317(f317(f89(x79631),x79632),x79634)),f317(f317(f89(x79631),x79633),x79634))) % 168.22/168.06 [7965]~P76(x79651)+P22(f317(f317(f226(x79651),x79652),x79653))+~P22(f317(f317(f226(x79651),f317(f317(f89(x79651),x79654),x79652)),f317(f317(f89(x79651),x79654),x79653))) % 168.22/168.06 [7967]~P76(x79671)+P22(f317(f317(f226(x79671),x79672),x79673))+~P22(f317(f317(f226(x79671),f317(f317(f89(x79671),x79672),x79674)),f317(f317(f89(x79671),x79673),x79674))) % 168.22/168.06 [8017]P22(f317(x80171,x80172))+~E(f317(f317(f132(x80173),f317(f189(f850(x80173)),f170(x80173,x80171,x80174))),x80174),f125(x80173))+~P22(f317(f317(f319(x80173),x80172),f317(f166(x80173),x80174))) % 168.22/168.06 [8143]P22(f317(x81431,x81432))+~P22(f317(f317(f319(x81433),x81432),f317(f166(x81433),x81434)))+P22(f317(f317(f226(a849),f317(f189(f850(x81433)),f317(f130(x81433,x81431),x81434))),f317(f189(f850(x81433)),x81434))) % 168.22/168.06 [8272]E(x82721,x82722)+P22(f317(f317(f194(x82723),x82721),f422(x82722,x82721,x82723,x82724)))+~P22(f317(f317(f194(f35(x82724,x82723)),x82721),x82722)) % 168.22/168.06 [8273]E(x82731,x82732)+P22(f317(f317(f194(x82733),x82731),f462(x82732,x82731,x82733,x82734)))+~P22(f317(f317(f194(f35(x82734,x82733)),x82731),x82732)) % 168.22/168.06 [8303]~P22(f317(x83034,x83032))+P22(f317(f317(f194(x83031),x83032),f422(x83033,x83032,x83031,x83034)))+~P22(f317(f317(f194(f35(x83034,x83031)),x83032),x83033)) % 168.22/168.06 [8304]~P22(f317(x83044,x83042))+P22(f317(f317(f194(x83041),x83042),f462(x83043,x83042,x83041,x83044)))+~P22(f317(f317(f194(f35(x83044,x83041)),x83042),x83043)) % 168.22/168.06 [8624]~P22(f317(x86241,f736(x86241,x86243,x86242,x86244)))+P22(f317(x86241,f317(f317(f159(x86242),x86243),x86244)))+~P22(f317(f317(f226(a849),x86244),f317(f189(f850(x86242)),x86243))) % 168.22/168.06 [8647]~P19(x86474,x86473,x86471,f233(f858(x86474,a842)))+E(f317(x86471,f840(x86472,x86471,x86473,x86474)),x86472)+~P22(f317(f317(f319(x86473),x86472),f317(f287(x86474,x86473,x86471),f233(f858(x86474,a842))))) % 168.22/168.06 [8710]E(f170(x87101,x87102,x87103),f317(f317(f167(x87101),x87104),x87103))+P22(f317(f317(f226(a849),f681(x87102,x87103,x87101,x87104)),x87104))+P22(f317(f317(f226(a849),x87104),f317(f189(f850(x87101)),x87103))) % 168.22/168.06 [8713]E(f170(x87131,x87132,x87133),f317(f317(f167(x87131),x87134),x87133))+P22(f317(f317(f226(a849),f681(x87132,x87133,x87131,x87134)),x87134))+P22(f317(x87132,f317(f317(f159(x87131),x87133),x87134))) % 168.22/168.06 [8741]P22(f317(x87411,x87412))+~P22(f317(f317(f319(x87414),x87412),f317(f166(x87414),x87413)))+P22(f317(f317(f226(a849),f697(x87412,x87411,x87413,x87414)),f317(f189(f850(x87414)),x87413))) % 168.22/168.06 [8744]E(f170(x87441,x87442,x87443),f317(f317(f167(x87441),x87444),x87443))+P22(f317(f317(f226(a849),x87444),f317(f189(f850(x87441)),x87443)))+P22(f317(f317(f226(a849),f681(x87442,x87443,x87441,x87444)),f317(f189(f850(x87441)),x87443))) % 168.22/168.06 [8750]E(f170(x87501,x87502,x87503),f317(f317(f167(x87501),x87504),x87503))+P22(f317(x87502,f317(f317(f159(x87501),x87503),x87504)))+P22(f317(f317(f226(a849),f681(x87502,x87503,x87501,x87504)),f317(f189(f850(x87501)),x87503))) % 168.22/168.06 [8809]~P22(f317(f71(x88091),x88094))+P22(f317(f317(f319(x88091),f523(x88092,x88093,x88094,x88091)),x88094))+P22(f317(f71(f857(x88091,x88093)),f317(f317(f245(x88091,x88093),x88094),x88092))) % 168.22/168.06 [8843]P22(f317(f317(f319(x88432),f736(x88431,x88433,x88432,x88434)),f317(f166(x88432),x88433)))+P22(f317(x88431,f317(f317(f159(x88432),x88433),x88434)))+~P22(f317(f317(f226(a849),x88434),f317(f189(f850(x88432)),x88433))) % 168.22/168.06 [8858]E(x88581,x88582)+P22(f317(f317(f194(f35(x88583,x88584)),f422(x88581,x88582,x88584,x88583)),x88581))+~P22(f317(f317(f194(f35(x88583,x88584)),x88582),x88581)) % 168.22/168.06 [8859]E(x88591,x88592)+P22(f317(f317(f194(f35(x88593,x88594)),f462(x88591,x88592,x88594,x88593)),x88591))+~P22(f317(f317(f194(f35(x88593,x88594)),x88592),x88591)) % 168.22/168.06 [8880]~P22(f317(x88801,x88804))+P22(f317(f317(f194(f35(x88801,x88802)),f422(x88803,x88804,x88802,x88801)),x88803))+~P22(f317(f317(f194(f35(x88801,x88802)),x88804),x88803)) % 168.22/168.06 [8881]~P22(f317(x88811,x88814))+P22(f317(f317(f194(f35(x88811,x88812)),f462(x88813,x88814,x88812,x88811)),x88813))+~P22(f317(f317(f194(f35(x88811,x88812)),x88814),x88813)) % 168.22/168.06 [8973]P22(f317(f317(f225(a849),x89734),f317(f189(f850(x89732)),f170(x89732,x89733,x89731))))+P22(f317(f317(f226(a849),f682(x89731,x89732,x89733,x89734)),x89734))+~P22(f317(f317(f225(a849),x89734),f317(f189(f850(x89732)),x89731))) % 168.22/168.06 [9074]~E(f317(f317(f171(x90741,x90742),x90743),f704(x90744,x90743,x90742,x90741)),f317(f317(f171(x90741,x90742),x90744),f704(x90744,x90743,x90742,x90741)))+E(f317(f171(x90741,x90742),x90743),f317(f171(x90741,x90742),x90744))+~E(f317(f166(x90741),f317(f317(f148(f857(x90741,x90742),x90741),f244(x90741,x90742)),x90743)),f317(f166(x90741),f317(f317(f148(f857(x90741,x90742),x90741),f244(x90741,x90742)),x90744))) % 168.22/168.06 [9120]E(f170(x91201,x91202,x91203),f317(f317(f167(x91201),x91204),x91203))+~P22(f317(x91202,f317(f317(f159(x91201),x91203),f681(x91202,x91203,x91201,x91204))))+P22(f317(f317(f226(a849),x91204),f317(f189(f850(x91201)),x91203))) % 168.22/168.06 [9124]E(f170(x91241,x91242,x91243),f317(f317(f167(x91241),x91244),x91243))+~P22(f317(x91242,f317(f317(f159(x91241),x91243),f681(x91242,x91243,x91241,x91244))))+P22(f317(x91242,f317(f317(f159(x91241),x91243),x91244))) % 168.22/168.06 [9131]~P22(f317(f71(x91311),x91313))+~P22(f317(f71(x91312),f317(x91314,f523(x91314,x91312,x91313,x91311))))+P22(f317(f71(f857(x91311,x91312)),f317(f317(f245(x91311,x91312),x91313),x91314))) % 168.22/168.06 [9145]~E(f317(f189(f850(x91454)),x91452),f317(f189(f850(x91454)),x91453))+P22(f317(f317(f319(f857(f850(x91454),f850(x91454))),f317(f317(f237(f850(x91454),f850(x91454)),x91453),x91452)),f152(x91454,x91451)))+P22(f317(f317(f226(a849),f599(x91451,x91452,x91453,x91454)),f317(f189(f850(x91454)),x91453))) % 168.22/168.06 [9199]~P22(f317(x91993,f317(f317(f159(x91992),x91994),f682(x91994,x91992,x91993,x91991))))+P22(f317(f317(f225(a849),x91991),f317(f189(f850(x91992)),f170(x91992,x91993,x91994))))+~P22(f317(f317(f225(a849),x91991),f317(f189(f850(x91992)),x91994))) % 168.22/168.06 [9274]E(f317(f317(f167(x92741),f601(x92742,x92743,x92744,x92741)),x92743),f317(f317(f167(x92741),f601(x92742,x92743,x92744,x92741)),x92744))+~P22(f317(f317(f319(f857(f850(x92741),f850(x92741))),f317(f317(f237(f850(x92741),f850(x92741)),x92744),x92743)),f141(x92741,x92742)))+P22(f317(f317(f226(a849),f317(f189(f850(x92741)),x92744)),f317(f189(f850(x92741)),x92743))) % 168.22/168.06 [9329]~P22(f317(f317(f226(a849),f2(a849)),x93293))+~P22(f317(f317(f226(a849),x93294),x93291))+P22(f317(f317(f226(a849),f317(f317(f89(a849),f317(f317(f90(a849),x93291),f55(a849,x93292,x93293))),x93294)),f317(f317(f90(a849),x93291),x93293))) % 168.22/168.06 [9516]~P102(x95162)+~P22(f317(f317(f225(x95162),f317(x95163,f793(x95164,x95163,x95161,x95162))),f317(x95164,f793(x95164,x95163,x95161,x95162))))+P22(f317(f317(f225(f858(x95161,x95162)),x95163),x95164)) % 168.22/168.06 [9617]~P25(x96171)+E(f317(f317(f6(a849,x96171),f317(f317(f18(a849,x96171,x96171),f317(f317(f8(x96171,f858(x96171,x96171),a849),f21(x96171)),x96172)),f317(f317(f8(a849,x96171,a849),x96172),f317(f317(f7(a849,a849,a849),f89(a849)),f87(a849))))),f279(a849,x96173,x96174)),f317(f317(f21(x96171),f317(x96172,x96173)),f317(x96172,f317(f317(f89(a849),x96174),f87(a849)))))+~P22(f317(f317(f225(a849),x96173),x96174)) % 168.22/168.06 [6701]E(f317(f317(f127(x67011),x67012),x67013),x67014)+~E(x67013,f317(f317(f132(x67011),f317(f189(f850(x67011)),x67012)),x67014))+~E(f317(f317(f167(x67011),f317(f189(f850(x67011)),x67012)),x67014),x67012) % 168.22/168.06 [6755]~P59(x67552)+E(x67551,f2(x67552))+E(f317(f317(f266(x67552),f317(f317(f238(x67552),x67553),x67554)),f317(f317(f238(x67552),x67551),x67554)),f317(f317(f238(x67552),f317(f317(f266(x67552),x67553),x67551)),x67554)) % 168.22/168.06 [6894]~E(f317(f189(f850(x68941)),x68943),f317(f189(f850(x68942)),x68944))+~P22(f317(f131(x68941),x68943))+E(f177(x68941,x68942,f317(f171(x68941,x68942),f317(f317(f175(x68941,x68942),x68943),x68944))),f317(f166(x68941),x68943)) % 168.22/168.06 [6914]~P98(x69141)+~P22(f317(f317(f225(x69141),x69143),x69144))+P22(f317(f317(f225(x69141),f317(f317(f113(x69141),x69142),x69143)),x69144)) % 168.22/168.06 [6915]~P98(x69151)+~P22(f317(f317(f225(x69151),x69152),x69154))+P22(f317(f317(f225(x69151),f317(f317(f113(x69151),x69152),x69153)),x69154)) % 168.22/168.06 [6917]~P103(x69171)+~P22(f317(f317(f225(x69171),x69173),x69174))+P22(f317(f317(f225(x69171),f317(f317(f223(x69171),x69172),x69173)),x69174)) % 168.22/168.06 [6919]~P103(x69191)+~P22(f317(f317(f225(x69191),x69192),x69194))+P22(f317(f317(f225(x69191),f317(f317(f223(x69191),x69192),x69193)),x69194)) % 168.22/168.06 [6920]~P98(x69201)+~P22(f317(f317(f226(x69201),x69203),x69204))+P22(f317(f317(f226(x69201),f317(f317(f113(x69201),x69202),x69203)),x69204)) % 168.22/168.06 [6921]~P98(x69211)+~P22(f317(f317(f226(x69211),x69212),x69214))+P22(f317(f317(f226(x69211),f317(f317(f113(x69211),x69212),x69213)),x69214)) % 168.22/168.06 [6923]~P103(x69231)+~P22(f317(f317(f226(x69231),x69233),x69234))+P22(f317(f317(f226(x69231),f317(f317(f223(x69231),x69232),x69233)),x69234)) % 168.22/168.06 [6925]~P103(x69251)+~P22(f317(f317(f226(x69251),x69252),x69254))+P22(f317(f317(f226(x69251),f317(f317(f223(x69251),x69252),x69253)),x69254)) % 168.22/168.06 [6944]~P22(f317(x69443,x69444))+~P22(f317(x69442,x69444))+P22(f317(f317(f317(f113(f858(x69441,a842)),x69442),x69443),x69444)) % 168.22/168.06 [7070]P18(x70701,x70702,x70703)+~P18(x70701,x70704,x70703)+~P22(f317(f317(f225(f858(f848(x70701),a842)),x70704),x70702)) % 168.22/168.06 [7071]P18(x70711,x70712,x70713)+~P18(x70711,x70712,x70714)+~P22(f317(f317(f225(f858(f848(x70711),a842)),x70713),x70714)) % 168.22/168.06 [7429]~P67(x74291)+E(f317(f317(f89(x74291),f317(x74292,x74293)),f317(f317(f6(a849,x74291),x74292),f317(f278(a849,f317(a124,x74293)),x74294))),f317(f317(f6(a849,x74291),x74292),f317(f278(a849,x74293),x74294)))+~P22(f317(f317(f226(a849),x74293),x74294)) % 168.22/168.06 [7459]~P103(x74591)+P22(f317(f317(f225(x74591),x74592),x74593))+~P22(f317(f317(f225(x74591),f317(f317(f224(x74591),x74594),x74592)),x74593)) % 168.22/168.06 [7461]~P103(x74611)+P22(f317(f317(f225(x74611),x74612),x74613))+~P22(f317(f317(f225(x74611),f317(f317(f224(x74611),x74612),x74614)),x74613)) % 168.22/168.06 [7463]~P92(x74631)+P22(f317(f317(f225(x74631),x74632),x74633))+~P22(f317(f317(f225(x74631),f317(f317(f122(x74631),x74634),x74632)),x74633)) % 168.22/168.06 [7465]~P92(x74651)+P22(f317(f317(f225(x74651),x74652),x74653))+~P22(f317(f317(f225(x74651),f317(f317(f122(x74651),x74652),x74654)),x74653)) % 168.22/168.06 [7466]~P103(x74661)+P22(f317(f317(f226(x74661),x74662),x74663))+~P22(f317(f317(f226(x74661),f317(f317(f224(x74661),x74664),x74662)),x74663)) % 168.22/168.06 [7467]~P103(x74671)+P22(f317(f317(f226(x74671),x74672),x74673))+~P22(f317(f317(f226(x74671),f317(f317(f224(x74671),x74672),x74674)),x74673)) % 168.22/168.06 [7542]~P22(f317(f317(f319(x75421),x75422),x75424))+P22(f317(f317(f319(x75421),x75422),x75423))+P22(f317(f317(f319(x75421),x75422),f317(f317(f21(f858(x75421,a842)),x75424),x75423))) % 168.22/168.06 [7626]P22(f317(x76261,x76262))+P22(f317(x76263,x76262))+~P22(f317(f317(f317(f122(f858(x76264,a842)),x76263),x76261),x76262)) % 168.22/168.06 [7637]~P22(f317(f317(f319(x76371),x76372),x76374))+~P22(f317(f317(f319(x76371),x76372),x76373))+P22(f317(f317(f319(x76371),x76372),f317(f317(f113(f858(x76371,a842)),x76373),x76374))) % 168.22/168.06 [7689]~P92(x76891)+~P22(f317(f71(x76891),x76894))+E(f317(f317(f74(x76891,x76891,f122(x76891)),x76892),f317(f317(f286(x76891),x76893),x76894)),f317(f317(f122(x76891),x76893),f317(f317(f74(x76891,x76891,f122(x76891)),x76892),x76894))) % 168.22/168.06 [7690]~P98(x76901)+~P22(f317(f71(x76901),x76904))+E(f317(f317(f74(x76901,x76901,f113(x76901)),x76902),f317(f317(f286(x76901),x76903),x76904)),f317(f317(f113(x76901),x76903),f317(f317(f74(x76901,x76901,f113(x76901)),x76902),x76904))) % 168.22/168.06 [7691]~P103(x76911)+~P22(f317(f71(x76911),x76914))+E(f317(f317(f74(x76911,x76911,f223(x76911)),x76912),f317(f317(f286(x76911),x76913),x76914)),f317(f317(f223(x76911),x76913),f317(f317(f74(x76911,x76911,f223(x76911)),x76912),x76914))) % 168.22/168.06 [7692]~P103(x76921)+~P22(f317(f71(x76921),x76924))+E(f317(f317(f74(x76921,x76921,f224(x76921)),x76922),f317(f317(f286(x76921),x76923),x76924)),f317(f317(f224(x76921),x76923),f317(f317(f74(x76921,x76921,f224(x76921)),x76922),x76924))) % 168.22/168.06 [7693]~P134(x76931)+~P88(x76931)+E(f317(f317(f89(x76931),f317(f317(f90(x76931),f317(f115(x76931),x76932)),x76933)),f317(f317(f90(x76931),f317(f115(x76931),x76932)),x76934)),f317(f317(f90(x76931),f317(f115(x76931),x76932)),f317(f317(f89(x76931),x76933),x76934))) % 168.22/168.06 [7694]~P126(x76941)+~P88(x76941)+E(f317(f317(f21(x76941),f317(f317(f90(x76941),f317(f115(x76941),x76942)),x76943)),f317(f317(f90(x76941),f317(f115(x76941),x76942)),x76944)),f317(f317(f90(x76941),f317(f115(x76941),x76942)),f317(f317(f21(x76941),x76943),x76944))) % 168.22/168.06 [7803]E(x78031,x78032)+P22(f317(f317(f319(x78033),x78031),f317(f166(x78033),x78034)))+~P22(f317(f317(f319(x78033),x78031),f317(f166(x78033),f317(f317(f145(x78033),x78032),x78034)))) % 168.22/168.06 [7825]~P57(x78251)+~E(f317(f189(f850(x78252)),x78253),f317(f189(f850(x78251)),f65(x78251)))+E(f317(f317(f171(x78251,x78252),f317(f317(f175(x78251,x78252),f65(x78251)),x78253)),x78254),f317(f217(x78252),f670(x78254,x78253,x78252,x78251))) % 168.22/168.06 [7974]P49(x79741,x79742,x79743)+~P49(x79741,x79742,x79744)+~P22(f317(f317(f225(f858(f857(x79741,x79742),a842)),x79743),x79744)) % 168.22/168.06 [8020]P22(f317(f317(f319(x80201),x80202),x80203))+P22(f317(f317(f319(x80201),x80202),x80204))+~P22(f317(f317(f319(x80201),x80202),f317(f317(f122(f858(x80201,a842)),x80204),x80203))) % 168.22/168.06 [8031]~P45(x80311,x80314,x80313)+~P22(f317(f317(f319(x80311),x80312),x80314))+P22(f317(f317(f319(f857(x80311,x80311)),f317(f317(f237(x80311,x80311),x80312),x80312)),x80313)) % 168.22/168.06 [8047]~P22(f317(f71(x80472),x80474))+~P22(f317(f71(x80471),x80473))+P22(f317(f71(f857(x80471,x80472)),f317(f317(f245(x80471,x80472),x80473),f317(f16(f858(x80472,a842),x80471),x80474)))) % 168.22/168.06 [8048]~P22(f317(f317(f319(x80481),x80482),x80484))+~P22(f317(f317(f225(f858(x80481,a842)),x80483),x80484))+P22(f317(f317(f225(f858(x80481,a842)),f317(f317(f286(x80481),x80482),x80483)),x80484)) % 168.22/168.06 [8056]~P110(x80562)+~P70(x80562)+E(f317(f317(f9(x80561,x80562),f317(f317(f8(a849,x80562,x80561),f112(x80562)),x80563)),x80564),f317(f112(x80562),f317(f317(f9(x80561,a849),x80563),x80564))) % 168.22/168.06 [8057]~P111(x80572)+~P70(x80572)+E(f317(f317(f9(x80571,x80572),f317(f317(f8(a1,x80572,x80571),f114(x80572)),x80573)),x80574),f317(f114(x80572),f317(f317(f9(x80571,a1),x80573),x80574))) % 168.22/168.06 [8081]E(f317(f317(f21(f858(x80811,a842)),x80812),f317(f317(f21(f858(x80811,a842)),x80813),x80814)),x80814)+~P22(f317(f317(f225(f858(x80811,a842)),x80812),x80813))+~P22(f317(f317(f225(f858(x80811,a842)),x80814),x80812)) % 168.22/168.06 [8178]~P22(f317(f71(x81781),x81784))+E(f317(f317(f21(a849),f317(f317(f6(x81781,a849),x81782),x81783)),f317(f317(f6(x81781,a849),x81782),x81784)),f317(f317(f6(x81781,a849),x81782),f317(f317(f21(f858(x81781,a842)),x81783),x81784)))+~P22(f317(f317(f225(f858(x81781,a842)),x81784),x81783)) % 168.22/168.06 [8338]~P6(x83381,x83384,x83383)+~P22(f317(f317(f319(x83381),x83382),x83384))+P22(f317(f317(f319(x83381),x83382),f317(f262(x83381,x83381,x83383),f317(f317(f286(x83381),x83382),f188(f858(x83381,a842)))))) % 168.22/168.06 [8402]~P22(f317(f317(f225(f858(x84021,a842)),x84022),x84023))+~P22(f317(f317(f225(f858(x84021,a842)),x84022),x84024))+P22(f317(f317(f225(f858(x84021,a842)),x84022),f317(f317(f113(f858(x84021,a842)),x84023),x84024))) % 168.22/168.06 [8505]E(x85051,f188(f858(x85052,a842)))+P22(f317(f71(x85053),x85054))+~P22(f317(f71(f857(x85053,x85052)),f317(f317(f245(x85053,x85052),x85054),f317(f16(f858(x85052,a842),x85053),x85051)))) % 168.22/168.06 [8506]E(x85061,f188(f858(x85062,a842)))+P22(f317(f71(x85063),x85064))+~P22(f317(f71(f857(x85062,x85063)),f317(f317(f245(x85062,x85063),x85061),f317(f16(f858(x85063,a842),x85062),x85064)))) % 168.22/168.06 [8567]P22(f317(f317(f319(x85671),x85672),f306(x85671,x85673)))+~P22(f317(f317(f319(x85671),x85674),f306(x85671,x85673)))+~P22(f317(f317(f319(f857(x85671,x85671)),f317(f317(f237(x85671,x85671),x85672),x85674)),x85673)) % 168.22/168.06 [8619]~P37(x86191,x86194)+P22(f317(f317(f319(f857(x86191,x86191)),f317(f317(f237(x86191,x86191),x86193),x86192)),f284(x86191,x86194)))+P37(x86191,f317(f317(f286(f857(x86191,x86191)),f317(f317(f237(x86191,x86191),x86192),x86193)),x86194)) % 168.22/168.06 [8620]~P52(x86201,x86204)+P22(f317(f317(f319(f857(x86201,x86201)),f317(f317(f237(x86201,x86201),x86203),x86202)),f284(x86201,x86204)))+P52(x86201,f317(f317(f286(f857(x86201,x86201)),f317(f317(f237(x86201,x86201),x86202),x86203)),x86204)) % 168.22/168.06 [8695]~E(x86952,x86953)+~P22(f317(f317(f319(x86951),x86952),f317(f166(x86951),x86954)))+P22(f317(f317(f319(f857(x86951,x86951)),f317(f317(f237(x86951,x86951),x86952),x86953)),f317(f166(f857(x86951,x86951)),f317(f317(f175(x86951,x86951),x86954),x86954)))) % 168.22/168.06 [8775]~E(x87753,x87754)+P22(f317(f317(f247(x87751,x87751,a842),a314),x87752))+~P22(f317(f317(f319(f857(x87751,x87751)),x87752),f317(f166(f857(x87751,x87751)),f317(f317(f175(x87751,x87751),x87753),x87754)))) % 168.22/168.06 [8800]~P22(f317(x88004,x88002))+P22(f317(f317(f317(f317(a197,x88001),x88002),x88003),f379(x88003,x88002,x88001,x88004)))+~P22(f317(f317(f317(f317(a197,f35(x88004,x88001)),x88002),x88003),x88002)) % 168.22/168.06 [8827]P22(f317(f317(f319(f857(f850(x88271),f850(x88271))),f317(f317(f237(f850(x88271),f850(x88271)),x88272),x88273)),f141(x88271,x88274)))+~E(f317(f317(f167(x88271),f317(f189(f850(x88271)),x88272)),x88273),x88272)+~P22(f317(f317(f226(a849),f317(f189(f850(x88271)),x88272)),f317(f189(f850(x88271)),x88273))) % 168.22/168.06 [8928]~P22(f317(f71(x89281),x89284))+P22(f317(f317(f319(x89281),f483(x89282,x89283,x89284,x89281)),x89284))+P22(f317(f71(x89283),f317(f317(f51(x89281,f858(x89283,a842)),x89284),x89282))) % 168.22/168.06 [8929]~P22(f317(f71(x89291),x89294))+P22(f317(f317(f319(x89291),f582(x89292,x89293,x89294,x89291)),x89294))+P22(f317(f71(x89293),f317(f317(f51(x89291,f858(x89293,a842)),x89294),x89292))) % 168.22/168.06 [9006]P22(f317(f317(f319(f857(x90061,x90061)),x90062),f317(f317(f265(x90061,x90061,x90061),x90063),f284(x90061,x90063))))+~P22(f317(f317(f226(a849),f2(a849)),x90064))+~P22(f317(f317(f319(f857(x90061,x90061)),x90062),f317(f317(f182(f857(x90061,x90061),a842),x90064),x90063))) % 168.22/168.06 [9014]~P37(x90141,x90142)+~P22(f317(f317(f319(f857(x90141,x90141)),f317(f317(f237(x90141,x90141),x90144),x90143)),x90142))+~P22(f317(f317(f319(f857(x90141,x90141)),f317(f317(f237(x90141,x90141),x90143),x90144)),x90142)) % 168.22/168.06 [9139]~P22(f317(f71(x91391),x91394))+E(f317(f317(f6(x91391,a849),f317(f317(f8(f858(x91392,a842),a849,x91391),f54(x91392)),x91393)),x91394),f317(f54(f857(x91391,x91392)),f317(f317(f245(x91391,x91392),x91394),x91393)))+P22(f317(f317(f319(x91391),f524(x91393,x91392,x91394,x91391)),x91394)) % 168.22/168.06 [9141]~P22(f317(f131(x91411),x91412))+P22(f317(f131(x91411),f317(f317(f153(x91411,x91412),x91413),x91414)))+P22(f317(f317(f319(x91411),x91414),f317(f317(f21(f858(x91411,a842)),f317(f166(x91411),x91412)),f317(f317(f286(x91411),f317(f317(f159(x91411),x91412),x91413)),f188(f858(x91411,a842)))))) % 168.22/168.06 [9158]~P22(f317(f71(x91582),x91583))+~P22(f317(f71(x91581),f317(x91584,f483(x91584,x91581,x91583,x91582))))+P22(f317(f71(x91581),f317(f317(f51(x91582,f858(x91581,a842)),x91583),x91584))) % 168.22/168.06 [9159]~P22(f317(f71(x91592),x91593))+~P22(f317(f71(x91591),f317(x91594,f582(x91594,x91591,x91593,x91592))))+P22(f317(f71(x91591),f317(f317(f51(x91592,f858(x91591,a842)),x91593),x91594))) % 168.22/168.06 [9235]~P22(f317(f317(f319(f857(x92351,x92351)),x92352),f317(f317(f265(x92351,x92351,x92351),x92354),f284(x92351,x92354))))+P22(f317(f317(f319(f857(x92351,x92351)),x92352),f317(f317(f265(x92351,x92351,x92351),x92353),f284(x92351,x92353))))+~P22(f317(f317(f225(f858(f857(x92351,x92351),a842)),x92354),x92353)) % 168.22/168.06 [9241]E(f317(f317(f167(x92411),f601(x92414,x92413,x92412,x92411)),x92413),f317(f317(f167(x92411),f601(x92414,x92413,x92412,x92411)),x92412))+~P22(f317(f317(f319(f857(f850(x92411),f850(x92411))),f317(f317(f237(f850(x92411),f850(x92411)),x92412),x92413)),f141(x92411,x92414)))+E(f317(f317(f167(x92411),f317(f189(f850(x92411)),x92412)),x92413),x92412) % 168.22/168.06 [9259]~P22(f317(f71(x92591),x92594))+E(f317(f317(f6(x92591,a849),f317(f317(f8(f858(x92592,a842),a849,x92591),f54(x92592)),x92593)),x92594),f317(f54(f857(x92591,x92592)),f317(f317(f245(x92591,x92592),x92594),x92593)))+~P22(f317(f71(x92592),f317(x92593,f524(x92593,x92592,x92594,x92591)))) % 168.22/168.06 [9263]~E(f317(f189(f850(x92631)),x92633),f317(f189(f850(x92631)),x92632))+P22(f317(f317(f319(f857(f850(x92631),f850(x92631))),f317(f317(f237(f850(x92631),f850(x92631)),x92632),x92633)),f152(x92631,x92634)))+P22(f317(f317(f319(f857(x92631,x92631)),f588(x92634,x92633,x92632,x92631)),f317(f166(f857(x92631,x92631)),f317(f317(f175(x92631,x92631),x92632),x92633)))) % 168.22/168.06 [9341]~P22(f317(f317(f319(f857(f850(x93411),f850(x93411))),f317(f317(f237(f850(x93411),f850(x93411)),x93412),x93413)),f141(x93411,x93414)))+E(f317(f317(f167(x93411),f317(f189(f850(x93411)),x93412)),x93413),x93412)+P22(f317(f317(f226(a849),f601(x93414,x93413,x93412,x93411)),f317(f317(f223(a849),f317(f189(f850(x93411)),x93412)),f317(f189(f850(x93411)),x93413)))) % 168.22/168.06 [9342]E(f317(f171(x93421,x93422),x93423),f317(f171(x93421,x93422),x93424))+~E(f317(f166(x93421),f317(f317(f148(f857(x93421,x93422),x93421),f244(x93421,x93422)),x93423)),f317(f166(x93421),f317(f317(f148(f857(x93421,x93422),x93421),f244(x93421,x93422)),x93424)))+P22(f317(f317(f319(x93421),f704(x93423,x93424,x93422,x93421)),f317(f166(x93421),f317(f317(f148(f857(x93421,x93422),x93421),f244(x93421,x93422)),x93424)))) % 168.22/168.06 [9355]~P22(f317(x93551,x93554))+P22(f317(f317(f317(f317(a197,f35(x93551,x93552)),f379(x93553,x93554,x93552,x93551)),x93553),x93554))+~P22(f317(f317(f317(f317(a197,f35(x93551,x93552)),x93554),x93553),x93554)) % 168.22/168.06 [9360]~P22(f317(f317(f319(f857(f850(x93601),f850(x93601))),f317(f317(f237(f850(x93601),f850(x93601)),x93602),x93603)),f141(x93601,x93604)))+P22(f317(f317(f226(a849),f317(f189(f850(x93601)),x93602)),f317(f189(f850(x93601)),x93603)))+P22(f317(f317(f226(a849),f601(x93604,x93603,x93602,x93601)),f317(f317(f223(a849),f317(f189(f850(x93601)),x93602)),f317(f189(f850(x93601)),x93603)))) % 168.22/168.06 [9653]~P22(f317(f317(f317(x96531,f344(x96531,x96534,x96533,x96532)),f347(x96531,x96534,x96533,x96532)),f348(x96531,x96534,x96533,x96532)))+P22(f317(f317(f317(x96531,x96532),x96533),x96534))+~P22(f317(f305(f857(f858(a1,f853(f850(a313))),f857(a1,a1)),a295),f317(f317(f237(f858(a1,f853(f850(a313))),f857(a1,a1)),x96532),f317(f317(f237(a1,a1),x96533),x96534)))) % 168.22/168.06 [9732]P22(f317(f317(f317(x97321,x97322),x97323),x97324))+P22(f317(f305(f857(f858(a1,f853(f850(a313))),f857(a1,a1)),a295),f317(f317(f237(f858(a1,f853(f850(a313))),f857(a1,a1)),f344(x97321,x97324,x97323,x97322)),f317(f317(f237(a1,a1),f347(x97321,x97324,x97323,x97322)),f348(x97321,x97324,x97323,x97322)))))+~P22(f317(f305(f857(f858(a1,f853(f850(a313))),f857(a1,a1)),a295),f317(f317(f237(f858(a1,f853(f850(a313))),f857(a1,a1)),x97322),f317(f317(f237(a1,a1),x97323),x97324)))) % 168.22/168.06 [9772]~P22(f317(f317(f319(f857(f850(x97721),f850(x97721))),f317(f317(f237(f850(x97721),f850(x97721)),x97722),x97723)),f141(x97721,x97724)))+E(f317(f317(f167(x97721),f317(f189(f850(x97721)),x97722)),x97723),x97722)+P22(f317(f317(f319(f857(x97721,x97721)),f317(f317(f237(x97721,x97721),f317(f317(f159(x97721),x97722),f601(x97724,x97723,x97722,x97721))),f317(f317(f159(x97721),x97723),f601(x97724,x97723,x97722,x97721)))),x97724)) % 168.22/168.06 [9775]~P22(f317(f317(f319(f857(f850(x97751),f850(x97751))),f317(f317(f237(f850(x97751),f850(x97751)),x97752),x97753)),f141(x97751,x97754)))+P22(f317(f317(f226(a849),f317(f189(f850(x97751)),x97752)),f317(f189(f850(x97751)),x97753)))+P22(f317(f317(f319(f857(x97751,x97751)),f317(f317(f237(x97751,x97751),f317(f317(f159(x97751),x97752),f601(x97754,x97753,x97752,x97751))),f317(f317(f159(x97751),x97753),f601(x97754,x97753,x97752,x97751)))),x97754)) % 168.22/168.06 [9834]~E(f317(f189(f850(x98341)),x98342),f317(f189(f850(x98341)),x98343))+P22(f317(f317(f319(f857(f850(x98341),f850(x98341))),f317(f317(f237(f850(x98341),f850(x98341)),x98342),x98343)),f152(x98341,x98344)))+~P22(f317(f317(f319(f857(x98341,x98341)),f317(f317(f237(x98341,x98341),f317(f317(f159(x98341),x98342),f599(x98344,x98343,x98342,x98341))),f317(f317(f159(x98341),x98343),f599(x98344,x98343,x98342,x98341)))),x98344)) % 168.22/168.06 [9971]~P67(x99711)+~P22(f317(f71(x99712),x99714))+E(f317(f160(x99711),f317(f317(f148(x99712,x99711),x99713),f99(f850(x99712),f317(f317(f18(f850(x99712),a842,a842),f317(f317(f8(a842,f858(a842,a842),f850(x99712)),a315),f317(f317(f7(f850(x99712),f858(x99712,a842),a842),f317(f317(f8(f858(x99712,a842),f858(f858(x99712,a842),a842),f850(x99712)),a314),f166(x99712))),x99714))),f131(x99712))))),f216(x99712,x99711,x99713,x99714)) % 168.22/168.06 [7197]~P55(x71972)+E(x71971,f2(x71972))+E(f317(f48(x71972,f317(f317(f89(x71972),x71973),f317(f317(f90(x71972),x71974),x71971))),x71971),f317(f317(f89(x71972),x71974),f317(f48(x71972,x71973),x71971))) % 168.22/168.06 [7198]~P55(x71982)+E(x71981,f2(x71982))+E(f317(f48(x71982,f317(f317(f89(x71982),x71983),f317(f317(f90(x71982),x71981),x71984))),x71981),f317(f317(f89(x71982),x71984),f317(f48(x71982,x71983),x71981))) % 168.22/168.06 [7275]~P58(x72752)+E(x72751,f2(x72752))+E(f317(f317(f266(x72752),f317(f317(f89(x72752),x72753),f317(f317(f90(x72752),x72754),x72751))),x72751),f317(f317(f89(x72752),x72754),f317(f317(f266(x72752),x72753),x72751))) % 168.22/168.06 [7506]~P58(x75062)+E(x75061,f2(x75062))+E(f317(f317(f266(x75062),f317(f317(f89(x75062),x75063),f317(f317(f90(x75062),x75064),x75061))),x75061),f317(f317(f89(x75062),f317(f317(f266(x75062),x75063),x75061)),x75064)) % 168.22/168.06 [7507]~P59(x75072)+E(x75071,f2(x75072))+E(f317(f317(f266(x75072),f317(f317(f89(x75072),x75073),f317(f317(f90(x75072),x75071),x75074))),x75071),f317(f317(f89(x75072),f317(f317(f266(x75072),x75073),x75071)),x75074)) % 168.22/168.06 [7508]~P59(x75082)+E(x75081,f2(x75082))+E(f317(f317(f266(x75082),f317(f317(f21(x75082),x75083),f317(f317(f90(x75082),x75081),x75084))),x75081),f317(f317(f21(x75082),f317(f317(f266(x75082),x75083),x75081)),x75084)) % 168.22/168.06 [8206]~P22(f317(f154(x82061,x82063),x82064))+~P22(f317(f154(x82061,x82062),x82064))+P22(f317(f154(x82061,f317(f317(f113(f858(x82061,a842)),x82062),x82063)),x82064)) % 168.22/168.06 [8581]~E(f317(f317(f265(x85811,x85811,x85811),x85812),x85814),f188(f858(f857(x85811,x85811),a842)))+~E(f317(f317(f265(x85811,x85811,x85811),x85812),x85813),f188(f858(f857(x85811,x85811),a842)))+E(f317(f317(f265(x85811,x85811,x85811),x85812),f317(f317(f122(f858(f857(x85811,x85811),a842)),x85813),x85814)),f188(f858(f857(x85811,x85811),a842))) % 168.22/168.06 [8696]~P22(f317(f317(f225(f858(x86961,a842)),x86963),x86964))+~P22(f317(f317(f225(f858(x86961,a842)),x86962),x86964))+P22(f317(f317(f225(f858(x86961,a842)),f317(f317(f122(f858(x86961,a842)),x86962),x86963)),x86964)) % 168.22/168.06 [9068]~P22(f317(f71(x90681),x90684))+~P22(f317(f71(x90681),x90683))+E(f317(f317(f21(a849),f317(f317(f89(a849),f317(f317(f6(x90681,a849),x90682),x90683)),f317(f317(f6(x90681,a849),x90682),x90684))),f317(f317(f6(x90681,a849),x90682),f317(f317(f113(f858(x90681,a842)),x90683),x90684))),f317(f317(f6(x90681,a849),x90682),f317(f317(f122(f858(x90681,a842)),x90683),x90684))) % 168.22/168.06 [9154]~P22(f317(f317(f319(x91541),x91543),x91542))+~P22(f317(f317(f225(f858(x91541,a842)),x91542),f317(f317(f286(x91541),x91543),x91544)))+P22(f317(f317(f225(f858(x91541,a842)),f317(f317(f21(f858(x91541,a842)),x91542),f317(f317(f286(x91541),x91543),f188(f858(x91541,a842))))),x91544)) % 168.22/168.06 [9313]~P22(f317(f317(f319(x93131),x93133),x93132))+P22(f317(f317(f225(f858(x93131,a842)),x93132),f317(f317(f286(x93131),x93133),x93134)))+~P22(f317(f317(f225(f858(x93131,a842)),f317(f317(f21(f858(x93131,a842)),x93132),f317(f317(f286(x93131),x93133),f188(f858(x93131,a842))))),x93134)) % 168.22/168.06 [9404]~P22(f317(f317(f225(a849),x94041),x94043))+~P22(f317(f317(f226(a849),x94042),x94044))+P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),f317(f317(f237(a849,a849),x94041),x94042)),f317(f317(f237(a849,a849),x94043),x94044))),a45)) % 168.22/168.06 [9405]~P22(f317(f317(f225(a849),x94052),x94054))+~P22(f317(f317(f225(a849),x94051),x94053))+P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),f317(f317(f237(a849,a849),x94051),x94052)),f317(f317(f237(a849,a849),x94053),x94054))),a79)) % 168.22/168.06 [9689]~P22(f317(f317(f319(f850(x96891)),x96894),f155(x96891,x96893)))+~P22(f317(f317(f319(f850(x96891)),x96894),f155(x96891,x96892)))+P22(f317(f154(x96891,f317(f317(f113(f858(x96891,a842)),f317(f317(f7(x96891,f858(x96891,a842),a842),f319(x96891)),x96892)),f317(f317(f7(x96891,f858(x96891,a842),a842),f319(x96891)),x96893))),x96894)) % 168.22/168.06 [9799]~P19(x97991,f858(f858(x97991,a842),a842),f317(f317(f7(x97991,f858(f857(x97991,x97991),a842),f858(f858(x97991,a842),a842)),f317(f317(f8(f858(x97991,a842),f858(f858(f857(x97991,x97991),a842),f858(f858(x97991,a842),a842)),x97991),f70(x97991)),f317(f317(f7(x97991,f858(x97991,a842),f858(x97991,a842)),f286(x97991)),f188(f858(x97991,a842))))),x97993),x97992)+~P22(f317(f317(f319(x97991),x97994),x97992))+E(f317(f317(f21(f858(f858(x97991,a842),a842)),f317(f317(f70(x97991),x97992),x97993)),f317(f317(f70(x97991),f317(f317(f286(x97991),x97994),f188(f858(x97991,a842)))),x97993)),f317(f317(f70(x97991),f317(f317(f21(f858(x97991,a842)),x97992),f317(f317(f286(x97991),x97994),f188(f858(x97991,a842))))),x97993)) % 168.22/168.06 [9937]~P45(x99371,x99372,x99374)+~P22(f317(f317(f319(f857(x99371,x99371)),x99373),x99374))+P22(f317(f317(f247(x99371,x99371,a842),f317(f317(f7(x99371,f858(x99371,a842),f858(x99371,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x99371,a842),f858(x99371,a842)),x99371),f8(a842,a842,x99371)),f317(f317(f8(a842,f858(a842,a842),x99371),a315),f317(f317(f7(x99371,f858(x99371,a842),a842),f319(x99371)),x99372)))),f317(f317(f7(x99371,f858(x99371,a842),a842),f319(x99371)),x99372))),x99373)) % 168.22/168.06 [9949]P22(f317(f71(x99491),x99492))+~P22(f317(f71(x99493),f317(f287(x99491,x99493,x99494),x99492)))+~P22(f317(f71(x99491),f317(f230(x99491),f317(f317(f18(x99491,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99491),a315),f317(f317(f7(x99491,f858(x99491,a842),a842),f319(x99491)),x99492))),f317(f317(f7(x99491,x99493,a842),f317(f317(f8(x99493,f858(x99493,a842),x99491),a314),x99494)),f317(x99494,f567(x99494,x99493,x99492,x99491))))))) % 168.22/168.06 [7956]~P59(x79562)+E(x79561,f2(x79562))+E(f317(f317(f266(x79562),f317(f317(f89(x79562),f317(f317(f90(x79562),x79561),x79563)),x79564)),x79561),f317(f317(f89(x79562),x79563),f317(f317(f266(x79562),x79564),x79561))) % 168.22/168.06 [7957]~P59(x79572)+E(x79571,f2(x79572))+E(f317(f317(f266(x79572),f317(f317(f21(x79572),f317(f317(f90(x79572),x79571),x79573)),x79574)),x79571),f317(f317(f21(x79572),x79573),f317(f317(f266(x79572),x79574),x79571))) % 168.22/168.06 [8857]~E(f317(f317(f265(x88571,x88571,x88571),x88573),x88574),f188(f858(f857(x88571,x88571),a842)))+~E(f317(f317(f265(x88571,x88571,x88571),x88572),x88574),f188(f858(f857(x88571,x88571),a842)))+E(f317(f317(f265(x88571,x88571,x88571),f317(f317(f122(f858(f857(x88571,x88571),a842)),x88572),x88573)),x88574),f188(f858(f857(x88571,x88571),a842))) % 168.22/168.06 [9882]~P137(x98821)+~P137(x98822)+E(f317(f317(f294(x98821),f317(f317(f7(x98821,a111,f853(f850(a313))),f317(f317(f8(f858(x98822,f853(f850(a313))),f858(a111,f853(f850(a313))),x98821),f294(x98822)),f317(f317(f8(f858(x98822,f857(x98821,x98822)),f858(x98822,f853(f850(a313))),x98821),f317(f8(f857(x98821,x98822),f853(f850(a313)),x98822),x98823)),f237(x98821,x98822)))),x98824)),x98824),f317(f317(f294(f857(x98821,x98822)),x98823),x98824)) % 168.22/168.06 [9602]~P22(f317(f154(x96021,x96023),x96024))+~P22(f317(f154(x96021,x96022),x96024))+P22(f317(f154(x96021,f317(f317(f18(x96021,a842,a842),f317(f317(f8(a842,f858(a842,a842),x96021),a315),x96022)),x96023)),x96024)) % 168.22/168.06 [9874]P22(f317(x98741,f551(x98742,x98743,x98741,x98744)))+~P22(f317(f71(x98744),f317(f230(x98744),x98741)))+P22(f317(f71(x98743),f317(f230(x98743),f317(f317(f8(f858(x98744,a842),a842,x98743),f96(x98744)),f317(f317(f8(f858(x98744,a842),f858(x98744,a842),x98743),f317(f18(x98744,a842,a842),f317(f317(f8(a842,f858(a842,a842),x98744),a315),x98741))),x98742))))) % 168.22/168.06 [9893]~P22(f317(f71(x98932),f317(f230(x98932),x98933)))+~P22(f317(f71(x98931),f317(f230(x98931),f317(f317(f7(x98931,x98932,a842),x98934),f551(x98934,x98931,x98933,x98932)))))+P22(f317(f71(x98931),f317(f230(x98931),f317(f317(f8(f858(x98932,a842),a842,x98931),f96(x98932)),f317(f317(f8(f858(x98932,a842),f858(x98932,a842),x98931),f317(f18(x98932,a842,a842),f317(f317(f8(a842,f858(a842,a842),x98932),a315),x98933))),x98934))))) % 168.22/168.06 [7648]~P32(x76481,x76482,x76483,x76485)+P32(x76481,x76482,x76483,x76484)+~P32(x76481,x76482,x76485,x76484) % 168.22/168.06 [6428]E(x64281,x64282)+~E(f317(x64283,x64281),f317(x64283,x64282))+~P19(x64284,x64285,x64283,f233(f858(x64284,a842))) % 168.22/168.06 [6588]~E(f317(x65883,x65885),f191(x65882))+~E(f317(x65884,x65885),f191(x65882))+E(f317(f178(x65881,x65882,x65883,x65884),x65885),f191(x65882)) % 168.22/168.06 [7309]E(x73091,x73092)+~P19(x73093,x73094,x73095,f233(f858(x73093,a842)))+~E(f317(f287(x73093,x73094,x73095),x73091),f317(f287(x73093,x73094,x73095),x73092)) % 168.22/168.06 [7450]~P32(x74504,x74505,x74501,x74503)+E(f317(x74501,x74502),f317(x74503,x74502))+~P22(f317(f317(f319(x74504),x74502),f177(x74504,x74505,x74501))) % 168.22/168.06 [7558]P19(x75582,x75583,f815(x75584,x75583,x75582,x75581),x75581)+~E(f317(f287(x75583,x75582,x75585),x75584),x75581)+E(x75581,f188(f858(x75582,a842))) % 168.22/168.06 [8093]~P22(f317(f317(x80933,x80932),x80935))+~P22(f317(f317(x80933,x80934),x80932))+P22(f317(f317(f319(x80931),x80932),f275(x80931,x80933,x80934,x80935))) % 168.22/168.06 [8094]~P22(f317(f317(x80943,x80942),x80945))+~P22(f317(f317(x80943,x80944),x80942))+P22(f317(f317(f319(x80941),x80942),f272(x80941,x80943,x80944,x80945))) % 168.22/168.06 [8656]~P19(x86561,x86563,x86565,f233(f858(x86561,a842)))+~P19(x86563,x86562,x86564,f233(f858(x86563,a842)))+P19(x86561,x86562,f317(f82(x86563,x86562,x86561,x86564),x86565),f233(f858(x86561,a842))) % 168.22/168.06 [9213]P22(f317(f317(f319(f857(x92131,x92131)),f317(f317(f237(x92131,x92131),x92132),x92133)),f284(x92131,x92134)))+~P22(f317(f317(f319(f857(x92131,x92131)),f317(f317(f237(x92131,x92131),x92132),x92135)),f284(x92131,x92134)))+~P22(f317(f317(f319(f857(x92131,x92131)),f317(f317(f237(x92131,x92131),x92135),x92133)),f284(x92131,x92134))) % 168.22/168.06 [9248]~P103(x92482)+~P22(f317(f131(x92481),x92485))+P22(f317(f131(x92481),f144(x92481,x92482,x92483,x92484,x92485))) % 168.22/168.06 [9402]E(f317(f297(x94022,x94021),f792(x94023,x94024,x94025,x94022,x94021)),x94025)+E(f317(f288(x94021,x94022),f788(x94023,x94024,x94025,x94022,x94021)),x94025)+~P22(f317(f317(f319(f856(x94021,x94022)),x94025),f298(x94021,x94022,x94024,x94023))) % 168.22/168.06 [5286]~E(x52862,f125(x52861))+E(f317(f317(f127(x52861),x52862),x52863),f317(f317(f145(x52861),x52864),x52865))+~E(x52863,f317(f317(f145(x52861),x52864),x52865)) % 168.22/168.06 [5287]~E(x52872,f125(x52871))+E(f317(f317(f127(x52871),x52872),x52873),f317(f317(f145(x52871),x52874),x52875))+~E(f317(f317(f145(x52871),x52874),x52875),x52873) % 168.22/168.06 [6386]~E(f317(f189(f850(x63861)),x63865),f317(f189(f850(x63862)),x63864))+E(f317(f317(f148(f857(x63861,x63862),x63862),f246(x63861,x63862)),x63863),x63864)+~E(f317(f317(f175(x63861,x63862),x63865),x63864),x63863) % 168.22/168.06 [6387]~E(f317(f189(f850(x63871)),x63874),f317(f189(f850(x63872)),x63875))+E(f317(f317(f148(f857(x63871,x63872),x63871),f244(x63871,x63872)),x63873),x63874)+~E(f317(f317(f175(x63871,x63872),x63874),x63875),x63873) % 168.22/168.06 [6847]~P103(x68471)+~P29(x68471,f317(f317(f148(x68472,x68471),x68473),x68475))+P29(x68471,f317(f317(f148(x68472,x68471),x68473),f317(f130(x68472,x68474),x68475))) % 168.22/168.06 [6900]~P22(f317(x69003,x69005))+~P22(f317(f317(x69002,x69004),x69005))+P22(f317(f317(f103(x69001,x69002,x69003),x69004),x69005)) % 168.22/168.06 [6999]~P103(x69991)+P29(x69991,f317(f317(f148(x69992,x69991),x69993),f164(x69992,x69994,x69995)))+~P29(x69991,f317(f317(f148(x69992,x69991),x69993),x69995)) % 168.22/168.06 [7020]~P49(x70203,x70202,x70205)+~P49(x70201,x70203,x70204)+P49(x70201,x70202,f317(f317(f265(x70201,x70203,x70202),x70204),x70205)) % 168.22/168.06 [7114]E(x71141,x71142)+~P19(x71143,x71144,x71145,f233(f858(x71143,a842)))+~E(f317(f317(f148(x71143,x71144),x71145),x71141),f317(f317(f148(x71143,x71144),x71145),x71142)) % 168.22/168.06 [7260]~P22(f317(f317(f225(a849),x72601),f317(x72603,x72605)))+P22(f317(f317(f225(a849),x72601),f149(x72602,x72603,x72604)))+~P22(f317(f317(f319(x72602),x72605),f317(f166(x72602),x72604))) % 168.22/168.06 [7261]~P22(f317(f317(f226(a849),x72611),f317(x72613,x72615)))+P22(f317(f317(f226(a849),x72611),f149(x72612,x72613,x72614)))+~P22(f317(f317(f319(x72612),x72615),f317(f166(x72612),x72614))) % 168.22/168.06 [7664]~P104(x76641)+P22(f317(f317(f225(f858(x76641,a842)),f279(x76641,x76642,x76643)),f279(x76641,x76644,x76645)))+P22(f317(f317(f225(x76641),x76642),x76643)) % 168.22/168.06 [7687]~P27(x76871)+P22(f317(f317(f225(x76871),f317(f317(f52(x76872,x76871),x76873),x76874)),f317(x76874,x76875)))+~P22(f317(f317(f319(x76872),x76875),x76873)) % 168.22/168.06 [7754]~P19(x77541,x77542,x77544,x77543)+E(f317(f86(x77541,x77542,x77543,x77544),f317(x77544,x77545)),x77545)+~P22(f317(f317(f319(x77541),x77545),x77543)) % 168.22/168.06 [7944]~P22(f317(x79441,x79445))+P22(f317(x79441,f804(x79441,x79442,x79443,x79444)))+~P22(f317(f317(f319(x79444),x79445),x79443)) % 168.22/168.06 [7945]~P22(f317(x79451,x79455))+P22(f317(x79451,f804(x79451,x79452,x79453,x79454)))+~P22(f317(f317(f319(x79454),x79455),x79452)) % 168.22/168.06 [8044]P22(f317(f71(x80441),x80442))+~P22(f317(f71(x80443),x80444))+~P22(f317(f317(f225(f858(x80441,a842)),x80442),f317(f287(x80443,x80441,x80445),x80444))) % 168.22/168.06 [8209]E(x82091,x82092)+~P19(x82093,x82094,x82095,f317(f317(f122(f858(x82093,a842)),f317(f166(x82093),x82091)),f317(f166(x82093),x82092)))+~E(f317(f317(f148(x82093,x82094),x82095),x82091),f317(f317(f148(x82093,x82094),x82095),x82092)) % 168.22/168.06 [8266]~P104(x82661)+~P22(f317(f317(f226(f858(x82661,a842)),f279(x82661,x82664,x82665)),f279(x82661,x82662,x82663)))+P22(f317(f317(f225(x82661),x82662),x82663)) % 168.22/168.06 [8336]~P19(x83361,x83364,x83365,f233(f858(x83361,a842)))+~P22(f317(f317(f319(x83364),f317(x83365,x83362)),f317(f287(x83361,x83364,x83365),x83363)))+P22(f317(f317(f319(x83361),x83362),x83363)) % 168.22/168.06 [8418]P22(f317(x84181,x84182))+~P22(f317(x84181,f794(x84181,x84183,x84184,x84185)))+~P22(f317(f317(f319(x84185),x84182),x84184)) % 168.22/168.06 [8419]P22(f317(x84191,x84192))+~P22(f317(x84191,f794(x84191,x84193,x84194,x84195)))+~P22(f317(f317(f319(x84195),x84192),x84193)) % 168.22/168.06 [8693]~P19(x86932,x86933,x86931,x86934)+E(f317(x86931,f317(f86(x86932,x86933,x86934,x86931),x86935)),x86935)+~P22(f317(f317(f319(x86933),x86935),f317(f287(x86932,x86933,x86931),x86934))) % 168.22/168.06 [8795]E(x87951,f125(x87952))+E(f317(f317(f145(x87952),x87953),f617(x87954,x87953,x87955,x87951,x87952)),x87951)+~E(f317(f317(f127(x87952),x87951),x87955),f317(f317(f145(x87952),x87953),x87954)) % 168.22/168.06 [8796]E(x87961,f125(x87962))+E(f317(f317(f145(x87962),x87963),f618(x87964,x87961,x87965,x87963,x87962)),x87961)+~E(f317(f317(f127(x87962),x87961),x87964),f317(f317(f145(x87962),x87963),x87965)) % 168.22/168.06 [8813]E(f317(f317(f145(x88132),x88133),f617(x88134,x88133,x88131,x88135,x88132)),x88135)+~E(f317(f317(f127(x88132),x88135),x88131),f317(f317(f145(x88132),x88133),x88134))+E(x88131,f317(f317(f145(x88132),x88133),x88134)) % 168.22/168.06 [8814]E(f317(f317(f145(x88141),x88142),f618(x88144,x88145,x88143,x88142,x88141)),x88145)+~E(f317(f317(f127(x88141),x88145),x88144),f317(f317(f145(x88141),x88142),x88143))+E(f317(f317(f145(x88141),x88142),x88143),x88144) % 168.22/168.06 [8898]~E(f317(f287(x88983,x88982,x88984),f233(f858(x88983,a842))),f233(f858(x88982,a842)))+~E(f317(f287(x88981,x88983,x88985),f233(f858(x88981,a842))),f233(f858(x88983,a842)))+E(f317(f287(x88981,x88982,f317(f82(x88983,x88982,x88981,x88984),x88985)),f233(f858(x88981,a842))),f233(f858(x88982,a842))) % 168.22/168.06 [9256]E(x92561,f125(x92562))+~E(f317(f317(f127(x92562),x92561),x92563),f317(f317(f145(x92562),x92565),x92564))+E(f317(f317(f127(x92562),f618(x92563,x92561,x92564,x92565,x92562)),x92563),x92564) % 168.22/168.06 [9257]E(x92571,f125(x92572))+~E(f317(f317(f127(x92572),x92571),x92575),f317(f317(f145(x92572),x92574),x92573))+E(f317(f317(f127(x92572),f617(x92573,x92574,x92575,x92571,x92572)),x92575),x92573) % 168.22/168.06 [9264]E(f317(f317(f127(x92642),f617(x92644,x92643,x92641,x92645,x92642)),x92641),x92644)+~E(f317(f317(f127(x92642),x92645),x92641),f317(f317(f145(x92642),x92643),x92644))+E(x92641,f317(f317(f145(x92642),x92643),x92644)) % 168.22/168.06 [9265]~E(f317(f317(f127(x92651),x92655),x92654),f317(f317(f145(x92651),x92652),x92653))+E(f317(f317(f127(x92651),f618(x92654,x92655,x92653,x92652,x92651)),x92654),x92653)+E(f317(f317(f145(x92651),x92652),x92653),x92654) % 168.22/168.06 [9266]E(f317(f317(f127(x92661),x92665),f620(x92663,x92662,x92664,x92665,x92661)),x92662)+E(f317(f317(f127(x92661),x92662),f619(x92663,x92662,x92664,x92665,x92661)),x92665)+~E(f317(f317(f127(x92661),x92665),x92664),f317(f317(f127(x92661),x92662),x92663)) % 168.22/168.06 [9298]~P103(x92981)+P29(x92981,f317(f317(f148(x92982,x92981),x92983),f144(x92982,x92981,x92983,x92984,x92985)))+~P29(x92981,f317(f317(f148(x92982,x92981),x92983),x92985)) % 168.22/168.06 [9310]~P53(x93105,x93101,x93104,x93103)+P22(f317(f317(x93101,x93102),f507(x93103,x93104,x93101,x93105,x93102)))+~P22(f317(f317(f319(x93105),x93102),x93104)) % 168.22/168.06 [9416]~P22(f317(f317(f319(f857(x94161,x94161)),f317(f317(f237(x94161,x94161),x94165),x94163)),f284(x94161,x94164)))+P22(f317(f317(f319(f857(x94161,x94161)),f317(f317(f237(x94161,x94161),x94162),x94163)),f317(f317(f265(x94161,x94161,x94161),x94164),f284(x94161,x94164))))+~P22(f317(f317(f319(f857(x94161,x94161)),f317(f317(f237(x94161,x94161),x94162),x94165)),f317(f317(f265(x94161,x94161,x94161),x94164),f284(x94161,x94164)))) % 168.22/168.06 [9417]~P22(f317(f317(f319(f857(x94171,x94171)),f317(f317(f237(x94171,x94171),x94172),x94175)),f284(x94171,x94174)))+P22(f317(f317(f319(f857(x94171,x94171)),f317(f317(f237(x94171,x94171),x94172),x94173)),f317(f317(f265(x94171,x94171,x94171),x94174),f284(x94171,x94174))))+~P22(f317(f317(f319(f857(x94171,x94171)),f317(f317(f237(x94171,x94171),x94175),x94173)),f317(f317(f265(x94171,x94171,x94171),x94174),f284(x94171,x94174)))) % 168.22/168.06 [9420]P22(f317(f317(f319(f857(f850(x94201),f850(x94201))),f317(f317(f237(f850(x94201),f850(x94201)),x94202),x94203)),f152(x94201,f284(x94201,x94204))))+~P22(f317(f317(f319(f857(f850(x94201),f850(x94201))),f317(f317(f237(f850(x94201),f850(x94201)),x94202),x94205)),f152(x94201,f284(x94201,x94204))))+~P22(f317(f317(f319(f857(f850(x94201),f850(x94201))),f317(f317(f237(f850(x94201),f850(x94201)),x94205),x94203)),f152(x94201,f284(x94201,x94204)))) % 168.22/168.06 [9425]E(f317(f317(f127(x94251),x94252),f619(x94253,x94252,x94254,x94255,x94251)),x94255)+E(f317(f317(f127(x94251),f620(x94253,x94252,x94254,x94255,x94251)),x94253),x94254)+~E(f317(f317(f127(x94251),x94252),x94253),f317(f317(f127(x94251),x94255),x94254)) % 168.22/168.06 [9426]E(f317(f317(f127(x94261),x94262),f620(x94263,x94264,x94265,x94262,x94261)),x94264)+E(f317(f317(f127(x94261),f619(x94263,x94264,x94265,x94262,x94261)),x94265),x94263)+~E(f317(f317(f127(x94261),x94262),x94265),f317(f317(f127(x94261),x94264),x94263)) % 168.22/168.06 [9479]P22(f317(f317(f319(f857(x94791,x94791)),f317(f317(f237(x94791,x94791),x94792),x94793)),f317(f317(f265(x94791,x94791,x94791),x94794),f284(x94791,x94794))))+~P22(f317(f317(f319(f857(x94791,x94791)),f317(f317(f237(x94791,x94791),x94792),x94795)),f317(f317(f265(x94791,x94791,x94791),x94794),f284(x94791,x94794))))+~P22(f317(f317(f319(f857(x94791,x94791)),f317(f317(f237(x94791,x94791),x94795),x94793)),f317(f317(f265(x94791,x94791,x94791),x94794),f284(x94791,x94794)))) % 168.22/168.06 [9505]P35(x95051,x95052,x95053,x95054,x95055)+~E(f317(f189(f850(x95051)),x95054),f317(f189(f850(x95052)),x95055))+~P22(f317(f317(f247(x95051,x95052,a842),x95053),f683(x95055,x95054,x95053,x95052,x95051))) % 168.22/168.06 [9506]P35(x95061,x95062,x95063,x95064,x95065)+~E(f317(f189(f850(x95061)),x95064),f317(f189(f850(x95062)),x95065))+~P22(f317(f317(f247(x95061,x95062,a842),x95063),f693(x95063,x95065,x95064,x95062,x95061))) % 168.22/168.06 [9510]E(f317(f317(f127(x95101),f619(x95102,x95103,x95104,x95105,x95101)),x95104),x95102)+~E(f317(f317(f127(x95101),x95103),x95102),f317(f317(f127(x95101),x95105),x95104))+E(f317(f317(f127(x95101),f620(x95102,x95103,x95104,x95105,x95101)),x95102),x95104) % 168.22/168.06 [9521]~P103(x95212)+E(f317(f317(f143(x95211,x95212,x95213),x95214),x95215),f317(f317(f145(x95211),x95214),x95215))+P22(f317(f317(f319(x95211),f718(x95214,x95213,x95215,x95211,x95212)),f317(f166(x95211),x95215))) % 168.22/168.06 [9527]~P53(x95271,x95274,x95273,x95272)+~P22(f317(f317(f319(x95271),x95275),x95273))+P22(f317(f317(f319(x95271),f507(x95272,x95273,x95274,x95271,x95275)),x95272)) % 168.22/168.06 [9632]E(f317(f288(x96321,x96322),f788(x96323,x96324,x96325,x96322,x96321)),x96325)+~P22(f317(f317(f319(f856(x96321,x96322)),x96325),f298(x96321,x96322,x96324,x96323)))+P22(f317(f317(f319(x96322),f792(x96323,x96324,x96325,x96322,x96321)),x96323)) % 168.22/168.06 [9633]E(f317(f297(x96331,x96332),f792(x96333,x96334,x96335,x96331,x96332)),x96335)+~P22(f317(f317(f319(f856(x96332,x96331)),x96335),f298(x96332,x96331,x96334,x96333)))+P22(f317(f317(f319(x96332),f788(x96333,x96334,x96335,x96331,x96332)),x96334)) % 168.22/168.06 [9643]~P22(f317(f317(f319(f857(f858(x96431,a842),f858(x96431,a842))),f317(f317(f237(f858(x96431,a842),f858(x96431,a842)),x96434),x96433)),f309(x96431,x96432)))+~P22(f317(f317(f319(x96431),x96435),x96434))+P22(f317(f317(f319(x96431),f738(x96432,x96433,x96434,x96431,x96435)),x96433)) % 168.22/168.06 [9656]~P103(x96562)+E(f317(f317(f143(x96561,x96562,x96563),x96564),x96565),f317(f317(f145(x96561),x96564),x96565))+~P22(f317(f317(f225(x96562),f317(x96563,x96564)),f317(x96563,f718(x96564,x96563,x96565,x96561,x96562)))) % 168.22/168.06 [9723]~P22(f317(f317(f319(f856(x97231,x97235)),x97234),f298(x97231,x97235,x97233,x97232)))+P22(f317(f317(f319(x97235),f792(x97232,x97233,x97234,x97235,x97231)),x97232))+P22(f317(f317(f319(x97231),f788(x97232,x97233,x97234,x97235,x97231)),x97233)) % 168.22/168.06 [9851]P35(x98511,x98512,x98513,x98514,x98515)+~E(f317(f189(f850(x98511)),x98514),f317(f189(f850(x98512)),x98515))+~P22(f317(f317(x98513,f317(f317(f159(x98511),x98514),f694(x98515,x98514,x98513,x98512,x98511))),f317(f317(f159(x98512),x98515),f694(x98515,x98514,x98513,x98512,x98511)))) % 168.22/168.06 [9852]P35(x98521,x98522,x98523,x98524,x98525)+~E(f317(f189(f850(x98521)),x98524),f317(f189(f850(x98522)),x98525))+~P22(f317(f317(x98523,f317(f317(f159(x98521),x98524),f709(x98523,x98525,x98522,x98524,x98521))),f317(f317(f159(x98522),x98525),f709(x98523,x98525,x98522,x98524,x98521)))) % 168.22/168.06 [6457]~P12(x64572,x64575,x64571)+~P22(f317(f71(x64572),x64574))+E(f317(x64571,f317(f317(f286(x64572),x64573),x64574)),f317(f317(f74(x64572,x64572,x64575),x64573),x64574)) % 168.22/168.06 [6458]~E(x64583,x64584)+~E(x64582,x64585)+E(f317(f317(f286(x64581),x64582),f317(f317(f286(x64581),x64583),f188(f858(x64581,a842)))),f317(f317(f286(x64581),x64584),f317(f317(f286(x64581),x64585),f188(f858(x64581,a842))))) % 168.22/168.06 [6471]P22(f317(x64712,x64715))+E(f170(x64711,x64712,f317(f317(f127(x64711),x64713),x64714)),f170(x64711,x64712,x64713))+~P22(f317(f317(f319(x64711),x64715),f317(f166(x64711),x64713))) % 168.22/168.06 [6504]E(f317(x65041,x65042),f188(f858(x65043,a842)))+~E(f317(f317(f51(x65044,f858(x65043,a842)),x65045),x65041),f188(f858(x65043,a842)))+~P22(f317(f317(f319(x65044),x65042),x65045)) % 168.22/168.06 [6505]E(f317(x65051,x65052),f233(f858(x65053,a842)))+~E(f317(f317(f52(x65054,f858(x65053,a842)),x65055),x65051),f233(f858(x65053,a842)))+~P22(f317(f317(f319(x65054),x65052),x65055)) % 168.22/168.06 [6796]~P22(f317(f317(f194(x67961),x67963),x67965))+~P22(f317(f317(f194(x67962),x67965),x67964))+P22(f317(f317(f194(f36(x67961,x67962)),x67963),x67964)) % 168.22/168.06 [7007]~E(x70072,x70074)+~P109(x70071)+E(f317(f317(f89(x70071),f317(f317(f90(x70071),x70072),x70073)),f317(f317(f90(x70071),x70074),x70075)),f317(f317(f89(x70071),f317(f317(f90(x70071),x70072),x70075)),f317(f317(f90(x70071),x70074),x70073))) % 168.22/168.06 [7069]~P27(x70691)+~P22(f317(f317(f319(x70694),x70693),x70695))+P22(f317(f317(f225(x70691),f317(x70692,x70693)),f317(f317(f51(x70694,x70691),x70695),x70692))) % 168.22/168.06 [7119]~P102(x71191)+P22(f317(f317(f225(x71191),f317(x71192,x71193)),f317(x71194,x71193)))+~P22(f317(f317(f225(f858(x71195,x71191)),x71192),x71194)) % 168.22/168.06 [7230]E(x72301,x72302)+E(x72303,x72301)+~E(f317(f317(f286(x72304),x72301),f317(f317(f286(x72304),x72305),f188(f858(x72304,a842)))),f317(f317(f286(x72304),x72302),f317(f317(f286(x72304),x72303),f188(f858(x72304,a842))))) % 168.22/168.06 [7231]E(x72311,x72312)+E(x72313,x72311)+~E(f317(f317(f286(x72314),x72313),f317(f317(f286(x72314),x72312),f188(f858(x72314,a842)))),f317(f317(f286(x72314),x72315),f317(f317(f286(x72314),x72311),f188(f858(x72314,a842))))) % 168.22/168.06 [7232]E(x72321,x72322)+E(x72321,x72323)+~E(f317(f317(f286(x72324),x72323),f317(f317(f286(x72324),x72322),f188(f858(x72324,a842)))),f317(f317(f286(x72324),x72325),f317(f317(f286(x72324),x72321),f188(f858(x72324,a842))))) % 168.22/168.06 [7233]E(x72331,x72332)+E(x72331,x72333)+~E(f317(f317(f286(x72334),x72331),f317(f317(f286(x72334),x72335),f188(f858(x72334,a842)))),f317(f317(f286(x72334),x72332),f317(f317(f286(x72334),x72333),f188(f858(x72334,a842))))) % 168.22/168.06 [7763]P19(x77631,x77632,x77633,x77634)+~P19(x77631,x77632,x77633,x77635)+~P22(f317(f317(f225(f858(x77631,a842)),x77634),x77635)) % 168.22/168.06 [7769]~P22(f317(f317(f225(a849),x77695),x77693))+~P22(f317(f317(f317(f317(a197,x77691),x77692),x77695),x77694))+P22(f317(f317(f317(f317(a197,x77691),x77692),x77693),x77694)) % 168.22/168.06 [7858]P22(f317(x78581,x78582))+~P22(f317(f317(f194(x78584),x78582),x78585))+P22(f317(f317(f194(f33(x78581,x78583,x78584)),x78582),x78585)) % 168.22/168.06 [7885]~P22(f317(x78851,x78854))+~P22(f317(f317(f194(x78852),x78854),x78855))+P22(f317(f317(f194(f33(x78851,x78852,x78853)),x78854),x78855)) % 168.22/168.06 [7934]E(x79341,x79342)+~E(f317(f287(x79343,x79344,x79345),x79341),f317(f287(x79343,x79344,x79345),x79342))+~P19(x79343,x79344,x79345,f317(f317(f122(f858(x79343,a842)),x79341),x79342)) % 168.22/168.06 [8010]P22(f317(x80102,x80104))+E(f317(f317(f132(x80101),f317(f189(f850(x80101)),f170(x80101,x80102,x80103))),x80103),f317(f317(f145(x80101),x80104),x80105))+~E(f317(f317(f127(x80101),f170(x80101,x80102,x80103)),f317(f317(f145(x80101),x80104),x80105)),x80103) % 168.22/168.06 [8041]~P19(x80411,x80412,x80413,x80415)+~P19(x80411,x80412,x80413,x80414)+P19(x80411,x80412,x80413,f317(f317(f113(f858(x80411,a842)),x80414),x80415)) % 168.22/168.06 [8151]~P67(x81511)+E(f317(f317(f89(x81511),f317(x81512,x81513)),f317(f160(x81511),f317(f317(f148(x81514,x81511),x81512),f164(x81514,x81513,x81515)))),f317(f160(x81511),f317(f317(f148(x81514,x81511),x81512),x81515)))+~P22(f317(f317(f319(x81514),x81513),f317(f166(x81514),x81515))) % 168.22/168.06 [8244]~P103(x82441)+~P29(x82441,f317(f317(f148(x82442,x82441),x82443),x82445))+P29(x82441,f317(f317(f148(x82442,x82441),x82443),f317(f317(f143(x82442,x82441,x82443),x82444),x82445))) % 168.22/168.06 [8320]P22(f317(x83201,x83202))+P22(f317(f317(f194(x83203),x83202),x83204))+~P22(f317(f317(f194(f33(x83201,x83205,x83203)),x83202),x83204)) % 168.22/168.06 [8331]~P27(x83311)+P22(f317(f317(f225(x83311),f317(f317(f51(x83312,x83311),x83313),x83314)),f317(f317(f51(x83312,x83311),x83315),x83314)))+~P22(f317(f317(f225(f858(x83312,a842)),x83313),x83315)) % 168.22/168.06 [8332]~P27(x83321)+P22(f317(f317(f225(x83321),f317(f317(f52(x83322,x83321),x83323),x83324)),f317(f317(f52(x83322,x83321),x83325),x83324)))+~P22(f317(f317(f225(f858(x83322,a842)),x83325),x83323)) % 168.22/168.06 [8344]~P22(f317(x83444,x83442))+P22(f317(f317(f194(x83441),x83442),x83443))+~P22(f317(f317(f194(f33(x83444,x83441,x83445)),x83442),x83443)) % 168.22/168.06 [8368]~P103(x83683)+P22(f317(f131(x83681),x83682))+~P22(f317(f131(x83681),f317(f317(f143(x83681,x83683,x83684),x83685),x83682))) % 168.22/168.06 [8379]P22(f317(f317(f194(x83791),x83792),x83793))+P22(f317(f317(f194(x83794),x83792),x83793))+~P22(f317(f317(f194(f33(x83795,x83791,x83794)),x83792),x83793)) % 168.22/168.06 [8514]~P103(x85141)+~P22(f317(f317(f319(x85142),x85143),f317(f166(x85142),x85144)))+~P22(f317(f131(x85142),f317(f317(f143(x85142,x85141,x85145),x85143),x85144))) % 168.22/168.06 [8591]~P103(x85911)+P29(x85911,f317(f317(f148(x85912,x85911),x85913),x85914))+~P29(x85911,f317(f317(f148(x85912,x85911),x85913),f317(f317(f143(x85912,x85911,x85913),x85915),x85914))) % 168.22/168.06 [8682]~P103(x86822)+E(f317(f317(f143(x86821,x86822,x86823),x86824),x86825),f144(x86821,x86822,x86823,x86824,x86825))+P22(f317(f317(f319(x86822),f317(x86823,x86824)),f317(f287(x86821,x86822,x86823),f317(f166(x86821),x86825)))) % 168.22/168.06 [8753]~P103(x87532)+E(f144(x87531,x87532,x87533,x87534,x87535),x87535)+~P22(f317(f317(f319(x87532),f317(x87533,x87534)),f317(f287(x87531,x87532,x87533),f317(f166(x87531),x87535)))) % 168.22/168.06 [8769]~P19(x87692,x87691,x87693,x87695)+P22(f317(f317(f226(f858(x87691,a842)),f317(f287(x87692,x87691,x87693),x87694)),f317(f287(x87692,x87691,x87693),x87695)))+~P22(f317(f317(f226(f858(x87692,a842)),x87694),x87695)) % 168.22/168.06 [8939]~P19(x89391,x89392,x89393,f233(f858(x89391,a842)))+~P22(f317(f317(f225(f858(x89392,a842)),x89394),f317(f287(x89391,x89392,x89393),x89395)))+P22(f317(f317(f225(f858(x89391,a842)),f317(f289(x89391,x89392,x89393),x89394)),x89395)) % 168.22/168.06 [8958]~E(f317(f287(x89583,x89581,x89584),f233(f858(x89583,a842))),f233(f858(x89581,a842)))+P22(f317(f317(f225(f858(x89581,a842)),x89582),f317(f287(x89583,x89581,x89584),x89585)))+~P22(f317(f317(f225(f858(x89583,a842)),f317(f289(x89583,x89581,x89584),x89582)),x89585)) % 168.22/168.06 [8981]~E(f317(f217(x89812),x89814),f317(f317(f171(x89811,x89812),x89815),x89813))+~P22(f317(f131(x89811),f317(f317(f148(f857(x89811,x89812),x89811),f244(x89811,x89812)),x89815)))+P22(f317(f317(f319(f857(x89811,x89812)),f317(f317(f237(x89811,x89812),x89813),x89814)),f317(f166(f857(x89811,x89812)),x89815))) % 168.22/168.06 [9060]~P19(x90601,x90604,x90605,f233(f858(x90601,a842)))+~P22(f317(f317(f225(f858(x90604,a842)),f317(f287(x90601,x90604,x90605),x90602)),f317(f287(x90601,x90604,x90605),x90603)))+P22(f317(f317(f225(f858(x90601,a842)),x90602),x90603)) % 168.22/168.06 [9125]E(f317(f217(x91251),x91252),f317(f317(f171(x91253,x91251),x91254),x91255))+~P22(f317(f131(x91253),f317(f317(f148(f857(x91253,x91251),x91253),f244(x91253,x91251)),x91254)))+~P22(f317(f317(f319(f857(x91253,x91251)),f317(f317(f237(x91253,x91251),x91255),x91252)),f317(f166(f857(x91253,x91251)),x91254))) % 168.22/168.06 [9127]E(f317(f317(f171(x91271,x91272),x91273),x91274),f317(f217(x91272),x91275))+~P22(f317(f131(x91271),f317(f317(f148(f857(x91271,x91272),x91271),f244(x91271,x91272)),x91273)))+~P22(f317(f317(f319(f857(x91271,x91272)),f317(f317(f237(x91271,x91272),x91274),x91275)),f317(f166(f857(x91271,x91272)),x91273))) % 168.22/168.06 [9182]~P66(x91821)+~E(f317(x91823,f662(x91823,x91824,x91825,x91822,x91821)),f2(x91821))+E(f317(f160(x91821),f317(f317(f148(x91822,x91821),x91823),f317(f130(x91822,x91824),x91825))),f317(f160(x91821),f317(f317(f148(x91822,x91821),x91823),x91825))) % 168.22/168.06 [9449]~P66(x94491)+~P22(f317(x94494,f662(x94493,x94494,x94495,x94492,x94491)))+E(f317(f160(x94491),f317(f317(f148(x94492,x94491),x94493),f317(f130(x94492,x94494),x94495))),f317(f160(x94491),f317(f317(f148(x94492,x94491),x94493),x94495))) % 168.22/168.06 [9525]~P27(x95255)+P22(f317(f317(f319(x95251),f635(x95252,x95253,x95251,x95254,x95255)),x95253))+P22(f317(f317(f225(x95255),x95254),f317(f317(f52(x95251,x95255),x95253),x95252))) % 168.22/168.06 [9528]~P66(x95281)+E(f317(f160(x95281),f317(f317(f148(x95282,x95281),x95283),f317(f130(x95282,x95284),x95285))),f317(f160(x95281),f317(f317(f148(x95282,x95281),x95283),x95285)))+P22(f317(f317(f319(x95282),f662(x95283,x95284,x95285,x95282,x95281)),f317(f166(x95282),x95285))) % 168.22/168.06 [9569]P35(x95691,x95692,x95693,x95694,x95695)+~E(f317(f189(f850(x95692)),x95695),f317(f189(f850(x95691)),x95694))+P22(f317(f317(f226(a849),f694(x95695,x95694,x95693,x95692,x95691)),f317(f189(f850(x95691)),x95694))) % 168.22/168.06 [9570]P35(x95701,x95702,x95703,x95704,x95705)+~E(f317(f189(f850(x95702)),x95705),f317(f189(f850(x95701)),x95704))+P22(f317(f317(f226(a849),f709(x95703,x95705,x95702,x95704,x95701)),f317(f189(f850(x95701)),x95704))) % 168.22/168.06 [9657]~P27(x96571)+~P22(f317(f317(f225(x96571),x96572),f317(x96575,f635(x96575,x96574,x96573,x96572,x96571))))+P22(f317(f317(f225(x96571),x96572),f317(f317(f52(x96573,x96571),x96574),x96575))) % 168.22/168.06 [9687]~P70(x96871)+~P22(f317(f71(x96872),x96875))+E(f317(f317(f317(f75(x96871,x96872,f90(x96871)),f317(f317(f18(x96872,x96871,x96871),f317(f317(f8(x96871,f858(x96871,x96871),x96872),f90(x96871)),x96873)),x96874)),f87(x96871)),x96875),f317(f317(f90(x96871),f317(f317(f317(f75(x96871,x96872,f90(x96871)),x96873),f87(x96871)),x96875)),f317(f317(f317(f75(x96871,x96872,f90(x96871)),x96874),f87(x96871)),x96875))) % 168.22/168.06 [9753]~P22(f317(f317(f319(f857(f858(x97531,a842),f858(x97531,a842))),f317(f317(f237(f858(x97531,a842),f858(x97531,a842)),x97535),x97534)),f309(x97531,x97533)))+~P22(f317(f317(f319(x97531),x97532),x97535))+P22(f317(f317(f319(f857(x97531,x97531)),f317(f317(f237(x97531,x97531),x97532),f738(x97533,x97534,x97535,x97531,x97532))),x97533)) % 168.22/168.06 [9892]~P22(f317(f317(f319(f857(f850(x98921),f850(x98921))),f317(f317(f237(f850(x98921),f850(x98921)),f317(f317(f127(x98921),x98925),x98922)),f317(f317(f127(x98921),x98925),x98923))),f141(x98921,x98924)))+P22(f317(f317(f319(f857(f850(x98921),f850(x98921))),f317(f317(f237(f850(x98921),f850(x98921)),x98922),x98923)),f141(x98921,x98924)))+P22(f317(f317(f319(f857(x98921,x98921)),f317(f317(f237(x98921,x98921),f626(x98924,x98923,x98922,x98925,x98921)),f626(x98924,x98923,x98922,x98925,x98921))),x98924)) % 168.22/168.06 [7048]~E(f317(f189(f850(x70481)),x70483),f317(f189(f850(x70482)),x70484))+E(f317(f317(f171(x70481,x70482),f317(f317(f175(x70481,x70482),x70483),x70484)),x70485),f191(x70482))+P22(f317(f317(f319(x70481),x70485),f317(f166(x70481),x70483))) % 168.22/168.06 [7122]~E(x71223,x71225)+E(f317(f317(f159(x71221),f317(f317(f153(x71221,x71222),x71223),x71224)),x71225),x71224)+~P22(f317(f317(f226(a849),x71223),f317(f189(f850(x71221)),x71222))) % 168.22/168.06 [7223]~E(f317(f317(f127(x72231),x72232),x72234),f317(f317(f127(x72231),x72233),x72235))+E(f317(f317(f167(x72231),f317(f189(f850(x72231)),x72232)),x72233),x72232)+P22(f317(f317(f225(a849),f317(f189(f850(x72231)),x72233)),f317(f189(f850(x72231)),x72232))) % 168.22/168.06 [7242]~E(x72425,x72422)+P22(f317(x72421,x72422))+P22(f317(f317(f317(f317(a197,f35(x72421,x72423)),x72422),x72424),x72425)) % 168.22/168.06 [7726]~E(f317(f317(f127(x77261),x77262),x77264),f317(f317(f127(x77261),x77263),x77265))+E(f317(f317(f167(x77261),f317(f189(f850(x77261)),x77262)),x77263),x77262)+~P22(f317(f317(f225(a849),f317(f189(f850(x77261)),x77262)),f317(f189(f850(x77261)),x77263))) % 168.22/168.06 [7750]~P22(f317(f71(x77501),f317(x77504,x77505)))+~P22(f317(f317(f319(x77502),x77505),x77503))+P22(f317(f71(x77501),f317(f317(f52(x77502,f858(x77501,a842)),x77503),x77504))) % 168.22/168.06 [7797]~E(f317(f189(f850(x77971)),x77972),f317(f189(f850(x77973)),x77974))+~E(f317(f317(f171(x77971,x77973),f317(f317(f175(x77971,x77973),x77972),x77974)),x77975),f191(x77973))+~P22(f317(f317(f319(x77971),x77975),f317(f166(x77971),x77972))) % 168.22/168.06 [7919]~P45(x79191,x79193,x79195)+~P45(x79191,x79192,x79194)+P45(x79191,f317(f317(f122(f858(x79191,a842)),x79192),x79193),f317(f317(f122(f858(f857(x79191,x79191),a842)),x79194),x79195)) % 168.22/168.06 [7920]~P45(x79201,x79203,x79205)+~P45(x79201,x79202,x79204)+P45(x79201,f317(f317(f113(f858(x79201,a842)),x79202),x79203),f317(f317(f113(f858(f857(x79201,x79201),a842)),x79204),x79205)) % 168.22/168.06 [8003]E(x80031,x80032)+P22(f317(x80033,x80031))+~P22(f317(f317(f317(f317(a197,f35(x80033,x80034)),x80031),x80035),x80032)) % 168.22/168.06 [8281]E(f317(f317(f237(x82811,x82812),f317(f317(f159(x82811),x82813),x82814)),f317(f317(f159(x82812),x82815),x82814)),f317(f317(f159(f857(x82811,x82812)),f317(f317(f175(x82811,x82812),x82813),x82815)),x82814))+~P22(f317(f317(f226(a849),x82814),f317(f189(f850(x82811)),x82813)))+~P22(f317(f317(f226(a849),x82814),f317(f189(f850(x82812)),x82815))) % 168.22/168.06 [8447]~P45(x84471,x84473,x84474)+P22(f317(f317(f319(x84471),x84472),x84473))+~P22(f317(f317(f319(f857(x84471,x84471)),f317(f317(f237(x84471,x84471),x84475),x84472)),x84474)) % 168.22/168.06 [8448]~P45(x84481,x84483,x84484)+P22(f317(f317(f319(x84481),x84482),x84483))+~P22(f317(f317(f319(f857(x84481,x84481)),f317(f317(f237(x84481,x84481),x84482),x84485)),x84484)) % 168.22/168.06 [8449]~P6(x84491,x84493,x84494)+P22(f317(f317(f319(x84491),x84492),x84493))+~P22(f317(f317(f319(f857(x84491,x84491)),f317(f317(f237(x84491,x84491),x84495),x84492)),x84494)) % 168.22/168.06 [8450]~P6(x84501,x84503,x84504)+P22(f317(f317(f319(x84501),x84502),x84503))+~P22(f317(f317(f319(f857(x84501,x84501)),f317(f317(f237(x84501,x84501),x84502),x84505)),x84504)) % 168.22/168.06 [8703]~P6(x87031,x87035,x87032)+E(f317(f262(x87031,x87031,x87032),f317(f317(f286(x87031),x87033),f188(f858(x87031,a842)))),f317(f262(x87031,x87031,x87032),f317(f317(f286(x87031),x87034),f188(f858(x87031,a842)))))+~P22(f317(f317(f319(f857(x87031,x87031)),f317(f317(f237(x87031,x87031),x87033),x87034)),x87032)) % 168.22/168.06 [8783]~P22(f317(f317(f317(f317(a197,x87832),x87833),x87834),x87835))+~P22(f317(f317(f317(f317(a197,f35(x87831,x87832)),x87835),x87834),x87833))+P22(f317(f317(f317(f317(a197,f35(x87831,x87832)),x87833),x87834),x87833)) % 168.22/168.06 [8895]P22(f317(x88951,x88952))+~P22(f317(f317(f319(x88953),x88952),x88955))+P22(f317(f317(f319(x88953),f794(x88951,x88954,x88955,x88953)),f317(f317(f122(f858(x88953,a842)),x88955),x88954))) % 168.22/168.06 [8896]P22(f317(x88961,x88962))+~P22(f317(f317(f319(x88963),x88962),x88964))+P22(f317(f317(f319(x88963),f794(x88961,x88964,x88965,x88963)),f317(f317(f122(f858(x88963,a842)),x88965),x88964))) % 168.22/168.06 [8904]~P22(f317(x89042,x89045))+~P22(f317(f317(f319(x89041),x89045),x89044))+P22(f317(f317(f319(x89041),f804(x89042,x89043,x89044,x89041)),f317(f317(f122(f858(x89041,a842)),x89044),x89043))) % 168.22/168.06 [8905]~P22(f317(x89052,x89055))+~P22(f317(f317(f319(x89051),x89055),x89053))+P22(f317(f317(f319(x89051),f804(x89052,x89053,x89054,x89051)),f317(f317(f122(f858(x89051,a842)),x89054),x89053))) % 168.22/168.06 [8920]~P22(f317(f317(f225(f858(x89201,a842)),x89205),x89203))+~P22(f317(f317(f225(f858(x89201,a842)),x89202),x89204))+P22(f317(f317(f225(f858(x89201,a842)),f317(f317(f21(f858(x89201,a842)),x89202),x89203)),f317(f317(f21(f858(x89201,a842)),x89204),x89205))) % 168.22/168.06 [8921]~P22(f317(f317(f225(f858(x89211,a842)),x89213),x89215))+~P22(f317(f317(f225(f858(x89211,a842)),x89212),x89214))+P22(f317(f317(f225(f858(x89211,a842)),f317(f317(f122(f858(x89211,a842)),x89212),x89213)),f317(f317(f122(f858(x89211,a842)),x89214),x89215))) % 168.22/168.06 [8922]~P22(f317(f317(f225(f858(x89221,a842)),x89223),x89225))+~P22(f317(f317(f225(f858(x89221,a842)),x89222),x89224))+P22(f317(f317(f225(f858(x89221,a842)),f317(f317(f113(f858(x89221,a842)),x89222),x89223)),f317(f317(f113(f858(x89221,a842)),x89224),x89225))) % 168.22/168.06 [9005]~E(f317(f189(f850(x90051)),x90053),f317(f189(f850(x90052)),x90054))+E(f317(f317(f171(x90051,x90052),f317(f317(f175(x90051,x90052),x90053),x90054)),x90055),f317(f217(x90052),f587(x90055,x90054,x90052,x90053,x90051)))+~P22(f317(f317(f319(x90051),x90055),f317(f166(x90051),x90053))) % 168.22/168.06 [9009]P22(f317(f317(f319(f857(x90091,x90091)),f317(f317(f237(x90091,x90091),x90092),x90093)),f311(x90091,x90094,x90095)))+~P22(f317(f317(f225(a849),f317(x90094,x90092)),f317(x90094,x90093)))+~P22(f317(f317(f319(f857(x90091,x90091)),f317(f317(f237(x90091,x90091),x90092),x90093)),x90095)) % 168.22/168.06 [9192]P22(f317(f317(f319(f857(x91921,x91921)),f317(f317(f237(x91921,x91921),x91922),x91923)),f284(x91921,x91924)))+~P22(f317(f317(f319(f857(x91921,x91921)),f317(f317(f237(x91921,x91921),x91922),x91925)),f284(x91921,x91924)))+~P22(f317(f317(f319(f857(x91921,x91921)),f317(f317(f237(x91921,x91921),x91925),x91923)),x91924)) % 168.22/168.06 [9193]P22(f317(f317(f319(f857(x91931,x91931)),f317(f317(f237(x91931,x91931),x91932),x91933)),f284(x91931,x91934)))+~P22(f317(f317(f319(f857(x91931,x91931)),f317(f317(f237(x91931,x91931),x91935),x91933)),f284(x91931,x91934)))+~P22(f317(f317(f319(f857(x91931,x91931)),f317(f317(f237(x91931,x91931),x91932),x91935)),x91934)) % 168.22/168.06 [9287]E(x92871,x92872)+E(f317(a124,f758(x92873,x92874,x92871,x92872,x92875)),x92874)+~P22(f317(f317(f319(f857(x92875,x92875)),f317(f317(f237(x92875,x92875),x92872),x92871)),f317(f317(f182(f857(x92875,x92875),a842),x92874),x92873))) % 168.22/168.06 [9288]E(x92881,x92882)+E(f317(a124,f760(x92883,x92884,x92881,x92882,x92885)),x92884)+~P22(f317(f317(f319(f857(x92885,x92885)),f317(f317(f237(x92885,x92885),x92882),x92881)),f317(f317(f182(f857(x92885,x92885),a842),x92884),x92883))) % 168.22/168.06 [9289]E(x92891,f2(a849))+E(f317(a124,f758(x92892,x92891,x92893,x92894,x92895)),x92891)+~P22(f317(f317(f319(f857(x92895,x92895)),f317(f317(f237(x92895,x92895),x92894),x92893)),f317(f317(f182(f857(x92895,x92895),a842),x92891),x92892))) % 168.22/168.06 [9290]E(x92901,f2(a849))+E(f317(a124,f760(x92902,x92901,x92903,x92904,x92905)),x92901)+~P22(f317(f317(f319(f857(x92905,x92905)),f317(f317(f237(x92905,x92905),x92904),x92903)),f317(f317(f182(f857(x92905,x92905),a842),x92901),x92902))) % 168.22/168.06 [9306]P22(f317(f317(f319(f857(x93061,x93061)),f317(f317(f237(x93061,x93061),x93062),x93063)),f317(f317(f265(x93061,x93061,x93061),x93064),f284(x93061,x93064))))+~P22(f317(f317(f319(f857(x93061,x93061)),f317(f317(f237(x93061,x93061),x93062),x93065)),x93064))+~P22(f317(f317(f319(f857(x93061,x93061)),f317(f317(f237(x93061,x93061),x93065),x93063)),x93064)) % 168.22/168.06 [9314]~P22(f317(f317(f319(f857(x93141,x93141)),f317(f317(f237(x93141,x93141),x93142),x93145)),f284(x93141,x93144)))+P22(f317(f317(f319(f857(x93141,x93141)),f317(f317(f237(x93141,x93141),x93142),x93143)),f317(f317(f265(x93141,x93141,x93141),x93144),f284(x93141,x93144))))+~P22(f317(f317(f319(f857(x93141,x93141)),f317(f317(f237(x93141,x93141),x93145),x93143)),x93144)) % 168.22/168.06 [9351]~P6(x93511,x93515,x93512)+~P22(f317(f317(f319(f857(x93511,x93511)),f317(f317(f237(x93511,x93511),x93513),x93514)),x93512))+P22(f317(f317(f225(f858(x93511,a842)),f317(f262(x93511,x93511,x93512),f317(f317(f286(x93511),x93513),f188(f858(x93511,a842))))),f317(f262(x93511,x93511,x93512),f317(f317(f286(x93511),x93514),f188(f858(x93511,a842)))))) % 168.22/168.06 [9373]E(x93731,x93732)+P22(f317(f317(f317(f317(a197,x93733),x93731),x93734),f393(x93732,x93734,x93731,x93733,x93735)))+~P22(f317(f317(f317(f317(a197,f35(x93735,x93733)),x93731),x93734),x93732)) % 168.22/168.06 [9374]E(x93741,x93742)+P22(f317(f317(f317(f317(a197,x93743),x93741),x93744),f476(x93742,x93744,x93741,x93743,x93745)))+~P22(f317(f317(f317(f317(a197,f35(x93745,x93743)),x93741),x93744),x93742)) % 168.22/168.06 [9379]~P22(f317(x93795,x93792))+P22(f317(f317(f317(f317(a197,x93791),x93792),x93793),f393(x93794,x93793,x93792,x93791,x93795)))+~P22(f317(f317(f317(f317(a197,f35(x93795,x93791)),x93792),x93793),x93794)) % 168.22/168.06 [9380]~P22(f317(x93805,x93802))+P22(f317(f317(f317(f317(a197,x93801),x93802),x93803),f476(x93804,x93803,x93802,x93801,x93805)))+~P22(f317(f317(f317(f317(a197,f35(x93805,x93801)),x93802),x93803),x93804)) % 168.22/168.06 [9409]P22(f317(f317(f319(f857(x94091,x94091)),f317(f317(f237(x94091,x94091),x94092),x94093)),f317(f317(f265(x94091,x94091,x94091),x94094),f284(x94091,x94094))))+~P22(f317(f317(f319(f857(x94091,x94091)),f317(f317(f237(x94091,x94091),x94092),x94095)),f317(f317(f265(x94091,x94091,x94091),x94094),f284(x94091,x94094))))+~P22(f317(f317(f319(f857(x94091,x94091)),f317(f317(f237(x94091,x94091),x94095),x94093)),x94094)) % 168.22/168.06 [9410]P22(f317(f317(f319(f857(x94101,x94101)),f317(f317(f237(x94101,x94101),x94102),x94103)),f317(f317(f265(x94101,x94101,x94101),x94104),f284(x94101,x94104))))+~P22(f317(f317(f319(f857(x94101,x94101)),f317(f317(f237(x94101,x94101),x94105),x94103)),f317(f317(f265(x94101,x94101,x94101),x94104),f284(x94101,x94104))))+~P22(f317(f317(f319(f857(x94101,x94101)),f317(f317(f237(x94101,x94101),x94102),x94105)),x94104)) % 168.22/168.06 [9458]~P22(f317(f76(x94581,x94581,x94584,x94582,x94583),x94585))+P22(f317(f317(f319(x94581),x94582),x94583))+P22(f317(f72(x94581,x94584,f317(f317(f286(x94581),x94582),x94583)),x94585)) % 168.22/168.06 [9499]~E(f317(f287(x94993,x94992,x94995),x94994),x94991)+E(x94991,f188(f858(x94992,a842)))+P22(f317(f317(f225(f858(x94993,a842)),f317(f287(x94992,x94993,f815(x94994,x94993,x94992,x94991)),x94991)),x94994)) % 168.22/168.06 [9540]~P27(x95405)+P22(f317(f317(f319(x95401),f493(x95402,x95403,x95404,x95401,x95405)),x95404))+P22(f317(f317(f225(x95405),f317(f317(f51(x95401,x95405),x95404),x95403)),x95402)) % 168.22/168.06 [9589]P35(x95891,x95892,x95893,x95894,x95895)+~E(f317(f189(f850(x95891)),x95894),f317(f189(f850(x95892)),x95895))+P22(f317(f317(f319(f857(x95891,x95892)),f683(x95895,x95894,x95893,x95892,x95891)),f317(f166(f857(x95891,x95892)),f317(f317(f175(x95891,x95892),x95894),x95895)))) % 168.22/168.06 [9590]P35(x95901,x95902,x95903,x95904,x95905)+~E(f317(f189(f850(x95901)),x95904),f317(f189(f850(x95902)),x95905))+P22(f317(f317(f319(f857(x95901,x95902)),f693(x95903,x95905,x95904,x95902,x95901)),f317(f166(f857(x95901,x95902)),f317(f317(f175(x95901,x95902),x95904),x95905)))) % 168.22/168.06 [9718]E(x97181,x97182)+P22(f317(f317(f317(f317(a197,f35(x97183,x97184)),f393(x97181,x97185,x97182,x97184,x97183)),x97185),x97181))+~P22(f317(f317(f317(f317(a197,f35(x97183,x97184)),x97182),x97185),x97181)) % 168.22/168.06 [9719]E(x97191,x97192)+P22(f317(f317(f317(f317(a197,f35(x97193,x97194)),f476(x97191,x97195,x97192,x97194,x97193)),x97195),x97191))+~P22(f317(f317(f317(f317(a197,f35(x97193,x97194)),x97192),x97195),x97191)) % 168.22/168.06 [9721]~P22(f317(x97211,x97215))+P22(f317(f317(f317(f317(a197,f35(x97211,x97212)),f393(x97213,x97214,x97215,x97212,x97211)),x97214),x97213))+~P22(f317(f317(f317(f317(a197,f35(x97211,x97212)),x97215),x97214),x97213)) % 168.22/168.06 [9722]~P22(f317(x97221,x97225))+P22(f317(f317(f317(f317(a197,f35(x97221,x97222)),f476(x97223,x97224,x97225,x97222,x97221)),x97224),x97223))+~P22(f317(f317(f317(f317(a197,f35(x97221,x97222)),x97225),x97224),x97223)) % 168.22/168.06 [9730]E(x97301,x97302)+P22(f317(f317(f319(f857(x97303,x97303)),f317(f317(f237(x97303,x97303),x97301),f761(x97304,x97305,x97302,x97301,x97303))),x97304))+~P22(f317(f317(f319(f857(x97303,x97303)),f317(f317(f237(x97303,x97303),x97301),x97302)),f317(f317(f182(f857(x97303,x97303),a842),x97305),x97304))) % 168.22/168.06 [9731]E(x97311,f2(a849))+P22(f317(f317(f319(f857(x97312,x97312)),f317(f317(f237(x97312,x97312),x97313),f761(x97314,x97311,x97315,x97313,x97312))),x97314))+~P22(f317(f317(f319(f857(x97312,x97312)),f317(f317(f237(x97312,x97312),x97313),x97315)),f317(f317(f182(f857(x97312,x97312),a842),x97311),x97314))) % 168.22/168.06 [9778]~P27(x97781)+~P22(f317(f317(f225(x97781),f317(x97784,f493(x97785,x97784,x97783,x97782,x97781))),x97785))+P22(f317(f317(f225(x97781),f317(f317(f51(x97782,x97781),x97783),x97784)),x97785)) % 168.22/168.06 [9821]E(x98211,x98212)+P22(f317(f317(f319(f857(x98213,x98213)),f317(f317(f237(x98213,x98213),f759(x98214,x98215,x98211,x98212,x98213)),x98211)),x98214))+~P22(f317(f317(f319(f857(x98213,x98213)),f317(f317(f237(x98213,x98213),x98212),x98211)),f317(f317(f182(f857(x98213,x98213),a842),x98215),x98214))) % 168.22/168.06 [9822]E(x98221,f2(a849))+P22(f317(f317(f319(f857(x98222,x98222)),f317(f317(f237(x98222,x98222),f759(x98223,x98221,x98224,x98225,x98222)),x98224)),x98223))+~P22(f317(f317(f319(f857(x98222,x98222)),f317(f317(f237(x98222,x98222),x98225),x98224)),f317(f317(f182(f857(x98222,x98222),a842),x98221),x98223))) % 168.22/168.06 [9826]E(x98261,x98262)+P22(f317(f317(f319(f857(x98263,x98263)),f317(f317(f237(x98263,x98263),x98261),f759(x98264,x98265,x98262,x98261,x98263))),f317(f317(f182(f857(x98263,x98263),a842),f758(x98264,x98265,x98262,x98261,x98263)),x98264)))+~P22(f317(f317(f319(f857(x98263,x98263)),f317(f317(f237(x98263,x98263),x98261),x98262)),f317(f317(f182(f857(x98263,x98263),a842),x98265),x98264))) % 168.22/168.06 [9827]E(x98271,f2(a849))+P22(f317(f317(f319(f857(x98272,x98272)),f317(f317(f237(x98272,x98272),x98273),f759(x98274,x98271,x98275,x98273,x98272))),f317(f317(f182(f857(x98272,x98272),a842),f758(x98274,x98271,x98275,x98273,x98272)),x98274)))+~P22(f317(f317(f319(f857(x98272,x98272)),f317(f317(f237(x98272,x98272),x98273),x98275)),f317(f317(f182(f857(x98272,x98272),a842),x98271),x98274))) % 168.22/168.06 [9883]E(x98831,x98832)+P22(f317(f317(f319(f857(x98833,x98833)),f317(f317(f237(x98833,x98833),f761(x98834,x98835,x98831,x98832,x98833)),x98831)),f317(f317(f182(f857(x98833,x98833),a842),f760(x98834,x98835,x98831,x98832,x98833)),x98834)))+~P22(f317(f317(f319(f857(x98833,x98833)),f317(f317(f237(x98833,x98833),x98832),x98831)),f317(f317(f182(f857(x98833,x98833),a842),x98835),x98834))) % 168.22/168.06 [9884]E(x98841,f2(a849))+P22(f317(f317(f319(f857(x98842,x98842)),f317(f317(f237(x98842,x98842),f761(x98843,x98841,x98844,x98845,x98842)),x98844)),f317(f317(f182(f857(x98842,x98842),a842),f760(x98843,x98841,x98844,x98845,x98842)),x98843)))+~P22(f317(f317(f319(f857(x98842,x98842)),f317(f317(f237(x98842,x98842),x98845),x98844)),f317(f317(f182(f857(x98842,x98842),a842),x98841),x98843))) % 168.22/168.06 [9915]~P67(x99152)+~P22(f317(f71(x99151),x99155))+E(f317(f317(f6(x99151,x99152),f317(f317(f7(x99151,x99152,x99152),f317(f317(f18(x99151,x99152,f858(x99152,x99152)),f317(f317(f8(a842,f858(x99152,f858(x99152,x99152)),x99151),f108(x99152)),f317(f317(f7(x99151,f858(x99151,a842),a842),f319(x99151)),x99153))),x99154)),f2(x99152))),x99155),f317(f317(f6(x99151,x99152),x99154),f317(f317(f113(f858(x99151,a842)),x99155),x99153))) % 168.22/168.06 [8511]~P70(x85111)+~P22(f317(f71(x85114),x85115))+E(f317(f317(f90(x85111),f317(x85112,x85113)),f317(f317(f9(x85114,x85111),x85112),f317(f317(f21(f858(x85114,a842)),x85115),f317(f317(f286(x85114),x85113),f188(f858(x85114,a842)))))),f317(f317(f9(x85114,x85111),x85112),f317(f317(f286(x85114),x85113),x85115))) % 168.22/168.06 [8512]~P67(x85121)+~P22(f317(f71(x85124),x85125))+E(f317(f317(f89(x85121),f317(x85122,x85123)),f317(f317(f6(x85124,x85121),x85122),f317(f317(f21(f858(x85124,a842)),x85125),f317(f317(f286(x85124),x85123),f188(f858(x85124,a842)))))),f317(f317(f6(x85124,x85121),x85122),f317(f317(f286(x85124),x85123),x85125))) % 168.22/168.06 [8823]~P103(x88232)+~P29(x88232,f317(f163(x88232),f317(f317(f148(x88231,x88232),x88234),x88235)))+E(f317(f130(x88231,f317(f317(f8(x88232,a842,x88231),f317(f226(x88232),x88233)),x88234)),x88235),f170(x88231,f317(f317(f8(x88232,a842,x88231),f317(f226(x88232),x88233)),x88234),x88235)) % 168.22/168.06 [8847]~P67(x88471)+E(f317(f317(f89(x88471),f317(f317(f6(a849,x88471),x88472),f279(a849,x88473,x88474))),f317(f317(f6(a849,x88471),x88472),f279(a849,f317(f317(f89(a849),x88474),f87(a849)),f317(f317(f89(a849),x88474),x88475)))),f317(f317(f6(a849,x88471),x88472),f279(a849,x88473,f317(f317(f89(a849),x88474),x88475))))+~P22(f317(f317(f225(a849),x88473),f317(f317(f89(a849),x88474),f87(a849)))) % 168.22/168.06 [8848]~P22(f317(f317(f319(x88481),x88484),x88485))+~P22(f317(f317(f225(f858(x88481,a842)),f317(f166(x88481),x88482)),x88485))+P22(f317(f317(f225(f858(x88481,a842)),f317(f166(x88481),f317(f317(f153(x88481,x88482),x88483),x88484))),x88485)) % 168.22/168.06 [9070]~P27(x90702)+~P22(f317(f71(x90701),x90705))+E(f317(f317(f74(x90701,x90702,f317(f317(f8(x90702,f858(x90702,x90702),x90701),f122(x90702)),x90703)),x90704),x90705),f317(f317(f122(x90702),x90704),f317(f317(f51(x90701,x90702),x90705),x90703))) % 168.22/168.06 [9071]~P27(x90712)+~P22(f317(f71(x90711),x90715))+E(f317(f317(f74(x90711,x90712,f317(f317(f8(x90712,f858(x90712,x90712),x90711),f113(x90712)),x90713)),x90714),x90715),f317(f317(f113(x90712),x90714),f317(f317(f52(x90711,x90712),x90715),x90713))) % 168.22/168.06 [9118]E(f317(x91181,x91182),f317(x91181,x91183))+P22(f317(f317(f226(a849),f317(x91181,x91182)),f317(x91181,x91183)))+~P22(f317(f317(f319(f857(x91184,x91184)),f317(f317(f237(x91184,x91184),x91182),x91183)),f147(x91184,f317(f317(f145(f858(x91184,a849)),x91181),x91185)))) % 168.22/168.06 [9148]~E(f317(x91484,x91482),f317(x91484,x91483))+~P22(f317(f317(f319(f857(x91481,x91481)),f317(f317(f237(x91481,x91481),x91482),x91483)),f147(x91481,x91485)))+P22(f317(f317(f319(f857(x91481,x91481)),f317(f317(f237(x91481,x91481),x91482),x91483)),f147(x91481,f317(f317(f145(f858(x91481,a849)),x91484),x91485)))) % 168.22/168.06 [9171]~P19(x91711,x91712,x91713,x91715)+P19(x91711,x91712,x91713,f317(f317(f286(x91711),x91714),x91715))+P22(f317(f317(f319(x91712),f317(x91713,x91714)),f317(f287(x91711,x91712,x91713),f317(f317(f21(f858(x91711,a842)),x91715),f317(f317(f286(x91711),x91714),f188(f858(x91711,a842))))))) % 168.22/168.06 [9175]P22(f317(x91752,x91755))+~P22(f317(f317(f319(x91751),x91755),f317(f166(x91751),x91753)))+E(f317(f317(f132(x91751),f317(f189(f850(x91751)),f170(x91751,x91752,f317(f317(f127(x91751),x91753),x91754)))),f317(f317(f127(x91751),x91753),x91754)),f317(f317(f127(x91751),f317(f317(f132(x91751),f317(f189(f850(x91751)),f170(x91751,x91752,x91753))),x91753)),x91754)) % 168.22/168.06 [9178]~P22(f317(f317(f319(f857(x91781,x91781)),f317(f317(f237(x91781,x91781),x91782),x91783)),f147(x91781,x91785)))+~P22(f317(f317(f225(a849),f317(x91784,x91782)),f317(x91784,x91783)))+P22(f317(f317(f319(f857(x91781,x91781)),f317(f317(f237(x91781,x91781),x91782),x91783)),f147(x91781,f317(f317(f145(f858(x91781,a849)),x91784),x91785)))) % 168.22/168.06 [9239]P22(f317(f317(f319(f857(x92394,x92394)),f317(f317(f237(x92394,x92394),x92392),x92393)),f147(x92394,x92395)))+P22(f317(f317(f226(a849),f317(x92391,x92392)),f317(x92391,x92393)))+~P22(f317(f317(f319(f857(x92394,x92394)),f317(f317(f237(x92394,x92394),x92392),x92393)),f147(x92394,f317(f317(f145(f858(x92394,a849)),x92391),x92395)))) % 168.22/168.06 [9383]~P22(f317(f317(f319(f857(f850(x93831),f850(x93831))),f317(f317(f237(f850(x93831),f850(x93831)),x93832),x93834)),f152(x93831,x93835)))+~P22(f317(f317(f226(a849),x93833),f317(f189(f850(x93831)),x93832)))+P22(f317(f317(f319(f857(x93831,x93831)),f317(f317(f237(x93831,x93831),f317(f317(f159(x93831),x93832),x93833)),f317(f317(f159(x93831),x93834),x93833))),x93835)) % 168.22/168.06 [9610]E(x96101,f2(a1))+~P22(f317(f58(x96103,x96101),f317(f317(f237(a1,a1),x96104),x96105)))+P22(f317(f58(f317(f317(f90(a1),x96102),x96103),x96101),f317(f317(f237(a1,a1),f317(f317(f89(a1),f317(f317(f90(a1),x96102),x96104)),f317(f48(a1,f317(f317(f90(a1),x96102),x96105)),x96101))),f55(a1,f317(f317(f90(a1),x96102),x96105),x96101)))) % 168.22/168.06 [9612]~P22(f317(f317(f226(a849),f2(a849)),x96123))+~P22(f317(f57(x96122,x96123),f317(f317(f237(a849,a849),x96124),x96125)))+P22(f317(f57(f317(f317(f90(a849),x96121),x96122),x96123),f317(f317(f237(a849,a849),f317(f317(f89(a849),f317(f317(f90(a849),x96121),x96124)),f317(f48(a849,f317(f317(f90(a849),x96121),x96125)),x96123))),f55(a849,f317(f317(f90(a849),x96121),x96125),x96123)))) % 168.22/168.06 [9938]~P67(x99382)+~P22(f317(f71(x99381),x99384))+E(f317(f317(f6(x99381,x99382),x99383),f317(f230(x99381),f317(f317(f18(x99381,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99381),a315),f317(f317(f7(x99381,f858(x99381,a842),a842),f319(x99381)),x99384))),f317(f317(f7(x99381,f858(x99381,a842),a842),f319(x99381)),x99385)))),f317(f317(f6(x99381,x99382),f317(f317(f7(x99381,x99382,x99382),f317(f317(f18(x99381,x99382,f858(x99382,x99382)),f317(f317(f8(a842,f858(x99382,f858(x99382,x99382)),x99381),f108(x99382)),f317(f317(f7(x99381,f858(x99381,a842),a842),f319(x99381)),x99385))),x99383)),f2(x99382))),x99384)) % 168.22/168.06 [8133]~E(f317(f317(f127(x81331),x81332),x81335),f317(f317(f127(x81331),x81333),x81334))+E(f317(f317(f127(x81331),f317(f317(f132(x81331),f317(f189(f850(x81331)),x81332)),x81333)),x81334),x81335)+P22(f317(f317(f225(a849),f317(f189(f850(x81331)),x81333)),f317(f189(f850(x81331)),x81332))) % 168.22/168.06 [8335]~E(f317(f317(f127(x83352),x83353),x83351),f317(f317(f127(x83352),x83354),x83355))+E(x83351,f317(f317(f127(x83352),f317(f317(f132(x83352),f317(f189(f850(x83352)),x83353)),x83354)),x83355))+~P22(f317(f317(f225(a849),f317(f189(f850(x83352)),x83353)),f317(f189(f850(x83352)),x83354))) % 168.22/168.06 [8429]~E(f317(f317(f89(a849),f317(f317(f90(a849),x84293),x84294)),x84291),f317(f317(f89(a849),f317(f317(f90(a849),x84292),x84294)),x84295))+~P22(f317(f317(f225(a849),x84293),x84292))+E(x84291,f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x84292),x84293)),x84294)),x84295)) % 168.22/168.06 [8430]~E(f317(f317(f89(a849),f317(f317(f90(a849),x84301),x84303)),x84304),f317(f317(f89(a849),f317(f317(f90(a849),x84302),x84303)),x84305))+~P22(f317(f317(f225(a849),x84302),x84301))+E(f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x84301),x84302)),x84303)),x84304),x84305) % 168.22/168.06 [8584]E(f317(f317(f89(a849),f317(f317(f90(a849),x85841),x85842)),x85843),f317(f317(f89(a849),f317(f317(f90(a849),x85844),x85842)),x85845))+~P22(f317(f317(f225(a849),x85844),x85841))+~E(x85845,f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x85841),x85844)),x85842)),x85843)) % 168.22/168.06 [8585]E(f317(f317(f89(a849),f317(f317(f90(a849),x85851),x85852)),x85853),f317(f317(f89(a849),f317(f317(f90(a849),x85854),x85852)),x85855))+~P22(f317(f317(f225(a849),x85854),x85851))+~E(f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x85851),x85854)),x85852)),x85853),x85855) % 168.22/168.06 [9435]~P58(x94352)+~P22(f317(f71(x94351),x94355))+E(f317(f317(f9(x94351,x94352),f317(f317(f18(x94351,x94352,x94352),f317(f317(f8(x94352,f858(x94352,x94352),x94351),f266(x94352)),x94353)),x94354)),x94355),f317(f317(f266(x94352),f317(f317(f9(x94351,x94352),x94353),x94355)),f317(f317(f9(x94351,x94352),x94354),x94355))) % 168.22/168.06 [9554]~E(f772(x95545,x95544,x95543,x95542,x95541),f762(x95545,x95544,x95543,x95542,x95541))+P22(f317(f317(f319(f857(x95541,x95541)),f317(f317(f237(x95541,x95541),x95542),x95543)),f284(x95541,x95544)))+~P22(f317(f317(f319(f857(x95541,x95541)),f317(f317(f237(x95541,x95541),x95542),x95543)),f284(x95541,f317(f317(f122(f858(f857(x95541,x95541),a842)),x95544),x95545)))) % 168.22/168.06 [9555]~E(f773(x95555,x95554,x95553,x95552,x95551),f774(x95555,x95554,x95553,x95552,x95551))+P22(f317(f317(f319(f857(x95551,x95551)),f317(f317(f237(x95551,x95551),x95552),x95553)),f284(x95551,x95554)))+~P22(f317(f317(f319(f857(x95551,x95551)),f317(f317(f237(x95551,x95551),x95552),x95553)),f284(x95551,f317(f317(f122(f858(f857(x95551,x95551),a842)),x95554),x95555)))) % 168.22/168.06 [9764]P22(f317(f317(f319(f857(x97641,x97641)),f317(f317(f237(x97641,x97641),x97642),f762(x97645,x97644,x97643,x97642,x97641))),f284(x97641,x97644)))+P22(f317(f317(f319(f857(x97641,x97641)),f317(f317(f237(x97641,x97641),x97642),x97643)),f284(x97641,x97644)))+~P22(f317(f317(f319(f857(x97641,x97641)),f317(f317(f237(x97641,x97641),x97642),x97643)),f284(x97641,f317(f317(f122(f858(f857(x97641,x97641),a842)),x97644),x97645)))) % 168.22/168.06 [9848]P22(f317(f317(f319(f857(x98481,x98481)),f317(f317(f237(x98481,x98481),f774(x98485,x98484,x98483,x98482,x98481)),x98483)),f284(x98481,x98484)))+P22(f317(f317(f319(f857(x98481,x98481)),f317(f317(f237(x98481,x98481),x98482),x98483)),f284(x98481,x98484)))+~P22(f317(f317(f319(f857(x98481,x98481)),f317(f317(f237(x98481,x98481),x98482),x98483)),f284(x98481,f317(f317(f122(f858(f857(x98481,x98481),a842)),x98484),x98485)))) % 168.22/168.06 [9890]P22(f317(f317(f319(f857(x98901,x98901)),f317(f317(f237(x98901,x98901),x98902),x98903)),f284(x98901,x98904)))+P22(f317(f317(f319(f857(x98901,x98901)),f317(f317(f237(x98901,x98901),f762(x98905,x98904,x98903,x98902,x98901)),f772(x98905,x98904,x98903,x98902,x98901))),x98905))+~P22(f317(f317(f319(f857(x98901,x98901)),f317(f317(f237(x98901,x98901),x98902),x98903)),f284(x98901,f317(f317(f122(f858(f857(x98901,x98901),a842)),x98904),x98905)))) % 168.22/168.06 [9891]P22(f317(f317(f319(f857(x98911,x98911)),f317(f317(f237(x98911,x98911),x98912),x98913)),f284(x98911,x98914)))+P22(f317(f317(f319(f857(x98911,x98911)),f317(f317(f237(x98911,x98911),f773(x98915,x98914,x98913,x98912,x98911)),f774(x98915,x98914,x98913,x98912,x98911))),x98915))+~P22(f317(f317(f319(f857(x98911,x98911)),f317(f317(f237(x98911,x98911),x98912),x98913)),f284(x98911,f317(f317(f122(f858(f857(x98911,x98911),a842)),x98914),x98915)))) % 168.22/168.06 [10009]~P22(f317(f317(f319(f857(f850(x100091),f850(x100091))),f317(f317(f237(f850(x100091),f850(x100091)),x100094),x100095)),f152(x100091,x100092)))+~P22(f317(f317(f319(f857(x100091,x100091)),x100093),f317(f166(f857(x100091,x100091)),f317(f317(f175(x100091,x100091),x100094),x100095))))+P22(f317(f317(f247(x100091,x100091,a842),f317(f317(f7(x100091,f858(f857(x100091,x100091),a842),f858(x100091,a842)),f317(f317(f8(f858(x100091,f858(f858(f857(x100091,x100091),a842),a842)),f858(f858(f857(x100091,x100091),a842),f858(x100091,a842)),x100091),f7(x100091,f858(f857(x100091,x100091),a842),a842)),f317(f317(f8(f858(x100091,f857(x100091,x100091)),f858(x100091,f858(f858(f857(x100091,x100091),a842),a842)),x100091),f317(f8(f857(x100091,x100091),f858(f858(f857(x100091,x100091),a842),a842),x100091),f319(f857(x100091,x100091)))),f237(x100091,x100091)))),x100092)),x100093)) % 168.22/168.06 [9462]~P22(f317(f317(f225(a849),x94623),x94622))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),f317(f317(f90(a849),x94623),x94624)),x94621)),f317(f317(f89(a849),f317(f317(f90(a849),x94622),x94624)),x94625)))+P22(f317(f317(f225(a849),x94621),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x94622),x94623)),x94624)),x94625))) % 168.22/168.06 [9463]~P22(f317(f317(f225(a849),x94633),x94632))+~P22(f317(f317(f226(a849),f317(f317(f89(a849),f317(f317(f90(a849),x94633),x94634)),x94631)),f317(f317(f89(a849),f317(f317(f90(a849),x94632),x94634)),x94635)))+P22(f317(f317(f226(a849),x94631),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x94632),x94633)),x94634)),x94635))) % 168.22/168.06 [9483]~P22(f317(f317(f225(a849),x94831),x94834))+P22(f317(f317(f225(a849),f317(f317(f89(a849),f317(f317(f90(a849),x94831),x94832)),x94833)),f317(f317(f89(a849),f317(f317(f90(a849),x94834),x94832)),x94835)))+~P22(f317(f317(f225(a849),x94833),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x94834),x94831)),x94832)),x94835))) % 168.22/168.06 [9484]~P22(f317(f317(f225(a849),x94841),x94844))+P22(f317(f317(f226(a849),f317(f317(f89(a849),f317(f317(f90(a849),x94841),x94842)),x94843)),f317(f317(f89(a849),f317(f317(f90(a849),x94844),x94842)),x94845)))+~P22(f317(f317(f226(a849),x94843),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x94844),x94841)),x94842)),x94845))) % 168.22/168.06 [9587]~P22(f317(f317(f225(a849),x95872),x95871))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),f317(f317(f90(a849),x95871),x95873)),x95874)),f317(f317(f89(a849),f317(f317(f90(a849),x95872),x95873)),x95875)))+P22(f317(f317(f225(a849),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x95871),x95872)),x95873)),x95874)),x95875)) % 168.22/168.06 [9588]~P22(f317(f317(f225(a849),x95882),x95881))+~P22(f317(f317(f226(a849),f317(f317(f89(a849),f317(f317(f90(a849),x95881),x95883)),x95884)),f317(f317(f89(a849),f317(f317(f90(a849),x95882),x95883)),x95885)))+P22(f317(f317(f226(a849),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x95881),x95882)),x95883)),x95884)),x95885)) % 168.22/168.06 [9640]~P22(f317(f317(f225(a849),x96404),x96401))+P22(f317(f317(f225(a849),f317(f317(f89(a849),f317(f317(f90(a849),x96401),x96402)),x96403)),f317(f317(f89(a849),f317(f317(f90(a849),x96404),x96402)),x96405)))+~P22(f317(f317(f225(a849),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x96401),x96404)),x96402)),x96403)),x96405)) % 168.22/168.06 [9641]~P22(f317(f317(f225(a849),x96414),x96411))+P22(f317(f317(f226(a849),f317(f317(f89(a849),f317(f317(f90(a849),x96411),x96412)),x96413)),f317(f317(f89(a849),f317(f317(f90(a849),x96414),x96412)),x96415)))+~P22(f317(f317(f226(a849),f317(f317(f89(a849),f317(f317(f90(a849),f317(f317(f21(a849),x96411),x96414)),x96412)),x96413)),x96415)) % 168.22/168.06 [9875]~P9(x98751,x98752,x98755,x98753)+~P22(f317(f317(f319(f857(x98751,x98751)),x98754),x98755))+P22(f317(f317(f247(x98751,x98751,a842),f317(f317(f7(x98751,f858(x98751,x98752),f858(x98751,a842)),f317(f317(f8(f858(x98752,a842),f858(f858(x98751,x98752),f858(x98751,a842)),x98751),f8(x98752,a842,x98751)),f317(f317(f8(x98752,f858(x98752,a842),x98751),a314),x98753))),x98753)),x98754)) % 168.22/168.06 [6692]~E(f317(x66924,x66925),f191(x66922))+E(f317(f178(x66921,x66922,x66923,x66924),x66925),f317(f217(x66922),x66926))+~E(f317(x66923,x66925),f317(f217(x66922),x66926)) % 168.22/168.06 [6785]~E(f317(x67853,x67856),f191(x67851))+E(f317(f220(f853(x67851),x67852,f191(x67851),x67853),f317(x67854,x67855)),f191(x67851))+~E(f317(x67854,x67855),f317(f217(x67852),x67856)) % 168.22/168.06 [7369]E(f317(x73691,x73692),f191(x73693))+~E(f317(f178(x73695,x73693,x73696,x73691),x73692),f317(f217(x73693),x73694))+E(f317(x73691,x73692),f317(f217(x73693),x73694)) % 168.22/168.06 [7402]~E(f317(f178(x74026,x74023,x74025,x74021),x74022),f317(f217(x74023),x74024))+E(f317(x74021,x74022),f317(f217(x74023),x74024))+E(f317(x74025,x74022),f317(f217(x74023),x74024)) % 168.22/168.06 [8294]~P14(x82946,x82941,x82942,x82944)+E(f317(f82(x82941,x82941,x82941,f317(x82942,x82943)),f317(x82944,x82945)),f317(f82(x82941,x82941,x82941,f317(x82944,x82945)),f317(x82942,x82943)))+~P22(f317(f71(x82946),x82945)) % 168.22/168.06 [8715]~P19(x87151,x87153,x87155,x87156)+~P19(x87153,x87152,x87154,f317(f287(x87151,x87153,x87155),x87156))+P19(x87151,x87152,f317(f82(x87153,x87152,x87151,x87154),x87155),x87156) % 168.22/168.06 [9272]~P22(f317(f317(x92723,x92722),x92726))+~P22(f317(f317(x92724,x92725),x92722))+P22(f317(f317(f319(x92721),x92722),f276(x92721,x92723,x92724,x92725,x92726))) % 168.22/168.06 [9273]~P22(f317(f317(x92734,x92732),x92736))+~P22(f317(f317(x92733,x92735),x92732))+P22(f317(f317(f319(x92731),x92732),f273(x92731,x92733,x92734,x92735,x92736))) % 168.22/168.06 [9384]E(x93841,x93842)+E(x93843,x93844)+~P22(f317(f317(f319(f857(f850(x93845),f850(x93845))),f317(f317(f237(f850(x93845),f850(x93845)),f317(f317(f145(x93845),x93843),x93841)),f317(f317(f145(x93845),x93844),x93842))),f151(x93845,x93846))) % 168.22/168.06 [9394]~E(x93942,x93944)+P22(f317(f317(f319(f857(f850(x93941),f850(x93941))),f317(f317(f237(f850(x93941),f850(x93941)),f317(f317(f145(x93941),x93942),x93943)),f317(f317(f145(x93941),x93944),x93945))),f139(x93941,x93946)))+~P22(f317(f317(f319(f857(f850(x93941),f850(x93941))),f317(f317(f237(f850(x93941),f850(x93941)),x93943),x93945)),f139(x93941,x93946))) % 168.22/168.06 [9395]~E(x93952,x93954)+P22(f317(f317(f319(f857(f850(x93951),f850(x93951))),f317(f317(f237(f850(x93951),f850(x93951)),f317(f317(f145(x93951),x93952),x93953)),f317(f317(f145(x93951),x93954),x93955))),f141(x93951,x93956)))+~P22(f317(f317(f319(f857(f850(x93951),f850(x93951))),f317(f317(f237(f850(x93951),f850(x93951)),x93953),x93955)),f141(x93951,x93956))) % 168.22/168.06 [9396]~E(x93962,x93964)+P22(f317(f317(f319(f857(f850(x93961),f850(x93961))),f317(f317(f237(f850(x93961),f850(x93961)),f317(f317(f145(x93961),x93962),x93963)),f317(f317(f145(x93961),x93964),x93965))),f151(x93961,x93966)))+~P22(f317(f317(f319(f857(f850(x93961),f850(x93961))),f317(f317(f237(f850(x93961),f850(x93961)),x93963),x93965)),f151(x93961,x93966))) % 168.22/168.06 [9397]~E(x93972,x93974)+P22(f317(f317(f319(f857(f850(x93971),f850(x93971))),f317(f317(f237(f850(x93971),f850(x93971)),f317(f317(f127(x93971),x93972),x93973)),f317(f317(f127(x93971),x93974),x93975))),f151(x93971,x93976)))+~P22(f317(f317(f319(f857(f850(x93971),f850(x93971))),f317(f317(f237(f850(x93971),f850(x93971)),x93973),x93975)),f151(x93971,x93976))) % 168.22/168.06 [9398]~E(x93983,x93985)+P22(f317(f317(f319(f857(f850(x93981),f850(x93981))),f317(f317(f237(f850(x93981),f850(x93981)),f317(f317(f127(x93981),x93982),x93983)),f317(f317(f127(x93981),x93984),x93985))),f151(x93981,x93986)))+~P22(f317(f317(f319(f857(f850(x93981),f850(x93981))),f317(f317(f237(f850(x93981),f850(x93981)),x93982),x93984)),f151(x93981,x93986))) % 168.22/168.06 [9450]E(x94501,x94502)+P22(f317(f317(f319(f857(f850(x94503),f850(x94503))),f317(f317(f237(f850(x94503),f850(x94503)),x94501),x94502)),f151(x94503,x94504)))+~P22(f317(f317(f319(f857(f850(x94503),f850(x94503))),f317(f317(f237(f850(x94503),f850(x94503)),f317(f317(f145(x94503),x94505),x94501)),f317(f317(f145(x94503),x94506),x94502))),f151(x94503,x94504))) % 168.22/168.06 [9591]~E(x95913,x95915)+P22(f317(f317(f319(f857(f850(x95911),f850(x95911))),f317(f317(f237(f850(x95911),f850(x95911)),f317(f317(f127(x95911),x95912),f317(f317(f145(x95911),x95913),f125(x95911)))),f317(f317(f127(x95911),x95914),f317(f317(f145(x95911),x95915),f125(x95911))))),f151(x95911,x95916)))+~P22(f317(f317(f319(f857(f850(x95911),f850(x95911))),f317(f317(f237(f850(x95911),f850(x95911)),x95912),x95914)),f151(x95911,x95916))) % 168.22/168.06 [9607]E(f317(x96071,x96072),f191(x96073))+~E(f317(f220(f853(x96076),x96073,f191(x96076),x96074),f317(x96071,x96072)),f191(x96076))+E(f317(x96074,f834(x96072,x96071,x96074,x96075,x96076,x96073)),f191(x96076)) % 168.22/168.06 [9608]E(f317(x96081,x96082),f191(x96083))+~E(f317(f220(f853(x96086),x96083,f191(x96086),x96084),f317(x96081,x96082)),f191(x96086))+E(f317(f217(x96083),f834(x96082,x96081,x96084,x96085,x96086,x96083)),f317(x96081,x96082)) % 168.22/168.06 [9644]E(x96441,x96442)+E(x96443,x96444)+~P22(f317(f317(f319(f857(f850(x96445),f850(x96445))),f317(f317(f237(f850(x96445),f850(x96445)),f317(f317(f127(x96445),x96443),f317(f317(f145(x96445),x96441),f125(x96445)))),f317(f317(f127(x96445),x96444),f317(f317(f145(x96445),x96442),f125(x96445))))),f151(x96445,x96446))) % 168.22/168.06 [9669]E(x96691,x96692)+~P22(f317(f317(f319(f857(f850(x96693),f850(x96693))),f317(f317(f237(f850(x96693),f850(x96693)),f317(f317(f127(x96693),x96691),f317(f317(f145(x96693),x96695),f125(x96693)))),f317(f317(f127(x96693),x96692),f317(f317(f145(x96693),x96696),f125(x96693))))),f151(x96693,x96694)))+P22(f317(f317(f319(f857(f850(x96693),f850(x96693))),f317(f317(f237(f850(x96693),f850(x96693)),x96691),x96692)),f151(x96693,x96694))) % 168.22/168.06 [9703]~P22(f317(f317(f319(f857(f858(x97031,a842),f858(x97031,a842))),f317(f317(f237(f858(x97031,a842),f858(x97031,a842)),x97032),x97034)),f309(x97031,x97036)))+~P22(f317(f317(f319(f857(f858(x97031,a842),f858(x97031,a842))),f317(f317(f237(f858(x97031,a842),f858(x97031,a842)),x97033),x97035)),f309(x97031,x97036)))+P22(f317(f317(f319(f857(f858(x97031,a842),f858(x97031,a842))),f317(f317(f237(f858(x97031,a842),f858(x97031,a842)),f317(f317(f122(f858(x97031,a842)),x97032),x97033)),f317(f317(f122(f858(x97031,a842)),x97034),x97035))),f309(x97031,x97036))) % 168.22/168.06 [5177]~E(f317(x51773,x51776),x51775)+~E(x51774,f317(f217(x51771),x51776))+E(f317(f317(f192(x51771,x51772),x51773),x51774),f317(f217(x51772),x51775)) % 168.22/168.06 [5586]~E(f317(f317(f127(x55861),x55866),x55863),x55865)+E(f317(f317(f127(x55861),x55862),x55863),f317(f317(f145(x55861),x55864),x55865))+~E(x55862,f317(f317(f145(x55861),x55864),x55866)) % 168.22/168.06 [5587]~E(f317(f317(f127(x55871),x55876),x55873),x55875)+E(f317(f317(f127(x55871),x55872),x55873),f317(f317(f127(x55871),x55874),x55875))+~E(x55872,f317(f317(f127(x55871),x55874),x55876)) % 168.22/168.06 [5589]E(f317(f317(f127(x55891),x55892),x55893),f317(f317(f145(x55891),x55894),x55895))+~E(f317(f317(f145(x55891),x55894),x55896),x55892)+~E(x55895,f317(f317(f127(x55891),x55896),x55893)) % 168.22/168.06 [5591]~E(f317(f317(f127(x55911),x55912),x55916),x55914)+E(f317(f317(f127(x55911),x55912),x55913),f317(f317(f127(x55911),x55914),x55915))+~E(x55913,f317(f317(f127(x55911),x55916),x55915)) % 168.22/168.06 [6686]E(f317(x66861,x66862),f317(x66863,x66862))+~E(f317(f317(f148(x66864,x66865),x66861),x66866),f317(f317(f148(x66864,x66865),x66863),x66866))+~P22(f317(f317(f319(x66864),x66862),f317(f166(x66864),x66866))) % 168.22/168.06 [7072]~P14(x70724,x70725,x70726,x70721)+E(f317(f317(x70721,x70722),x70723),f317(f317(f74(x70724,x70725,x70726),x70723),x70722))+~P22(f317(f71(x70724),x70722)) % 168.22/168.06 [7136]~E(x71362,f317(x71364,x71366))+~P22(f317(f317(f319(x71363),x71366),x71365))+P22(f317(f317(f319(x71361),x71362),f317(f287(x71363,x71361,x71364),x71365))) % 168.22/168.06 [7137]~E(f317(x71374,x71372),x71376)+~P22(f317(f317(f319(x71373),x71376),x71375))+P22(f317(f317(f319(x71371),x71372),f317(f289(x71371,x71373,x71374),x71375))) % 168.22/168.06 [7580]~P33(x75801,x75802,x75804,x75806)+P33(x75801,x75802,f317(f317(f145(x75801),x75803),x75804),f317(f317(f145(x75801),x75805),x75806))+~P22(f317(f317(x75802,x75803),x75805)) % 168.22/168.06 [8592]~P51(x85924,x85925,x85921,x85922,x85926)+E(f317(x85921,f317(x85922,x85923)),x85923)+~P22(f317(f317(f319(x85925),x85923),x85926)) % 168.22/168.06 [9386]E(x93861,x93862)+E(f317(f189(f850(x93863)),x93864),f317(f189(f850(x93863)),x93865))+~P22(f317(f317(f319(f857(f850(x93863),f850(x93863))),f317(f317(f237(f850(x93863),f850(x93863)),f317(f317(f145(x93863),x93861),x93864)),f317(f317(f145(x93863),x93862),x93865))),f139(x93863,x93866))) % 168.22/168.06 [9453]E(f317(f189(f850(x94531)),x94532),f317(f189(f850(x94531)),x94533))+P22(f317(f317(f319(f857(f850(x94531),f850(x94531))),f317(f317(f237(f850(x94531),f850(x94531)),x94532),x94533)),f139(x94531,x94534)))+~P22(f317(f317(f319(f857(f850(x94531),f850(x94531))),f317(f317(f237(f850(x94531),f850(x94531)),f317(f317(f145(x94531),x94535),x94532)),f317(f317(f145(x94531),x94536),x94533))),f139(x94531,x94534))) % 168.22/168.06 [9476]~P22(f317(f317(f319(f857(x94761,x94761)),f317(f317(f237(x94761,x94761),x94762),x94764)),f284(x94761,x94766)))+P22(f317(f317(f319(f857(f850(x94761),f850(x94761))),f317(f317(f237(f850(x94761),f850(x94761)),f317(f317(f145(x94761),x94762),x94763)),f317(f317(f145(x94761),x94764),x94765))),f284(f850(x94761),f151(x94761,x94766))))+~P22(f317(f317(f319(f857(f850(x94761),f850(x94761))),f317(f317(f237(f850(x94761),f850(x94761)),x94763),x94765)),f284(f850(x94761),f151(x94761,x94766)))) % 168.22/168.06 [9651]~P22(f317(x96512,x96516))+~E(f317(f130(x96511,x96512),x96513),f317(f317(f145(x96511),x96514),x96515))+~P22(f317(f317(f319(x96511),x96516),f317(f166(x96511),f724(x96515,x96514,x96513,x96512,x96511)))) % 168.22/168.06 [9652]~P22(f317(x96524,x96526))+~E(f317(f317(f145(x96521),x96522),x96523),f317(f130(x96521,x96524),x96525))+~P22(f317(f317(f319(x96521),x96526),f317(f166(x96521),f727(x96525,x96524,x96523,x96522,x96521)))) % 168.22/168.06 [9964]~P67(x99642)+E(f317(f317(f6(x99641,x99642),f317(f317(f8(f858(x99643,a842),x99642,x99641),f317(f6(x99643,x99642),x99644)),f317(f317(f8(f858(x99643,a842),f858(x99643,a842),x99641),f230(x99643)),f317(f317(f8(f858(x99643,a842),f858(x99643,a842),x99641),f317(f18(x99643,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99643),a315),f317(f317(f7(x99643,f858(x99643,a842),a842),f319(x99643)),x99645)))),f317(f7(x99643,x99641,a842),f317(f317(f8(x99641,f858(x99641,a842),x99643),a314),x99646)))))),f317(f287(x99643,x99641,x99646),x99645)),f317(f317(f6(x99643,x99642),x99644),x99645))+~P22(f317(f71(x99643),x99645)) % 168.22/168.06 [6739]~P103(x67393)+P22(f317(x67392,x67395))+E(f317(f130(x67391,x67392),f317(f317(f143(x67391,x67393,x67394),x67395),x67396)),f317(f130(x67391,x67392),x67396)) % 168.22/168.06 [6741]P22(f317(x67411,x67412))+~E(f161(x67413,x67411,x67414),f317(f317(f237(f850(x67413),f850(x67413)),x67415),x67416))+~P22(f317(f317(f319(x67413),x67412),f317(f166(x67413),x67415))) % 168.22/168.06 [6783]~P22(f317(x67832,x67836))+~E(f161(x67831,x67832,x67833),f317(f317(f237(f850(x67831),f850(x67831)),x67834),x67835))+~P22(f317(f317(f319(x67831),x67836),f317(f166(x67831),x67835))) % 168.22/168.06 [7446]~P11(x74461,x74462,x74463)+~P22(f317(f71(x74461),x74466))+E(f317(f317(f74(x74461,x74462,x74463),x74464),f317(f317(f286(x74461),x74465),x74466)),f317(f317(f74(x74461,x74462,x74463),f317(f317(x74463,x74465),x74464)),x74466)) % 168.22/168.06 [7497]~P103(x74972)+~P22(f317(f317(f225(x74972),f317(x74973,x74974)),f317(x74973,x74975)))+E(f317(f317(f143(x74971,x74972,x74973),x74974),f317(f317(f145(x74971),x74975),x74976)),f317(f317(f145(x74971),x74974),f317(f317(f145(x74971),x74975),x74976))) % 168.22/168.06 [7609]E(x76091,x76092)+~E(f317(f317(f245(x76093,x76094),x76091),f317(f16(f858(x76094,a842),x76093),x76095)),f317(f317(f245(x76093,x76094),x76092),f317(f16(f858(x76094,a842),x76093),x76095)))+~P22(f317(f317(f319(x76094),x76096),x76095)) % 168.22/168.06 [7677]~P11(x76771,x76772,x76773)+~P22(f317(f71(x76771),x76776))+E(f317(f317(f74(x76771,x76772,x76773),x76774),f317(f317(f286(x76771),x76775),x76776)),f317(f317(x76773,x76775),f317(f317(f74(x76771,x76772,x76773),x76774),x76776))) % 168.22/168.06 [7854]~P15(x78542,x78545,x78546,x78541)+~P22(f317(f71(x78542),x78544))+E(f317(x78541,f317(f317(f286(x78542),x78543),x78544)),f317(f82(x78545,x78545,x78545,f317(x78541,x78544)),f317(x78546,x78543))) % 168.22/168.06 [7891]~P103(x78912)+P22(f317(f317(f225(x78912),f317(x78913,x78914)),f317(x78913,x78915)))+E(f317(f317(f143(x78911,x78912,x78913),x78914),f317(f317(f145(x78911),x78915),x78916)),f317(f317(f145(x78911),x78915),f317(f317(f143(x78911,x78912,x78913),x78914),x78916))) % 168.22/168.06 [8033]~E(f317(f189(f850(x80331)),x80335),f317(f189(f850(x80332)),x80336))+~E(f317(f189(f850(x80331)),x80333),f317(f189(f850(x80332)),x80334))+E(f317(f317(f127(f857(x80331,x80332)),f317(f317(f175(x80331,x80332),x80333),x80334)),f317(f317(f175(x80331,x80332),x80335),x80336)),f317(f317(f175(x80331,x80332),f317(f317(f127(x80331),x80333),x80335)),f317(f317(f127(x80332),x80334),x80336))) % 168.22/168.06 [8148]~E(x81482,f317(f287(x81483,x81481,x81484),x81486))+P22(f317(f317(f225(f858(x81481,a842)),x81482),f317(f287(x81483,x81481,x81484),x81485)))+~P22(f317(f317(f225(f858(x81483,a842)),x81486),x81485)) % 168.22/168.06 [8252]~P103(x82525)+E(f317(x82521,x82522),f317(x82521,x82523))+E(f317(f317(f143(x82524,x82525,x82521),x82522),f317(f317(f143(x82524,x82525,x82521),x82523),x82526)),f317(f317(f143(x82524,x82525,x82521),x82523),f317(f317(f143(x82524,x82525,x82521),x82522),x82526))) % 168.22/168.06 [8287]~P19(x82873,x82871,x82874,x82875)+P19(x82873,x82871,f317(f317(f317(f81(x82873,x82871),x82874),x82876),x82872),x82875)+P22(f317(f317(f319(x82871),x82872),f317(f287(x82873,x82871,x82874),x82875))) % 168.22/168.06 [8439]~P22(f317(f317(f319(x84392),x84394),f317(x84396,x84393)))+~P22(f317(f317(f319(x84391),x84393),x84395))+P22(f317(f317(f319(f857(x84391,x84392)),f317(f317(f237(x84391,x84392),x84393),x84394)),f317(f317(f245(x84391,x84392),x84395),x84396))) % 168.22/168.06 [8893]~P70(x88932)+~P19(x88934,x88931,x88935,x88936)+E(f317(f317(f9(x88931,x88932),x88933),f317(f287(x88934,x88931,x88935),x88936)),f317(f317(f9(x88934,x88932),f317(f82(x88931,x88932,x88934,x88933),x88935)),x88936)) % 168.22/168.06 [8894]~P67(x88942)+~P19(x88944,x88941,x88945,x88946)+E(f317(f317(f6(x88941,x88942),x88943),f317(f287(x88944,x88941,x88945),x88946)),f317(f317(f6(x88944,x88942),f317(f82(x88941,x88942,x88944,x88943),x88945)),x88946)) % 168.22/168.06 [8941]~P35(x89412,x89415,x89411,x89413,x89416)+P22(f317(f317(x89411,f317(f317(f159(x89412),x89413),x89414)),f317(f317(f159(x89415),x89416),x89414)))+~P22(f317(f317(f226(a849),x89414),f317(f189(f850(x89415)),x89416))) % 168.22/168.06 [8942]~P35(x89422,x89425,x89421,x89423,x89426)+P22(f317(f317(x89421,f317(f317(f159(x89422),x89423),x89424)),f317(f317(f159(x89425),x89426),x89424)))+~P22(f317(f317(f226(a849),x89424),f317(f189(f850(x89422)),x89423))) % 168.22/168.06 [9138]~E(f317(f317(f317(a200,x91385),f40(x91381)),f317(f317(a201,x91384),x91381)),f317(f317(f317(a200,x91386),f40(x91381)),f317(f317(a201,x91384),x91381)))+~P22(f317(f317(f194(x91383),f317(f317(f317(a200,x91384),f40(x91381)),f317(x91382,x91384))),x91386))+P22(f317(f317(f194(f32(x91381,x91382,x91383)),x91384),f317(f317(f317(a200,x91385),f40(x91381)),f317(f317(a201,x91384),x91381)))) % 168.22/168.06 [9144]~P14(x91443,x91441,x91446,x91442)+~P22(f317(f71(x91443),x91444))+E(f317(f82(x91441,x91441,x91441,f317(x91442,f317(f317(f21(f858(x91443,a842)),x91444),f317(f317(f286(x91443),x91445),f188(f858(x91443,a842)))))),f317(x91446,x91445)),f317(x91442,f317(f317(f286(x91443),x91445),x91444))) % 168.22/168.06 [9549]~E(f317(f317(f317(a200,f317(f317(a202,x95495),f317(a201,x95494))),x95491),f317(f317(a201,x95495),a25)),f317(f317(f317(a200,f317(f317(a202,x95496),f317(a201,x95494))),x95491),f317(f317(a201,x95496),a25)))+~P22(f317(f317(f194(f317(a29,x95492)),f317(f317(f317(a200,f317(f317(a202,x95494),a203)),f40(a26)),f317(x95493,x95494))),x95496))+P22(f317(f317(f194(f31(x95491,x95492,x95493)),x95494),f317(f317(f317(a200,f317(f317(a202,x95495),f317(a201,x95494))),x95491),f317(f317(a201,x95495),a25)))) % 168.22/168.06 [9744]~E(f317(f287(x97442,x97444,x97446),f233(f858(x97442,a842))),f233(f858(x97444,a842)))+~E(f317(f287(x97441,x97443,x97445),f233(f858(x97441,a842))),f233(f858(x97443,a842)))+E(f317(f287(f857(x97441,x97442),f857(x97443,x97444),f248(x97441,x97443,x97442,x97444,x97445,x97446)),f233(f858(f857(x97441,x97442),a842))),f233(f858(f857(x97443,x97444),a842))) % 168.22/168.06 [9797]~P19(x97973,x97974,x97975,f317(x97976,f705(x97976,x97975,x97974,x97973,x97972,x97971)))+P19(x97973,x97974,x97975,f317(f317(f52(x97972,f858(x97973,a842)),x97971),x97976))+E(x97971,f188(f858(x97972,a842))) % 168.22/168.06 [9856]P19(x98566,x98565,x98564,f317(f317(f52(x98562,f858(x98566,a842)),x98561),x98563))+E(x98561,f188(f858(x98562,a842)))+P22(f317(f317(f319(x98562),f705(x98563,x98564,x98565,x98566,x98562,x98561)),x98561)) % 168.22/168.06 [9862]P22(f317(f317(f319(x98621),f729(x98622,x98623,x98624,x98625,x98626,x98621)),x98626))+P22(f317(f317(f225(f858(f857(x98621,x98624),a842)),f317(f317(f245(x98621,x98624),x98626),x98623)),f317(f317(f245(x98621,x98624),x98625),x98622)))+~P22(f317(f317(f225(f858(x98621,a842)),x98626),x98625)) % 168.22/168.06 [9902]P18(x99026,x99025,f317(f317(f286(f848(x99026)),f317(f317(f317(f100(x99026),x99021),x99023),x99022)),f188(f858(f848(x99026),a842))))+~P18(x99026,x99025,f317(f317(f286(f848(x99026)),f317(f317(f317(f100(x99026),x99024),x99023),x99022)),f188(f858(f848(x99026),a842))))+P22(f317(f317(x99021,f712(x99021,x99022,x99023,x99024,x99025,x99026)),f725(x99021,x99022,x99023,x99024,x99025,x99026))) % 168.22/168.06 [9903]P18(x99036,x99035,f317(f317(f286(f848(x99036)),f317(f317(f317(f100(x99036),x99034),x99033),x99032)),f188(f858(f848(x99036),a842))))+~P18(x99036,x99035,f317(f317(f286(f848(x99036)),f317(f317(f317(f100(x99036),x99034),x99033),x99031)),f188(f858(f848(x99036),a842))))+P22(f317(f317(x99031,f755(x99032,x99031,x99033,x99034,x99035,x99036)),f763(x99032,x99031,x99033,x99034,x99035,x99036))) % 168.22/168.06 [9941]~P18(x99411,x99412,f317(f317(f286(f848(x99411)),f317(f317(f317(f100(x99411),x99413),x99414),x99416)),f188(f858(f848(x99411),a842))))+P18(x99411,x99412,f317(f317(f286(f848(x99411)),f317(f317(f317(f100(x99411),x99413),x99414),x99415)),f188(f858(f848(x99411),a842))))+~P22(f317(f317(x99415,f755(x99415,x99416,x99414,x99413,x99412,x99411)),f763(x99415,x99416,x99414,x99413,x99412,x99411))) % 168.22/168.06 [9942]~P18(x99421,x99422,f317(f317(f286(f848(x99421)),f317(f317(f317(f100(x99421),x99426),x99424),x99425)),f188(f858(f848(x99421),a842))))+P18(x99421,x99422,f317(f317(f286(f848(x99421)),f317(f317(f317(f100(x99421),x99423),x99424),x99425)),f188(f858(f848(x99421),a842))))+~P22(f317(f317(x99426,f712(x99423,x99425,x99424,x99426,x99422,x99421)),f725(x99423,x99425,x99424,x99426,x99422,x99421))) % 168.22/168.06 [9976]~P22(f317(f317(f225(f858(x99762,a842)),f317(x99764,f729(x99766,x99764,x99762,x99765,x99763,x99761))),f317(x99766,f729(x99766,x99764,x99762,x99765,x99763,x99761))))+~P22(f317(f317(f225(f858(x99761,a842)),x99763),x99765))+P22(f317(f317(f225(f858(f857(x99761,x99762),a842)),f317(f317(f245(x99761,x99762),x99763),x99764)),f317(f317(f245(x99761,x99762),x99765),x99766))) % 168.22/168.06 [7631]~P22(f317(x76311,x76315))+~P22(f317(x76316,x76314))+P22(f317(x76311,f317(f246(x76312,x76313),f317(f317(f237(x76312,x76313),x76314),x76315)))) % 168.22/168.06 [7632]~P22(f317(x76321,x76324))+~P22(f317(x76326,x76325))+P22(f317(x76321,f317(f244(x76322,x76323),f317(f317(f237(x76322,x76323),x76324),x76325)))) % 168.22/168.06 [7654]~E(f317(f189(f850(x76541)),x76543),f317(f189(f850(x76544)),x76545))+~E(f317(f317(f171(x76541,x76544),f317(f317(f175(x76541,x76544),x76543),x76545)),x76542),f317(f217(x76544),x76546))+P22(f317(f317(f319(x76541),x76542),f317(f166(x76541),x76543))) % 168.22/168.06 [7682]~P22(f317(f317(x76824,x76826),x76825))+~P22(f317(f317(f319(x76821),x76826),x76823))+P22(f317(f317(f317(f51(x76821,f858(x76822,a842)),x76823),x76824),x76825)) % 168.22/168.06 [7980]~P22(f317(f317(f319(x79801),x79802),f317(x79805,x79806)))+~P22(f317(f317(f319(x79803),x79806),x79804))+P22(f317(f317(f319(x79801),x79802),f317(f317(f51(x79803,f858(x79801,a842)),x79804),x79805))) % 168.22/168.06 [8025]P22(f317(f317(x80251,x80252),x80253))+~P22(f317(f317(x80254,x80252),x80253))+~P22(f317(f317(f225(f858(x80255,f858(x80256,a842))),x80254),x80251)) % 168.22/168.06 [8172]P22(f317(f317(x81721,x81722),x81723))+~P22(f317(f317(f319(x81724),x81722),x81725))+~P22(f317(f317(f317(f52(x81724,f858(x81726,a842)),x81725),x81721),x81723)) % 168.22/168.06 [8311]P22(f317(f317(f319(x83111),x83112),f317(x83113,x83114)))+~P22(f317(f317(f319(x83115),x83114),x83116))+~P22(f317(f317(f319(x83111),x83112),f317(f317(f52(x83115,f858(x83111,a842)),x83116),x83113))) % 168.22/168.06 [8510]~P22(f317(f317(f317(f317(a197,x85101),x85103),x85104),x85106))+~P22(f317(f317(f317(f317(a197,x85102),x85106),x85104),x85105))+P22(f317(f317(f317(f317(a197,f36(x85101,x85102)),x85103),x85104),x85105)) % 168.22/168.06 [8574]~P9(x85744,x85745,x85746,x85741)+E(f317(x85741,x85742),f317(x85741,x85743))+~P22(f317(f317(f319(f857(x85744,x85744)),f317(f317(f237(x85744,x85744),x85742),x85743)),x85746)) % 168.22/168.06 [8605]P22(f317(f317(f225(f858(x86051,a842)),x86052),f317(x86053,x86054)))+~P22(f317(f317(f319(x86055),x86054),x86056))+~P22(f317(f317(f225(f858(x86051,a842)),x86052),f317(f317(f52(x86055,f858(x86051,a842)),x86056),x86053))) % 168.22/168.06 [8633]~P49(x86333,x86334,f317(f263(x86334,x86333),x86335))+E(x86331,f188(f858(x86332,a842)))+E(f317(f317(f52(x86332,f858(x86333,a842)),x86331),f317(f317(f8(f858(x86334,a842),f858(x86333,a842),x86332),f262(x86334,x86333,x86335)),x86336)),f317(f262(x86334,x86333,x86335),f317(f317(f52(x86332,f858(x86334,a842)),x86331),x86336))) % 168.22/168.06 [8706]P22(f317(f317(f319(x87061),x87062),f317(f262(x87063,x87061,x87064),x87065)))+~P22(f317(f317(f319(x87063),x87066),x87065))+~P22(f317(f317(f319(f857(x87063,x87061)),f317(f317(f237(x87063,x87061),x87066),x87062)),x87064)) % 168.22/168.06 [8822]P22(f317(x88221,x88222))+~P22(f317(f317(f317(f317(a197,x88224),x88222),x88225),x88226))+P22(f317(f317(f317(f317(a197,f33(x88221,x88223,x88224)),x88222),x88225),x88226)) % 168.22/168.06 [8838]~P22(f317(x88381,x88384))+~P22(f317(f317(f317(f317(a197,x88382),x88384),x88385),x88386))+P22(f317(f317(f317(f317(a197,f33(x88381,x88382,x88383)),x88384),x88385),x88386)) % 168.22/168.06 [9011]P22(f317(f317(f225(f858(x90111,a842)),f317(f262(x90112,x90111,x90113),x90114)),f317(f262(x90112,x90111,x90115),x90116)))+~P22(f317(f317(f225(f858(x90112,a842)),x90114),x90116))+~P22(f317(f317(f225(f858(f857(x90112,x90111),a842)),x90113),x90115)) % 168.22/168.06 [9097]P22(f317(x90971,x90972))+P22(f317(f317(f317(f317(a197,x90973),x90972),x90974),x90975))+~P22(f317(f317(f317(f317(a197,f33(x90971,x90976,x90973)),x90972),x90974),x90975)) % 168.22/168.06 [9102]~P22(f317(x91025,x91022))+P22(f317(f317(f317(f317(a197,x91021),x91022),x91023),x91024))+~P22(f317(f317(f317(f317(a197,f33(x91025,x91021,x91026)),x91022),x91023),x91024)) % 168.22/168.06 [9151]P22(f317(f317(f317(f317(a197,x91511),x91512),x91513),x91514))+P22(f317(f317(f317(f317(a197,x91515),x91512),x91513),x91514))+~P22(f317(f317(f317(f317(a197,f33(x91516,x91511,x91515)),x91512),x91513),x91514)) % 168.22/168.06 [9194]~P22(f317(f317(f319(x91942),x91946),x91944))+~P22(f317(f317(f225(f858(x91941,a842)),x91943),x91945))+P22(f317(f317(f225(f858(f857(x91941,x91942),a842)),f317(f317(f245(x91941,x91942),x91943),f317(f16(f858(x91942,a842),x91941),x91944))),f317(f317(f245(x91941,x91942),x91945),f317(f16(f858(x91942,a842),x91941),x91944)))) % 168.22/168.06 [9206]~P35(x92061,x92062,x92063,x92065,x92066)+P22(f317(f317(f247(x92061,x92062,a842),x92063),x92064))+~P22(f317(f317(f319(f857(x92061,x92062)),x92064),f317(f166(f857(x92061,x92062)),f317(f317(f175(x92061,x92062),x92065),x92066)))) % 168.22/168.06 [9339]~E(x93393,x93395)+P22(f317(f317(f319(f857(f850(x93391),f850(x93391))),f317(f317(f237(f850(x93391),f850(x93391)),f317(f317(f145(x93391),x93392),x93393)),f317(f317(f145(x93391),x93394),x93395))),f151(x93391,x93396)))+~P22(f317(f317(f319(f857(x93391,x93391)),f317(f317(f237(x93391,x93391),x93392),x93394)),x93396)) % 168.22/168.06 [9343]~E(f317(f189(f850(x93431)),x93435),f317(f189(f850(x93432)),x93436))+E(f180(x93431,x93432,f181(x93431,x93432,x93433,f317(f317(f21(f858(x93431,a842)),x93434),f317(f166(x93431),x93435))),x93435,x93436),f181(x93431,x93432,f180(x93431,x93432,x93433,x93435,x93436),x93434))+~P22(f317(f317(f225(f858(x93431,a842)),f317(f166(x93431),x93435)),x93434)) % 168.22/168.06 [9344]~E(f317(f189(f850(x93441)),x93443),f317(f189(f850(x93441)),x93445))+P22(f317(f317(f319(f857(f850(x93441),f850(x93441))),f317(f317(f237(f850(x93441),f850(x93441)),f317(f317(f145(x93441),x93442),x93443)),f317(f317(f145(x93441),x93444),x93445))),f139(x93441,x93446)))+~P22(f317(f317(f319(f857(x93441,x93441)),f317(f317(f237(x93441,x93441),x93442),x93444)),x93446)) % 168.22/168.06 [9376]P22(f317(f317(f319(f857(x93761,x93761)),f317(f317(f237(x93761,x93761),x93762),x93763)),f317(f317(f182(f857(x93761,x93761),a842),f317(a124,x93764)),x93765)))+~P22(f317(f317(f319(f857(x93761,x93761)),f317(f317(f237(x93761,x93761),x93766),x93763)),x93765))+~P22(f317(f317(f319(f857(x93761,x93761)),f317(f317(f237(x93761,x93761),x93762),x93766)),f317(f317(f182(f857(x93761,x93761),a842),x93764),x93765))) % 168.22/168.06 [9377]P22(f317(f317(f319(f857(x93771,x93771)),f317(f317(f237(x93771,x93771),x93772),x93773)),f317(f317(f182(f857(x93771,x93771),a842),f317(a124,x93774)),x93775)))+~P22(f317(f317(f319(f857(x93771,x93771)),f317(f317(f237(x93771,x93771),x93772),x93776)),x93775))+~P22(f317(f317(f319(f857(x93771,x93771)),f317(f317(f237(x93771,x93771),x93776),x93773)),f317(f317(f182(f857(x93771,x93771),a842),x93774),x93775))) % 168.22/168.06 [9382]~P22(f317(f317(f319(x93824),x93825),x93826))+P22(f317(f317(f225(f858(x93821,a842)),x93822),x93823))+~P22(f317(f317(f225(f858(f857(x93821,x93824),a842)),f317(f317(f245(x93821,x93824),x93822),f317(f16(f858(x93824,a842),x93821),x93826))),f317(f317(f245(x93821,x93824),x93823),f317(f16(f858(x93824,a842),x93821),x93826)))) % 168.22/168.06 [9427]E(x94271,x94272)+~P22(f317(f317(f319(f857(f850(x94273),f850(x94273))),f317(f317(f237(f850(x94273),f850(x94273)),f317(f317(f145(x94273),x94271),x94275)),f317(f317(f145(x94273),x94272),x94276))),f139(x94273,x94274)))+P22(f317(f317(f319(f857(x94273,x94273)),f317(f317(f237(x94273,x94273),x94271),x94272)),x94274)) % 168.22/168.06 [9428]E(x94281,x94282)+~P22(f317(f317(f319(f857(f850(x94283),f850(x94283))),f317(f317(f237(f850(x94283),f850(x94283)),f317(f317(f145(x94283),x94281),x94285)),f317(f317(f145(x94283),x94282),x94286))),f141(x94283,x94284)))+P22(f317(f317(f319(f857(x94283,x94283)),f317(f317(f237(x94283,x94283),x94281),x94282)),x94284)) % 168.22/168.06 [9429]E(x94291,x94292)+~P22(f317(f317(f319(f857(f850(x94293),f850(x94293))),f317(f317(f237(f850(x94293),f850(x94293)),f317(f317(f145(x94293),x94291),x94295)),f317(f317(f145(x94293),x94292),x94296))),f151(x94293,x94294)))+P22(f317(f317(f319(f857(x94293,x94293)),f317(f317(f237(x94293,x94293),x94291),x94292)),x94294)) % 168.22/168.06 [9461]P22(f317(f317(f319(f857(f850(x94611),f850(x94611))),f317(f317(f237(f850(x94611),f850(x94611)),f317(f317(f145(x94611),x94612),x94613)),f317(f317(f145(x94611),x94614),x94615))),f152(x94611,x94616)))+~P22(f317(f317(f319(f857(f850(x94611),f850(x94611))),f317(f317(f237(f850(x94611),f850(x94611)),x94613),x94615)),f152(x94611,x94616)))+~P22(f317(f317(f319(f857(x94611,x94611)),f317(f317(f237(x94611,x94611),x94612),x94614)),x94616)) % 168.22/168.06 [9481]P22(f317(x94811,x94812))+~P22(f317(x94811,f487(x94811,x94813,x94814,x94815,x94816)))+~P22(f317(f317(f319(x94816),x94812),f317(f317(f51(x94815,f858(x94816,a842)),x94814),x94813))) % 168.22/168.06 [9486]~P22(f317(f317(f319(f857(f850(x94861),f850(x94861))),f317(f317(f237(f850(x94861),f850(x94861)),f317(f317(f145(x94861),x94862),x94865)),f317(f317(f145(x94861),x94863),x94866))),f139(x94861,x94864)))+P22(f317(f317(f319(f857(f850(x94861),f850(x94861))),f317(f317(f237(f850(x94861),f850(x94861)),x94865),x94866)),f139(x94861,x94864)))+P22(f317(f317(f319(f857(x94861,x94861)),f317(f317(f237(x94861,x94861),x94862),x94863)),x94864)) % 168.22/168.06 [9487]~P22(f317(f317(f319(f857(f850(x94871),f850(x94871))),f317(f317(f237(f850(x94871),f850(x94871)),f317(f317(f145(x94871),x94872),x94875)),f317(f317(f145(x94871),x94873),x94876))),f141(x94871,x94874)))+P22(f317(f317(f319(f857(f850(x94871),f850(x94871))),f317(f317(f237(f850(x94871),f850(x94871)),x94875),x94876)),f141(x94871,x94874)))+P22(f317(f317(f319(f857(x94871,x94871)),f317(f317(f237(x94871,x94871),x94872),x94873)),x94874)) % 168.22/168.06 [9488]~P22(f317(f317(f319(f857(f850(x94881),f850(x94881))),f317(f317(f237(f850(x94881),f850(x94881)),f317(f317(f145(x94881),x94882),x94885)),f317(f317(f145(x94881),x94883),x94886))),f151(x94881,x94884)))+P22(f317(f317(f319(f857(f850(x94881),f850(x94881))),f317(f317(f237(f850(x94881),f850(x94881)),x94885),x94886)),f151(x94881,x94884)))+P22(f317(f317(f319(f857(x94881,x94881)),f317(f317(f237(x94881,x94881),x94882),x94883)),x94884)) % 168.22/168.06 [9564]P22(f317(x95641,x95642))+P22(f317(f317(f319(x95643),f488(x95641,x95644,x95645,x95643,x95646)),x95645))+~P22(f317(f317(f319(x95646),x95642),f317(f317(f51(x95643,f858(x95646,a842)),x95645),x95644))) % 168.22/168.06 [9573]~E(x95732,x95734)+P22(f317(f317(f319(f857(f850(x95731),f850(x95731))),f317(f317(f237(f850(x95731),f850(x95731)),f317(f317(f127(x95731),x95732),f317(f317(f145(x95731),x95733),f125(x95731)))),f317(f317(f127(x95731),x95734),f317(f317(f145(x95731),x95735),f125(x95731))))),f151(x95731,x95736)))+~P22(f317(f317(f319(f857(x95731,x95731)),f317(f317(f237(x95731,x95731),x95733),x95735)),x95736)) % 168.22/168.06 [9661]E(x96611,x96612)+~P22(f317(f317(f319(f857(f850(x96613),f850(x96613))),f317(f317(f237(f850(x96613),f850(x96613)),f317(f317(f127(x96613),x96615),f317(f317(f145(x96613),x96611),f125(x96613)))),f317(f317(f127(x96613),x96616),f317(f317(f145(x96613),x96612),f125(x96613))))),f151(x96613,x96614)))+P22(f317(f317(f319(f857(x96613,x96613)),f317(f317(f237(x96613,x96613),x96611),x96612)),x96614)) % 168.22/168.06 [9686]~P22(f317(f317(f319(f857(f850(x96861),f850(x96861))),f317(f317(f237(f850(x96861),f850(x96861)),f317(f317(f127(x96861),x96865),f317(f317(f145(x96861),x96862),f125(x96861)))),f317(f317(f127(x96861),x96866),f317(f317(f145(x96861),x96863),f125(x96861))))),f151(x96861,x96864)))+P22(f317(f317(f319(f857(f850(x96861),f850(x96861))),f317(f317(f237(f850(x96861),f850(x96861)),x96865),x96866)),f151(x96861,x96864)))+P22(f317(f317(f319(f857(x96861,x96861)),f317(f317(f237(x96861,x96861),x96862),x96863)),x96864)) % 168.22/168.06 [9704]P22(f317(x97041,x97042))+P22(f317(f317(f319(x97043),f487(x97041,x97044,x97045,x97046,x97043)),f317(x97044,f488(x97041,x97044,x97045,x97046,x97043))))+~P22(f317(f317(f319(x97043),x97042),f317(f317(f51(x97046,f858(x97043,a842)),x97045),x97044))) % 168.22/168.06 [8804]~E(f317(f317(f171(x88041,x88042),x88044),x88045),f317(f217(x88042),x88046))+~P22(f317(f317(x88043,x88045),x88046))+E(f317(f317(f171(x88041,x88042),f317(f130(f857(x88041,x88042),f317(f247(x88041,x88042,a842),x88043)),x88044)),x88045),f317(f217(x88042),x88046)) % 168.22/168.06 [9018]~P22(f317(f317(f319(x90185),x90183),x90186))+P22(f317(f317(f225(f858(x90181,a842)),f317(x90182,x90183)),x90184))+~P22(f317(f317(f225(f858(x90181,a842)),f317(f317(f51(x90185,f858(x90181,a842)),x90186),x90182)),x90184)) % 168.22/168.06 [9635]~P6(x96351,x96355,x96354)+P22(f317(f317(f319(f857(x96351,x96351)),f317(f317(f237(x96351,x96351),x96352),x96353)),x96354))+~P22(f317(f317(f319(x96351),x96356),f317(f317(f113(f858(x96351,a842)),f317(f262(x96351,x96351,x96354),f317(f317(f286(x96351),x96352),f188(f858(x96351,a842))))),f317(f262(x96351,x96351,x96354),f317(f317(f286(x96351),x96353),f188(f858(x96351,a842))))))) % 168.22/168.06 [8479]~P126(x84792)+~E(f317(f317(f89(x84792),f317(f317(f90(x84792),x84794),x84795)),x84791),f317(f317(f89(x84792),f317(f317(f90(x84792),x84793),x84795)),x84796))+E(x84791,f317(f317(f89(x84792),f317(f317(f90(x84792),f317(f317(f21(x84792),x84793),x84794)),x84795)),x84796)) % 168.22/168.06 [8480]~P126(x84801)+~E(f317(f317(f89(x84801),f317(f317(f90(x84801),x84802),x84804)),x84805),f317(f317(f89(x84801),f317(f317(f90(x84801),x84803),x84804)),x84806))+E(f317(f317(f89(x84801),f317(f317(f90(x84801),f317(f317(f21(x84801),x84802),x84803)),x84804)),x84805),x84806) % 168.22/168.06 [8636]~P126(x86361)+E(f317(f317(f89(x86361),f317(f317(f90(x86361),x86362),x86363)),x86364),f317(f317(f89(x86361),f317(f317(f90(x86361),x86365),x86363)),x86366))+~E(x86366,f317(f317(f89(x86361),f317(f317(f90(x86361),f317(f317(f21(x86361),x86362),x86365)),x86363)),x86364)) % 168.22/168.06 [8637]~P126(x86371)+E(f317(f317(f89(x86371),f317(f317(f90(x86371),x86372),x86373)),x86374),f317(f317(f89(x86371),f317(f317(f90(x86371),x86375),x86373)),x86376))+~E(f317(f317(f89(x86371),f317(f317(f90(x86371),f317(f317(f21(x86371),x86372),x86375)),x86373)),x86374),x86376) % 168.22/168.06 [8960]~P22(f317(f317(x89604,x89605),x89606))+~P22(f317(f317(x89603,x89605),x89606))+P22(f317(f317(f317(f317(f113(f858(x89601,f858(x89602,a842))),x89603),x89604),x89605),x89606)) % 168.22/168.06 [9214]P22(f317(f317(x92141,x92142),x92143))+P22(f317(f317(x92144,x92142),x92143))+~P22(f317(f317(f317(f317(f122(f858(x92145,f858(x92146,a842))),x92144),x92141),x92142),x92143)) % 168.22/168.06 [9501]~P128(x95011)+~P22(f317(f317(f225(x95011),f317(f317(f89(x95011),f317(f317(f90(x95011),x95014),x95015)),x95012)),f317(f317(f89(x95011),f317(f317(f90(x95011),x95013),x95015)),x95016)))+P22(f317(f317(f225(x95011),x95012),f317(f317(f89(x95011),f317(f317(f90(x95011),f317(f317(f21(x95011),x95013),x95014)),x95015)),x95016))) % 168.22/168.06 [9502]~P128(x95021)+~P22(f317(f317(f226(x95021),f317(f317(f89(x95021),f317(f317(f90(x95021),x95024),x95025)),x95022)),f317(f317(f89(x95021),f317(f317(f90(x95021),x95023),x95025)),x95026)))+P22(f317(f317(f226(x95021),x95022),f317(f317(f89(x95021),f317(f317(f90(x95021),f317(f317(f21(x95021),x95023),x95024)),x95025)),x95026))) % 168.22/168.06 [9519]~P128(x95191)+P22(f317(f317(f225(x95191),f317(f317(f89(x95191),f317(f317(f90(x95191),x95192),x95193)),x95194)),f317(f317(f89(x95191),f317(f317(f90(x95191),x95195),x95193)),x95196)))+~P22(f317(f317(f225(x95191),x95194),f317(f317(f89(x95191),f317(f317(f90(x95191),f317(f317(f21(x95191),x95195),x95192)),x95193)),x95196))) % 168.22/168.06 [9520]~P128(x95201)+P22(f317(f317(f226(x95201),f317(f317(f89(x95201),f317(f317(f90(x95201),x95202),x95203)),x95204)),f317(f317(f89(x95201),f317(f317(f90(x95201),x95205),x95203)),x95206)))+~P22(f317(f317(f226(x95201),x95204),f317(f317(f89(x95201),f317(f317(f90(x95201),f317(f317(f21(x95201),x95205),x95202)),x95203)),x95206))) % 168.22/168.06 [9622]~P128(x96221)+~P22(f317(f317(f225(x96221),f317(f317(f89(x96221),f317(f317(f90(x96221),x96222),x96224)),x96225)),f317(f317(f89(x96221),f317(f317(f90(x96221),x96223),x96224)),x96226)))+P22(f317(f317(f225(x96221),f317(f317(f89(x96221),f317(f317(f90(x96221),f317(f317(f21(x96221),x96222),x96223)),x96224)),x96225)),x96226)) % 168.22/168.06 [9623]~P128(x96231)+~P22(f317(f317(f226(x96231),f317(f317(f89(x96231),f317(f317(f90(x96231),x96232),x96234)),x96235)),f317(f317(f89(x96231),f317(f317(f90(x96231),x96233),x96234)),x96236)))+P22(f317(f317(f226(x96231),f317(f317(f89(x96231),f317(f317(f90(x96231),f317(f317(f21(x96231),x96232),x96233)),x96234)),x96235)),x96236)) % 168.22/168.06 [9671]~P128(x96711)+P22(f317(f317(f225(x96711),f317(f317(f89(x96711),f317(f317(f90(x96711),x96712),x96713)),x96714)),f317(f317(f89(x96711),f317(f317(f90(x96711),x96715),x96713)),x96716)))+~P22(f317(f317(f225(x96711),f317(f317(f89(x96711),f317(f317(f90(x96711),f317(f317(f21(x96711),x96712),x96715)),x96713)),x96714)),x96716)) % 168.22/168.06 [9672]~P128(x96721)+P22(f317(f317(f226(x96721),f317(f317(f89(x96721),f317(f317(f90(x96721),x96722),x96723)),x96724)),f317(f317(f89(x96721),f317(f317(f90(x96721),x96725),x96723)),x96726)))+~P22(f317(f317(f226(x96721),f317(f317(f89(x96721),f317(f317(f90(x96721),f317(f317(f21(x96721),x96722),x96725)),x96723)),x96724)),x96726)) % 168.22/168.06 [9849]~P67(x98492)+~P22(f317(f71(x98491),x98496))+E(f317(f317(f6(x98491,x98492),f317(f317(f18(x98491,x98492,x98492),f317(f317(f18(x98491,x98492,f858(x98492,x98492)),f317(f317(f8(a842,f858(x98492,f858(x98492,x98492)),x98491),f108(x98492)),x98493)),x98494)),x98495)),x98496),f317(f317(f89(x98492),f317(f317(f6(x98491,x98492),x98494),f317(f317(f113(f858(x98491,a842)),x98496),f317(f230(x98491),x98493)))),f317(f317(f6(x98491,x98492),x98495),f317(f317(f113(f858(x98491,a842)),x98496),f317(f88(f858(x98491,a842)),f317(f230(x98491),x98493)))))) % 168.22/168.06 [9911]P22(f317(f317(f319(x99112),x99114),x99116))+P22(f317(f317(f319(x99112),x99115),x99116))+E(f317(f289(x99111,x99112,f317(f317(f7(x99111,x99112,x99112),f317(f317(f7(x99111,x99112,f858(x99112,x99112)),f317(f317(f8(a842,f858(x99112,f858(x99112,x99112)),x99111),f108(x99112)),f317(f317(f7(x99111,f858(x99111,a842),a842),f319(x99111)),x99113))),x99114)),x99115)),x99116),f188(f858(x99111,a842))) % 168.22/168.06 [9912]P22(f317(f317(f319(x99122),x99125),x99126))+~P22(f317(f317(f319(x99122),x99124),x99126))+E(f317(f289(x99121,x99122,f317(f317(f7(x99121,x99122,x99122),f317(f317(f7(x99121,x99122,f858(x99122,x99122)),f317(f317(f8(a842,f858(x99122,f858(x99122,x99122)),x99121),f108(x99122)),f317(f317(f7(x99121,f858(x99121,a842),a842),f319(x99121)),x99123))),x99124)),x99125)),x99126),x99123) % 168.22/168.06 [9913]P22(f317(f317(f319(x99132),x99134),x99136))+~P22(f317(f317(f319(x99132),x99135),x99136))+E(f317(f289(x99131,x99132,f317(f317(f7(x99131,x99132,x99132),f317(f317(f7(x99131,x99132,f858(x99132,x99132)),f317(f317(f8(a842,f858(x99132,f858(x99132,x99132)),x99131),f108(x99132)),f317(f317(f7(x99131,f858(x99131,a842),a842),f319(x99131)),x99133))),x99134)),x99135)),x99136),f317(f88(f858(x99131,a842)),x99133)) % 168.22/168.06 [9914]~P22(f317(f317(f319(x99142),x99144),x99146))+~P22(f317(f317(f319(x99142),x99145),x99146))+E(f317(f289(x99141,x99142,f317(f317(f7(x99141,x99142,x99142),f317(f317(f7(x99141,x99142,f858(x99142,x99142)),f317(f317(f8(a842,f858(x99142,f858(x99142,x99142)),x99141),f108(x99142)),f317(f317(f7(x99141,f858(x99141,a842),a842),f319(x99141)),x99143))),x99144)),x99145)),x99146),f233(f858(x99141,a842))) % 168.22/168.06 [10042]P18(x100421,x100422,f317(f317(f286(f848(x100421)),f317(f317(f317(f100(x100421),f317(x100423,x100424)),f317(a29,x100424)),f317(x100425,x100424))),f188(f858(f848(x100421),a842))))+~P22(f317(f317(f319(a846),x100424),x100426))+~P18(x100421,f317(f317(f122(f858(f848(x100421),a842)),x100422),f317(f287(a846,f848(x100421),f317(f317(f18(a846,f858(x100421,f858(a845,a842)),f848(x100421)),f317(f317(f18(a846,a843,f858(f858(x100421,f858(a845,a842)),f848(x100421))),f317(f317(f8(f858(x100421,f858(a845,a842)),f858(a843,f858(f858(x100421,f858(a845,a842)),f848(x100421))),a846),f100(x100421)),x100423)),a29)),x100425)),x100426)),f317(f287(a846,f848(x100421),f317(f317(f18(a846,f858(x100421,f858(a845,a842)),f848(x100421)),f317(f317(f18(a846,a843,f858(f858(x100421,f858(a845,a842)),f848(x100421))),f317(f317(f8(f858(x100421,f858(a845,a842)),f858(a843,f858(f858(x100421,f858(a845,a842)),f848(x100421))),a846),f100(x100421)),x100423)),f317(f317(f8(f853(a843),a843,a846),f222(a843)),a27))),x100425)),x100426)) % 168.22/168.06 [8507]E(x85071,x85072)+~P51(x85074,x85075,x85073,x85076,x85077)+~E(f317(x85073,x85071),f317(x85073,x85072)) % 168.22/168.06 [6896]E(f317(f220(f853(x68961),x68962,f191(x68961),x68963),f317(x68964,x68965)),f317(f217(x68961),x68966))+~E(f317(x68964,x68965),f317(f217(x68962),x68967))+~E(f317(x68963,x68967),f317(f217(x68961),x68966)) % 168.22/168.06 [8532]~P3(x85326,x85325,x85327,x85324,x85321)+E(f317(f317(x85321,x85322),x85323),x85324)+P22(f317(f71(x85325),x85323)) % 168.22/168.06 [9363]P41(x93631,x93632,x93633,x93634,x93635,f317(f317(x93633,x93636),x93637))+~E(f317(f317(x93633,x93636),x93637),x93634)+~E(x93635,f188(f858(x93631,a842))) % 168.22/168.06 [9541]~P22(f317(x95416,x95413))+~P22(f317(f317(f319(f857(x95412,x95412)),f317(f317(f237(x95412,x95412),x95414),x95415)),f317(x95417,x95413)))+P22(f317(f317(f319(f857(f857(x95411,x95412),f857(x95411,x95412))),f317(f317(f237(f857(x95411,x95412),f857(x95411,x95412)),f317(f317(f237(x95411,x95412),x95413),x95414)),f317(f317(f237(x95411,x95412),x95413),x95415))),f260(x95411,x95412,x95416,x95417))) % 168.22/168.06 [9966]~P41(x99662,x99667,x99663,x99666,x99661,f317(f317(x99663,x99665),x99664))+E(f317(f317(x99663,f733(x99664,x99665,x99661,x99666,x99663,x99667,x99662)),f746(x99664,x99665,x99661,x99666,x99663,x99667,x99662)),f317(f317(x99663,x99665),x99664))+E(x99661,f188(f858(x99662,a842))) % 168.22/168.06 [9967]~P41(x99677,x99676,x99671,x99674,x99675,f317(f317(x99671,x99672),x99673))+E(f317(f317(x99671,f733(x99673,x99672,x99675,x99674,x99671,x99676,x99677)),f746(x99673,x99672,x99675,x99674,x99671,x99676,x99677)),f317(f317(x99671,x99672),x99673))+E(f317(f317(x99671,x99672),x99673),x99674) % 168.22/168.06 [9054]~P35(x90541,x90542,x90543,x90545,x90547)+P35(x90541,x90542,x90543,f317(f317(f145(x90541),x90544),x90545),f317(f317(f145(x90542),x90546),x90547))+~P22(f317(f317(x90543,x90544),x90546)) % 168.22/168.06 [9072]P35(x90721,x90722,x90723,x90724,x90725)+~P35(x90721,x90722,x90723,f317(f317(f127(x90721),x90726),x90724),f317(f317(f127(x90722),x90727),x90725))+~E(f317(f189(f850(x90721)),x90726),f317(f189(f850(x90722)),x90727)) % 168.22/168.06 [9073]P35(x90731,x90732,x90733,x90734,x90735)+~P35(x90731,x90732,x90733,f317(f317(f127(x90731),x90734),x90736),f317(f317(f127(x90732),x90735),x90737))+~E(f317(f189(f850(x90731)),x90734),f317(f189(f850(x90732)),x90735)) % 168.22/168.06 [9275]~P35(x92751,x92752,x92753,x92755,x92757)+~P35(x92751,x92752,x92753,x92754,x92756)+P35(x92751,x92752,x92753,f317(f317(f127(x92751),x92754),x92755),f317(f317(f127(x92752),x92756),x92757)) % 168.22/168.06 [9611]~P22(f317(f76(x96111,x96114,x96115,x96116,x96113),x96117))+P22(f317(f76(x96111,x96114,x96115,x96116,f317(f317(f286(x96111),x96112),x96113)),f317(f317(x96115,x96112),x96117)))+P22(f317(f317(f319(x96111),x96112),x96113)) % 168.22/168.06 [9742]~P19(x97423,x97421,x97424,f233(f858(x97423,a842)))+E(f317(f317(f171(x97421,x97422),f317(f317(f148(f857(x97423,x97422),f857(x97421,x97422)),f317(f247(x97423,x97422,f857(x97421,x97422)),f317(f317(f8(x97421,f858(x97422,f857(x97421,x97422)),x97423),f237(x97421,x97422)),x97424))),x97425)),f317(x97424,x97426)),f317(f217(x97422),x97427))+~E(f317(f317(f171(x97423,x97422),x97425),x97426),f317(f217(x97422),x97427)) % 168.22/168.06 [9990]~P41(x99902,x99907,x99906,x99905,x99901,f317(f317(x99906,x99904),x99903))+E(x99901,f188(f858(x99902,a842)))+P22(f317(f317(f319(x99902),f733(x99903,x99904,x99901,x99905,x99906,x99907,x99902)),x99901)) % 168.22/168.06 [9991]~P41(x99915,x99917,x99911,x99914,x99916,f317(f317(x99911,x99912),x99913))+E(f317(f317(x99911,x99912),x99913),x99914)+P22(f317(f317(f319(x99915),f733(x99913,x99912,x99916,x99914,x99911,x99917,x99915)),x99916)) % 168.22/168.06 [6685]~E(x66855,x66857)+~E(x66856,x66854)+E(f317(f317(f317(f317(f81(x66851,f853(x66852)),x66853),x66854),f317(f217(x66852),x66855)),x66856),f317(f217(x66852),x66857)) % 168.22/168.06 [6806]E(x68061,x68062)+~E(f317(x68065,x68061),f317(f217(x68064),x68067))+E(f317(f317(f317(f317(f81(x68063,f853(x68064)),x68065),x68062),f317(f217(x68064),x68066)),x68061),f317(f217(x68064),x68067)) % 168.22/168.06 [7522]E(x75221,x75222)+~E(x75223,x75224)+~E(f317(f317(f317(f317(f81(x75225,f853(x75226)),x75227),x75224),f317(f217(x75226),x75221)),x75223),f317(f217(x75226),x75222)) % 168.22/168.06 [7586]E(x75861,x75862)+E(f317(x75863,x75864),f317(f217(x75865),x75861))+~E(f317(f317(f317(f317(f81(x75866,f853(x75865)),x75863),x75867),f317(f217(x75865),x75862)),x75864),f317(f217(x75865),x75861)) % 168.22/168.06 [7587]E(x75871,x75872)+E(f317(x75873,x75871),f317(f217(x75874),x75875))+~E(f317(f317(f317(f317(f81(x75876,f853(x75874)),x75873),x75872),f317(f217(x75874),x75877)),x75871),f317(f217(x75874),x75875)) % 168.22/168.06 [8745]~P16(x87454,x87455,x87456,x87457,x87451)+~P22(f317(f71(x87455),x87453))+E(f317(f317(x87451,x87452),x87453),f317(f317(f317(f75(x87454,x87455,x87456),x87452),x87457),x87453)) % 168.22/168.06 [8746]~P3(x87464,x87465,x87466,x87467,x87461)+~P22(f317(f71(x87465),x87463))+E(f317(f317(x87461,x87462),x87463),f317(f317(f317(f75(x87464,x87465,x87466),x87462),x87467),x87463)) % 168.22/168.06 [9332]~P18(x93321,x93322,f317(f317(f286(f848(x93321)),f317(f317(f317(f100(x93321),x93323),x93324),x93327)),f188(f858(f848(x93321),a842))))+P18(x93321,x93322,f317(f317(f286(f848(x93321)),f317(f317(f317(f100(x93321),x93323),f36(x93324,x93325)),x93326)),f188(f858(f848(x93321),a842))))+~P18(x93321,x93322,f317(f317(f286(f848(x93321)),f317(f317(f317(f100(x93321),x93327),x93325),x93326)),f188(f858(f848(x93321),a842)))) % 168.22/168.06 [9515]~P17(x95153,x95154,x95155,x95157,x95156,x95151)+~P22(f317(f71(x95154),x95152))+E(f317(x95151,x95152),f317(f317(f317(f75(x95153,x95154,x95155),x95156),x95157),x95152)) % 168.22/168.06 [9666]P41(x96661,x96662,x96663,x96664,x96665,f317(f317(x96663,x96666),x96667))+~P41(x96661,x96662,x96663,x96664,f317(f317(f21(f858(x96661,a842)),x96665),f317(f317(f286(x96661),x96666),f188(f858(x96661,a842)))),x96667)+~P22(f317(f317(f319(x96661),x96666),x96665)) % 168.22/168.06 [9943]~P18(x99431,x99432,f317(f317(f286(f848(x99431)),f317(f317(f317(f100(x99431),f103(x99431,x99433,x99434)),x99435),x99437)),f188(f858(f848(x99431),a842))))+P18(x99431,x99432,f317(f317(f286(f848(x99431)),f317(f317(f317(f100(x99431),x99433),f33(x99434,x99435,x99436)),x99437)),f188(f858(f848(x99431),a842))))+~P18(x99431,x99432,f317(f317(f286(f848(x99431)),f317(f317(f317(f100(x99431),f103(x99431,x99433,f317(f82(a842,a842,a845,a312),x99434))),x99436),x99437)),f188(f858(f848(x99431),a842)))) % 168.22/168.06 [10014]~P41(x100142,x100143,x100144,x100145,x100141,f317(f317(x100144,x100147),x100146))+P41(x100142,x100143,x100144,x100145,f317(f317(f21(f858(x100142,a842)),x100141),f317(f317(f286(x100142),f733(x100146,x100147,x100141,x100145,x100144,x100143,x100142)),f188(f858(x100142,a842)))),f746(x100146,x100147,x100141,x100145,x100144,x100143,x100142))+E(x100141,f188(f858(x100142,a842))) % 168.22/168.06 [10015]~P41(x100155,x100156,x100151,x100154,x100157,f317(f317(x100151,x100152),x100153))+P41(x100155,x100156,x100151,x100154,f317(f317(f21(f858(x100155,a842)),x100157),f317(f317(f286(x100155),f733(x100153,x100152,x100157,x100154,x100151,x100156,x100155)),f188(f858(x100155,a842)))),f746(x100153,x100152,x100157,x100154,x100151,x100156,x100155))+E(f317(f317(x100151,x100152),x100153),x100154) % 168.22/168.06 [9061]E(f180(x90611,x90612,x90613,x90614,f317(f317(f153(x90612,x90615),x90616),x90617)),f180(x90611,x90612,x90613,x90614,x90615))+~P22(f317(f317(f226(a849),x90616),f317(f189(f850(x90612)),x90615)))+~P22(f317(f317(f225(a849),f317(f189(f850(x90611)),x90614)),x90616)) % 168.22/168.06 [9352]P22(f317(f317(f225(f858(f857(x93521,x93522),a842)),f317(f317(f265(x93521,x93523,x93522),x93524),x93525)),f317(f317(f265(x93521,x93523,x93522),x93526),x93527)))+~P22(f317(f317(f225(f858(f857(x93523,x93522),a842)),x93525),x93527))+~P22(f317(f317(f225(f858(f857(x93521,x93523),a842)),x93524),x93526)) % 168.22/168.06 [9403]~E(f317(f317(f317(a200,x94036),f40(x94031)),f317(f317(a201,x94034),x94031)),f317(f317(f317(a200,x94037),f40(x94031)),f317(f317(a201,x94034),x94031)))+P22(f317(f317(f317(f317(a197,f32(x94031,x94032,x94033)),x94034),x94035),f317(f317(f317(a200,x94036),f40(x94031)),f317(f317(a201,x94034),x94031))))+~P22(f317(f317(f317(f317(a197,x94033),f317(f317(f317(a200,x94034),f40(x94031)),f317(x94032,x94034))),x94035),x94037)) % 168.22/168.06 [9681]~E(f317(f317(f317(a200,f317(f317(a202,x96816),f317(a201,x96814))),x96811),f317(f317(a201,x96816),a25)),f317(f317(f317(a200,f317(f317(a202,x96817),f317(a201,x96814))),x96811),f317(f317(a201,x96817),a25)))+P22(f317(f317(f317(f317(a197,f31(x96811,x96812,x96813)),x96814),x96815),f317(f317(f317(a200,f317(f317(a202,x96816),f317(a201,x96814))),x96811),f317(f317(a201,x96816),a25))))+~P22(f317(f317(f317(f317(a197,f317(a29,x96812)),f317(f317(f317(a200,f317(f317(a202,x96814),a203)),f40(a26)),f317(x96813,x96814))),x96815),x96817)) % 168.22/168.06 [9677]~P22(f317(f317(f319(x96771),x96776),x96775))+P22(f317(f76(x96771,x96772,x96773,x96774,x96775),f317(f317(x96773,x96776),x96777)))+~P22(f317(f76(x96771,x96772,x96773,x96774,f317(f317(f21(f858(x96771,a842)),x96775),f317(f317(f286(x96771),x96776),f188(f858(x96771,a842))))),x96777)) % 168.22/168.06 [10072]~P135(x100721)+~P19(f857(x100722,x100723),x100721,f317(f247(x100722,x100723,x100721),f317(f317(f7(x100722,f858(x100723,x100721),f858(x100723,x100721)),f317(f317(f8(f858(x100721,x100721),f858(f858(x100723,x100721),f858(x100723,x100721)),x100722),f8(x100721,x100721,x100723)),f317(f317(f8(x100721,f858(x100721,x100721),x100722),f90(x100721)),x100724))),x100725)),f317(f317(f245(x100722,x100723),x100726),f317(f16(f858(x100723,a842),x100722),x100727)))+E(f317(f317(f6(x100721,x100721),f39(x100721)),f317(f230(x100721),f317(f317(f8(f858(x100722,a842),a842,x100721),f96(x100722)),f317(f317(f8(f858(x100722,f858(x100723,a842)),f858(x100722,a842),x100721),f317(f8(f858(x100723,a842),a842,x100722),f96(x100723))),f317(f317(f7(x100721,f858(x100722,f858(x100723,a842)),f858(x100722,f858(x100723,a842))),f317(f317(f8(f858(x100722,f858(f858(x100723,a842),f858(x100723,a842))),f858(f858(x100722,f858(x100723,a842)),f858(x100722,f858(x100723,a842))),x100721),f18(x100722,f858(x100723,a842),f858(x100723,a842))),f317(f317(f8(f858(x100722,f858(x100723,f858(a842,a842))),f858(x100722,f858(f858(x100723,a842),f858(x100723,a842))),x100721),f317(f8(f858(x100723,f858(a842,a842)),f858(f858(x100723,a842),f858(x100723,a842)),x100722),f18(x100723,a842,a842))),f317(f317(f8(f858(x100722,f858(x100723,a842)),f858(x100722,f858(x100723,f858(a842,a842))),x100721),f317(f8(f858(x100723,a842),f858(x100723,f858(a842,a842)),x100722),f317(f8(a842,f858(a842,a842),x100723),a315))),f317(f317(f7(x100721,f858(x100722,f858(x100723,x100721)),f858(x100722,f858(x100723,a842))),f317(f317(f8(f858(f858(x100723,x100721),f858(x100723,a842)),f858(f858(x100722,f858(x100723,x100721)),f858(x100722,f858(x100723,a842))),x100721),f8(f858(x100723,x100721),f858(x100723,a842),x100722)),f317(f317(f8(f858(x100721,a842),f858(f858(x100723,x100721),f858(x100723,a842)),x100721),f8(x100721,a842,x100723)),a314))),f317(f317(f7(x100722,f858(x100723,x100721),f858(x100723,x100721)),f317(f317(f8(f858(x100721,x100721),f858(f858(x100723,x100721),f858(x100723,x100721)),x100722),f8(x100721,x100721,x100723)),f317(f317(f8(x100721,f858(x100721,x100721),x100722),f90(x100721)),x100724))),x100725)))))),f317(f317(f7(x100722,f858(x100723,a842),f858(x100723,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x100723,a842),f858(x100723,a842)),x100722),f8(a842,a842,x100723)),f317(f317(f8(a842,f858(a842,a842),x100722),a315),f317(f317(f7(x100722,f858(x100722,a842),a842),f319(x100722)),x100726)))),f317(f317(f7(x100723,f858(x100723,a842),a842),f319(x100723)),x100727))))))),f317(f317(f90(x100721),f317(f317(f6(x100722,x100721),x100724),x100726)),f317(f317(f6(x100723,x100721),x100725),x100727))) % 168.22/168.06 [9774]P48(x97741,x97742,x97743,x97744,x97745,x97746,x97747)+~P22(f317(f317(x97744,x97746),x97748))+~P22(f317(f317(x97745,x97748),x97747)) % 168.22/168.06 [9122]~P14(x91228,x91221,x91223,x91225)+~P22(f317(f71(x91228),x91226))+E(f317(f82(x91221,x91221,x91222,f317(x91223,x91224)),f317(f82(x91221,x91221,x91222,f317(x91225,x91226)),x91227)),f317(f82(x91221,x91221,x91222,f317(x91225,x91226)),f317(f82(x91221,x91221,x91222,f317(x91223,x91224)),x91227))) % 168.22/168.06 [9619]~P19(x96192,x96194,x96196,x96198)+~P19(x96191,x96193,x96195,x96197)+P19(f857(x96191,x96192),f857(x96193,x96194),f248(x96191,x96193,x96192,x96194,x96195,x96196),f317(f317(f245(x96191,x96192),x96197),f317(f16(f858(x96192,a842),x96191),x96198))) % 168.22/168.06 [9299]P22(f317(f317(f319(f857(x92991,x92992)),f317(f317(f237(x92991,x92992),x92993),x92994)),f317(f317(f265(x92991,x92995,x92992),x92996),x92997)))+~P22(f317(f317(f319(f857(x92991,x92995)),f317(f317(f237(x92991,x92995),x92993),x92998)),x92996))+~P22(f317(f317(f319(f857(x92995,x92992)),f317(f317(f237(x92995,x92992),x92998),x92994)),x92997)) % 168.22/168.06 [9489]~P22(f317(f317(f225(f858(f857(x94893,x94892),a842)),x94895),f317(f317(f245(x94893,x94892),x94898),f317(f16(f858(x94892,a842),x94893),x94897))))+~P22(f317(f317(f225(f858(f857(x94891,x94893),a842)),x94894),f317(f317(f245(x94891,x94893),x94896),f317(f16(f858(x94893,a842),x94891),x94898))))+P22(f317(f317(f225(f858(f857(x94891,x94892),a842)),f317(f317(f265(x94891,x94893,x94892),x94894),x94895)),f317(f317(f245(x94891,x94892),x94896),f317(f16(f858(x94892,a842),x94891),x94897)))) % 168.22/168.06 [9537]~E(x95373,x95375)+P22(f317(f317(f319(f857(f857(x95371,x95372),f857(x95371,x95372))),f317(f317(f237(f857(x95371,x95372),f857(x95371,x95372)),f317(f317(f237(x95371,x95372),x95373),x95374)),f317(f317(f237(x95371,x95372),x95375),x95376))),f310(x95371,x95372,x95377,x95378)))+~P22(f317(f317(f319(f857(x95372,x95372)),f317(f317(f237(x95372,x95372),x95374),x95376)),x95378)) % 168.22/168.06 [9642]E(x96421,x96422)+~P22(f317(f317(f319(f857(f857(x96423,x96425),f857(x96423,x96425))),f317(f317(f237(f857(x96423,x96425),f857(x96423,x96425)),f317(f317(f237(x96423,x96425),x96421),x96426)),f317(f317(f237(x96423,x96425),x96422),x96427))),f310(x96423,x96425,x96424,x96428)))+P22(f317(f317(f319(f857(x96423,x96423)),f317(f317(f237(x96423,x96423),x96421),x96422)),x96424)) % 168.22/168.06 [9660]~P22(f317(f317(f319(f857(f857(x96601,x96605),f857(x96601,x96605))),f317(f317(f237(f857(x96601,x96605),f857(x96601,x96605)),f317(f317(f237(x96601,x96605),x96602),x96606)),f317(f317(f237(x96601,x96605),x96603),x96607))),f310(x96601,x96605,x96604,x96608)))+P22(f317(f317(f319(f857(x96601,x96601)),f317(f317(f237(x96601,x96601),x96602),x96603)),x96604))+P22(f317(f317(f319(f857(x96605,x96605)),f317(f317(f237(x96605,x96605),x96606),x96607)),x96608)) % 168.22/168.06 [9565]~P17(x95657,x95655,x95651,x95658,x95652,x95654)+~P22(f317(f71(x95655),x95656))+E(f317(f317(x95651,f317(x95652,x95653)),f317(x95654,f317(f317(f21(f858(x95655,a842)),x95656),f317(f317(f286(x95655),x95653),f188(f858(x95655,a842)))))),f317(x95654,f317(f317(f286(x95655),x95653),x95656))) % 168.22/168.06 [9080]~P22(f317(f317(f317(x90805,x90808),x90806),x90807))+~P22(f317(f317(f319(x90801),x90808),x90804))+P22(f317(f317(f317(f317(f51(x90801,f858(x90802,f858(x90803,a842))),x90804),x90805),x90806),x90807)) % 168.22/168.06 [9286]P22(f317(f317(f317(x92861,x92862),x92863),x92864))+~P22(f317(f317(f319(x92865),x92862),x92866))+~P22(f317(f317(f317(f317(f52(x92865,f858(x92867,f858(x92868,a842))),x92866),x92861),x92863),x92864)) % 168.22/168.06 [9482]~P16(x94823,x94822,x94824,x94828,x94821)+~P22(f317(f71(x94822),x94827))+E(f317(f317(x94821,f317(f317(f18(x94822,x94823,x94823),f317(f317(f8(x94823,f858(x94823,x94823),x94822),x94824),x94825)),x94826)),x94827),f317(f317(x94824,f317(f317(x94821,x94825),x94827)),f317(f317(x94821,x94826),x94827))) % 168.22/168.06 [9750]~E(f317(f287(x97502,x97504,x97506),x97508),x975010)+~E(f317(f287(x97501,x97503,x97505),x97507),x97509)+E(f317(f287(f857(x97501,x97502),f857(x97503,x97504),f248(x97501,x97503,x97502,x97504,x97505,x97506)),f317(f317(f245(x97501,x97502),x97507),f317(f16(f858(x97502,a842),x97501),x97508))),f317(f317(f245(x97503,x97504),x97509),f317(f16(f858(x97504,a842),x97503),x975010))) % 168.22/168.06 [4777]~P103(x47772)+~P29(x47772,x47771)+P29(x47772,f126(x47772,x47771))+E(x47771,f125(x47772)) % 168.22/168.06 [4778]~P103(x47782)+~P29(x47782,x47781)+P29(x47782,f654(x47781,x47782))+E(x47781,f125(x47782)) % 168.22/168.06 [5006]~P27(x50062)+E(f10(x50062,x50061),f49(x50062,x50061))+E(x50061,f188(f858(x50062,a842)))+~P22(f317(f71(x50062),x50061)) % 168.22/168.06 [5007]~P27(x50072)+E(f11(x50072,x50071),f50(x50072,x50071))+E(x50071,f188(f858(x50072,a842)))+~P22(f317(f71(x50072),x50071)) % 168.22/168.06 [5165]~P103(x51652)+~P29(x51652,x51651)+E(x51651,f125(x51652))+E(f317(f317(f145(x51652),f686(x51651,x51652)),f654(x51651,x51652)),x51651) % 168.22/168.06 [5943]~P93(x59432)+E(x59431,f188(f858(x59432,a842)))+P22(f317(f317(f225(x59432),f11(x59432,x59431)),f10(x59432,x59431)))+~P22(f317(f71(x59432),x59431)) % 168.22/168.06 [5952]~P39(x59522)+~P39(x59521)+E(x59521,x59522)+~E(f317(f287(a1,a849,a116),x59521),f317(f287(a1,a849,a116),x59522)) % 168.22/168.06 [8943]~P113(x89431)+~P22(f317(f317(f319(x89431),x89432),f121(x89431)))+P22(f317(f317(f226(x89431),f317(f317(f89(x89431),f317(f317(f89(x89431),f87(x89431)),x89432)),x89432)),f2(x89431)))+~P22(f317(f317(f226(x89431),x89432),f2(x89431))) % 168.22/168.06 [9177]~P113(x91771)+~P22(f317(f317(f319(x91771),x91772),f121(x91771)))+~P22(f317(f317(f226(x91771),f317(f317(f89(x91771),f317(f317(f89(x91771),f87(x91771)),x91772)),x91772)),f2(x91771)))+P22(f317(f317(f226(x91771),x91772),f2(x91771))) % 168.22/168.06 [4832]~P106(x48322)+~P135(x48322)+E(x48321,f2(a849))+E(f317(f317(f238(x48322),f2(x48322)),x48321),f2(x48322)) % 168.22/168.06 [4836]~P106(x48361)+~P135(x48361)+~E(x48362,f2(a849))+E(f317(f317(f238(x48361),f2(x48361)),x48362),f87(x48361)) % 168.22/168.06 [4993]~P133(x49932)+E(x49931,f87(x49932))+E(x49931,f317(f88(x49932),f87(x49932)))+~E(f317(f317(f90(x49932),x49931),x49931),f87(x49932)) % 168.22/168.06 [5243]~P82(x52432)+E(x52431,f2(x52432))+E(f91(x52432,x52431),f317(f88(x52432),f87(x52432)))+P22(f317(f317(f226(x52432),f2(x52432)),x52431)) % 168.22/168.06 [5471]~P82(x54712)+E(f91(x54712,x54711),f87(x54712))+E(x54711,f2(x54712))+~P22(f317(f317(f226(x54712),f2(x54712)),x54711)) % 168.22/168.06 [5482]E(x54821,x54822)+~E(f317(f115(a849),x54821),f317(f115(a849),x54822))+P22(f317(a193,f317(f115(a1),x54822)))+P22(f317(a193,f317(f115(a1),x54821))) % 168.22/168.06 [5517]E(x55171,f2(a1))+~E(f317(f48(a1,x55172),x55171),f2(a1))+P22(f317(f317(f226(a1),x55171),x55172))+P22(f317(f317(f226(a1),x55172),x55171)) % 168.22/168.06 [5535]~P87(x55351)+~E(x55352,f2(x55351))+E(f317(f317(f89(x55351),x55352),x55352),f2(x55351))+~P22(f317(f317(f319(x55351),x55352),f121(x55351))) % 168.22/168.06 [5546]E(x55461,f2(a1))+~E(f317(f48(a1,x55462),x55461),f2(a1))+P22(f317(f317(f225(a1),x55462),f2(a1)))+P22(f317(f317(f226(a1),x55462),x55461)) % 168.22/168.06 [5574]E(x55741,f2(a1))+~E(f317(f48(a1,x55742),x55741),f2(a1))+P22(f317(f317(f225(a1),f2(a1)),x55742))+P22(f317(f317(f226(a1),x55741),x55742)) % 168.22/168.06 [5668]~P87(x56682)+E(x56681,f2(x56682))+~E(f317(f317(f89(x56682),x56681),x56681),f2(x56682))+~P22(f317(f317(f319(x56682),x56681),f121(x56682))) % 168.22/168.06 [5724]E(f317(f115(a849),x57241),f317(f115(a849),x57242))+~E(f317(f115(a1),x57242),f2(a1))+P22(f317(a193,f317(f115(a1),x57242)))+~P22(f317(a193,f317(f115(a1),x57241))) % 168.22/168.06 [5746]~E(f317(f115(a849),x57462),f317(f115(a849),x57461))+E(f317(f115(a1),x57461),f2(a1))+P22(f317(a193,f317(f115(a1),x57461)))+~P22(f317(a193,f317(f115(a1),x57462))) % 168.22/168.06 [5755]~P103(x57552)+E(x57551,f188(f858(x57552,a842)))+~P22(f317(f71(x57552),x57551))+P22(f317(f317(f319(x57552),f14(x57552,x57551)),x57551)) % 168.22/168.06 [5756]~P103(x57562)+E(x57561,f188(f858(x57562,a842)))+~P22(f317(f71(x57562),x57561))+P22(f317(f317(f319(x57562),f15(x57562,x57561)),x57561)) % 168.22/168.06 [5924]~P113(x59241)+~P90(x59241)+P22(f317(f317(f225(x59241),f2(x59241)),f317(f115(x59241),x59242)))+~P22(f317(f317(f225(a1),a92),x59242)) % 168.22/168.06 [5925]~P113(x59251)+~P90(x59251)+P22(f317(f317(f226(x59251),f2(x59251)),f317(f115(x59251),x59252)))+~P22(f317(f317(f226(a1),a92),x59252)) % 168.22/168.06 [5942]~P113(x59421)+~P90(x59421)+E(f317(f84(x59421),f317(f115(x59421),x59422)),f317(f115(x59421),x59422))+P22(f317(f317(f226(x59421),f317(f115(x59421),x59422)),f2(x59421))) % 168.22/168.06 [5978]E(x59781,x59782)+~E(f317(a116,x59781),f317(a116,x59782))+~P22(f317(f317(f225(a1),f2(a1)),x59782))+~P22(f317(f317(f225(a1),f2(a1)),x59781)) % 168.22/168.06 [6168]~P90(x61682)+~P113(x61682)+~P22(f317(f317(f225(x61682),f2(x61682)),f317(f115(x61682),x61681)))+P22(f317(f317(f225(a1),a92),x61681)) % 168.22/168.06 [6169]~P90(x61692)+~P113(x61692)+~P22(f317(f317(f226(x61692),f2(x61692)),f317(f115(x61692),x61691)))+P22(f317(f317(f226(a1),a92),x61691)) % 168.22/168.06 [6174]~P113(x61741)+~P90(x61741)+P22(f317(f317(f225(x61741),f317(f115(x61741),x61742)),f2(x61741)))+~P22(f317(f317(f225(a1),x61742),a92)) % 168.22/168.06 [6175]~P113(x61751)+~P90(x61751)+P22(f317(f317(f226(x61751),f317(f115(x61751),x61752)),f2(x61751)))+~P22(f317(f317(f226(a1),x61752),a92)) % 168.22/168.06 [6478]~P90(x64782)+~P113(x64782)+~P22(f317(f317(f225(x64782),f317(f115(x64782),x64781)),f2(x64782)))+P22(f317(f317(f225(a1),x64781),a92)) % 168.22/168.06 [6479]~P90(x64792)+~P113(x64792)+~P22(f317(f317(f226(x64792),f317(f115(x64792),x64791)),f2(x64792)))+P22(f317(f317(f226(a1),x64791),a92)) % 168.22/168.06 [6568]~P113(x65681)+~P90(x65681)+E(f317(f84(x65681),f317(f115(x65681),x65682)),f317(f88(x65681),f317(f115(x65681),x65682)))+~P22(f317(f317(f226(x65681),f317(f115(x65681),x65682)),f2(x65681))) % 168.22/168.06 [6589]E(f317(f115(a849),x65891),f317(f115(a849),x65892))+~E(f317(f115(a1),x65892),f2(a1))+~P22(f317(f317(f225(a1),f317(f115(a1),x65891)),f2(a1)))+~P22(f317(a193,f317(f115(a1),x65891))) % 168.22/168.06 [7453]~P103(x74532)+E(x74531,f188(f858(x74532,a842)))+~P22(f317(f71(x74532),x74531))+P22(f317(f317(f225(x74532),f13(x74532,f223(x74532),x74531)),f12(x74532,f224(x74532),x74531))) % 168.22/168.06 [7768]~P39(x77682)+~P28(x77681)+P22(f317(f317(f319(a1),x77681),x77682))+~P22(f317(f317(f319(a849),f317(a116,x77681)),f317(f287(a1,a849,a116),x77682))) % 168.22/168.06 [8036]~P57(x80362)+P22(f317(x80361,f191(x80362)))+~P22(f317(f67(f853(x80362)),x80361))+P22(f317(f67(x80362),f317(f317(f8(f853(x80362),a842,x80362),x80361),f217(x80362)))) % 168.22/168.06 [8513]~P57(x85131)+~P22(f317(x85132,f191(x85131)))+P22(f317(f68(f853(x85131)),x85132))+~P22(f317(f68(x85131),f317(f317(f8(f853(x85131),a842,x85131),x85132),f217(x85131)))) % 168.22/168.06 [9319]E(x93191,f2(a1))+E(x93192,f2(a1))+E(f317(f317(f95(a1,f857(a1,a1)),f317(f317(a199,x93192),x93191)),f317(f317(f18(a1,a1,f857(a1,a1)),f317(f317(f8(a1,f858(a1,f857(a1,a1)),a1),f237(a1,a1)),f48(a1,x93192))),f48(a1,x93191))),f209(x93192,x93191))+P22(f317(f317(f226(a1),x93191),f2(a1))) % 168.22/168.06 [5752]~P111(x57522)+E(x57521,f2(a1))+E(f317(f88(x57522),f317(f114(x57522),f317(f88(a1),x57521))),f317(f114(x57522),x57521))+~P22(f317(f317(f226(a1),x57521),f2(a1))) % 168.22/168.06 [5825]~P87(x58251)+~P90(x58251)+~P31(x58251,f317(f115(x58251),x58252))+P31(x58251,f317(f115(x58251),f317(f317(f89(a1),x58252),x58252))) % 168.22/168.06 [6156]~P68(x61562)+E(x61561,f188(f858(x61562,a842)))+E(f15(x61562,f317(f287(x61562,x61562,f88(x61562)),x61561)),f317(f88(x61562),f14(x61562,x61561)))+~P22(f317(f71(x61562),x61561)) % 168.22/168.06 [6157]~P68(x61572)+E(x61571,f188(f858(x61572,a842)))+E(f14(x61572,f317(f287(x61572,x61572,f88(x61572)),x61571)),f317(f88(x61572),f15(x61572,x61571)))+~P22(f317(f71(x61572),x61571)) % 168.22/168.06 [6190]~P87(x61901)+~P90(x61901)+P31(x61901,f317(f115(x61901),x61902))+~P31(x61901,f317(f115(x61901),f317(f317(f89(a1),x61902),x61902))) % 168.22/168.06 [7129]E(x71291,f2(a1))+E(f317(f317(f237(a1,a1),f317(f48(a1,x71291),x71292)),f55(a1,x71291,x71292)),f317(a60,f59(f317(f88(a1),x71291),f317(f88(a1),x71292))))+P22(f317(f317(f225(a1),f2(a1)),x71292))+~P22(f317(f317(f225(a1),f2(a1)),x71291)) % 168.22/168.06 [8260]~P4(a5000)+~P22(f317(a24,x82601))+P18(a845,x82602,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),x82601),f194(x82601))),f188(f858(f848(a845),a842))))+P22(f317(f317(f319(a846),f691(x82601,x82602)),f177(a846,a843,a27))) % 168.22/168.06 [8555]~P39(x85552)+~P39(x85551)+P22(f317(f317(f226(f858(a849,a842)),f317(f287(a1,a849,a116),x85551)),f317(f287(a1,a849,a116),x85552)))+~P22(f317(f317(f226(f858(a1,a842)),x85551),x85552)) % 168.22/168.06 [8762]~E(f698(x87622,x87621),f699(x87622,x87621))+~P22(f317(f131(x87621),f700(x87622,x87621)))+~P22(f317(f131(f850(x87621)),x87622))+P22(f317(f131(x87621),f317(f136(f850(x87621),f850(x87621),f127(x87621),f125(x87621)),x87622))) % 168.22/168.06 [8860]~P39(x88602)+~P39(x88601)+~P22(f317(f317(f225(f858(a849,a842)),f317(f287(a1,a849,a116),x88601)),f317(f287(a1,a849,a116),x88602)))+P22(f317(f317(f225(f858(a1,a842)),x88601),x88602)) % 168.22/168.06 [8861]~P39(x88612)+~P39(x88611)+~P22(f317(f317(f226(f858(a849,a842)),f317(f287(a1,a849,a116),x88611)),f317(f287(a1,a849,a116),x88612)))+P22(f317(f317(f226(f858(a1,a842)),x88611),x88612)) % 168.22/168.06 [8868]~E(f698(x88682,x88681),f699(x88682,x88681))+~P22(f317(f131(f850(x88681)),x88682))+P22(f317(f131(x88681),f317(f136(f850(x88681),f850(x88681),f127(x88681),f125(x88681)),x88682)))+P22(f317(f317(f319(f850(x88681)),f700(x88682,x88681)),f317(f166(f850(x88681)),x88682))) % 168.22/168.06 [8911]~P22(f317(f131(x89111),f700(x89112,x89111)))+~P22(f317(f131(f850(x89111)),x89112))+P22(f317(f131(x89111),f317(f136(f850(x89111),f850(x89111),f127(x89111),f125(x89111)),x89112)))+P22(f317(f317(f319(f850(x89111)),f699(x89112,x89111)),f317(f166(f850(x89111)),x89112))) % 168.22/168.06 [8912]~P22(f317(f131(x89121),f700(x89122,x89121)))+~P22(f317(f131(f850(x89121)),x89122))+P22(f317(f131(x89121),f317(f136(f850(x89121),f850(x89121),f127(x89121),f125(x89121)),x89122)))+P22(f317(f317(f319(f850(x89121)),f698(x89122,x89121)),f317(f166(f850(x89121)),x89122))) % 168.22/168.06 [8984]~P22(f317(f131(f850(x89841)),x89842))+P22(f317(f131(x89841),f317(f136(f850(x89841),f850(x89841),f127(x89841),f125(x89841)),x89842)))+P22(f317(f317(f319(f850(x89841)),f699(x89842,x89841)),f317(f166(f850(x89841)),x89842)))+P22(f317(f317(f319(f850(x89841)),f700(x89842,x89841)),f317(f166(f850(x89841)),x89842))) % 168.22/168.06 [8985]~P22(f317(f131(f850(x89851)),x89852))+P22(f317(f131(x89851),f317(f136(f850(x89851),f850(x89851),f127(x89851),f125(x89851)),x89852)))+P22(f317(f317(f319(f850(x89851)),f698(x89852,x89851)),f317(f166(f850(x89851)),x89852)))+P22(f317(f317(f319(f850(x89851)),f700(x89852,x89851)),f317(f166(f850(x89851)),x89852))) % 168.22/168.06 [8997]~E(f317(f317(f113(f858(x89971,a842)),f317(f166(x89971),f699(x89972,x89971))),f317(f166(x89971),f698(x89972,x89971))),f188(f858(x89971,a842)))+~P22(f317(f131(x89971),f700(x89972,x89971)))+~P22(f317(f131(f850(x89971)),x89972))+P22(f317(f131(x89971),f317(f136(f850(x89971),f850(x89971),f127(x89971),f125(x89971)),x89972))) % 168.22/168.06 [9057]~E(f317(f317(f113(f858(x90571,a842)),f317(f166(x90571),f699(x90572,x90571))),f317(f166(x90571),f698(x90572,x90571))),f188(f858(x90571,a842)))+~P22(f317(f131(f850(x90571)),x90572))+P22(f317(f131(x90571),f317(f136(f850(x90571),f850(x90571),f127(x90571),f125(x90571)),x90572)))+P22(f317(f317(f319(f850(x90571)),f700(x90572,x90571)),f317(f166(f850(x90571)),x90572))) % 168.22/168.06 [9388]~P4(a5000)+~P22(f317(a24,x93882))+P18(a845,x93881,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),x93882),f194(x93882))),f188(f858(f848(a845),a842))))+~P18(a845,x93881,f317(f317(f286(f848(a845)),f317(f317(f317(f100(a845),a314),f317(a29,f691(x93882,x93881))),f194(f317(a29,f691(x93882,x93881))))),f188(f858(f848(a845),a842)))) % 168.22/168.06 [8097]~P90(x80972)+~P113(x80972)+~P22(f317(f317(f225(x80972),f317(f115(x80972),x80971)),f87(x80972)))+P22(f317(f317(f225(a1),x80971),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))) % 168.22/168.06 [8098]~P90(x80982)+~P113(x80982)+~P22(f317(f317(f226(x80982),f317(f115(x80982),x80981)),f87(x80982)))+P22(f317(f317(f226(a1),x80981),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))) % 168.22/168.06 [8381]~P113(x83811)+~P90(x83811)+P22(f317(f317(f225(x83811),f317(f115(x83811),x83812)),f87(x83811)))+~P22(f317(f317(f225(a1),x83812),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))) % 168.22/168.06 [8382]~P113(x83821)+~P90(x83821)+P22(f317(f317(f226(x83821),f317(f115(x83821),x83822)),f87(x83821)))+~P22(f317(f317(f226(a1),x83822),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))) % 168.22/168.06 [8579]~P90(x85792)+~P113(x85792)+~P22(f317(f317(f225(x85792),f87(x85792)),f317(f115(x85792),x85791)))+P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),x85791)) % 168.22/168.06 [8580]~P90(x85802)+~P113(x85802)+~P22(f317(f317(f226(x85802),f87(x85802)),f317(f115(x85802),x85801)))+P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),x85801)) % 168.22/168.06 [8949]~P113(x89491)+~P90(x89491)+P22(f317(f317(f225(x89491),f87(x89491)),f317(f115(x89491),x89492)))+~P22(f317(f317(f225(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),x89492)) % 168.22/168.06 [8950]~P113(x89501)+~P90(x89501)+P22(f317(f317(f226(x89501),f87(x89501)),f317(f115(x89501),x89502)))+~P22(f317(f317(f226(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),x89502)) % 168.22/168.06 [9452]~P133(x94522)+E(x94521,f87(x94522))+E(x94521,f317(f88(x94522),f87(x94522)))+~E(f317(f317(f238(x94522),x94521),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f87(x94522)) % 168.22/168.06 [9716]~P90(x97161)+~P60(x97161)+~P22(f317(f317(f226(x97161),f2(x97161)),x97162))+P22(f317(f317(f226(x97161),f2(x97161)),f317(f317(f266(x97161),x97162),f317(f115(x97161),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.22/168.06 [9784]~P90(x97841)+~P60(x97841)+P22(f317(f317(f226(x97841),f2(x97841)),x97842))+~P22(f317(f317(f226(x97841),f2(x97841)),f317(f317(f266(x97841),x97842),f317(f115(x97841),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.22/168.06 [10040]~P111(x100402)+E(x100401,f2(a1))+P22(f317(f317(f226(a1),x100401),f2(a1)))+E(f317(f317(f247(a1,a1,x100402),f317(f317(f7(a1,f858(a1,f858(x100402,x100402)),f858(a1,x100402)),f317(f317(f8(f858(f858(x100402,x100402),x100402),f858(f858(a1,f858(x100402,x100402)),f858(a1,x100402)),a1),f8(f858(x100402,x100402),x100402,a1)),f317(f317(f8(x100402,f858(f858(x100402,x100402),x100402),a1),f95(x100402,x100402)),f114(x100402)))),f317(f317(f7(a1,f858(x100402,x100402),f858(x100402,x100402)),f317(f317(f8(f858(x100402,f858(x100402,x100402)),f858(f858(x100402,x100402),f858(x100402,x100402)),a1),f18(x100402,x100402,x100402)),f317(f317(f7(a1,f858(x100402,x100402),f858(x100402,f858(x100402,x100402))),f317(f317(f8(f858(x100402,f858(x100402,x100402)),f858(f858(x100402,x100402),f858(x100402,f858(x100402,x100402))),a1),f8(x100402,f858(x100402,x100402),x100402)),f317(f317(f8(a842,f858(x100402,f858(x100402,x100402)),a1),f108(x100402)),f317(f317(f7(a1,a1,a842),a314),f2(a1))))),f317(f317(f18(x100402,x100402,x100402),f89(x100402)),f5(x100402))))),f317(f317(f7(x100402,x100402,x100402),f317(f317(f8(x100402,f858(x100402,x100402),x100402),f89(x100402)),f317(f317(f18(x100402,x100402,x100402),f89(x100402)),f5(x100402)))),f87(x100402))))),f317(f317(f237(a1,a1),f317(f48(a1,x100401),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f55(a1,x100401,f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f317(f114(x100402),x100401)) % 168.22/168.06 [4803]~P87(x48033)+~P90(x48033)+E(x48031,x48032)+~E(f317(f115(x48033),x48031),f317(f115(x48033),x48032)) % 168.22/168.06 [5933]~P22(f317(x59331,x59332))+~P22(f317(x59331,x59333))+~P22(f317(f317(f225(a849),x59333),f823(x59332,x59331)))+P22(f317(x59331,f2(a849))) % 168.22/168.06 [6339]P139(x63392,x63393,x63391)+E(x63391,f2(a1))+P22(f317(f317(f225(a1),f2(a1)),f766(x63391,x63393,x63392)))+P22(f317(f317(f226(a1),x63391),f2(a1))) % 168.22/168.06 [6340]P138(x63402,x63403,x63401)+E(x63401,f2(a1))+P22(f317(f317(f225(a1),f2(a1)),f786(x63401,x63403,x63402)))+P22(f317(f317(f226(a1),x63401),f2(a1))) % 168.22/168.06 [6459]P138(x64591,x64592,x64593)+~P22(f317(x64591,x64592))+P22(f317(f317(f225(a1),f2(a1)),f786(x64593,x64592,x64591)))+P22(f317(f317(f226(a1),x64593),f2(a1))) % 168.22/168.06 [6484]P139(x64841,x64842,x64843)+P22(f317(f317(f225(a1),f2(a1)),f766(x64843,x64842,x64841)))+~P22(f317(x64841,f2(a1)))+P22(f317(f317(f226(a1),x64843),f2(a1))) % 168.22/168.06 [6512]P139(x65122,x65123,x65121)+E(x65121,f2(a1))+~P22(f317(x65122,f767(x65121,x65123,x65122)))+P22(f317(f317(f226(a1),x65121),f2(a1))) % 168.22/168.06 [6513]P138(x65132,x65133,x65131)+E(x65131,f2(a1))+~P22(f317(x65132,f786(x65131,x65133,x65132)))+P22(f317(f317(f226(a1),x65131),f2(a1))) % 168.22/168.06 [6609]~P103(x66091)+~P27(x66091)+~P22(f317(f317(f226(x66091),x66092),f49(x66091,x66093)))+P22(f317(f317(f226(x66091),x66092),f673(x66093,x66092,x66091))) % 168.22/168.06 [6620]P138(x66201,x66202,x66203)+~P22(f317(x66201,x66202))+~P22(f317(x66201,f786(x66203,x66202,x66201)))+P22(f317(f317(f226(a1),x66203),f2(a1))) % 168.22/168.06 [6652]P139(x66521,x66522,x66523)+~P22(f317(x66521,f767(x66523,x66522,x66521)))+~P22(f317(x66521,f2(a1)))+P22(f317(f317(f226(a1),x66523),f2(a1))) % 168.22/168.06 [6901]P139(x69012,x69013,x69011)+E(x69011,f2(a1))+P22(f317(f317(f225(a1),f2(a1)),f766(x69011,x69013,x69012)))+P22(f317(f317(f226(a1),x69011),f765(x69011,x69013,x69012))) % 168.22/168.06 [6902]P138(x69022,x69023,x69021)+E(x69021,f2(a1))+P22(f317(f317(f225(a1),f2(a1)),f786(x69021,x69023,x69022)))+P22(f317(f317(f226(a1),x69021),f785(x69021,x69023,x69022))) % 168.22/168.06 [7019]P138(x70191,x70192,x70193)+~P22(f317(x70191,x70192))+P22(f317(f317(f225(a1),f2(a1)),f786(x70193,x70192,x70191)))+P22(f317(f317(f226(a1),x70193),f785(x70193,x70192,x70191))) % 168.22/168.06 [7037]P139(x70371,x70372,x70373)+P22(f317(f317(f225(a1),f2(a1)),f766(x70373,x70372,x70371)))+P22(f317(f317(f226(a1),x70373),f765(x70373,x70372,x70371)))+~P22(f317(x70371,f2(a1))) % 168.22/168.06 [7073]P139(x70732,x70733,x70731)+E(x70731,f2(a1))+~P22(f317(x70732,f767(x70731,x70733,x70732)))+P22(f317(f317(f226(a1),x70731),f765(x70731,x70733,x70732))) % 168.22/168.06 [7074]P138(x70742,x70743,x70741)+E(x70741,f2(a1))+~P22(f317(x70742,f786(x70741,x70743,x70742)))+P22(f317(f317(f226(a1),x70741),f785(x70741,x70743,x70742))) % 168.22/168.06 [7115]P139(x71152,x71153,x71151)+E(x71151,f2(a1))+P22(f317(f317(f225(a1),f2(a1)),f766(x71151,x71153,x71152)))+~P22(f317(x71152,f784(x71151,x71153,x71152))) % 168.22/168.06 [7116]P138(x71162,x71163,x71161)+E(x71161,f2(a1))+P22(f317(f317(f225(a1),f2(a1)),f786(x71161,x71163,x71162)))+~P22(f317(x71162,f785(x71161,x71163,x71162))) % 168.22/168.06 [7194]P138(x71941,x71942,x71943)+~P22(f317(x71941,x71942))+~P22(f317(x71941,f786(x71943,x71942,x71941)))+P22(f317(f317(f226(a1),x71943),f785(x71943,x71942,x71941))) % 168.22/168.06 [7212]P139(x72121,x72122,x72123)+~P22(f317(x72121,f767(x72123,x72122,x72121)))+P22(f317(f317(f226(a1),x72123),f765(x72123,x72122,x72121)))+~P22(f317(x72121,f2(a1))) % 168.22/168.06 [7216]P138(x72161,x72162,x72163)+~P22(f317(x72161,x72162))+P22(f317(f317(f225(a1),f2(a1)),f786(x72163,x72162,x72161)))+~P22(f317(x72161,f785(x72163,x72162,x72161))) % 168.22/168.06 [7236]P139(x72361,x72362,x72363)+P22(f317(f317(f225(a1),f2(a1)),f766(x72363,x72362,x72361)))+~P22(f317(x72361,f784(x72363,x72362,x72361)))+~P22(f317(x72361,f2(a1))) % 168.22/168.06 [7258]P139(x72582,x72583,x72581)+E(x72581,f2(a1))+~P22(f317(x72582,f767(x72581,x72583,x72582)))+~P22(f317(x72582,f784(x72581,x72583,x72582))) % 168.22/168.06 [7259]P138(x72592,x72593,x72591)+E(x72591,f2(a1))+~P22(f317(x72592,f786(x72591,x72593,x72592)))+~P22(f317(x72592,f785(x72591,x72593,x72592))) % 168.22/168.06 [7349]P138(x73491,x73492,x73493)+~P22(f317(x73491,x73492))+~P22(f317(x73491,f786(x73493,x73492,x73491)))+~P22(f317(x73491,f785(x73493,x73492,x73491))) % 168.22/168.06 [7367]P139(x73671,x73672,x73673)+~P22(f317(x73671,f767(x73673,x73672,x73671)))+~P22(f317(x73671,f784(x73673,x73672,x73671)))+~P22(f317(x73671,f2(a1))) % 168.22/168.06 [7412]P139(x74122,x74123,x74121)+E(x74121,f2(a1))+P22(f317(f317(f225(a1),f2(a1)),f766(x74121,x74123,x74122)))+P22(f317(f317(f225(a1),f765(x74121,x74123,x74122)),f2(a1))) % 168.22/168.06 [7413]P138(x74132,x74133,x74131)+E(x74131,f2(a1))+P22(f317(f317(f225(a1),f2(a1)),f786(x74131,x74133,x74132)))+P22(f317(f317(f225(a1),f785(x74131,x74133,x74132)),f2(a1))) % 168.22/168.06 [7414]~P111(x74141)+~P22(f317(f317(f319(x74141),x74143),f121(x74141)))+~P22(f317(f317(f319(x74141),x74142),f121(x74141)))+P22(f317(f317(f319(x74141),f317(f317(f89(x74141),x74142),x74143)),f121(x74141))) % 168.22/168.06 [7415]~P110(x74151)+~P22(f317(f317(f319(x74151),x74153),f185(x74151)))+~P22(f317(f317(f319(x74151),x74152),f185(x74151)))+P22(f317(f317(f319(x74151),f317(f317(f89(x74151),x74152),x74153)),f185(x74151))) % 168.22/168.06 [7416]~P111(x74161)+~P22(f317(f317(f319(x74161),x74163),f121(x74161)))+~P22(f317(f317(f319(x74161),x74162),f121(x74161)))+P22(f317(f317(f319(x74161),f317(f317(f21(x74161),x74162),x74163)),f121(x74161))) % 168.22/168.06 [7417]~P111(x74171)+~P22(f317(f317(f319(x74171),x74173),f121(x74171)))+~P22(f317(f317(f319(x74171),x74172),f121(x74171)))+P22(f317(f317(f319(x74171),f317(f317(f90(x74171),x74172),x74173)),f121(x74171))) % 168.22/168.06 [7418]~P110(x74181)+~P22(f317(f317(f319(x74181),x74183),f185(x74181)))+~P22(f317(f317(f319(x74181),x74182),f185(x74181)))+P22(f317(f317(f319(x74181),f317(f317(f90(x74181),x74182),x74183)),f185(x74181))) % 168.22/168.06 [7419]~P80(x74191)+~P22(f317(f317(f225(x74191),x74193),f2(x74191)))+~P22(f317(f317(f225(x74191),x74192),f2(x74191)))+P22(f317(f317(f225(x74191),f317(f317(f89(x74191),x74192),x74193)),f2(x74191))) % 168.22/168.06 [7420]~P80(x74201)+~P22(f317(f317(f225(x74201),x74203),f2(x74201)))+~P22(f317(f317(f226(x74201),x74202),f2(x74201)))+P22(f317(f317(f226(x74201),f317(f317(f89(x74201),x74202),x74203)),f2(x74201))) % 168.22/168.06 [7421]~P80(x74211)+~P22(f317(f317(f225(x74211),x74212),f2(x74211)))+~P22(f317(f317(f226(x74211),x74213),f2(x74211)))+P22(f317(f317(f226(x74211),f317(f317(f89(x74211),x74212),x74213)),f2(x74211))) % 168.22/168.06 [7422]~P80(x74221)+~P22(f317(f317(f226(x74221),x74223),f2(x74221)))+~P22(f317(f317(f226(x74221),x74222),f2(x74221)))+P22(f317(f317(f226(x74221),f317(f317(f89(x74221),x74222),x74223)),f2(x74221))) % 168.22/168.06 [7448]P139(x74483,x74482,x74481)+E(x74481,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x74481),f767(x74481,x74482,x74483))),f766(x74481,x74482,x74483)),x74482)+P22(f317(f317(f226(a1),x74481),f2(a1))) % 168.22/168.06 [7449]P138(x74493,x74492,x74491)+E(x74491,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x74491),f787(x74491,x74492,x74493))),f786(x74491,x74492,x74493)),x74492)+P22(f317(f317(f226(a1),x74491),f2(a1))) % 168.22/168.06 [7533]P138(x75331,x75332,x75333)+~P22(f317(x75331,x75332))+P22(f317(f317(f225(a1),f2(a1)),f786(x75333,x75332,x75331)))+P22(f317(f317(f225(a1),f785(x75333,x75332,x75331)),f2(a1))) % 168.22/168.06 [7559]P139(x75591,x75592,x75593)+P22(f317(f317(f225(a1),f2(a1)),f766(x75593,x75592,x75591)))+~P22(f317(x75591,f2(a1)))+P22(f317(f317(f225(a1),f765(x75593,x75592,x75591)),f2(a1))) % 168.22/168.06 [7569]P138(x75693,x75692,x75691)+~P22(f317(x75693,x75692))+E(f317(f317(f89(a1),f317(f317(f90(a1),x75691),f787(x75691,x75692,x75693))),f786(x75691,x75692,x75693)),x75692)+P22(f317(f317(f226(a1),x75691),f2(a1))) % 168.22/168.06 [7575]P139(x75752,x75753,x75751)+E(x75751,f2(a1))+~P22(f317(x75752,f767(x75751,x75753,x75752)))+P22(f317(f317(f225(a1),f765(x75751,x75753,x75752)),f2(a1))) % 168.22/168.06 [7576]P138(x75762,x75763,x75761)+E(x75761,f2(a1))+~P22(f317(x75762,f786(x75761,x75763,x75762)))+P22(f317(f317(f225(a1),f785(x75761,x75763,x75762)),f2(a1))) % 168.22/168.06 [7581]P139(x75813,x75812,x75811)+E(f317(f317(f89(a1),f317(f317(f90(a1),x75811),f767(x75811,x75812,x75813))),f766(x75811,x75812,x75813)),x75812)+~P22(f317(x75813,f2(a1)))+P22(f317(f317(f226(a1),x75811),f2(a1))) % 168.22/168.06 [7638]P138(x76381,x76382,x76383)+~P22(f317(x76381,x76382))+~P22(f317(x76381,f786(x76383,x76382,x76381)))+P22(f317(f317(f225(a1),f785(x76383,x76382,x76381)),f2(a1))) % 168.22/168.06 [7643]P139(x76431,x76432,x76433)+~P22(f317(x76431,f767(x76433,x76432,x76431)))+~P22(f317(x76431,f2(a1)))+P22(f317(f317(f225(a1),f765(x76433,x76432,x76431)),f2(a1))) % 168.22/168.06 [7712]~P118(x77121)+~P22(f317(f317(f225(x77121),f317(f317(f90(x77121),x77123),x77122)),f2(x77121)))+P22(f317(f317(f225(x77121),x77122),f2(x77121)))+P22(f317(f317(f225(x77121),x77123),f2(x77121))) % 168.22/168.06 [7713]~P60(x77131)+~P22(f317(f317(f225(x77131),f317(f317(f266(x77131),x77133),x77132)),f2(x77131)))+P22(f317(f317(f225(x77131),x77132),f2(x77131)))+P22(f317(f317(f225(x77131),x77133),f2(x77131))) % 168.22/168.06 [7714]~P60(x77141)+~P22(f317(f317(f226(x77141),f317(f317(f266(x77141),x77143),x77142)),f2(x77141)))+P22(f317(f317(f226(x77141),x77142),f2(x77141)))+P22(f317(f317(f226(x77141),x77143),f2(x77141))) % 168.22/168.06 [7820]P139(x78203,x78202,x78201)+E(x78201,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x78201),f767(x78201,x78202,x78203))),f766(x78201,x78202,x78203)),x78202)+P22(f317(f317(f226(a1),x78201),f765(x78201,x78202,x78203))) % 168.22/168.06 [7821]P138(x78213,x78212,x78211)+E(x78211,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x78211),f787(x78211,x78212,x78213))),f786(x78211,x78212,x78213)),x78212)+P22(f317(f317(f226(a1),x78211),f785(x78211,x78212,x78213))) % 168.22/168.06 [7832]P139(x78323,x78322,x78321)+E(x78321,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x78321),f784(x78321,x78322,x78323))),f765(x78321,x78322,x78323)),x78322)+P22(f317(f317(f225(a1),f2(a1)),f766(x78321,x78322,x78323))) % 168.22/168.06 [7833]P138(x78333,x78332,x78331)+E(x78331,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x78331),f789(x78331,x78332,x78333))),f785(x78331,x78332,x78333)),x78332)+P22(f317(f317(f225(a1),f2(a1)),f786(x78331,x78332,x78333))) % 168.22/168.06 [7876]P138(x78763,x78762,x78761)+~P22(f317(x78763,x78762))+E(f317(f317(f89(a1),f317(f317(f90(a1),x78761),f787(x78761,x78762,x78763))),f786(x78761,x78762,x78763)),x78762)+P22(f317(f317(f226(a1),x78761),f785(x78761,x78762,x78763))) % 168.22/168.06 [7888]P139(x78883,x78882,x78881)+E(f317(f317(f89(a1),f317(f317(f90(a1),x78881),f767(x78881,x78882,x78883))),f766(x78881,x78882,x78883)),x78882)+P22(f317(f317(f226(a1),x78881),f765(x78881,x78882,x78883)))+~P22(f317(x78883,f2(a1))) % 168.22/168.06 [7894]P138(x78943,x78942,x78941)+~P22(f317(x78943,x78942))+E(f317(f317(f89(a1),f317(f317(f90(a1),x78941),f789(x78941,x78942,x78943))),f785(x78941,x78942,x78943)),x78942)+P22(f317(f317(f225(a1),f2(a1)),f786(x78941,x78942,x78943))) % 168.22/168.06 [7900]P139(x79003,x79002,x79001)+E(f317(f317(f89(a1),f317(f317(f90(a1),x79001),f784(x79001,x79002,x79003))),f765(x79001,x79002,x79003)),x79002)+P22(f317(f317(f225(a1),f2(a1)),f766(x79001,x79002,x79003)))+~P22(f317(x79003,f2(a1))) % 168.22/168.06 [7911]P139(x79113,x79112,x79111)+E(x79111,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x79111),f767(x79111,x79112,x79113))),f766(x79111,x79112,x79113)),x79112)+~P22(f317(x79113,f784(x79111,x79112,x79113))) % 168.22/168.06 [7912]P138(x79123,x79122,x79121)+E(x79121,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x79121),f787(x79121,x79122,x79123))),f786(x79121,x79122,x79123)),x79122)+~P22(f317(x79123,f785(x79121,x79122,x79123))) % 168.22/168.06 [7913]P139(x79133,x79132,x79131)+E(x79131,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x79131),f784(x79131,x79132,x79133))),f765(x79131,x79132,x79133)),x79132)+~P22(f317(x79133,f767(x79131,x79132,x79133))) % 168.22/168.06 [7914]P138(x79143,x79142,x79141)+E(x79141,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x79141),f789(x79141,x79142,x79143))),f785(x79141,x79142,x79143)),x79142)+~P22(f317(x79143,f786(x79141,x79142,x79143))) % 168.22/168.06 [7972]P138(x79723,x79722,x79721)+~P22(f317(x79723,x79722))+E(f317(f317(f89(a1),f317(f317(f90(a1),x79721),f787(x79721,x79722,x79723))),f786(x79721,x79722,x79723)),x79722)+~P22(f317(x79723,f785(x79721,x79722,x79723))) % 168.22/168.06 [7973]P138(x79733,x79732,x79731)+~P22(f317(x79733,x79732))+E(f317(f317(f89(a1),f317(f317(f90(a1),x79731),f789(x79731,x79732,x79733))),f785(x79731,x79732,x79733)),x79732)+~P22(f317(x79733,f786(x79731,x79732,x79733))) % 168.22/168.06 [7982]P139(x79823,x79822,x79821)+E(f317(f317(f89(a1),f317(f317(f90(a1),x79821),f767(x79821,x79822,x79823))),f766(x79821,x79822,x79823)),x79822)+~P22(f317(x79823,f784(x79821,x79822,x79823)))+~P22(f317(x79823,f2(a1))) % 168.22/168.06 [7983]P139(x79833,x79832,x79831)+E(f317(f317(f89(a1),f317(f317(f90(a1),x79831),f784(x79831,x79832,x79833))),f765(x79831,x79832,x79833)),x79832)+~P22(f317(x79833,f767(x79831,x79832,x79833)))+~P22(f317(x79833,f2(a1))) % 168.22/168.06 [8090]P139(x80903,x80902,x80901)+E(x80901,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x80901),f767(x80901,x80902,x80903))),f766(x80901,x80902,x80903)),x80902)+P22(f317(f317(f225(a1),f765(x80901,x80902,x80903)),f2(a1))) % 168.22/168.06 [8091]P138(x80913,x80912,x80911)+E(x80911,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x80911),f787(x80911,x80912,x80913))),f786(x80911,x80912,x80913)),x80912)+P22(f317(f317(f225(a1),f785(x80911,x80912,x80913)),f2(a1))) % 168.22/168.06 [8132]P138(x81323,x81322,x81321)+~P22(f317(x81323,x81322))+E(f317(f317(f89(a1),f317(f317(f90(a1),x81321),f787(x81321,x81322,x81323))),f786(x81321,x81322,x81323)),x81322)+P22(f317(f317(f225(a1),f785(x81321,x81322,x81323)),f2(a1))) % 168.22/168.06 [8137]P139(x81373,x81372,x81371)+E(f317(f317(f89(a1),f317(f317(f90(a1),x81371),f767(x81371,x81372,x81373))),f766(x81371,x81372,x81373)),x81372)+~P22(f317(x81373,f2(a1)))+P22(f317(f317(f225(a1),f765(x81371,x81372,x81373)),f2(a1))) % 168.22/168.06 [8267]P139(x82673,x82672,x82671)+E(x82671,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x82671),f784(x82671,x82672,x82673))),f765(x82671,x82672,x82673)),x82672)+E(f317(f317(f89(a1),f317(f317(f90(a1),x82671),f767(x82671,x82672,x82673))),f766(x82671,x82672,x82673)),x82672) % 168.22/168.06 [8268]P138(x82683,x82682,x82681)+E(x82681,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x82681),f789(x82681,x82682,x82683))),f785(x82681,x82682,x82683)),x82682)+E(f317(f317(f89(a1),f317(f317(f90(a1),x82681),f787(x82681,x82682,x82683))),f786(x82681,x82682,x82683)),x82682) % 168.22/168.06 [8293]P138(x82933,x82932,x82931)+~P22(f317(x82933,x82932))+E(f317(f317(f89(a1),f317(f317(f90(a1),x82931),f789(x82931,x82932,x82933))),f785(x82931,x82932,x82933)),x82932)+E(f317(f317(f89(a1),f317(f317(f90(a1),x82931),f787(x82931,x82932,x82933))),f786(x82931,x82932,x82933)),x82932) % 168.22/168.06 [8306]P139(x83063,x83062,x83061)+E(f317(f317(f89(a1),f317(f317(f90(a1),x83061),f784(x83061,x83062,x83063))),f765(x83061,x83062,x83063)),x83062)+E(f317(f317(f89(a1),f317(f317(f90(a1),x83061),f767(x83061,x83062,x83063))),f766(x83061,x83062,x83063)),x83062)+~P22(f317(x83063,f2(a1))) % 168.22/168.06 [8954]~P118(x89541)+~E(x89543,f2(x89541))+~E(x89542,f2(x89541))+P22(f317(f317(f225(x89541),f317(f317(f89(x89541),f317(f317(f90(x89541),x89542),x89542)),f317(f317(f90(x89541),x89543),x89543))),f2(x89541))) % 168.22/168.06 [9993]~P113(x99931)+~E(x99933,f2(x99931))+~E(x99932,f2(x99931))+P22(f317(f317(f225(x99931),f317(f317(f89(x99931),f317(f317(f238(x99931),x99932),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x99931),x99933),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))),f2(x99931))) % 168.22/168.06 [4752]~E(x47523,x47521)+~P115(x47522)+E(x47521,f2(x47522))+E(f317(f317(f266(x47522),x47523),x47521),f87(x47522)) % 168.22/168.06 [4804]~P94(x48041)+~E(x48043,f188(x48041))+~E(x48042,f188(x48041))+E(f317(f317(f122(x48041),x48042),x48043),f188(x48041)) % 168.22/168.06 [4805]~P97(x48051)+~E(x48053,f233(x48051))+~E(x48052,f233(x48051))+E(f317(f317(f113(x48051),x48052),x48053),f233(x48051)) % 168.22/168.06 [4892]~P115(x48923)+E(x48921,x48922)+E(x48922,f2(x48923))+~E(f317(f317(f266(x48923),x48921),x48922),f87(x48923)) % 168.22/168.06 [4910]~P132(x49102)+E(x49101,f2(x49102))+E(x49103,f2(x49102))+~E(f317(f317(f90(x49102),x49103),x49101),f2(x49102)) % 168.22/168.06 [4912]~P125(x49122)+E(x49121,f2(x49122))+E(x49123,f2(x49122))+~E(f317(f317(f90(x49122),x49123),x49121),f2(x49122)) % 168.22/168.06 [5279]~P114(x52793)+E(x52791,x52792)+E(x52791,f317(f88(x52793),x52792))+~E(f317(f317(f90(x52793),x52791),x52791),f317(f317(f90(x52793),x52792),x52792)) % 168.22/168.06 [5315]~P86(x53151)+E(f317(f88(x53151),x53152),x53153)+~E(f317(f317(f122(x53151),x53152),x53153),f233(x53151))+~E(f317(f317(f113(x53151),x53152),x53153),f188(x53151)) % 168.22/168.06 [5395]~P113(x53953)+E(x53951,x53952)+P22(f317(f317(f226(x53953),x53952),x53951))+P22(f317(f317(f226(x53953),x53951),x53952)) % 168.22/168.06 [5396]~P103(x53963)+E(x53961,x53962)+P22(f317(f317(f226(x53963),x53962),x53961))+P22(f317(f317(f226(x53963),x53961),x53962)) % 168.22/168.06 [5397]~E(x53972,x53973)+~P103(x53971)+P22(f317(f317(f226(x53971),x53972),x53973))+P22(f317(f317(f225(x53971),x53972),x53973)) % 168.22/168.06 [5650]~P104(x56503)+E(x56501,x56502)+~P22(f317(f317(f225(x56503),x56502),x56501))+P22(f317(f317(f226(x56503),x56502),x56501)) % 168.22/168.06 [5652]~P103(x56523)+E(x56521,x56522)+~P22(f317(f317(f225(x56523),x56521),x56522))+P22(f317(f317(f226(x56523),x56521),x56522)) % 168.22/168.06 [5658]~P104(x56583)+E(x56581,x56582)+~P22(f317(f317(f225(x56583),x56581),x56582))+P22(f317(f317(f226(x56583),x56581),x56582)) % 168.22/168.06 [5749]P138(x57491,x57492,x57493)+~P22(f317(x57491,x57492))+P22(f317(f317(f226(a1),x57493),f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x57493)) % 168.22/168.06 [5798]P139(x57981,x57982,x57983)+~P22(f317(x57981,f2(a1)))+P22(f317(f317(f226(a1),x57983),f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x57983)) % 168.22/168.06 [5802]~P93(x58021)+E(f317(f317(f122(x58021),x58022),f11(x58021,x58023)),x58022)+~P22(f317(f71(x58021),x58023))+~P22(f317(f317(f319(x58021),x58022),x58023)) % 168.22/168.06 [5803]~P93(x58031)+E(f317(f317(f113(x58031),x58032),f10(x58031,x58033)),x58032)+~P22(f317(f71(x58031),x58033))+~P22(f317(f317(f319(x58031),x58032),x58033)) % 168.22/168.06 [5835]~P93(x58351)+E(f317(f317(f122(x58351),x58352),f10(x58351,x58353)),f10(x58351,x58353))+~P22(f317(f71(x58351),x58353))+~P22(f317(f317(f319(x58351),x58352),x58353)) % 168.22/168.06 [5836]~P93(x58361)+E(f317(f317(f113(x58361),x58362),f11(x58361,x58363)),f11(x58361,x58363))+~P22(f317(f71(x58361),x58363))+~P22(f317(f317(f319(x58361),x58362),x58363)) % 168.22/168.06 [5837]~P103(x58371)+E(f317(f317(f223(x58371),x58372),f15(x58371,x58373)),f15(x58371,x58373))+~P22(f317(f71(x58371),x58373))+~P22(f317(f317(f319(x58371),x58372),x58373)) % 168.22/168.06 [5838]~P103(x58381)+E(f317(f317(f224(x58381),x58382),f14(x58381,x58383)),f14(x58381,x58383))+~P22(f317(f71(x58381),x58383))+~P22(f317(f317(f319(x58381),x58382),x58383)) % 168.22/168.06 [5883]E(x58831,x58832)+~P104(x58833)+~P22(f317(f317(f225(x58833),x58832),x58831))+~P22(f317(f317(f225(x58833),x58831),x58832)) % 168.22/168.06 [6020]~P101(x60201)+P22(f317(f317(f226(x60201),x60203),x60202))+~P22(f317(f317(f225(x60201),x60203),x60202))+P22(f317(f317(f225(x60201),x60202),x60203)) % 168.22/168.06 [6041]~P103(x60411)+~P22(f317(f71(x60411),x60413))+P22(f317(f317(f225(x60411),x60412),f14(x60411,x60413)))+~P22(f317(f317(f319(x60411),x60412),x60413)) % 168.22/168.06 [6090]~P103(x60901)+E(f317(f317(f223(x60901),x60902),f12(x60901,f224(x60901),x60903)),x60902)+~P22(f317(f71(x60901),x60903))+~P22(f317(f317(f319(x60901),x60902),x60903)) % 168.22/168.06 [6091]~P103(x60911)+E(f317(f317(f224(x60911),x60912),f13(x60911,f223(x60911),x60913)),x60912)+~P22(f317(f71(x60911),x60913))+~P22(f317(f317(f319(x60911),x60912),x60913)) % 168.22/168.06 [6226]E(x62261,x62262)+~E(f317(f317(f21(a849),x62261),x62263),f317(f317(f21(a849),x62262),x62263))+~P22(f317(f317(f225(a849),x62263),x62261))+~P22(f317(f317(f225(a849),x62263),x62262)) % 168.22/168.06 [6255]~P103(x62551)+~P22(f317(f71(x62551),x62552))+~P22(f317(f317(f319(x62551),x62553),x62552))+P22(f317(f317(f225(x62551),f15(x62551,x62552)),x62553)) % 168.22/168.06 [6317]P139(x63172,x63173,x63171)+E(x63171,f2(a1))+P22(f317(f317(f226(a1),x63171),f765(x63171,x63173,x63172)))+P22(f317(f317(f226(a1),f2(a1)),x63171)) % 168.22/168.06 [6318]P138(x63182,x63183,x63181)+E(x63181,f2(a1))+P22(f317(f317(f226(a1),x63181),f785(x63181,x63183,x63182)))+P22(f317(f317(f226(a1),f2(a1)),x63181)) % 168.22/168.06 [6320]~P103(x63201)+E(f317(f317(f223(x63201),x63202),f13(x63201,f223(x63201),x63203)),f13(x63201,f223(x63201),x63203))+~P22(f317(f71(x63201),x63203))+~P22(f317(f317(f319(x63201),x63202),x63203)) % 168.22/168.06 [6321]~P103(x63211)+E(f317(f317(f224(x63211),x63212),f12(x63211,f224(x63211),x63213)),f12(x63211,f224(x63211),x63213))+~P22(f317(f71(x63211),x63213))+~P22(f317(f317(f319(x63211),x63212),x63213)) % 168.22/168.06 [6328]~P22(f317(x63281,x63282))+P22(f317(x63281,f735(x63282,x63281,x63283)))+P22(f317(x63281,f2(a849)))+~P22(f317(f317(f226(a849),x63282),x63283)) % 168.22/168.06 [6381]~P22(f317(x63811,x63812))+~P22(f317(f71(x63813),x63812))+P22(f317(x63811,f390(x63811,x63812,x63813)))+P22(f317(x63811,f188(f858(x63813,a842)))) % 168.22/168.06 [6394]~P113(x63941)+~P90(x63941)+P22(f317(f317(f225(x63941),f317(f115(x63941),x63942)),f317(f115(x63941),x63943)))+~P22(f317(f317(f225(a1),x63942),x63943)) % 168.22/168.06 [6395]~P113(x63951)+~P90(x63951)+P22(f317(f317(f226(x63951),f317(f115(x63951),x63952)),f317(f115(x63951),x63953)))+~P22(f317(f317(f226(a1),x63952),x63953)) % 168.22/168.06 [6399]~P22(f317(x63991,x63993))+~P22(f317(f71(x63992),x63993))+P22(f317(f71(x63992),f390(x63991,x63993,x63992)))+P22(f317(x63991,f188(f858(x63992,a842)))) % 168.22/168.06 [6430]P138(x64301,x64302,x64303)+~P22(f317(x64301,x64302))+P22(f317(f317(f226(a1),x64303),f785(x64303,x64302,x64301)))+P22(f317(f317(f226(a1),f2(a1)),x64303)) % 168.22/168.06 [6468]P139(x64681,x64682,x64683)+P22(f317(f317(f226(a1),x64683),f765(x64683,x64682,x64681)))+~P22(f317(x64681,f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x64683)) % 168.22/168.06 [6495]~P102(x64951)+~P88(x64951)+E(f317(f317(f223(x64951),f317(f115(x64951),x64952)),f317(f115(x64951),x64953)),f317(f115(x64951),x64953))+P22(f317(f317(f225(x64951),f317(f115(x64951),x64952)),f317(f115(x64951),x64953))) % 168.22/168.06 [6496]~P102(x64961)+~P88(x64961)+E(f317(f317(f224(x64961),f317(f115(x64961),x64962)),f317(f115(x64961),x64963)),f317(f115(x64961),x64962))+P22(f317(f317(f225(x64961),f317(f115(x64961),x64962)),f317(f115(x64961),x64963))) % 168.22/168.06 [6553]P139(x65532,x65533,x65531)+E(x65531,f2(a1))+~P22(f317(x65532,f784(x65531,x65533,x65532)))+P22(f317(f317(f226(a1),f2(a1)),x65531)) % 168.22/168.06 [6554]P138(x65542,x65543,x65541)+E(x65541,f2(a1))+~P22(f317(x65542,f785(x65541,x65543,x65542)))+P22(f317(f317(f226(a1),f2(a1)),x65541)) % 168.22/168.06 [6641]P138(x66411,x66412,x66413)+~P22(f317(x66411,x66412))+~P22(f317(x66411,f785(x66413,x66412,x66411)))+P22(f317(f317(f226(a1),f2(a1)),x66413)) % 168.22/168.06 [6670]P139(x66701,x66702,x66703)+~P22(f317(x66701,f784(x66703,x66702,x66701)))+~P22(f317(x66701,f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x66703)) % 168.22/168.06 [6771]~P90(x67713)+~P113(x67713)+~P22(f317(f317(f225(x67713),f317(f115(x67713),x67711)),f317(f115(x67713),x67712)))+P22(f317(f317(f225(a1),x67711),x67712)) % 168.22/168.06 [6772]~P90(x67723)+~P113(x67723)+~P22(f317(f317(f226(x67723),f317(f115(x67723),x67721)),f317(f115(x67723),x67722)))+P22(f317(f317(f226(a1),x67721),x67722)) % 168.22/168.06 [6798]~P103(x67981)+~P29(x67981,x67983)+P29(x67981,f317(f317(f145(x67981),x67982),x67983))+~P22(f317(f317(f225(x67981),x67982),f645(x67983,x67982,x67981))) % 168.22/168.06 [6799]~P103(x67991)+~P29(x67991,x67993)+P29(x67991,f317(f317(f145(x67991),x67992),x67993))+~P22(f317(f317(f225(x67991),x67992),f646(x67993,x67992,x67991))) % 168.22/168.06 [6800]~P103(x68001)+~P29(x68001,x68003)+P29(x68001,f317(f317(f145(x68001),x68002),x68003))+~P22(f317(f317(f225(x68001),x68002),f739(x68002,x68003,x68001))) % 168.22/168.06 [6888]P139(x68882,x68883,x68881)+E(x68881,f2(a1))+P22(f317(f317(f226(a1),x68881),f2(a1)))+P22(f317(f317(f226(a1),f766(x68881,x68883,x68882)),x68881)) % 168.22/168.06 [6889]P138(x68892,x68893,x68891)+E(x68891,f2(a1))+P22(f317(f317(f226(a1),x68891),f2(a1)))+P22(f317(f317(f226(a1),f786(x68891,x68893,x68892)),x68891)) % 168.22/168.06 [6933]P139(x69332,x69333,x69331)+E(x69331,f2(a1))+P22(f317(f317(f225(a1),f765(x69331,x69333,x69332)),f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x69331)) % 168.22/168.06 [6934]P138(x69342,x69343,x69341)+E(x69341,f2(a1))+P22(f317(f317(f225(a1),f785(x69341,x69343,x69342)),f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x69341)) % 168.22/168.06 [6954]~P103(x69541)+~P29(x69541,x69543)+E(f317(f317(f143(x69541,x69541,f5(x69541)),x69542),f164(x69541,x69542,x69543)),x69543)+~P22(f317(f317(f319(x69541),x69542),f317(f166(x69541),x69543))) % 168.22/168.06 [7004]P138(x70041,x70042,x70043)+~P22(f317(x70041,x70042))+P22(f317(f317(f226(a1),x70043),f2(a1)))+P22(f317(f317(f226(a1),f786(x70043,x70042,x70041)),x70043)) % 168.22/168.06 [7008]~P102(x70081)+~P88(x70081)+E(f317(f317(f223(x70081),f317(f115(x70081),x70082)),f317(f115(x70081),x70083)),f317(f115(x70081),x70082))+~P22(f317(f317(f225(x70081),f317(f115(x70081),x70082)),f317(f115(x70081),x70083))) % 168.22/168.06 [7009]~P102(x70091)+~P88(x70091)+E(f317(f317(f224(x70091),f317(f115(x70091),x70092)),f317(f115(x70091),x70093)),f317(f115(x70091),x70093))+~P22(f317(f317(f225(x70091),f317(f115(x70091),x70092)),f317(f115(x70091),x70093))) % 168.22/168.06 [7024]P139(x70241,x70242,x70243)+~P22(f317(x70241,f2(a1)))+P22(f317(f317(f226(a1),x70243),f2(a1)))+P22(f317(f317(f226(a1),f766(x70243,x70242,x70241)),x70243)) % 168.22/168.06 [7030]P138(x70301,x70302,x70303)+~P22(f317(x70301,x70302))+P22(f317(f317(f225(a1),f785(x70303,x70302,x70301)),f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x70303)) % 168.22/168.06 [7057]P139(x70571,x70572,x70573)+~P22(f317(x70571,f2(a1)))+P22(f317(f317(f225(a1),f765(x70573,x70572,x70571)),f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x70573)) % 168.22/168.06 [7086]~P22(f317(x70861,x70862))+P22(f317(x70861,f2(a849)))+~P22(f317(f317(f226(a849),x70862),x70863))+P22(f317(f317(f226(a849),f735(x70862,x70861,x70863)),x70863)) % 168.22/168.06 [7102]~P103(x71021)+~P29(x71021,x71023)+P29(x71021,f317(f317(f145(x71021),x71022),x71023))+P22(f317(f317(f319(x71021),f645(x71023,x71022,x71021)),f317(f166(x71021),x71023))) % 168.22/168.06 [7103]~P103(x71031)+~P29(x71031,x71033)+P29(x71031,f317(f317(f145(x71031),x71032),x71033))+P22(f317(f317(f319(x71031),f646(x71033,x71032,x71031)),f317(f166(x71031),x71033))) % 168.22/168.06 [7104]~P103(x71041)+~P29(x71041,x71043)+P29(x71041,f317(f317(f145(x71041),x71042),x71043))+P22(f317(f317(f319(x71041),f739(x71042,x71043,x71041)),f317(f166(x71041),x71043))) % 168.22/168.06 [7200]~P103(x72001)+~P27(x72001)+~P22(f317(f317(f226(x72001),x72003),f49(x72001,x72002)))+P22(f317(f317(f319(x72001),f673(x72002,x72003,x72001)),x72002)) % 168.22/168.06 [7365]~P103(x73651)+~P27(x73651)+~P22(f317(f317(f226(x73651),f50(x73651,x73653)),x73652))+P22(f317(f317(f319(x73651),f680(x73652,x73653,x73651)),x73653)) % 168.22/168.06 [7366]~P103(x73661)+~P27(x73661)+~P22(f317(f317(f226(x73661),f50(x73661,x73663)),x73662))+P22(f317(f317(f226(x73661),f680(x73662,x73663,x73661)),x73662)) % 168.22/168.06 [7379]P139(x73792,x73793,x73791)+E(x73791,f2(a1))+P22(f317(f317(f226(a1),x73791),f765(x73791,x73793,x73792)))+P22(f317(f317(f226(a1),f766(x73791,x73793,x73792)),x73791)) % 168.22/168.06 [7380]P138(x73802,x73803,x73801)+E(x73801,f2(a1))+P22(f317(f317(f226(a1),x73801),f785(x73801,x73803,x73802)))+P22(f317(f317(f226(a1),f786(x73801,x73803,x73802)),x73801)) % 168.22/168.06 [7470]P139(x74703,x74702,x74701)+E(x74701,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x74701),f784(x74701,x74702,x74703))),f765(x74701,x74702,x74703)),x74702)+P22(f317(f317(f226(a1),f2(a1)),x74701)) % 168.22/168.06 [7471]P138(x74713,x74712,x74711)+E(x74711,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x74711),f789(x74711,x74712,x74713))),f785(x74711,x74712,x74713)),x74712)+P22(f317(f317(f226(a1),f2(a1)),x74711)) % 168.22/168.06 [7474]~P127(x74741)+~P22(f317(f317(f225(x74741),x74743),f2(x74741)))+P22(f317(f317(f225(x74741),f317(f317(f90(x74741),x74742),x74743)),f2(x74741)))+~P22(f317(f317(f225(x74741),f2(x74741)),x74742)) % 168.22/168.06 [7476]~P127(x74761)+~P22(f317(f317(f225(x74761),x74762),f2(x74761)))+P22(f317(f317(f225(x74761),f317(f317(f90(x74761),x74762),x74763)),f2(x74761)))+~P22(f317(f317(f225(x74761),f2(x74761)),x74763)) % 168.22/168.06 [7477]~P118(x74771)+~P22(f317(f317(f225(x74771),x74773),f2(x74771)))+P22(f317(f317(f225(x74771),f317(f317(f90(x74771),x74772),x74773)),f2(x74771)))+~P22(f317(f317(f225(x74771),f2(x74771)),x74772)) % 168.22/168.06 [7478]~P118(x74781)+~P22(f317(f317(f225(x74781),x74782),f2(x74781)))+P22(f317(f317(f225(x74781),f317(f317(f90(x74781),x74782),x74783)),f2(x74781)))+~P22(f317(f317(f225(x74781),f2(x74781)),x74783)) % 168.22/168.06 [7479]~P61(x74791)+~P22(f317(f317(f225(x74791),x74792),f2(x74791)))+P22(f317(f317(f225(x74791),f317(f317(f266(x74791),x74792),x74793)),f2(x74791)))+~P22(f317(f317(f226(x74791),f2(x74791)),x74793)) % 168.22/168.06 [7480]~P61(x74801)+~P22(f317(f317(f226(x74801),x74803),f2(x74801)))+P22(f317(f317(f225(x74801),f317(f317(f266(x74801),x74802),x74803)),f2(x74801)))+~P22(f317(f317(f225(x74801),f2(x74801)),x74802)) % 168.22/168.06 [7481]~P60(x74811)+~P22(f317(f317(f225(x74811),x74813),f2(x74811)))+P22(f317(f317(f225(x74811),f317(f317(f266(x74811),x74812),x74813)),f2(x74811)))+~P22(f317(f317(f225(x74811),f2(x74811)),x74812)) % 168.22/168.06 [7482]~P60(x74821)+~P22(f317(f317(f225(x74821),x74822),f2(x74821)))+P22(f317(f317(f225(x74821),f317(f317(f266(x74821),x74822),x74823)),f2(x74821)))+~P22(f317(f317(f225(x74821),f2(x74821)),x74823)) % 168.22/168.06 [7484]~P124(x74841)+~P22(f317(f317(f226(x74841),x74843),f2(x74841)))+P22(f317(f317(f226(x74841),f317(f317(f90(x74841),x74842),x74843)),f2(x74841)))+~P22(f317(f317(f226(x74841),f2(x74841)),x74842)) % 168.22/168.06 [7485]~P124(x74851)+~P22(f317(f317(f226(x74851),x74852),f2(x74851)))+P22(f317(f317(f226(x74851),f317(f317(f90(x74851),x74852),x74853)),f2(x74851)))+~P22(f317(f317(f226(x74851),f2(x74851)),x74853)) % 168.22/168.06 [7486]~P61(x74861)+~P22(f317(f317(f226(x74861),x74863),f2(x74861)))+P22(f317(f317(f226(x74861),f317(f317(f266(x74861),x74862),x74863)),f2(x74861)))+~P22(f317(f317(f226(x74861),f2(x74861)),x74862)) % 168.22/168.06 [7487]~P61(x74871)+~P22(f317(f317(f226(x74871),x74872),f2(x74871)))+P22(f317(f317(f226(x74871),f317(f317(f266(x74871),x74872),x74873)),f2(x74871)))+~P22(f317(f317(f226(x74871),f2(x74871)),x74873)) % 168.22/168.06 [7488]~P60(x74881)+~P22(f317(f317(f226(x74881),x74883),f2(x74881)))+P22(f317(f317(f226(x74881),f317(f317(f266(x74881),x74882),x74883)),f2(x74881)))+~P22(f317(f317(f226(x74881),f2(x74881)),x74882)) % 168.22/168.06 [7489]~P60(x74891)+~P22(f317(f317(f226(x74891),x74892),f2(x74891)))+P22(f317(f317(f226(x74891),f317(f317(f266(x74891),x74892),x74893)),f2(x74891)))+~P22(f317(f317(f226(x74891),f2(x74891)),x74893)) % 168.22/168.06 [7504]P138(x75041,x75042,x75043)+~P22(f317(x75041,x75042))+P22(f317(f317(f226(a1),x75043),f785(x75043,x75042,x75041)))+P22(f317(f317(f226(a1),f786(x75043,x75042,x75041)),x75043)) % 168.22/168.06 [7517]P139(x75171,x75172,x75173)+P22(f317(f317(f226(a1),x75173),f765(x75173,x75172,x75171)))+~P22(f317(x75171,f2(a1)))+P22(f317(f317(f226(a1),f766(x75173,x75172,x75171)),x75173)) % 168.22/168.06 [7565]P139(x75652,x75653,x75651)+E(x75651,f2(a1))+~P22(f317(x75652,f784(x75651,x75653,x75652)))+P22(f317(f317(f226(a1),f766(x75651,x75653,x75652)),x75651)) % 168.22/168.06 [7566]P138(x75662,x75663,x75661)+E(x75661,f2(a1))+~P22(f317(x75662,f785(x75661,x75663,x75662)))+P22(f317(f317(f226(a1),f786(x75661,x75663,x75662)),x75661)) % 168.22/168.06 [7578]P138(x75783,x75782,x75781)+~P22(f317(x75783,x75782))+E(f317(f317(f89(a1),f317(f317(f90(a1),x75781),f789(x75781,x75782,x75783))),f785(x75781,x75782,x75783)),x75782)+P22(f317(f317(f226(a1),f2(a1)),x75781)) % 168.22/168.06 [7595]P139(x75953,x75952,x75951)+E(f317(f317(f89(a1),f317(f317(f90(a1),x75951),f784(x75951,x75952,x75953))),f765(x75951,x75952,x75953)),x75952)+~P22(f317(x75953,f2(a1)))+P22(f317(f317(f226(a1),f2(a1)),x75951)) % 168.22/168.06 [7621]~P22(f317(x76211,x76213))+~P22(f317(f71(x76212),x76213))+P22(f317(f317(f319(x76212),f403(x76211,x76213,x76212)),f390(x76211,x76213,x76212)))+P22(f317(x76211,f188(f858(x76212,a842)))) % 168.22/168.06 [7624]~P22(f317(f317(f226(a1),x76241),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x76242))+~P22(f317(f317(f225(a1),x76242),x76243))+P22(f317(f317(f225(a1),f317(f48(a1,x76241),x76242)),f317(f48(a1,x76241),x76243))) % 168.22/168.06 [7633]P138(x76331,x76332,x76333)+~P22(f317(x76331,x76332))+~P22(f317(x76331,f785(x76333,x76332,x76331)))+P22(f317(f317(f226(a1),f786(x76333,x76332,x76331)),x76333)) % 168.22/168.06 [7635]~P22(f317(f317(f225(a1),f2(a1)),x76351))+~P22(f317(f317(f226(a1),f2(a1)),x76353))+~P22(f317(f317(f225(a1),x76353),x76352))+P22(f317(f317(f225(a1),f317(f48(a1,x76351),x76352)),f317(f48(a1,x76351),x76353))) % 168.22/168.06 [7639]P139(x76391,x76392,x76393)+~P22(f317(x76391,f784(x76393,x76392,x76391)))+~P22(f317(x76391,f2(a1)))+P22(f317(f317(f226(a1),f766(x76393,x76392,x76391)),x76393)) % 168.22/168.06 [7744]~P118(x77441)+~P22(f317(f317(f225(x77441),f317(f317(f90(x77441),x77443),x77442)),f2(x77441)))+P22(f317(f317(f225(x77441),x77442),f2(x77441)))+P22(f317(f317(f225(x77441),f2(x77441)),x77442)) % 168.22/168.06 [7745]~P118(x77451)+~P22(f317(f317(f225(x77451),f317(f317(f90(x77451),x77452),x77453)),f2(x77451)))+P22(f317(f317(f225(x77451),x77452),f2(x77451)))+P22(f317(f317(f225(x77451),f2(x77451)),x77452)) % 168.22/168.06 [7746]~P60(x77461)+~P22(f317(f317(f225(x77461),f317(f317(f266(x77461),x77463),x77462)),f2(x77461)))+P22(f317(f317(f225(x77461),x77462),f2(x77461)))+P22(f317(f317(f225(x77461),f2(x77461)),x77462)) % 168.22/168.06 [7747]~P60(x77471)+~P22(f317(f317(f225(x77471),f317(f317(f266(x77471),x77472),x77473)),f2(x77471)))+P22(f317(f317(f225(x77471),x77472),f2(x77471)))+P22(f317(f317(f225(x77471),f2(x77471)),x77472)) % 168.22/168.06 [7748]~P60(x77481)+~P22(f317(f317(f226(x77481),f317(f317(f266(x77481),x77483),x77482)),f2(x77481)))+P22(f317(f317(f226(x77481),x77482),f2(x77481)))+P22(f317(f317(f226(x77481),f2(x77481)),x77482)) % 168.22/168.06 [7749]~P60(x77491)+~P22(f317(f317(f226(x77491),f317(f317(f266(x77491),x77492),x77493)),f2(x77491)))+P22(f317(f317(f226(x77491),x77492),f2(x77491)))+P22(f317(f317(f226(x77491),f2(x77491)),x77492)) % 168.22/168.06 [7770]~P118(x77701)+~P22(f317(f317(f225(x77701),f317(f317(f90(x77701),x77702),x77703)),f2(x77701)))+P22(f317(f317(f225(x77701),f2(x77701)),x77702))+P22(f317(f317(f225(x77701),f2(x77701)),x77703)) % 168.22/168.06 [7771]~P60(x77711)+~P22(f317(f317(f225(x77711),f317(f317(f266(x77711),x77712),x77713)),f2(x77711)))+P22(f317(f317(f225(x77711),f2(x77711)),x77712))+P22(f317(f317(f225(x77711),f2(x77711)),x77713)) % 168.22/168.06 [7772]~P60(x77721)+~P22(f317(f317(f226(x77721),f317(f317(f266(x77721),x77722),x77723)),f2(x77721)))+P22(f317(f317(f226(x77721),f2(x77721)),x77722))+P22(f317(f317(f226(x77721),f2(x77721)),x77723)) % 168.22/168.06 [7792]P139(x77922,x77923,x77921)+E(x77921,f2(a1))+P22(f317(f317(f225(a1),f765(x77921,x77923,x77922)),f2(a1)))+P22(f317(f317(f226(a1),f766(x77921,x77923,x77922)),x77921)) % 168.22/168.06 [7793]P138(x77932,x77933,x77931)+E(x77931,f2(a1))+P22(f317(f317(f225(a1),f785(x77931,x77933,x77932)),f2(a1)))+P22(f317(f317(f226(a1),f786(x77931,x77933,x77932)),x77931)) % 168.22/168.06 [7798]~P112(x77981)+~P22(f317(f317(f226(x77981),x77982),f87(x77981)))+P22(f317(f317(f226(x77981),f317(f317(f238(x77981),x77982),f317(a124,x77983))),f87(x77981)))+~P22(f317(f317(f226(x77981),f2(x77981)),x77982)) % 168.22/168.06 [7849]~P103(x78491)+~E(x78493,f125(x78491))+~P29(x78491,f317(f163(x78491),x78493))+E(f317(f136(x78491,x78491,f317(f7(x78491,x78491,x78491),f224(x78491)),x78492),f317(f163(x78491),x78493)),x78492) % 168.22/168.06 [7851]P138(x78511,x78512,x78513)+~P22(f317(x78511,x78512))+P22(f317(f317(f225(a1),f785(x78513,x78512,x78511)),f2(a1)))+P22(f317(f317(f226(a1),f786(x78513,x78512,x78511)),x78513)) % 168.22/168.06 [7860]P139(x78601,x78602,x78603)+~P22(f317(x78601,f2(a1)))+P22(f317(f317(f225(a1),f765(x78603,x78602,x78601)),f2(a1)))+P22(f317(f317(f226(a1),f766(x78603,x78602,x78601)),x78603)) % 168.22/168.06 [8084]P139(x80843,x80842,x80841)+E(x80841,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x80841),f784(x80841,x80842,x80843))),f765(x80841,x80842,x80843)),x80842)+P22(f317(f317(f226(a1),f766(x80841,x80842,x80843)),x80841)) % 168.22/168.06 [8085]P138(x80853,x80852,x80851)+E(x80851,f2(a1))+E(f317(f317(f89(a1),f317(f317(f90(a1),x80851),f789(x80851,x80852,x80853))),f785(x80851,x80852,x80853)),x80852)+P22(f317(f317(f226(a1),f786(x80851,x80852,x80853)),x80851)) % 168.22/168.06 [8122]P138(x81223,x81222,x81221)+~P22(f317(x81223,x81222))+E(f317(f317(f89(a1),f317(f317(f90(a1),x81221),f789(x81221,x81222,x81223))),f785(x81221,x81222,x81223)),x81222)+P22(f317(f317(f226(a1),f786(x81221,x81222,x81223)),x81221)) % 168.22/168.06 [8123]~P67(x81231)+~P70(x81231)+~P39(x81233)+E(f317(f317(f9(a849,x81231),f317(f317(f8(a1,x81231,a849),x81232),f112(a1))),f317(f287(a1,a849,a116),x81233)),f317(f317(f9(a1,x81231),x81232),x81233)) % 168.22/168.06 [8124]~P67(x81241)+~P70(x81241)+~P39(x81243)+E(f317(f317(f6(a849,x81241),f317(f317(f8(a1,x81241,a849),x81242),f112(a1))),f317(f287(a1,a849,a116),x81243)),f317(f317(f6(a1,x81241),x81242),x81243)) % 168.22/168.06 [8134]P139(x81343,x81342,x81341)+E(f317(f317(f89(a1),f317(f317(f90(a1),x81341),f784(x81341,x81342,x81343))),f765(x81341,x81342,x81343)),x81342)+~P22(f317(x81343,f2(a1)))+P22(f317(f317(f226(a1),f766(x81341,x81342,x81343)),x81341)) % 168.22/168.06 [8153]~E(x81532,f2(a849))+~E(f317(f244(a849,a849),x81533),f2(a849))+~E(x81531,f317(f317(f89(a849),f317(f317(f90(a849),f317(f244(a849,a849),x81533)),x81532)),f317(f246(a849,a849),x81533)))+P22(f317(f57(x81531,x81532),x81533)) % 168.22/168.06 [8413]~P57(x84132)+~P57(x84131)+~P22(f317(f68(f856(x84132,x84131)),x84133))+P22(f317(f68(x84131),f317(f317(f8(f856(x84132,x84131),a842,x84131),x84133),f297(x84131,x84132)))) % 168.22/168.06 [8414]~P57(x84142)+~P57(x84141)+~P22(f317(f68(f856(x84141,x84142)),x84143))+P22(f317(f68(x84141),f317(f317(f8(f856(x84141,x84142),a842,x84141),x84143),f288(x84141,x84142)))) % 168.22/168.06 [8780]~P57(x87801)+~P57(x87802)+P22(f317(f67(f856(x87801,x87802)),x87803))+~P22(f317(f67(x87802),f317(f317(f8(f856(x87801,x87802),a842,x87802),x87803),f297(x87802,x87801)))) % 168.22/168.06 [8781]~P57(x87812)+~P57(x87811)+P22(f317(f67(f856(x87811,x87812)),x87813))+~P22(f317(f67(x87811),f317(f317(f8(f856(x87811,x87812),a842,x87811),x87813),f288(x87811,x87812)))) % 168.22/168.06 [9053]P22(f317(f317(f225(a1),x90531),f2(a1)))+~P22(f317(f317(f226(a1),f317(f317(f89(a1),f317(f317(f90(a1),x90533),x90531)),x90532)),f2(a1)))+~P22(f317(f317(f225(a1),f2(a1)),x90532))+~P22(f317(f317(f226(a1),f2(a1)),x90533)) % 168.22/168.06 [5715]~P93(x57152)+E(x57151,f188(f858(x57152,a842)))+~P22(f317(f71(x57152),x57151))+E(f11(x57152,f317(f317(f286(x57152),x57153),x57151)),f317(f317(f113(x57152),x57153),f11(x57152,x57151))) % 168.22/168.06 [5716]~P93(x57162)+E(x57161,f188(f858(x57162,a842)))+~P22(f317(f71(x57162),x57161))+E(f10(x57162,f317(f317(f286(x57162),x57163),x57161)),f317(f317(f122(x57162),x57163),f10(x57162,x57161))) % 168.22/168.06 [5717]~P103(x57172)+E(x57171,f188(f858(x57172,a842)))+~P22(f317(f71(x57172),x57171))+E(f14(x57172,f317(f317(f286(x57172),x57173),x57171)),f317(f317(f224(x57172),x57173),f14(x57172,x57171))) % 168.22/168.06 [5718]~P103(x57182)+E(x57181,f188(f858(x57182,a842)))+~P22(f317(f71(x57182),x57181))+E(f15(x57182,f317(f317(f286(x57182),x57183),x57181)),f317(f317(f223(x57182),x57183),f15(x57182,x57181))) % 168.22/168.06 [6018]~P118(x60181)+~E(x60183,f2(x60181))+~E(x60182,f2(x60181))+E(f317(f317(f89(x60181),f317(f317(f90(x60181),x60182),x60182)),f317(f317(f90(x60181),x60183),x60183)),f2(x60181)) % 168.22/168.06 [6084]~P91(x60842)+E(x60841,f188(f858(x60842,a842)))+~P22(f317(f71(x60842),x60841))+E(f317(f73(x60842,f90(x60842)),f317(f317(f286(x60842),x60843),x60841)),f317(f317(f90(x60842),x60843),f317(f73(x60842,f90(x60842)),x60841))) % 168.22/168.06 [6209]~P103(x62092)+E(x62091,f188(f858(x62092,a842)))+~P22(f317(f71(x62092),x62091))+E(f12(x62092,f224(x62092),f317(f317(f286(x62092),x62093),x62091)),f317(f317(f224(x62092),x62093),f12(x62092,f224(x62092),x62091))) % 168.22/168.06 [6210]~P103(x62102)+E(x62101,f188(f858(x62102,a842)))+~P22(f317(f71(x62102),x62101))+E(f13(x62102,f223(x62102),f317(f317(f286(x62102),x62103),x62101)),f317(f317(f223(x62102),x62103),f13(x62102,f223(x62102),x62101))) % 168.22/168.06 [6776]~E(f317(f317(f89(a1),x67762),f317(f317(f90(a1),x67763),x67761)),x67763)+~P22(f317(f317(f226(a1),f2(a1)),x67763))+P22(f317(f317(f225(a1),f87(a1)),x67761))+~P22(f317(f317(f226(a1),x67762),x67763)) % 168.22/168.06 [6805]~E(f317(f317(f89(a1),x68052),f317(f317(f90(a1),x68053),x68051)),x68053)+P22(f317(f317(f225(a1),x68051),f87(a1)))+~P22(f317(f317(f225(a1),f2(a1)),x68052))+~P22(f317(f317(f226(a1),f2(a1)),x68053)) % 168.22/168.06 [6823]E(x68231,f2(a849))+~P22(f317(f57(x68233,x68231),x68232))+~P22(f317(f317(f226(a849),f2(a849)),x68231))+P22(f317(f317(f226(a849),f317(f246(a849,a849),x68232)),x68231)) % 168.22/168.06 [6854]~P131(x68541)+~P22(f317(f317(f225(x68541),x68542),f2(x68541)))+~P22(f317(f317(f225(x68541),x68543),f2(x68541)))+E(f317(f317(f90(x68541),f317(f84(x68541),x68542)),f317(f84(x68541),x68543)),f317(f84(x68541),f317(f317(f90(x68541),x68542),x68543))) % 168.22/168.06 [6910]~P131(x69101)+~P22(f317(f317(f225(x69101),x69102),f2(x69101)))+E(f317(f317(f90(x69101),f317(f84(x69101),x69102)),f317(f84(x69101),x69103)),f317(f84(x69101),f317(f317(f90(x69101),x69102),x69103)))+~P22(f317(f317(f225(x69101),f2(x69101)),x69103)) % 168.22/168.06 [6911]~P131(x69111)+~P22(f317(f317(f225(x69111),x69113),f2(x69111)))+E(f317(f317(f90(x69111),f317(f84(x69111),x69112)),f317(f84(x69111),x69113)),f317(f84(x69111),f317(f317(f90(x69111),x69112),x69113)))+~P22(f317(f317(f225(x69111),f2(x69111)),x69112)) % 168.22/168.06 [6964]~P131(x69641)+E(f317(f317(f90(x69641),f317(f84(x69641),x69642)),f317(f84(x69641),x69643)),f317(f84(x69641),f317(f317(f90(x69641),x69642),x69643)))+~P22(f317(f317(f225(x69641),f2(x69641)),x69642))+~P22(f317(f317(f225(x69641),f2(x69641)),x69643)) % 168.22/168.06 [6981]~P128(x69811)+~P22(f317(f317(f225(x69811),x69813),f2(x69811)))+~P22(f317(f317(f225(x69811),x69812),f2(x69811)))+P22(f317(f317(f225(x69811),f2(x69811)),f317(f317(f90(x69811),x69812),x69813))) % 168.22/168.06 [6982]~P118(x69821)+~P22(f317(f317(f225(x69821),x69823),f2(x69821)))+~P22(f317(f317(f225(x69821),x69822),f2(x69821)))+P22(f317(f317(f225(x69821),f2(x69821)),f317(f317(f90(x69821),x69822),x69823))) % 168.22/168.06 [6983]~P61(x69831)+~P22(f317(f317(f226(x69831),x69833),f2(x69831)))+~P22(f317(f317(f225(x69831),x69832),f2(x69831)))+P22(f317(f317(f225(x69831),f2(x69831)),f317(f317(f266(x69831),x69832),x69833))) % 168.22/168.06 [6984]~P60(x69841)+~P22(f317(f317(f225(x69841),x69843),f2(x69841)))+~P22(f317(f317(f225(x69841),x69842),f2(x69841)))+P22(f317(f317(f225(x69841),f2(x69841)),f317(f317(f266(x69841),x69842),x69843))) % 168.22/168.06 [6985]~P118(x69851)+~P22(f317(f317(f226(x69851),x69853),f2(x69851)))+~P22(f317(f317(f226(x69851),x69852),f2(x69851)))+P22(f317(f317(f226(x69851),f2(x69851)),f317(f317(f90(x69851),x69852),x69853))) % 168.22/168.06 [6986]~P61(x69861)+~P22(f317(f317(f226(x69861),x69863),f2(x69861)))+~P22(f317(f317(f226(x69861),x69862),f2(x69861)))+P22(f317(f317(f226(x69861),f2(x69861)),f317(f317(f266(x69861),x69862),x69863))) % 168.22/168.06 [6987]~P60(x69871)+~P22(f317(f317(f226(x69871),x69873),f2(x69871)))+~P22(f317(f317(f226(x69871),x69872),f2(x69871)))+P22(f317(f317(f226(x69871),f2(x69871)),f317(f317(f266(x69871),x69872),x69873))) % 168.22/168.06 [6988]~P112(x69881)+~P22(f317(f317(f226(a849),f2(a849)),x69883))+~P22(f317(f317(f226(x69881),f87(x69881)),x69882))+P22(f317(f317(f226(x69881),f87(x69881)),f317(f317(f238(x69881),x69882),x69883))) % 168.22/168.06 [7088]~P127(x70881)+~P22(f317(f317(f225(x70881),f2(x70881)),x70883))+~P22(f317(f317(f225(x70881),f2(x70881)),x70882))+P22(f317(f317(f225(x70881),f2(x70881)),f317(f317(f90(x70881),x70882),x70883))) % 168.22/168.06 [7089]~P128(x70891)+~P22(f317(f317(f225(x70891),f2(x70891)),x70893))+~P22(f317(f317(f225(x70891),f2(x70891)),x70892))+P22(f317(f317(f225(x70891),f2(x70891)),f317(f317(f90(x70891),x70892),x70893))) % 168.22/168.06 [7090]~P118(x70901)+~P22(f317(f317(f225(x70901),f2(x70901)),x70903))+~P22(f317(f317(f225(x70901),f2(x70901)),x70902))+P22(f317(f317(f225(x70901),f2(x70901)),f317(f317(f90(x70901),x70902),x70903))) % 168.22/168.06 [7091]~P61(x70911)+~P22(f317(f317(f226(x70911),f2(x70911)),x70913))+~P22(f317(f317(f225(x70911),f2(x70911)),x70912))+P22(f317(f317(f225(x70911),f2(x70911)),f317(f317(f266(x70911),x70912),x70913))) % 168.22/168.06 [7092]~P60(x70921)+~P22(f317(f317(f225(x70921),f2(x70921)),x70923))+~P22(f317(f317(f225(x70921),f2(x70921)),x70922))+P22(f317(f317(f225(x70921),f2(x70921)),f317(f317(f266(x70921),x70922),x70923))) % 168.22/168.06 [7095]~P80(x70951)+~P22(f317(f317(f226(x70951),f2(x70951)),x70953))+~P22(f317(f317(f226(x70951),f2(x70951)),x70952))+P22(f317(f317(f226(x70951),f2(x70951)),f317(f317(f89(x70951),x70952),x70953))) % 168.22/168.06 [7096]~P124(x70961)+~P22(f317(f317(f226(x70961),f2(x70961)),x70963))+~P22(f317(f317(f226(x70961),f2(x70961)),x70962))+P22(f317(f317(f226(x70961),f2(x70961)),f317(f317(f90(x70961),x70962),x70963))) % 168.22/168.06 [7097]~P61(x70971)+~P22(f317(f317(f226(x70971),f2(x70971)),x70973))+~P22(f317(f317(f226(x70971),f2(x70971)),x70972))+P22(f317(f317(f226(x70971),f2(x70971)),f317(f317(f266(x70971),x70972),x70973))) % 168.22/168.06 [7098]~P60(x70981)+~P22(f317(f317(f226(x70981),f2(x70981)),x70983))+~P22(f317(f317(f226(x70981),f2(x70981)),x70982))+P22(f317(f317(f226(x70981),f2(x70981)),f317(f317(f266(x70981),x70982),x70983))) % 168.22/168.06 [7099]~P112(x70991)+~P22(f317(f317(f226(x70991),f87(x70991)),x70993))+~P22(f317(f317(f226(x70991),f87(x70991)),x70992))+P22(f317(f317(f226(x70991),f87(x70991)),f317(f317(f90(x70991),x70992),x70993))) % 168.22/168.06 [7168]~P93(x71681)+~P22(f317(f71(x71681),x71683))+E(f11(x71681,f317(f317(f286(x71681),x71682),x71683)),x71682)+~E(f317(f317(f21(f858(x71681,a842)),x71683),f317(f317(f286(x71681),x71682),f188(f858(x71681,a842)))),f188(f858(x71681,a842))) % 168.22/168.06 [7169]~P93(x71691)+~P22(f317(f71(x71691),x71693))+E(f10(x71691,f317(f317(f286(x71691),x71692),x71693)),x71692)+~E(f317(f317(f21(f858(x71691,a842)),x71693),f317(f317(f286(x71691),x71692),f188(f858(x71691,a842)))),f188(f858(x71691,a842))) % 168.22/168.06 [7170]~P103(x71701)+~P22(f317(f71(x71701),x71703))+E(f14(x71701,f317(f317(f286(x71701),x71702),x71703)),x71702)+~E(f317(f317(f21(f858(x71701,a842)),x71703),f317(f317(f286(x71701),x71702),f188(f858(x71701,a842)))),f188(f858(x71701,a842))) % 168.22/168.06 [7171]~P103(x71711)+~P22(f317(f71(x71711),x71713))+E(f15(x71711,f317(f317(f286(x71711),x71712),x71713)),x71712)+~E(f317(f317(f21(f858(x71711,a842)),x71713),f317(f317(f286(x71711),x71712),f188(f858(x71711,a842)))),f188(f858(x71711,a842))) % 168.22/168.06 [7172]~P118(x71721)+P22(f317(f317(f225(x71721),x71722),f2(x71721)))+P22(f317(f317(f225(x71721),f2(x71721)),x71723))+~P22(f317(f317(f225(x71721),f2(x71721)),f317(f317(f90(x71721),x71723),x71722))) % 168.22/168.06 [7173]~P118(x71731)+P22(f317(f317(f225(x71731),x71732),f2(x71731)))+P22(f317(f317(f225(x71731),f2(x71731)),x71733))+~P22(f317(f317(f225(x71731),f2(x71731)),f317(f317(f90(x71731),x71732),x71733))) % 168.22/168.06 [7174]~P60(x71741)+P22(f317(f317(f225(x71741),x71742),f2(x71741)))+P22(f317(f317(f225(x71741),f2(x71741)),x71743))+~P22(f317(f317(f225(x71741),f2(x71741)),f317(f317(f266(x71741),x71743),x71742))) % 168.22/168.06 [7175]~P60(x71751)+P22(f317(f317(f225(x71751),x71752),f2(x71751)))+P22(f317(f317(f225(x71751),f2(x71751)),x71753))+~P22(f317(f317(f225(x71751),f2(x71751)),f317(f317(f266(x71751),x71752),x71753))) % 168.22/168.06 [7176]~P118(x71761)+P22(f317(f317(f225(x71761),x71762),f2(x71761)))+P22(f317(f317(f225(x71761),f2(x71761)),x71762))+~P22(f317(f317(f225(x71761),f2(x71761)),f317(f317(f90(x71761),x71763),x71762))) % 168.22/168.06 [7177]~P118(x71771)+P22(f317(f317(f225(x71771),x71772),f2(x71771)))+P22(f317(f317(f225(x71771),f2(x71771)),x71772))+~P22(f317(f317(f225(x71771),f2(x71771)),f317(f317(f90(x71771),x71772),x71773))) % 168.22/168.06 [7178]~P60(x71781)+P22(f317(f317(f225(x71781),x71782),f2(x71781)))+P22(f317(f317(f225(x71781),f2(x71781)),x71782))+~P22(f317(f317(f225(x71781),f2(x71781)),f317(f317(f266(x71781),x71783),x71782))) % 168.22/168.06 [7179]~P60(x71791)+P22(f317(f317(f225(x71791),x71792),f2(x71791)))+P22(f317(f317(f225(x71791),f2(x71791)),x71792))+~P22(f317(f317(f225(x71791),f2(x71791)),f317(f317(f266(x71791),x71792),x71793))) % 168.22/168.06 [7180]~P60(x71801)+P22(f317(f317(f226(x71801),x71802),f2(x71801)))+P22(f317(f317(f226(x71801),f2(x71801)),x71803))+~P22(f317(f317(f226(x71801),f2(x71801)),f317(f317(f266(x71801),x71803),x71802))) % 168.22/168.06 [7181]~P60(x71811)+P22(f317(f317(f226(x71811),x71812),f2(x71811)))+P22(f317(f317(f226(x71811),f2(x71811)),x71813))+~P22(f317(f317(f226(x71811),f2(x71811)),f317(f317(f266(x71811),x71812),x71813))) % 168.22/168.06 [7182]~P60(x71821)+P22(f317(f317(f226(x71821),x71822),f2(x71821)))+P22(f317(f317(f226(x71821),f2(x71821)),x71822))+~P22(f317(f317(f226(x71821),f2(x71821)),f317(f317(f266(x71821),x71823),x71822))) % 168.22/168.06 [7183]~P60(x71831)+P22(f317(f317(f226(x71831),x71832),f2(x71831)))+P22(f317(f317(f226(x71831),f2(x71831)),x71832))+~P22(f317(f317(f226(x71831),f2(x71831)),f317(f317(f266(x71831),x71832),x71833))) % 168.22/168.06 [7266]~E(f317(f317(f113(f858(x72661,a842)),f317(f166(x72661),x72662)),f317(f166(x72661),x72663)),f188(f858(x72661,a842)))+~P22(f317(f131(x72661),x72663))+~P22(f317(f131(x72661),x72662))+P22(f317(f131(x72661),f317(f317(f127(x72661),x72662),x72663))) % 168.22/168.06 [7267]~P103(x72671)+~P22(f317(f71(x72671),x72673))+E(f12(x72671,f224(x72671),f317(f317(f286(x72671),x72672),x72673)),x72672)+~E(f317(f317(f21(f858(x72671,a842)),x72673),f317(f317(f286(x72671),x72672),f188(f858(x72671,a842)))),f188(f858(x72671,a842))) % 168.22/168.06 [7268]~P103(x72681)+~P22(f317(f71(x72681),x72683))+E(f13(x72681,f223(x72681),f317(f317(f286(x72681),x72682),x72683)),x72682)+~E(f317(f317(f21(f858(x72681,a842)),x72683),f317(f317(f286(x72681),x72682),f188(f858(x72681,a842)))),f188(f858(x72681,a842))) % 168.22/168.06 [7285]~P79(x72851)+~P22(f317(f317(f225(x72851),x72852),x72853))+~P22(f317(f317(f225(x72851),f317(f88(x72851),x72852)),x72853))+P22(f317(f317(f225(x72851),f317(f84(x72851),x72852)),x72853)) % 168.22/168.06 [7286]~P113(x72861)+~P22(f317(f317(f226(x72861),x72862),x72863))+~P22(f317(f317(f226(x72861),f317(f88(x72861),x72862)),x72863))+P22(f317(f317(f226(x72861),f317(f84(x72861),x72862)),x72863)) % 168.22/168.06 [7353]~P124(x73531)+P22(f317(f317(f226(x73531),f2(x73531)),x73532))+~P22(f317(f317(f226(x73531),f2(x73531)),x73533))+~P22(f317(f317(f226(x73531),f2(x73531)),f317(f317(f90(x73531),x73533),x73532))) % 168.22/168.06 [7354]~P124(x73541)+P22(f317(f317(f226(x73541),f2(x73541)),x73542))+~P22(f317(f317(f226(x73541),f2(x73541)),x73543))+~P22(f317(f317(f226(x73541),f2(x73541)),f317(f317(f90(x73541),x73542),x73543))) % 168.22/168.06 [7656]E(x76561,x76562)+~P22(f317(f71(x76563),x76561))+~P22(f317(f317(f225(a849),f317(f54(x76563),x76561)),f317(f54(x76563),x76562)))+~P22(f317(f317(f225(f858(x76563,a842)),x76562),x76561)) % 168.22/168.06 [7939]E(f317(x79391,f828(x79392,x79391,x79393)),x79392)+~P22(f317(f317(f225(a1),x79392),f317(x79391,x79393)))+P22(f317(f317(f226(a849),f829(x79392,x79391,x79393)),x79393))+~P22(f317(f317(f225(a1),f317(x79391,f2(a849))),x79392)) % 168.22/168.06 [7940]E(f317(x79401,f830(x79402,x79401,x79403)),x79402)+~P22(f317(f317(f225(a1),x79402),f317(x79401,x79403)))+P22(f317(f317(f226(a849),f831(x79402,x79401,x79403)),x79403))+~P22(f317(f317(f225(a1),f317(x79401,f2(a849))),x79402)) % 168.22/168.06 [8046]~P22(f317(f71(x80461),x80463))+~P22(f317(f317(f226(a849),f317(f54(x80461),x80462)),f317(f54(x80461),x80463)))+~P22(f317(f317(f225(f858(x80461,a842)),x80462),x80463))+P22(f317(f317(f226(f858(x80461,a842)),x80462),x80463)) % 168.22/168.06 [8075]E(f317(f317(f21(a1),f437(x80753,x80751,x80752)),f424(x80753,x80751,x80752)),x80751)+E(f317(f317(f89(a1),x80751),x80752),x80751)+~P22(f317(f317(f226(a1),f2(a1)),x80752))+~P22(f317(f317(f319(a1),f317(f317(f89(a1),x80751),f87(a1))),x80753)) % 168.22/168.06 [8076]E(f317(f317(f89(a1),f425(x80763,x80761,x80762)),f426(x80763,x80761,x80762)),x80761)+E(f317(f317(f21(a1),x80761),x80762),x80761)+~P22(f317(f317(f226(a1),f2(a1)),x80762))+~P22(f317(f317(f319(a1),f317(f317(f21(a1),x80761),f87(a1))),x80763)) % 168.22/168.06 [8130]~P22(f317(f317(f225(a849),x81303),x81301))+P22(f317(f317(f225(a849),x81301),x81302))+~P22(f317(f317(f225(a849),x81303),x81302))+~P22(f317(f317(f225(a849),f317(f317(f21(a849),x81301),x81303)),f317(f317(f21(a849),x81302),x81303))) % 168.22/168.06 [8131]~P22(f317(f317(f225(a849),x81313),x81311))+P22(f317(f317(f226(a849),x81311),x81312))+~P22(f317(f317(f225(a849),x81313),x81312))+~P22(f317(f317(f226(a849),f317(f317(f21(a849),x81311),x81313)),f317(f317(f21(a849),x81312),x81313))) % 168.22/168.06 [8146]~P103(x81462)+E(x81461,f125(x81462))+~P29(x81462,f317(f163(x81462),x81461))+E(f317(f136(x81462,x81462,f317(f7(x81462,x81462,x81462),f224(x81462)),x81463),f317(f163(x81462),x81461)),f317(f317(f224(x81462),f317(f317(f159(x81462),x81461),f2(a849))),x81463)) % 168.22/168.06 [8211]E(f317(f317(f89(a1),x82111),x82112),x82111)+~P22(f317(f317(f226(a1),f2(a1)),x82112))+P22(f317(f317(f319(a1),f437(x82113,x82111,x82112)),x82113))+~P22(f317(f317(f319(a1),f317(f317(f89(a1),x82111),f87(a1))),x82113)) % 168.22/168.06 [8212]E(f317(f317(f21(a1),x82121),x82122),x82121)+~P22(f317(f317(f226(a1),f2(a1)),x82122))+P22(f317(f317(f319(a1),f425(x82123,x82121,x82122)),x82123))+~P22(f317(f317(f319(a1),f317(f317(f21(a1),x82121),f87(a1))),x82123)) % 168.22/168.06 [8291]~P22(f317(f317(f225(a1),x82911),f317(x82912,x82913)))+P22(f317(f317(f226(a849),f829(x82911,x82912,x82913)),x82913))+P22(f317(f317(f225(a849),f828(x82911,x82912,x82913)),x82913))+~P22(f317(f317(f225(a1),f317(x82912,f2(a849))),x82911)) % 168.22/168.06 [8292]~P22(f317(f317(f225(a1),x82921),f317(x82922,x82923)))+P22(f317(f317(f226(a849),f831(x82921,x82922,x82923)),x82923))+P22(f317(f317(f225(a849),f830(x82921,x82922,x82923)),x82923))+~P22(f317(f317(f225(a1),f317(x82922,f2(a849))),x82921)) % 168.22/168.06 [8371]E(f317(f317(f89(a1),x83711),x83712),x83711)+~P22(f317(f317(f226(a1),f2(a1)),x83712))+P22(f317(f317(f319(a1),f424(x83713,x83711,x83712)),f279(a1,f87(a1),x83712)))+~P22(f317(f317(f319(a1),f317(f317(f89(a1),x83711),f87(a1))),x83713)) % 168.22/168.06 [8372]E(f317(f317(f21(a1),x83721),x83722),x83721)+~P22(f317(f317(f226(a1),f2(a1)),x83722))+P22(f317(f317(f319(a1),f426(x83723,x83721,x83722)),f279(a1,f87(a1),x83722)))+~P22(f317(f317(f319(a1),f317(f317(f21(a1),x83721),f87(a1))),x83723)) % 168.22/168.06 [8508]~P112(x85081)+~P22(f317(f317(f226(x85081),x85082),f87(x85081)))+~P22(f317(f317(f226(x85081),f2(x85081)),x85082))+P22(f317(f317(f226(x85081),f317(f317(f90(x85081),x85082),f317(f317(f238(x85081),x85082),x85083))),f317(f317(f238(x85081),x85082),x85083))) % 168.22/168.06 [8586]~P22(f317(x85861,x85862))+P22(f317(x85861,f2(a849)))+~P22(f317(f317(f226(a849),x85862),x85863))+~P22(f317(x85861,f55(a849,f317(a124,f735(x85862,x85861,x85863)),x85863))) % 168.22/168.06 [8721]E(f353(x87211,x87212,x87213),f2(a849))+P22(f317(f317(x87211,x87213),x87212))+P22(f317(f317(x87211,f353(x87211,x87212,x87213)),f55(a849,f352(x87211,x87212,x87213),f353(x87211,x87212,x87213))))+~P22(f317(f305(f857(a849,a849),a210),f317(f317(f237(a849,a849),x87213),x87212))) % 168.22/168.06 [8759]~P19(x87591,x87591,x87592,x87593)+E(f317(f287(x87591,x87591,x87592),x87593),x87593)+~P22(f317(f71(x87591),x87593))+~P22(f317(f317(f225(f858(x87591,a842)),f317(f287(x87591,x87591,x87592),x87593)),x87593)) % 168.22/168.06 [8996]P22(f317(f317(x89961,x89962),x89963))+~P22(f317(f317(f226(a1),f351(x89961,x89963,x89962)),f2(a1)))+P22(f317(f317(x89961,f317(f88(a1),f350(x89961,x89963,x89962))),f317(f88(a1),f351(x89961,x89963,x89962))))+~P22(f317(f305(f857(a1,a1),a211),f317(f317(f237(a1,a1),x89962),x89963))) % 168.22/168.06 [9181]P22(f317(f317(x91811,x91812),x91813))+P22(f317(f317(x91811,f317(f317(f89(a1),f614(x91811,x91813,x91812)),f87(a1))),f616(x91811,x91813,x91812)))+~P22(f317(f317(f225(a1),f614(x91811,x91813,x91812)),f616(x91811,x91813,x91812)))+~P22(f317(f305(f857(a1,a1),a176),f317(f317(f237(a1,a1),x91812),x91813))) % 168.22/168.06 [9597]~P57(x95972)+~P57(x95971)+~P22(f317(f68(f857(x95971,x95972)),x95973))+P22(f317(f68(x95971),f317(f317(f8(f858(x95972,a842),a842,x95971),f68(x95972)),f317(f317(f8(f858(x95972,f857(x95971,x95972)),f858(x95972,a842),x95971),f317(f8(f857(x95971,x95972),a842,x95972),x95973)),f237(x95971,x95972))))) % 168.22/168.06 [9598]~P57(x95982)+~P57(x95981)+~P22(f317(f67(f857(x95981,x95982)),x95983))+P22(f317(f67(x95981),f317(f317(f8(f858(x95982,a842),a842,x95981),f67(x95982)),f317(f317(f8(f858(x95982,f857(x95981,x95982)),f858(x95982,a842),x95981),f317(f8(f857(x95981,x95982),a842,x95982),x95983)),f237(x95981,x95982))))) % 168.22/168.06 [9696]~P57(x96962)+~P57(x96961)+P22(f317(f68(f857(x96961,x96962)),x96963))+~P22(f317(f68(x96961),f317(f317(f8(f858(x96962,a842),a842,x96961),f68(x96962)),f317(f317(f8(f858(x96962,f857(x96961,x96962)),f858(x96962,a842),x96961),f317(f8(f857(x96961,x96962),a842,x96962),x96963)),f237(x96961,x96962))))) % 168.22/168.06 [9697]~P57(x96972)+~P57(x96971)+P22(f317(f67(f857(x96971,x96972)),x96973))+~P22(f317(f67(x96971),f317(f317(f8(f858(x96972,a842),a842,x96971),f67(x96972)),f317(f317(f8(f858(x96972,f857(x96971,x96972)),f858(x96972,a842),x96971),f317(f8(f857(x96971,x96972),a842,x96972),x96973)),f237(x96971,x96972))))) % 168.22/168.06 [9880]E(f317(x98801,f828(x98802,x98801,x98803)),x98802)+~P22(f317(f317(f225(a1),x98802),f317(x98801,x98803)))+~P22(f317(f317(f225(a1),f317(f84(a1),f317(f317(f21(a1),f317(x98801,f317(f317(f89(a849),f829(x98802,x98801,x98803)),f87(a849)))),f317(x98801,f829(x98802,x98801,x98803))))),f87(a1)))+~P22(f317(f317(f225(a1),f317(x98801,f2(a849))),x98802)) % 168.22/168.06 [9881]E(f317(x98811,f830(x98812,x98811,x98813)),x98812)+~P22(f317(f317(f225(a1),x98812),f317(x98811,x98813)))+~P22(f317(f317(f225(a1),f317(f84(a1),f317(f317(f21(a1),f317(x98811,f317(f317(f89(a849),f831(x98812,x98811,x98813)),f87(a849)))),f317(x98811,f831(x98812,x98811,x98813))))),f87(a1)))+~P22(f317(f317(f225(a1),f317(x98811,f2(a849))),x98812)) % 168.22/168.06 [9885]~P22(f317(f317(f225(a1),x98851),f317(x98852,x98853)))+~P22(f317(f317(f225(a1),f317(f84(a1),f317(f317(f21(a1),f317(x98852,f317(f317(f89(a849),f829(x98851,x98852,x98853)),f87(a849)))),f317(x98852,f829(x98851,x98852,x98853))))),f87(a1)))+P22(f317(f317(f225(a849),f828(x98851,x98852,x98853)),x98853))+~P22(f317(f317(f225(a1),f317(x98852,f2(a849))),x98851)) % 168.22/168.06 [9886]~P22(f317(f317(f225(a1),x98861),f317(x98862,x98863)))+~P22(f317(f317(f225(a1),f317(f84(a1),f317(f317(f21(a1),f317(x98862,f317(f317(f89(a849),f831(x98861,x98862,x98863)),f87(a849)))),f317(x98862,f831(x98861,x98862,x98863))))),f87(a1)))+P22(f317(f317(f225(a849),f830(x98861,x98862,x98863)),x98863))+~P22(f317(f317(f225(a1),f317(x98862,f2(a849))),x98861)) % 168.22/168.06 [9939]E(x99391,x99392)+~E(f317(f136(f850(x99393),f850(x99393),f127(x99393),f125(x99393)),x99391),f317(f136(f850(x99393),f850(x99393),f127(x99393),f125(x99393)),x99392))+~E(f317(f189(f850(f850(x99393))),x99391),f317(f189(f850(f850(x99393))),x99392))+~P22(f317(f317(f247(f850(x99393),f850(x99393),a842),f317(f317(f7(f850(x99393),f858(f850(x99393),a849),f858(f850(x99393),a842)),f317(f317(f8(f858(a849,a842),f858(f858(f850(x99393),a849),f858(f850(x99393),a842)),f850(x99393)),f8(a849,a842,f850(x99393))),f317(f317(f8(a849,f858(a849,a842),f850(x99393)),a314),f189(f850(x99393))))),f189(f850(x99393)))),f659(x99391,x99392,x99393))) % 168.22/168.06 [9940]E(x99401,x99402)+~E(f317(f136(f850(x99403),f850(x99403),f127(x99403),f125(x99403)),x99401),f317(f136(f850(x99403),f850(x99403),f127(x99403),f125(x99403)),x99402))+~E(f317(f189(f850(f850(x99403))),x99401),f317(f189(f850(f850(x99403))),x99402))+~P22(f317(f317(f247(f850(x99403),f850(x99403),a842),f317(f317(f7(f850(x99403),f858(f850(x99403),a849),f858(f850(x99403),a842)),f317(f317(f8(f858(a849,a842),f858(f858(f850(x99403),a849),f858(f850(x99403),a842)),f850(x99403)),f8(a849,a842,f850(x99403))),f317(f317(f8(a849,f858(a849,a842),f850(x99403)),a314),f189(f850(x99403))))),f189(f850(x99403)))),f660(x99402,x99401,x99403))) % 168.22/168.06 [6690]~E(f87(a849),f2(a849))+~P22(f317(f71(x66901),x66903))+~P22(f317(f71(x66901),x66902))+E(f317(f317(f89(a849),f317(f54(x66901),x66902)),f317(f54(x66901),x66903)),f317(f54(x66901),f317(f317(f122(f858(x66901,a842)),x66902),x66903))) % 168.22/168.06 [7105]~P98(x71051)+~P22(f317(f71(x71051),x71052))+~P22(f317(f317(f319(x71051),x71053),x71052))+P22(f317(f317(f225(x71051),f317(f73(x71051,f113(x71051)),x71052)),x71053)) % 168.22/168.06 [7106]~P103(x71061)+~P22(f317(f71(x71061),x71062))+~P22(f317(f317(f319(x71061),x71063),x71062))+P22(f317(f317(f225(x71061),f317(f73(x71061,f223(x71061)),x71062)),x71063)) % 168.22/168.06 [7348]~P22(f317(f71(x73481),x73483))+~P22(f317(f71(x73481),x73482))+~E(f317(f317(f113(f858(x73481,a842)),x73482),x73483),f188(f858(x73481,a842)))+E(f317(f317(f89(a849),f317(f54(x73481),x73482)),f317(f54(x73481),x73483)),f317(f54(x73481),f317(f317(f122(f858(x73481,a842)),x73482),x73483))) % 168.22/168.06 [8135]~P37(x81351,x81353)+~P37(x81351,x81352)+~E(f317(f317(f113(f858(x81351,a842)),f317(f236(x81351,x81351),x81352)),f317(f234(x81351,x81351),x81353)),f188(f858(x81351,a842)))+P37(x81351,f317(f317(f122(f858(f857(x81351,x81351),a842)),x81352),x81353)) % 168.22/168.06 [8216]E(x82161,f317(f48(a849,x82162),x82163))+~P22(f317(f317(f226(a849),f2(a849)),x82163))+~P22(f317(f317(f226(a849),x82162),f317(f317(f90(a849),x82163),f317(a124,x82161))))+~P22(f317(f317(f225(a849),f317(f317(f90(a849),x82163),x82161)),x82162)) % 168.22/168.06 [8369]~P22(f317(f71(x83691),x83692))+~P22(f317(f71(x83691),x83693))+E(f317(f317(f89(a849),f317(f54(x83691),x83692)),f317(f54(x83691),x83693)),f317(f54(x83691),f317(f317(f122(f858(x83691,a842)),x83692),x83693)))+P22(f317(f317(f319(x83691),f378(x83693,x83692,x83691)),f317(f317(f113(f858(x83691,a842)),x83692),x83693))) % 168.22/168.06 [8733]~P118(x87332)+~E(x87331,f2(x87332))+~E(x87333,f2(x87332))+~P22(f317(f317(f226(x87332),f2(x87332)),f317(f317(f89(x87332),f317(f317(f90(x87332),x87333),x87333)),f317(f317(f90(x87332),x87331),x87331)))) % 168.22/168.06 [9258]~P37(x92581,x92583)+~P37(x92581,x92582)+P37(x92581,f317(f317(f122(f858(f857(x92581,x92581),a842)),x92582),x92583))+~P22(f317(f317(f225(f858(f857(x92581,x92581),a842)),f317(f317(f265(x92581,x92581,x92581),x92582),x92583)),x92582)) % 168.22/168.06 [9385]~P22(f317(x93851,x93853))+~P22(f317(f71(x93852),x93853))+P22(f317(x93851,f188(f858(x93852,a842))))+~P22(f317(x93851,f317(f317(f21(f858(x93852,a842)),f390(x93851,x93853,x93852)),f317(f317(f286(x93852),f403(x93851,x93853,x93852)),f188(f858(x93852,a842)))))) % 168.22/168.06 [9627]~P57(x96271)+~P57(x96272)+P8(x96271,f317(f317(f8(f858(x96272,x96271),a842,f850(x96271)),x96273),f317(f317(f8(f858(x96272,f853(x96271)),f858(x96272,x96271),f850(x96271)),f82(f853(x96271),x96271,x96272,f222(x96271))),f317(f317(f8(f850(f857(x96272,x96271)),f858(x96272,f853(x96271)),f850(x96271)),f171(x96272,x96271)),f317(f175(x96272,x96271),f65(x96272))))),f317(f189(f850(x96272)),f65(x96272)))+~P22(f317(f68(f858(x96272,x96271)),x96273)) % 168.22/168.06 [9628]~P57(x96281)+~P57(x96282)+P7(x96281,f317(f317(f8(f858(x96282,x96281),a842,f850(x96281)),x96283),f317(f317(f8(f858(x96282,f853(x96281)),f858(x96282,x96281),f850(x96281)),f82(f853(x96281),x96281,x96282,f222(x96281))),f317(f317(f8(f850(f857(x96282,x96281)),f858(x96282,f853(x96281)),f850(x96281)),f171(x96282,x96281)),f317(f175(x96282,x96281),f65(x96282))))),f317(f189(f850(x96282)),f65(x96282)))+~P22(f317(f67(f858(x96282,x96281)),x96283)) % 168.22/168.06 [9724]~P57(x97241)+~P57(x97242)+~P8(x97242,f317(f317(f8(f858(x97241,x97242),a842,f850(x97242)),x97243),f317(f317(f8(f858(x97241,f853(x97242)),f858(x97241,x97242),f850(x97242)),f82(f853(x97242),x97242,x97241,f222(x97242))),f317(f317(f8(f850(f857(x97241,x97242)),f858(x97241,f853(x97242)),f850(x97242)),f171(x97241,x97242)),f317(f175(x97241,x97242),f65(x97241))))),f317(f189(f850(x97241)),f65(x97241)))+P22(f317(f68(f858(x97241,x97242)),x97243)) % 168.22/168.06 [9725]~P57(x97251)+~P57(x97252)+~P7(x97252,f317(f317(f8(f858(x97251,x97252),a842,f850(x97252)),x97253),f317(f317(f8(f858(x97251,f853(x97252)),f858(x97251,x97252),f850(x97252)),f82(f853(x97252),x97252,x97251,f222(x97252))),f317(f317(f8(f850(f857(x97251,x97252)),f858(x97251,f853(x97252)),f850(x97252)),f171(x97251,x97252)),f317(f175(x97251,x97252),f65(x97251))))),f317(f189(f850(x97251)),f65(x97251)))+P22(f317(f67(f858(x97251,x97252)),x97253)) % 168.22/168.06 [8540]~P22(f317(f317(f226(a1),f2(a1)),x85403))+P22(f317(f317(f225(a1),f2(a1)),x85401))+~P22(f317(f317(f226(a1),x85402),x85403))+~P22(f317(f317(f225(a1),f2(a1)),f317(f317(f89(a1),f317(f317(f90(a1),x85403),x85401)),x85402))) % 168.22/168.06 [8560]~P93(x85601)+~P22(f317(f71(x85601),x85602))+E(f317(f317(f21(f858(x85601,a842)),x85602),f317(f317(f286(x85601),x85603),f188(f858(x85601,a842)))),f188(f858(x85601,a842)))+E(f317(f317(f113(x85601),x85603),f11(x85601,f317(f317(f21(f858(x85601,a842)),x85602),f317(f317(f286(x85601),x85603),f188(f858(x85601,a842)))))),f11(x85601,f317(f317(f286(x85601),x85603),x85602))) % 168.22/168.06 [8561]~P93(x85611)+~P22(f317(f71(x85611),x85612))+E(f317(f317(f21(f858(x85611,a842)),x85612),f317(f317(f286(x85611),x85613),f188(f858(x85611,a842)))),f188(f858(x85611,a842)))+E(f317(f317(f122(x85611),x85613),f10(x85611,f317(f317(f21(f858(x85611,a842)),x85612),f317(f317(f286(x85611),x85613),f188(f858(x85611,a842)))))),f10(x85611,f317(f317(f286(x85611),x85613),x85612))) % 168.22/168.06 [8562]~P103(x85621)+~P22(f317(f71(x85621),x85622))+E(f317(f317(f21(f858(x85621,a842)),x85622),f317(f317(f286(x85621),x85623),f188(f858(x85621,a842)))),f188(f858(x85621,a842)))+E(f317(f317(f224(x85621),x85623),f14(x85621,f317(f317(f21(f858(x85621,a842)),x85622),f317(f317(f286(x85621),x85623),f188(f858(x85621,a842)))))),f14(x85621,f317(f317(f286(x85621),x85623),x85622))) % 168.22/168.06 [8563]~P103(x85631)+~P22(f317(f71(x85631),x85632))+E(f317(f317(f21(f858(x85631,a842)),x85632),f317(f317(f286(x85631),x85633),f188(f858(x85631,a842)))),f188(f858(x85631,a842)))+E(f317(f317(f223(x85631),x85633),f15(x85631,f317(f317(f21(f858(x85631,a842)),x85632),f317(f317(f286(x85631),x85633),f188(f858(x85631,a842)))))),f15(x85631,f317(f317(f286(x85631),x85633),x85632))) % 168.22/168.06 [8627]~P103(x86271)+~P22(f317(f71(x86271),x86272))+E(f317(f317(f21(f858(x86271,a842)),x86272),f317(f317(f286(x86271),x86273),f188(f858(x86271,a842)))),f188(f858(x86271,a842)))+E(f317(f317(f224(x86271),x86273),f12(x86271,f224(x86271),f317(f317(f21(f858(x86271,a842)),x86272),f317(f317(f286(x86271),x86273),f188(f858(x86271,a842)))))),f12(x86271,f224(x86271),f317(f317(f286(x86271),x86273),x86272))) % 168.22/168.06 [8628]~P103(x86281)+~P22(f317(f71(x86281),x86282))+E(f317(f317(f21(f858(x86281,a842)),x86282),f317(f317(f286(x86281),x86283),f188(f858(x86281,a842)))),f188(f858(x86281,a842)))+E(f317(f317(f223(x86281),x86283),f13(x86281,f223(x86281),f317(f317(f21(f858(x86281,a842)),x86282),f317(f317(f286(x86281),x86283),f188(f858(x86281,a842)))))),f13(x86281,f223(x86281),f317(f317(f286(x86281),x86283),x86282))) % 168.22/168.06 [9200]E(x92001,x92002)+~E(f317(f136(f850(x92003),f850(x92003),f127(x92003),f125(x92003)),x92001),f317(f136(f850(x92003),f850(x92003),f127(x92003),f125(x92003)),x92002))+~E(f317(f189(f850(f850(x92003))),x92001),f317(f189(f850(f850(x92003))),x92002))+P22(f317(f317(f319(f857(f850(x92003),f850(x92003))),f659(x92001,x92002,x92003)),f317(f166(f857(f850(x92003),f850(x92003))),f317(f317(f175(f850(x92003),f850(x92003)),x92002),x92001)))) % 168.22/168.06 [9201]E(x92011,x92012)+~E(f317(f136(f850(x92013),f850(x92013),f127(x92013),f125(x92013)),x92011),f317(f136(f850(x92013),f850(x92013),f127(x92013),f125(x92013)),x92012))+~E(f317(f189(f850(f850(x92013))),x92011),f317(f189(f850(f850(x92013))),x92012))+P22(f317(f317(f319(f857(f850(x92013),f850(x92013))),f660(x92012,x92011,x92013)),f317(f166(f857(f850(x92013),f850(x92013))),f317(f317(f175(f850(x92013),f850(x92013)),x92011),x92012)))) % 168.22/168.06 [10024]~P72(x100242)+E(x100241,f188(f858(x100242,a842)))+~P22(f317(f71(x100242),x100241))+E(f14(x100242,f317(f230(x100242),f317(f317(f8(f858(x100242,a842),a842,x100242),f96(x100242)),f317(f317(f7(x100242,f858(x100242,a842),f858(x100242,a842)),f317(f317(f8(f858(x100242,f858(a842,a842)),f858(f858(x100242,a842),f858(x100242,a842)),x100242),f18(x100242,a842,a842)),f317(f317(f8(f858(x100242,a842),f858(x100242,f858(a842,a842)),x100242),f317(f8(a842,f858(a842,a842),x100242),a315)),f317(f317(f7(x100242,f858(x100242,x100242),f858(x100242,a842)),f317(f317(f8(f858(x100242,a842),f858(f858(x100242,x100242),f858(x100242,a842)),x100242),f8(x100242,a842,x100242)),a314)),f317(f89(x100242),x100243))))),f317(f317(f7(x100242,f858(x100242,a842),a842),f319(x100242)),x100241))))),f317(f317(f89(x100242),x100243),f14(x100242,x100241))) % 168.22/168.06 [10025]~P72(x100252)+E(x100251,f188(f858(x100252,a842)))+~P22(f317(f71(x100252),x100251))+E(f15(x100252,f317(f230(x100252),f317(f317(f8(f858(x100252,a842),a842,x100252),f96(x100252)),f317(f317(f7(x100252,f858(x100252,a842),f858(x100252,a842)),f317(f317(f8(f858(x100252,f858(a842,a842)),f858(f858(x100252,a842),f858(x100252,a842)),x100252),f18(x100252,a842,a842)),f317(f317(f8(f858(x100252,a842),f858(x100252,f858(a842,a842)),x100252),f317(f8(a842,f858(a842,a842),x100252),a315)),f317(f317(f7(x100252,f858(x100252,x100252),f858(x100252,a842)),f317(f317(f8(f858(x100252,a842),f858(f858(x100252,x100252),f858(x100252,a842)),x100252),f8(x100252,a842,x100252)),a314)),f317(f89(x100252),x100253))))),f317(f317(f7(x100252,f858(x100252,a842),a842),f319(x100252)),x100251))))),f317(f317(f89(x100252),x100253),f15(x100252,x100251))) % 168.22/168.06 [10026]~P96(x100262)+E(x100261,f188(f858(x100262,a842)))+~P22(f317(f71(x100262),x100261))+E(f11(x100262,f317(f230(x100262),f317(f317(f8(f858(x100262,a842),a842,x100262),f96(x100262)),f317(f317(f7(x100262,f858(x100262,a842),f858(x100262,a842)),f317(f317(f8(f858(x100262,f858(a842,a842)),f858(f858(x100262,a842),f858(x100262,a842)),x100262),f18(x100262,a842,a842)),f317(f317(f8(f858(x100262,a842),f858(x100262,f858(a842,a842)),x100262),f317(f8(a842,f858(a842,a842),x100262),a315)),f317(f317(f7(x100262,f858(x100262,x100262),f858(x100262,a842)),f317(f317(f8(f858(x100262,a842),f858(f858(x100262,x100262),f858(x100262,a842)),x100262),f8(x100262,a842,x100262)),a314)),f317(f122(x100262),x100263))))),f317(f317(f7(x100262,f858(x100262,a842),a842),f319(x100262)),x100261))))),f317(f317(f122(x100262),x100263),f11(x100262,x100261))) % 168.22/168.06 [10027]~P96(x100272)+E(x100271,f188(f858(x100272,a842)))+~P22(f317(f71(x100272),x100271))+E(f10(x100272,f317(f230(x100272),f317(f317(f8(f858(x100272,a842),a842,x100272),f96(x100272)),f317(f317(f7(x100272,f858(x100272,a842),f858(x100272,a842)),f317(f317(f8(f858(x100272,f858(a842,a842)),f858(f858(x100272,a842),f858(x100272,a842)),x100272),f18(x100272,a842,a842)),f317(f317(f8(f858(x100272,a842),f858(x100272,f858(a842,a842)),x100272),f317(f8(a842,f858(a842,a842),x100272),a315)),f317(f317(f7(x100272,f858(x100272,x100272),f858(x100272,a842)),f317(f317(f8(f858(x100272,a842),f858(f858(x100272,x100272),f858(x100272,a842)),x100272),f8(x100272,a842,x100272)),a314)),f317(f113(x100272),x100273))))),f317(f317(f7(x100272,f858(x100272,a842),a842),f319(x100272)),x100271))))),f317(f317(f113(x100272),x100273),f10(x100272,x100271))) % 168.22/168.06 [10028]~P103(x100282)+E(x100281,f188(f858(x100282,a842)))+~P22(f317(f71(x100282),x100281))+E(f12(x100282,f224(x100282),f317(f230(x100282),f317(f317(f8(f858(x100282,a842),a842,x100282),f96(x100282)),f317(f317(f7(x100282,f858(x100282,a842),f858(x100282,a842)),f317(f317(f8(f858(x100282,f858(a842,a842)),f858(f858(x100282,a842),f858(x100282,a842)),x100282),f18(x100282,a842,a842)),f317(f317(f8(f858(x100282,a842),f858(x100282,f858(a842,a842)),x100282),f317(f8(a842,f858(a842,a842),x100282),a315)),f317(f317(f7(x100282,f858(x100282,x100282),f858(x100282,a842)),f317(f317(f8(f858(x100282,a842),f858(f858(x100282,x100282),f858(x100282,a842)),x100282),f8(x100282,a842,x100282)),a314)),f317(f223(x100282),x100283))))),f317(f317(f7(x100282,f858(x100282,a842),a842),f319(x100282)),x100281))))),f317(f317(f223(x100282),x100283),f12(x100282,f224(x100282),x100281))) % 168.22/168.06 [10029]~P103(x100292)+E(x100291,f188(f858(x100292,a842)))+~P22(f317(f71(x100292),x100291))+E(f13(x100292,f223(x100292),f317(f230(x100292),f317(f317(f8(f858(x100292,a842),a842,x100292),f96(x100292)),f317(f317(f7(x100292,f858(x100292,a842),f858(x100292,a842)),f317(f317(f8(f858(x100292,f858(a842,a842)),f858(f858(x100292,a842),f858(x100292,a842)),x100292),f18(x100292,a842,a842)),f317(f317(f8(f858(x100292,a842),f858(x100292,f858(a842,a842)),x100292),f317(f8(a842,f858(a842,a842),x100292),a315)),f317(f317(f7(x100292,f858(x100292,x100292),f858(x100292,a842)),f317(f317(f8(f858(x100292,a842),f858(f858(x100292,x100292),f858(x100292,a842)),x100292),f8(x100292,a842,x100292)),a314)),f317(f224(x100292),x100293))))),f317(f317(f7(x100292,f858(x100292,a842),a842),f319(x100292)),x100291))))),f317(f317(f224(x100292),x100293),f13(x100292,f223(x100292),x100291))) % 168.22/168.06 [9777]~P113(x97771)+~E(x97773,f2(x97771))+~E(x97772,f2(x97771))+E(f317(f317(f89(x97771),f317(f317(f238(x97771),x97772),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x97771),x97773),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f2(x97771)) % 168.22/168.06 [9923]~P112(x99231)+~P22(f317(f317(f225(x99231),f2(x99231)),x99233))+P22(f317(f317(f225(x99231),x99232),x99233))+~P22(f317(f317(f225(x99231),f317(f317(f238(x99231),x99232),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x99231),x99233),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))))) % 168.22/168.06 [9968]~P113(x99682)+~E(x99681,f2(x99682))+~E(x99683,f2(x99682))+~P22(f317(f317(f226(x99682),f2(x99682)),f317(f317(f89(x99682),f317(f317(f238(x99682),x99683),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))),f317(f317(f238(x99682),x99681),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))))) % 168.22/168.06 [9163]E(x91631,x91632)+~E(f603(x91631,x91632,x91634,x91633),f604(x91631,x91632,x91634,x91633))+P22(f317(f317(f319(f857(f850(x91633),f850(x91633))),f317(f317(f237(f850(x91633),f850(x91633)),x91632),x91631)),f141(x91633,x91634)))+P22(f317(f317(f319(f857(f850(x91633),f850(x91633))),f317(f317(f237(f850(x91633),f850(x91633)),x91631),x91632)),f141(x91633,x91634))) % 168.22/168.06 [4790]~P58(x47902)+~E(x47904,f2(x47902))+~E(x47901,f2(x47902))+E(x47901,f317(f317(f266(x47902),x47903),x47904)) % 168.22/168.06 [4791]~P58(x47911)+~E(x47913,f2(x47911))+~E(x47914,f2(x47911))+E(f317(f317(f266(x47911),x47912),x47913),x47914) % 168.22/168.06 [4901]~P58(x49012)+E(x49011,f2(x49012))+~E(x49013,f2(x49012))+~E(x49011,f317(f317(f266(x49012),x49014),x49013)) % 168.22/168.06 [4902]~P58(x49022)+E(x49021,f2(x49022))+~E(x49023,f2(x49022))+~E(f317(f317(f266(x49022),x49024),x49023),x49021) % 168.22/168.06 [5073]~P115(x50732)+E(x50731,f2(x50732))+~E(f317(f317(f266(x50732),x50733),x50731),x50734)+E(x50733,f317(f317(f90(x50732),x50734),x50731)) % 168.22/168.06 [5075]~P115(x50752)+E(x50751,f2(x50752))+~E(f317(f317(f90(x50752),x50753),x50751),x50754)+E(x50753,f317(f317(f266(x50752),x50754),x50751)) % 168.22/168.06 [5076]~P58(x50762)+E(x50761,f2(x50762))+~E(f317(f317(f266(x50762),x50763),x50761),x50764)+E(x50763,f317(f317(f90(x50762),x50764),x50761)) % 168.22/168.06 [5077]~P58(x50772)+E(x50771,f2(x50772))+~E(f317(f317(f90(x50772),x50773),x50771),x50774)+E(x50773,f317(f317(f266(x50772),x50774),x50771)) % 168.22/168.06 [5078]~P115(x50782)+E(x50781,f2(x50782))+~E(x50783,f317(f317(f266(x50782),x50784),x50781))+E(f317(f317(f90(x50782),x50783),x50781),x50784) % 168.22/168.06 [5080]~P115(x50802)+E(x50801,f2(x50802))+~E(x50803,f317(f317(f90(x50802),x50804),x50801))+E(f317(f317(f266(x50802),x50803),x50801),x50804) % 168.22/168.06 [5081]~P58(x50812)+E(x50811,f2(x50812))+~E(x50813,f317(f317(f266(x50812),x50814),x50811))+E(f317(f317(f90(x50812),x50813),x50811),x50814) % 168.22/168.06 [5082]~P58(x50822)+E(x50821,f2(x50822))+~E(x50823,f317(f317(f90(x50822),x50824),x50821))+E(f317(f317(f266(x50822),x50823),x50821),x50824) % 168.22/168.06 [5115]~P58(x51152)+~E(x51151,f2(x51152))+~E(f317(f317(f90(x51152),x51151),x51154),x51153)+E(x51151,f317(f317(f266(x51152),x51153),x51154)) % 168.22/168.06 [5116]~P58(x51161)+~E(x51164,f2(x51161))+~E(x51162,f317(f317(f90(x51161),x51164),x51163))+E(f317(f317(f266(x51161),x51162),x51163),x51164) % 168.22/168.06 [5187]~E(x51873,x51874)+~E(x51872,x51873)+~P104(x51871)+E(f279(x51871,x51872,x51873),f317(f317(f286(x51871),x51874),f188(f858(x51871,a842)))) % 168.22/168.06 [5385]~E(f126(x53852,x53851),x53853)+~E(f138(x53852,x53851),x53854)+E(x53851,f125(x53852))+E(f317(f317(f127(x53852),x53853),f317(f317(f145(x53852),x53854),f125(x53852))),x53851) % 168.22/168.06 [5987]~P112(x59873)+E(x59871,x59872)+~E(f317(f317(f238(x59873),x59874),x59871),f317(f317(f238(x59873),x59874),x59872))+~P22(f317(f317(f226(x59873),f87(x59873)),x59874)) % 168.22/168.06 [5988]E(x59881,x59882)+~E(f317(f317(f286(x59883),x59884),x59881),f317(f317(f286(x59883),x59884),x59882))+P22(f317(f317(f319(x59883),x59884),x59882))+P22(f317(f317(f319(x59883),x59884),x59881)) % 168.22/168.06 [6024]E(f317(x60241,x60242),f2(a849))+~E(f317(f317(f6(x60243,a849),x60241),x60244),f2(a849))+~P22(f317(f71(x60243),x60244))+~P22(f317(f317(f319(x60243),x60242),x60244)) % 168.22/168.06 [6025]E(f317(x60251,x60252),f87(a849))+~E(f317(f317(f9(x60253,a849),x60251),x60254),f87(a849))+~P22(f317(f71(x60253),x60254))+~P22(f317(f317(f319(x60253),x60252),x60254)) % 168.22/168.06 [6238]~P104(x62381)+~P22(f317(f317(f225(x62381),x62384),x62383))+P22(f317(f317(f225(x62381),x62382),x62383))+~P22(f317(f317(f225(x62381),x62382),x62384)) % 168.22/168.06 [6239]~P101(x62391)+~P22(f317(f317(f225(x62391),x62392),x62394))+P22(f317(f317(f225(x62391),x62392),x62393))+~P22(f317(f317(f225(x62391),x62394),x62393)) % 168.22/168.06 [6240]~P104(x62401)+~P22(f317(f317(f226(x62401),x62404),x62403))+P22(f317(f317(f226(x62401),x62402),x62403))+~P22(f317(f317(f225(x62401),x62402),x62404)) % 168.22/168.06 [6241]~P104(x62411)+~P22(f317(f317(f226(x62411),x62412),x62414))+P22(f317(f317(f226(x62411),x62412),x62413))+~P22(f317(f317(f225(x62411),x62414),x62413)) % 168.22/168.06 [6242]~P104(x62421)+~P22(f317(f317(f226(x62421),x62424),x62423))+P22(f317(f317(f226(x62421),x62422),x62423))+~P22(f317(f317(f226(x62421),x62422),x62424)) % 168.22/168.06 [6243]~P101(x62431)+~P22(f317(f317(f226(x62431),x62432),x62434))+P22(f317(f317(f226(x62431),x62432),x62433))+~P22(f317(f317(f225(x62431),x62434),x62433)) % 168.22/168.06 [6244]~P101(x62441)+~P22(f317(f317(f226(x62441),x62444),x62443))+P22(f317(f317(f226(x62441),x62442),x62443))+~P22(f317(f317(f225(x62441),x62442),x62444)) % 168.22/168.06 [6245]~P101(x62451)+~P22(f317(f317(f226(x62451),x62452),x62454))+P22(f317(f317(f226(x62451),x62452),x62453))+~P22(f317(f317(f226(x62451),x62454),x62453)) % 168.22/168.06 [6472]~P27(x64721)+~P22(f317(f317(f225(x64721),x64722),f50(x64721,x64724)))+P22(f317(f317(f225(x64721),x64722),x64723))+~P22(f317(f317(f319(x64721),x64723),x64724)) % 168.22/168.06 [6612]~P103(x66121)+~P29(x66121,f317(f317(f145(x66121),x66122),x66124))+~P22(f317(f317(f319(x66121),x66123),f317(f166(x66121),x66124)))+P22(f317(f317(f225(x66121),x66122),x66123)) % 168.22/168.06 [6699]~P27(x66991)+~P22(f317(f317(f225(x66991),f49(x66991,x66994)),x66993))+P22(f317(f317(f225(x66991),x66992),x66993))+~P22(f317(f317(f319(x66991),x66992),x66994)) % 168.22/168.06 [7108]~P103(x71081)+E(f317(f317(f122(f858(x71081,a842)),f317(f278(x71081,x71082),x71083)),f317(f278(x71081,x71083),x71084)),f317(f278(x71081,x71082),x71084))+~P22(f317(f317(f225(x71081),x71083),x71084))+~P22(f317(f317(f225(x71081),x71082),x71083)) % 168.22/168.06 [7211]~P103(x72111)+E(f317(f317(f122(f858(x72111,a842)),f317(f278(x72111,x72112),x72113)),f279(x72111,x72113,x72114)),f279(x72111,x72112,x72114))+~P22(f317(f317(f225(x72111),x72113),x72114))+~P22(f317(f317(f225(x72111),x72112),x72113)) % 168.22/168.06 [7276]~P103(x72761)+E(f317(f317(f122(f858(x72761,a842)),f282(x72761,x72762,x72763)),f317(f278(x72761,x72763),x72764)),f282(x72761,x72762,x72764))+~P22(f317(f317(f225(x72761),x72763),x72764))+~P22(f317(f317(f226(x72761),x72762),x72763)) % 168.22/168.06 [7298]~P103(x72981)+E(f317(f317(f122(f858(x72981,a842)),f279(x72981,x72982,x72983)),f282(x72981,x72983,x72984)),f317(f278(x72981,x72982),x72984))+~P22(f317(f317(f225(x72981),x72982),x72983))+~P22(f317(f317(f226(x72981),x72983),x72984)) % 168.22/168.06 [7328]~P103(x73281)+E(f317(f317(f122(f858(x73281,a842)),f282(x73281,x73282,x73283)),f279(x73281,x73283,x73284)),f281(x73281,x73282,x73284))+~P22(f317(f317(f225(x73281),x73283),x73284))+~P22(f317(f317(f226(x73281),x73282),x73283)) % 168.22/168.06 [7329]~P103(x73291)+E(f317(f317(f122(f858(x73291,a842)),f281(x73291,x73292,x73293)),f282(x73291,x73293,x73294)),f282(x73291,x73292,x73294))+~P22(f317(f317(f225(x73291),x73292),x73293))+~P22(f317(f317(f226(x73291),x73293),x73294)) % 168.22/168.06 [7330]~P103(x73301)+E(f317(f317(f122(f858(x73301,a842)),f281(x73301,x73302,x73303)),f281(x73301,x73303,x73304)),f281(x73301,x73302,x73304))+~P22(f317(f317(f225(x73301),x73303),x73304))+~P22(f317(f317(f225(x73301),x73302),x73303)) % 168.22/168.06 [7331]~P103(x73311)+E(f317(f317(f122(f858(x73311,a842)),f279(x73311,x73312,x73313)),f281(x73311,x73313,x73314)),f279(x73311,x73312,x73314))+~P22(f317(f317(f225(x73311),x73313),x73314))+~P22(f317(f317(f225(x73311),x73312),x73313)) % 168.22/168.06 [8118]P19(x81181,x81182,f366(x81183,x81182,x81184,x81181),x81184)+~P22(f317(f71(x81182),x81183))+~P22(f317(f71(x81181),x81184))+~P22(f317(f317(f225(a849),f317(f54(x81181),x81184)),f317(f54(x81182),x81183))) % 168.22/168.06 [8191]~P70(x81911)+~E(f317(x81913,f732(x81913,x81914,x81912,x81911)),f87(x81911))+E(f317(f317(f317(f75(x81911,x81912,f90(x81911)),x81913),f87(x81911)),x81914),f87(x81911))+~P22(f317(f71(x81912),x81914)) % 168.22/168.06 [8477]~P112(x84771)+~P22(f317(f317(f225(x84771),f2(x84771)),x84773))+P22(f317(f317(f225(x84771),x84772),x84773))+~P22(f317(f317(f225(x84771),f317(f317(f238(x84771),x84772),f317(a124,x84774))),f317(f317(f238(x84771),x84773),f317(a124,x84774)))) % 168.22/168.06 [8844]~P70(x88441)+E(f317(f317(f317(f75(x88441,x88442,f90(x88441)),x88443),f87(x88441)),x88444),f87(x88441))+~P22(f317(f71(x88442),x88444))+P22(f317(f317(f319(x88442),f732(x88443,x88444,x88442,x88441)),x88444)) % 168.22/168.06 [9325]~P22(f317(f317(f225(a1),x93254),f2(a1)))+P22(f317(f317(f225(a1),f317(f317(f89(a1),f317(f317(f90(a1),x93251),f55(a1,x93252,x93253))),x93254)),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x93253))+~P22(f317(f317(f226(a1),x93251),x93254)) % 168.22/168.06 [9766]~P22(f317(f71(x97661),x97662))+~P22(f317(f317(f319(x97661),x97664),x97662))+~P22(f317(f317(f319(x97661),x97663),x97662))+P22(f317(f317(f226(a849),f317(f54(x97661),f317(f317(f21(f858(x97661,a842)),f317(f317(f21(f858(x97661,a842)),x97662),f317(f317(f286(x97661),x97663),f188(f858(x97661,a842))))),f317(f317(f286(x97661),x97664),f188(f858(x97661,a842)))))),f317(f54(x97661),x97662))) % 168.22/168.06 [6810]~P98(x68101)+~P22(f317(f317(f225(x68101),x68102),x68104))+~P22(f317(f317(f225(x68101),x68102),x68103))+P22(f317(f317(f225(x68101),x68102),f317(f317(f113(x68101),x68103),x68104))) % 168.22/168.06 [6813]~P103(x68131)+~P22(f317(f317(f225(x68131),x68132),x68134))+~P22(f317(f317(f225(x68131),x68132),x68133))+P22(f317(f317(f225(x68131),x68132),f317(f317(f223(x68131),x68133),x68134))) % 168.22/168.06 [6814]~P103(x68141)+~P22(f317(f317(f226(x68141),x68142),x68144))+~P22(f317(f317(f226(x68141),x68142),x68143))+P22(f317(f317(f226(x68141),x68142),f317(f317(f223(x68141),x68143),x68144))) % 168.22/168.06 [6836]~P59(x68362)+E(x68361,f2(x68362))+E(f317(f317(f266(x68362),f317(f317(f238(x68362),x68361),x68363)),f317(f317(f238(x68362),x68361),x68364)),f317(f317(f238(x68362),x68361),f317(f317(f21(a849),x68363),x68364)))+~P22(f317(f317(f225(a849),x68364),x68363)) % 168.22/168.06 [6882]~P103(x68821)+~P29(x68821,f317(f317(f145(x68821),x68823),x68824))+P29(x68821,f317(f317(f145(x68821),x68822),f317(f317(f145(x68821),x68823),x68824)))+~P22(f317(f317(f225(x68821),x68822),x68823)) % 168.22/168.06 [6926]~P80(x69261)+~P22(f317(f317(f225(x69261),f2(x69261)),x69264))+~P22(f317(f317(f225(x69261),x69262),x69263))+P22(f317(f317(f225(x69261),x69262),f317(f317(f89(x69261),x69263),x69264))) % 168.22/168.06 [6927]~P80(x69271)+~P22(f317(f317(f225(x69271),f2(x69271)),x69273))+~P22(f317(f317(f225(x69271),x69272),x69274))+P22(f317(f317(f225(x69271),x69272),f317(f317(f89(x69271),x69273),x69274))) % 168.22/168.06 [6928]~P80(x69281)+~P22(f317(f317(f225(x69281),x69282),x69284))+~P22(f317(f317(f226(x69281),f2(x69281)),x69283))+P22(f317(f317(f226(x69281),x69282),f317(f317(f89(x69281),x69283),x69284))) % 168.22/168.06 [6929]~P80(x69291)+~P22(f317(f317(f225(x69291),f2(x69291)),x69293))+~P22(f317(f317(f226(x69291),x69292),x69294))+P22(f317(f317(f226(x69291),x69292),f317(f317(f89(x69291),x69293),x69294))) % 168.22/168.06 [6930]~P112(x69301)+~P22(f317(f317(f226(x69301),f2(x69301)),x69303))+~P22(f317(f317(f226(x69301),x69302),x69304))+P22(f317(f317(f226(x69301),x69302),f317(f317(f89(x69301),x69303),x69304))) % 168.22/168.06 [6967]~P103(x69671)+P22(f317(f317(f225(x69671),x69672),x69673))+P22(f317(f317(f225(x69671),x69672),x69674))+~P22(f317(f317(f225(x69671),x69672),f317(f317(f224(x69671),x69674),x69673))) % 168.22/168.06 [6968]~P103(x69681)+P22(f317(f317(f226(x69681),x69682),x69683))+P22(f317(f317(f226(x69681),x69682),x69684))+~P22(f317(f317(f226(x69681),x69682),f317(f317(f224(x69681),x69684),x69683))) % 168.22/168.06 [7251]~P104(x72512)+~P57(x72511)+~P22(f317(f317(f226(f858(x72511,x72512)),x72513),x72514))+P22(f317(f317(f225(f858(x72511,x72512)),x72513),x72514)) % 168.22/168.06 [7615]~P61(x76151)+~P22(f317(f317(f226(x76151),x76154),f2(x76151)))+~P22(f317(f317(f225(x76151),x76153),f317(f317(f266(x76151),x76152),x76154)))+P22(f317(f317(f225(x76151),x76152),f317(f317(f90(x76151),x76153),x76154))) % 168.22/168.06 [7616]~P61(x76161)+~P22(f317(f317(f226(x76161),x76164),f2(x76161)))+~P22(f317(f317(f225(x76161),x76163),f317(f317(f90(x76161),x76162),x76164)))+P22(f317(f317(f225(x76161),x76162),f317(f317(f266(x76161),x76163),x76164))) % 168.22/168.06 [7617]~P61(x76171)+~P22(f317(f317(f226(x76171),x76174),f2(x76171)))+~P22(f317(f317(f226(x76171),x76173),f317(f317(f266(x76171),x76172),x76174)))+P22(f317(f317(f226(x76171),x76172),f317(f317(f90(x76171),x76173),x76174))) % 168.22/168.06 [7618]~P61(x76181)+~P22(f317(f317(f226(x76181),x76184),f2(x76181)))+~P22(f317(f317(f226(x76181),x76183),f317(f317(f90(x76181),x76182),x76184)))+P22(f317(f317(f226(x76181),x76182),f317(f317(f266(x76181),x76183),x76184))) % 168.22/168.06 [7727]~P128(x77271)+~P22(f317(f317(f225(x77271),x77272),f2(x77271)))+~P22(f317(f317(f225(x77271),x77274),x77273))+P22(f317(f317(f225(x77271),f317(f317(f90(x77271),x77272),x77273)),f317(f317(f90(x77271),x77272),x77274))) % 168.22/168.06 [7728]~P118(x77281)+~P22(f317(f317(f226(x77281),x77282),f2(x77281)))+~P22(f317(f317(f225(x77281),x77284),x77283))+P22(f317(f317(f225(x77281),f317(f317(f90(x77281),x77282),x77283)),f317(f317(f90(x77281),x77282),x77284))) % 168.22/168.06 [7729]~P128(x77291)+~P22(f317(f317(f225(x77291),x77293),f2(x77291)))+~P22(f317(f317(f225(x77291),x77294),x77292))+P22(f317(f317(f225(x77291),f317(f317(f90(x77291),x77292),x77293)),f317(f317(f90(x77291),x77294),x77293))) % 168.22/168.06 [7730]~P60(x77301)+~P22(f317(f317(f225(x77301),x77303),f2(x77301)))+~P22(f317(f317(f225(x77301),x77304),x77302))+P22(f317(f317(f225(x77301),f317(f317(f266(x77301),x77302),x77303)),f317(f317(f266(x77301),x77304),x77303))) % 168.22/168.06 [7734]~P118(x77341)+~P22(f317(f317(f226(x77341),x77343),f2(x77341)))+~P22(f317(f317(f226(x77341),x77344),x77342))+P22(f317(f317(f226(x77341),f317(f317(f90(x77341),x77342),x77343)),f317(f317(f90(x77341),x77344),x77343))) % 168.22/168.06 [7735]~P118(x77351)+~P22(f317(f317(f226(x77351),x77352),f2(x77351)))+~P22(f317(f317(f226(x77351),x77354),x77353))+P22(f317(f317(f226(x77351),f317(f317(f90(x77351),x77352),x77353)),f317(f317(f90(x77351),x77352),x77354))) % 168.22/168.06 [7736]~P61(x77361)+~P22(f317(f317(f226(x77361),x77363),f2(x77361)))+~P22(f317(f317(f226(x77361),x77364),x77362))+P22(f317(f317(f226(x77361),f317(f317(f266(x77361),x77362),x77363)),f317(f317(f266(x77361),x77364),x77363))) % 168.22/168.06 [7737]~P112(x77371)+~P22(f317(f317(f226(x77371),f87(x77371)),x77372))+~P22(f317(f317(f225(a849),x77373),x77374))+P22(f317(f317(f225(x77371),f317(f317(f238(x77371),x77372),x77373)),f317(f317(f238(x77371),x77372),x77374))) % 168.22/168.06 [7738]~P112(x77381)+~P22(f317(f317(f225(x77381),f87(x77381)),x77382))+~P22(f317(f317(f225(a849),x77383),x77384))+P22(f317(f317(f225(x77381),f317(f317(f238(x77381),x77382),x77383)),f317(f317(f238(x77381),x77382),x77384))) % 168.22/168.06 [7740]~P112(x77401)+~P22(f317(f317(f226(x77401),f87(x77401)),x77402))+~P22(f317(f317(f226(a849),x77403),x77404))+P22(f317(f317(f226(x77401),f317(f317(f238(x77401),x77402),x77403)),f317(f317(f238(x77401),x77402),x77404))) % 168.22/168.06 [7765]P22(f317(f317(f226(a849),f2(a849)),f317(x77651,x77652)))+~P22(f317(f71(x77653),x77654))+~P22(f317(f317(f319(x77653),x77652),x77654))+~P22(f317(f317(f226(a849),f2(a849)),f317(f317(f9(x77653,a849),x77651),x77654))) % 168.22/168.06 [7773]~P130(x77731)+~P22(f317(f317(f225(x77731),x77733),x77734))+~P22(f317(f317(f225(x77731),f2(x77731)),x77732))+P22(f317(f317(f225(x77731),f317(f317(f90(x77731),x77732),x77733)),f317(f317(f90(x77731),x77732),x77734))) % 168.22/168.06 [7774]~P129(x77741)+~P22(f317(f317(f225(x77741),x77743),x77744))+~P22(f317(f317(f225(x77741),f2(x77741)),x77742))+P22(f317(f317(f225(x77741),f317(f317(f90(x77741),x77742),x77743)),f317(f317(f90(x77741),x77742),x77744))) % 168.22/168.06 [7775]~P118(x77751)+~P22(f317(f317(f226(x77751),f2(x77751)),x77752))+~P22(f317(f317(f225(x77751),x77753),x77754))+P22(f317(f317(f225(x77751),f317(f317(f90(x77751),x77752),x77753)),f317(f317(f90(x77751),x77752),x77754))) % 168.22/168.06 [7776]~P130(x77761)+~P22(f317(f317(f225(x77761),x77762),x77764))+~P22(f317(f317(f225(x77761),f2(x77761)),x77763))+P22(f317(f317(f225(x77761),f317(f317(f90(x77761),x77762),x77763)),f317(f317(f90(x77761),x77764),x77763))) % 168.22/168.06 [7777]~P112(x77771)+~P22(f317(f317(f225(x77771),x77772),x77774))+~P22(f317(f317(f225(x77771),f2(x77771)),x77772))+P22(f317(f317(f225(x77771),f317(f317(f238(x77771),x77772),x77773)),f317(f317(f238(x77771),x77774),x77773))) % 168.22/168.06 [7778]~P60(x77781)+~P22(f317(f317(f225(x77781),x77782),x77784))+~P22(f317(f317(f225(x77781),f2(x77781)),x77783))+P22(f317(f317(f225(x77781),f317(f317(f266(x77781),x77782),x77783)),f317(f317(f266(x77781),x77784),x77783))) % 168.22/168.06 [7780]~P117(x77801)+~P22(f317(f317(f226(x77801),x77803),x77804))+~P22(f317(f317(f226(x77801),f2(x77801)),x77802))+P22(f317(f317(f226(x77801),f317(f317(f90(x77801),x77802),x77803)),f317(f317(f90(x77801),x77802),x77804))) % 168.22/168.06 [7781]~P124(x77811)+~P22(f317(f317(f226(x77811),x77813),x77814))+~P22(f317(f317(f226(x77811),f2(x77811)),x77812))+P22(f317(f317(f226(x77811),f317(f317(f90(x77811),x77812),x77813)),f317(f317(f90(x77811),x77812),x77814))) % 168.22/168.06 [7782]~P118(x77821)+~P22(f317(f317(f226(x77821),x77822),x77824))+~P22(f317(f317(f226(x77821),f2(x77821)),x77823))+P22(f317(f317(f226(x77821),f317(f317(f90(x77821),x77822),x77823)),f317(f317(f90(x77821),x77824),x77823))) % 168.22/168.06 [7783]~P124(x77831)+~P22(f317(f317(f226(x77831),x77832),x77834))+~P22(f317(f317(f226(x77831),f2(x77831)),x77833))+P22(f317(f317(f226(x77831),f317(f317(f90(x77831),x77832),x77833)),f317(f317(f90(x77831),x77834),x77833))) % 168.22/168.06 [7784]~P118(x77841)+~P22(f317(f317(f226(x77841),x77843),x77844))+~P22(f317(f317(f226(x77841),f2(x77841)),x77842))+P22(f317(f317(f226(x77841),f317(f317(f90(x77841),x77842),x77843)),f317(f317(f90(x77841),x77842),x77844))) % 168.22/168.06 [7785]~P61(x77851)+~P22(f317(f317(f226(x77851),x77852),x77854))+~P22(f317(f317(f226(x77851),f2(x77851)),x77853))+P22(f317(f317(f226(x77851),f317(f317(f266(x77851),x77852),x77853)),f317(f317(f266(x77851),x77854),x77853))) % 168.22/168.06 [7822]~P102(x78222)+P22(f317(f317(f226(f858(x78221,x78222)),x78224),x78223))+~P22(f317(f317(f225(f858(x78221,x78222)),x78224),x78223))+P22(f317(f317(f225(f858(x78221,x78222)),x78223),x78224)) % 168.22/168.06 [7862]P22(f317(f317(f319(x78621),x78622),x78623))+P22(f317(f317(f319(x78621),x78622),x78624))+~P22(f317(f317(f225(f858(x78621,a842)),x78624),x78623))+P22(f317(f317(f226(f858(x78621,a842)),x78624),f317(f317(f286(x78621),x78622),x78623))) % 168.22/168.06 [8023]P22(f317(f317(f319(x80231),x80232),x80233))+P22(f317(f317(f319(x80231),x80232),x80234))+~P22(f317(f317(f226(f858(x80231,a842)),x80234),f317(f317(f286(x80231),x80232),x80233)))+P22(f317(f317(f225(f858(x80231,a842)),x80234),x80233)) % 168.22/168.06 [8032]~P57(x80321)+P7(x80321,x80322,x80323)+~P22(f317(x80322,x80324))+~P22(f317(f317(f319(f850(x80321)),x80324),f317(f166(f850(x80321)),f64(x80321,x80323,f65(x80321))))) % 168.22/168.06 [8042]~P8(x80423,x80421,x80424)+~P57(x80423)+P22(f317(x80421,x80422))+~P22(f317(f317(f319(f850(x80423)),x80422),f317(f166(f850(x80423)),f64(x80423,x80424,f65(x80423))))) % 168.22/168.06 [8095]~P118(x80951)+P22(f317(f317(f226(x80951),x80953),x80952))+P22(f317(f317(f226(x80951),x80952),x80953))+~P22(f317(f317(f226(x80951),f317(f317(f90(x80951),x80954),x80952)),f317(f317(f90(x80951),x80954),x80953))) % 168.22/168.06 [8096]~P118(x80961)+P22(f317(f317(f226(x80961),x80963),x80962))+P22(f317(f317(f226(x80961),x80962),x80963))+~P22(f317(f317(f226(x80961),f317(f317(f90(x80961),x80962),x80964)),f317(f317(f90(x80961),x80963),x80964))) % 168.22/168.06 [8107]~P118(x81071)+P22(f317(f317(f226(x81071),x81074),f2(x81071)))+P22(f317(f317(f226(x81071),x81072),x81073))+~P22(f317(f317(f226(x81071),f317(f317(f90(x81071),x81072),x81074)),f317(f317(f90(x81071),x81073),x81074))) % 168.22/168.06 [8108]~P118(x81081)+P22(f317(f317(f226(x81081),x81084),f2(x81081)))+P22(f317(f317(f226(x81081),x81082),x81083))+~P22(f317(f317(f226(x81081),f317(f317(f90(x81081),x81084),x81082)),f317(f317(f90(x81081),x81084),x81083))) % 168.22/168.06 [8112]~P118(x81121)+P22(f317(f317(f226(x81121),x81122),x81123))+P22(f317(f317(f226(x81121),f2(x81121)),x81124))+~P22(f317(f317(f226(x81121),f317(f317(f90(x81121),x81124),x81123)),f317(f317(f90(x81121),x81124),x81122))) % 168.22/168.06 [8113]~P118(x81131)+P22(f317(f317(f226(x81131),x81132),x81133))+P22(f317(f317(f226(x81131),f2(x81131)),x81134))+~P22(f317(f317(f226(x81131),f317(f317(f90(x81131),x81133),x81134)),f317(f317(f90(x81131),x81132),x81134))) % 168.22/168.06 [8126]~P118(x81261)+P22(f317(f317(f226(x81261),x81262),f2(x81261)))+P22(f317(f317(f226(x81261),f2(x81261)),x81262))+~P22(f317(f317(f226(x81261),f317(f317(f90(x81261),x81263),x81262)),f317(f317(f90(x81261),x81264),x81262))) % 168.22/168.06 [8127]~P118(x81271)+P22(f317(f317(f226(x81271),x81272),f2(x81271)))+P22(f317(f317(f226(x81271),f2(x81271)),x81272))+~P22(f317(f317(f226(x81271),f317(f317(f90(x81271),x81272),x81273)),f317(f317(f90(x81271),x81272),x81274))) % 168.22/168.06 [8154]~P118(x81541)+~P22(f317(f317(f226(x81541),x81544),f2(x81541)))+P22(f317(f317(f225(x81541),x81542),x81543))+~P22(f317(f317(f225(x81541),f317(f317(f90(x81541),x81544),x81543)),f317(f317(f90(x81541),x81544),x81542))) % 168.22/168.06 [8155]~P118(x81551)+~P22(f317(f317(f226(x81551),x81554),f2(x81551)))+P22(f317(f317(f226(x81551),x81552),x81553))+~P22(f317(f317(f226(x81551),f317(f317(f90(x81551),x81554),x81553)),f317(f317(f90(x81551),x81554),x81552))) % 168.22/168.06 [8167]~P112(x81673)+~P22(f317(f317(f226(x81673),f87(x81673)),x81674))+P22(f317(f317(f225(a849),x81671),x81672))+~P22(f317(f317(f225(x81673),f317(f317(f238(x81673),x81674),x81671)),f317(f317(f238(x81673),x81674),x81672))) % 168.22/168.06 [8169]~P112(x81693)+~P22(f317(f317(f226(x81693),f87(x81693)),x81694))+P22(f317(f317(f226(a849),x81691),x81692))+~P22(f317(f317(f226(x81693),f317(f317(f238(x81693),x81694),x81691)),f317(f317(f238(x81693),x81694),x81692))) % 168.22/168.06 [8179]~P118(x81791)+P22(f317(f317(f225(x81791),x81792),x81793))+~P22(f317(f317(f226(x81791),f2(x81791)),x81794))+~P22(f317(f317(f225(x81791),f317(f317(f90(x81791),x81794),x81792)),f317(f317(f90(x81791),x81794),x81793))) % 168.22/168.06 [8180]~P124(x81801)+P22(f317(f317(f225(x81801),x81802),x81803))+~P22(f317(f317(f226(x81801),f2(x81801)),x81804))+~P22(f317(f317(f225(x81801),f317(f317(f90(x81801),x81804),x81802)),f317(f317(f90(x81801),x81804),x81803))) % 168.22/168.06 [8181]~P124(x81811)+P22(f317(f317(f225(x81811),x81812),x81813))+~P22(f317(f317(f226(x81811),f2(x81811)),x81814))+~P22(f317(f317(f225(x81811),f317(f317(f90(x81811),x81812),x81814)),f317(f317(f90(x81811),x81813),x81814))) % 168.22/168.06 [8182]~P118(x81821)+P22(f317(f317(f226(x81821),x81822),x81823))+~P22(f317(f317(f226(x81821),f2(x81821)),x81824))+~P22(f317(f317(f226(x81821),f317(f317(f90(x81821),x81824),x81822)),f317(f317(f90(x81821),x81824),x81823))) % 168.22/168.06 [8183]~P124(x81831)+P22(f317(f317(f226(x81831),x81832),x81833))+~P22(f317(f317(f225(x81831),f2(x81831)),x81834))+~P22(f317(f317(f226(x81831),f317(f317(f90(x81831),x81834),x81832)),f317(f317(f90(x81831),x81834),x81833))) % 168.22/168.06 [8184]~P121(x81841)+P22(f317(f317(f226(x81841),x81842),x81843))+~P22(f317(f317(f225(x81841),f2(x81841)),x81844))+~P22(f317(f317(f226(x81841),f317(f317(f90(x81841),x81844),x81842)),f317(f317(f90(x81841),x81844),x81843))) % 168.22/168.06 [8185]~P112(x81851)+~P22(f317(f317(f225(x81851),f2(x81851)),x81853))+P22(f317(f317(f226(x81851),x81852),x81853))+~P22(f317(f317(f226(x81851),f317(f317(f238(x81851),x81852),x81854)),f317(f317(f238(x81851),x81853),x81854))) % 168.22/168.06 [8186]~P124(x81861)+P22(f317(f317(f226(x81861),x81862),x81863))+~P22(f317(f317(f225(x81861),f2(x81861)),x81864))+~P22(f317(f317(f226(x81861),f317(f317(f90(x81861),x81862),x81864)),f317(f317(f90(x81861),x81863),x81864))) % 168.22/168.06 [8187]~P121(x81871)+P22(f317(f317(f226(x81871),x81872),x81873))+~P22(f317(f317(f225(x81871),f2(x81871)),x81874))+~P22(f317(f317(f226(x81871),f317(f317(f90(x81871),x81872),x81874)),f317(f317(f90(x81871),x81873),x81874))) % 168.22/168.06 [8233]P22(f317(f317(f319(x82331),x82332),x82333))+~P22(f317(f317(f225(f858(x82331,a842)),x82333),x82334))+~P22(f317(f317(f226(f858(x82331,a842)),x82333),x82334))+P22(f317(f317(f226(f858(x82331,a842)),x82333),f317(f317(f286(x82331),x82332),x82334))) % 168.22/168.06 [8607]E(f317(f317(f21(a1),f439(x86071,x86072,x86073,x86074)),f440(x86071,x86072,x86073,x86074)),x86074)+~P22(f317(f317(f226(a1),f2(a1)),x86073))+~P22(f317(f317(f225(a1),x86071),x86074))+P22(f317(f317(f225(a1),x86071),f317(f317(f89(a1),x86074),x86073))) % 168.22/168.06 [8608]E(f317(f317(f21(a1),f448(x86081,x86082,x86083,x86084)),f449(x86081,x86082,x86083,x86084)),x86084)+~P22(f317(f317(f226(a1),f2(a1)),x86083))+~P22(f317(f317(f226(a1),x86081),x86084))+P22(f317(f317(f226(a1),x86081),f317(f317(f89(a1),x86084),x86083))) % 168.22/168.06 [8740]~E(f317(f317(f159(x87401),x87403),f615(x87404,x87403,x87401,x87402)),f317(f317(f159(x87401),x87404),f615(x87404,x87403,x87401,x87402)))+E(f317(f317(f167(x87401),x87402),x87403),f317(f317(f167(x87401),x87402),x87404))+~P22(f317(f317(f225(a849),x87402),f317(f189(f850(x87401)),x87403)))+~P22(f317(f317(f225(a849),x87402),f317(f189(f850(x87401)),x87404))) % 168.22/168.06 [8810]~P22(f317(f317(f226(a1),f2(a1)),x88103))+~P22(f317(f317(f225(a1),x88101),x88104))+P22(f317(f317(f319(a1),f439(x88101,x88102,x88103,x88104)),x88102))+P22(f317(f317(f225(a1),x88101),f317(f317(f89(a1),x88104),x88103))) % 168.22/168.06 [8811]~P22(f317(f317(f226(a1),f2(a1)),x88113))+~P22(f317(f317(f226(a1),x88111),x88114))+P22(f317(f317(f319(a1),f448(x88111,x88112,x88113,x88114)),x88112))+P22(f317(f317(f226(a1),x88111),f317(f317(f89(a1),x88114),x88113))) % 168.22/168.06 [8853]~P98(x88531)+~P22(f317(f71(x88531),x88533))+~P22(f317(f317(f319(x88531),x88534),x88533))+P22(f317(f317(f225(x88531),f317(f317(f74(x88531,x88531,f113(x88531)),x88532),x88533)),f317(f317(f113(x88531),x88534),x88532))) % 168.22/168.06 [8854]~P103(x88541)+~P22(f317(f71(x88541),x88543))+~P22(f317(f317(f319(x88541),x88544),x88543))+P22(f317(f317(f225(x88541),f317(f317(f74(x88541,x88541,f223(x88541)),x88542),x88543)),f317(f317(f223(x88541),x88544),x88542))) % 168.22/168.06 [8903]E(f317(f317(f167(x89031),x89032),x89033),f317(f317(f167(x89031),x89032),x89034))+P22(f317(f317(f226(a849),f615(x89033,x89034,x89031,x89032)),x89032))+~P22(f317(f317(f225(a849),x89032),f317(f189(f850(x89031)),x89033)))+~P22(f317(f317(f225(a849),x89032),f317(f189(f850(x89031)),x89034))) % 168.22/168.06 [8908]~P22(f317(f317(f226(a1),f2(a1)),x89083))+~P22(f317(f317(f225(a1),x89081),x89082))+P22(f317(f317(f319(a1),f440(x89081,x89084,x89083,x89082)),f279(a1,f87(a1),x89083)))+P22(f317(f317(f225(a1),x89081),f317(f317(f89(a1),x89082),x89083))) % 168.22/168.06 [8909]~P22(f317(f317(f226(a1),f2(a1)),x89093))+~P22(f317(f317(f226(a1),x89091),x89092))+P22(f317(f317(f319(a1),f449(x89091,x89094,x89093,x89092)),f279(a1,f87(a1),x89093)))+P22(f317(f317(f226(a1),x89091),f317(f317(f89(a1),x89092),x89093))) % 168.22/168.06 [9066]~E(f317(f171(x90661,x90662),x90663),f317(f171(x90661,x90662),x90664))+E(f317(f166(f857(x90661,x90662)),x90663),f317(f166(f857(x90661,x90662)),x90664))+~P22(f317(f131(x90661),f317(f317(f148(f857(x90661,x90662),x90661),f244(x90661,x90662)),x90664)))+~P22(f317(f131(x90661),f317(f317(f148(f857(x90661,x90662),x90661),f244(x90661,x90662)),x90663))) % 168.22/168.06 [9078]E(f317(f171(x90781,x90782),x90783),f317(f171(x90781,x90782),x90784))+~E(f317(f166(f857(x90781,x90782)),x90783),f317(f166(f857(x90781,x90782)),x90784))+~P22(f317(f131(x90781),f317(f317(f148(f857(x90781,x90782),x90781),f244(x90781,x90782)),x90784)))+~P22(f317(f131(x90781),f317(f317(f148(f857(x90781,x90782),x90781),f244(x90781,x90782)),x90783))) % 168.22/168.06 [9345]~P22(f317(f317(f225(a1),f2(a1)),x93454))+~P22(f317(f317(f226(a1),f2(a1)),x93453))+~P22(f317(f317(f226(a1),x93454),x93451))+P22(f317(f317(f226(a1),f317(f317(f89(a1),f317(f317(f90(a1),x93451),f55(a1,x93452,x93453))),x93454)),f317(f317(f90(a1),x93451),x93453))) % 168.22/168.06 [9735]E(x97351,x97352)+P22(f317(f317(f319(f857(f850(x97353),f850(x97353))),f317(f317(f237(f850(x97353),f850(x97353)),x97352),x97351)),f141(x97353,x97354)))+P22(f317(f317(f319(f857(f850(x97353),f850(x97353))),f317(f317(f237(f850(x97353),f850(x97353)),x97351),x97352)),f141(x97353,x97354)))+~P22(f317(f317(f319(f857(x97353,x97353)),f317(f317(f237(x97353,x97353),f603(x97351,x97352,x97354,x97353)),f604(x97351,x97352,x97354,x97353))),x97354)) % 168.22/168.06 [9736]E(x97361,x97362)+P22(f317(f317(f319(f857(f850(x97363),f850(x97363))),f317(f317(f237(f850(x97363),f850(x97363)),x97362),x97361)),f141(x97363,x97364)))+P22(f317(f317(f319(f857(f850(x97363),f850(x97363))),f317(f317(f237(f850(x97363),f850(x97363)),x97361),x97362)),f141(x97363,x97364)))+~P22(f317(f317(f319(f857(x97363,x97363)),f317(f317(f237(x97363,x97363),f604(x97361,x97362,x97364,x97363)),f603(x97361,x97362,x97364,x97363))),x97364)) % 168.22/168.06 [7318]~P92(x73181)+~P22(f317(f317(f225(x73181),x73183),x73184))+~P22(f317(f317(f225(x73181),x73182),x73184))+P22(f317(f317(f225(x73181),f317(f317(f122(x73181),x73182),x73183)),x73184)) % 168.22/168.06 [7321]~P103(x73211)+~P22(f317(f317(f225(x73211),x73213),x73214))+~P22(f317(f317(f225(x73211),x73212),x73214))+P22(f317(f317(f225(x73211),f317(f317(f224(x73211),x73212),x73213)),x73214)) % 168.22/168.06 [7322]~P103(x73221)+~P22(f317(f317(f226(x73221),x73223),x73224))+~P22(f317(f317(f226(x73221),x73222),x73224))+P22(f317(f317(f226(x73221),f317(f317(f224(x73221),x73222),x73223)),x73224)) % 168.22/168.06 [7640]~E(x76401,x76403)+E(f133(a849,f317(f278(a849,x76401),x76402)),f317(f317(f145(a849),x76403),x76404))+~E(f133(a849,f317(f278(a849,f317(f317(f89(a849),x76401),f87(a849))),x76402)),x76404)+~P22(f317(f317(f226(a849),x76401),x76402)) % 168.22/168.06 [7651]~P103(x76511)+P22(f317(f317(f225(x76511),x76512),x76513))+P22(f317(f317(f225(x76511),x76514),x76513))+~P22(f317(f317(f225(x76511),f317(f317(f223(x76511),x76514),x76512)),x76513)) % 168.22/168.06 [7652]~P103(x76521)+P22(f317(f317(f226(x76521),x76522),x76523))+P22(f317(f317(f226(x76521),x76524),x76523))+~P22(f317(f317(f226(x76521),f317(f317(f223(x76521),x76524),x76522)),x76523)) % 168.22/168.06 [7921]~P60(x79211)+~P22(f317(f317(f226(x79211),f2(x79211)),x79213))+~P22(f317(f317(f225(x79211),x79212),f317(f317(f266(x79211),x79214),x79213)))+P22(f317(f317(f225(x79211),f317(f317(f90(x79211),x79212),x79213)),x79214)) % 168.22/168.06 [7922]~P61(x79221)+~P22(f317(f317(f226(x79221),f2(x79221)),x79223))+~P22(f317(f317(f225(x79221),x79222),f317(f317(f266(x79221),x79224),x79223)))+P22(f317(f317(f225(x79221),f317(f317(f90(x79221),x79222),x79223)),x79224)) % 168.22/168.06 [7924]~P60(x79241)+~P22(f317(f317(f226(x79241),f2(x79241)),x79243))+~P22(f317(f317(f225(x79241),x79242),f317(f317(f90(x79241),x79244),x79243)))+P22(f317(f317(f225(x79241),f317(f317(f266(x79241),x79242),x79243)),x79244)) % 168.22/168.06 [7925]~P61(x79251)+~P22(f317(f317(f226(x79251),f2(x79251)),x79253))+~P22(f317(f317(f225(x79251),x79252),f317(f317(f90(x79251),x79254),x79253)))+P22(f317(f317(f225(x79251),f317(f317(f266(x79251),x79252),x79253)),x79254)) % 168.22/168.06 [7926]~P60(x79261)+~P22(f317(f317(f226(x79261),f2(x79261)),x79263))+~P22(f317(f317(f226(x79261),x79262),f317(f317(f266(x79261),x79264),x79263)))+P22(f317(f317(f226(x79261),f317(f317(f90(x79261),x79262),x79263)),x79264)) % 168.22/168.06 [7927]~P61(x79271)+~P22(f317(f317(f226(x79271),f2(x79271)),x79273))+~P22(f317(f317(f226(x79271),x79272),f317(f317(f266(x79271),x79274),x79273)))+P22(f317(f317(f226(x79271),f317(f317(f90(x79271),x79272),x79273)),x79274)) % 168.22/168.06 [7929]~P60(x79291)+~P22(f317(f317(f226(x79291),f2(x79291)),x79293))+~P22(f317(f317(f226(x79291),x79292),f317(f317(f90(x79291),x79294),x79293)))+P22(f317(f317(f226(x79291),f317(f317(f266(x79291),x79292),x79293)),x79294)) % 168.22/168.06 [7930]~P61(x79301)+~P22(f317(f317(f226(x79301),f2(x79301)),x79303))+~P22(f317(f317(f226(x79301),x79302),f317(f317(f90(x79301),x79304),x79303)))+P22(f317(f317(f226(x79301),f317(f317(f266(x79301),x79302),x79303)),x79304)) % 168.22/168.06 [8065]~P60(x80651)+~P22(f317(f317(f226(x80651),f2(x80651)),x80654))+P22(f317(f317(f225(x80651),x80652),f317(f317(f90(x80651),x80653),x80654)))+~P22(f317(f317(f225(x80651),f317(f317(f266(x80651),x80652),x80654)),x80653)) % 168.22/168.06 [8067]~P60(x80671)+~P22(f317(f317(f226(x80671),f2(x80671)),x80674))+P22(f317(f317(f225(x80671),x80672),f317(f317(f266(x80671),x80673),x80674)))+~P22(f317(f317(f225(x80671),f317(f317(f90(x80671),x80672),x80674)),x80673)) % 168.22/168.06 [8068]~P61(x80681)+~P22(f317(f317(f226(x80681),f2(x80681)),x80684))+P22(f317(f317(f225(x80681),x80682),f317(f317(f90(x80681),x80683),x80684)))+~P22(f317(f317(f225(x80681),f317(f317(f266(x80681),x80682),x80684)),x80683)) % 168.22/168.06 [8069]~P61(x80691)+~P22(f317(f317(f226(x80691),f2(x80691)),x80694))+P22(f317(f317(f225(x80691),x80692),f317(f317(f266(x80691),x80693),x80694)))+~P22(f317(f317(f225(x80691),f317(f317(f90(x80691),x80692),x80694)),x80693)) % 168.22/168.06 [8070]~P60(x80701)+~P22(f317(f317(f226(x80701),f2(x80701)),x80704))+P22(f317(f317(f226(x80701),x80702),f317(f317(f90(x80701),x80703),x80704)))+~P22(f317(f317(f226(x80701),f317(f317(f266(x80701),x80702),x80704)),x80703)) % 168.22/168.06 [8072]~P60(x80721)+~P22(f317(f317(f226(x80721),f2(x80721)),x80724))+P22(f317(f317(f226(x80721),x80722),f317(f317(f266(x80721),x80723),x80724)))+~P22(f317(f317(f226(x80721),f317(f317(f90(x80721),x80722),x80724)),x80723)) % 168.22/168.06 [8073]~P61(x80731)+~P22(f317(f317(f226(x80731),f2(x80731)),x80734))+P22(f317(f317(f226(x80731),x80732),f317(f317(f90(x80731),x80733),x80734)))+~P22(f317(f317(f226(x80731),f317(f317(f266(x80731),x80732),x80734)),x80733)) % 168.22/168.06 [8074]~P61(x80741)+~P22(f317(f317(f226(x80741),f2(x80741)),x80744))+P22(f317(f317(f226(x80741),x80742),f317(f317(f266(x80741),x80743),x80744)))+~P22(f317(f317(f226(x80741),f317(f317(f90(x80741),x80742),x80744)),x80743)) % 168.22/168.06 [8232]~P22(f317(x82321,x82324))+P22(f317(x82321,f317(f48(a849,x82322),x82323)))+~P22(f317(f317(f226(a849),x82322),f317(f317(f90(a849),x82323),f317(a124,x82324))))+~P22(f317(f317(f225(a849),f317(f317(f90(a849),x82323),x82324)),x82322)) % 168.22/168.06 [8238]~P61(x82381)+~P22(f317(f317(f226(x82381),x82383),f2(x82381)))+~P22(f317(f317(f225(x82381),f317(f317(f266(x82381),x82384),x82383)),x82382))+P22(f317(f317(f225(x82381),f317(f317(f90(x82381),x82382),x82383)),x82384)) % 168.22/168.06 [8239]~P61(x82391)+~P22(f317(f317(f226(x82391),x82393),f2(x82391)))+~P22(f317(f317(f225(x82391),f317(f317(f90(x82391),x82394),x82393)),x82392))+P22(f317(f317(f225(x82391),f317(f317(f266(x82391),x82392),x82393)),x82394)) % 168.22/168.06 [8240]~P61(x82401)+~P22(f317(f317(f226(x82401),x82403),f2(x82401)))+~P22(f317(f317(f226(x82401),f317(f317(f266(x82401),x82404),x82403)),x82402))+P22(f317(f317(f226(x82401),f317(f317(f90(x82401),x82402),x82403)),x82404)) % 168.22/168.06 [8241]~P61(x82411)+~P22(f317(f317(f226(x82411),x82413),f2(x82411)))+~P22(f317(f317(f226(x82411),f317(f317(f90(x82411),x82414),x82413)),x82412))+P22(f317(f317(f226(x82411),f317(f317(f266(x82411),x82412),x82413)),x82414)) % 168.22/168.06 [8472]~P92(x84721)+~P22(f317(f71(x84721),x84724))+~P22(f317(f317(f319(x84721),x84722),x84724))+P22(f317(f317(f225(x84721),f317(f317(f122(x84721),x84722),x84723)),f317(f317(f74(x84721,x84721,f122(x84721)),x84723),x84724))) % 168.22/168.06 [8473]~P103(x84731)+~P22(f317(f71(x84731),x84734))+~P22(f317(f317(f319(x84731),x84732),x84734))+P22(f317(f317(f225(x84731),f317(f317(f224(x84731),x84732),x84733)),f317(f317(f74(x84731,x84731,f224(x84731)),x84733),x84734))) % 168.22/168.06 [8609]~P22(f317(f71(x86091),x86092))+E(f317(f54(x86091),f317(f317(f21(f858(x86091,a842)),x86092),f317(f317(f286(x86091),x86093),x86094))),f317(f317(f21(a849),f317(f54(x86091),f317(f317(f21(f858(x86091,a842)),x86092),x86094))),f87(a849)))+P22(f317(f317(f319(x86091),x86093),x86094))+~P22(f317(f317(f319(x86091),x86093),x86092)) % 168.22/168.06 [8678]E(f317(f317(f89(a1),f441(x86781,x86782,x86783,x86784)),f442(x86781,x86782,x86783,x86784)),x86784)+~P22(f317(f317(f226(a1),f2(a1)),x86783))+~P22(f317(f317(f225(a1),x86784),x86781))+P22(f317(f317(f225(a1),f317(f317(f21(a1),x86784),x86783)),x86781)) % 168.22/168.06 [8679]E(f317(f317(f89(a1),f450(x86791,x86792,x86793,x86794)),f447(x86791,x86792,x86793,x86794)),x86794)+~P22(f317(f317(f226(a1),f2(a1)),x86793))+~P22(f317(f317(f226(a1),x86794),x86791))+P22(f317(f317(f226(a1),f317(f317(f21(a1),x86794),x86793)),x86791)) % 168.22/168.06 [8888]~P22(f317(f317(f226(a1),f2(a1)),x88883))+~P22(f317(f317(f225(a1),x88884),x88881))+P22(f317(f317(f319(a1),f441(x88881,x88882,x88883,x88884)),x88882))+P22(f317(f317(f225(a1),f317(f317(f21(a1),x88884),x88883)),x88881)) % 168.22/168.06 [8889]~P22(f317(f317(f226(a1),f2(a1)),x88893))+~P22(f317(f317(f226(a1),x88894),x88891))+P22(f317(f317(f319(a1),f450(x88891,x88892,x88893,x88894)),x88892))+P22(f317(f317(f226(a1),f317(f317(f21(a1),x88894),x88893)),x88891)) % 168.22/168.06 [8971]~P22(f317(f317(f226(a1),f2(a1)),x89712))+~P22(f317(f317(f225(a1),x89711),x89713))+P22(f317(f317(f319(a1),f442(x89713,x89714,x89712,x89711)),f279(a1,f87(a1),x89712)))+P22(f317(f317(f225(a1),f317(f317(f21(a1),x89711),x89712)),x89713)) % 168.22/168.06 [8972]~P22(f317(f317(f226(a1),f2(a1)),x89722))+~P22(f317(f317(f226(a1),x89721),x89723))+P22(f317(f317(f319(a1),f447(x89723,x89724,x89722,x89721)),f279(a1,f87(a1),x89722)))+P22(f317(f317(f226(a1),f317(f317(f21(a1),x89721),x89722)),x89723)) % 168.22/168.06 [8988]~P22(f317(f317(f225(a1),f2(a1)),x89884))+~P22(f317(f317(f226(a1),f2(a1)),x89883))+~P22(f317(f317(f226(a1),x89884),x89881))+P22(f317(f317(f225(a1),f2(a1)),f317(f317(f89(a1),f317(f317(f90(a1),x89881),f55(a1,x89882,x89883))),x89884))) % 168.22/168.06 [9065]~P22(f317(f317(f225(a1),x90654),f2(a1)))+~P22(f317(f317(f226(a1),f2(a1)),x90652))+~P22(f317(f317(f226(a1),x90651),x90654))+P22(f317(f317(f226(a1),f317(f317(f90(a1),x90651),x90652)),f317(f317(f89(a1),f317(f317(f90(a1),x90651),f55(a1,x90653,x90652))),x90654))) % 168.22/168.06 [9087]P22(f317(f71(x90871),x90872))+~P22(f317(f71(x90871),x90873))+~P22(f317(f317(f319(f858(x90871,a842)),x90872),f317(f317(f70(x90871),x90873),x90874)))+~P22(f317(f317(f225(f858(f857(x90871,x90871),a842)),x90874),f317(f317(f245(x90871,x90871),x90873),f317(f16(f858(x90871,a842),x90871),x90873)))) % 168.22/168.06 [9508]~P22(f317(f71(x95082),x95084))+~P22(f317(f71(x95081),x95083))+~P22(f317(f317(f225(a849),f317(f54(x95082),x95084)),f317(f54(x95081),x95083)))+P22(f317(f317(f225(f858(x95081,a842)),f317(f287(x95082,x95081,f366(x95083,x95081,x95084,x95082)),x95084)),x95083)) % 168.22/168.06 [9162]~P22(f317(f317(f319(x91621),x91622),x91624))+P22(f317(f317(f319(x91621),x91622),x91623))+~P22(f317(f317(f226(f858(x91621,a842)),x91624),f317(f317(f286(x91621),x91622),x91623)))+P22(f317(f317(f226(f858(x91621,a842)),f317(f317(f21(f858(x91621,a842)),x91624),f317(f317(f286(x91621),x91622),f188(f858(x91621,a842))))),x91623)) % 168.22/168.06 [9322]~P22(f317(f317(f319(x93221),x93222),x93224))+P22(f317(f317(f319(x93221),x93222),x93223))+P22(f317(f317(f226(f858(x93221,a842)),x93224),f317(f317(f286(x93221),x93222),x93223)))+~P22(f317(f317(f226(f858(x93221,a842)),f317(f317(f21(f858(x93221,a842)),x93224),f317(f317(f286(x93221),x93222),f188(f858(x93221,a842))))),x93223)) % 168.22/168.06 [9348]P22(f317(f317(f319(x93481),x93482),x93483))+~P22(f317(f317(f225(f858(x93481,a842)),x93484),x93483))+P22(f317(f317(f226(f858(x93481,a842)),x93484),f317(f317(f286(x93481),x93482),x93483)))+~P22(f317(f317(f226(f858(x93481,a842)),f317(f317(f21(f858(x93481,a842)),x93484),f317(f317(f286(x93481),x93482),f188(f858(x93481,a842))))),x93483)) % 168.22/168.06 [9353]~P22(f317(f317(f319(x93531),x93533),x93532))+~P22(f317(f317(f226(f858(x93531,a842)),x93532),x93534))+P22(f317(f317(f226(f858(x93531,a842)),x93532),f317(f317(f286(x93531),x93533),x93534)))+~P22(f317(f317(f226(f858(x93531,a842)),f317(f317(f21(f858(x93531,a842)),x93532),f317(f317(f286(x93531),x93533),f188(f858(x93531,a842))))),x93534)) % 168.22/168.06 [9365]~P22(f317(f317(f225(f858(x93651,a842)),x93652),x93654))+~P22(f317(f317(f226(f858(x93651,a842)),x93652),x93654))+P22(f317(f317(f226(f858(x93651,a842)),x93652),f317(f317(f286(x93651),x93653),x93654)))+~P22(f317(f317(f226(f858(x93651,a842)),f317(f317(f21(f858(x93651,a842)),x93652),f317(f317(f286(x93651),x93653),f188(f858(x93651,a842))))),x93654)) % 168.22/168.06 [9413]~P104(x94132)+~P57(x94131)+~P22(f317(f317(f225(f858(x94131,x94132)),x94133),x94134))+P22(f317(f68(x94131),f317(f317(f18(x94131,x94132,a842),f317(f317(f8(x94132,f858(x94132,a842),x94131),f225(x94132)),x94133)),x94134))) % 168.22/168.06 [9552]~P104(x95522)+~P57(x95521)+P22(f317(f317(f225(f858(x95521,x95522)),x95523),x95524))+~P22(f317(f68(x95521),f317(f317(f18(x95521,x95522,a842),f317(f317(f8(x95522,f858(x95522,a842),x95521),f225(x95522)),x95523)),x95524))) % 168.22/168.06 [9717]E(f317(f317(f159(x97171),f317(f317(f159(f850(x97171)),f173(x97171,x97172)),x97173)),x97174),f317(f317(f159(x97171),f317(f317(f159(f850(x97171)),x97172),x97174)),x97173))+~P22(f317(f317(f226(a849),x97173),f317(f189(f850(f850(x97171))),f173(x97171,x97172))))+~P29(a849,f317(f163(a849),f317(f317(f148(f850(x97171),a849),f189(f850(x97171))),x97172)))+~P22(f317(f317(f226(a849),x97174),f317(f189(f850(f850(x97171))),f317(f130(f850(x97171),f317(f317(f8(a849,a842,f850(x97171)),f317(f226(a849),x97173)),f189(f850(x97171)))),x97172)))) % 168.22/168.06 [9748]~P22(f317(f317(f319(f857(a849,a849)),x97484),x97481))+~P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),x97484),x97482)),a45))+~P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),x97481),x97483)),a46))+P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),x97481),f317(f317(f286(f857(a849,a849)),x97482),x97483))),a46)) % 168.22/168.06 [9749]~P22(f317(f317(f319(f857(a849,a849)),x97494),x97491))+~P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),x97494),x97492)),a79))+~P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),x97491),x97493)),a80))+P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),x97491),f317(f317(f286(f857(a849,a849)),x97492),x97493))),a80)) % 168.22/168.06 [9634]~P104(x96342)+~P57(x96341)+~P22(f317(f317(f226(f858(x96341,x96342)),x96343),x96344))+P22(f317(f67(x96341),f317(f317(f8(a842,a842,x96341),a312),f317(f317(f18(x96341,x96342,a842),f317(f317(f8(x96342,f858(x96342,a842),x96341),a314),x96343)),x96344)))) % 168.22/168.07 [9762]~P22(f317(f317(f319(f857(a849,a849)),x97624),x97623))+~P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),x97621),x97624)),a45))+~P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),x97622),x97623)),a47))+P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),f317(f317(f286(f857(a849,a849)),x97621),x97622)),x97623)),a47)) % 168.22/168.07 [9763]~P22(f317(f317(f319(f857(a849,a849)),x97634),x97633))+~P22(f317(f317(f319(f857(f857(a849,a849),f857(a849,a849))),f317(f317(f237(f857(a849,a849),f857(a849,a849)),x97631),x97634)),a79))+~P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),x97632),x97633)),a78))+P22(f317(f317(f319(f857(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842))),f317(f317(f237(f858(f857(a849,a849),a842),f858(f857(a849,a849),a842)),f317(f317(f286(f857(a849,a849)),x97631),x97632)),x97633)),a78)) % 168.22/168.07 [8817]~P32(x88171,x88172,x88174,x88175)+~P32(x88171,x88172,x88173,x88175)+~P32(x88171,x88172,x88173,f178(x88171,x88172,x88173,x88174))+P32(x88171,x88172,f178(x88171,x88172,x88173,x88174),x88175) % 168.22/168.07 [5941]~P5(x59414,x59411)+~P22(f317(f317(x59411,x59412),x59415))+P22(f317(f317(x59411,x59412),x59413))+~P22(f317(f317(x59411,x59415),x59413)) % 168.22/168.07 [5218]~P25(x52185)+E(x52181,x52182)+~E(x52183,x52184)+~E(f317(f317(f21(x52185),x52183),x52184),f317(f317(f21(x52185),x52181),x52182)) % 168.22/168.07 [6042]~P12(x60425,x60421,x60423)+E(f317(f317(x60421,x60422),f317(x60423,x60424)),f317(x60423,x60424))+~P22(f317(f71(x60425),x60424))+~P22(f317(f317(f319(x60425),x60422),x60424)) % 168.22/168.07 [6229]~P78(x62291)+~E(f317(f317(f21(x62291),x62294),x62295),f317(f317(f21(x62291),x62292),x62293))+~P22(f317(f317(f225(x62291),x62294),x62295))+P22(f317(f317(f225(x62291),x62292),x62293)) % 168.22/168.07 [6231]~P78(x62311)+~E(f317(f317(f21(x62311),x62314),x62315),f317(f317(f21(x62311),x62312),x62313))+~P22(f317(f317(f226(x62311),x62314),x62315))+P22(f317(f317(f226(x62311),x62312),x62313)) % 168.22/168.07 [7184]~E(x71842,f317(f317(f145(x71841),x71844),x71845))+P22(f317(f317(f319(f850(x71841)),x71842),f155(x71841,x71843)))+~P22(f317(f317(f319(f850(x71841)),x71845),f155(x71841,x71843)))+~P22(f317(f317(f319(x71841),x71844),x71843)) % 168.22/168.07 [7590]~E(f317(f189(f850(x75901)),x75903),f317(f189(f850(x75902)),x75904))+~E(f317(f317(f148(f857(x75901,x75902),x75902),f246(x75901,x75902)),x75905),x75904)+~E(f317(f317(f148(f857(x75901,x75902),x75901),f244(x75901,x75902)),x75905),x75903)+E(f317(f317(f175(x75901,x75902),x75903),x75904),x75905) % 168.22/168.07 [7918]~P104(x79181)+P22(f317(f317(f226(f858(x79181,a842)),f279(x79181,x79182,x79183)),f279(x79181,x79184,x79185)))+~P22(f317(f317(f225(x79181),x79184),x79185))+P22(f317(f317(f225(x79181),x79182),x79183)) % 168.22/168.07 [8016]~P104(x80161)+P22(f317(f317(f225(f858(x80161,a842)),f279(x80161,x80162,x80163)),f279(x80161,x80164,x80165)))+~P22(f317(f317(f225(x80161),x80163),x80165))+~P22(f317(f317(f225(x80161),x80164),x80162)) % 168.22/168.07 [8141]~P103(x81411)+P22(f317(f317(f225(x81411),x81412),x81413))+P22(f317(f317(f225(x81411),x81414),x81413))+~P22(f317(f317(f225(f858(x81411,a842)),f317(f278(x81411,x81413),x81412)),f317(f278(x81411,x81414),x81415))) % 168.22/168.07 [8142]~P103(x81421)+P22(f317(f317(f225(x81421),x81422),x81423))+P22(f317(f317(f225(x81421),x81422),x81424))+~P22(f317(f317(f225(f858(x81421,a842)),f317(f278(x81421,x81423),x81422)),f317(f278(x81421,x81425),x81424))) % 168.22/168.07 [8387]~P104(x83871)+~P22(f317(f317(f225(f858(x83871,a842)),f279(x83871,x83874,x83872)),f279(x83871,x83875,x83873)))+P22(f317(f317(f225(x83871),x83872),x83873))+~P22(f317(f317(f225(x83871),x83874),x83872)) % 168.22/168.07 [8388]~P104(x83881)+~P22(f317(f317(f226(f858(x83881,a842)),f279(x83881,x83884,x83882)),f279(x83881,x83885,x83883)))+P22(f317(f317(f225(x83881),x83882),x83883))+~P22(f317(f317(f225(x83881),x83884),x83882)) % 168.22/168.07 [8389]~P104(x83891)+~P22(f317(f317(f225(f858(x83891,a842)),f279(x83891,x83893,x83894)),f279(x83891,x83892,x83895)))+P22(f317(f317(f225(x83891),x83892),x83893))+~P22(f317(f317(f225(x83891),x83893),x83894)) % 168.22/168.07 [8390]~P104(x83901)+~P22(f317(f317(f226(f858(x83901,a842)),f279(x83901,x83903,x83904)),f279(x83901,x83902,x83905)))+P22(f317(f317(f225(x83901),x83902),x83903))+~P22(f317(f317(f225(x83901),x83903),x83904)) % 168.22/168.07 [5940]~P12(x59402,x59405,x59403)+E(x59401,f188(f858(x59402,a842)))+~P22(f317(f71(x59402),x59401))+E(f317(x59403,f317(f317(f286(x59402),x59404),x59401)),f317(f317(x59405,x59404),f317(x59403,x59401))) % 168.22/168.07 [6689]~E(x66891,x66892)+~E(f317(f317(f113(f858(x66893,a842)),x66894),x66895),f188(f858(x66893,a842)))+~P22(f317(f317(f319(x66893),x66892),x66895))+~P22(f317(f317(f319(x66893),x66891),x66894)) % 168.22/168.07 [6765]~P13(x67652,x67655,x67651)+~P22(f317(f71(x67652),x67654))+E(f317(x67651,f317(f317(f286(x67652),x67653),x67654)),f317(f317(f74(x67652,x67652,x67655),x67653),x67654))+P22(f317(f317(f319(x67652),x67653),x67654)) % 168.22/168.07 [6831]~P70(x68312)+~P22(f317(f71(x68311),x68315))+E(f317(f317(f9(x68311,x68312),x68313),f317(f317(f286(x68311),x68314),x68315)),f317(f317(f90(x68312),f317(x68313,x68314)),f317(f317(f9(x68311,x68312),x68313),x68315)))+P22(f317(f317(f319(x68311),x68314),x68315)) % 168.22/168.07 [6833]~P67(x68332)+~P22(f317(f71(x68331),x68335))+E(f317(f317(f6(x68331,x68332),x68333),f317(f317(f286(x68331),x68334),x68335)),f317(f317(f89(x68332),f317(x68333,x68334)),f317(f317(f6(x68331,x68332),x68333),x68335)))+P22(f317(f317(f319(x68331),x68334),x68335)) % 168.22/168.07 [7333]~P13(x73332,x73335,x73331)+~P22(f317(f71(x73332),x73334))+E(f317(x73331,f317(f317(f286(x73332),x73333),x73334)),x73333)+~E(f317(f317(f21(f858(x73332,a842)),x73334),f317(f317(f286(x73332),x73333),f188(f858(x73332,a842)))),f188(f858(x73332,a842))) % 168.22/168.07 [7645]~P22(f317(x76451,x76453))+~P22(f317(f317(f194(x76452),x76453),x76455))+~P22(f317(f317(f194(f35(x76451,x76452)),x76455),x76454))+P22(f317(f317(f194(f35(x76451,x76452)),x76453),x76454)) % 168.22/168.07 [7696]~P77(x76961)+~P22(f317(f317(f225(x76961),x76963),x76965))+~P22(f317(f317(f225(x76961),x76962),x76964))+P22(f317(f317(f225(x76961),f317(f317(f89(x76961),x76962),x76963)),f317(f317(f89(x76961),x76964),x76965))) % 168.22/168.07 [7697]~P92(x76971)+~P22(f317(f317(f225(x76971),x76973),x76975))+~P22(f317(f317(f225(x76971),x76972),x76974))+P22(f317(f317(f225(x76971),f317(f317(f122(x76971),x76972),x76973)),f317(f317(f122(x76971),x76974),x76975))) % 168.22/168.07 [7698]~P98(x76981)+~P22(f317(f317(f225(x76981),x76983),x76985))+~P22(f317(f317(f225(x76981),x76982),x76984))+P22(f317(f317(f225(x76981),f317(f317(f113(x76981),x76982),x76983)),f317(f317(f113(x76981),x76984),x76985))) % 168.22/168.07 [7699]~P103(x76991)+~P22(f317(f317(f225(x76991),x76993),x76995))+~P22(f317(f317(f225(x76991),x76992),x76994))+P22(f317(f317(f225(x76991),f317(f317(f223(x76991),x76992),x76993)),f317(f317(f223(x76991),x76994),x76995))) % 168.22/168.07 [7700]~P103(x77001)+~P22(f317(f317(f225(x77001),x77003),x77005))+~P22(f317(f317(f225(x77001),x77002),x77004))+P22(f317(f317(f225(x77001),f317(f317(f224(x77001),x77002),x77003)),f317(f317(f224(x77001),x77004),x77005))) % 168.22/168.07 [7701]~P81(x77011)+~P22(f317(f317(f225(x77011),x77013),x77015))+~P22(f317(f317(f226(x77011),x77012),x77014))+P22(f317(f317(f226(x77011),f317(f317(f89(x77011),x77012),x77013)),f317(f317(f89(x77011),x77014),x77015))) % 168.22/168.07 [7702]~P81(x77021)+~P22(f317(f317(f225(x77021),x77022),x77024))+~P22(f317(f317(f226(x77021),x77023),x77025))+P22(f317(f317(f226(x77021),f317(f317(f89(x77021),x77022),x77023)),f317(f317(f89(x77021),x77024),x77025))) % 168.22/168.07 [7703]~P81(x77031)+~P22(f317(f317(f226(x77031),x77033),x77035))+~P22(f317(f317(f226(x77031),x77032),x77034))+P22(f317(f317(f226(x77031),f317(f317(f89(x77031),x77032),x77033)),f317(f317(f89(x77031),x77034),x77035))) % 168.22/168.07 [7831]~P109(x78315)+E(x78311,x78312)+E(x78313,x78314)+~E(f317(f317(f89(x78315),f317(f317(f90(x78315),x78313),x78311)),f317(f317(f90(x78315),x78314),x78312)),f317(f317(f89(x78315),f317(f317(f90(x78315),x78313),x78312)),f317(f317(f90(x78315),x78314),x78311))) % 168.22/168.07 [7969]P30(x79691,x79692,x79693)+~P21(x79691,x79694,x79695)+~P30(x79691,x79692,f578(x79695,x79694,x79691,x79692))+~P22(f317(f317(f319(f848(x79691)),x79693),x79695)) % 168.22/168.07 [8039]~P103(x80394)+~P22(f317(f131(x80391),x80393))+P22(f317(f317(f319(x80391),x80392),f317(f166(x80391),x80393)))+P22(f317(f131(x80391),f317(f317(f143(x80391,x80394,x80395),x80392),x80393))) % 168.22/168.07 [8188]~P67(x81881)+E(f317(f317(f89(x81881),f317(f317(f6(a849,x81881),x81882),f317(f278(a849,x81883),x81884))),f317(f317(f6(a849,x81881),x81882),f317(f278(a849,x81884),x81885))),f317(f317(f6(a849,x81881),x81882),f317(f278(a849,x81883),x81885)))+~P22(f317(f317(f225(a849),x81884),x81885))+~P22(f317(f317(f225(a849),x81883),x81884)) % 168.22/168.07 [8189]~P25(x81891)+E(f317(f317(f21(x81891),f317(f317(f6(a849,x81891),x81892),f317(f278(a849,x81893),x81894))),f317(f317(f6(a849,x81891),x81892),f317(f278(a849,x81893),x81895))),f317(f317(f6(a849,x81891),x81892),f317(f278(a849,x81895),x81894)))+~P22(f317(f317(f225(a849),x81895),x81894))+~P22(f317(f317(f225(a849),x81893),x81895)) % 168.22/168.07 [8526]~P59(x85262)+E(x85261,f2(x85262))+E(x85263,f2(x85262))+E(f317(f317(f266(x85262),f317(f317(f89(x85262),f317(f317(f90(x85262),x85264),x85261)),f317(f317(f90(x85262),x85265),x85263))),f317(f317(f90(x85262),x85263),x85261)),f317(f317(f89(x85262),f317(f317(f266(x85262),x85264),x85263)),f317(f317(f266(x85262),x85265),x85261))) % 168.22/168.07 [8527]~P59(x85272)+E(x85271,f2(x85272))+E(x85273,f2(x85272))+E(f317(f317(f266(x85272),f317(f317(f21(x85272),f317(f317(f90(x85272),x85274),x85271)),f317(f317(f90(x85272),x85275),x85273))),f317(f317(f90(x85272),x85273),x85271)),f317(f317(f21(x85272),f317(f317(f266(x85272),x85274),x85273)),f317(f317(f266(x85272),x85275),x85271))) % 168.22/168.07 [8536]~E(x85362,f317(x85363,x85361))+E(x85361,f840(x85362,x85363,x85364,x85365))+~P19(x85365,x85364,x85363,f233(f858(x85365,a842)))+~P22(f317(f317(f319(x85364),x85362),f317(f287(x85365,x85364,x85363),f233(f858(x85365,a842))))) % 168.22/168.07 [8725]~P113(x87251)+~P22(f317(f317(f226(x87251),f317(f84(x87251),x87252)),x87254))+P22(f317(f317(f226(x87251),f317(f317(f90(x87251),f317(f84(x87251),x87252)),f317(f84(x87251),x87253))),f317(f317(f90(x87251),x87254),x87255)))+~P22(f317(f317(f226(x87251),f317(f84(x87251),x87253)),x87255)) % 168.22/168.07 [8742]~P21(x87421,x87425,x87424)+P30(x87421,x87422,x87423)+P22(f317(f317(f319(f848(x87421)),f578(x87424,x87425,x87421,x87422)),x87425))+~P22(f317(f317(f319(f848(x87421)),x87423),x87424)) % 168.22/168.07 [8845]~P19(x88451,x88453,x88455,x88452)+~P22(f317(f71(x88453),x88454))+P22(f317(f317(f225(a849),f317(f54(x88451),x88452)),f317(f54(x88453),x88454)))+~P22(f317(f317(f225(f858(x88453,a842)),f317(f287(x88451,x88453,x88455),x88452)),x88454)) % 168.22/168.07 [8917]~P70(x89172)+~P19(x89171,x89171,x89174,x89175)+~P22(f317(f71(x89171),x89175))+E(f317(f317(f9(x89171,x89172),f317(f82(x89171,x89172,x89171,x89173),x89174)),x89175),f317(f317(f9(x89171,x89172),x89173),f317(f287(x89171,x89171,x89174),x89175))) % 168.22/168.07 [8918]~P67(x89182)+~P19(x89181,x89181,x89184,x89185)+~P22(f317(f71(x89181),x89185))+E(f317(f317(f6(x89181,x89182),f317(f82(x89181,x89182,x89181,x89183),x89184)),x89185),f317(f317(f6(x89181,x89182),x89183),f317(f287(x89181,x89181,x89184),x89185))) % 168.22/168.07 [9064]~P19(x90642,x90643,x90645,x90641)+E(x90641,f188(f858(x90642,a842)))+E(f317(f287(x90643,x90642,f816(x90644,x90643,x90642,x90641)),x90644),x90641)+~P22(f317(f317(f225(f858(x90643,a842)),f317(f287(x90642,x90643,x90645),x90641)),x90644)) % 168.22/168.07 [9534]~P103(x95345)+~P27(x95345)+P22(f317(f317(f319(x95341),f492(x95342,x95343,x95341,x95344,x95345)),x95343))+~P22(f317(f317(f226(x95345),x95344),f317(f317(f51(x95341,x95345),x95343),x95342))) % 168.22/168.07 [9538]~P103(x95381)+~P27(x95381)+P22(f317(f317(f226(x95381),x95382),f317(x95383,f492(x95383,x95384,x95385,x95382,x95381))))+~P22(f317(f317(f226(x95381),x95382),f317(f317(f51(x95385,x95381),x95384),x95383))) % 168.22/168.07 [9614]~P64(x96141)+~P22(f317(f76(x96141,x96141,f90(x96141),x96142,x96143),x96145))+P22(f317(f317(f319(x96141),x96142),x96143))+P22(f317(f76(x96141,x96141,f90(x96141),x96144,f317(f317(f286(x96141),x96142),x96143)),f317(f317(f90(x96141),x96144),x96145))) % 168.22/168.07 [9835]~P70(x98352)+~P22(f317(f71(x98351),x98355))+E(f317(f317(f9(x98351,x98352),f317(f317(f7(x98351,x98352,x98352),f317(f317(f18(x98351,x98352,f858(x98352,x98352)),f317(f317(f8(a842,f858(x98352,f858(x98352,x98352)),x98351),f108(x98352)),f317(a314,x98353))),x98354)),f87(x98352))),x98355),f87(x98352))+P22(f317(f317(f319(x98351),x98353),x98355)) % 168.22/168.07 [9836]~P67(x98362)+~P22(f317(f71(x98361),x98365))+E(f317(f317(f6(x98361,x98362),f317(f317(f7(x98361,x98362,x98362),f317(f317(f18(x98361,x98362,f858(x98362,x98362)),f317(f317(f8(a842,f858(x98362,f858(x98362,x98362)),x98361),f108(x98362)),f317(a314,x98363))),x98364)),f2(x98362))),x98365),f2(x98362))+P22(f317(f317(f319(x98361),x98363),x98365)) % 168.22/168.07 [9837]~P70(x98372)+~P22(f317(f71(x98371),x98375))+E(f317(f317(f9(x98371,x98372),f317(f317(f7(x98371,x98372,x98372),f317(f317(f18(x98371,x98372,f858(x98372,x98372)),f317(f317(f8(a842,f858(x98372,f858(x98372,x98372)),x98371),f108(x98372)),f317(a314,x98373))),x98374)),f87(x98372))),x98375),f317(x98374,x98373))+~P22(f317(f317(f319(x98371),x98373),x98375)) % 168.22/168.07 [9838]~P67(x98382)+~P22(f317(f71(x98381),x98385))+E(f317(f317(f6(x98381,x98382),f317(f317(f7(x98381,x98382,x98382),f317(f317(f18(x98381,x98382,f858(x98382,x98382)),f317(f317(f8(a842,f858(x98382,f858(x98382,x98382)),x98381),f108(x98382)),f317(a314,x98383))),x98384)),f2(x98382))),x98385),f317(x98384,x98383))+~P22(f317(f317(f319(x98381),x98383),x98385)) % 168.22/168.07 [9897]~P70(x98972)+~P22(f317(f71(x98971),x98975))+E(f317(f317(f9(x98971,x98972),f317(f317(f7(x98971,x98972,x98972),f317(f317(f18(x98971,x98972,f858(x98972,x98972)),f317(f317(f8(a842,f858(x98972,f858(x98972,x98972)),x98971),f108(x98972)),f317(f317(f7(x98971,x98971,a842),a314),x98973))),x98974)),f87(x98972))),x98975),f87(x98972))+P22(f317(f317(f319(x98971),x98973),x98975)) % 168.22/168.07 [9898]~P67(x98982)+~P22(f317(f71(x98981),x98985))+E(f317(f317(f6(x98981,x98982),f317(f317(f7(x98981,x98982,x98982),f317(f317(f18(x98981,x98982,f858(x98982,x98982)),f317(f317(f8(a842,f858(x98982,f858(x98982,x98982)),x98981),f108(x98982)),f317(f317(f7(x98981,x98981,a842),a314),x98983))),x98984)),f2(x98982))),x98985),f2(x98982))+P22(f317(f317(f319(x98981),x98983),x98985)) % 168.22/168.07 [9900]~P70(x99002)+~P22(f317(f71(x99001),x99005))+E(f317(f317(f9(x99001,x99002),f317(f317(f7(x99001,x99002,x99002),f317(f317(f18(x99001,x99002,f858(x99002,x99002)),f317(f317(f8(a842,f858(x99002,f858(x99002,x99002)),x99001),f108(x99002)),f317(f317(f7(x99001,x99001,a842),a314),x99003))),x99004)),f87(x99002))),x99005),f317(x99004,x99003))+~P22(f317(f317(f319(x99001),x99003),x99005)) % 168.22/168.07 [9901]~P67(x99012)+~P22(f317(f71(x99011),x99015))+E(f317(f317(f6(x99011,x99012),f317(f317(f7(x99011,x99012,x99012),f317(f317(f18(x99011,x99012,f858(x99012,x99012)),f317(f317(f8(a842,f858(x99012,f858(x99012,x99012)),x99011),f108(x99012)),f317(f317(f7(x99011,x99011,a842),a314),x99013))),x99014)),f2(x99012))),x99015),f317(x99014,x99013))+~P22(f317(f317(f319(x99011),x99013),x99015)) % 168.22/168.07 [7695]~P25(x76952)+~P22(f317(f71(x76951),x76954))+E(f317(f317(f6(x76951,x76952),x76953),f317(f317(f21(f858(x76951,a842)),x76954),f317(f317(f286(x76951),x76955),f188(f858(x76951,a842))))),f317(f317(f6(x76951,x76952),x76953),x76954))+P22(f317(f317(f319(x76951),x76955),x76954)) % 168.22/168.07 [8194]~P126(x81942)+~P22(f317(f71(x81941),x81944))+E(f317(f317(f6(x81941,x81942),x81943),f317(f317(f21(f858(x81941,a842)),x81944),f317(f317(f286(x81941),x81945),f188(f858(x81941,a842))))),f317(f317(f21(x81942),f317(f317(f6(x81941,x81942),x81943),x81944)),f317(x81943,x81945)))+~P22(f317(f317(f319(x81941),x81945),x81944)) % 168.22/168.07 [8195]~P25(x81952)+~P22(f317(f71(x81951),x81954))+E(f317(f317(f6(x81951,x81952),x81953),f317(f317(f21(f858(x81951,a842)),x81954),f317(f317(f286(x81951),x81955),f188(f858(x81951,a842))))),f317(f317(f21(x81952),f317(f317(f6(x81951,x81952),x81953),x81954)),f317(x81953,x81955)))+~P22(f317(f317(f319(x81951),x81955),x81954)) % 168.22/168.07 [8228]~P25(x82281)+~P22(f317(f71(x82282),x82284))+E(f317(f317(f21(x82281),f317(f317(f6(x82282,x82281),x82283),x82284)),f317(f317(f6(x82282,x82281),x82283),x82285)),f317(f317(f6(x82282,x82281),x82283),f317(f317(f21(f858(x82282,a842)),x82284),x82285)))+~P22(f317(f317(f225(f858(x82282,a842)),x82285),x82284)) % 168.22/168.07 [8250]P22(f317(f71(x82501),f317(x82502,x82503)))+~P22(f317(f71(x82504),x82505))+~P22(f317(f317(f319(x82504),x82503),x82505))+~P22(f317(f71(x82501),f317(f317(f51(x82504,f858(x82501,a842)),x82505),x82502))) % 168.22/168.07 [8689]~P6(x86891,x86895,x86894)+~E(f317(f262(x86891,x86891,x86894),f317(f317(f286(x86891),x86892),f188(f858(x86891,a842)))),f317(f262(x86891,x86891,x86894),f317(f317(f286(x86891),x86893),f188(f858(x86891,a842)))))+~P22(f317(f317(f319(x86891),x86893),x86895))+P22(f317(f317(f319(f857(x86891,x86891)),f317(f317(f237(x86891,x86891),x86892),x86893)),x86894)) % 168.22/168.07 [8986]~P22(f317(x89861,x89865))+P22(f317(x89861,f805(x89861,x89862,x89863,x89864)))+P22(f317(x89861,f795(x89861,x89862,x89863,x89864)))+~P22(f317(f317(f319(x89864),x89865),f317(f317(f122(f858(x89864,a842)),x89863),x89862))) % 168.22/168.07 [9167]~P22(f317(x91671,x91675))+P22(f317(x91671,f795(x91671,x91672,x91673,x91674)))+P22(f317(f317(f319(x91674),f805(x91671,x91672,x91673,x91674)),x91672))+~P22(f317(f317(f319(x91674),x91675),f317(f317(f122(f858(x91674,a842)),x91673),x91672))) % 168.22/168.07 [9168]~P22(f317(x91681,x91685))+P22(f317(x91681,f805(x91681,x91682,x91683,x91684)))+P22(f317(f317(f319(x91684),f795(x91681,x91682,x91683,x91684)),x91683))+~P22(f317(f317(f319(x91684),x91685),f317(f317(f122(f858(x91684,a842)),x91683),x91682))) % 168.22/168.07 [9174]P22(f317(x91741,x91742))+~P22(f317(x91741,f797(x91741,x91743,x91744,x91745)))+~P22(f317(x91741,f796(x91741,x91743,x91744,x91745)))+~P22(f317(f317(f319(x91745),x91742),f317(f317(f122(f858(x91745,a842)),x91744),x91743))) % 168.22/168.07 [9215]E(x92151,x92152)+~P22(f317(f317(f319(f857(x92153,x92153)),f317(f317(f237(x92153,x92153),x92151),x92152)),f284(x92153,x92155)))+P22(f317(f317(f319(x92153),x92151),x92154))+~P22(f317(f317(f225(f858(f857(x92153,x92153),a842)),x92155),f317(f317(f245(x92153,x92153),x92154),f317(f16(f858(x92153,a842),x92153),x92154)))) % 168.22/168.07 [9232]P22(f317(x92321,x92322))+~P22(f317(x92321,f796(x92321,x92324,x92325,x92323)))+P22(f317(f317(f319(x92323),f797(x92321,x92324,x92325,x92323)),x92324))+~P22(f317(f317(f319(x92323),x92322),f317(f317(f122(f858(x92323,a842)),x92325),x92324))) % 168.22/168.07 [9233]P22(f317(x92331,x92332))+~P22(f317(x92331,f797(x92331,x92334,x92335,x92333)))+P22(f317(f317(f319(x92333),f796(x92331,x92334,x92335,x92333)),x92335))+~P22(f317(f317(f319(x92333),x92332),f317(f317(f122(f858(x92333,a842)),x92335),x92334))) % 168.22/168.07 [9294]P22(f317(x92941,x92942))+P22(f317(f317(f319(x92943),f797(x92941,x92944,x92945,x92943)),x92944))+P22(f317(f317(f319(x92943),f796(x92941,x92944,x92945,x92943)),x92945))+~P22(f317(f317(f319(x92943),x92942),f317(f317(f122(f858(x92943,a842)),x92945),x92944))) % 168.22/168.07 [9296]~P22(f317(x92962,x92965))+P22(f317(f317(f319(x92961),f805(x92962,x92963,x92964,x92961)),x92963))+P22(f317(f317(f319(x92961),f795(x92962,x92963,x92964,x92961)),x92964))+~P22(f317(f317(f319(x92961),x92965),f317(f317(f122(f858(x92961,a842)),x92964),x92963))) % 168.22/168.07 [9445]~P6(x94451,x94455,x94454)+~P22(f317(f317(f319(x94451),x94453),x94455))+P22(f317(f317(f319(f857(x94451,x94451)),f317(f317(f237(x94451,x94451),x94452),x94453)),x94454))+~P22(f317(f317(f225(f858(x94451,a842)),f317(f262(x94451,x94451,x94454),f317(f317(f286(x94451),x94453),f188(f858(x94451,a842))))),f317(f262(x94451,x94451,x94454),f317(f317(f286(x94451),x94452),f188(f858(x94451,a842)))))) % 168.22/168.07 [9562]~P103(x95625)+~P27(x95625)+P22(f317(f317(f319(x95621),f638(x95622,x95623,x95624,x95621,x95625)),x95624))+~P22(f317(f317(f226(x95625),f317(f317(f52(x95621,x95625),x95624),x95623)),x95622)) % 168.22/168.07 [9593]~P66(x95935)+~P77(x95935)+P22(f317(f317(f319(x95931),f610(x95932,x95933,x95934,x95931,x95935)),f317(f166(x95931),x95934)))+P22(f317(f317(f225(x95935),f317(f160(x95935),f317(f317(f148(x95931,x95935),x95933),x95934))),f317(f160(x95935),f317(f317(f148(x95931,x95935),x95932),x95934)))) % 168.22/168.07 [9705]~P103(x97051)+~P27(x97051)+P22(f317(f317(f226(x97051),f317(x97052,f638(x97053,x97052,x97054,x97055,x97051))),x97053))+~P22(f317(f317(f226(x97051),f317(f317(f52(x97055,x97051),x97054),x97052)),x97053)) % 168.22/168.07 [9854]~P66(x98541)+~P77(x98541)+~P22(f317(f317(f225(x98541),f317(x98543,f610(x98545,x98543,x98544,x98542,x98541))),f317(x98545,f610(x98545,x98543,x98544,x98542,x98541))))+P22(f317(f317(f225(x98541),f317(f160(x98541),f317(f317(f148(x98542,x98541),x98543),x98544))),f317(f160(x98541),f317(f317(f148(x98542,x98541),x98545),x98544)))) % 168.22/168.07 [8543]~P70(x85431)+~P22(f317(f71(x85434),x85435))+~P22(f317(f317(f319(x85434),x85433),x85435))+E(f317(f317(f90(x85431),f317(x85432,x85433)),f317(f317(f9(x85434,x85431),x85432),f317(f317(f21(f858(x85434,a842)),x85435),f317(f317(f286(x85434),x85433),f188(f858(x85434,a842)))))),f317(f317(f9(x85434,x85431),x85432),x85435)) % 168.22/168.07 [8545]~P67(x85451)+~P22(f317(f71(x85454),x85455))+~P22(f317(f317(f319(x85454),x85453),x85455))+E(f317(f317(f89(x85451),f317(x85452,x85453)),f317(f317(f6(x85454,x85451),x85452),f317(f317(f21(f858(x85454,a842)),x85455),f317(f317(f286(x85454),x85453),f188(f858(x85454,a842)))))),f317(f317(f6(x85454,x85451),x85452),x85455)) % 168.22/168.07 [8598]~P13(x85981,x85984,x85985)+~P22(f317(f71(x85981),x85982))+E(f317(f317(f21(f858(x85981,a842)),x85982),f317(f317(f286(x85981),x85983),f188(f858(x85981,a842)))),f188(f858(x85981,a842)))+E(f317(f317(x85984,x85983),f317(x85985,f317(f317(f21(f858(x85981,a842)),x85982),f317(f317(f286(x85981),x85983),f188(f858(x85981,a842)))))),f317(x85985,f317(f317(f286(x85981),x85983),x85982))) % 168.22/168.07 [8966]~P67(x89661)+~P22(f317(f71(x89662),x89665))+~P22(f317(f71(x89662),x89664))+E(f317(f317(f89(x89661),f317(f317(f6(x89662,x89661),x89663),f317(f317(f122(f858(x89662,a842)),x89664),x89665))),f317(f317(f6(x89662,x89661),x89663),f317(f317(f113(f858(x89662,a842)),x89664),x89665))),f317(f317(f89(x89661),f317(f317(f6(x89662,x89661),x89663),x89664)),f317(f317(f6(x89662,x89661),x89663),x89665))) % 168.22/168.07 [8968]~P70(x89681)+~P22(f317(f71(x89682),x89685))+~P22(f317(f71(x89682),x89684))+E(f317(f317(f90(x89681),f317(f317(f9(x89682,x89681),x89683),f317(f317(f122(f858(x89682,a842)),x89684),x89685))),f317(f317(f9(x89682,x89681),x89683),f317(f317(f113(f858(x89682,a842)),x89684),x89685))),f317(f317(f90(x89681),f317(f317(f9(x89682,x89681),x89683),x89684)),f317(f317(f9(x89682,x89681),x89683),x89685))) % 168.22/168.07 [9106]~P25(x91061)+~P22(f317(f71(x91062),x91065))+~P22(f317(f71(x91062),x91064))+E(f317(f317(f21(x91061),f317(f317(f89(x91061),f317(f317(f6(x91062,x91061),x91063),x91064)),f317(f317(f6(x91062,x91061),x91063),x91065))),f317(f317(f6(x91062,x91061),x91063),f317(f317(f113(f858(x91062,a842)),x91064),x91065))),f317(f317(f6(x91062,x91061),x91063),f317(f317(f122(f858(x91062,a842)),x91064),x91065))) % 168.22/168.07 [9305]~P19(x93051,x93052,x93053,x93055)+~P19(x93051,x93052,x93053,x93054)+P19(x93051,x93052,x93053,f317(f317(f122(f858(x93051,a842)),x93054),x93055))+~E(f317(f317(f113(f858(x93052,a842)),f317(f287(x93051,x93052,x93053),f317(f317(f21(f858(x93051,a842)),x93054),x93055))),f317(f287(x93051,x93052,x93053),f317(f317(f21(f858(x93051,a842)),x93055),x93054))),f188(f858(x93052,a842))) % 168.22/168.07 [9414]E(x94141,f2(a1))+~P22(f317(f317(f226(a1),f2(a1)),x94143))+~P22(f317(f58(x94142,x94141),f317(f317(f237(a1,a1),x94144),x94145)))+P22(f317(f58(x94142,f317(f317(f90(a1),x94141),x94143)),f317(f317(f237(a1,a1),f317(f48(a1,x94144),x94143)),f317(f317(f89(a1),f317(f317(f90(a1),x94141),f55(a1,x94144,x94143))),x94145)))) % 168.22/168.07 [9422]~P22(f317(f317(f226(a849),f2(a849)),x94223))+~P22(f317(f317(f226(a849),f2(a849)),x94222))+~P22(f317(f57(x94221,x94222),f317(f317(f237(a849,a849),x94224),x94225)))+P22(f317(f57(x94221,f317(f317(f90(a849),x94222),x94223)),f317(f317(f237(a849,a849),f317(f48(a849,x94224),x94223)),f317(f317(f89(a849),f317(f317(f90(a849),x94222),f55(a849,x94224,x94223))),x94225)))) % 168.22/168.07 [9478]~P70(x94781)+~P22(f317(f71(x94782),x94785))+~P22(f317(f71(x94782),x94784))+E(f317(f317(f90(x94781),f317(f317(f317(f75(x94781,x94782,f90(x94781)),x94783),f87(x94781)),f317(f317(f122(f858(x94782,a842)),x94784),x94785))),f317(f317(f317(f75(x94781,x94782,f90(x94781)),x94783),f87(x94781)),f317(f317(f113(f858(x94782,a842)),x94784),x94785))),f317(f317(f90(x94781),f317(f317(f317(f75(x94781,x94782,f90(x94781)),x94783),f87(x94781)),x94784)),f317(f317(f317(f75(x94781,x94782,f90(x94781)),x94783),f87(x94781)),x94785))) % 168.22/168.07 [9480]~E(f317(f317(f167(x94801),x94805),x94802),f317(f317(f167(x94801),x94805),x94803))+P22(f317(f317(f319(f857(f850(x94801),f850(x94801))),f317(f317(f237(f850(x94801),f850(x94801)),x94802),x94803)),f141(x94801,x94804)))+~P22(f317(f317(f226(a849),x94805),f317(f317(f223(a849),f317(f189(f850(x94801)),x94802)),f317(f189(f850(x94801)),x94803))))+~P22(f317(f317(f319(f857(x94801,x94801)),f317(f317(f237(x94801,x94801),f317(f317(f159(x94801),x94802),x94805)),f317(f317(f159(x94801),x94803),x94805))),x94804)) % 168.22/168.07 [9581]~P110(x95815)+~P77(x95815)+P22(f317(f317(f319(x95811),f455(x95812,x95813,x95814,x95811,x95815)),x95814))+P22(f317(f317(f225(x95815),f317(f317(f6(x95811,x95815),x95813),x95814)),f317(f317(f90(x95815),f317(f112(x95815),f317(f54(x95811),x95814))),x95812))) % 168.22/168.07 [9780]~P110(x97801)+~P77(x97801)+~P22(f317(f317(f225(x97801),f317(x97803,f455(x97805,x97803,x97804,x97802,x97801))),x97805))+P22(f317(f317(f225(x97801),f317(f317(f6(x97802,x97801),x97803),x97804)),f317(f317(f90(x97801),f317(f112(x97801),f317(f54(x97802),x97804))),x97805))) % 168.22/168.07 [8570]E(f317(f317(f127(x85701),x85702),x85703),f317(f317(f127(x85701),x85704),x85705))+~E(f317(f317(f167(x85701),f317(f189(f850(x85701)),x85702)),x85704),x85702)+~E(f317(f317(f127(x85701),f317(f317(f132(x85701),f317(f189(f850(x85701)),x85702)),x85704)),x85705),x85703)+P22(f317(f317(f225(a849),f317(f189(f850(x85701)),x85704)),f317(f189(f850(x85701)),x85702))) % 168.22/168.07 [8688]E(f317(f317(f127(x86881),x86882),x86883),f317(f317(f127(x86881),x86884),x86885))+~E(f317(f317(f167(x86881),f317(f189(f850(x86881)),x86882)),x86884),x86882)+~E(x86883,f317(f317(f127(x86881),f317(f317(f132(x86881),f317(f189(f850(x86881)),x86882)),x86884)),x86885))+~P22(f317(f317(f225(a849),f317(f189(f850(x86881)),x86882)),f317(f189(f850(x86881)),x86884))) % 168.22/168.07 [9919]~P22(f317(x99195,x99194))+~P22(f317(f71(x99192),f317(f230(x99192),x99195)))+P22(f317(f71(x99191),f317(f230(x99191),f317(f317(f7(x99191,x99192,a842),x99193),x99194))))+~P22(f317(f71(x99191),f317(f230(x99191),f317(f317(f8(f858(x99192,a842),a842,x99191),f96(x99192)),f317(f317(f8(f858(x99192,a842),f858(x99192,a842),x99191),f317(f18(x99192,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99192),a315),x99195))),x99193))))) % 168.22/168.07 [8363]~P14(x83635,x83631,x83636,x83632)+E(f317(f82(x83631,x83631,x83631,f317(x83632,x83633)),f317(x83632,x83634)),f317(f82(x83631,x83631,x83631,f317(x83632,x83634)),f317(x83632,x83633)))+~P22(f317(f71(x83635),x83634))+~P22(f317(f71(x83635),x83633)) % 168.22/168.07 [7752]~P19(x77521,x77522,x77524,x77523)+~E(f317(x77524,x77526),x77525)+E(f317(f86(x77521,x77522,x77523,x77524),x77525),x77526)+~P22(f317(f317(f319(x77521),x77526),x77523)) % 168.22/168.07 [7938]~P15(x79386,x79381,x79384,x79382)+E(f317(f82(x79381,x79381,x79381,f317(x79382,x79383)),f317(x79384,x79385)),f317(x79382,x79383))+~P22(f317(f71(x79386),x79383))+~P22(f317(f317(f319(x79386),x79385),x79383)) % 168.22/168.07 [9152]~P14(x91523,x91521,x91526,x91522)+E(f317(f82(x91521,x91521,x91521,f317(x91522,f317(f317(f21(f858(x91523,a842)),x91524),f317(f317(f286(x91523),x91525),f188(f858(x91523,a842)))))),f317(x91526,x91525)),f317(x91522,x91524))+~P22(f317(f71(x91523),x91524))+~P22(f317(f317(f319(x91523),x91525),x91524)) % 168.22/168.07 [6837]~P55(x68371)+~E(f55(x68371,x68373,x68374),f55(x68371,x68376,x68374))+~E(f55(x68371,x68372,x68374),f55(x68371,x68375,x68374))+E(f55(x68371,f317(f317(f89(x68371),x68372),x68373),x68374),f55(x68371,f317(f317(f89(x68371),x68375),x68376),x68374)) % 168.22/168.07 [6838]~P26(x68381)+~E(f55(x68381,x68383,x68384),f55(x68381,x68386,x68384))+~E(f55(x68381,x68382,x68384),f55(x68381,x68385,x68384))+E(f55(x68381,f317(f317(f21(x68381),x68382),x68383),x68384),f55(x68381,f317(f317(f21(x68381),x68385),x68386),x68384)) % 168.22/168.07 [6839]~P55(x68391)+~E(f55(x68391,x68393,x68394),f55(x68391,x68396,x68394))+~E(f55(x68391,x68392,x68394),f55(x68391,x68395,x68394))+E(f55(x68391,f317(f317(f90(x68391),x68392),x68393),x68394),f55(x68391,f317(f317(f90(x68391),x68395),x68396),x68394)) % 168.22/168.07 [7709]~P27(x77091)+P22(f317(f317(f225(x77091),x77092),f317(x77093,x77094)))+~P22(f317(f317(f319(x77095),x77094),x77096))+~P22(f317(f317(f225(x77091),x77092),f317(f317(f52(x77095,x77091),x77096),x77093))) % 168.22/168.07 [7954]~P103(x79543)+~P22(f317(x79542,x79545))+~P29(x79543,f317(f317(f148(x79541,x79543),x79544),x79546))+E(f317(f130(x79541,x79542),f317(f317(f143(x79541,x79543,x79544),x79545),x79546)),f317(f317(f143(x79541,x79543,x79544),x79545),f317(f130(x79541,x79542),x79546))) % 168.22/168.07 [7977]E(x79771,x79772)+E(x79773,f2(a1))+~P22(f317(f58(x79774,x79773),f317(f317(f237(a1,a1),x79775),x79772)))+~P22(f317(f58(x79774,x79773),f317(f317(f237(a1,a1),x79776),x79771))) % 168.22/168.07 [7978]E(x79781,x79782)+E(x79783,f2(a1))+~P22(f317(f58(x79784,x79783),f317(f317(f237(a1,a1),x79782),x79785)))+~P22(f317(f58(x79784,x79783),f317(f317(f237(a1,a1),x79781),x79786))) % 168.22/168.07 [7998]~P14(x79982,x79985,x79986,x79981)+~P22(f317(f71(x79982),x79984))+E(f317(x79981,f317(f317(f286(x79982),x79983),x79984)),f317(f82(x79985,x79985,x79985,f317(x79981,x79984)),f317(x79986,x79983)))+P22(f317(f317(f319(x79982),x79983),x79984)) % 168.22/168.07 [8231]~P15(x82315,x82311,x82316,x82312)+E(f317(f82(x82311,x82311,x82311,f317(x82312,x82313)),f317(x82312,x82314)),f317(x82312,x82313))+~P22(f317(f71(x82315),x82313))+~P22(f317(f317(f225(f858(x82315,a842)),x82314),x82313)) % 168.22/168.07 [9350]~P19(x93501,x93502,x93504,x93503)+~P22(f317(f317(f319(x93502),x93505),f317(f287(x93501,x93502,x93504),x93503)))+P22(f317(f317(f319(x93501),f317(f86(x93501,x93502,x93503,x93504),x93505)),x93506))+~P22(f317(f317(f225(f858(x93501,a842)),x93503),x93506)) % 168.22/168.07 [9720]~P67(x97202)+~E(f477(x97201,x97203,x97205,x97206,x97204,x97202),f478(x97201,x97203,x97205,x97206,x97204,x97202))+~P22(f317(f71(x97204),x97206))+E(f317(f317(f6(x97201,x97202),x97203),f317(f287(x97204,x97201,x97205),x97206)),f317(f317(f6(x97204,x97202),f317(f82(x97201,x97202,x97204,x97203),x97205)),x97206)) % 168.22/168.07 [9758]~P67(x97586)+E(f317(x97581,f477(x97582,x97583,x97581,x97584,x97585,x97586)),f317(x97581,f478(x97582,x97583,x97581,x97584,x97585,x97586)))+E(f317(f317(f6(x97582,x97586),x97583),f317(f287(x97585,x97582,x97581),x97584)),f317(f317(f6(x97585,x97586),f317(f82(x97582,x97586,x97585,x97583),x97581)),x97584))+~P22(f317(f71(x97585),x97584)) % 168.22/168.07 [9803]~P67(x98032)+~E(f317(x98033,f317(x98035,f478(x98031,x98033,x98035,x98036,x98034,x98032))),f2(x98032))+~P22(f317(f71(x98034),x98036))+E(f317(f317(f6(x98031,x98032),x98033),f317(f287(x98034,x98031,x98035),x98036)),f317(f317(f6(x98034,x98032),f317(f82(x98031,x98032,x98034,x98033),x98035)),x98036)) % 168.22/168.07 [9864]~P67(x98642)+~P22(f317(f71(x98644),x98646))+E(f317(f317(f6(x98641,x98642),x98643),f317(f287(x98644,x98641,x98645),x98646)),f317(f317(f6(x98644,x98642),f317(f82(x98641,x98642,x98644,x98643),x98645)),x98646))+P22(f317(f317(f319(x98644),f478(x98641,x98643,x98645,x98646,x98644,x98642)),x98646)) % 168.22/168.07 [9865]~P67(x98652)+~P22(f317(f71(x98654),x98656))+E(f317(f317(f6(x98651,x98652),x98653),f317(f287(x98654,x98651,x98655),x98656)),f317(f317(f6(x98654,x98652),f317(f82(x98651,x98652,x98654,x98653),x98655)),x98656))+P22(f317(f317(f319(x98654),f477(x98651,x98653,x98655,x98656,x98654,x98652)),x98656)) % 168.22/168.07 [9977]~P70(x99771)+~P22(f317(f71(x99772),x99776))+E(f317(f317(f317(f75(x99771,x99772,f90(x99771)),f317(f317(f18(x99772,f858(x99773,a842),x99771),f317(f317(f7(x99772,x99771,f858(f858(x99773,a842),x99771)),f317(f317(f8(f858(x99773,x99771),f858(x99771,f858(f858(x99773,a842),x99771)),x99772),f75(x99771,x99773,f90(x99771))),x99774)),f87(x99771))),x99775)),f87(x99771)),x99776),f317(f317(f317(f75(x99771,f857(x99772,x99773),f90(x99771)),f317(f247(x99772,x99773,x99771),x99774)),f87(x99771)),f317(f317(f245(x99772,x99773),x99776),x99775)))+P22(f317(f317(f319(x99772),f526(x99774,x99775,x99773,x99776,x99772,x99771)),x99776)) % 168.22/168.07 [9997]~P70(x99971)+~P22(f317(f71(x99972),x99976))+E(f317(f317(f317(f75(x99971,x99972,f90(x99971)),f317(f317(f18(x99972,f858(x99973,a842),x99971),f317(f317(f7(x99972,x99971,f858(f858(x99973,a842),x99971)),f317(f317(f8(f858(x99973,x99971),f858(x99971,f858(f858(x99973,a842),x99971)),x99972),f75(x99971,x99973,f90(x99971))),x99974)),f87(x99971))),x99975)),f87(x99971)),x99976),f317(f317(f317(f75(x99971,f857(x99972,x99973),f90(x99971)),f317(f247(x99972,x99973,x99971),x99974)),f87(x99971)),f317(f317(f245(x99972,x99973),x99976),x99975)))+~P22(f317(f71(x99973),f317(x99975,f526(x99974,x99975,x99973,x99976,x99972,x99971)))) % 168.22/168.07 [8140]~P15(x81402,x81405,x81406,x81401)+~P22(f317(f71(x81402),x81404))+~P22(f317(f71(x81402),x81403))+E(f317(x81401,f317(f317(f122(f858(x81402,a842)),x81403),x81404)),f317(f82(x81405,x81405,x81405,f317(x81401,x81403)),f317(x81401,x81404))) % 168.22/168.07 [8364]~P27(x83641)+P22(f317(f317(f225(x83641),f317(x83642,x83643)),x83644))+~P22(f317(f317(f319(x83645),x83643),x83646))+~P22(f317(f317(f225(x83641),f317(f317(f51(x83645,x83641),x83646),x83642)),x83644)) % 168.22/168.07 [8765]~P19(x87652,x87651,x87653,x87656)+E(f317(f317(f21(f858(x87651,a842)),f317(f287(x87652,x87651,x87653),x87654)),f317(f287(x87652,x87651,x87653),x87655)),f317(f287(x87652,x87651,x87653),f317(f317(f21(f858(x87652,a842)),x87654),x87655)))+~P22(f317(f317(f225(f858(x87652,a842)),x87655),x87656))+~P22(f317(f317(f225(f858(x87652,a842)),x87654),x87656)) % 168.22/168.07 [8766]~P19(x87662,x87661,x87663,x87666)+E(f317(f317(f113(f858(x87661,a842)),f317(f287(x87662,x87661,x87663),x87664)),f317(f287(x87662,x87661,x87663),x87665)),f317(f287(x87662,x87661,x87663),f317(f317(f113(f858(x87662,a842)),x87664),x87665)))+~P22(f317(f317(f225(f858(x87662,a842)),x87665),x87666))+~P22(f317(f317(f225(f858(x87662,a842)),x87664),x87666)) % 168.22/168.07 [8803]~P22(f317(x88031,x88033))+~P22(f317(f317(f317(f317(a197,x88032),x88033),x88034),x88036))+~P22(f317(f317(f317(f317(a197,f35(x88031,x88032)),x88036),x88034),x88035))+P22(f317(f317(f317(f317(a197,f35(x88031,x88032)),x88033),x88034),x88035)) % 168.22/168.07 [9031]E(x90311,x90312)+~P49(x90313,x90314,x90315)+~P22(f317(f317(f319(f857(x90313,x90314)),f317(f317(f237(x90313,x90314),x90316),x90312)),x90315))+~P22(f317(f317(f319(f857(x90313,x90314)),f317(f317(f237(x90313,x90314),x90316),x90311)),x90315)) % 168.22/168.07 [9647]~P67(x96471)+~P22(f317(f71(x96473),x96476))+~P22(f317(f71(x96472),x96475))+E(f317(f317(f89(x96471),f317(f317(f6(x96472,x96471),f317(f82(f856(x96472,x96473),x96471,x96472,x96474),f288(x96472,x96473))),x96475)),f317(f317(f6(x96473,x96471),f317(f82(f856(x96472,x96473),x96471,x96473,x96474),f297(x96473,x96472))),x96476)),f317(f317(f6(f856(x96472,x96473),x96471),x96474),f298(x96472,x96473,x96475,x96476))) % 168.22/168.07 [9798]~P64(x97981)+~E(f317(x97983,f744(x97984,x97986,x97983,x97985,x97982,x97981)),f317(x97986,f744(x97984,x97986,x97983,x97985,x97982,x97981)))+~P22(f317(f71(x97982),x97985))+E(f317(f317(f317(f75(x97981,x97982,f90(x97981)),x97983),x97984),x97985),f317(f317(f317(f75(x97981,x97982,f90(x97981)),x97986),x97984),x97985)) % 168.22/168.07 [9861]~P64(x98611)+~P22(f317(f71(x98612),x98615))+E(f317(f317(f317(f75(x98611,x98612,f90(x98611)),x98613),x98614),x98615),f317(f317(f317(f75(x98611,x98612,f90(x98611)),x98616),x98614),x98615))+P22(f317(f317(f319(x98612),f744(x98614,x98613,x98616,x98615,x98612,x98611)),x98615)) % 168.22/168.07 [8583]~P64(x85831)+~P22(f317(f71(x85832),x85836))+P22(f317(f317(f319(x85832),x85835),x85836))+E(f317(f317(f317(f75(x85831,x85832,f90(x85831)),x85833),x85834),f317(f317(f286(x85832),x85835),x85836)),f317(f317(f90(x85831),f317(x85833,x85835)),f317(f317(f317(f75(x85831,x85832,f90(x85831)),x85833),x85834),x85836))) % 168.22/168.07 [8629]~P6(x86291,x86296,x86293)+~P9(x86291,f858(x86292,a842),x86293,x86295)+~P22(f317(f317(f319(x86291),x86294),x86296))+E(f317(f317(f51(x86291,f858(x86292,a842)),f317(f262(x86291,x86291,x86293),f317(f317(f286(x86291),x86294),f188(f858(x86291,a842))))),x86295),f317(x86295,x86294)) % 168.22/168.07 [9043]~P14(x90433,x90431,x90436,x90432)+~P22(f317(f71(x90433),x90435))+~P22(f317(f71(x90433),x90434))+E(f317(f82(x90431,x90431,x90431,f317(x90432,f317(f317(f122(f858(x90433,a842)),x90434),x90435))),f317(x90432,f317(f317(f113(f858(x90433,a842)),x90434),x90435))),f317(f82(x90431,x90431,x90431,f317(x90432,x90434)),f317(x90432,x90435))) % 168.22/168.07 [9369]~E(x93693,f317(f317(f153(x93691,x93692),x93695),x93696))+P22(f317(f317(f319(f857(f850(x93691),f850(x93691))),f317(f317(f237(f850(x93691),f850(x93691)),x93692),x93693)),f151(x93691,x93694)))+~P22(f317(f317(f226(a849),x93695),f317(f189(f850(x93691)),x93692)))+~P22(f317(f317(f319(f857(x93691,x93691)),f317(f317(f237(x93691,x93691),f317(f317(f159(x93691),x93692),x93695)),x93696)),x93694)) % 168.22/168.07 [9878]~P70(x98782)+~P22(f317(f71(x98781),x98786))+P22(f317(f317(f319(x98781),f527(x98784,x98785,x98783,x98786,x98781,x98782)),x98786))+E(f317(f317(f9(x98781,x98782),f317(f317(f18(x98781,f858(x98783,a842),x98782),f317(f317(f8(f858(x98783,x98782),f858(f858(x98783,a842),x98782),x98781),f9(x98783,x98782)),x98784)),x98785)),x98786),f317(f317(f9(f857(x98781,x98783),x98782),f317(f247(x98781,x98783,x98782),x98784)),f317(f317(f245(x98781,x98783),x98786),x98785))) % 168.22/168.07 [9879]~P67(x98792)+~P22(f317(f71(x98791),x98796))+P22(f317(f317(f319(x98791),f528(x98794,x98795,x98793,x98796,x98791,x98792)),x98796))+E(f317(f317(f6(x98791,x98792),f317(f317(f18(x98791,f858(x98793,a842),x98792),f317(f317(f8(f858(x98793,x98792),f858(f858(x98793,a842),x98792),x98791),f6(x98793,x98792)),x98794)),x98795)),x98796),f317(f317(f6(f857(x98791,x98793),x98792),f317(f247(x98791,x98793,x98792),x98794)),f317(f317(f245(x98791,x98793),x98796),x98795))) % 168.22/168.07 [9916]~P70(x99162)+~P22(f317(f71(x99161),x99166))+~P22(f317(f71(x99163),f317(x99165,f527(x99164,x99165,x99163,x99166,x99161,x99162))))+E(f317(f317(f9(x99161,x99162),f317(f317(f18(x99161,f858(x99163,a842),x99162),f317(f317(f8(f858(x99163,x99162),f858(f858(x99163,a842),x99162),x99161),f9(x99163,x99162)),x99164)),x99165)),x99166),f317(f317(f9(f857(x99161,x99163),x99162),f317(f247(x99161,x99163,x99162),x99164)),f317(f317(f245(x99161,x99163),x99166),x99165))) % 168.22/168.07 [9917]~P67(x99172)+~P22(f317(f71(x99171),x99176))+~P22(f317(f71(x99173),f317(x99175,f528(x99174,x99175,x99173,x99176,x99171,x99172))))+E(f317(f317(f6(x99171,x99172),f317(f317(f18(x99171,f858(x99173,a842),x99172),f317(f317(f8(f858(x99173,x99172),f858(f858(x99173,a842),x99172),x99171),f6(x99173,x99172)),x99174)),x99175)),x99176),f317(f317(f6(f857(x99171,x99173),x99172),f317(f247(x99171,x99173,x99172),x99174)),f317(f317(f245(x99171,x99173),x99176),x99175))) % 168.22/168.07 [9899]~P70(x98992)+~P22(f317(f71(x98991),x98996))+P22(f317(f317(f319(x98991),x98993),x98996))+E(f317(f317(f9(x98991,x98992),f317(f317(f7(x98991,x98992,x98992),f317(f317(f18(x98991,x98992,f858(x98992,x98992)),f317(f317(f8(a842,f858(x98992,f858(x98992,x98992)),x98991),f108(x98992)),f317(f317(f7(x98991,x98991,a842),a314),x98993))),x98994)),x98995)),x98996),f317(f317(f238(x98992),x98995),f317(f54(x98991),x98996))) % 168.22/168.07 [9904]~P70(x99042)+~P22(f317(f71(x99041),x99046))+~P22(f317(f317(f319(x99041),x99043),x99046))+E(f317(f317(f9(x99041,x99042),f317(f317(f7(x99041,x99042,x99042),f317(f317(f18(x99041,x99042,f858(x99042,x99042)),f317(f317(f8(a842,f858(x99042,f858(x99042,x99042)),x99041),f108(x99042)),f317(f317(f7(x99041,x99041,a842),a314),x99043))),x99044)),x99045)),x99046),f317(f317(f90(x99042),f317(x99044,x99043)),f317(f317(f238(x99042),x99045),f317(f317(f21(a849),f317(f54(x99041),x99046)),f87(a849))))) % 168.22/168.07 [9969]~P22(f317(f71(x99691),x99695))+~P22(f317(f71(x99692),x99693))+P22(f317(f317(f319(x99692),f552(x99696,x99694,x99693,x99692,x99695,x99691)),x99693))+E(f317(f317(f6(x99691,a849),f317(f317(f8(f858(x99692,a842),a849,x99691),f54(x99692)),f317(f317(f8(f858(x99692,a842),f858(x99692,a842),x99691),f230(x99692)),f317(f317(f8(f858(x99692,a842),f858(x99692,a842),x99691),f317(f18(x99692,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99692),a315),f317(f317(f7(x99692,f858(x99692,a842),a842),f319(x99692)),x99693)))),x99694)))),x99695),f317(f317(f90(a849),x99696),f317(f54(x99692),x99693))) % 168.22/168.07 [9970]~P22(f317(f71(x99701),x99705))+~P22(f317(f71(x99702),x99703))+P22(f317(f317(f319(x99702),f553(x99706,x99704,x99703,x99702,x99705,x99701)),x99703))+E(f317(f317(f6(x99701,a849),f317(f317(f8(f858(x99702,a842),a849,x99701),f54(x99702)),f317(f317(f8(f858(x99702,a842),f858(x99702,a842),x99701),f230(x99702)),f317(f317(f8(f858(x99702,a842),f858(x99702,a842),x99701),f317(f18(x99702,a842,a842),f317(f317(f8(a842,f858(a842,a842),x99702),a315),f317(f317(f7(x99702,f858(x99702,a842),a842),f319(x99702)),x99703)))),x99704)))),x99705),f317(f317(f6(x99702,a849),x99706),x99703)) % 168.22/168.07 [10001]~P22(f317(f71(x100012),x100013))+~P22(f317(f71(x100011),x100015))+~E(f317(f54(x100011),f317(f230(x100011),f317(f317(f18(x100011,a842,a842),f317(f317(f8(a842,f858(a842,a842),x100011),a315),f317(f317(f7(x100011,f858(x100011,a842),a842),f319(x100011)),x100015))),f317(f317(f7(x100011,x100012,a842),x100014),f552(x100016,x100014,x100013,x100012,x100015,x100011))))),x100016)+E(f317(f317(f6(x100011,a849),f317(f317(f8(f858(x100012,a842),a849,x100011),f54(x100012)),f317(f317(f8(f858(x100012,a842),f858(x100012,a842),x100011),f230(x100012)),f317(f317(f8(f858(x100012,a842),f858(x100012,a842),x100011),f317(f18(x100012,a842,a842),f317(f317(f8(a842,f858(a842,a842),x100012),a315),f317(f317(f7(x100012,f858(x100012,a842),a842),f319(x100012)),x100013)))),x100014)))),x100015),f317(f317(f90(a849),x100016),f317(f54(x100012),x100013))) % 168.22/168.07 [10003]~P22(f317(f71(x100032),x100033))+~P22(f317(f71(x100031),x100035))+~E(f317(f54(x100031),f317(f230(x100031),f317(f317(f18(x100031,a842,a842),f317(f317(f8(a842,f858(a842,a842),x100031),a315),f317(f317(f7(x100031,f858(x100031,a842),a842),f319(x100031)),x100035))),f317(f317(f7(x100031,x100032,a842),x100034),f553(x100036,x100034,x100033,x100032,x100035,x100031))))),f317(x100036,f553(x100036,x100034,x100033,x100032,x100035,x100031)))+E(f317(f317(f6(x100031,a849),f317(f317(f8(f858(x100032,a842),a849,x100031),f54(x100032)),f317(f317(f8(f858(x100032,a842),f858(x100032,a842),x100031),f230(x100032)),f317(f317(f8(f858(x100032,a842),f858(x100032,a842),x100031),f317(f18(x100032,a842,a842),f317(f317(f8(a842,f858(a842,a842),x100032),a315),f317(f317(f7(x100032,f858(x100032,a842),a842),f319(x100032)),x100033)))),x100034)))),x100035),f317(f317(f6(x100032,a849),x100036),x100033)) % 168.22/168.07 [9447]P22(f317(x94471,x94472))+~P22(f317(f317(f319(x94477),x94472),f317(x94476,x94474)))+~P22(f317(x94471,f485(x94471,x94476,x94475,x94473,x94477)))+~P22(f317(f317(f319(x94473),x94474),x94475)) % 168.22/168.07 [9346]~P64(x93461)+~P19(x93465,x93462,x93466,x93467)+~P22(f317(f71(x93465),x93467))+E(f317(f317(f317(f75(x93461,x93462,f90(x93461)),x93463),x93464),f317(f287(x93465,x93462,x93466),x93467)),f317(f317(f317(f75(x93461,x93465,f90(x93461)),f317(f82(x93462,x93461,x93465,x93463),x93466)),x93464),x93467)) % 168.22/168.07 [9472]~E(f317(f317(f286(x94721),x94725),x94726),f317(f317(f286(x94721),x94722),x94723))+~P22(f317(f76(x94721,x94721,x94724,x94722,x94723),x94727))+P22(f317(f317(f319(x94721),x94722),x94723))+P22(f317(f72(x94721,x94724,f317(f317(f286(x94721),x94725),x94726)),x94727)) % 168.22/168.07 [9551]P22(f317(x95511,x95512))+~P22(f317(f317(f319(x95513),x95512),f317(x95514,x95517)))+~P22(f317(f317(f319(x95516),x95517),x95515))+P22(f317(f317(f319(x95513),f485(x95511,x95514,x95515,x95516,x95513)),f317(f317(f51(x95516,f858(x95513,a842)),x95515),x95514))) % 168.22/168.07 [9563]~P19(x95632,x95631,x95635,x95634)+~P19(x95631,x95633,x95636,f317(f287(x95632,x95631,x95635),x95634))+E(f317(f317(f82(x95631,x95632,x95633,f86(x95632,x95631,x95634,x95635)),f86(x95631,x95633,f317(f287(x95632,x95631,x95635),x95634),x95636)),x95637),f317(f86(x95632,x95633,x95634,f317(f82(x95631,x95633,x95632,x95636),x95635)),x95637))+~P22(f317(f317(f319(x95633),x95637),f317(f287(x95631,x95633,x95636),f317(f287(x95632,x95631,x95635),x95634)))) % 168.22/168.07 [9620]E(x96201,f2(a1))+~P22(f317(f58(x96203,x96201),f317(f317(f237(a1,a1),x96205),x96207)))+~P22(f317(f58(x96202,x96201),f317(f317(f237(a1,a1),x96204),x96206)))+P22(f317(f58(f317(f317(f89(a1),x96202),x96203),x96201),f317(f317(f237(a1,a1),f317(f317(f89(a1),f317(f317(f89(a1),x96204),x96205)),f317(f48(a1,f317(f317(f89(a1),x96206),x96207)),x96201))),f55(a1,f317(f317(f89(a1),x96206),x96207),x96201)))) % 168.22/168.07 [9626]~P22(f317(f317(f226(a849),f2(a849)),x96263))+~P22(f317(f57(x96262,x96263),f317(f317(f237(a849,a849),x96265),x96267)))+~P22(f317(f57(x96261,x96263),f317(f317(f237(a849,a849),x96264),x96266)))+P22(f317(f57(f317(f317(f89(a849),x96261),x96262),x96263),f317(f317(f237(a849,a849),f317(f317(f89(a849),f317(f317(f89(a849),x96264),x96265)),f317(f48(a849,f317(f317(f89(a849),x96266),x96267)),x96263))),f55(a849,f317(f317(f89(a849),x96266),x96267),x96263)))) % 168.22/168.07 [10000]~P67(x100002)+~P22(f317(f71(x100003),x100005))+~P22(f317(f71(x100001),x100007))+E(f317(f317(f6(x100001,x100002),f317(f317(f18(x100001,f858(x100003,a842),x100002),f317(f317(f8(f858(x100003,x100002),f858(f858(x100003,a842),x100002),x100001),f6(x100003,x100002)),x100004)),f317(f317(f8(f858(x100003,a842),f858(x100003,a842),x100001),f230(x100003)),f317(f317(f8(f858(x100003,a842),f858(x100003,a842),x100001),f317(f18(x100003,a842,a842),f317(f317(f8(a842,f858(a842,a842),x100003),a315),f317(f317(f7(x100003,f858(x100003,a842),a842),f319(x100003)),x100005)))),x100006)))),x100007),f317(f317(f6(x100003,x100002),f317(f317(f18(x100003,f858(x100001,a842),x100002),f317(f317(f8(f858(x100001,x100002),f858(f858(x100001,a842),x100002),x100003),f6(x100001,x100002)),f317(f7(x100001,x100003,x100002),x100004))),f317(f317(f8(f858(x100001,a842),f858(x100001,a842),x100003),f230(x100001)),f317(f317(f8(f858(x100001,a842),f858(x100001,a842),x100003),f317(f18(x100001,a842,a842),f317(f317(f8(a842,f858(a842,a842),x100001),a315),f317(f317(f7(x100001,f858(x100001,a842),a842),f319(x100001)),x100007)))),f317(f7(x100001,x100003,a842),x100006))))),x100005)) % 168.22/168.07 [9511]~P10(x95116,x95111,x95112,x95118,x95113,x95114)+~P6(x95116,x95117,x95118)+P9(x95111,x95112,x95113,f317(x95114,x95115))+~P22(f317(f317(f319(x95116),x95115),x95117)) % 168.22/168.07 [7955]~P30(x79558,x79557,f317(f317(f317(f100(x79558),x79554),x79556),x79551))+P22(f317(f317(x79551,x79552),x79553))+~P22(f317(f317(x79554,x79552),x79555))+~P22(f317(f317(f317(f317(a197,x79556),x79555),x79557),x79553)) % 168.22/168.07 [9135]~P14(x91357,x91351,x91358,x91353)+~P22(f317(f71(x91357),x91355))+~P22(f317(f71(x91357),x91354))+E(f317(f82(x91351,x91351,x91352,f317(x91353,x91354)),f317(f82(x91351,x91351,x91352,f317(x91353,x91355)),x91356)),f317(f82(x91351,x91351,x91352,f317(x91353,x91355)),f317(f82(x91351,x91351,x91352,f317(x91353,x91354)),x91356))) % 168.22/168.07 [9142]~P35(x91421,x91422,x91423,x91424,x91427)+P35(x91421,x91422,x91423,f317(f317(f153(x91421,x91424),x91425),x91426),f317(f317(f153(x91422,x91427),x91425),x91428))+~P22(f317(f317(x91423,x91426),x91428))+~P22(f317(f317(f226(a849),x91425),f317(f189(f850(x91421)),x91424))) % 168.22/168.07 [9143]~P35(x91431,x91432,x91433,x91434,x91437)+P35(x91431,x91432,x91433,f317(f317(f153(x91431,x91434),x91435),x91436),f317(f317(f153(x91432,x91437),x91435),x91438))+~P22(f317(f317(x91433,x91436),x91438))+~P22(f317(f317(f226(a849),x91435),f317(f189(f850(x91432)),x91437))) % 168.22/168.07 [9220]~P19(x92202,x92202,x92205,x92206)+~P16(x92203,x92202,x92207,x92208,x92201)+~P22(f317(f71(x92202),x92206))+E(f317(f317(x92201,f317(f82(x92202,x92203,x92202,x92204),x92205)),x92206),f317(f317(x92201,x92204),f317(f287(x92202,x92202,x92205),x92206))) % 168.22/168.07 [9509]~P17(x95097,x95092,x95095,x95098,x95096,x95091)+~P22(f317(f71(x95092),x95094))+E(f317(x95091,f317(f317(f286(x95092),x95093),x95094)),f317(f317(x95095,f317(x95096,x95093)),f317(x95091,x95094)))+P22(f317(f317(f319(x95092),x95093),x95094)) % 168.22/168.07 [9121]P22(f317(f317(f319(f857(f850(x91211),f850(x91211))),f317(f317(f237(f850(x91211),f850(x91211)),x91212),x91213)),f151(x91211,x91214)))+~E(x91213,f317(f317(f127(x91211),x91215),f317(f317(f145(x91211),x91216),x91217)))+~E(x91212,f317(f317(f127(x91211),x91215),f317(f317(f145(x91211),x91218),x91217)))+~P22(f317(f317(f319(f857(x91211,x91211)),f317(f317(f237(x91211,x91211),x91218),x91216)),x91214)) % 168.22/168.07 [10038]~P19(x100384,x100382,x100385,x100388)+E(f317(f317(f52(x100381,f858(x100382,a842)),x100383),f317(f317(f8(f858(x100384,a842),f858(x100382,a842),x100381),f287(x100384,x100382,x100385)),x100386)),f317(f287(x100384,x100382,x100385),f317(f317(f52(x100381,f858(x100384,a842)),x100383),x100386)))+~P22(f317(f317(f319(x100381),x100387),x100383))+P22(f317(f317(f319(x100381),f671(x100387,x100386,x100383,x100381,x100388,x100385,x100382,x100384)),x100383)) % 168.22/168.07 [10060]~P19(x100604,x100602,x100605,x100607)+E(f317(f317(f52(x100601,f858(x100602,a842)),x100603),f317(f317(f8(f858(x100604,a842),f858(x100602,a842),x100601),f287(x100604,x100602,x100605)),x100606)),f317(f287(x100604,x100602,x100605),f317(f317(f52(x100601,f858(x100604,a842)),x100603),x100606)))+~P22(f317(f317(f319(x100601),x100608),x100603))+~P22(f317(f317(f225(f858(x100604,a842)),f317(x100606,f671(x100608,x100606,x100603,x100601,x100607,x100605,x100602,x100604))),x100607)) % 168.22/168.07 [9571]~P17(x95717,x95715,x95711,x95718,x95712,x95714)+~P22(f317(f71(x95715),x95716))+~P22(f317(f317(f319(x95715),x95713),x95716))+E(f317(f317(x95711,f317(x95712,x95713)),f317(x95714,f317(f317(f21(f858(x95715,a842)),x95716),f317(f317(f286(x95715),x95713),f188(f858(x95715,a842)))))),f317(x95714,x95716)) % 168.22/168.07 [9579]~P17(x95796,x95793,x95791,x95797,x95798,x95792)+~P22(f317(f71(x95793),x95795))+~P22(f317(f71(x95793),x95794))+E(f317(f317(x95791,f317(x95792,f317(f317(f122(f858(x95793,a842)),x95794),x95795))),f317(x95792,f317(f317(f113(f858(x95793,a842)),x95794),x95795))),f317(f317(x95791,f317(x95792,x95794)),f317(x95792,x95795))) % 168.22/168.07 [9670]P41(x96701,x96702,x96703,x96704,x96705,f317(f317(x96703,x96706),x96707))+~P41(x96701,x96702,x96703,x96704,f317(f317(f21(f858(x96701,a842)),x96705),f317(f317(f286(x96701),x96708),f188(f858(x96701,a842)))),x96709)+~E(f317(f317(x96703,x96706),x96707),f317(f317(x96703,x96708),x96709))+~P22(f317(f317(f319(x96701),x96708),x96705)) % 168.22/168.07 [10076]P18(x100761,x100762,f317(f317(f286(f848(x100761)),f317(f317(f317(f100(x100761),f317(x100763,f357(x100764,x100765,x100766,x100767,x100763,x100762,x100761,x100768,x100769))),f317(x100767,f357(x100764,x100765,x100766,x100767,x100763,x100762,x100761,x100768,x100769))),f317(x100766,f357(x100764,x100765,x100766,x100767,x100763,x100762,x100761,x100768,x100769)))),f188(f858(f848(x100761),a842))))+~P22(f317(f71(x100769),x100768))+~P18(x100761,x100762,f317(f287(x100769,f848(x100761),f317(f317(f18(x100769,f858(x100761,f858(a845,a842)),f848(x100761)),f317(f317(f18(x100769,a843,f858(f858(x100761,f858(a845,a842)),f848(x100761))),f317(f317(f8(f858(x100761,f858(a845,a842)),f858(a843,f858(f858(x100761,f858(a845,a842)),f848(x100761))),x100769),f100(x100761)),x100763)),x100767)),x100766)),x100768))+P18(x100761,x100762,f317(f287(x100769,f848(x100761),f317(f317(f18(x100769,f858(x100761,f858(a845,a842)),f848(x100761)),f317(f317(f18(x100769,a843,f858(f858(x100761,f858(a845,a842)),f848(x100761))),f317(f317(f8(f858(x100761,f858(a845,a842)),f858(a843,f858(f858(x100761,f858(a845,a842)),f848(x100761))),x100769),f100(x100761)),x100765)),x100767)),x100764)),x100768)) % 168.22/168.07 [10077]~P18(x100771,x100772,f317(f317(f286(f848(x100771)),f317(f317(f317(f100(x100771),f317(x100774,f357(x100776,x100774,x100778,x100775,x100779,x100772,x100771,x100777,x100773))),f317(x100775,f357(x100776,x100774,x100778,x100775,x100779,x100772,x100771,x100777,x100773))),f317(x100776,f357(x100776,x100774,x100778,x100775,x100779,x100772,x100771,x100777,x100773)))),f188(f858(f848(x100771),a842))))+~P22(f317(f71(x100773),x100777))+~P18(x100771,x100772,f317(f287(x100773,f848(x100771),f317(f317(f18(x100773,f858(x100771,f858(a845,a842)),f848(x100771)),f317(f317(f18(x100773,a843,f858(f858(x100771,f858(a845,a842)),f848(x100771))),f317(f317(f8(f858(x100771,f858(a845,a842)),f858(a843,f858(f858(x100771,f858(a845,a842)),f848(x100771))),x100773),f100(x100771)),x100779)),x100775)),x100778)),x100777))+P18(x100771,x100772,f317(f287(x100773,f848(x100771),f317(f317(f18(x100773,f858(x100771,f858(a845,a842)),f848(x100771)),f317(f317(f18(x100773,a843,f858(f858(x100771,f858(a845,a842)),f848(x100771))),f317(f317(f8(f858(x100771,f858(a845,a842)),f858(a843,f858(f858(x100771,f858(a845,a842)),f848(x100771))),x100773),f100(x100771)),x100774)),x100775)),x100776)),x100777)) % 168.22/168.07 [9605]~P10(x96056,x96057,x96058,x96059,x960510,x96051)+E(f317(f317(x96051,x96052),x96053),f317(f317(x96051,x96054),x96055))+~P22(f317(f317(f319(f857(x96057,x96057)),f317(f317(f237(x96057,x96057),x96053),x96055)),x960510))+~P22(f317(f317(f319(f857(x96056,x96056)),f317(f317(f237(x96056,x96056),x96052),x96054)),x96059)) % 168.22/168.07 [9222]~P93(x92222)+E(x92221,f188(f858(x92222,a842)))+~P22(f317(f71(x92222),x92221))+P22(f317(f317(f319(x92222),f11(x92222,x92221)),x92221))+~P22(f317(f317(f319(x92222),f317(f317(f113(x92222),f370(x92221,x92222)),f373(x92221,x92222))),f317(f317(f286(x92222),f370(x92221,x92222)),f317(f317(f286(x92222),f373(x92221,x92222)),f188(f858(x92222,a842)))))) % 168.22/168.07 [9223]~P93(x92232)+E(x92231,f188(f858(x92232,a842)))+~P22(f317(f71(x92232),x92231))+P22(f317(f317(f319(x92232),f10(x92232,x92231)),x92231))+~P22(f317(f317(f319(x92232),f317(f317(f122(x92232),f374(x92231,x92232)),f375(x92231,x92232))),f317(f317(f286(x92232),f374(x92231,x92232)),f317(f317(f286(x92232),f375(x92231,x92232)),f188(f858(x92232,a842)))))) % 168.22/168.07 [9254]~P64(x92542)+E(x92541,f188(f858(x92542,a842)))+~P22(f317(f71(x92542),x92541))+P22(f317(f317(f319(x92542),f317(f73(x92542,f90(x92542)),x92541)),x92541))+~P22(f317(f317(f319(x92542),f317(f317(f90(x92542),f529(x92541,x92542)),f530(x92541,x92542))),f317(f317(f286(x92542),f529(x92541,x92542)),f317(f317(f286(x92542),f530(x92541,x92542)),f188(f858(x92542,a842)))))) % 168.22/168.07 [9261]~P103(x92612)+E(x92611,f188(f858(x92612,a842)))+~P22(f317(f71(x92612),x92611))+P22(f317(f317(f319(x92612),f12(x92612,f224(x92612),x92611)),x92611))+~P22(f317(f317(f319(x92612),f317(f317(f224(x92612),f380(x92611,x92612)),f381(x92611,x92612))),f317(f317(f286(x92612),f380(x92611,x92612)),f317(f317(f286(x92612),f381(x92611,x92612)),f188(f858(x92612,a842)))))) % 168.22/168.07 [9262]~P103(x92622)+E(x92621,f188(f858(x92622,a842)))+~P22(f317(f71(x92622),x92621))+P22(f317(f317(f319(x92622),f13(x92622,f223(x92622),x92621)),x92621))+~P22(f317(f317(f319(x92622),f317(f317(f223(x92622),f382(x92621,x92622)),f383(x92621,x92622))),f317(f317(f286(x92622),f382(x92621,x92622)),f317(f317(f286(x92622),f383(x92621,x92622)),f188(f858(x92622,a842)))))) % 168.22/168.07 [6418]~P80(x64182)+E(x64181,f2(x64182))+~E(f317(f317(f89(x64182),x64183),x64181),f2(x64182))+~P22(f317(f317(f225(x64182),f2(x64182)),x64183))+~P22(f317(f317(f225(x64182),f2(x64182)),x64181)) % 168.22/168.07 [6419]~P80(x64192)+E(x64191,f2(x64192))+~E(f317(f317(f89(x64192),x64191),x64193),f2(x64192))+~P22(f317(f317(f225(x64192),f2(x64192)),x64193))+~P22(f317(f317(f225(x64192),f2(x64192)),x64191)) % 168.22/168.07 [6943]~P103(x69432)+~P29(x69432,x69431)+E(x69431,f125(x69432))+~P22(f317(f317(f319(x69432),x69433),f317(f166(x69432),f654(x69431,x69432))))+P22(f317(f317(f225(x69432),f686(x69431,x69432)),x69433)) % 168.22/168.07 [7110]~P103(x71101)+E(f15(x71101,x71102),x71103)+~P22(f317(f71(x71101),x71102))+~P22(f317(f317(f225(x71101),x71103),f742(x71103,x71102,x71101)))+~P22(f317(f317(f319(x71101),x71103),x71102)) % 168.22/168.07 [7139]~P103(x71391)+~P29(x71391,x71392)+~P29(x71391,x71393)+P29(x71391,f317(f317(f127(x71391),x71392),x71393))+P22(f317(f317(f319(x71391),f647(x71393,x71392,x71391)),f317(f166(x71391),x71392))) % 168.22/168.07 [7140]~P103(x71401)+~P29(x71401,x71402)+~P29(x71401,x71403)+P29(x71401,f317(f317(f127(x71401),x71402),x71403))+P22(f317(f317(f319(x71401),f648(x71403,x71402,x71401)),f317(f166(x71401),x71403))) % 168.22/168.07 [7188]~P103(x71881)+E(f14(x71881,x71882),x71883)+~P22(f317(f71(x71881),x71882))+P22(f317(f317(f319(x71881),f743(x71883,x71882,x71881)),x71882))+~P22(f317(f317(f319(x71881),x71883),x71882)) % 168.22/168.07 [7189]~P103(x71891)+E(f15(x71891,x71892),x71893)+~P22(f317(f71(x71891),x71892))+P22(f317(f317(f319(x71891),f742(x71893,x71892,x71891)),x71892))+~P22(f317(f317(f319(x71891),x71893),x71892)) % 168.22/168.07 [7767]~P103(x77671)+E(f14(x77671,x77672),x77673)+~P22(f317(f71(x77671),x77672))+~P22(f317(f317(f319(x77671),x77673),x77672))+~P22(f317(f317(f225(x77671),f743(x77673,x77672,x77671)),x77673)) % 168.22/168.07 [8087]~P103(x80871)+~P29(x80871,x80872)+~P29(x80871,x80873)+P29(x80871,f317(f317(f127(x80871),x80872),x80873))+~P22(f317(f317(f225(x80871),f647(x80873,x80872,x80871)),f648(x80873,x80872,x80871))) % 168.22/168.07 [8871]~P93(x88712)+E(x88711,f188(f858(x88712,a842)))+~E(f317(f317(f113(x88712),f317(x88713,f404(x88711,x88713,x88712))),f317(x88713,f407(x88711,x88713,x88712))),f317(x88713,f317(f317(f113(x88712),f404(x88711,x88713,x88712)),f407(x88711,x88713,x88712))))+E(f11(x88712,f317(f287(x88712,x88712,x88713),x88711)),f317(x88713,f11(x88712,x88711)))+~P22(f317(f71(x88712),x88711)) % 168.22/168.07 [8872]~P93(x88722)+E(x88721,f188(f858(x88722,a842)))+~E(f317(f317(f122(x88722),f317(x88723,f408(x88721,x88723,x88722))),f317(x88723,f409(x88721,x88723,x88722))),f317(x88723,f317(f317(f122(x88722),f408(x88721,x88723,x88722)),f409(x88721,x88723,x88722))))+E(f10(x88722,f317(f287(x88722,x88722,x88723),x88721)),f317(x88723,f10(x88722,x88721)))+~P22(f317(f71(x88722),x88721)) % 168.22/168.07 [8873]~P103(x88732)+E(x88731,f188(f858(x88732,a842)))+~E(f317(f317(f224(x88732),f317(x88733,f398(x88731,x88733,x88732))),f317(x88733,f402(x88731,x88733,x88732))),f317(x88733,f317(f317(f224(x88732),f398(x88731,x88733,x88732)),f402(x88731,x88733,x88732))))+E(f14(x88732,f317(f287(x88732,x88732,x88733),x88731)),f317(x88733,f14(x88732,x88731)))+~P22(f317(f71(x88732),x88731)) % 168.22/168.07 [8874]~P103(x88742)+E(x88741,f188(f858(x88742,a842)))+~E(f317(f317(f223(x88742),f317(x88743,f405(x88741,x88743,x88742))),f317(x88743,f406(x88741,x88743,x88742))),f317(x88743,f317(f317(f223(x88742),f405(x88741,x88743,x88742)),f406(x88741,x88743,x88742))))+E(f15(x88742,f317(f287(x88742,x88742,x88743),x88741)),f317(x88743,f15(x88742,x88741)))+~P22(f317(f71(x88742),x88741)) % 168.22/168.07 [8944]~P103(x89442)+E(x89441,f188(f858(x89442,a842)))+~E(f317(f317(f224(x89442),f317(x89443,f388(x89441,x89443,x89442))),f317(x89443,f389(x89441,x89443,x89442))),f317(x89443,f317(f317(f224(x89442),f388(x89441,x89443,x89442)),f389(x89441,x89443,x89442))))+E(f12(x89442,f224(x89442),f317(f287(x89442,x89442,x89443),x89441)),f317(x89443,f12(x89442,f224(x89442),x89441)))+~P22(f317(f71(x89442),x89441)) % 168.22/168.07 [8945]~P103(x89452)+E(x89451,f188(f858(x89452,a842)))+~E(f317(f317(f223(x89452),f317(x89453,f399(x89451,x89453,x89452))),f317(x89453,f401(x89451,x89453,x89452))),f317(x89453,f317(f317(f223(x89452),f399(x89451,x89453,x89452)),f401(x89451,x89453,x89452))))+E(f13(x89452,f223(x89452),f317(f287(x89452,x89452,x89453),x89451)),f317(x89453,f13(x89452,f223(x89452),x89451)))+~P22(f317(f71(x89452),x89451)) % 168.22/168.07 [9028]~P57(x90281)+~P57(x90282)+~P22(f317(f67(f856(x90282,x90281)),x90283))+P22(f317(f67(x90282),f317(f317(f8(f856(x90282,x90281),a842,x90282),x90283),f288(x90282,x90281))))+P22(f317(f67(x90281),f317(f317(f8(f856(x90282,x90281),a842,x90281),x90283),f297(x90281,x90282)))) % 168.22/168.07 [9255]~P57(x92552)+~P57(x92551)+P22(f317(f68(f856(x92551,x92552)),x92553))+~P22(f317(f68(x92552),f317(f317(f8(f856(x92551,x92552),a842,x92552),x92553),f297(x92552,x92551))))+~P22(f317(f68(x92551),f317(f317(f8(f856(x92551,x92552),a842,x92551),x92553),f288(x92551,x92552)))) % 168.22/168.07 [6432]~P64(x64322)+E(x64321,f188(f858(x64322,a842)))+~P22(f317(f71(x64322),x64321))+E(f317(f73(x64322,f90(x64322)),f317(f317(f286(x64322),x64323),x64321)),f317(f317(f90(x64322),x64323),f317(f73(x64322,f90(x64322)),x64321)))+P22(f317(f317(f319(x64322),x64323),x64321)) % 168.22/168.07 [6948]~P93(x69482)+E(f317(f317(f122(x69482),f10(x69482,x69481)),f10(x69482,x69483)),f10(x69482,x69483))+E(x69481,f188(f858(x69482,a842)))+~P22(f317(f71(x69482),x69483))+~P22(f317(f317(f225(f858(x69482,a842)),x69481),x69483)) % 168.22/168.07 [6949]~P93(x69492)+E(f317(f317(f113(x69492),f11(x69492,x69491)),f11(x69492,x69493)),f11(x69492,x69493))+E(x69491,f188(f858(x69492,a842)))+~P22(f317(f71(x69492),x69493))+~P22(f317(f317(f225(f858(x69492,a842)),x69491),x69493)) % 168.22/168.07 [6950]~P103(x69502)+E(f317(f317(f223(x69502),f15(x69502,x69501)),f15(x69502,x69503)),f15(x69502,x69503))+E(x69501,f188(f858(x69502,a842)))+~P22(f317(f71(x69502),x69503))+~P22(f317(f317(f225(f858(x69502,a842)),x69501),x69503)) % 168.22/168.07 [6951]~P103(x69512)+E(f317(f317(f224(x69512),f14(x69512,x69511)),f14(x69512,x69513)),f14(x69512,x69513))+E(x69511,f188(f858(x69512,a842)))+~P22(f317(f71(x69512),x69513))+~P22(f317(f317(f225(f858(x69512,a842)),x69511),x69513)) % 168.22/168.07 [7244]~P103(x72442)+E(x72441,f188(f858(x72442,a842)))+~P22(f317(f71(x72442),x72443))+P22(f317(f317(f225(x72442),f14(x72442,x72441)),f14(x72442,x72443)))+~P22(f317(f317(f225(f858(x72442,a842)),x72441),x72443)) % 168.22/168.07 [7245]~P103(x72452)+E(x72451,f188(f858(x72452,a842)))+~P22(f317(f71(x72452),x72453))+P22(f317(f317(f225(x72452),f15(x72452,x72453)),f15(x72452,x72451)))+~P22(f317(f317(f225(f858(x72452,a842)),x72451),x72453)) % 168.22/168.07 [7302]~P93(x73021)+E(f11(x73021,x73022),x73023)+~P22(f317(f71(x73021),x73022))+~E(f317(f317(f21(f858(x73021,a842)),x73022),f317(f317(f286(x73021),x73023),f188(f858(x73021,a842)))),f188(f858(x73021,a842)))+~P22(f317(f317(f319(x73021),x73023),x73022)) % 168.22/168.07 [7303]~P93(x73031)+E(f10(x73031,x73032),x73033)+~P22(f317(f71(x73031),x73032))+~E(f317(f317(f21(f858(x73031,a842)),x73032),f317(f317(f286(x73031),x73033),f188(f858(x73031,a842)))),f188(f858(x73031,a842)))+~P22(f317(f317(f319(x73031),x73033),x73032)) % 168.22/168.07 [7304]~P103(x73041)+E(f14(x73041,x73042),x73043)+~P22(f317(f71(x73041),x73042))+~E(f317(f317(f21(f858(x73041,a842)),x73042),f317(f317(f286(x73041),x73043),f188(f858(x73041,a842)))),f188(f858(x73041,a842)))+~P22(f317(f317(f319(x73041),x73043),x73042)) % 168.22/168.07 [7305]~P103(x73051)+E(f15(x73051,x73052),x73053)+~P22(f317(f71(x73051),x73052))+~E(f317(f317(f21(f858(x73051,a842)),x73052),f317(f317(f286(x73051),x73053),f188(f858(x73051,a842)))),f188(f858(x73051,a842)))+~P22(f317(f317(f319(x73051),x73053),x73052)) % 168.22/168.07 [7399]~P103(x73991)+E(f12(x73991,f224(x73991),x73992),x73993)+~P22(f317(f71(x73991),x73992))+~E(f317(f317(f21(f858(x73991,a842)),x73992),f317(f317(f286(x73991),x73993),f188(f858(x73991,a842)))),f188(f858(x73991,a842)))+~P22(f317(f317(f319(x73991),x73993),x73992)) % 168.22/168.07 [7400]~P103(x74001)+E(f13(x74001,f223(x74001),x74002),x74003)+~P22(f317(f71(x74001),x74002))+~E(f317(f317(f21(f858(x74001,a842)),x74002),f317(f317(f286(x74001),x74003),f188(f858(x74001,a842)))),f188(f858(x74001,a842)))+~P22(f317(f317(f319(x74001),x74003),x74002)) % 168.22/168.07 [7436]~P98(x74362)+E(x74361,f188(f858(x74362,a842)))+~P22(f317(f71(x74362),x74361))+~P22(f317(f317(f225(x74362),x74363),f481(x74363,x74361,x74362)))+P22(f317(f317(f225(x74362),x74363),f317(f73(x74362,f113(x74362)),x74361))) % 168.22/168.07 [7437]~P103(x74372)+E(x74371,f188(f858(x74372,a842)))+~P22(f317(f71(x74372),x74371))+~P22(f317(f317(f225(x74372),x74373),f514(x74373,x74371,x74372)))+P22(f317(f317(f225(x74372),x74373),f317(f73(x74372,f223(x74372)),x74371))) % 168.22/168.07 [7438]~P103(x74382)+E(x74381,f188(f858(x74382,a842)))+~P22(f317(f71(x74382),x74381))+~P22(f317(f317(f226(x74382),x74383),f515(x74383,x74381,x74382)))+P22(f317(f317(f226(x74382),x74383),f317(f73(x74382,f223(x74382)),x74381))) % 168.22/168.07 [7525]~P98(x75252)+E(x75251,f188(f858(x75252,a842)))+~P22(f317(f71(x75252),x75251))+P22(f317(f317(f319(x75252),f481(x75253,x75251,x75252)),x75251))+P22(f317(f317(f225(x75252),x75253),f317(f73(x75252,f113(x75252)),x75251))) % 168.22/168.07 [7526]~P103(x75262)+E(x75261,f188(f858(x75262,a842)))+~P22(f317(f71(x75262),x75261))+P22(f317(f317(f319(x75262),f514(x75263,x75261,x75262)),x75261))+P22(f317(f317(f225(x75262),x75263),f317(f73(x75262,f223(x75262)),x75261))) % 168.22/168.07 [7527]~P103(x75272)+E(x75271,f188(f858(x75272,a842)))+~P22(f317(f71(x75272),x75271))+P22(f317(f317(f319(x75272),f515(x75273,x75271,x75272)),x75271))+P22(f317(f317(f226(x75272),x75273),f317(f73(x75272,f223(x75272)),x75271))) % 168.22/168.07 [7649]~P103(x76492)+E(x76491,f188(f858(x76492,a842)))+E(f317(f317(f223(x76492),f13(x76492,f223(x76492),x76491)),f13(x76492,f223(x76492),x76493)),f13(x76492,f223(x76492),x76493))+~P22(f317(f71(x76492),x76493))+~P22(f317(f317(f225(f858(x76492,a842)),x76491),x76493)) % 168.22/168.07 [7650]~P103(x76502)+E(x76501,f188(f858(x76502,a842)))+E(f317(f317(f224(x76502),f12(x76502,f224(x76502),x76501)),f12(x76502,f224(x76502),x76503)),f12(x76502,f224(x76502),x76503))+~P22(f317(f71(x76502),x76503))+~P22(f317(f317(f225(f858(x76502,a842)),x76501),x76503)) % 168.22/168.07 [7839]~E(f688(x78391,x78393,x78392),f689(x78391,x78393,x78392))+~E(f317(f54(x78392),f690(x78391,x78393,x78392)),x78391)+E(f317(f317(f90(a849),x78391),f317(f54(f858(x78392,a842)),x78393)),f317(f54(x78392),f49(f858(x78392,a842),x78393)))+~P22(f317(f71(x78392),f49(f858(x78392,a842),x78393)))+~P22(f317(f71(f858(x78392,a842)),x78393)) % 168.22/168.07 [8021]~P103(x80212)+E(x80211,f188(f858(x80212,a842)))+~P22(f317(f71(x80212),x80213))+P22(f317(f317(f225(x80212),f317(f73(x80212,f223(x80212)),x80213)),f317(f73(x80212,f223(x80212)),x80211)))+~P22(f317(f317(f225(f858(x80212,a842)),x80211),x80213)) % 168.22/168.07 [8334]~E(f688(x83341,x83343,x83342),f689(x83341,x83343,x83342))+E(f317(f317(f90(a849),x83341),f317(f54(f858(x83342,a842)),x83343)),f317(f54(x83342),f49(f858(x83342,a842),x83343)))+P22(f317(f317(f319(f858(x83342,a842)),f690(x83341,x83343,x83342)),x83343))+~P22(f317(f71(x83342),f49(f858(x83342,a842),x83343)))+~P22(f317(f71(f858(x83342,a842)),x83343)) % 168.22/168.07 [8360]~E(f317(f54(x83602),f690(x83601,x83603,x83602)),x83601)+E(f317(f317(f90(a849),x83601),f317(f54(f858(x83602,a842)),x83603)),f317(f54(x83602),f49(f858(x83602,a842),x83603)))+P22(f317(f317(f319(f858(x83602,a842)),f689(x83601,x83603,x83602)),x83603))+~P22(f317(f71(x83602),f49(f858(x83602,a842),x83603)))+~P22(f317(f71(f858(x83602,a842)),x83603)) % 168.22/168.07 [8361]~E(f317(f54(x83612),f690(x83611,x83613,x83612)),x83611)+E(f317(f317(f90(a849),x83611),f317(f54(f858(x83612,a842)),x83613)),f317(f54(x83612),f49(f858(x83612,a842),x83613)))+P22(f317(f317(f319(f858(x83612,a842)),f688(x83611,x83613,x83612)),x83613))+~P22(f317(f71(x83612),f49(f858(x83612,a842),x83613)))+~P22(f317(f71(f858(x83612,a842)),x83613)) % 168.22/168.07 [8391]~E(f317(f54(x83912),f690(x83911,x83913,x83912)),x83911)+~E(f317(f317(f113(f858(x83912,a842)),f689(x83911,x83913,x83912)),f688(x83911,x83913,x83912)),f188(f858(x83912,a842)))+E(f317(f317(f90(a849),x83911),f317(f54(f858(x83912,a842)),x83913)),f317(f54(x83912),f49(f858(x83912,a842),x83913)))+~P22(f317(f71(f858(x83912,a842)),x83913))+~P22(f317(f71(x83912),f49(f858(x83912,a842),x83913))) % 168.22/168.07 [8634]E(f317(f317(f90(a849),x86341),f317(f54(f858(x86342,a842)),x86343)),f317(f54(x86342),f49(f858(x86342,a842),x86343)))+P22(f317(f317(f319(f858(x86342,a842)),f690(x86341,x86343,x86342)),x86343))+P22(f317(f317(f319(f858(x86342,a842)),f689(x86341,x86343,x86342)),x86343))+~P22(f317(f71(f858(x86342,a842)),x86343))+~P22(f317(f71(x86342),f49(f858(x86342,a842),x86343))) % 168.22/168.07 [8635]E(f317(f317(f90(a849),x86351),f317(f54(f858(x86352,a842)),x86353)),f317(f54(x86352),f49(f858(x86352,a842),x86353)))+P22(f317(f317(f319(f858(x86352,a842)),f690(x86351,x86353,x86352)),x86353))+P22(f317(f317(f319(f858(x86352,a842)),f688(x86351,x86353,x86352)),x86353))+~P22(f317(f71(f858(x86352,a842)),x86353))+~P22(f317(f71(x86352),f49(f858(x86352,a842),x86353))) % 168.22/168.07 [8660]~E(f317(f317(f113(f858(x86602,a842)),f689(x86601,x86603,x86602)),f688(x86601,x86603,x86602)),f188(f858(x86602,a842)))+E(f317(f317(f90(a849),x86601),f317(f54(f858(x86602,a842)),x86603)),f317(f54(x86602),f49(f858(x86602,a842),x86603)))+~P22(f317(f71(f858(x86602,a842)),x86603))+P22(f317(f317(f319(f858(x86602,a842)),f690(x86601,x86603,x86602)),x86603))+~P22(f317(f71(x86602),f49(f858(x86602,a842),x86603))) % 168.22/168.07 [8919]~P91(x89192)+E(x89191,f188(f858(x89192,a842)))+~E(f317(f317(f90(x89192),f317(x89193,f531(x89191,x89193,x89192))),f317(x89193,f532(x89191,x89193,x89192))),f317(x89193,f317(f317(f90(x89192),f531(x89191,x89193,x89192)),f532(x89191,x89193,x89192))))+~P22(f317(f71(x89192),x89191))+E(f317(f73(x89192,f90(x89192)),f317(f287(x89192,x89192,x89193),x89191)),f317(x89193,f317(f73(x89192,f90(x89192)),x89191))) % 168.22/168.07 [9833]P22(f317(f317(x98331,x98332),x98333))+P22(f317(f317(f226(a1),f346(x98331,x98333,x98332)),f349(x98331,x98333,x98332)))+P22(f317(f317(f225(a1),f349(x98331,x98333,x98332)),f2(a1)))+P22(f317(f317(x98331,f346(x98331,x98333,x98332)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f349(x98331,x98333,x98332))))+~P22(f317(f305(f857(a1,a1),a66),f317(f317(f237(a1,a1),x98332),x98333))) % 168.22/168.07 [9839]P22(f317(f317(x98391,x98392),x98393))+P22(f317(f317(f225(a1),f343(x98391,x98393,x98392)),f2(a1)))+P22(f317(f317(x98391,f342(x98391,x98393,x98392)),f317(f317(f90(a1),f317(f115(a1),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f343(x98391,x98393,x98392))))+P22(f317(f317(f225(a1),f2(a1)),f317(f317(f89(a1),f342(x98391,x98393,x98392)),f343(x98391,x98393,x98392))))+~P22(f317(f305(f857(a1,a1),a61),f317(f317(f237(a1,a1),x98392),x98393))) % 168.22/168.07 [7811]~P113(x78111)+~P22(f317(f317(f225(x78111),x78112),f87(x78111)))+~P22(f317(f317(f225(x78111),f2(x78111)),x78112))+~P22(f317(f317(f225(x78111),f2(x78111)),x78113))+P22(f317(f317(f225(x78111),f317(f317(f90(x78111),x78112),x78113)),x78113)) % 168.22/168.07 [7812]~P113(x78121)+~P22(f317(f317(f225(x78121),x78123),f87(x78121)))+~P22(f317(f317(f225(x78121),f2(x78121)),x78123))+~P22(f317(f317(f225(x78121),f2(x78121)),x78122))+P22(f317(f317(f225(x78121),f317(f317(f90(x78121),x78122),x78123)),x78122)) % 168.22/168.07 [8173]~P103(x81732)+E(x81731,f188(f858(x81732,a842)))+~P22(f317(f71(x81732),x81731))+P22(f317(f317(f319(x81732),f516(x81733,x81731,x81732)),x81731))+~P22(f317(f317(f225(x81732),f317(f73(x81732,f223(x81732)),x81731)),x81733)) % 168.22/168.07 [8174]~P103(x81742)+E(x81741,f188(f858(x81742,a842)))+~P22(f317(f71(x81742),x81741))+P22(f317(f317(f319(x81742),f517(x81743,x81741,x81742)),x81741))+~P22(f317(f317(f226(x81742),f317(f73(x81742,f223(x81742)),x81741)),x81743)) % 168.22/168.07 [8175]~P103(x81752)+E(x81751,f188(f858(x81752,a842)))+~P22(f317(f71(x81752),x81751))+P22(f317(f317(f225(x81752),f516(x81753,x81751,x81752)),x81753))+~P22(f317(f317(f225(x81752),f317(f73(x81752,f223(x81752)),x81751)),x81753)) % 168.22/168.07 [8176]~P103(x81762)+E(x81761,f188(f858(x81762,a842)))+~P22(f317(f71(x81762),x81761))+P22(f317(f317(f226(x81762),f517(x81763,x81761,x81762)),x81763))+~P22(f317(f317(f226(x81762),f317(f73(x81762,f223(x81762)),x81761)),x81763)) % 168.22/168.07 [8262]~P22(f317(x82621,x82623))+P22(f317(x82621,f443(x82621,x82622)))+P22(f317(x82621,f438(x82621,x82622)))+~P22(f317(f317(f226(a1),f2(a1)),x82622))+P22(f317(x82621,f317(f317(f21(a1),f438(x82621,x82622)),f317(f317(f90(a1),f444(x82621,x82622)),x82622)))) % 168.22/168.07 [8494]~P22(f317(x84941,x84943))+P22(f317(x84941,f438(x84941,x84942)))+~P22(f317(f317(f226(a1),f2(a1)),x84942))+P22(f317(f317(f319(a1),f443(x84941,x84942)),f279(a1,f87(a1),x84942)))+P22(f317(x84941,f317(f317(f21(a1),f438(x84941,x84942)),f317(f317(f90(a1),f444(x84941,x84942)),x84942)))) % 168.22/168.07 [8681]~P22(f317(x86811,x86813))+~P22(f317(x86811,f438(x86811,x86812)))+P22(f317(x86811,f443(x86811,x86812)))+~P22(f317(f317(f226(a1),f2(a1)),x86812))+~P22(f317(x86811,f317(f317(f21(a1),f438(x86811,x86812)),f317(f317(f90(a1),f444(x86811,x86812)),x86812)))) % 168.22/168.07 [8801]~P22(f317(x88011,x88013))+~P22(f317(x88011,f438(x88011,x88012)))+~P22(f317(f317(f226(a1),f2(a1)),x88012))+P22(f317(f317(f319(a1),f443(x88011,x88012)),f279(a1,f87(a1),x88012)))+~P22(f317(x88011,f317(f317(f21(a1),f438(x88011,x88012)),f317(f317(f90(a1),f444(x88011,x88012)),x88012)))) % 168.22/168.07 [8594]~P93(x85941)+~P22(f317(f71(x85941),x85942))+E(f317(f317(f21(f858(x85941,a842)),x85942),f317(f317(f286(x85941),x85943),f188(f858(x85941,a842)))),f188(f858(x85941,a842)))+~P22(f317(f317(f319(x85941),x85943),x85942))+E(f317(f317(f113(x85941),x85943),f11(x85941,f317(f317(f21(f858(x85941,a842)),x85942),f317(f317(f286(x85941),x85943),f188(f858(x85941,a842)))))),f11(x85941,x85942)) % 168.22/168.07 [8595]~P93(x85951)+~P22(f317(f71(x85951),x85952))+E(f317(f317(f21(f858(x85951,a842)),x85952),f317(f317(f286(x85951),x85953),f188(f858(x85951,a842)))),f188(f858(x85951,a842)))+~P22(f317(f317(f319(x85951),x85953),x85952))+E(f317(f317(f122(x85951),x85953),f10(x85951,f317(f317(f21(f858(x85951,a842)),x85952),f317(f317(f286(x85951),x85953),f188(f858(x85951,a842)))))),f10(x85951,x85952)) % 168.22/168.07 [8596]~P103(x85961)+~P22(f317(f71(x85961),x85962))+E(f317(f317(f21(f858(x85961,a842)),x85962),f317(f317(f286(x85961),x85963),f188(f858(x85961,a842)))),f188(f858(x85961,a842)))+~P22(f317(f317(f319(x85961),x85963),x85962))+E(f317(f317(f224(x85961),x85963),f14(x85961,f317(f317(f21(f858(x85961,a842)),x85962),f317(f317(f286(x85961),x85963),f188(f858(x85961,a842)))))),f14(x85961,x85962)) % 168.22/168.07 [8597]~P103(x85971)+~P22(f317(f71(x85971),x85972))+E(f317(f317(f21(f858(x85971,a842)),x85972),f317(f317(f286(x85971),x85973),f188(f858(x85971,a842)))),f188(f858(x85971,a842)))+~P22(f317(f317(f319(x85971),x85973),x85972))+E(f317(f317(f223(x85971),x85973),f15(x85971,f317(f317(f21(f858(x85971,a842)),x85972),f317(f317(f286(x85971),x85973),f188(f858(x85971,a842)))))),f15(x85971,x85972)) % 168.22/168.07 [8654]~P103(x86541)+~P22(f317(f71(x86541),x86542))+E(f317(f317(f21(f858(x86541,a842)),x86542),f317(f317(f286(x86541),x86543),f188(f858(x86541,a842)))),f188(f858(x86541,a842)))+~P22(f317(f317(f319(x86541),x86543),x86542))+E(f317(f317(f224(x86541),x86543),f12(x86541,f224(x86541),f317(f317(f21(f858(x86541,a842)),x86542),f317(f317(f286(x86541),x86543),f188(f858(x86541,a842)))))),f12(x86541,f224(x86541),x86542)) % 168.22/168.07 [8655]~P103(x86551)+~P22(f317(f71(x86551),x86552))+E(f317(f317(f21(f858(x86551,a842)),x86552),f317(f317(f286(x86551),x86553),f188(f858(x86551,a842)))),f188(f858(x86551,a842)))+~P22(f317(f317(f319(x86551),x86553),x86552))+E(f317(f317(f223(x86551),x86553),f13(x86551,f223(x86551),f317(f317(f21(f858(x86551,a842)),x86552),f317(f317(f286(x86551),x86553),f188(f858(x86551,a842)))))),f13(x86551,f223(x86551),x86552)) % 168.22/168.07 [8668]~P93(x86681)+~P22(f317(f71(x86681),x86683))+~P22(f317(f71(x86681),x86682))+E(f317(f317(f113(f858(x86681,a842)),x86682),x86683),f188(f858(x86681,a842)))+E(f317(f317(f122(x86681),f10(x86681,f317(f317(f122(f858(x86681,a842)),x86682),x86683))),f10(x86681,f317(f317(f113(f858(x86681,a842)),x86682),x86683))),f317(f317(f122(x86681),f10(x86681,x86682)),f10(x86681,x86683))) % 168.22/168.07 [8669]~P93(x86691)+~P22(f317(f71(x86691),x86693))+~P22(f317(f71(x86691),x86692))+E(f317(f317(f113(f858(x86691,a842)),x86692),x86693),f188(f858(x86691,a842)))+E(f317(f317(f113(x86691),f11(x86691,f317(f317(f122(f858(x86691,a842)),x86692),x86693))),f11(x86691,f317(f317(f113(f858(x86691,a842)),x86692),x86693))),f317(f317(f113(x86691),f11(x86691,x86692)),f11(x86691,x86693))) % 168.22/168.07 [8670]~P103(x86701)+~P22(f317(f71(x86701),x86703))+~P22(f317(f71(x86701),x86702))+E(f317(f317(f113(f858(x86701,a842)),x86702),x86703),f188(f858(x86701,a842)))+E(f317(f317(f223(x86701),f15(x86701,f317(f317(f122(f858(x86701,a842)),x86702),x86703))),f15(x86701,f317(f317(f113(f858(x86701,a842)),x86702),x86703))),f317(f317(f223(x86701),f15(x86701,x86702)),f15(x86701,x86703))) % 168.22/168.07 [8671]~P103(x86711)+~P22(f317(f71(x86711),x86713))+~P22(f317(f71(x86711),x86712))+E(f317(f317(f113(f858(x86711,a842)),x86712),x86713),f188(f858(x86711,a842)))+E(f317(f317(f224(x86711),f14(x86711,f317(f317(f122(f858(x86711,a842)),x86712),x86713))),f14(x86711,f317(f317(f113(f858(x86711,a842)),x86712),x86713))),f317(f317(f224(x86711),f14(x86711,x86712)),f14(x86711,x86713))) % 168.22/168.07 [8891]~P103(x88911)+~P22(f317(f71(x88911),x88913))+~P22(f317(f71(x88911),x88912))+E(f317(f317(f113(f858(x88911,a842)),x88912),x88913),f188(f858(x88911,a842)))+E(f317(f317(f223(x88911),f13(x88911,f223(x88911),f317(f317(f122(f858(x88911,a842)),x88912),x88913))),f13(x88911,f223(x88911),f317(f317(f113(f858(x88911,a842)),x88912),x88913))),f317(f317(f223(x88911),f13(x88911,f223(x88911),x88912)),f13(x88911,f223(x88911),x88913))) % 168.22/168.07 [8892]~P103(x88921)+~P22(f317(f71(x88921),x88923))+~P22(f317(f71(x88921),x88922))+E(f317(f317(f113(f858(x88921,a842)),x88922),x88923),f188(f858(x88921,a842)))+E(f317(f317(f224(x88921),f12(x88921,f224(x88921),f317(f317(f122(f858(x88921,a842)),x88922),x88923))),f12(x88921,f224(x88921),f317(f317(f113(f858(x88921,a842)),x88922),x88923))),f317(f317(f224(x88921),f12(x88921,f224(x88921),x88922)),f12(x88921,f224(x88921),x88923))) % 168.22/168.07 [9667]~P112(x96673)+E(x96671,x96672)+~P22(f317(f317(f225(x96673),f2(x96673)),x96672))+~P22(f317(f317(f225(x96673),f2(x96673)),x96671))+~E(f317(f317(f238(x96673),x96671),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)))),f317(f317(f238(x96673),x96672),f317(f115(a849),f317(f317(f89(a1),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109)),f317(f317(f21(a1),f317(f317(f89(a1),a92),a92)),a109))))) % 168.22/168.07 [6233]E(f451(x62331,x62332,x62333),x62334)+E(f317(x62331,x62334),f2(a849))+~E(f317(f317(f6(x62333,a849),x62331),x62332),f87(a849))+~P22(f317(f71(x62333),x62332))+~P22(f317(f317(f319(x62333),x62334),x62332)) % 168.22/168.07 [6295]E(f458(x62951,x62952,x62953),x62954)+E(f317(x62951,x62954),f2(a849))+~E(f317(f317(f6(x62953,a849),x62951),x62952),f317(a124,f2(a849)))+~P22(f317(f71(x62953),x62952))+~P22(f317(f317(f319(x62953),x62954),x62952)) % 168.22/168.07 [6403]~P103(x64031)+~P27(x64031)+P22(f317(f317(f226(x64031),x64032),f49(x64031,x64033)))+~P22(f317(f317(f226(x64031),x64032),x64034))+~P22(f317(f317(f319(x64031),x64034),x64033)) % 168.22/168.07 [6571]~P103(x65711)+~P27(x65711)+~P22(f317(f317(f226(x65711),x65714),x65713))+P22(f317(f317(f226(x65711),f50(x65711,x65712)),x65713))+~P22(f317(f317(f319(x65711),x65714),x65712)) % 168.22/168.07 [6822]~P112(x68223)+E(x68221,x68222)+~E(f317(f317(f238(x68223),x68221),f317(a124,x68224)),f317(f317(f238(x68223),x68222),f317(a124,x68224)))+~P22(f317(f317(f225(x68223),f2(x68223)),x68222))+~P22(f317(f317(f225(x68223),f2(x68223)),x68221)) % 168.22/168.07 [7036]~E(f461(x70362,x70363,x70361,x70364),x70364)+~E(f317(x70362,x70364),f87(a849))+E(f317(f317(f6(x70361,a849),x70362),x70363),f87(a849))+~P22(f317(f71(x70361),x70363))+~P22(f317(f317(f319(x70361),x70364),x70363)) % 168.22/168.07 [7043]~P84(x70434)+~P125(x70434)+E(f317(x70431,f387(x70431,x70432,x70433,x70434)),f2(x70434))+~E(f317(f317(f9(x70433,x70434),x70431),x70432),f2(x70434))+~P22(f317(f71(x70433),x70432)) % 168.22/168.07 [7130]~E(f459(x71302,x71303,x71301,x71304),x71304)+~E(f317(x71302,x71304),f317(a124,f2(a849)))+E(f317(f317(f6(x71301,a849),x71302),x71303),f317(a124,f2(a849)))+~P22(f317(f71(x71301),x71303))+~P22(f317(f317(f319(x71301),x71304),x71303)) % 168.22/168.07 [7850]~E(f317(x78502,x78504),f87(a849))+~E(f317(x78502,f461(x78502,x78503,x78501,x78504)),f2(a849))+E(f317(f317(f6(x78501,a849),x78502),x78503),f87(a849))+~P22(f317(f71(x78501),x78503))+~P22(f317(f317(f319(x78501),x78504),x78503)) % 168.22/168.07 [7893]~E(f317(x78932,x78934),f317(a124,f2(a849)))+~E(f317(x78932,f459(x78932,x78933,x78931,x78934)),f2(a849))+E(f317(f317(f6(x78931,a849),x78932),x78933),f317(a124,f2(a849)))+~P22(f317(f71(x78931),x78933))+~P22(f317(f317(f319(x78931),x78934),x78933)) % 168.22/168.07 [8462]~P103(x84621)+~P29(x84621,x84624)+P29(x84621,x84622)+~E(x84622,f317(f317(f145(x84621),x84623),x84624))+~P22(f317(f317(f225(x84621),x84623),f692(x84622,x84621,x84624,x84623))) % 168.22/168.07 [8498]E(x84981,x84982)+E(f317(f317(f89(a1),f427(x84983,x84982,x84984,x84981)),f428(x84983,x84982,x84984,x84981)),x84981)+~E(f317(f317(f21(a1),x84981),x84984),x84982)+~P22(f317(f317(f226(a1),f2(a1)),x84984))+~P22(f317(f317(f319(a1),x84982),x84983)) % 168.22/168.07 [8499]E(x84991,x84992)+E(f317(f317(f21(a1),f415(x84993,x84992,x84994,x84991)),f416(x84993,x84992,x84994,x84991)),x84991)+~E(f317(f317(f89(a1),x84991),x84994),x84992)+~P22(f317(f317(f226(a1),f2(a1)),x84994))+~P22(f317(f317(f319(a1),x84992),x84993)) % 168.22/168.07 [8666]E(f317(x86661,f832(x86662,x86661,x86663,x86664)),x86662)+P22(f317(f317(f225(a849),x86664),f833(x86662,x86661,x86663,x86664)))+~P22(f317(f317(f225(a1),x86662),f317(x86661,x86663)))+~P22(f317(f317(f226(a849),x86664),x86663))+~P22(f317(f317(f225(a1),f317(x86661,x86664)),x86662)) % 168.22/168.07 [8667]~P103(x86671)+~P29(x86671,x86673)+P29(x86671,x86672)+~E(x86672,f317(f317(f145(x86671),x86674),x86673))+P22(f317(f317(f319(x86671),f692(x86672,x86671,x86673,x86674)),f317(f166(x86671),x86673))) % 168.22/168.07 [8684]~P84(x86844)+~P125(x86844)+~E(f317(f317(f9(x86841,x86844),x86842),x86843),f2(x86844))+~P22(f317(f71(x86841),x86843))+P22(f317(f317(f319(x86841),f387(x86842,x86843,x86841,x86844)),x86843)) % 168.22/168.07 [8718]~E(f317(x87182,x87184),f87(a849))+E(f317(f317(f6(x87181,a849),x87182),x87183),f87(a849))+~P22(f317(f71(x87181),x87183))+~P22(f317(f317(f319(x87181),x87184),x87183))+P22(f317(f317(f319(x87181),f461(x87182,x87183,x87181,x87184)),x87183)) % 168.22/168.07 [8726]E(x87261,x87262)+~E(f317(f317(f89(a1),x87262),x87264),x87261)+~P22(f317(f317(f226(a1),f2(a1)),x87264))+~P22(f317(f317(f319(a1),x87261),x87263))+P22(f317(f317(f319(a1),f415(x87263,x87261,x87264,x87262)),x87263)) % 168.22/168.07 [8727]E(x87271,x87272)+~E(f317(f317(f21(a1),x87272),x87274),x87271)+~P22(f317(f317(f226(a1),f2(a1)),x87274))+~P22(f317(f317(f319(a1),x87271),x87273))+P22(f317(f317(f319(a1),f427(x87273,x87271,x87274,x87272)),x87273)) % 168.22/168.07 [8729]~E(f317(x87292,x87294),f317(a124,f2(a849)))+E(f317(f317(f6(x87291,a849),x87292),x87293),f317(a124,f2(a849)))+~P22(f317(f71(x87291),x87293))+~P22(f317(f317(f319(x87291),x87294),x87293))+P22(f317(f317(f319(x87291),f459(x87292,x87293,x87291,x87294)),x87293)) % 168.22/168.07 [8734]P53(x87342,x87343,x87344,x87341)+E(x87341,f188(f858(x87342,a842)))+~P22(f317(f71(x87342),x87344))+~P22(f317(f71(x87342),x87341))+P22(f317(f317(f319(x87342),f506(x87341,x87344,x87343,x87342)),x87344)) % 168.22/168.07 [8815]E(x88151,x88152)+~E(f317(f317(f89(a1),x88152),x88154),x88151)+~P22(f317(f317(f226(a1),f2(a1)),x88154))+~P22(f317(f317(f319(a1),x88151),x88153))+P22(f317(f317(f319(a1),f416(x88153,x88151,x88154,x88152)),f279(a1,f87(a1),x88154))) % 168.22/168.07 [8816]E(x88161,x88162)+~E(f317(f317(f21(a1),x88162),x88164),x88161)+~P22(f317(f317(f226(a1),f2(a1)),x88164))+~P22(f317(f317(f319(a1),x88161),x88163))+P22(f317(f317(f319(a1),f428(x88163,x88161,x88164,x88162)),f279(a1,f87(a1),x88164))) % 168.22/168.07 [8897]P22(f317(f317(f225(a849),x88971),f832(x88972,x88973,x88974,x88971)))+~P22(f317(f317(f225(a1),x88972),f317(x88973,x88974)))+P22(f317(f317(f225(a849),x88971),f833(x88972,x88973,x88974,x88971)))+~P22(f317(f317(f226(a849),x88971),x88974))+~P22(f317(f317(f225(a1),f317(x88973,x88971)),x88972)) % 168.22/168.07 [9003]E(f317(x90031,f832(x90032,x90031,x90033,x90034)),x90032)+~P22(f317(f317(f225(a1),x90032),f317(x90031,x90033)))+P22(f317(f317(f226(a849),f833(x90032,x90031,x90033,x90034)),x90033))+~P22(f317(f317(f226(a849),x90034),x90033))+~P22(f317(f317(f225(a1),f317(x90031,x90034)),x90032)) % 168.22/168.07 [9132]~P22(f317(f317(f225(a1),x91322),f317(x91323,x91324)))+P22(f317(f317(f225(a849),x91321),f833(x91322,x91323,x91324,x91321)))+P22(f317(f317(f225(a849),f832(x91322,x91323,x91324,x91321)),x91324))+~P22(f317(f317(f226(a849),x91321),x91324))+~P22(f317(f317(f225(a1),f317(x91323,x91321)),x91322)) % 168.22/168.07 [9133]~P22(f317(f317(f225(a1),x91332),f317(x91333,x91334)))+P22(f317(f317(f225(a849),x91331),f832(x91332,x91333,x91334,x91331)))+P22(f317(f317(f226(a849),f833(x91332,x91333,x91334,x91331)),x91334))+~P22(f317(f317(f226(a849),x91331),x91334))+~P22(f317(f317(f225(a1),f317(x91333,x91331)),x91332)) % 168.22/168.07 [9237]~P22(f317(f317(f225(a1),x92371),f317(x92372,x92373)))+P22(f317(f317(f226(a849),f833(x92371,x92372,x92373,x92374)),x92373))+~P22(f317(f317(f226(a849),x92374),x92373))+~P22(f317(f317(f225(a1),f317(x92372,x92374)),x92371))+P22(f317(f317(f225(a849),f832(x92371,x92372,x92373,x92374)),x92373)) % 168.22/168.07 [9316]E(x93161,f188(f858(x93162,a842)))+~P22(f317(f71(x93162),x93164))+~P22(f317(f71(x93162),x93161))+P22(f317(f317(f319(f857(f858(x93162,a842),f858(x93162,a842))),f317(f317(f237(f858(x93162,a842),f858(x93162,a842)),x93164),x93161)),f309(x93162,x93163)))+P22(f317(f317(f319(x93162),f509(x93163,x93161,x93164,x93162)),x93164)) % 168.22/168.07 [9317]E(x93171,f188(f858(x93172,a842)))+~P22(f317(f71(x93172),x93174))+~P22(f317(f71(x93172),x93171))+P22(f317(f317(f319(f857(f858(x93172,a842),f858(x93172,a842))),f317(f317(f237(f858(x93172,a842),f858(x93172,a842)),x93174),x93171)),f309(x93172,x93173)))+P22(f317(f317(f319(x93172),f737(x93173,x93171,x93174,x93172)),x93174)) % 168.22/168.07 [9978]E(f317(x99781,f832(x99782,x99781,x99783,x99784)),x99782)+~P22(f317(f317(f225(a1),x99782),f317(x99781,x99783)))+~P22(f317(f317(f225(a1),f317(f84(a1),f317(f317(f21(a1),f317(x99781,f317(f317(f89(a849),f833(x99782,x99781,x99783,x99784)),f87(a849)))),f317(x99781,f833(x99782,x99781,x99783,x99784))))),f87(a1)))+~P22(f317(f317(f226(a849),x99784),x99783))+~P22(f317(f317(f225(a1),f317(x99781,x99784)),x99782)) % 168.22/168.07 [9979]~P22(f317(f317(f225(a1),x99792),f317(x99793,x99794)))+P22(f317(f317(f225(a849),x99791),f832(x99792,x99793,x99794,x99791)))+~P22(f317(f317(f225(a1),f317(f84(a1),f317(f317(f21(a1),f317(x99793,f317(f317(f89(a849),f833(x99792,x99793,x99794,x99791)),f87(a849)))),f317(x99793,f833(x99792,x99793,x99794,x99791))))),f87(a1)))+~P22(f317(f317(f226(a849),x99791),x99794))+~P22(f317(f317(f225(a1),f317(x99793,x99791)),x99792)) % 168.22/168.07 [9980]~P22(f317(f317(f225(a1),x99801),f317(x99802,x99803)))+~P22(f317(f317(f225(a1),f317(f84(a1),f317(f317(f21(a1),f317(x99802,f317(f317(f89(a849),f833(x99801,x99802,x99803,x99804)),f87(a849)))),f317(x99802,f833(x99801,x99802,x99803,x99804))))),f87(a1)))+~P22(f317(f317(f226(a849),x99804),x99803))+~P22(f317(f317(f225(a1),f317(x99802,x99804)),x99801))+P22(f317(f317(f225(a849),f832(x99801,x99802,x99803,x99804)),x99803)) % 168.22/168.07 [7100]~P60(x71001)+P22(f317(f317(f226(x71001),x71002),f2(x71001)))+~P22(f317(f317(f225(x71001),x71003),f2(x71001)))+P22(f317(f317(f226(x71001),f2(x71001)),x71002))+P22(f317(f317(f225(x71001),x71003),f317(f317(f266(x71001),x71004),x71002))) % 168.22/168.07 [7101]~P60(x71011)+P22(f317(f317(f226(x71011),x71012),f2(x71011)))+~P22(f317(f317(f226(x71011),x71013),f2(x71011)))+P22(f317(f317(f226(x71011),f2(x71011)),x71012))+P22(f317(f317(f226(x71011),x71013),f317(f317(f266(x71011),x71014),x71012))) % 168.22/168.07 [7339]~P60(x73391)+P22(f317(f317(f225(x73391),x73392),f2(x73391)))+P22(f317(f317(f226(x73391),x73393),f2(x73391)))+P22(f317(f317(f226(x73391),f2(x73391)),x73393))+~P22(f317(f317(f225(x73391),x73392),f317(f317(f266(x73391),x73394),x73393))) % 168.22/168.07 [7340]~P60(x73401)+P22(f317(f317(f226(x73401),x73402),f2(x73401)))+P22(f317(f317(f226(x73401),x73403),f2(x73401)))+P22(f317(f317(f226(x73401),f2(x73401)),x73403))+~P22(f317(f317(f226(x73401),x73402),f317(f317(f266(x73401),x73404),x73403))) % 168.22/168.07 [7457]E(x74571,x74572)+~E(f317(f317(f159(x74573),x74574),x74571),f317(f317(f159(x74573),x74574),x74572))+~P22(f317(f131(x74573),x74574))+~P22(f317(f317(f226(a849),x74572),f317(f189(f850(x74573)),x74574)))+~P22(f317(f317(f226(a849),x74571),f317(f189(f850(x74573)),x74574))) % 168.22/168.07 [7813]~P60(x78131)+~P22(f317(f317(f225(x78131),x78133),f2(x78131)))+P22(f317(f317(f226(x78131),f2(x78131)),x78132))+~P22(f317(f317(f225(x78131),x78134),f317(f317(f90(x78131),x78133),x78132)))+P22(f317(f317(f225(x78131),x78133),f317(f317(f266(x78131),x78134),x78132))) % 168.22/168.07 [7814]~P60(x78141)+~P22(f317(f317(f226(x78141),x78143),f2(x78141)))+P22(f317(f317(f226(x78141),f2(x78141)),x78142))+~P22(f317(f317(f226(x78141),x78144),f317(f317(f90(x78141),x78143),x78142)))+P22(f317(f317(f226(x78141),x78143),f317(f317(f266(x78141),x78144),x78142))) % 168.22/168.07 [7815]~P60(x78151)+~P22(f317(f317(f226(x78151),x78152),f2(x78151)))+P22(f317(f317(f226(x78151),f2(x78151)),x78152))+~P22(f317(f317(f225(x78151),x78154),f317(f317(f90(x78151),x78153),x78152)))+P22(f317(f317(f225(x78151),x78153),f317(f317(f266(x78151),x78154),x78152))) % 168.22/168.07 [7816]~P60(x78161)+~P22(f317(f317(f226(x78161),x78162),f2(x78161)))+P22(f317(f317(f226(x78161),f2(x78161)),x78162))+~P22(f317(f317(f225(x78161),x78164),f317(f317(f266(x78161),x78163),x78162)))+P22(f317(f317(f225(x78161),x78163),f317(f317(f90(x78161),x78164),x78162))) % 168.22/168.07 [7817]~P60(x78171)+~P22(f317(f317(f226(x78171),x78172),f2(x78171)))+P22(f317(f317(f226(x78171),f2(x78171)),x78172))+~P22(f317(f317(f226(x78171),x78174),f317(f317(f90(x78171),x78173),x78172)))+P22(f317(f317(f226(x78171),x78173),f317(f317(f266(x78171),x78174),x78172))) % 168.22/168.07 [7818]~P60(x78181)+~P22(f317(f317(f226(x78181),x78182),f2(x78181)))+P22(f317(f317(f226(x78181),f2(x78181)),x78182))+~P22(f317(f317(f226(x78181),x78184),f317(f317(f266(x78181),x78183),x78182)))+P22(f317(f317(f226(x78181),x78183),f317(f317(f90(x78181),x78184),x78182))) % 168.22/168.07 [7959]~P103(x79591)+~P29(x79591,x79592)+~P22(f317(f317(f225(a849),x79593),x79594))+P22(f317(f317(f225(x79591),f317(f317(f159(x79591),x79592),x79593)),f317(f317(f159(x79591),x79592),x79594)))+~P22(f317(f317(f226(a849),x79594),f317(f189(f850(x79591)),x79592))) % 168.22/168.07 [8012]~P112(x80121)+~P22(f317(f317(f225(x80121),x80122),f87(x80121)))+~P22(f317(f317(f225(x80121),f2(x80121)),x80122))+~P22(f317(f317(f225(a849),x80124),x80123))+P22(f317(f317(f225(x80121),f317(f317(f238(x80121),x80122),x80123)),f317(f317(f238(x80121),x80122),x80124))) % 168.22/168.07 [8013]~P112(x80131)+~P22(f317(f317(f226(x80131),x80132),f87(x80131)))+~P22(f317(f317(f226(x80131),f2(x80131)),x80132))+~P22(f317(f317(f226(a849),x80134),x80133))+P22(f317(f317(f226(x80131),f317(f317(f238(x80131),x80132),x80133)),f317(f317(f238(x80131),x80132),x80134))) % 168.22/168.07 [8014]~P112(x80141)+~P22(f317(f317(f225(x80141),f2(x80141)),x80142))+~P22(f317(f317(f226(a849),f2(a849)),x80143))+~P22(f317(f317(f226(x80141),x80142),x80144))+P22(f317(f317(f226(x80141),f317(f317(f238(x80141),x80142),x80143)),f317(f317(f238(x80141),x80144),x80143))) % 168.22/168.07 [8034]~P103(x80341)+~P29(x80341,f317(f163(x80341),x80342))+~P22(f317(f317(f225(a849),x80344),x80343))+P22(f317(f317(f225(x80341),f317(f317(f159(x80341),x80342),x80343)),f317(f317(f159(x80341),x80342),x80344)))+~P22(f317(f317(f226(a849),x80343),f317(f189(f850(x80341)),x80342))) % 168.22/168.07 [8284]~P60(x82841)+~P22(f317(f317(f225(x82841),x82842),f2(x82841)))+~P22(f317(f317(f225(x82841),x82843),x82844))+~P22(f317(f317(f226(x82841),f2(x82841)),f317(f317(f90(x82841),x82843),x82844)))+P22(f317(f317(f225(x82841),f317(f317(f266(x82841),x82842),x82843)),f317(f317(f266(x82841),x82842),x82844))) % 168.22/168.07 [8285]~P61(x82851)+~P22(f317(f317(f226(x82851),x82852),f2(x82851)))+~P22(f317(f317(f226(x82851),x82853),x82854))+~P22(f317(f317(f226(x82851),f2(x82851)),f317(f317(f90(x82851),x82853),x82854)))+P22(f317(f317(f226(x82851),f317(f317(f266(x82851),x82852),x82853)),f317(f317(f266(x82851),x82852),x82854))) % 168.22/168.07 [8296]~P61(x82961)+~P22(f317(f317(f225(x82961),x82964),x82963))+~P22(f317(f317(f225(x82961),f2(x82961)),x82962))+~P22(f317(f317(f226(x82961),f2(x82961)),f317(f317(f90(x82961),x82963),x82964)))+P22(f317(f317(f225(x82961),f317(f317(f266(x82961),x82962),x82963)),f317(f317(f266(x82961),x82962),x82964))) % 168.22/168.07 [8297]~P61(x82971)+~P22(f317(f317(f226(x82971),x82974),x82973))+~P22(f317(f317(f226(x82971),f2(x82971)),x82972))+~P22(f317(f317(f226(x82971),f2(x82971)),f317(f317(f90(x82971),x82973),x82974)))+P22(f317(f317(f226(x82971),f317(f317(f266(x82971),x82972),x82973)),f317(f317(f266(x82971),x82972),x82974))) % 168.22/168.07 [8407]P22(f317(x84071,x84072))+~P22(f317(f71(x84074),x84072))+P22(f317(x84071,f468(x84071,x84073,x84072,x84074)))+~P22(f317(x84071,f188(f858(x84074,a842))))+~P22(f317(f317(f225(f858(x84074,a842)),x84072),x84073)) % 168.22/168.07 [8417]P22(f317(x84171,x84172))+P22(f317(f71(x84173),f468(x84171,x84174,x84172,x84173)))+~P22(f317(f71(x84173),x84172))+~P22(f317(x84171,f188(f858(x84173,a842))))+~P22(f317(f317(f225(f858(x84173,a842)),x84172),x84174)) % 168.22/168.07 [8662]E(f317(f317(f89(a1),f429(x86621,x86622,x86623,x86624)),f430(x86621,x86622,x86623,x86624)),x86624)+~P22(f317(f317(f226(a1),f2(a1)),x86623))+~P22(f317(f317(f226(a1),x86622),x86624))+~P22(f317(f317(f319(a1),x86622),x86621))+P22(f317(f317(f226(a1),x86622),f317(f317(f21(a1),x86624),x86623))) % 168.22/168.07 [8877]~P22(f317(f317(f226(a1),f2(a1)),x88773))+~P22(f317(f317(f226(a1),x88772),x88774))+~P22(f317(f317(f319(a1),x88772),x88771))+P22(f317(f317(f319(a1),f429(x88771,x88772,x88773,x88774)),x88771))+P22(f317(f317(f226(a1),x88772),f317(f317(f21(a1),x88774),x88773))) % 168.22/168.07 [8890]P22(f317(x88901,x88902))+~P22(f317(f71(x88903),x88902))+P22(f317(f317(f319(x88903),f469(x88901,x88904,x88902,x88903)),x88904))+~P22(f317(x88901,f188(f858(x88903,a842))))+~P22(f317(f317(f225(f858(x88903,a842)),x88902),x88904)) % 168.22/168.07 [8907]E(f317(f317(f89(a1),f417(x89071,x89072,x89073,x89074)),f418(x89071,x89072,x89073,x89074)),x89074)+~P22(f317(f317(f226(a1),f2(a1)),x89073))+~P22(f317(f317(f225(a1),x89072),x89074))+P22(f317(f317(f225(a1),x89072),f317(f317(f21(a1),x89074),x89073)))+~P22(f317(f317(f319(a1),f317(f317(f21(a1),x89072),f87(a1))),x89071)) % 168.22/168.07 [8957]~P22(f317(f317(f226(a1),f2(a1)),x89573))+~P22(f317(f317(f226(a1),x89571),x89572))+~P22(f317(f317(f319(a1),x89571),x89574))+P22(f317(f317(f319(a1),f430(x89574,x89571,x89573,x89572)),f279(a1,f87(a1),x89573)))+P22(f317(f317(f226(a1),x89571),f317(f317(f21(a1),x89572),x89573))) % 168.22/168.07 [9050]~P22(f317(f317(f226(a1),f2(a1)),x90503))+~P22(f317(f317(f225(a1),x90502),x90504))+P22(f317(f317(f319(a1),f417(x90501,x90502,x90503,x90504)),x90501))+P22(f317(f317(f225(a1),x90502),f317(f317(f21(a1),x90504),x90503)))+~P22(f317(f317(f319(a1),f317(f317(f21(a1),x90502),f87(a1))),x90501)) % 168.22/168.07 [9088]~P22(f317(f317(f226(a1),f2(a1)),x90883))+~P22(f317(f317(f225(a1),x90881),x90882))+P22(f317(f317(f319(a1),f418(x90884,x90881,x90883,x90882)),f279(a1,f87(a1),x90883)))+P22(f317(f317(f225(a1),x90881),f317(f317(f21(a1),x90882),x90883)))+~P22(f317(f317(f319(a1),f317(f317(f21(a1),x90881),f87(a1))),x90884)) % 168.22/168.07 [9320]P22(f317(x93201,x93202))+~P22(f317(f317(f319(x93203),f469(x93201,x93204,x93202,x93203)),f468(x93201,x93204,x93202,x93203)))+~P22(f317(f71(x93203),x93202))+~P22(f317(x93201,f188(f858(x93203,a842))))+~P22(f317(f317(f225(f858(x93203,a842)),x93202),x93204)) % 168.22/168.07 [9531]P22(f317(x95311,x95312))+~P22(f317(f71(x95313),x95312))+~P22(f317(x95311,f317(f317(f286(x95313),f469(x95311,x95314,x95312,x95313)),f468(x95311,x95314,x95312,x95313))))+~P22(f317(x95311,f188(f858(x95313,a842))))+~P22(f317(f317(f225(f858(x95313,a842)),x95312),x95314)) % 168.22/168.07 [7591]~P60(x75911)+P22(f317(f317(f226(x75911),x75912),f2(x75911)))+~P22(f317(f317(f225(x75911),f2(x75911)),x75914))+P22(f317(f317(f226(x75911),f2(x75911)),x75912))+P22(f317(f317(f225(x75911),f317(f317(f266(x75911),x75913),x75912)),x75914)) % 168.22/168.07 [7592]~P60(x75921)+P22(f317(f317(f226(x75921),x75922),f2(x75921)))+P22(f317(f317(f226(x75921),f2(x75921)),x75922))+~P22(f317(f317(f226(x75921),f2(x75921)),x75924))+P22(f317(f317(f226(x75921),f317(f317(f266(x75921),x75923),x75922)),x75924)) % 168.22/168.07 [7865]~P22(f317(f317(f225(a1),x78654),f2(a1)))+~E(x78652,f317(f317(f89(a1),f317(f317(f90(a1),x78651),x78653)),x78654))+P22(f317(f317(f226(a1),f2(a1)),x78651))+~P22(f317(f317(f226(a1),x78651),x78654))+P22(f317(f58(x78652,x78651),f317(f317(f237(a1,a1),x78653),x78654))) % 168.22/168.07 [7902]~P22(f317(x79021,x79024))+P22(f317(x79021,f822(x79022,x79021,x79023)))+~P22(f317(f317(f225(a1),f2(a1)),x79022))+~P22(f317(f317(f226(a1),f2(a1)),x79023))+P22(f317(x79021,f317(f317(f21(a1),x79024),f317(f317(f90(a1),x79022),x79023)))) % 168.22/168.07 [7903]~P22(f317(x79031,x79034))+P22(f317(x79031,f824(x79032,x79031,x79033)))+~P22(f317(f317(f225(a1),f2(a1)),x79032))+~P22(f317(f317(f226(a1),f2(a1)),x79033))+P22(f317(x79031,f317(f317(f89(a1),x79034),f317(f317(f90(a1),x79032),x79033)))) % 168.22/168.07 [7904]~P60(x79041)+P22(f317(f317(f226(x79041),x79042),f2(x79041)))+P22(f317(f317(f226(x79041),f2(x79041)),x79042))+P22(f317(f317(f225(x79041),f2(x79041)),x79043))+~P22(f317(f317(f225(x79041),f317(f317(f266(x79041),x79044),x79042)),x79043)) % 168.22/168.07 [7905]~P60(x79051)+P22(f317(f317(f226(x79051),x79052),f2(x79051)))+P22(f317(f317(f226(x79051),f2(x79051)),x79052))+P22(f317(f317(f226(x79051),f2(x79051)),x79053))+~P22(f317(f317(f226(x79051),f317(f317(f266(x79051),x79054),x79052)),x79053)) % 168.22/168.07 [7953]~E(x79531,f317(f317(f89(a1),f317(f317(f90(a1),x79532),x79533)),x79534))+~P22(f317(f317(f225(a1),f2(a1)),x79534))+~P22(f317(f317(f226(a1),f2(a1)),x79532))+~P22(f317(f317(f226(a1),x79534),x79532))+P22(f317(f58(x79531,x79532),f317(f317(f237(a1,a1),x79533),x79534))) % 168.22/168.07 [8078]~P60(x80781)+P22(f317(f317(f226(x80781),x80782),f2(x80781)))+~P22(f317(f317(f225(x80781),f2(x80781)),x80784))+~P22(f317(f317(f225(x80781),x80783),f317(f317(f90(x80781),x80784),x80782)))+P22(f317(f317(f225(x80781),f317(f317(f266(x80781),x80783),x80782)),x80784)) % 168.22/168.07 [8079]~P60(x80791)+P22(f317(f317(f226(x80791),x80792),f2(x80791)))+~P22(f317(f317(f226(x80791),f2(x80791)),x80794))+~P22(f317(f317(f226(x80791),x80793),f317(f317(f90(x80791),x80794),x80792)))+P22(f317(f317(f226(x80791),f317(f317(f266(x80791),x80793),x80792)),x80794)) % 168.22/168.07 [8161]~P60(x81611)+P22(f317(f317(f226(x81611),x81612),f2(x81611)))+~P22(f317(f317(f225(x81611),x81613),f2(x81611)))+P22(f317(f317(f225(x81611),x81613),f317(f317(f266(x81611),x81614),x81612)))+~P22(f317(f317(f225(x81611),f317(f317(f90(x81611),x81613),x81612)),x81614)) % 168.22/168.07 [8162]~P60(x81621)+P22(f317(f317(f226(x81621),x81622),f2(x81621)))+~P22(f317(f317(f226(x81621),x81623),f2(x81621)))+P22(f317(f317(f226(x81621),x81623),f317(f317(f266(x81621),x81624),x81622)))+~P22(f317(f317(f226(x81621),f317(f317(f90(x81621),x81623),x81622)),x81624)) % 168.22/168.07 [8322]~P60(x83221)+~P22(f317(f317(f226(x83221),x83222),f2(x83221)))+P22(f317(f317(f226(x83221),f2(x83221)),x83222))+~P22(f317(f317(f225(x83221),f317(f317(f266(x83221),x83224),x83222)),x83223))+P22(f317(f317(f225(x83221),f317(f317(f90(x83221),x83223),x83222)),x83224)) % 168.22/168.07 [8323]~P60(x83231)+~P22(f317(f317(f226(x83231),x83232),f2(x83231)))+P22(f317(f317(f226(x83231),f2(x83231)),x83232))+~P22(f317(f317(f225(x83231),f317(f317(f90(x83231),x83234),x83232)),x83233))+P22(f317(f317(f225(x83231),f317(f317(f266(x83231),x83233),x83232)),x83234)) % 168.22/168.07 [8324]~P60(x83241)+~P22(f317(f317(f226(x83241),x83242),f2(x83241)))+P22(f317(f317(f226(x83241),f2(x83241)),x83242))+~P22(f317(f317(f226(x83241),f317(f317(f266(x83241),x83244),x83242)),x83243))+P22(f317(f317(f226(x83241),f317(f317(f90(x83241),x83243),x83242)),x83244)) % 168.22/168.07 [8325]~P60(x83251)+~P22(f317(f317(f226(x83251),x83252),f2(x83251)))+P22(f317(f317(f226(x83251),f2(x83251)),x83252))+~P22(f317(f317(f226(x83251),f317(f317(f90(x83251),x83254),x83252)),x83253))+P22(f317(f317(f226(x83251),f317(f317(f266(x83251),x83253),x83252)),x83254)) % 168.22/168.07 [8348]~P60(x83481)+~P22(f317(f317(f225(x83481),f2(x83481)),x83484))+P22(f317(f317(f226(x83481),f2(x83481)),x83482))+~P22(f317(f317(f225(x83481),f317(f317(f90(x83481),x83484),x83482)),x83483))+P22(f317(f317(f225(x83481),f317(f317(f266(x83481),x83483),x83482)),x83484)) % 168.22/168.07 [8349]~P60(x83491)+~P22(f317(f317(f226(x83491),f2(x83491)),x83494))+P22(f317(f317(f226(x83491),f2(x83491)),x83492))+~P22(f317(f317(f226(x83491),f317(f317(f90(x83491),x83494),x83492)),x83493))+P22(f317(f317(f226(x83491),f317(f317(f266(x83491),x83493),x83492)),x83494)) % 168.22/168.07 [8425]~P60(x84251)+~P22(f317(f317(f226(x84251),x84254),f2(x84251)))+~P22(f317(f317(f225(x84251),x84253),f317(f317(f90(x84251),x84252),x84254)))+P22(f317(f317(f225(x84251),x84252),f317(f317(f266(x84251),x84253),x84254)))+~P22(f317(f317(f225(x84251),f317(f317(f90(x84251),x84252),x84254)),x84253)) % 168.22/168.07 [8426]~P60(x84261)+~P22(f317(f317(f225(x84261),x84262),f2(x84261)))+~P22(f317(f317(f225(x84261),x84263),f317(f317(f90(x84261),x84262),x84264)))+P22(f317(f317(f225(x84261),x84262),f317(f317(f266(x84261),x84263),x84264)))+~P22(f317(f317(f225(x84261),f317(f317(f90(x84261),x84262),x84264)),x84263)) % 168.22/168.07 [8427]~P60(x84271)+~P22(f317(f317(f226(x84271),x84274),f2(x84271)))+~P22(f317(f317(f226(x84271),x84273),f317(f317(f90(x84271),x84272),x84274)))+P22(f317(f317(f226(x84271),x84272),f317(f317(f266(x84271),x84273),x84274)))+~P22(f317(f317(f226(x84271),f317(f317(f90(x84271),x84272),x84274)),x84273)) % 168.22/168.07 [8428]~P60(x84281)+~P22(f317(f317(f226(x84281),x84282),f2(x84281)))+~P22(f317(f317(f226(x84281),x84283),f317(f317(f90(x84281),x84282),x84284)))+P22(f317(f317(f226(x84281),x84282),f317(f317(f266(x84281),x84283),x84284)))+~P22(f317(f317(f226(x84281),f317(f317(f90(x84281),x84282),x84284)),x84283)) % 168.22/168.07 [8541]~P60(x85411)+~P22(f317(f317(f226(x85411),x85413),f2(x85411)))+~P22(f317(f317(f225(x85411),x85412),f317(f317(f90(x85411),x85414),x85413)))+~P22(f317(f317(f225(x85411),f317(f317(f90(x85411),x85414),x85413)),x85412))+P22(f317(f317(f225(x85411),f317(f317(f266(x85411),x85412),x85413)),x85414)) % 168.22/168.07 [8542]~P60(x85421)+~P22(f317(f317(f226(x85421),x85423),f2(x85421)))+~P22(f317(f317(f226(x85421),x85422),f317(f317(f90(x85421),x85424),x85423)))+~P22(f317(f317(f226(x85421),f317(f317(f90(x85421),x85424),x85423)),x85422))+P22(f317(f317(f226(x85421),f317(f317(f266(x85421),x85422),x85423)),x85424)) % 168.22/168.07 [8556]~P60(x85561)+~P22(f317(f317(f225(x85561),f2(x85561)),x85564))+~P22(f317(f317(f225(x85561),x85562),f317(f317(f90(x85561),x85564),x85563)))+~P22(f317(f317(f225(x85561),f317(f317(f90(x85561),x85564),x85563)),x85562))+P22(f317(f317(f225(x85561),f317(f317(f266(x85561),x85562),x85563)),x85564)) % 168.22/168.07 [8557]~P60(x85571)+~P22(f317(f317(f226(x85571),f2(x85571)),x85574))+~P22(f317(f317(f226(x85571),x85572),f317(f317(f90(x85571),x85574),x85573)))+~P22(f317(f317(f226(x85571),f317(f317(f90(x85571),x85574),x85573)),x85572))+P22(f317(f317(f226(x85571),f317(f317(f266(x85571),x85572),x85573)),x85574)) % 168.22/168.07 [8720]E(f317(f317(f21(a1),f431(x87201,x87202,x87203,x87204)),f432(x87201,x87202,x87203,x87204)),x87204)+~P22(f317(f317(f226(a1),f2(a1)),x87203))+~P22(f317(f317(f319(a1),x87202),x87201))+~P22(f317(f317(f226(a1),x87204),x87202))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x87204),x87203)),x87202)) % 168.22/168.07 [8797]~P22(f317(x87971,x87972))+~P22(f317(f317(f225(a1),f2(a1)),x87973))+~P22(f317(f317(f226(a1),f2(a1)),x87974))+~P22(f317(x87971,f317(f317(f89(a1),f824(x87973,x87971,x87974)),x87974)))+P22(f317(x87971,f317(f317(f89(a1),x87972),f317(f317(f90(a1),x87973),x87974)))) % 168.22/168.07 [8798]~P22(f317(x87981,x87982))+~P22(f317(f317(f225(a1),f2(a1)),x87983))+~P22(f317(f317(f226(a1),f2(a1)),x87984))+~P22(f317(x87981,f317(f317(f21(a1),f822(x87983,x87981,x87984)),x87984)))+P22(f317(x87981,f317(f317(f21(a1),x87982),f317(f317(f90(a1),x87983),x87984)))) % 168.22/168.07 [8952]~P22(f317(f317(f226(a1),f2(a1)),x89523))+~P22(f317(f317(f319(a1),x89522),x89521))+~P22(f317(f317(f226(a1),x89524),x89522))+P22(f317(f317(f319(a1),f431(x89521,x89522,x89523,x89524)),x89521))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x89524),x89523)),x89522)) % 168.22/168.07 [8970]E(f317(f317(f21(a1),f419(x89701,x89702,x89703,x89704)),f420(x89701,x89702,x89703,x89704)),x89704)+~P22(f317(f317(f226(a1),f2(a1)),x89703))+~P22(f317(f317(f225(a1),x89704),x89702))+~P22(f317(f317(f319(a1),f317(f317(f89(a1),x89702),f87(a1))),x89701))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x89704),x89703)),x89702)) % 168.22/168.07 [8995]~P22(f317(f317(f226(a1),f2(a1)),x89952))+~P22(f317(f317(f319(a1),x89953),x89954))+~P22(f317(f317(f226(a1),x89951),x89953))+P22(f317(f317(f319(a1),f432(x89954,x89953,x89952,x89951)),f279(a1,f87(a1),x89952)))+P22(f317(f317(f226(a1),f317(f317(f89(a1),x89951),x89952)),x89953)) % 168.22/168.07 [9083]~P22(f317(f317(f226(a1),f2(a1)),x90833))+~P22(f317(f317(f225(a1),x90834),x90832))+P22(f317(f317(f319(a1),f419(x90831,x90832,x90833,x90834)),x90831))+~P22(f317(f317(f319(a1),f317(f317(f89(a1),x90832),f87(a1))),x90831))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x90834),x90833)),x90832)) % 168.22/168.07 [9128]~P22(f317(f317(f226(a1),f2(a1)),x91282))+~P22(f317(f317(f225(a1),x91281),x91283))+P22(f317(f317(f319(a1),f420(x91284,x91283,x91282,x91281)),f279(a1,f87(a1),x91282)))+~P22(f317(f317(f319(a1),f317(f317(f89(a1),x91283),f87(a1))),x91284))+P22(f317(f317(f225(a1),f317(f317(f89(a1),x91281),x91282)),x91283)) % 168.22/168.07 [9412]~P37(x94121,x94123)+~P20(x94121,x94124)+P37(x94121,f317(f317(f122(f858(f857(x94121,x94121),a842)),x94122),x94123))+~P22(f317(f317(f225(f858(f857(x94121,x94121),a842)),x94122),f317(f244(f858(f857(x94121,x94121),a842),f858(f857(x94121,x94121),a842)),x94124)))+~P22(f317(f317(f225(f858(f857(x94121,x94121),a842)),x94123),f317(f246(f858(f857(x94121,x94121),a842),f858(f857(x94121,x94121),a842)),x94124))) % 168.22/168.07 [9693]~E(f317(f344(x96931,x96934,x96933,x96932),f348(x96931,x96934,x96933,x96932)),f191(f850(a313)))+P22(f317(f317(f226(a1),f347(x96931,x96934,x96933,x96932)),f348(x96931,x96934,x96933,x96932)))+P22(f317(f317(f317(x96931,x96932),x96933),x96934))+P22(f317(f317(f317(x96931,f344(x96931,x96934,x96933,x96932)),f347(x96931,x96934,x96933,x96932)),f317(f317(f89(a1),f348(x96931,x96934,x96933,x96932)),f87(a1))))+~P22(f317(f305(f857(f858(a1,f853(f850(a313))),f857(a1,a1)),a295),f317(f317(f237(f858(a1,f853(f850(a313))),f857(a1,a1)),x96932),f317(f317(f237(a1,a1),x96933),x96934)))) % 168.22/168.07 [9802]~P13(x98022,x98024,x98023)+E(x98021,f188(f858(x98022,a842)))+~P22(f317(f71(x98022),x98021))+P22(f317(f317(f319(x98022),f317(x98023,x98021)),x98021))+~P22(f317(f317(f319(x98022),f317(f317(x98024,f376(x98021,x98023,x98024,x98022)),f377(x98021,x98023,x98024,x98022))),f317(f317(f286(x98022),f376(x98021,x98023,x98024,x98022)),f317(f317(f286(x98022),f377(x98021,x98023,x98024,x98022)),f188(f858(x98022,a842)))))) % 168.22/168.07 [9729]~P104(x97292)+~P57(x97291)+~P22(f317(f317(f225(f858(x97291,x97292)),x97293),x97294))+P22(f317(f317(f226(f858(x97291,x97292)),x97293),x97294))+~P22(f317(f67(x97291),f317(f317(f8(a842,a842,x97291),a312),f317(f317(f18(x97291,x97292,a842),f317(f317(f8(x97292,f858(x97292,a842),x97291),a314),x97293)),x97294)))) % 168.22/168.07 [9327]~P49(x93271,x93271,x93274)+P22(f317(f317(f319(f857(x93271,x93271)),f317(f317(f237(x93271,x93271),x93272),x93273)),f284(x93271,x93274)))+P22(f317(f317(f319(f857(x93271,x93271)),f317(f317(f237(x93271,x93271),x93273),x93272)),f284(x93271,x93274)))+~P22(f317(f317(f319(f857(x93271,x93271)),f317(f317(f237(x93271,x93271),x93275),x93272)),f284(x93271,x93274)))+~P22(f317(f317(f319(f857(x93271,x93271)),f317(f317(f237(x93271,x93271),x93275),x93273)),f284(x93271,x93274))) % 168.22/168.07 [5543]E(x55431,f2(a849))+~E(f317(f54(x55432),x55435),x55431)+E(f317(f54(x55432),x55433),f317(a124,x55431))+~E(x55433,f317(f317(f286(x55432),x55434),x55435))+P22(f317(f317(f319(x55432),x55434),x55435)) % 168.22/168.07 [5664]~P59(x56642)+E(x56641,f2(x56642))+E(x56643,f2(x56642))+~E(f317(f317(f266(x56642),x56644),x56643),f317(f317(f266(x56642),x56645),x56641))+E(f317(f317(f90(x56642),x56644),x56641),f317(f317(f90(x56642),x56645),x56643)) % 168.22/168.07 [5665]~P59(x56652)+E(x56651,f2(x56652))+E(x56653,f2(x56652))+~E(f317(f317(f90(x56652),x56654),x56653),f317(f317(f90(x56652),x56655),x56651))+E(f317(f317(f266(x56652),x56654),x56651),f317(f317(f266(x56652),x56655),x56653)) % 168.22/168.07 [5725]~E(f317(f54(x57251),x57255),x57253)+~E(x57255,f188(f858(x57251,a842)))+E(f317(f54(x57251),x57252),f317(a124,x57253))+~E(x57252,f317(f317(f286(x57251),x57254),x57255))+P22(f317(f317(f319(x57251),x57254),x57255)) % 168.22/168.07 [5947]~P84(x59472)+~E(f317(x59473,x59475),f2(x59472))+E(f317(f317(f9(x59471,x59472),x59473),x59474),f2(x59472))+~P22(f317(f71(x59471),x59474))+~P22(f317(f317(f319(x59471),x59475),x59474)) % 168.22/168.07 [6309]~P103(x63093)+E(x63091,x63092)+~E(f317(f278(x63093,x63094),x63091),f317(f278(x63093,x63095),x63092))+~P22(f317(f317(f226(x63093),x63095),x63092))+~P22(f317(f317(f226(x63093),x63094),x63091)) % 168.22/168.07 [6310]~P103(x63103)+E(x63101,x63102)+~E(f317(f278(x63103,x63101),x63104),f317(f278(x63103,x63102),x63105))+~P22(f317(f317(f226(x63103),x63102),x63105))+~P22(f317(f317(f226(x63103),x63101),x63104)) % 168.22/168.07 [7355]~P103(x73551)+~P29(x73551,f317(f317(f127(x73551),x73554),x73555))+~P22(f317(f317(f319(x73551),x73553),f317(f166(x73551),x73555)))+~P22(f317(f317(f319(x73551),x73552),f317(f166(x73551),x73554)))+P22(f317(f317(f225(x73551),x73552),x73553)) % 168.22/168.07 [8464]~P104(x84641)+~P22(f317(f317(f226(f858(x84641,a842)),f279(x84641,x84645,x84642)),f279(x84641,x84644,x84643)))+~P22(f317(f317(f225(x84641),x84645),x84642))+P22(f317(f317(f226(x84641),x84642),x84643))+P22(f317(f317(f226(x84641),x84644),x84645)) % 168.22/168.07 [9845]~P12(x98452,x98455,x98453)+E(x98451,f188(f858(x98452,a842)))+~E(f317(f317(x98455,f317(x98454,f540(x98451,x98454,x98453,x98455,x98452))),f317(x98454,f541(x98451,x98454,x98453,x98455,x98452))),f317(x98454,f317(f317(x98455,f540(x98451,x98454,x98453,x98455,x98452)),f541(x98451,x98454,x98453,x98455,x98452))))+E(f317(x98453,f317(f287(x98452,x98452,x98454),x98451)),f317(x98454,f317(x98453,x98451)))+~P22(f317(f71(x98452),x98451)) % 168.22/168.07 [6304]~P13(x63042,x63045,x63043)+E(x63041,f188(f858(x63042,a842)))+~P22(f317(f71(x63042),x63041))+E(f317(x63043,f317(f317(f286(x63042),x63044),x63041)),f317(f317(x63045,x63044),f317(x63043,x63041)))+P22(f317(f317(f319(x63042),x63044),x63041)) % 168.22/168.07 [7123]~P12(x71232,x71233,x71234)+E(f317(f317(x71233,f317(x71234,x71231)),f317(x71234,x71235)),f317(x71234,x71235))+E(x71231,f188(f858(x71232,a842)))+~P22(f317(f71(x71232),x71235))+~P22(f317(f317(f225(f858(x71232,a842)),x71231),x71235)) % 168.22/168.07 [7490]~P13(x74904,x74905,x74901)+E(f317(x74901,x74902),x74903)+~P22(f317(f71(x74904),x74902))+~E(f317(f317(f21(f858(x74904,a842)),x74902),f317(f317(f286(x74904),x74903),f188(f858(x74904,a842)))),f188(f858(x74904,a842)))+~P22(f317(f317(f319(x74904),x74903),x74902)) % 168.22/168.07 [7574]E(x75741,x75742)+~E(f317(f189(f850(x75743)),x75742),f317(f189(f850(x75744)),x75745))+~E(f317(f189(f850(x75743)),x75741),f317(f189(f850(x75744)),x75745))+~E(f317(f171(x75744,x75743),f317(f317(f175(x75744,x75743),x75745),x75741)),f317(f171(x75744,x75743),f317(f317(f175(x75744,x75743),x75745),x75742)))+~P22(f317(f131(x75744),x75745)) % 168.22/168.07 [8433]E(x84331,x84332)+~P6(x84333,x84334,x84335)+E(f317(f317(f113(f858(x84333,a842)),x84331),x84332),f188(f858(x84333,a842)))+~P22(f317(f317(f319(f858(x84333,a842)),x84332),f317(f317(f70(x84333),x84334),x84335)))+~P22(f317(f317(f319(f858(x84333,a842)),x84331),f317(f317(f70(x84333),x84334),x84335))) % 168.22/168.07 [9209]~P70(x92092)+~E(f317(x92093,f410(x92093,x92094,x92095,x92091,x92092)),f87(x92092))+E(f317(f317(f9(x92091,x92092),x92093),x92094),f317(f317(f9(x92091,x92092),x92093),x92095))+~P22(f317(f71(x92091),x92095))+~P22(f317(f317(f225(f858(x92091,a842)),x92094),x92095)) % 168.22/168.07 [9210]~P70(x92102)+~E(f317(x92103,f412(x92103,x92104,x92105,x92101,x92102)),f87(x92102))+E(f317(f317(f9(x92101,x92102),x92103),x92104),f317(f317(f9(x92101,x92102),x92103),x92105))+~P22(f317(f71(x92101),x92105))+~P22(f317(f317(f225(f858(x92101,a842)),x92104),x92105)) % 168.22/168.07 [9211]~P67(x92112)+~E(f317(x92113,f470(x92113,x92114,x92115,x92111,x92112)),f2(x92112))+E(f317(f317(f6(x92111,x92112),x92113),x92114),f317(f317(f6(x92111,x92112),x92113),x92115))+~P22(f317(f71(x92111),x92115))+~P22(f317(f317(f225(f858(x92111,a842)),x92114),x92115)) % 168.22/168.07 [9212]~P67(x92122)+~E(f317(x92123,f472(x92123,x92124,x92125,x92121,x92122)),f2(x92122))+E(f317(f317(f6(x92121,x92122),x92123),x92124),f317(f317(f6(x92121,x92122),x92123),x92125))+~P22(f317(f71(x92121),x92125))+~P22(f317(f317(f225(f858(x92121,a842)),x92124),x92125)) % 168.22/168.07 [9675]~P80(x96751)+~P22(f317(f71(x96752),x96755))+~P22(f317(f317(f225(x96751),f2(x96751)),f317(x96753,f456(x96753,x96754,x96755,x96752,x96751))))+P22(f317(f317(f225(x96751),f317(f317(f6(x96752,x96751),x96753),x96754)),f317(f317(f6(x96752,x96751),x96753),x96755)))+~P22(f317(f317(f225(f858(x96752,a842)),x96754),x96755)) % 168.22/168.07 [7225]E(x72251,f2(a849))+P22(f317(x72252,x72253))+~E(x72254,f317(f317(f89(a849),f317(f317(f90(a849),x72251),x72253)),x72255))+~P22(f317(x72252,f317(f48(a849,x72254),x72251)))+~P22(f317(f317(f226(a849),x72255),x72251)) % 168.22/168.07 [7430]E(x74301,f2(a849))+P22(f317(x74302,x74303))+~P22(f317(x74302,f55(a849,x74304,x74301)))+~E(x74304,f317(f317(f89(a849),f317(f317(f90(a849),x74301),x74305)),x74303))+~P22(f317(f317(f226(a849),x74303),x74301)) % 168.22/168.07 [7723]~P59(x77233)+E(f317(x77231,x77232),f2(x77233))+~P22(f317(f71(x77234),x77235))+E(f317(f317(f9(x77234,x77233),x77231),f317(f317(f21(f858(x77234,a842)),x77235),f317(f317(f286(x77234),x77232),f188(f858(x77234,a842))))),f317(f317(f9(x77234,x77233),x77231),x77235))+P22(f317(f317(f319(x77234),x77232),x77235)) % 168.22/168.07 [8120]~P70(x81201)+~P22(f317(f71(x81202),x81205))+~P22(f317(f71(x81202),x81204))+~E(f317(f317(f113(f858(x81202,a842)),x81204),x81205),f188(f858(x81202,a842)))+E(f317(f317(f90(x81201),f317(f317(f9(x81202,x81201),x81203),x81204)),f317(f317(f9(x81202,x81201),x81203),x81205)),f317(f317(f9(x81202,x81201),x81203),f317(f317(f122(f858(x81202,a842)),x81204),x81205))) % 168.22/168.07 [8121]~P67(x81211)+~P22(f317(f71(x81212),x81215))+~P22(f317(f71(x81212),x81214))+~E(f317(f317(f113(f858(x81212,a842)),x81214),x81215),f188(f858(x81212,a842)))+E(f317(f317(f89(x81211),f317(f317(f6(x81212,x81211),x81213),x81214)),f317(f317(f6(x81212,x81211),x81213),x81215)),f317(f317(f6(x81212,x81211),x81213),f317(f317(f122(f858(x81212,a842)),x81214),x81215))) % 168.22/168.07 [8214]~P59(x82143)+E(f317(x82141,x82142),f2(x82143))+~P22(f317(f71(x82144),x82145))+E(f317(f317(f9(x82144,x82143),x82141),f317(f317(f21(f858(x82144,a842)),x82145),f317(f317(f286(x82144),x82142),f188(f858(x82144,a842))))),f317(f317(f266(x82143),f317(f317(f9(x82144,x82143),x82141),x82145)),f317(x82141,x82142)))+~P22(f317(f317(f319(x82144),x82142),x82145)) % 168.22/168.07 [8932]~P6(x89321,x89325,x89324)+~E(f317(f317(f70(x89321),f317(f317(f286(x89321),x89322),f188(f858(x89321,a842)))),x89324),f317(f317(f70(x89321),f317(f317(f286(x89321),x89323),f188(f858(x89321,a842)))),x89324))+~P22(f317(f317(f319(x89321),x89323),x89325))+~P22(f317(f317(f319(x89321),x89322),x89325))+P22(f317(f317(f319(f857(x89321,x89321)),f317(f317(f237(x89321,x89321),x89322),x89323)),x89324)) % 168.22/168.07 [8951]~P6(x89511,x89515,x89513)+E(f317(f317(f70(x89511),f317(f317(f286(x89511),x89512),f188(f858(x89511,a842)))),x89513),f317(f317(f70(x89511),f317(f317(f286(x89511),x89514),f188(f858(x89511,a842)))),x89513))+~P22(f317(f317(f319(x89511),x89514),x89515))+~P22(f317(f317(f319(x89511),x89512),x89515))+~P22(f317(f317(f319(f857(x89511,x89511)),f317(f317(f237(x89511,x89511),x89512),x89514)),x89513)) % 168.22/168.07 [9236]~P70(x92361)+~P22(f317(f71(x92362),x92365))+~P22(f317(f71(x92362),x92364))+~E(f317(f317(f113(f858(x92362,a842)),x92364),x92365),f188(f858(x92362,a842)))+E(f317(f317(f90(x92361),f317(f317(f317(f75(x92361,x92362,f90(x92361)),x92363),f87(x92361)),x92364)),f317(f317(f317(f75(x92361,x92362,f90(x92361)),x92363),f87(x92361)),x92365)),f317(f317(f317(f75(x92361,x92362,f90(x92361)),x92363),f87(x92361)),f317(f317(f122(f858(x92362,a842)),x92364),x92365))) % 168.22/168.07 [9244]~P70(x92441)+~E(f317(x92443,f395(x92443,x92445,x92444,x92442,x92441)),f87(x92441))+~P22(f317(f71(x92442),x92444))+~P22(f317(f71(x92442),x92445))+E(f317(f317(f90(x92441),f317(f317(f9(x92442,x92441),x92443),x92444)),f317(f317(f9(x92442,x92441),x92443),x92445)),f317(f317(f9(x92442,x92441),x92443),f317(f317(f122(f858(x92442,a842)),x92444),x92445))) % 168.22/168.07 [9245]~P70(x92451)+~E(f317(x92453,f397(x92453,x92455,x92454,x92452,x92451)),f87(x92451))+~P22(f317(f71(x92452),x92454))+~P22(f317(f71(x92452),x92455))+E(f317(f317(f90(x92451),f317(f317(f9(x92452,x92451),x92453),x92454)),f317(f317(f9(x92452,x92451),x92453),x92455)),f317(f317(f9(x92452,x92451),x92453),f317(f317(f122(f858(x92452,a842)),x92454),x92455))) % 168.22/168.07 [9246]~P67(x92461)+~E(f317(x92463,f454(x92463,x92465,x92464,x92462,x92461)),f2(x92461))+~P22(f317(f71(x92462),x92464))+~P22(f317(f71(x92462),x92465))+E(f317(f317(f89(x92461),f317(f317(f6(x92462,x92461),x92463),x92464)),f317(f317(f6(x92462,x92461),x92463),x92465)),f317(f317(f6(x92462,x92461),x92463),f317(f317(f122(f858(x92462,a842)),x92464),x92465))) % 168.22/168.07 [9247]~P67(x92471)+~E(f317(x92473,f464(x92473,x92475,x92474,x92472,x92471)),f2(x92471))+~P22(f317(f71(x92472),x92474))+~P22(f317(f71(x92472),x92475))+E(f317(f317(f89(x92471),f317(f317(f6(x92472,x92471),x92473),x92474)),f317(f317(f6(x92472,x92471),x92473),x92475)),f317(f317(f6(x92472,x92471),x92473),f317(f317(f122(f858(x92472,a842)),x92474),x92475))) % 168.22/168.07 [9454]~P70(x94541)+~E(f317(x94543,f396(x94543,x94545,x94544,x94542,x94541)),f87(x94541))+~P22(f317(f71(x94542),x94544))+~P22(f317(f71(x94542),x94545))+E(f317(f317(f90(x94541),f317(f317(f317(f75(x94541,x94542,f90(x94541)),x94543),f87(x94541)),x94544)),f317(f317(f317(f75(x94541,x94542,f90(x94541)),x94543),f87(x94541)),x94545)),f317(f317(f317(f75(x94541,x94542,f90(x94541)),x94543),f87(x94541)),f317(f317(f122(f858(x94542,a842)),x94544),x94545))) % 168.22/168.07 [9556]~P70(x95562)+E(f317(f317(f9(x95561,x95562),x95563),x95564),f317(f317(f9(x95561,x95562),x95563),x95565))+~P22(f317(f71(x95561),x95565))+~P22(f317(f317(f225(f858(x95561,a842)),x95564),x95565))+P22(f317(f317(f319(x95561),f410(x95563,x95564,x95565,x95561,x95562)),f317(f317(f21(f858(x95561,a842)),x95565),x95564))) % 168.22/168.07 [9557]~P70(x95572)+E(f317(f317(f9(x95571,x95572),x95573),x95574),f317(f317(f9(x95571,x95572),x95573),x95575))+~P22(f317(f71(x95571),x95575))+~P22(f317(f317(f225(f858(x95571,a842)),x95574),x95575))+P22(f317(f317(f319(x95571),f412(x95573,x95574,x95575,x95571,x95572)),f317(f317(f21(f858(x95571,a842)),x95575),x95574))) % 168.22/168.07 [9558]~P67(x95582)+E(f317(f317(f6(x95581,x95582),x95583),x95584),f317(f317(f6(x95581,x95582),x95583),x95585))+~P22(f317(f71(x95581),x95585))+~P22(f317(f317(f225(f858(x95581,a842)),x95584),x95585))+P22(f317(f317(f319(x95581),f470(x95583,x95584,x95585,x95581,x95582)),f317(f317(f21(f858(x95581,a842)),x95585),x95584))) % 168.22/168.07 [9559]~P67(x95592)+E(f317(f317(f6(x95591,x95592),x95593),x95594),f317(f317(f6(x95591,x95592),x95593),x95595))+~P22(f317(f71(x95591),x95595))+~P22(f317(f317(f225(f858(x95591,a842)),x95594),x95595))+P22(f317(f317(f319(x95591),f472(x95593,x95594,x95595,x95591,x95592)),f317(f317(f21(f858(x95591,a842)),x95595),x95594))) % 168.22/168.07 [9575]~P70(x95751)+~P22(f317(f71(x95752),x95754))+~P22(f317(f71(x95752),x95755))+E(f317(f317(f90(x95751),f317(f317(f9(x95752,x95751),x95753),x95754)),f317(f317(f9(x95752,x95751),x95753),x95755)),f317(f317(f9(x95752,x95751),x95753),f317(f317(f122(f858(x95752,a842)),x95754),x95755)))+P22(f317(f317(f319(x95752),f395(x95753,x95755,x95754,x95752,x95751)),f317(f317(f113(f858(x95752,a842)),x95754),x95755))) % 168.22/168.07 [9576]~P70(x95761)+~P22(f317(f71(x95762),x95764))+~P22(f317(f71(x95762),x95765))+E(f317(f317(f90(x95761),f317(f317(f9(x95762,x95761),x95763),x95764)),f317(f317(f9(x95762,x95761),x95763),x95765)),f317(f317(f9(x95762,x95761),x95763),f317(f317(f122(f858(x95762,a842)),x95764),x95765)))+P22(f317(f317(f319(x95762),f397(x95763,x95765,x95764,x95762,x95761)),f317(f317(f113(f858(x95762,a842)),x95764),x95765))) % 168.22/168.07 [9577]~P67(x95771)+~P22(f317(f71(x95772),x95774))+~P22(f317(f71(x95772),x95775))+E(f317(f317(f89(x95771),f317(f317(f6(x95772,x95771),x95773),x95774)),f317(f317(f6(x95772,x95771),x95773),x95775)),f317(f317(f6(x95772,x95771),x95773),f317(f317(f122(f858(x95772,a842)),x95774),x95775)))+P22(f317(f317(f319(x95772),f454(x95773,x95775,x95774,x95772,x95771)),f317(f317(f113(f858(x95772,a842)),x95774),x95775))) % 168.22/168.07 [9578]~P67(x95781)+~P22(f317(f71(x95782),x95784))+~P22(f317(f71(x95782),x95785))+E(f317(f317(f89(x95781),f317(f317(f6(x95782,x95781),x95783),x95784)),f317(f317(f6(x95782,x95781),x95783),x95785)),f317(f317(f6(x95782,x95781),x95783),f317(f317(f122(f858(x95782,a842)),x95784),x95785)))+P22(f317(f317(f319(x95782),f464(x95783,x95785,x95784,x95782,x95781)),f317(f317(f113(f858(x95782,a842)),x95784),x95785))) % 168.22/168.07 [9585]~P80(x95855)+~P22(f317(f71(x95851),x95854))+P22(f317(f317(f225(x95855),f317(f317(f6(x95851,x95855),x95852),x95853)),f317(f317(f6(x95851,x95855),x95852),x95854)))+~P22(f317(f317(f225(f858(x95851,a842)),x95853),x95854))+P22(f317(f317(f319(x95851),f456(x95852,x95853,x95854,x95851,x95855)),f317(f317(f21(f858(x95851,a842)),x95854),x95853))) % 168.22/168.07 [9638]~P70(x96381)+~P22(f317(f71(x96382),x96384))+~P22(f317(f71(x96382),x96385))+E(f317(f317(f90(x96381),f317(f317(f317(f75(x96381,x96382,f90(x96381)),x96383),f87(x96381)),x96384)),f317(f317(f317(f75(x96381,x96382,f90(x96381)),x96383),f87(x96381)),x96385)),f317(f317(f317(f75(x96381,x96382,f90(x96381)),x96383),f87(x96381)),f317(f317(f122(f858(x96382,a842)),x96384),x96385)))+P22(f317(f317(f319(x96382),f396(x96383,x96385,x96384,x96382,x96381)),f317(f317(f113(f858(x96382,a842)),x96384),x96385))) % 168.22/168.07 [8623]~P13(x86231,x86234,x86235)+~P22(f317(f71(x86231),x86232))+E(f317(f317(f21(f858(x86231,a842)),x86232),f317(f317(f286(x86231),x86233),f188(f858(x86231,a842)))),f188(f858(x86231,a842)))+~P22(f317(f317(f319(x86231),x86233),x86232))+E(f317(f317(x86234,x86233),f317(x86235,f317(f317(f21(f858(x86231,a842)),x86232),f317(f317(f286(x86231),x86233),f188(f858(x86231,a842)))))),f317(x86235,x86232)) % 168.22/168.07 [8694]~P13(x86941,x86944,x86945)+~P22(f317(f71(x86941),x86943))+~P22(f317(f71(x86941),x86942))+E(f317(f317(f113(f858(x86941,a842)),x86942),x86943),f188(f858(x86941,a842)))+E(f317(f317(x86944,f317(x86945,f317(f317(f122(f858(x86941,a842)),x86942),x86943))),f317(x86945,f317(f317(f113(f858(x86941,a842)),x86942),x86943))),f317(f317(x86944,f317(x86945,x86942)),f317(x86945,x86943))) % 168.22/168.07 [9249]~P22(f317(f317(f225(a1),x92494),f2(a1)))+~P22(f317(f317(f226(a1),x92493),x92495))+P22(f317(f317(f225(a1),x92491),x92492))+~P22(f317(f317(f226(a1),x92493),x92494))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),f317(f317(f90(a1),x92493),x92492)),x92495)),f317(f317(f89(a1),f317(f317(f90(a1),x92493),x92491)),x92494))) % 168.22/168.07 [9251]~P22(f317(f317(f225(a1),f2(a1)),x92515))+P22(f317(f317(f225(a1),x92511),x92512))+~P22(f317(f317(f226(a1),x92513),x92514))+~P22(f317(f317(f226(a1),x92515),x92514))+~P22(f317(f317(f225(a1),f317(f317(f89(a1),f317(f317(f90(a1),x92514),x92511)),x92515)),f317(f317(f89(a1),f317(f317(f90(a1),x92514),x92512)),x92513))) % 168.22/168.07 [9361]~P59(x93615)+E(f317(x93611,f400(x93611,x93612,x93613,x93614,x93615)),f2(x93615))+~P22(f317(f71(x93614),x93613))+~P22(f317(f71(x93614),x93612))+E(f317(f317(f266(x93615),f317(f317(f90(x93615),f317(f317(f9(x93614,x93615),x93611),x93613)),f317(f317(f9(x93614,x93615),x93611),x93612))),f317(f317(f9(x93614,x93615),x93611),f317(f317(f113(f858(x93614,a842)),x93613),x93612))),f317(f317(f9(x93614,x93615),x93611),f317(f317(f122(f858(x93614,a842)),x93613),x93612))) % 168.22/168.07 [9631]~P59(x96311)+~P22(f317(f71(x96312),x96314))+~P22(f317(f71(x96312),x96315))+E(f317(f317(f266(x96311),f317(f317(f90(x96311),f317(f317(f9(x96312,x96311),x96313),x96314)),f317(f317(f9(x96312,x96311),x96313),x96315))),f317(f317(f9(x96312,x96311),x96313),f317(f317(f113(f858(x96312,a842)),x96314),x96315))),f317(f317(f9(x96312,x96311),x96313),f317(f317(f122(f858(x96312,a842)),x96314),x96315)))+P22(f317(f317(f319(x96312),f400(x96313,x96315,x96314,x96312,x96311)),f317(f317(f113(f858(x96312,a842)),x96314),x96315))) % 168.22/168.07 [8969]E(f317(f317(f127(x89691),x89692),x89693),f317(f317(f127(x89691),x89694),x89695))+~E(f317(f317(f167(x89691),f317(f189(f850(x89691)),x89694)),x89692),x89694)+~E(f317(f317(f167(x89691),f317(f189(f850(x89691)),x89692)),x89694),x89692)+~E(x89695,f317(f317(f127(x89691),f317(f317(f132(x89691),f317(f189(f850(x89691)),x89694)),x89692)),x89693))+~E(f317(f317(f127(x89691),f317(f317(f132(x89691),f317(f189(f850(x89691)),x89692)),x89694)),x89695),x89693) % 168.22/168.07 [9359]~P103(x93592)+E(f317(f317(f143(x93591,x93592,x93593),x93594),f164(x93591,x93594,x93595)),x93595)+~P29(x93592,f317(f317(f148(x93591,x93592),x93593),x93595))+~P22(f317(f317(f319(x93591),x93594),f317(f166(x93591),x93595)))+~E(f317(f135(x93591),f317(f130(x93591,f317(f317(f8(x93592,a842,x93591),f317(a314,f317(x93593,x93594))),x93593)),x93595)),x93594) % 168.22/168.07 [9690]~P64(x96901)+~P22(f317(f76(x96901,x96901,f90(x96901),x96902,x96903),x96905))+~P22(f317(f317(f319(x96901),x96904),x96903))+P22(f317(f317(f319(x96901),x96902),x96903))+P22(f317(f76(x96901,x96901,f90(x96901),x96904,f317(f317(f286(x96901),x96902),f317(f317(f21(f858(x96901,a842)),x96903),f317(f317(f286(x96901),x96904),f188(f858(x96901,a842)))))),x96905)) % 168.22/168.07 [7128]E(x71281,x71282)+~P19(x71284,x71285,x71283,x71286)+~E(f317(x71283,x71281),f317(x71283,x71282))+~P22(f317(f317(f319(x71284),x71282),x71286))+~P22(f317(f317(f319(x71284),x71281),x71286)) % 168.22/168.07 [6398]~P109(x63984)+E(x63981,x63982)+~E(x63985,x63986)+E(x63983,f2(x63984))+~E(f317(f317(f89(x63984),x63985),f317(f317(f90(x63984),x63983),x63981)),f317(f317(f89(x63984),x63986),f317(f317(f90(x63984),x63983),x63982))) % 168.22/168.07 [7411]~P103(x74111)+~P27(x74111)+~P22(f317(f317(f226(x74111),x74112),f317(x74115,x74116)))+~P22(f317(f317(f319(x74113),x74116),x74114))+P22(f317(f317(f226(x74111),x74112),f317(f317(f51(x74113,x74111),x74114),x74115))) % 168.22/168.07 [8089]~P103(x80891)+~P27(x80891)+~P22(f317(f317(f226(x80891),f317(x80894,x80896)),x80895))+~P22(f317(f317(f319(x80892),x80896),x80893))+P22(f317(f317(f226(x80891),f317(f317(f52(x80892,x80891),x80893),x80894)),x80895)) % 168.22/168.07 [8354]~P14(x83542,x83545,x83546,x83541)+~P22(f317(f71(x83542),x83544))+~P22(f317(f71(x83542),x83543))+~E(f317(f317(f113(f858(x83542,a842)),x83543),x83544),f188(f858(x83542,a842)))+E(f317(x83541,f317(f317(f122(f858(x83542,a842)),x83543),x83544)),f317(f82(x83545,x83545,x83545,f317(x83541,x83543)),f317(x83541,x83544))) % 168.22/168.07 [8665]E(x86651,x86652)+~P51(x86654,x86655,x86656,x86653,x86657)+~E(f317(x86653,x86651),f317(x86653,x86652))+~P22(f317(f317(f319(x86655),x86652),x86657))+~P22(f317(f317(f319(x86655),x86651),x86657)) % 168.22/168.07 [9947]~P22(f317(x99472,x99474))+~E(x99475,f317(f130(x99471,x99472),x99477))+E(f317(f130(x99471,x99472),x99473),f317(f317(f145(x99471),x99474),x99475))+~E(x99473,f317(f317(f127(x99471),x99476),f317(f317(f145(x99471),x99474),x99477)))+P22(f317(x99472,f728(x99475,x99474,x99473,x99472,x99471,x99476,x99477))) % 168.22/168.07 [9948]~P22(f317(x99484,x99482))+~E(x99483,f317(f130(x99481,x99484),x99487))+E(f317(f317(f145(x99481),x99482),x99483),f317(f130(x99481,x99484),x99485))+~E(x99485,f317(f317(f127(x99481),x99486),f317(f317(f145(x99481),x99482),x99487)))+P22(f317(x99484,f730(x99485,x99484,x99483,x99482,x99481,x99486,x99487))) % 168.22/168.07 [9981]~P22(f317(x99812,x99814))+~E(x99815,f317(f130(x99811,x99812),x99817))+E(f317(f130(x99811,x99812),x99813),f317(f317(f145(x99811),x99814),x99815))+~E(x99813,f317(f317(f127(x99811),x99816),f317(f317(f145(x99811),x99814),x99817)))+P22(f317(f317(f319(x99811),f728(x99815,x99814,x99813,x99812,x99811,x99816,x99817)),f317(f166(x99811),x99816))) % 168.22/168.07 [9982]~P22(f317(x99824,x99822))+~E(x99823,f317(f130(x99821,x99824),x99827))+E(f317(f317(f145(x99821),x99822),x99823),f317(f130(x99821,x99824),x99825))+~E(x99825,f317(f317(f127(x99821),x99826),f317(f317(f145(x99821),x99822),x99827)))+P22(f317(f317(f319(x99821),f730(x99825,x99824,x99823,x99822,x99821,x99826,x99827)),f317(f166(x99821),x99826))) % 168.22/168.07 [9985]~P6(x99851,x99857,x99856)+~P9(x99851,f858(x99855,a842),x99856,x99854)+P22(f317(f317(f319(x99851),f504(x99852,x99853,x99854,x99855,x99856,x99857,x99851)),x99857))+~P22(f317(f317(f319(f858(x99851,a842)),x99853),f317(f317(f70(x99851),x99857),x99856)))+P22(f317(f317(f319(f858(x99855,a842)),f317(f317(f51(x99851,f858(x99855,a842)),x99853),x99854)),x99852)) % 168.22/168.07 [10031]~P6(x100312,x100316,x100317)+~P9(x100312,f858(x100311,a842),x100317,x100314)+~P22(f317(f317(f319(f858(x100312,a842)),x100313),f317(f317(f70(x100312),x100316),x100317)))+~P22(f317(f317(f319(f858(x100311,a842)),f317(x100314,f504(x100315,x100313,x100314,x100311,x100317,x100316,x100312))),x100315))+P22(f317(f317(f319(f858(x100311,a842)),f317(f317(f51(x100312,f858(x100311,a842)),x100313),x100314)),x100315)) % 168.22/168.07 [8261]~P70(x82612)+~P19(x82611,x82615,x82618,x82614)+~E(x82613,f317(f82(x82615,x82612,x82611,x82616),x82618))+~E(x82617,f317(f287(x82611,x82615,x82618),x82614))+E(f317(f317(f9(x82611,x82612),x82613),x82614),f317(f317(f9(x82615,x82612),x82616),x82617)) % 168.22/168.07 [10034]~P70(x100342)+~P19(x100345,x100341,x100348,x100347)+~E(f317(x100346,f479(x100343,x100346,x100344,x100347,x100348,x100341,x100345,x100342)),f317(f317(f82(x100341,x100342,x100345,x100343),x100348),f479(x100343,x100346,x100344,x100347,x100348,x100341,x100345,x100342)))+~E(x100344,f317(f287(x100345,x100341,x100348),x100347))+E(f317(f317(f9(x100341,x100342),x100343),x100344),f317(f317(f9(x100345,x100342),x100346),x100347)) % 168.22/168.07 [10036]~P70(x100362)+~P19(x100361,x100365,x100368,x100364)+~E(x100367,f317(f287(x100361,x100365,x100368),x100364))+E(f317(f317(f9(x100361,x100362),x100363),x100364),f317(f317(f9(x100365,x100362),x100366),x100367))+P22(f317(f317(f319(x100361),f479(x100366,x100363,x100367,x100364,x100368,x100365,x100361,x100362)),x100364)) % 168.22/168.07 [10037]~P67(x100372)+~P19(x100371,x100375,x100378,x100374)+~E(x100377,f317(f287(x100371,x100375,x100378),x100374))+E(f317(f317(f6(x100371,x100372),x100373),x100374),f317(f317(f6(x100375,x100372),x100376),x100377))+P22(f317(f317(f319(x100371),f747(x100376,x100373,x100377,x100374,x100378,x100375,x100371,x100372)),x100374)) % 168.22/168.07 [10043]~P67(x100432)+~P19(x100435,x100431,x100438,x100437)+~E(x100434,f317(f287(x100435,x100431,x100438),x100437))+~E(f317(x100436,f747(x100433,x100436,x100434,x100437,x100438,x100431,x100435,x100432)),f317(x100433,f317(x100438,f747(x100433,x100436,x100434,x100437,x100438,x100431,x100435,x100432))))+E(f317(f317(f6(x100431,x100432),x100433),x100434),f317(f317(f6(x100435,x100432),x100436),x100437)) % 168.22/168.07 [9418]~E(f317(f189(f850(x94182)),x94185),f317(f189(f850(x94181)),x94183))+~E(f317(f189(f850(x94182)),x94184),f317(f189(f850(x94181)),x94183))+~E(f317(f317(f317(f81(x94181,f853(x94182)),f317(f171(x94181,x94182),f317(f317(f175(x94181,x94182),x94183),x94184))),x94186),f317(f217(x94182),x94187)),f317(f317(f317(f81(x94181,f853(x94182)),f317(f171(x94181,x94182),f317(f317(f175(x94181,x94182),x94183),x94185))),x94186),f317(f217(x94182),x94188)))+E(f317(f171(x94181,x94182),f317(f317(f175(x94181,x94182),x94183),x94184)),f317(f171(x94181,x94182),f317(f317(f175(x94181,x94182),x94183),x94185)))+P22(f317(f317(f319(x94181),x94186),f317(f166(x94181),x94183))) % 168.22/168.07 [9526]~P17(x95266,x95262,x95265,x95267,x95268,x95261)+~P22(f317(f71(x95262),x95264))+~P22(f317(f71(x95262),x95263))+~E(f317(f317(f113(f858(x95262,a842)),x95263),x95264),f188(f858(x95262,a842)))+E(f317(x95261,f317(f317(f122(f858(x95262,a842)),x95263),x95264)),f317(f317(x95265,f317(x95261,x95263)),f317(x95261,x95264))) % 168.22/168.07 [9934]~P17(x99348,x99342,x99345,x99347,x99346,x99341)+~E(f317(x99346,f544(x99344,x99343,x99341,x99346,x99347,x99345,x99342)),x99347)+~P22(f317(f71(x99342),x99343))+~P22(f317(f71(x99342),x99344))+E(f317(x99341,f317(f317(f122(f858(x99342,a842)),x99343),x99344)),f317(f317(x99345,f317(x99341,x99343)),f317(x99341,x99344))) % 168.22/168.07 [9992]~P17(x99928,x99922,x99925,x99927,x99926,x99921)+~P22(f317(f71(x99922),x99923))+~P22(f317(f71(x99922),x99924))+E(f317(x99921,f317(f317(f122(f858(x99922,a842)),x99923),x99924)),f317(f317(x99925,f317(x99921,x99923)),f317(x99921,x99924)))+P22(f317(f317(f319(x99922),f544(x99924,x99923,x99921,x99926,x99927,x99925,x99922)),f317(f317(f113(f858(x99922,a842)),x99923),x99924))) % 168.22/168.07 [9678]~P6(x96784,x96788,x96785)+~P6(x96781,x96789,x96783)+~P10(x96781,x96784,f858(x96782,a842),x96783,x96785,x96787)+P9(x96781,f858(x96782,a842),x96783,f317(f317(f8(f858(x96784,f858(x96782,a842)),f858(x96782,a842),x96781),f317(f51(x96784,f858(x96782,a842)),f317(f262(x96784,x96784,x96785),f317(f317(f286(x96784),x96786),f188(f858(x96784,a842)))))),x96787))+~P22(f317(f317(f319(x96784),x96786),x96788)) % 168.22/168.07 [5344]~P103(x53443)+~P29(x53443,x53441)+E(x53441,f685(x53442,x53443))+~E(f317(f166(x53443),x53441),x53442)+~P22(f317(f71(x53443),x53442))+~P22(f317(f131(x53443),x53441)) % 168.22/168.07 [4974]~P136(x49742)+~P123(x49742)+~P125(x49742)+~P106(x49742)+E(x49741,f2(x49742))+~E(f317(f317(f238(x49742),x49741),x49743),f2(x49742)) % 168.22/168.07 [4975]~P136(x49752)+~P123(x49752)+~P125(x49752)+~P106(x49752)+~E(x49751,f2(a849))+~E(f317(f317(f238(x49752),x49753),x49751),f2(x49752)) % 168.22/168.07 [6379]~P80(x63791)+~E(x63793,f2(x63791))+~E(x63792,f2(x63791))+E(f317(f317(f89(x63791),x63792),x63793),f2(x63791))+~P22(f317(f317(f225(x63791),f2(x63791)),x63793))+~P22(f317(f317(f225(x63791),f2(x63791)),x63792)) % 168.22/168.07 [8724]~E(f317(f244(a849,a849),x87243),f2(a849))+~E(x87241,f317(f317(f89(a849),f317(f317(f90(a849),f317(f244(a849,a849),x87243)),x87242)),f317(f246(a849,a849),x87243)))+P22(f317(f57(x87241,x87242),x87243))+~P22(f317(f317(f225(a849),f317(f246(a849,a849),x87243)),f2(a849)))+P22(f317(f317(f226(a849),f2(a849)),x87242))+~P22(f317(f317(f226(a849),x87242),f317(f246(a849,a849),x87243))) % 168.22/168.07 [8732]E(x87321,f2(a849))+~E(x87322,f317(f317(f89(a849),f317(f317(f90(a849),f317(f244(a849,a849),x87323)),x87321)),f317(f246(a849,a849),x87323)))+P22(f317(f57(x87322,x87321),x87323))+~P22(f317(f317(f226(a849),f2(a849)),x87321))+~P22(f317(f317(f225(a849),f2(a849)),f317(f246(a849,a849),x87323)))+~P22(f317(f317(f226(a849),f317(f246(a849,a849),x87323)),x87321)) % 168.22/168.07 [8749]~E(f317(f244(a849,a849),x87493),f2(a849))+~E(x87491,f317(f317(f89(a849),f317(f317(f90(a849),f317(f244(a849,a849),x87493)),x87492)),f317(f246(a849,a849),x87493)))+P22(f317(f57(x87491,x87492),x87493))+~P22(f317(f317(f226(a849),f2(a849)),x87492))+~P22(f317(f317(f225(a849),f2(a849)),f317(f246(a849,a849),x87493)))+~P22(f317(f317(f226(a849),f317(f246(a849,a849),x87493)),x87492)) % 168.22/168.07 [6749]~P93(x67492)+E(x67491,f188(f858(x67492,a842)))+E(x67493,f188(f858(x67492,a842)))+~P22(f317(f71(x67492),x67491))+~P22(f317(f71(x67492),x67493))+E(f11(x67492,f317(f317(f122(f858(x67492,a842)),x67493),x67491)),f317(f317(f113(x67492),f11(x67492,x67493)),f11(x67492,x67491))) % 168.22/168.07 [6750]~P93(x67502)+E(x67501,f188(f858(x67502,a842)))+E(x67503,f188(f858(x67502,a842)))+~P22(f317(f71(x67502),x67501))+~P22(f317(f71(x67502),x67503))+E(f10(x67502,f317(f317(f122(f858(x67502,a842)),x67503),x67501)),f317(f317(f122(x67502),f10(x67502,x67503)),f10(x67502,x67501))) % 168.22/168.07 [6751]~P103(x67512)+E(x67511,f188(f858(x67512,a842)))+E(x67513,f188(f858(x67512,a842)))+~P22(f317(f71(x67512),x67511))+~P22(f317(f71(x67512),x67513))+E(f14(x67512,f317(f317(f122(f858(x67512,a842)),x67513),x67511)),f317(f317(f224(x67512),f14(x67512,x67513)),f14(x67512,x67511))) % 168.22/168.07 [6752]~P103(x67522)+E(x67521,f188(f858(x67522,a842)))+E(x67523,f188(f858(x67522,a842)))+~P22(f317(f71(x67522),x67521))+~P22(f317(f71(x67522),x67523))+E(f15(x67522,f317(f317(f122(f858(x67522,a842)),x67523),x67521)),f317(f317(f223(x67522),f15(x67522,x67523)),f15(x67522,x67521))) % 168.22/168.07 [7386]~P91(x73862)+E(x73861,f188(f858(x73862,a842)))+E(x73863,f188(f858(x73862,a842)))+~P22(f317(f71(x73862),x73861))+~P22(f317(f71(x73862),x73863))+E(f317(f317(f90(x73862),f317(f73(x73862,f90(x73862)),x73863)),f317(f73(x73862,f90(x73862)),x73861)),f317(f73(x73862,f90(x73862)),f317(f317(f122(f858(x73862,a842)),x73863),x73861))) % 168.22/168.07 [7543]~P103(x75432)+E(x75431,f188(f858(x75432,a842)))+E(x75433,f188(f858(x75432,a842)))+~P22(f317(f71(x75432),x75431))+~P22(f317(f71(x75432),x75433))+E(f317(f317(f224(x75432),f12(x75432,f224(x75432),x75433)),f12(x75432,f224(x75432),x75431)),f12(x75432,f224(x75432),f317(f317(f122(f858(x75432,a842)),x75433),x75431))) % 168.22/168.07 [7544]~P103(x75442)+E(x75441,f188(f858(x75442,a842)))+E(x75443,f188(f858(x75442,a842)))+~P22(f317(f71(x75442),x75441))+~P22(f317(f71(x75442),x75443))+E(f317(f317(f223(x75442),f13(x75442,f223(x75442),x75443)),f13(x75442,f223(x75442),x75441)),f13(x75442,f223(x75442),f317(f317(f122(f858(x75442,a842)),x75443),x75441))) % 168.22/168.07 [8576]~P22(f317(x85761,x85763))+P22(f317(x85761,f446(x85761,x85762)))+P22(f317(x85761,f438(x85761,x85762)))+~P22(f317(f317(f226(a1),f2(a1)),x85762))+~P22(f317(f317(f319(a1),x85763),f279(a1,f87(a1),x85762)))+P22(f317(x85761,f317(f317(f21(a1),f438(x85761,x85762)),f317(f317(f90(a1),f444(x85761,x85762)),x85762)))) % 168.22/168.07 [8870]~P22(f317(x88701,x88703))+~P22(f317(x88701,f438(x88701,x88702)))+P22(f317(x88701,f446(x88701,x88702)))+~P22(f317(f317(f226(a1),f2(a1)),x88702))+~P22(f317(f317(f319(a1),x88703),f279(a1,f87(a1),x88702)))+~P22(f317(x88701,f317(f317(f21(a1),f438(x88701,x88702)),f317(f317(f90(a1),f444(x88701,x88702)),x88702)))) % 168.22/168.07 [10067]~P96(x100672)+E(x100671,f188(f858(x100672,a842)))+E(x100673,f188(f858(x100672,a842)))+~P22(f317(f71(x100672),x100671))+~P22(f317(f71(x100672),x100673))+E(f11(x100672,f317(f230(x100672),f317(f317(f8(f858(x100672,a842),a842,x100672),f96(x100672)),f317(f317(f8(f858(x100672,f858(x100672,a842)),f858(x100672,a842),x100672),f317(f8(f858(x100672,a842),a842,x100672),f96(x100672))),f317(f317(f7(x100672,f858(x100672,f858(x100672,a842)),f858(x100672,f858(x100672,a842))),f317(f317(f8(f858(x100672,f858(f858(x100672,a842),f858(x100672,a842))),f858(f858(x100672,f858(x100672,a842)),f858(x100672,f858(x100672,a842))),x100672),f18(x100672,f858(x100672,a842),f858(x100672,a842))),f317(f317(f8(f858(x100672,f858(x100672,f858(a842,a842))),f858(x100672,f858(f858(x100672,a842),f858(x100672,a842))),x100672),f317(f8(f858(x100672,f858(a842,a842)),f858(f858(x100672,a842),f858(x100672,a842)),x100672),f18(x100672,a842,a842))),f317(f317(f8(f858(x100672,f858(x100672,a842)),f858(x100672,f858(x100672,f858(a842,a842))),x100672),f317(f8(f858(x100672,a842),f858(x100672,f858(a842,a842)),x100672),f317(f8(a842,f858(a842,a842),x100672),a315))),f317(f317(f7(x100672,f858(x100672,f858(x100672,x100672)),f858(x100672,f858(x100672,a842))),f317(f317(f8(f858(f858(x100672,x100672),f858(x100672,a842)),f858(f858(x100672,f858(x100672,x100672)),f858(x100672,f858(x100672,a842))),x100672),f8(f858(x100672,x100672),f858(x100672,a842),x100672)),f317(f317(f8(f858(x100672,a842),f858(f858(x100672,x100672),f858(x100672,a842)),x100672),f8(x100672,a842,x100672)),a314))),f122(x100672)))))),f317(f317(f7(x100672,f858(x100672,a842),f858(x100672,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x100672,a842),f858(x100672,a842)),x100672),f8(a842,a842,x100672)),f317(f317(f8(a842,f858(a842,a842),x100672),a315),f317(f317(f7(x100672,f858(x100672,a842),a842),f319(x100672)),x100673)))),f317(f317(f7(x100672,f858(x100672,a842),a842),f319(x100672)),x100671))))))),f317(f317(f122(x100672),f11(x100672,x100673)),f11(x100672,x100671))) % 168.22/168.07 [10068]~P96(x100682)+E(x100681,f188(f858(x100682,a842)))+E(x100683,f188(f858(x100682,a842)))+~P22(f317(f71(x100682),x100681))+~P22(f317(f71(x100682),x100683))+E(f10(x100682,f317(f230(x100682),f317(f317(f8(f858(x100682,a842),a842,x100682),f96(x100682)),f317(f317(f8(f858(x100682,f858(x100682,a842)),f858(x100682,a842),x100682),f317(f8(f858(x100682,a842),a842,x100682),f96(x100682))),f317(f317(f7(x100682,f858(x100682,f858(x100682,a842)),f858(x100682,f858(x100682,a842))),f317(f317(f8(f858(x100682,f858(f858(x100682,a842),f858(x100682,a842))),f858(f858(x100682,f858(x100682,a842)),f858(x100682,f858(x100682,a842))),x100682),f18(x100682,f858(x100682,a842),f858(x100682,a842))),f317(f317(f8(f858(x100682,f858(x100682,f858(a842,a842))),f858(x100682,f858(f858(x100682,a842),f858(x100682,a842))),x100682),f317(f8(f858(x100682,f858(a842,a842)),f858(f858(x100682,a842),f858(x100682,a842)),x100682),f18(x100682,a842,a842))),f317(f317(f8(f858(x100682,f858(x100682,a842)),f858(x100682,f858(x100682,f858(a842,a842))),x100682),f317(f8(f858(x100682,a842),f858(x100682,f858(a842,a842)),x100682),f317(f8(a842,f858(a842,a842),x100682),a315))),f317(f317(f7(x100682,f858(x100682,f858(x100682,x100682)),f858(x100682,f858(x100682,a842))),f317(f317(f8(f858(f858(x100682,x100682),f858(x100682,a842)),f858(f858(x100682,f858(x100682,x100682)),f858(x100682,f858(x100682,a842))),x100682),f8(f858(x100682,x100682),f858(x100682,a842),x100682)),f317(f317(f8(f858(x100682,a842),f858(f858(x100682,x100682),f858(x100682,a842)),x100682),f8(x100682,a842,x100682)),a314))),f113(x100682)))))),f317(f317(f7(x100682,f858(x100682,a842),f858(x100682,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x100682,a842),f858(x100682,a842)),x100682),f8(a842,a842,x100682)),f317(f317(f8(a842,f858(a842,a842),x100682),a315),f317(f317(f7(x100682,f858(x100682,a842),a842),f319(x100682)),x100683)))),f317(f317(f7(x100682,f858(x100682,a842),a842),f319(x100682)),x100681))))))),f317(f317(f113(x100682),f10(x100682,x100683)),f10(x100682,x100681))) % 168.22/168.07 [10069]~P103(x100692)+E(x100691,f188(f858(x100692,a842)))+E(x100693,f188(f858(x100692,a842)))+~P22(f317(f71(x100692),x100691))+~P22(f317(f71(x100692),x100693))+E(f12(x100692,f224(x100692),f317(f230(x100692),f317(f317(f8(f858(x100692,a842),a842,x100692),f96(x100692)),f317(f317(f8(f858(x100692,f858(x100692,a842)),f858(x100692,a842),x100692),f317(f8(f858(x100692,a842),a842,x100692),f96(x100692))),f317(f317(f7(x100692,f858(x100692,f858(x100692,a842)),f858(x100692,f858(x100692,a842))),f317(f317(f8(f858(x100692,f858(f858(x100692,a842),f858(x100692,a842))),f858(f858(x100692,f858(x100692,a842)),f858(x100692,f858(x100692,a842))),x100692),f18(x100692,f858(x100692,a842),f858(x100692,a842))),f317(f317(f8(f858(x100692,f858(x100692,f858(a842,a842))),f858(x100692,f858(f858(x100692,a842),f858(x100692,a842))),x100692),f317(f8(f858(x100692,f858(a842,a842)),f858(f858(x100692,a842),f858(x100692,a842)),x100692),f18(x100692,a842,a842))),f317(f317(f8(f858(x100692,f858(x100692,a842)),f858(x100692,f858(x100692,f858(a842,a842))),x100692),f317(f8(f858(x100692,a842),f858(x100692,f858(a842,a842)),x100692),f317(f8(a842,f858(a842,a842),x100692),a315))),f317(f317(f7(x100692,f858(x100692,f858(x100692,x100692)),f858(x100692,f858(x100692,a842))),f317(f317(f8(f858(f858(x100692,x100692),f858(x100692,a842)),f858(f858(x100692,f858(x100692,x100692)),f858(x100692,f858(x100692,a842))),x100692),f8(f858(x100692,x100692),f858(x100692,a842),x100692)),f317(f317(f8(f858(x100692,a842),f858(f858(x100692,x100692),f858(x100692,a842)),x100692),f8(x100692,a842,x100692)),a314))),f223(x100692)))))),f317(f317(f7(x100692,f858(x100692,a842),f858(x100692,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x100692,a842),f858(x100692,a842)),x100692),f8(a842,a842,x100692)),f317(f317(f8(a842,f858(a842,a842),x100692),a315),f317(f317(f7(x100692,f858(x100692,a842),a842),f319(x100692)),x100693)))),f317(f317(f7(x100692,f858(x100692,a842),a842),f319(x100692)),x100691))))))),f317(f317(f223(x100692),f12(x100692,f224(x100692),x100693)),f12(x100692,f224(x100692),x100691))) % 168.22/168.07 [10070]~P103(x100702)+E(x100701,f188(f858(x100702,a842)))+E(x100703,f188(f858(x100702,a842)))+~P22(f317(f71(x100702),x100701))+~P22(f317(f71(x100702),x100703))+E(f13(x100702,f223(x100702),f317(f230(x100702),f317(f317(f8(f858(x100702,a842),a842,x100702),f96(x100702)),f317(f317(f8(f858(x100702,f858(x100702,a842)),f858(x100702,a842),x100702),f317(f8(f858(x100702,a842),a842,x100702),f96(x100702))),f317(f317(f7(x100702,f858(x100702,f858(x100702,a842)),f858(x100702,f858(x100702,a842))),f317(f317(f8(f858(x100702,f858(f858(x100702,a842),f858(x100702,a842))),f858(f858(x100702,f858(x100702,a842)),f858(x100702,f858(x100702,a842))),x100702),f18(x100702,f858(x100702,a842),f858(x100702,a842))),f317(f317(f8(f858(x100702,f858(x100702,f858(a842,a842))),f858(x100702,f858(f858(x100702,a842),f858(x100702,a842))),x100702),f317(f8(f858(x100702,f858(a842,a842)),f858(f858(x100702,a842),f858(x100702,a842)),x100702),f18(x100702,a842,a842))),f317(f317(f8(f858(x100702,f858(x100702,a842)),f858(x100702,f858(x100702,f858(a842,a842))),x100702),f317(f8(f858(x100702,a842),f858(x100702,f858(a842,a842)),x100702),f317(f8(a842,f858(a842,a842),x100702),a315))),f317(f317(f7(x100702,f858(x100702,f858(x100702,x100702)),f858(x100702,f858(x100702,a842))),f317(f317(f8(f858(f858(x100702,x100702),f858(x100702,a842)),f858(f858(x100702,f858(x100702,x100702)),f858(x100702,f858(x100702,a842))),x100702),f8(f858(x100702,x100702),f858(x100702,a842),x100702)),f317(f317(f8(f858(x100702,a842),f858(f858(x100702,x100702),f858(x100702,a842)),x100702),f8(x100702,a842,x100702)),a314))),f224(x100702)))))),f317(f317(f7(x100702,f858(x100702,a842),f858(x100702,a842)),f317(f317(f8(f858(a842,a842),f858(f858(x100702,a842),f858(x100702,a842)),x100702),f8(a842,a842,x100702)),f317(f317(f8(a842,f858(a842,a842),x100702),a315),f317(f317(f7(x100702,f858(x100702,a842),a842),f319(x100702)),x100703)))),f317(f317(f7(x100702,f858(x100702,a842),a842),f319(x100702)),x100701))))))),f317(f317(f224(x100702),f13(x100702,f223(x100702),x100703)),f13(x100702,f223(x100702),x100701))) % 168.22/168.07 [7083]~P112(x70833)+E(x70831,x70832)+~E(f317(f317(f238(x70833),x70831),x70834),f317(f317(f238(x70833),x70832),x70834))+~P22(f317(f317(f225(x70833),f2(x70833)),x70832))+~P22(f317(f317(f225(x70833),f2(x70833)),x70831))+~P22(f317(f317(f226(a849),f2(a849)),x70834)) % 168.22/168.07 [7345]~P103(x73452)+E(x73451,f188(f858(x73452,a842)))+~P22(f317(f71(x73452),x73451))+~P22(f317(f317(f319(x73452),x73454),x73451))+P22(f317(f317(f225(x73452),x73453),x73454))+~P22(f317(f317(f225(x73452),x73453),f317(f73(x73452,f223(x73452)),x73451))) % 168.22/168.07 [7346]~P98(x73462)+E(x73461,f188(f858(x73462,a842)))+~P22(f317(f71(x73462),x73461))+~P22(f317(f317(f319(x73462),x73464),x73461))+P22(f317(f317(f225(x73462),x73463),x73464))+~P22(f317(f317(f225(x73462),x73463),f317(f73(x73462,f113(x73462)),x73461))) % 168.22/168.07 [7347]~P103(x73472)+E(x73471,f188(f858(x73472,a842)))+~P22(f317(f71(x73472),x73471))+~P22(f317(f317(f319(x73472),x73474),x73471))+P22(f317(f317(f226(x73472),x73473),x73474))+~P22(f317(f317(f226(x73472),x73473),f317(f73(x73472,f223(x73472)),x73471))) % 168.22/168.07 [7224]E(x72241,f2(a1))+E(f317(f48(a1,x72242),x72241),x72243)+~P22(f317(f317(f225(a1),x72244),f2(a1)))+~E(x72242,f317(f317(f89(a1),f317(f317(f90(a1),x72241),x72243)),x72244))+P22(f317(f317(f226(a1),f2(a1)),x72241))+~P22(f317(f317(f226(a1),x72241),x72244)) % 168.22/168.07 [7263]E(f55(a1,x72632,x72631),x72633)+E(x72631,f2(a1))+~P22(f317(f317(f225(a1),x72633),f2(a1)))+~E(x72632,f317(f317(f89(a1),f317(f317(f90(a1),x72631),x72634)),x72633))+P22(f317(f317(f226(a1),f2(a1)),x72631))+~P22(f317(f317(f226(a1),x72631),x72633)) % 168.22/168.07 [7373]E(x73731,f2(a1))+E(f317(f48(a1,x73732),x73731),x73733)+~E(x73732,f317(f317(f89(a1),f317(f317(f90(a1),x73731),x73733)),x73734))+~P22(f317(f317(f225(a1),f2(a1)),x73734))+~P22(f317(f317(f226(a1),f2(a1)),x73731))+~P22(f317(f317(f226(a1),x73734),x73731)) % 168.22/168.07 [7407]E(f55(a1,x74072,x74071),x74073)+E(x74071,f2(a1))+~E(x74072,f317(f317(f89(a1),f317(f317(f90(a1),x74071),x74074)),x74073))+~P22(f317(f317(f225(a1),f2(a1)),x74073))+~P22(f317(f317(f226(a1),f2(a1)),x74071))+~P22(f317(f317(f226(a1),x74073),x74071)) % 168.22/168.07 [7546]~P103(x75462)+E(x75461,f188(f858(x75462,a842)))+~P22(f317(f71(x75462),x75461))+~P22(f317(f317(f225(x75462),x75464),x75463))+~P22(f317(f317(f319(x75462),x75464),x75461))+P22(f317(f317(f225(x75462),f317(f73(x75462,f223(x75462)),x75461)),x75463)) % 168.22/168.07 [7547]~P103(x75472)+E(x75471,f188(f858(x75472,a842)))+~P22(f317(f71(x75472),x75471))+~P22(f317(f317(f226(x75472),x75474),x75473))+~P22(f317(f317(f319(x75472),x75474),x75471))+P22(f317(f317(f226(x75472),f317(f73(x75472,f223(x75472)),x75471)),x75473)) % 168.22/168.07 [8114]~P22(f317(f317(f225(a1),x81144),f2(a1)))+~E(x81141,f317(f317(f89(a1),f317(f317(f90(a1),x81142),x81143)),x81144))+~P22(f317(f317(f225(a1),f2(a1)),x81144))+~P22(f317(f317(f226(a1),x81144),x81142))+~P22(f317(f317(f226(a1),x81142),x81144))+P22(f317(f58(x81141,x81142),f317(f317(f237(a1,a1),x81143),x81144))) % 168.22/168.07 [9058]~P57(x90583)+~P57(x90584)+E(x90581,x90582)+~E(f317(f189(f850(x90583)),x90582),f317(f189(f850(x90584)),f65(x90584)))+~E(f317(f189(f850(x90583)),x90581),f317(f189(f850(x90584)),f65(x90584)))+~E(f317(f82(f853(x90583),x90583,x90584,f222(x90583)),f317(f171(x90584,x90583),f317(f317(f175(x90584,x90583),f65(x90584)),x90581))),f317(f82(f853(x90583),x90583,x90584,f222(x90583)),f317(f171(x90584,x90583),f317(f317(f175(x90584,x90583),f65(x90584)),x90582)))) % 168.22/168.07 [8282]~P104(x82821)+P22(f317(f317(f226(f858(x82821,a842)),f279(x82821,x82822,x82823)),f279(x82821,x82824,x82825)))+~P22(f317(f317(f225(x82821),x82824),x82822))+~P22(f317(f317(f225(x82821),x82824),x82825))+~P22(f317(f317(f225(x82821),x82823),x82825))+~P22(f317(f317(f226(x82821),x82823),x82825)) % 168.22/168.07 [8283]~P104(x82831)+P22(f317(f317(f226(f858(x82831,a842)),f279(x82831,x82832,x82833)),f279(x82831,x82834,x82835)))+~P22(f317(f317(f225(x82831),x82833),x82835))+~P22(f317(f317(f225(x82831),x82834),x82835))+~P22(f317(f317(f225(x82831),x82834),x82832))+~P22(f317(f317(f226(x82831),x82834),x82832)) % 168.22/168.07 [9123]P53(x91232,x91233,x91234,x91231)+E(x91231,f188(f858(x91232,a842)))+~P22(f317(f71(x91232),x91234))+~P22(f317(f71(x91232),x91231))+~P22(f317(f317(x91233,f506(x91231,x91234,x91233,x91232)),x91235))+~P22(f317(f317(f319(x91232),x91235),x91231)) % 168.22/168.07 [9269]~E(x92693,x92695)+~P67(x92691)+~P70(x92691)+~P39(x92693)+E(f317(f317(f9(a1,x92691),x92692),x92693),f317(f317(f9(a1,x92691),x92694),x92695))+P22(f317(f317(f225(a1),f2(a1)),f475(x92692,x92694,x92693,x92695,x92691))) % 168.22/168.07 [9270]~E(x92703,x92705)+~P67(x92701)+~P70(x92701)+~P39(x92703)+E(f317(f317(f6(a1,x92701),x92702),x92703),f317(f317(f6(a1,x92701),x92704),x92705))+P22(f317(f317(f225(a1),f2(a1)),f484(x92702,x92704,x92703,x92705,x92701))) % 168.22/168.07 [9438]~E(x94385,x94383)+~P67(x94381)+~P70(x94381)+~P39(x94385)+~E(f317(x94382,f475(x94384,x94382,x94385,x94383,x94381)),f317(x94384,f475(x94384,x94382,x94385,x94383,x94381)))+E(f317(f317(f9(a1,x94381),x94382),x94383),f317(f317(f9(a1,x94381),x94384),x94385)) % 168.22/168.07 [9439]~E(x94395,x94393)+~P67(x94391)+~P70(x94391)+~P39(x94395)+~E(f317(x94392,f484(x94394,x94392,x94395,x94393,x94391)),f317(x94394,f484(x94394,x94392,x94395,x94393,x94391)))+E(f317(f317(f6(a1,x94391),x94392),x94393),f317(f317(f6(a1,x94391),x94394),x94395)) % 168.22/168.07 [9522]~P78(x95223)+E(f317(x95221,x95222),f2(x95223))+~E(f317(f317(f6(x95224,x95223),x95221),x95225),f2(x95223))+~P22(f317(f71(x95224),x95225))+P22(f317(f317(f319(x95224),f465(x95222,x95221,x95225,x95224,x95223)),x95225))+~P22(f317(f317(f319(x95224),x95222),x95225)) % 168.22/168.07 [9655]~P78(x96553)+E(f317(x96551,x96552),f2(x96553))+~E(f317(f317(f6(x96554,x96553),x96551),x96555),f2(x96553))+~P22(f317(f71(x96554),x96555))+~P22(f317(f317(f319(x96554),x96552),x96555))+~P22(f317(f317(f225(x96553),f2(x96553)),f317(x96551,f465(x96552,x96551,x96555,x96554,x96553)))) % 168.22/168.07 [8196]~P130(x81961)+~P22(f317(f317(f225(x81961),x81963),x81965))+~P22(f317(f317(f225(x81961),x81962),x81964))+~P22(f317(f317(f225(x81961),f2(x81961)),x81963))+~P22(f317(f317(f225(x81961),f2(x81961)),x81964))+P22(f317(f317(f225(x81961),f317(f317(f90(x81961),x81962),x81963)),f317(f317(f90(x81961),x81964),x81965))) % 168.22/168.07 [8197]~P130(x81971)+~P22(f317(f317(f225(x81971),x81973),x81975))+~P22(f317(f317(f225(x81971),x81972),x81974))+~P22(f317(f317(f225(x81971),f2(x81971)),x81973))+~P22(f317(f317(f225(x81971),f2(x81971)),x81972))+P22(f317(f317(f225(x81971),f317(f317(f90(x81971),x81972),x81973)),f317(f317(f90(x81971),x81974),x81975))) % 168.22/168.07 [8198]~P61(x81981)+~P22(f317(f317(f226(x81981),f2(x81981)),x81985))+~P22(f317(f317(f225(x81981),x81985),x81983))+~P22(f317(f317(f225(x81981),x81982),x81984))+~P22(f317(f317(f225(x81981),f2(x81981)),x81982))+P22(f317(f317(f225(x81981),f317(f317(f266(x81981),x81982),x81983)),f317(f317(f266(x81981),x81984),x81985))) % 168.22/168.07 [8199]~P124(x81991)+~P22(f317(f317(f225(x81991),x81993),x81995))+~P22(f317(f317(f225(x81991),f2(x81991)),x81992))+~P22(f317(f317(f226(x81991),x81992),x81994))+~P22(f317(f317(f226(x81991),f2(x81991)),x81993))+P22(f317(f317(f226(x81991),f317(f317(f90(x81991),x81992),x81993)),f317(f317(f90(x81991),x81994),x81995))) % 168.22/168.07 [8200]~P124(x82001)+~P22(f317(f317(f225(x82001),x82002),x82004))+~P22(f317(f317(f225(x82001),f2(x82001)),x82003))+~P22(f317(f317(f226(x82001),x82003),x82005))+~P22(f317(f317(f226(x82001),f2(x82001)),x82002))+P22(f317(f317(f226(x82001),f317(f317(f90(x82001),x82002),x82003)),f317(f317(f90(x82001),x82004),x82005))) % 168.22/168.07 [8201]~P124(x82011)+~P22(f317(f317(f225(x82011),f2(x82011)),x82013))+~P22(f317(f317(f225(x82011),f2(x82011)),x82012))+~P22(f317(f317(f226(x82011),x82013),x82015))+~P22(f317(f317(f226(x82011),x82012),x82014))+P22(f317(f317(f226(x82011),f317(f317(f90(x82011),x82012),x82013)),f317(f317(f90(x82011),x82014),x82015))) % 168.22/168.07 [8202]~P124(x82021)+~P22(f317(f317(f225(x82021),f2(x82021)),x82023))+~P22(f317(f317(f226(x82021),x82023),x82025))+~P22(f317(f317(f226(x82021),x82022),x82024))+~P22(f317(f317(f226(x82021),f2(x82021)),x82024))+P22(f317(f317(f226(x82021),f317(f317(f90(x82021),x82022),x82023)),f317(f317(f90(x82021),x82024),x82025))) % 168.22/168.07 [8203]~P61(x82031)+~P22(f317(f317(f225(x82031),x82035),x82033))+~P22(f317(f317(f225(x82031),f2(x82031)),x82032))+~P22(f317(f317(f226(x82031),x82032),x82034))+~P22(f317(f317(f226(x82031),f2(x82031)),x82035))+P22(f317(f317(f226(x82031),f317(f317(f266(x82031),x82032),x82033)),f317(f317(f266(x82031),x82034),x82035))) % 168.22/168.07 [8204]~P61(x82041)+~P22(f317(f317(f225(x82041),x82042),x82044))+~P22(f317(f317(f226(x82041),x82045),x82043))+~P22(f317(f317(f226(x82041),f2(x82041)),x82045))+~P22(f317(f317(f226(x82041),f2(x82041)),x82042))+P22(f317(f317(f226(x82041),f317(f317(f266(x82041),x82042),x82043)),f317(f317(f266(x82041),x82044),x82045))) % 168.22/168.07 [9560]~P67(x95605)+~P81(x95605)+E(x95601,f188(f858(x95602,a842)))+~P22(f317(f71(x95602),x95601))+P22(f317(f317(f319(x95602),f473(x95603,x95604,x95601,x95602,x95605)),x95601))+P22(f317(f317(f226(x95605),f317(f317(f6(x95602,x95605),x95604),x95601)),f317(f317(f6(x95602,x95605),x95603),x95601))) % 168.22/168.07 [9676]~P67(x96761)+~P77(x96761)+~P22(f317(f71(x96762),x96765))+~P22(f317(f317(f225(x96761),f2(x96761)),f317(x96763,f466(x96763,x96764,x96765,x96762,x96761))))+P22(f317(f317(f225(x96761),f317(f317(f6(x96762,x96761),x96763),x96764)),f317(f317(f6(x96762,x96761),x96763),x96765)))+~P22(f317(f317(f225(f858(x96762,a842)),x96764),x96765)) % 168.22/168.07 [9850]~P67(x98503)+~P81(x98503)+E(x98501,f188(f858(x98502,a842)))+~P22(f317(f71(x98502),x98501))+~P22(f317(f317(f226(x98503),f317(x98504,f473(x98505,x98504,x98501,x98502,x98503))),f317(x98505,f473(x98505,x98504,x98501,x98502,x98503))))+P22(f317(f317(f226(x98503),f317(f317(f6(x98502,x98503),x98504),x98501)),f317(f317(f6(x98502,x98503),x98505),x98501))) % 168.22/168.07 [6940]~P12(x69402,x69405,x69404)+E(x69401,f188(f858(x69402,a842)))+E(x69403,f188(f858(x69402,a842)))+~P22(f317(f71(x69402),x69401))+~P22(f317(f71(x69402),x69403))+E(f317(x69404,f317(f317(f122(f858(x69402,a842)),x69403),x69401)),f317(f317(x69405,f317(x69404,x69403)),f317(x69404,x69401))) % 168.22/168.07 [7515]~P139(x75151,x75153,x75154)+P22(f317(x75151,x75152))+~P22(f317(f317(f226(a1),x75154),f2(a1)))+~P22(f317(f317(f225(a1),x75155),f2(a1)))+~E(x75153,f317(f317(f89(a1),f317(f317(f90(a1),x75154),x75152)),x75155))+~P22(f317(f317(f226(a1),x75154),x75155)) % 168.22/168.07 [7516]~P138(x75161,x75163,x75164)+P22(f317(x75161,x75162))+~P22(f317(f317(f226(a1),x75164),f2(a1)))+~P22(f317(f317(f225(a1),x75162),f2(a1)))+~E(x75163,f317(f317(f89(a1),f317(f317(f90(a1),x75164),x75165)),x75162))+~P22(f317(f317(f226(a1),x75164),x75162)) % 168.22/168.07 [7555]~P139(x75551,x75553,x75554)+P22(f317(x75551,x75552))+~E(x75553,f317(f317(f89(a1),f317(f317(f90(a1),x75554),x75552)),x75555))+~P22(f317(f317(f225(a1),f2(a1)),x75555))+~P22(f317(f317(f226(a1),f2(a1)),x75554))+~P22(f317(f317(f226(a1),x75555),x75554)) % 168.22/168.07 [7556]~P138(x75561,x75563,x75564)+P22(f317(x75561,x75562))+~E(x75563,f317(f317(f89(a1),f317(f317(f90(a1),x75564),x75565)),x75562))+~P22(f317(f317(f225(a1),f2(a1)),x75562))+~P22(f317(f317(f226(a1),f2(a1)),x75564))+~P22(f317(f317(f226(a1),x75562),x75564)) % 168.22/168.07 [8431]P22(f317(f317(x84311,x84312),x84313))+~P22(f317(f317(x84311,f317(f48(a1,x84314),x84315)),f55(a1,x84314,x84315)))+~P22(f317(f317(f226(a1),x84315),f2(a1)))+~P22(f317(f317(f225(a1),x84313),f2(a1)))+~E(x84314,f317(f317(f89(a1),f317(f317(f90(a1),x84315),x84312)),x84313))+~P22(f317(f317(f226(a1),x84315),x84313)) % 168.22/168.07 [8451]P22(f317(f317(x84511,x84512),x84513))+~P22(f317(f317(x84511,f317(f48(a1,x84514),x84515)),f55(a1,x84514,x84515)))+~E(x84514,f317(f317(f89(a1),f317(f317(f90(a1),x84515),x84512)),x84513))+~P22(f317(f317(f225(a1),f2(a1)),x84513))+~P22(f317(f317(f226(a1),f2(a1)),x84515))+~P22(f317(f317(f226(a1),x84513),x84515)) % 168.22/168.07 [8739]E(x87391,x87392)+~P50(x87393,x87395,x87394)+~P22(f317(f317(f319(x87393),x87392),x87395))+~P22(f317(f317(f319(x87393),x87391),x87395))+P22(f317(f317(f319(f857(x87393,x87393)),f317(f317(f237(x87393,x87393),x87391),x87392)),x87394))+P22(f317(f317(f319(f857(x87393,x87393)),f317(f317(f237(x87393,x87393),x87392),x87391)),x87394)) % 168.22/168.07 [9586]~P67(x95865)+~P77(x95865)+~P22(f317(f71(x95861),x95864))+P22(f317(f317(f225(x95865),f317(f317(f6(x95861,x95865),x95862),x95863)),f317(f317(f6(x95861,x95865),x95862),x95864)))+~P22(f317(f317(f225(f858(x95861,a842)),x95863),x95864))+P22(f317(f317(f319(x95861),f466(x95862,x95863,x95864,x95861,x95865)),f317(f317(f21(f858(x95861,a842)),x95864),x95863))) % 168.22/168.07 [9682]E(x96821,f188(f858(x96822,a842)))+~P22(f317(f71(x96822),x96823))+~P22(f317(f71(x96822),x96821))+P22(f317(f317(f319(f857(f858(x96822,a842),f858(x96822,a842))),f317(f317(f237(f858(x96822,a842),f858(x96822,a842)),x96823),x96821)),f309(x96822,x96824)))+~P22(f317(f317(f319(x96822),x96825),x96821))+~P22(f317(f317(f319(f857(x96822,x96822)),f317(f317(f237(x96822,x96822),f509(x96824,x96821,x96823,x96822)),x96825)),x96824)) % 168.22/168.07 [9683]E(x96831,f188(f858(x96832,a842)))+~P22(f317(f71(x96832),x96833))+~P22(f317(f71(x96832),x96831))+P22(f317(f317(f319(f857(f858(x96832,a842),f858(x96832,a842))),f317(f317(f237(f858(x96832,a842),f858(x96832,a842)),x96833),x96831)),f309(x96832,x96834)))+~P22(f317(f317(f319(x96832),x96835),x96831))+~P22(f317(f317(f319(f857(x96832,x96832)),f317(f317(f237(x96832,x96832),f737(x96834,x96831,x96833,x96832)),x96835)),x96834)) % 168.22/168.07 [9855]~P78(x98551)+~E(f317(f317(f6(x98555,x98551),x98552),x98556),x98554)+~P22(f317(f71(x98555),x98556))+P22(f317(f317(f319(x98555),f467(x98553,x98554,x98552,x98556,x98555,x98551)),x98556))+P22(f317(f317(f225(x98551),f317(x98552,x98553)),x98554))+~P22(f317(f317(f319(x98555),x98553),x98556)) % 168.22/168.07 [9905]~P78(x99051)+~E(f317(f317(f6(x99055,x99051),x99052),x99056),x99054)+~P22(f317(f71(x99055),x99056))+~P22(f317(f317(f319(x99055),x99053),x99056))+~P22(f317(f317(f225(x99051),f2(x99051)),f317(x99052,f467(x99053,x99054,x99052,x99056,x99055,x99051))))+P22(f317(f317(f225(x99051),f317(x99052,x99053)),x99054)) % 168.22/168.07 [10017]~E(x100175,x100178)+~E(x100174,x100177)+~P67(x100172)+~P102(x100171)+E(f317(f317(f6(x100171,x100172),x100173),f317(f278(x100171,x100174),x100175)),f317(f317(f6(x100171,x100172),x100176),f317(f278(x100171,x100177),x100178)))+P22(f317(f317(f225(x100171),x100174),f749(x100173,x100176,x100175,x100178,x100174,x100177,x100171,x100172))) % 168.22/168.07 [10033]~E(x100337,x100334)+~E(x100338,x100335)+~P67(x100332)+~P102(x100331)+~E(f317(x100333,f749(x100336,x100333,x100338,x100335,x100337,x100334,x100331,x100332)),f317(x100336,f749(x100336,x100333,x100338,x100335,x100337,x100334,x100331,x100332)))+E(f317(f317(f6(x100331,x100332),x100333),f317(f278(x100331,x100334),x100335)),f317(f317(f6(x100331,x100332),x100336),f317(f278(x100331,x100337),x100338))) % 168.22/168.07 [10035]~E(x100354,x100357)+~E(x100355,x100358)+~P67(x100352)+~P102(x100351)+E(f317(f317(f6(x100351,x100352),x100353),f317(f278(x100351,x100354),x100355)),f317(f317(f6(x100351,x100352),x100356),f317(f278(x100351,x100357),x100358)))+P22(f317(f317(f226(x100351),f749(x100353,x100356,x100355,x100358,x100354,x100357,x100351,x100352)),x100355)) % 168.22/168.07 [9688]~P6(x96885,x96889,x96886)+~P6(x96881,x968810,x96883)+~P10(x96881,x96885,f858(x96882,a842),x96883,x96886,x96888)+~P22(f317(f317(f319(x96885),x96887),x96889))+~P22(f317(f317(f319(x96881),x96884),x968810))+E(f317(f317(f51(x96881,f858(x96882,a842)),f317(f262(x96881,x96881,x96883),f317(f317(f286(x96881),x96884),f188(f858(x96881,a842))))),f317(f317(f8(f858(x96885,f858(x96882,a842)),f858(x96882,a842),x96881),f317(f51(x96885,f858(x96882,a842)),f317(f262(x96885,x96885,x96886),f317(f317(f286(x96885),x96887),f188(f858(x96885,a842)))))),x96888)),f317(f317(x96888,x96884),x96887)) % 168.22/168.07 [5512]~P103(x55123)+~P29(x55123,x55122)+~P29(x55123,x55121)+E(x55121,x55122)+~E(f317(f166(x55123),x55121),f317(f166(x55123),x55122))+~P22(f317(f131(x55123),x55122))+~P22(f317(f131(x55123),x55121)) % 168.22/168.07 [4864]~P136(x48642)+~P123(x48642)+~P125(x48642)+~P106(x48642)+~E(x48643,f2(x48642))+E(x48641,f2(a849))+E(f317(f317(f238(x48642),x48643),x48641),f2(x48642)) % 168.22/168.07 [9001]E(x90011,f2(a849))+~E(x90012,f317(f317(f89(a849),f317(f317(f90(a849),f317(f244(a849,a849),x90013)),x90011)),f317(f246(a849,a849),x90013)))+P22(f317(f57(x90012,x90011),x90013))+~P22(f317(f317(f225(a849),f317(f246(a849,a849),x90013)),f2(a849)))+~P22(f317(f317(f225(a849),f2(a849)),f317(f246(a849,a849),x90013)))+~P22(f317(f317(f226(a849),x90011),f317(f246(a849,a849),x90013)))+~P22(f317(f317(f226(a849),f317(f246(a849,a849),x90013)),x90011)) % 168.22/168.07 [9010]~E(f317(f244(a849,a849),x90103),f2(a849))+~E(x90101,f317(f317(f89(a849),f317(f317(f90(a849),f317(f244(a849,a849),x90103)),x90102)),f317(f246(a849,a849),x90103)))+P22(f317(f57(x90101,x90102),x90103))+~P22(f317(f317(f225(a849),f317(f246(a849,a849),x90103)),f2(a849)))+~P22(f317(f317(f225(a849),f2(a849)),f317(f246(a849,a849),x90103)))+~P22(f317(f317(f226(a849),x90102),f317(f246(a849,a849),x90103)))+~P22(f317(f317(f226(a849),f317(f246(a849,a849),x90103)),x90102)) % 168.22/168.07 [7861]~P64(x78612)+E(x78611,f188(f858(x78612,a842)))+E(x78613,f188(f858(x78612,a842)))+~P22(f317(f71(x78612),x78611))+~P22(f317(f71(x78612),x78613))+~E(f317(f317(f113(f858(x78612,a842)),x78613),x78611),f188(f858(x78612,a842)))+E(f317(f317(f90(x78612),f317(f73(x78612,f90(x78612)),x78613)),f317(f73(x78612,f90(x78612)),x78611)),f317(f73(x78612,f90(x78612)),f317(f317(f122(f858(x78612,a842)),x78613),x78611))) % 168.22/168.07 [7642]E(x76421,f2(a1))+E(f317(f48(a1,x76422),x76421),x76423)+~P22(f317(f317(f225(a1),x76424),f2(a1)))+~E(x76422,f317(f317(f89(a1),f317(f317(f90(a1),x76421),x76423)),x76424))+~P22(f317(f317(f225(a1),f2(a1)),x76424))+~P22(f317(f317(f226(a1),x76424),x76421))+~P22(f317(f317(f226(a1),x76421),x76424)) % 168.22/168.07 [7660]E(f55(a1,x76602,x76601),x76603)+E(x76601,f2(a1))+~P22(f317(f317(f225(a1),x76603),f2(a1)))+~E(x76602,f317(f317(f89(a1),f317(f317(f90(a1),x76601),x76604)),x76603))+~P22(f317(f317(f225(a1),f2(a1)),x76603))+~P22(f317(f317(f226(a1),x76603),x76601))+~P22(f317(f317(f226(a1),x76601),x76603)) % 168.22/168.07 [7563]~P13(x75632,x75635,x75634)+E(x75631,f188(f858(x75632,a842)))+E(x75633,f188(f858(x75632,a842)))+~P22(f317(f71(x75632),x75631))+~P22(f317(f71(x75632),x75633))+~E(f317(f317(f113(f858(x75632,a842)),x75633),x75631),f188(f858(x75632,a842)))+E(f317(x75634,f317(f317(f122(f858(x75632,a842)),x75633),x75631)),f317(f317(x75635,f317(x75634,x75633)),f317(x75634,x75631))) % 168.22/168.07 [9240]~P19(x92403,x92401,x92405,x92404)+~P19(x92401,x92403,x92406,x92402)+E(f317(f54(x92401),x92402),f317(f54(x92403),x92404))+~P22(f317(f71(x92403),x92404))+~P22(f317(f71(x92401),x92402))+~P22(f317(f317(f225(f858(x92403,a842)),f317(f287(x92401,x92403,x92406),x92402)),x92404))+~P22(f317(f317(f225(f858(x92401,a842)),f317(f287(x92403,x92401,x92405),x92404)),x92402)) % 168.22/168.07 [9188]~P22(f317(f317(f226(a1),f317(f317(f89(a1),f317(f317(f90(a1),x91885),x91881)),x91886)),f2(a1)))+~E(f317(f317(f89(a1),f317(f317(f90(a1),x91883),x91882)),x91884),f317(f317(f89(a1),f317(f317(f90(a1),x91885),x91881)),x91886))+~P22(f317(f317(f225(a1),f2(a1)),x91886))+~P22(f317(f317(f226(a1),f2(a1)),x91885))+~P22(f317(f317(f225(a1),x91885),x91883))+~P22(f317(f317(f226(a1),x91884),x91883))+P22(f317(f317(f225(a1),x91881),x91882)) % 168.22/168.07 [8956]~E(f317(f317(f89(a1),f317(f317(f90(a1),x89563),x89561)),x89564),f317(f317(f89(a1),f317(f317(f90(a1),x89565),x89562)),x89566))+~P22(f317(f317(f225(a1),f2(a1)),x89564))+~P22(f317(f317(f226(a1),f2(a1)),x89565))+~P22(f317(f317(f225(a1),x89565),x89563))+~P22(f317(f317(f226(a1),x89566),x89565))+P22(f317(f317(f225(a1),x89561),x89562))+~P22(f317(f317(f225(a1),f2(a1)),f317(f317(f89(a1),f317(f317(f90(a1),x89565),x89562)),x89566))) % 168.22/168.07 [9129]~P122(x91291)+~E(f317(f317(f89(x91291),x91292),x91294),f87(x91291))+~P22(f317(f317(f225(x91291),x91295),x91296))+~P22(f317(f317(f225(x91291),x91293),x91296))+~P22(f317(f317(f225(x91291),f2(x91291)),x91294))+~P22(f317(f317(f225(x91291),f2(x91291)),x91292))+P22(f317(f317(f225(x91291),f317(f317(f89(x91291),f317(f317(f90(x91291),x91292),x91293)),f317(f317(f90(x91291),x91294),x91295))),x91296)) % 168.22/168.07 [9130]~P120(x91301)+~E(f317(f317(f89(x91301),x91302),x91304),f87(x91301))+~P22(f317(f317(f225(x91301),f2(x91301)),x91304))+~P22(f317(f317(f225(x91301),f2(x91301)),x91302))+~P22(f317(f317(f226(x91301),x91305),x91306))+~P22(f317(f317(f226(x91301),x91303),x91306))+P22(f317(f317(f226(x91301),f317(f317(f89(x91301),f317(f317(f90(x91301),x91302),x91303)),f317(f317(f90(x91301),x91304),x91305))),x91306)) % 168.22/168.07 [9950]~P6(x99507,x99506,x99505)+E(x99501,x99502)+~P9(x99507,f858(x99504,a842),x99505,x99503)+E(f317(x99503,f497(x99501,x99502,x99503,x99504,x99505,x99506,x99507)),f317(x99503,f498(x99501,x99502,x99503,x99504,x99505,x99506,x99507)))+~E(f317(f317(f51(x99507,f858(x99504,a842)),x99501),x99503),f317(f317(f51(x99507,f858(x99504,a842)),x99502),x99503))+~P22(f317(f317(f319(f858(x99507,a842)),x99502),f317(f317(f70(x99507),x99506),x99505)))+~P22(f317(f317(f319(f858(x99507,a842)),x99501),f317(f317(f70(x99507),x99506),x99505))) % 168.22/168.07 [9983]~P6(x99833,x99837,x99836)+E(x99831,x99832)+~P9(x99833,f858(x99835,a842),x99836,x99834)+~E(f317(f317(f51(x99833,f858(x99835,a842)),x99831),x99834),f317(f317(f51(x99833,f858(x99835,a842)),x99832),x99834))+P22(f317(f317(f319(x99833),f498(x99831,x99832,x99834,x99835,x99836,x99837,x99833)),x99837))+~P22(f317(f317(f319(f858(x99833,a842)),x99832),f317(f317(f70(x99833),x99837),x99836)))+~P22(f317(f317(f319(f858(x99833,a842)),x99831),f317(f317(f70(x99833),x99837),x99836))) % 168.22/168.07 [9984]~P6(x99843,x99847,x99846)+E(x99841,x99842)+~P9(x99843,f858(x99845,a842),x99846,x99844)+~E(f317(f317(f51(x99843,f858(x99845,a842)),x99841),x99844),f317(f317(f51(x99843,f858(x99845,a842)),x99842),x99844))+P22(f317(f317(f319(x99843),f497(x99841,x99842,x99844,x99845,x99846,x99847,x99843)),x99847))+~P22(f317(f317(f319(f858(x99843,a842)),x99842),f317(f317(f70(x99843),x99847),x99846)))+~P22(f317(f317(f319(f858(x99843,a842)),x99841),f317(f317(f70(x99843),x99847),x99846))) % 168.22/168.07 [10051]E(x100511,x100512)+~P6(x100513,x100516,x100517)+~P9(x100513,f858(x100514,a842),x100517,x100515)+~E(f317(f317(f51(x100513,f858(x100514,a842)),x100511),x100515),f317(f317(f51(x100513,f858(x100514,a842)),x100512),x100515))+~P22(f317(f317(f319(f857(x100513,x100513)),f317(f317(f237(x100513,x100513),f498(x100511,x100512,x100515,x100514,x100517,x100516,x100513)),f497(x100511,x100512,x100515,x100514,x100517,x100516,x100513))),x100517))+~P22(f317(f317(f319(f858(x100513,a842)),x100512),f317(f317(f70(x100513),x100516),x100517)))+~P22(f317(f317(f319(f858(x100513,a842)),x100511),f317(f317(f70(x100513),x100516),x100517))) % 168.22/168.07 [8955]~P6(x89551,x89557,x89554)+~E(x89555,x89556)+~P22(f317(f317(f319(x89551),x89553),x89556))+~P22(f317(f317(f319(x89551),x89552),x89555))+~P22(f317(f317(f319(f858(x89551,a842)),x89556),f317(f317(f70(x89551),x89557),x89554)))+~P22(f317(f317(f319(f858(x89551,a842)),x89555),f317(f317(f70(x89551),x89557),x89554)))+P22(f317(f317(f319(f857(x89551,x89551)),f317(f317(f237(x89551,x89551),x89552),x89553)),x89554)) % 168.22/168.07 [9086]E(x90861,x90862)+~P6(x90863,x90864,x90865)+~P22(f317(f317(f319(x90863),x90866),x90862))+~P22(f317(f317(f319(x90863),x90867),x90861))+~P22(f317(f317(f319(f858(x90863,a842)),x90862),f317(f317(f70(x90863),x90864),x90865)))+~P22(f317(f317(f319(f858(x90863,a842)),x90861),f317(f317(f70(x90863),x90864),x90865)))+~P22(f317(f317(f319(f857(x90863,x90863)),f317(f317(f237(x90863,x90863),x90867),x90866)),x90865)) % 168.22/168.07 [10074]~P6(x100749,x100748,x100747)+~P6(x100741,x1007411,x1007410)+~P10(x100741,x100749,f858(x100746,a842),x1007410,x100747,x100745)+P22(f317(f317(f319(x100741),f499(x100742,x100743,x100744,x100745,x100746,x100747,x100748,x100749,x1007410,x1007411,x100741)),x1007411))+~P22(f317(f317(f319(f858(x100749,a842)),x100743),f317(f317(f70(x100749),x100748),x100747)))+~P22(f317(f317(f319(f858(x100741,a842)),x100744),f317(f317(f70(x100741),x1007411),x1007410)))+P22(f317(f317(f319(f858(x100746,a842)),f317(f317(f51(x100741,f858(x100746,a842)),x100744),f317(f317(f8(f858(x100749,f858(x100746,a842)),f858(x100746,a842),x100741),f317(f51(x100749,f858(x100746,a842)),x100743)),x100745))),x100742)) % 168.22/168.07 [10075]~P6(x1007511,x1007510,x100759)+~P6(x100751,x100758,x100757)+~P10(x1007511,x100751,f858(x100756,a842),x100759,x100757,x100755)+P22(f317(f317(f319(x100751),f500(x100752,x100753,x100754,x100755,x100756,x100757,x100758,x100751,x100759,x1007510,x1007511)),x100758))+~P22(f317(f317(f319(f858(x1007511,a842)),x100754),f317(f317(f70(x1007511),x1007510),x100759)))+~P22(f317(f317(f319(f858(x100751,a842)),x100753),f317(f317(f70(x100751),x100758),x100757)))+P22(f317(f317(f319(f858(x100756,a842)),f317(f317(f51(x1007511,f858(x100756,a842)),x100754),f317(f317(f8(f858(x100751,f858(x100756,a842)),f858(x100756,a842),x1007511),f317(f51(x100751,f858(x100756,a842)),x100753)),x100755))),x100752)) % 168.22/168.07 [10078]~P6(x100782,x100788,x100789)+~P6(x100784,x1007810,x1007811)+~P10(x100782,x100784,f858(x100781,a842),x100789,x1007811,x100786)+~P22(f317(f317(f319(f858(x100782,a842)),x100783),f317(f317(f70(x100782),x100788),x100789)))+~P22(f317(f317(f319(f858(x100784,a842)),x100785),f317(f317(f70(x100784),x1007810),x1007811)))+~P22(f317(f317(f319(f858(x100781,a842)),f317(f317(x100786,f499(x100787,x100785,x100783,x100786,x100781,x1007811,x1007810,x100784,x100789,x100788,x100782)),f500(x100787,x100785,x100783,x100786,x100781,x1007811,x1007810,x100784,x100789,x100788,x100782))),x100787))+P22(f317(f317(f319(f858(x100781,a842)),f317(f317(f51(x100782,f858(x100781,a842)),x100783),f317(f317(f8(f858(x100784,f858(x100781,a842)),f858(x100781,a842),x100782),f317(f51(x100784,f858(x100781,a842)),x100785)),x100786))),x100787)) % 168.22/168.07 [8989]E(x89891,x89892)+~P103(x89894)+~P19(x89893,x89894,x89895,f317(f317(f122(f858(x89893,a842)),f317(f166(x89893),x89891)),f317(f166(x89893),x89892)))+~E(f317(f166(x89893),x89891),f317(f166(x89893),x89892))+~P29(x89894,f317(f317(f148(x89893,x89894),x89895),x89892))+~P29(x89894,f317(f317(f148(x89893,x89894),x89895),x89891))+~P22(f317(f131(x89894),f317(f317(f148(x89893,x89894),x89895),x89892)))+~P22(f317(f131(x89894),f317(f317(f148(x89893,x89894),x89895),x89891))) % 168.22/168.07 %EqnAxiom % 168.22/168.07 [1]E(x11,x11) % 168.22/168.07 [2]E(x22,x21)+~E(x21,x22) % 168.22/168.07 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 168.22/168.07 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 168.22/168.07 [5]~E(x51,x52)+E(f112(x51),f112(x52)) % 168.22/168.07 [6]~E(x61,x62)+E(f21(x61),f21(x62)) % 168.22/168.07 [7]~E(x71,x72)+E(f34(x71),f34(x72)) % 168.22/168.07 [8]~E(x81,x82)+E(f317(x81,x83),f317(x82,x83)) % 168.22/168.07 [9]~E(x91,x92)+E(f317(x93,x91),f317(x93,x92)) % 168.22/168.07 [10]~E(x101,x102)+E(f93(x101),f93(x102)) % 168.22/168.07 [11]~E(x111,x112)+E(f8(x111,x113,x114),f8(x112,x113,x114)) % 168.22/168.07 [12]~E(x121,x122)+E(f8(x123,x121,x124),f8(x123,x122,x124)) % 168.22/168.07 [13]~E(x131,x132)+E(f8(x133,x134,x131),f8(x133,x134,x132)) % 168.22/168.07 [14]~E(x141,x142)+E(f226(x141),f226(x142)) % 168.22/168.07 [15]~E(x151,x152)+E(f858(x151,x153),f858(x152,x153)) % 168.22/168.07 [16]~E(x161,x162)+E(f858(x163,x161),f858(x163,x162)) % 168.22/168.07 [17]~E(x171,x172)+E(f188(x171),f188(x172)) % 168.22/168.07 [18]~E(x181,x182)+E(f500(x181,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812),f500(x182,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812)) % 168.22/168.07 [19]~E(x191,x192)+E(f500(x193,x191,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912),f500(x193,x192,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912)) % 168.22/168.07 [20]~E(x201,x202)+E(f500(x203,x204,x201,x205,x206,x207,x208,x209,x2010,x2011,x2012),f500(x203,x204,x202,x205,x206,x207,x208,x209,x2010,x2011,x2012)) % 168.22/168.07 [21]~E(x211,x212)+E(f500(x213,x214,x215,x211,x216,x217,x218,x219,x2110,x2111,x2112),f500(x213,x214,x215,x212,x216,x217,x218,x219,x2110,x2111,x2112)) % 168.22/168.07 [22]~E(x221,x222)+E(f500(x223,x224,x225,x226,x221,x227,x228,x229,x2210,x2211,x2212),f500(x223,x224,x225,x226,x222,x227,x228,x229,x2210,x2211,x2212)) % 168.22/168.07 [23]~E(x231,x232)+E(f500(x233,x234,x235,x236,x237,x231,x238,x239,x2310,x2311,x2312),f500(x233,x234,x235,x236,x237,x232,x238,x239,x2310,x2311,x2312)) % 168.22/168.07 [24]~E(x241,x242)+E(f500(x243,x244,x245,x246,x247,x248,x241,x249,x2410,x2411,x2412),f500(x243,x244,x245,x246,x247,x248,x242,x249,x2410,x2411,x2412)) % 168.22/168.07 [25]~E(x251,x252)+E(f500(x253,x254,x255,x256,x257,x258,x259,x251,x2510,x2511,x2512),f500(x253,x254,x255,x256,x257,x258,x259,x252,x2510,x2511,x2512)) % 168.22/168.07 [26]~E(x261,x262)+E(f500(x263,x264,x265,x266,x267,x268,x269,x2610,x261,x2611,x2612),f500(x263,x264,x265,x266,x267,x268,x269,x2610,x262,x2611,x2612)) % 168.22/168.07 [27]~E(x271,x272)+E(f500(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x271,x2712),f500(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x272,x2712)) % 168.22/168.07 [28]~E(x281,x282)+E(f500(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x281),f500(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x282)) % 168.22/168.07 [29]~E(x291,x292)+E(f113(x291),f113(x292)) % 168.22/168.07 [30]~E(x301,x302)+E(f223(x301),f223(x302)) % 168.22/168.07 [31]~E(x311,x312)+E(f122(x311),f122(x312)) % 168.22/168.07 [32]~E(x321,x322)+E(f224(x321),f224(x322)) % 168.22/168.07 [33]~E(x331,x332)+E(f114(x331),f114(x332)) % 168.22/168.07 [34]~E(x341,x342)+E(f39(x341),f39(x342)) % 168.22/168.07 [35]~E(x351,x352)+E(f90(x351),f90(x352)) % 168.22/168.07 [36]~E(x361,x362)+E(f87(x361),f87(x362)) % 168.22/168.07 [37]~E(x371,x372)+E(f499(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f499(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 168.22/168.07 [38]~E(x381,x382)+E(f499(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f499(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 168.22/168.07 [39]~E(x391,x392)+E(f499(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f499(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912)) % 168.22/168.07 [40]~E(x401,x402)+E(f499(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f499(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012)) % 168.22/168.07 [41]~E(x411,x412)+E(f499(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f499(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112)) % 168.22/168.07 [42]~E(x421,x422)+E(f499(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f499(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212)) % 168.22/168.07 [43]~E(x431,x432)+E(f499(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f499(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312)) % 168.22/168.07 [44]~E(x441,x442)+E(f499(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f499(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412)) % 168.22/168.07 [45]~E(x451,x452)+E(f499(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f499(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512)) % 168.22/168.07 [46]~E(x461,x462)+E(f499(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f499(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612)) % 168.22/168.07 [47]~E(x471,x472)+E(f499(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f499(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472)) % 168.22/168.07 [48]~E(x481,x482)+E(f123(x481),f123(x482)) % 168.22/168.07 [49]~E(x491,x492)+E(f319(x491),f319(x492)) % 168.22/168.07 [50]~E(x501,x502)+E(f225(x501),f225(x502)) % 168.22/168.07 [51]~E(x511,x512)+E(f4(x511),f4(x512)) % 168.22/168.07 [52]~E(x521,x522)+E(f6(x521,x523),f6(x522,x523)) % 168.22/168.07 [53]~E(x531,x532)+E(f6(x533,x531),f6(x533,x532)) % 168.22/168.07 [54]~E(x541,x542)+E(f853(x541),f853(x542)) % 168.22/168.07 [55]~E(x551,x552)+E(f848(x551),f848(x552)) % 168.22/168.07 [56]~E(x561,x562)+E(f850(x561),f850(x562)) % 168.22/168.07 [57]~E(x571,x572)+E(f851(x571),f851(x572)) % 168.22/168.07 [58]~E(x581,x582)+E(f40(x581),f40(x582)) % 168.22/168.07 [59]~E(x591,x592)+E(f42(x591),f42(x592)) % 168.22/168.07 [60]~E(x601,x602)+E(f18(x601,x603,x604),f18(x602,x603,x604)) % 168.22/168.07 [61]~E(x611,x612)+E(f18(x613,x611,x614),f18(x613,x612,x614)) % 168.22/168.07 [62]~E(x621,x622)+E(f18(x623,x624,x621),f18(x623,x624,x622)) % 168.22/168.07 [63]~E(x631,x632)+E(f41(x631),f41(x632)) % 168.22/168.07 [64]~E(x641,x642)+E(f857(x641,x643),f857(x642,x643)) % 168.22/168.07 [65]~E(x651,x652)+E(f857(x653,x651),f857(x653,x652)) % 168.22/168.07 [66]~E(x661,x662)+E(f89(x661),f89(x662)) % 168.22/168.07 [67]~E(x671,x672)+E(f88(x671),f88(x672)) % 168.22/168.07 [68]~E(x681,x682)+E(f71(x681),f71(x682)) % 168.22/168.07 [69]~E(x691,x692)+E(f189(x691),f189(x692)) % 168.22/168.07 [70]~E(x701,x702)+E(f278(x701,x703),f278(x702,x703)) % 168.22/168.07 [71]~E(x711,x712)+E(f278(x713,x711),f278(x713,x712)) % 168.22/168.07 [72]~E(x721,x722)+E(f115(x721),f115(x722)) % 168.22/168.07 [73]~E(x731,x732)+E(f289(x731,x733,x734),f289(x732,x733,x734)) % 168.22/168.07 [74]~E(x741,x742)+E(f289(x743,x741,x744),f289(x743,x742,x744)) % 168.22/168.07 [75]~E(x751,x752)+E(f289(x753,x754,x751),f289(x753,x754,x752)) % 168.22/168.07 [76]~E(x761,x762)+E(f70(x761),f70(x762)) % 168.22/168.07 [77]~E(x771,x772)+E(f245(x771,x773),f245(x772,x773)) % 168.22/168.07 [78]~E(x781,x782)+E(f245(x783,x781),f245(x783,x782)) % 168.22/168.07 [79]~E(x791,x792)+E(f233(x791),f233(x792)) % 168.22/168.07 [80]~E(x801,x802)+E(f51(x801,x803),f51(x802,x803)) % 168.22/168.07 [81]~E(x811,x812)+E(f51(x813,x811),f51(x813,x812)) % 168.22/168.07 [82]~E(x821,x822)+E(f7(x821,x823,x824),f7(x822,x823,x824)) % 168.22/168.07 [83]~E(x831,x832)+E(f7(x833,x831,x834),f7(x833,x832,x834)) % 168.22/168.07 [84]~E(x841,x842)+E(f7(x843,x844,x841),f7(x843,x844,x842)) % 168.22/168.07 [85]~E(x851,x852)+E(f280(x851),f280(x852)) % 168.22/168.07 [86]~E(x861,x862)+E(f131(x861),f131(x862)) % 168.22/168.07 [87]~E(x871,x872)+E(f222(x871),f222(x872)) % 168.22/168.07 [88]~E(x881,x882)+E(f159(x881),f159(x882)) % 168.22/168.07 [89]~E(x891,x892)+E(f230(x891),f230(x892)) % 168.22/168.07 [90]~E(x901,x902)+E(f96(x901),f96(x902)) % 168.22/168.07 [91]~E(x911,x912)+E(f238(x911),f238(x912)) % 168.22/168.07 [92]~E(x921,x922)+E(f143(x921,x923,x924),f143(x922,x923,x924)) % 168.22/168.07 [93]~E(x931,x932)+E(f143(x933,x931,x934),f143(x933,x932,x934)) % 168.22/168.07 [94]~E(x941,x942)+E(f143(x943,x944,x941),f143(x943,x944,x942)) % 168.22/168.07 [95]~E(x951,x952)+E(f287(x951,x953,x954),f287(x952,x953,x954)) % 168.22/168.07 [96]~E(x961,x962)+E(f287(x963,x961,x964),f287(x963,x962,x964)) % 168.22/168.07 [97]~E(x971,x972)+E(f287(x973,x974,x971),f287(x973,x974,x972)) % 168.22/168.07 [98]~E(x981,x982)+E(f54(x981),f54(x982)) % 168.22/168.07 [99]~E(x991,x992)+E(f281(x991,x993,x994),f281(x992,x993,x994)) % 168.22/168.07 [100]~E(x1001,x1002)+E(f281(x1003,x1001,x1004),f281(x1003,x1002,x1004)) % 168.22/168.07 [101]~E(x1011,x1012)+E(f281(x1013,x1014,x1011),f281(x1013,x1014,x1012)) % 168.22/168.07 [102]~E(x1021,x1022)+E(f266(x1021),f266(x1022)) % 168.22/168.07 [103]~E(x1031,x1032)+E(f785(x1031,x1033,x1034),f785(x1032,x1033,x1034)) % 168.22/168.07 [104]~E(x1041,x1042)+E(f785(x1043,x1041,x1044),f785(x1043,x1042,x1044)) % 168.22/168.07 [105]~E(x1051,x1052)+E(f785(x1053,x1054,x1051),f785(x1053,x1054,x1052)) % 168.22/168.07 [106]~E(x1061,x1062)+E(f237(x1061,x1063),f237(x1062,x1063)) % 168.22/168.07 [107]~E(x1071,x1072)+E(f237(x1073,x1071),f237(x1073,x1072)) % 168.22/168.07 [108]~E(x1081,x1082)+E(f778(x1081,x1083,x1084),f778(x1082,x1083,x1084)) % 168.22/168.07 [109]~E(x1091,x1092)+E(f778(x1093,x1091,x1094),f778(x1093,x1092,x1094)) % 168.22/168.07 [110]~E(x1101,x1102)+E(f778(x1103,x1104,x1101),f778(x1103,x1104,x1102)) % 168.22/168.07 [111]~E(x1111,x1112)+E(f145(x1111),f145(x1112)) % 168.22/168.07 [112]~E(x1121,x1122)+E(f279(x1121,x1123,x1124),f279(x1122,x1123,x1124)) % 168.22/168.07 [113]~E(x1131,x1132)+E(f279(x1133,x1131,x1134),f279(x1133,x1132,x1134)) % 168.22/168.07 [114]~E(x1141,x1142)+E(f279(x1143,x1144,x1141),f279(x1143,x1144,x1142)) % 168.22/168.07 [115]~E(x1151,x1152)+E(f502(x1151,x1153,x1154,x1155),f502(x1152,x1153,x1154,x1155)) % 168.22/168.07 [116]~E(x1161,x1162)+E(f502(x1163,x1161,x1164,x1165),f502(x1163,x1162,x1164,x1165)) % 168.22/168.07 [117]~E(x1171,x1172)+E(f502(x1173,x1174,x1171,x1175),f502(x1173,x1174,x1172,x1175)) % 168.22/168.07 [118]~E(x1181,x1182)+E(f502(x1183,x1184,x1185,x1181),f502(x1183,x1184,x1185,x1182)) % 168.22/168.07 [119]~E(x1191,x1192)+E(f286(x1191),f286(x1192)) % 168.22/168.07 [120]~E(x1201,x1202)+E(f14(x1201,x1203),f14(x1202,x1203)) % 168.22/168.07 [121]~E(x1211,x1212)+E(f14(x1213,x1211),f14(x1213,x1212)) % 168.22/168.07 [122]~E(x1221,x1222)+E(f82(x1221,x1223,x1224,x1225),f82(x1222,x1223,x1224,x1225)) % 168.22/168.07 [123]~E(x1231,x1232)+E(f82(x1233,x1231,x1234,x1235),f82(x1233,x1232,x1234,x1235)) % 168.22/168.07 [124]~E(x1241,x1242)+E(f82(x1243,x1244,x1241,x1245),f82(x1243,x1244,x1242,x1245)) % 168.22/168.07 [125]~E(x1251,x1252)+E(f82(x1253,x1254,x1255,x1251),f82(x1253,x1254,x1255,x1252)) % 168.22/168.07 [126]~E(x1261,x1262)+E(f529(x1261,x1263),f529(x1262,x1263)) % 168.22/168.07 [127]~E(x1271,x1272)+E(f529(x1273,x1271),f529(x1273,x1272)) % 168.22/168.07 [128]~E(x1281,x1282)+E(f125(x1281),f125(x1282)) % 168.22/168.07 [129]~E(x1291,x1292)+E(f234(x1291,x1293),f234(x1292,x1293)) % 168.22/168.07 [130]~E(x1301,x1302)+E(f234(x1303,x1301),f234(x1303,x1302)) % 168.22/168.07 [131]~E(x1311,x1312)+E(f765(x1311,x1313,x1314),f765(x1312,x1313,x1314)) % 168.22/168.07 [132]~E(x1321,x1322)+E(f765(x1323,x1321,x1324),f765(x1323,x1322,x1324)) % 168.22/168.07 [133]~E(x1331,x1332)+E(f765(x1333,x1334,x1331),f765(x1333,x1334,x1332)) % 168.22/168.07 [134]~E(x1341,x1342)+E(f72(x1341,x1343,x1344),f72(x1342,x1343,x1344)) % 168.22/168.07 [135]~E(x1351,x1352)+E(f72(x1353,x1351,x1354),f72(x1353,x1352,x1354)) % 168.22/168.07 [136]~E(x1361,x1362)+E(f72(x1363,x1364,x1361),f72(x1363,x1364,x1362)) % 168.22/168.07 [137]~E(x1371,x1372)+E(f13(x1371,x1373,x1374),f13(x1372,x1373,x1374)) % 168.22/168.07 [138]~E(x1381,x1382)+E(f13(x1383,x1381,x1384),f13(x1383,x1382,x1384)) % 168.22/168.07 [139]~E(x1391,x1392)+E(f13(x1393,x1394,x1391),f13(x1393,x1394,x1392)) % 168.22/168.07 [140]~E(x1401,x1402)+E(f400(x1401,x1403,x1404,x1405,x1406),f400(x1402,x1403,x1404,x1405,x1406)) % 168.22/168.07 [141]~E(x1411,x1412)+E(f400(x1413,x1411,x1414,x1415,x1416),f400(x1413,x1412,x1414,x1415,x1416)) % 168.22/168.07 [142]~E(x1421,x1422)+E(f400(x1423,x1424,x1421,x1425,x1426),f400(x1423,x1424,x1422,x1425,x1426)) % 168.22/168.07 [143]~E(x1431,x1432)+E(f400(x1433,x1434,x1435,x1431,x1436),f400(x1433,x1434,x1435,x1432,x1436)) % 168.22/168.07 [144]~E(x1441,x1442)+E(f400(x1443,x1444,x1445,x1446,x1441),f400(x1443,x1444,x1445,x1446,x1442)) % 168.22/168.07 [145]~E(x1451,x1452)+E(f171(x1451,x1453),f171(x1452,x1453)) % 168.22/168.07 [146]~E(x1461,x1462)+E(f171(x1463,x1461),f171(x1463,x1462)) % 168.22/168.07 [147]~E(x1471,x1472)+E(f12(x1471,x1473,x1474),f12(x1472,x1473,x1474)) % 168.22/168.07 [148]~E(x1481,x1482)+E(f12(x1483,x1481,x1484),f12(x1483,x1482,x1484)) % 168.22/168.07 [149]~E(x1491,x1492)+E(f12(x1493,x1494,x1491),f12(x1493,x1494,x1492)) % 168.22/168.07 [150]~E(x1501,x1502)+E(f170(x1501,x1503,x1504),f170(x1502,x1503,x1504)) % 168.22/168.07 [151]~E(x1511,x1512)+E(f170(x1513,x1511,x1514),f170(x1513,x1512,x1514)) % 168.22/168.07 [152]~E(x1521,x1522)+E(f170(x1523,x1524,x1521),f170(x1523,x1524,x1522)) % 168.22/168.07 [153]~E(x1531,x1532)+E(f84(x1531),f84(x1532)) % 168.22/168.07 [154]~E(x1541,x1542)+E(f94(x1541,x1543),f94(x1542,x1543)) % 168.22/168.07 [155]~E(x1551,x1552)+E(f94(x1553,x1551),f94(x1553,x1552)) % 168.22/168.07 [156]~E(x1561,x1562)+E(f248(x1561,x1563,x1564,x1565,x1566,x1567),f248(x1562,x1563,x1564,x1565,x1566,x1567)) % 168.22/168.07 [157]~E(x1571,x1572)+E(f248(x1573,x1571,x1574,x1575,x1576,x1577),f248(x1573,x1572,x1574,x1575,x1576,x1577)) % 168.22/168.07 [158]~E(x1581,x1582)+E(f248(x1583,x1584,x1581,x1585,x1586,x1587),f248(x1583,x1584,x1582,x1585,x1586,x1587)) % 168.22/168.07 [159]~E(x1591,x1592)+E(f248(x1593,x1594,x1595,x1591,x1596,x1597),f248(x1593,x1594,x1595,x1592,x1596,x1597)) % 168.22/168.07 [160]~E(x1601,x1602)+E(f248(x1603,x1604,x1605,x1606,x1601,x1607),f248(x1603,x1604,x1605,x1606,x1602,x1607)) % 168.22/168.07 [161]~E(x1611,x1612)+E(f248(x1613,x1614,x1615,x1616,x1617,x1611),f248(x1613,x1614,x1615,x1616,x1617,x1612)) % 168.22/168.07 [162]~E(x1621,x1622)+E(f117(x1621),f117(x1622)) % 168.22/168.07 [163]~E(x1631,x1632)+E(f119(x1631),f119(x1632)) % 168.22/168.07 [164]~E(x1641,x1642)+E(f318(x1641),f318(x1642)) % 168.22/168.07 [165]~E(x1651,x1652)+E(f506(x1651,x1653,x1654,x1655),f506(x1652,x1653,x1654,x1655)) % 168.22/168.07 [166]~E(x1661,x1662)+E(f506(x1663,x1661,x1664,x1665),f506(x1663,x1662,x1664,x1665)) % 168.22/168.07 [167]~E(x1671,x1672)+E(f506(x1673,x1674,x1671,x1675),f506(x1673,x1674,x1672,x1675)) % 168.22/168.07 [168]~E(x1681,x1682)+E(f506(x1683,x1684,x1685,x1681),f506(x1683,x1684,x1685,x1682)) % 168.22/168.07 [169]~E(x1691,x1692)+E(f191(x1691),f191(x1692)) % 168.22/168.07 [170]~E(x1701,x1702)+E(f5(x1701),f5(x1702)) % 168.22/168.07 [171]~E(x1711,x1712)+E(f49(x1711,x1713),f49(x1712,x1713)) % 168.22/168.07 [172]~E(x1721,x1722)+E(f49(x1723,x1721),f49(x1723,x1722)) % 168.22/168.07 [173]~E(x1731,x1732)+E(f148(x1731,x1733),f148(x1732,x1733)) % 168.22/168.07 [174]~E(x1741,x1742)+E(f148(x1743,x1741),f148(x1743,x1742)) % 168.22/168.07 [175]~E(x1751,x1752)+E(f175(x1751,x1753),f175(x1752,x1753)) % 168.22/168.07 [176]~E(x1761,x1762)+E(f175(x1763,x1761),f175(x1763,x1762)) % 168.22/168.07 [177]~E(x1771,x1772)+E(f163(x1771),f163(x1772)) % 168.22/168.07 [178]~E(x1781,x1782)+E(f308(x1781,x1783),f308(x1782,x1783)) % 168.22/168.07 [179]~E(x1791,x1792)+E(f308(x1793,x1791),f308(x1793,x1792)) % 168.22/168.07 [180]~E(x1801,x1802)+E(f463(x1801,x1803,x1804),f463(x1802,x1803,x1804)) % 168.22/168.07 [181]~E(x1811,x1812)+E(f463(x1813,x1811,x1814),f463(x1813,x1812,x1814)) % 168.22/168.07 [182]~E(x1821,x1822)+E(f463(x1823,x1824,x1821),f463(x1823,x1824,x1822)) % 168.22/168.07 [183]~E(x1831,x1832)+E(f65(x1831),f65(x1832)) % 168.22/168.07 [184]~E(x1841,x1842)+E(f166(x1841),f166(x1842)) % 168.22/168.07 [185]~E(x1851,x1852)+E(f371(x1851,x1853),f371(x1852,x1853)) % 168.22/168.07 [186]~E(x1861,x1862)+E(f371(x1863,x1861),f371(x1863,x1862)) % 168.22/168.07 [187]~E(x1871,x1872)+E(f766(x1871,x1873,x1874),f766(x1872,x1873,x1874)) % 168.22/168.07 [188]~E(x1881,x1882)+E(f766(x1883,x1881,x1884),f766(x1883,x1882,x1884)) % 168.22/168.07 [189]~E(x1891,x1892)+E(f766(x1893,x1894,x1891),f766(x1893,x1894,x1892)) % 168.22/168.07 [190]~E(x1901,x1902)+E(f262(x1901,x1903,x1904),f262(x1902,x1903,x1904)) % 168.22/168.07 [191]~E(x1911,x1912)+E(f262(x1913,x1911,x1914),f262(x1913,x1912,x1914)) % 168.22/168.07 [192]~E(x1921,x1922)+E(f262(x1923,x1924,x1921),f262(x1923,x1924,x1922)) % 168.22/168.07 [193]~E(x1931,x1932)+E(f133(x1931,x1933),f133(x1932,x1933)) % 168.22/168.07 [194]~E(x1941,x1942)+E(f133(x1943,x1941),f133(x1943,x1942)) % 168.22/168.07 [195]~E(x1951,x1952)+E(f52(x1951,x1953),f52(x1952,x1953)) % 168.22/168.07 [196]~E(x1961,x1962)+E(f52(x1963,x1961),f52(x1963,x1962)) % 168.22/168.07 [197]~E(x1971,x1972)+E(f786(x1971,x1973,x1974),f786(x1972,x1973,x1974)) % 168.22/168.07 [198]~E(x1981,x1982)+E(f786(x1983,x1981,x1984),f786(x1983,x1982,x1984)) % 168.22/168.07 [199]~E(x1991,x1992)+E(f786(x1993,x1994,x1991),f786(x1993,x1994,x1992)) % 168.22/168.07 [200]~E(x2001,x2002)+E(f698(x2001,x2003),f698(x2002,x2003)) % 168.22/168.07 [201]~E(x2011,x2012)+E(f698(x2013,x2011),f698(x2013,x2012)) % 168.22/168.07 [202]~E(x2021,x2022)+E(f31(x2021,x2023,x2024),f31(x2022,x2023,x2024)) % 168.22/168.07 [203]~E(x2031,x2032)+E(f31(x2033,x2031,x2034),f31(x2033,x2032,x2034)) % 168.22/168.07 [204]~E(x2041,x2042)+E(f31(x2043,x2044,x2041),f31(x2043,x2044,x2042)) % 168.22/168.07 [205]~E(x2051,x2052)+E(f708(x2051,x2053,x2054,x2055),f708(x2052,x2053,x2054,x2055)) % 168.22/168.07 [206]~E(x2061,x2062)+E(f708(x2063,x2061,x2064,x2065),f708(x2063,x2062,x2064,x2065)) % 168.22/168.07 [207]~E(x2071,x2072)+E(f708(x2073,x2074,x2071,x2075),f708(x2073,x2074,x2072,x2075)) % 168.22/168.07 [208]~E(x2081,x2082)+E(f708(x2083,x2084,x2085,x2081),f708(x2083,x2084,x2085,x2082)) % 168.22/168.07 [209]~E(x2091,x2092)+E(f76(x2091,x2093,x2094,x2095,x2096),f76(x2092,x2093,x2094,x2095,x2096)) % 168.22/168.07 [210]~E(x2101,x2102)+E(f76(x2103,x2101,x2104,x2105,x2106),f76(x2103,x2102,x2104,x2105,x2106)) % 168.22/168.07 [211]~E(x2111,x2112)+E(f76(x2113,x2114,x2111,x2115,x2116),f76(x2113,x2114,x2112,x2115,x2116)) % 168.22/168.07 [212]~E(x2121,x2122)+E(f76(x2123,x2124,x2125,x2121,x2126),f76(x2123,x2124,x2125,x2122,x2126)) % 168.22/168.07 [213]~E(x2131,x2132)+E(f76(x2133,x2134,x2135,x2136,x2131),f76(x2133,x2134,x2135,x2136,x2132)) % 168.22/168.07 [214]~E(x2141,x2142)+E(f306(x2141,x2143),f306(x2142,x2143)) % 168.22/168.07 [215]~E(x2151,x2152)+E(f306(x2153,x2151),f306(x2153,x2152)) % 168.22/168.07 [216]~E(x2161,x2162)+E(f184(x2161,x2163,x2164,x2165),f184(x2162,x2163,x2164,x2165)) % 168.22/168.07 [217]~E(x2171,x2172)+E(f184(x2173,x2171,x2174,x2175),f184(x2173,x2172,x2174,x2175)) % 168.22/168.07 [218]~E(x2181,x2182)+E(f184(x2183,x2184,x2181,x2185),f184(x2183,x2184,x2182,x2185)) % 168.22/168.07 [219]~E(x2191,x2192)+E(f184(x2193,x2194,x2195,x2191),f184(x2193,x2194,x2195,x2192)) % 168.22/168.07 [220]~E(x2201,x2202)+E(f177(x2201,x2203,x2204),f177(x2202,x2203,x2204)) % 168.22/168.07 [221]~E(x2211,x2212)+E(f177(x2213,x2211,x2214),f177(x2213,x2212,x2214)) % 168.22/168.07 [222]~E(x2221,x2222)+E(f177(x2223,x2224,x2221),f177(x2223,x2224,x2222)) % 168.22/168.07 [223]~E(x2231,x2232)+E(f274(x2231,x2233,x2234),f274(x2232,x2233,x2234)) % 168.22/168.07 [224]~E(x2241,x2242)+E(f274(x2243,x2241,x2244),f274(x2243,x2242,x2244)) % 168.22/168.07 [225]~E(x2251,x2252)+E(f274(x2253,x2254,x2251),f274(x2253,x2254,x2252)) % 168.22/168.07 [226]~E(x2261,x2262)+E(f194(x2261),f194(x2262)) % 168.22/168.07 [227]~E(x2271,x2272)+E(f9(x2271,x2273),f9(x2272,x2273)) % 168.22/168.07 [228]~E(x2281,x2282)+E(f9(x2283,x2281),f9(x2283,x2282)) % 168.22/168.07 [229]~E(x2291,x2292)+E(f259(x2291,x2293),f259(x2292,x2293)) % 168.22/168.07 [230]~E(x2301,x2302)+E(f259(x2303,x2301),f259(x2303,x2302)) % 168.22/168.07 [231]~E(x2311,x2312)+E(f35(x2311,x2313),f35(x2312,x2313)) % 168.22/168.07 [232]~E(x2321,x2322)+E(f35(x2323,x2321),f35(x2323,x2322)) % 168.22/168.07 [233]~E(x2331,x2332)+E(f265(x2331,x2333,x2334),f265(x2332,x2333,x2334)) % 168.22/168.07 [234]~E(x2341,x2342)+E(f265(x2343,x2341,x2344),f265(x2343,x2342,x2344)) % 168.22/168.07 [235]~E(x2351,x2352)+E(f265(x2353,x2354,x2351),f265(x2353,x2354,x2352)) % 168.22/168.07 [236]~E(x2361,x2362)+E(f167(x2361),f167(x2362)) % 168.22/168.07 [237]~E(x2371,x2372)+E(f127(x2371),f127(x2372)) % 168.22/168.07 [238]~E(x2381,x2382)+E(f38(x2381,x2383,x2384,x2385,x2386,x2387,x2388,x2389,x23810,x23811),f38(x2382,x2383,x2384,x2385,x2386,x2387,x2388,x2389,x23810,x23811)) % 168.22/168.07 [239]~E(x2391,x2392)+E(f38(x2393,x2391,x2394,x2395,x2396,x2397,x2398,x2399,x23910,x23911),f38(x2393,x2392,x2394,x2395,x2396,x2397,x2398,x2399,x23910,x23911)) % 168.22/168.07 [240]~E(x2401,x2402)+E(f38(x2403,x2404,x2401,x2405,x2406,x2407,x2408,x2409,x24010,x24011),f38(x2403,x2404,x2402,x2405,x2406,x2407,x2408,x2409,x24010,x24011)) % 168.22/168.07 [241]~E(x2411,x2412)+E(f38(x2413,x2414,x2415,x2411,x2416,x2417,x2418,x2419,x24110,x24111),f38(x2413,x2414,x2415,x2412,x2416,x2417,x2418,x2419,x24110,x24111)) % 168.22/168.07 [242]~E(x2421,x2422)+E(f38(x2423,x2424,x2425,x2426,x2421,x2427,x2428,x2429,x24210,x24211),f38(x2423,x2424,x2425,x2426,x2422,x2427,x2428,x2429,x24210,x24211)) % 168.22/168.07 [243]~E(x2431,x2432)+E(f38(x2433,x2434,x2435,x2436,x2437,x2431,x2438,x2439,x24310,x24311),f38(x2433,x2434,x2435,x2436,x2437,x2432,x2438,x2439,x24310,x24311)) % 168.22/168.07 [244]~E(x2441,x2442)+E(f38(x2443,x2444,x2445,x2446,x2447,x2448,x2441,x2449,x24410,x24411),f38(x2443,x2444,x2445,x2446,x2447,x2448,x2442,x2449,x24410,x24411)) % 168.22/168.07 [245]~E(x2451,x2452)+E(f38(x2453,x2454,x2455,x2456,x2457,x2458,x2459,x2451,x24510,x24511),f38(x2453,x2454,x2455,x2456,x2457,x2458,x2459,x2452,x24510,x24511)) % 168.22/168.07 [246]~E(x2461,x2462)+E(f38(x2463,x2464,x2465,x2466,x2467,x2468,x2469,x24610,x2461,x24611),f38(x2463,x2464,x2465,x2466,x2467,x2468,x2469,x24610,x2462,x24611)) % 168.22/168.07 [247]~E(x2471,x2472)+E(f38(x2473,x2474,x2475,x2476,x2477,x2478,x2479,x24710,x24711,x2471),f38(x2473,x2474,x2475,x2476,x2477,x2478,x2479,x24710,x24711,x2472)) % 168.22/168.07 [248]~E(x2481,x2482)+E(f298(x2481,x2483,x2484,x2485),f298(x2482,x2483,x2484,x2485)) % 168.22/168.07 [249]~E(x2491,x2492)+E(f298(x2493,x2491,x2494,x2495),f298(x2493,x2492,x2494,x2495)) % 168.22/168.07 [250]~E(x2501,x2502)+E(f298(x2503,x2504,x2501,x2505),f298(x2503,x2504,x2502,x2505)) % 168.22/168.07 [251]~E(x2511,x2512)+E(f298(x2513,x2514,x2515,x2511),f298(x2513,x2514,x2515,x2512)) % 168.22/168.07 [252]~E(x2521,x2522)+E(f121(x2521),f121(x2522)) % 168.22/168.07 [253]~E(x2531,x2532)+E(f610(x2531,x2533,x2534,x2535,x2536),f610(x2532,x2533,x2534,x2535,x2536)) % 168.22/168.07 [254]~E(x2541,x2542)+E(f610(x2543,x2541,x2544,x2545,x2546),f610(x2543,x2542,x2544,x2545,x2546)) % 168.22/168.07 [255]~E(x2551,x2552)+E(f610(x2553,x2554,x2551,x2555,x2556),f610(x2553,x2554,x2552,x2555,x2556)) % 168.22/168.07 [256]~E(x2561,x2562)+E(f610(x2563,x2564,x2565,x2561,x2566),f610(x2563,x2564,x2565,x2562,x2566)) % 168.22/168.07 [257]~E(x2571,x2572)+E(f610(x2573,x2574,x2575,x2576,x2571),f610(x2573,x2574,x2575,x2576,x2572)) % 168.22/168.07 [258]~E(x2581,x2582)+E(f735(x2581,x2583,x2584),f735(x2582,x2583,x2584)) % 168.22/168.07 [259]~E(x2591,x2592)+E(f735(x2593,x2591,x2594),f735(x2593,x2592,x2594)) % 168.22/168.07 [260]~E(x2601,x2602)+E(f735(x2603,x2604,x2601),f735(x2603,x2604,x2602)) % 168.22/168.07 [261]~E(x2611,x2612)+E(f108(x2611),f108(x2612)) % 168.22/168.07 [262]~E(x2621,x2622)+E(f149(x2621,x2623,x2624),f149(x2622,x2623,x2624)) % 168.22/168.07 [263]~E(x2631,x2632)+E(f149(x2633,x2631,x2634),f149(x2633,x2632,x2634)) % 168.22/168.07 [264]~E(x2641,x2642)+E(f149(x2643,x2644,x2641),f149(x2643,x2644,x2642)) % 168.22/168.07 [265]~E(x2651,x2652)+E(f284(x2651,x2653),f284(x2652,x2653)) % 168.22/168.07 [266]~E(x2661,x2662)+E(f284(x2663,x2661),f284(x2663,x2662)) % 168.22/168.07 [267]~E(x2671,x2672)+E(f232(x2671),f232(x2672)) % 168.22/168.07 [268]~E(x2681,x2682)+E(f73(x2681,x2683),f73(x2682,x2683)) % 168.22/168.07 [269]~E(x2691,x2692)+E(f73(x2693,x2691),f73(x2693,x2692)) % 168.22/168.07 [270]~E(x2701,x2702)+E(f126(x2701,x2703),f126(x2702,x2703)) % 168.22/168.07 [271]~E(x2711,x2712)+E(f126(x2713,x2711),f126(x2713,x2712)) % 168.22/168.07 [272]~E(x2721,x2722)+E(f236(x2721,x2723),f236(x2722,x2723)) % 168.22/168.07 [273]~E(x2731,x2732)+E(f236(x2733,x2731),f236(x2733,x2732)) % 168.22/168.07 [274]~E(x2741,x2742)+E(f772(x2741,x2743,x2744,x2745,x2746),f772(x2742,x2743,x2744,x2745,x2746)) % 168.22/168.07 [275]~E(x2751,x2752)+E(f772(x2753,x2751,x2754,x2755,x2756),f772(x2753,x2752,x2754,x2755,x2756)) % 168.22/168.07 [276]~E(x2761,x2762)+E(f772(x2763,x2764,x2761,x2765,x2766),f772(x2763,x2764,x2762,x2765,x2766)) % 168.22/168.07 [277]~E(x2771,x2772)+E(f772(x2773,x2774,x2775,x2771,x2776),f772(x2773,x2774,x2775,x2772,x2776)) % 168.22/168.07 [278]~E(x2781,x2782)+E(f772(x2783,x2784,x2785,x2786,x2781),f772(x2783,x2784,x2785,x2786,x2782)) % 168.22/168.07 [279]~E(x2791,x2792)+E(f146(x2791,x2793),f146(x2792,x2793)) % 168.22/168.07 [280]~E(x2801,x2802)+E(f146(x2803,x2801),f146(x2803,x2802)) % 168.22/168.07 [281]~E(x2811,x2812)+E(f81(x2811,x2813),f81(x2812,x2813)) % 168.22/168.07 [282]~E(x2821,x2822)+E(f81(x2823,x2821),f81(x2823,x2822)) % 168.22/168.07 [283]~E(x2831,x2832)+E(f640(x2831,x2833,x2834),f640(x2832,x2833,x2834)) % 168.22/168.07 [284]~E(x2841,x2842)+E(f640(x2843,x2841,x2844),f640(x2843,x2842,x2844)) % 168.22/168.07 [285]~E(x2851,x2852)+E(f640(x2853,x2854,x2851),f640(x2853,x2854,x2852)) % 168.22/168.07 [286]~E(x2861,x2862)+E(f48(x2861,x2863),f48(x2862,x2863)) % 168.22/168.07 [287]~E(x2871,x2872)+E(f48(x2873,x2871),f48(x2873,x2872)) % 168.22/168.07 [288]~E(x2881,x2882)+E(f459(x2881,x2883,x2884,x2885),f459(x2882,x2883,x2884,x2885)) % 168.22/168.07 [289]~E(x2891,x2892)+E(f459(x2893,x2891,x2894,x2895),f459(x2893,x2892,x2894,x2895)) % 168.22/168.07 [290]~E(x2901,x2902)+E(f459(x2903,x2904,x2901,x2905),f459(x2903,x2904,x2902,x2905)) % 168.22/168.07 [291]~E(x2911,x2912)+E(f459(x2913,x2914,x2915,x2911),f459(x2913,x2914,x2915,x2912)) % 168.22/168.07 [292]~E(x2921,x2922)+E(f132(x2921),f132(x2922)) % 168.22/168.07 [293]~E(x2931,x2932)+E(f601(x2931,x2933,x2934,x2935),f601(x2932,x2933,x2934,x2935)) % 168.22/168.07 [294]~E(x2941,x2942)+E(f601(x2943,x2941,x2944,x2945),f601(x2943,x2942,x2944,x2945)) % 168.22/168.07 [295]~E(x2951,x2952)+E(f601(x2953,x2954,x2951,x2955),f601(x2953,x2954,x2952,x2955)) % 168.22/168.07 [296]~E(x2961,x2962)+E(f601(x2963,x2964,x2965,x2961),f601(x2963,x2964,x2965,x2962)) % 168.22/168.07 [297]~E(x2971,x2972)+E(f55(x2971,x2973,x2974),f55(x2972,x2973,x2974)) % 168.22/168.07 [298]~E(x2981,x2982)+E(f55(x2983,x2981,x2984),f55(x2983,x2982,x2984)) % 168.22/168.07 [299]~E(x2991,x2992)+E(f55(x2993,x2994,x2991),f55(x2993,x2994,x2992)) % 168.22/168.07 [300]~E(x3001,x3002)+E(f173(x3001,x3003),f173(x3002,x3003)) % 168.22/168.07 [301]~E(x3011,x3012)+E(f173(x3013,x3011),f173(x3013,x3012)) % 168.22/168.07 [302]~E(x3021,x3022)+E(f100(x3021),f100(x3022)) % 168.22/168.07 [303]~E(x3031,x3032)+E(f192(x3031,x3033),f192(x3032,x3033)) % 168.22/168.07 [304]~E(x3041,x3042)+E(f192(x3043,x3041),f192(x3043,x3042)) % 168.22/168.07 [305]~E(x3051,x3052)+E(f303(x3051,x3053,x3054,x3055,x3056),f303(x3052,x3053,x3054,x3055,x3056)) % 168.22/168.07 [306]~E(x3061,x3062)+E(f303(x3063,x3061,x3064,x3065,x3066),f303(x3063,x3062,x3064,x3065,x3066)) % 168.22/168.07 [307]~E(x3071,x3072)+E(f303(x3073,x3074,x3071,x3075,x3076),f303(x3073,x3074,x3072,x3075,x3076)) % 168.22/168.07 [308]~E(x3081,x3082)+E(f303(x3083,x3084,x3085,x3081,x3086),f303(x3083,x3084,x3085,x3082,x3086)) % 168.22/168.07 [309]~E(x3091,x3092)+E(f303(x3093,x3094,x3095,x3096,x3091),f303(x3093,x3094,x3095,x3096,x3092)) % 168.22/168.07 [310]~E(x3101,x3102)+E(f305(x3101,x3103),f305(x3102,x3103)) % 168.22/168.07 [311]~E(x3111,x3112)+E(f305(x3113,x3111),f305(x3113,x3112)) % 168.22/168.07 [312]~E(x3121,x3122)+E(f217(x3121),f217(x3122)) % 168.22/168.07 [313]~E(x3131,x3132)+E(f466(x3131,x3133,x3134,x3135,x3136),f466(x3132,x3133,x3134,x3135,x3136)) % 168.22/168.07 [314]~E(x3141,x3142)+E(f466(x3143,x3141,x3144,x3145,x3146),f466(x3143,x3142,x3144,x3145,x3146)) % 168.22/168.07 [315]~E(x3151,x3152)+E(f466(x3153,x3154,x3151,x3155,x3156),f466(x3153,x3154,x3152,x3155,x3156)) % 168.22/168.07 [316]~E(x3161,x3162)+E(f466(x3163,x3164,x3165,x3161,x3166),f466(x3163,x3164,x3165,x3162,x3166)) % 168.22/168.07 [317]~E(x3171,x3172)+E(f466(x3173,x3174,x3175,x3176,x3171),f466(x3173,x3174,x3175,x3176,x3172)) % 168.22/168.07 [318]~E(x3181,x3182)+E(f244(x3181,x3183),f244(x3182,x3183)) % 168.22/168.07 [319]~E(x3191,x3192)+E(f244(x3193,x3191),f244(x3193,x3192)) % 168.22/168.07 [320]~E(x3201,x3202)+E(f513(x3201,x3203,x3204,x3205,x3206),f513(x3202,x3203,x3204,x3205,x3206)) % 168.22/168.07 [321]~E(x3211,x3212)+E(f513(x3213,x3211,x3214,x3215,x3216),f513(x3213,x3212,x3214,x3215,x3216)) % 168.22/168.07 [322]~E(x3221,x3222)+E(f513(x3223,x3224,x3221,x3225,x3226),f513(x3223,x3224,x3222,x3225,x3226)) % 168.22/168.07 [323]~E(x3231,x3232)+E(f513(x3233,x3234,x3235,x3231,x3236),f513(x3233,x3234,x3235,x3232,x3236)) % 168.22/168.07 [324]~E(x3241,x3242)+E(f513(x3243,x3244,x3245,x3246,x3241),f513(x3243,x3244,x3245,x3246,x3242)) % 168.22/168.07 [325]~E(x3251,x3252)+E(f290(x3251,x3253),f290(x3252,x3253)) % 168.22/168.07 [326]~E(x3261,x3262)+E(f290(x3263,x3261),f290(x3263,x3262)) % 168.22/168.07 [327]~E(x3271,x3272)+E(f67(x3271),f67(x3272)) % 168.22/168.07 [328]~E(x3281,x3282)+E(f854(x3281,x3283),f854(x3282,x3283)) % 168.22/168.07 [329]~E(x3291,x3292)+E(f854(x3293,x3291),f854(x3293,x3292)) % 168.22/168.07 [330]~E(x3301,x3302)+E(f856(x3301,x3303),f856(x3302,x3303)) % 168.22/168.07 [331]~E(x3311,x3312)+E(f856(x3313,x3311),f856(x3313,x3312)) % 168.22/168.07 [332]~E(x3321,x3322)+E(f162(x3321),f162(x3322)) % 168.22/168.07 [333]~E(x3331,x3332)+E(f150(x3331,x3333,x3334,x3335),f150(x3332,x3333,x3334,x3335)) % 168.22/168.07 [334]~E(x3341,x3342)+E(f150(x3343,x3341,x3344,x3345),f150(x3343,x3342,x3344,x3345)) % 168.22/168.07 [335]~E(x3351,x3352)+E(f150(x3353,x3354,x3351,x3355),f150(x3353,x3354,x3352,x3355)) % 168.22/168.07 [336]~E(x3361,x3362)+E(f150(x3363,x3364,x3365,x3361),f150(x3363,x3364,x3365,x3362)) % 168.22/168.07 [337]~E(x3371,x3372)+E(f516(x3371,x3373,x3374),f516(x3372,x3373,x3374)) % 168.22/168.07 [338]~E(x3381,x3382)+E(f516(x3383,x3381,x3384),f516(x3383,x3382,x3384)) % 168.22/168.07 [339]~E(x3391,x3392)+E(f516(x3393,x3394,x3391),f516(x3393,x3394,x3392)) % 168.22/168.07 [340]~E(x3401,x3402)+E(f57(x3401,x3403),f57(x3402,x3403)) % 168.22/168.07 [341]~E(x3411,x3412)+E(f57(x3413,x3411),f57(x3413,x3412)) % 168.22/168.07 [342]~E(x3421,x3422)+E(f16(x3421,x3423),f16(x3422,x3423)) % 168.22/168.07 [343]~E(x3431,x3432)+E(f16(x3433,x3431),f16(x3433,x3432)) % 168.22/168.07 [344]~E(x3441,x3442)+E(f165(x3441),f165(x3442)) % 168.22/168.07 [345]~E(x3451,x3452)+E(f480(x3451),f480(x3452)) % 168.22/168.07 [346]~E(x3461,x3462)+E(f360(x3461,x3463,x3464),f360(x3462,x3463,x3464)) % 168.22/168.07 [347]~E(x3471,x3472)+E(f360(x3473,x3471,x3474),f360(x3473,x3472,x3474)) % 168.22/168.07 [348]~E(x3481,x3482)+E(f360(x3483,x3484,x3481),f360(x3483,x3484,x3482)) % 168.22/168.07 [349]~E(x3491,x3492)+E(f364(x3491),f364(x3492)) % 168.22/168.07 [350]~E(x3501,x3502)+E(f246(x3501,x3503),f246(x3502,x3503)) % 168.22/168.07 [351]~E(x3511,x3512)+E(f246(x3513,x3511),f246(x3513,x3512)) % 168.22/168.07 [352]~E(x3521,x3522)+E(f402(x3521,x3523,x3524),f402(x3522,x3523,x3524)) % 168.22/168.07 [353]~E(x3531,x3532)+E(f402(x3533,x3531,x3534),f402(x3533,x3532,x3534)) % 168.22/168.07 [354]~E(x3541,x3542)+E(f402(x3543,x3544,x3541),f402(x3543,x3544,x3542)) % 168.22/168.07 [355]~E(x3551,x3552)+E(f86(x3551,x3553,x3554,x3555),f86(x3552,x3553,x3554,x3555)) % 168.22/168.07 [356]~E(x3561,x3562)+E(f86(x3563,x3561,x3564,x3565),f86(x3563,x3562,x3564,x3565)) % 168.22/168.07 [357]~E(x3571,x3572)+E(f86(x3573,x3574,x3571,x3575),f86(x3573,x3574,x3572,x3575)) % 168.22/168.07 [358]~E(x3581,x3582)+E(f86(x3583,x3584,x3585,x3581),f86(x3583,x3584,x3585,x3582)) % 168.22/168.07 [359]~E(x3591,x3592)+E(f736(x3591,x3593,x3594,x3595),f736(x3592,x3593,x3594,x3595)) % 168.22/168.07 [360]~E(x3601,x3602)+E(f736(x3603,x3601,x3604,x3605),f736(x3603,x3602,x3604,x3605)) % 168.22/168.07 [361]~E(x3611,x3612)+E(f736(x3613,x3614,x3611,x3615),f736(x3613,x3614,x3612,x3615)) % 168.22/168.07 [362]~E(x3621,x3622)+E(f736(x3623,x3624,x3625,x3621),f736(x3623,x3624,x3625,x3622)) % 168.22/168.07 [363]~E(x3631,x3632)+E(f626(x3631,x3633,x3634,x3635,x3636),f626(x3632,x3633,x3634,x3635,x3636)) % 168.22/168.07 [364]~E(x3641,x3642)+E(f626(x3643,x3641,x3644,x3645,x3646),f626(x3643,x3642,x3644,x3645,x3646)) % 168.22/168.07 [365]~E(x3651,x3652)+E(f626(x3653,x3654,x3651,x3655,x3656),f626(x3653,x3654,x3652,x3655,x3656)) % 168.22/168.07 [366]~E(x3661,x3662)+E(f626(x3663,x3664,x3665,x3661,x3666),f626(x3663,x3664,x3665,x3662,x3666)) % 168.22/168.07 [367]~E(x3671,x3672)+E(f626(x3673,x3674,x3675,x3676,x3671),f626(x3673,x3674,x3675,x3676,x3672)) % 168.22/168.07 [368]~E(x3681,x3682)+E(f10(x3681,x3683),f10(x3682,x3683)) % 168.22/168.07 [369]~E(x3691,x3692)+E(f10(x3693,x3691),f10(x3693,x3692)) % 168.22/168.07 [370]~E(x3701,x3702)+E(f180(x3701,x3703,x3704,x3705,x3706),f180(x3702,x3703,x3704,x3705,x3706)) % 168.22/168.07 [371]~E(x3711,x3712)+E(f180(x3713,x3711,x3714,x3715,x3716),f180(x3713,x3712,x3714,x3715,x3716)) % 168.22/168.07 [372]~E(x3721,x3722)+E(f180(x3723,x3724,x3721,x3725,x3726),f180(x3723,x3724,x3722,x3725,x3726)) % 168.22/168.07 [373]~E(x3731,x3732)+E(f180(x3733,x3734,x3735,x3731,x3736),f180(x3733,x3734,x3735,x3732,x3736)) % 168.22/168.07 [374]~E(x3741,x3742)+E(f180(x3743,x3744,x3745,x3746,x3741),f180(x3743,x3744,x3745,x3746,x3742)) % 168.22/168.07 [375]~E(x3751,x3752)+E(f533(x3751,x3753,x3754),f533(x3752,x3753,x3754)) % 168.22/168.07 [376]~E(x3761,x3762)+E(f533(x3763,x3761,x3764),f533(x3763,x3762,x3764)) % 168.22/168.07 [377]~E(x3771,x3772)+E(f533(x3773,x3774,x3771),f533(x3773,x3774,x3772)) % 168.22/168.07 [378]~E(x3781,x3782)+E(f30(x3781,x3783),f30(x3782,x3783)) % 168.22/168.07 [379]~E(x3791,x3792)+E(f30(x3793,x3791),f30(x3793,x3792)) % 168.22/168.07 [380]~E(x3801,x3802)+E(f255(x3801,x3803),f255(x3802,x3803)) % 168.22/168.07 [381]~E(x3811,x3812)+E(f255(x3813,x3811),f255(x3813,x3812)) % 168.22/168.07 [382]~E(x3821,x3822)+E(f264(x3821,x3823),f264(x3822,x3823)) % 168.22/168.07 [383]~E(x3831,x3832)+E(f264(x3833,x3831),f264(x3833,x3832)) % 168.22/168.07 [384]~E(x3841,x3842)+E(f333(x3841,x3843,x3844),f333(x3842,x3843,x3844)) % 168.22/168.07 [385]~E(x3851,x3852)+E(f333(x3853,x3851,x3854),f333(x3853,x3852,x3854)) % 168.22/168.07 [386]~E(x3861,x3862)+E(f333(x3863,x3864,x3861),f333(x3863,x3864,x3862)) % 168.22/168.07 [387]~E(x3871,x3872)+E(f32(x3871,x3873,x3874),f32(x3872,x3873,x3874)) % 168.22/168.07 [388]~E(x3881,x3882)+E(f32(x3883,x3881,x3884),f32(x3883,x3882,x3884)) % 168.22/168.07 [389]~E(x3891,x3892)+E(f32(x3893,x3894,x3891),f32(x3893,x3894,x3892)) % 168.22/168.07 [390]~E(x3901,x3902)+E(f151(x3901,x3903),f151(x3902,x3903)) % 168.22/168.07 [391]~E(x3911,x3912)+E(f151(x3913,x3911),f151(x3913,x3912)) % 168.22/168.07 [392]~E(x3921,x3922)+E(f263(x3921,x3923),f263(x3922,x3923)) % 168.22/168.07 [393]~E(x3931,x3932)+E(f263(x3933,x3931),f263(x3933,x3932)) % 168.22/168.07 [394]~E(x3941,x3942)+E(f142(x3941,x3943,x3944,x3945),f142(x3942,x3943,x3944,x3945)) % 168.22/168.07 [395]~E(x3951,x3952)+E(f142(x3953,x3951,x3954,x3955),f142(x3953,x3952,x3954,x3955)) % 168.22/168.07 [396]~E(x3961,x3962)+E(f142(x3963,x3964,x3961,x3965),f142(x3963,x3964,x3962,x3965)) % 168.22/168.07 [397]~E(x3971,x3972)+E(f142(x3973,x3974,x3975,x3971),f142(x3973,x3974,x3975,x3972)) % 168.22/168.07 [398]~E(x3981,x3982)+E(f309(x3981,x3983),f309(x3982,x3983)) % 168.22/168.07 [399]~E(x3991,x3992)+E(f309(x3993,x3991),f309(x3993,x3992)) % 168.22/168.07 [400]~E(x4001,x4002)+E(f59(x4001,x4003),f59(x4002,x4003)) % 168.22/168.07 [401]~E(x4011,x4012)+E(f59(x4013,x4011),f59(x4013,x4012)) % 168.22/168.07 [402]~E(x4021,x4022)+E(f589(x4021,x4023,x4024,x4025,x4026),f589(x4022,x4023,x4024,x4025,x4026)) % 168.22/168.07 [403]~E(x4031,x4032)+E(f589(x4033,x4031,x4034,x4035,x4036),f589(x4033,x4032,x4034,x4035,x4036)) % 168.22/168.07 [404]~E(x4041,x4042)+E(f589(x4043,x4044,x4041,x4045,x4046),f589(x4043,x4044,x4042,x4045,x4046)) % 168.22/168.07 [405]~E(x4051,x4052)+E(f589(x4053,x4054,x4055,x4051,x4056),f589(x4053,x4054,x4055,x4052,x4056)) % 168.22/168.07 [406]~E(x4061,x4062)+E(f589(x4063,x4064,x4065,x4066,x4061),f589(x4063,x4064,x4065,x4066,x4062)) % 168.22/168.07 [407]~E(x4071,x4072)+E(f153(x4071,x4073),f153(x4072,x4073)) % 168.22/168.07 [408]~E(x4081,x4082)+E(f153(x4083,x4081),f153(x4083,x4082)) % 168.22/168.07 [409]~E(x4091,x4092)+E(f436(x4091,x4093),f436(x4092,x4093)) % 168.22/168.07 [410]~E(x4101,x4102)+E(f436(x4103,x4101),f436(x4103,x4102)) % 168.22/168.07 [411]~E(x4111,x4112)+E(f642(x4111,x4113,x4114,x4115,x4116),f642(x4112,x4113,x4114,x4115,x4116)) % 168.22/168.07 [412]~E(x4121,x4122)+E(f642(x4123,x4121,x4124,x4125,x4126),f642(x4123,x4122,x4124,x4125,x4126)) % 168.22/168.07 [413]~E(x4131,x4132)+E(f642(x4133,x4134,x4131,x4135,x4136),f642(x4133,x4134,x4132,x4135,x4136)) % 168.22/168.07 [414]~E(x4141,x4142)+E(f642(x4143,x4144,x4145,x4141,x4146),f642(x4143,x4144,x4145,x4142,x4146)) % 168.22/168.07 [415]~E(x4151,x4152)+E(f642(x4153,x4154,x4155,x4156,x4151),f642(x4153,x4154,x4155,x4156,x4152)) % 168.22/168.07 [416]~E(x4161,x4162)+E(f615(x4161,x4163,x4164,x4165),f615(x4162,x4163,x4164,x4165)) % 168.22/168.07 [417]~E(x4171,x4172)+E(f615(x4173,x4171,x4174,x4175),f615(x4173,x4172,x4174,x4175)) % 168.22/168.07 [418]~E(x4181,x4182)+E(f615(x4183,x4184,x4181,x4185),f615(x4183,x4184,x4182,x4185)) % 168.22/168.07 [419]~E(x4191,x4192)+E(f615(x4193,x4194,x4195,x4191),f615(x4193,x4194,x4195,x4192)) % 168.22/168.07 [420]~E(x4201,x4202)+E(f416(x4201,x4203,x4204,x4205),f416(x4202,x4203,x4204,x4205)) % 168.22/168.07 [421]~E(x4211,x4212)+E(f416(x4213,x4211,x4214,x4215),f416(x4213,x4212,x4214,x4215)) % 168.22/168.07 [422]~E(x4221,x4222)+E(f416(x4223,x4224,x4221,x4225),f416(x4223,x4224,x4222,x4225)) % 168.22/168.07 [423]~E(x4231,x4232)+E(f416(x4233,x4234,x4235,x4231),f416(x4233,x4234,x4235,x4232)) % 168.22/168.07 [424]~E(x4241,x4242)+E(f652(x4241,x4243,x4244,x4245,x4246),f652(x4242,x4243,x4244,x4245,x4246)) % 168.22/168.07 [425]~E(x4251,x4252)+E(f652(x4253,x4251,x4254,x4255,x4256),f652(x4253,x4252,x4254,x4255,x4256)) % 168.22/168.07 [426]~E(x4261,x4262)+E(f652(x4263,x4264,x4261,x4265,x4266),f652(x4263,x4264,x4262,x4265,x4266)) % 168.22/168.07 [427]~E(x4271,x4272)+E(f652(x4273,x4274,x4275,x4271,x4276),f652(x4273,x4274,x4275,x4272,x4276)) % 168.22/168.07 [428]~E(x4281,x4282)+E(f652(x4283,x4284,x4285,x4286,x4281),f652(x4283,x4284,x4285,x4286,x4282)) % 168.22/168.07 [429]~E(x4291,x4292)+E(f36(x4291,x4293),f36(x4292,x4293)) % 168.22/168.07 [430]~E(x4301,x4302)+E(f36(x4303,x4301),f36(x4303,x4302)) % 168.22/168.07 [431]~E(x4311,x4312)+E(f178(x4311,x4313,x4314,x4315),f178(x4312,x4313,x4314,x4315)) % 168.22/168.07 [432]~E(x4321,x4322)+E(f178(x4323,x4321,x4324,x4325),f178(x4323,x4322,x4324,x4325)) % 168.22/168.07 [433]~E(x4331,x4332)+E(f178(x4333,x4334,x4331,x4335),f178(x4333,x4334,x4332,x4335)) % 168.22/168.07 [434]~E(x4341,x4342)+E(f178(x4343,x4344,x4345,x4341),f178(x4343,x4344,x4345,x4342)) % 168.22/168.07 [435]~E(x4351,x4352)+E(f754(x4351,x4353,x4354),f754(x4352,x4353,x4354)) % 168.22/168.07 [436]~E(x4361,x4362)+E(f754(x4363,x4361,x4364),f754(x4363,x4362,x4364)) % 168.22/168.07 [437]~E(x4371,x4372)+E(f754(x4373,x4374,x4371),f754(x4373,x4374,x4372)) % 168.22/168.07 [438]~E(x4381,x4382)+E(f288(x4381,x4383),f288(x4382,x4383)) % 168.22/168.07 [439]~E(x4391,x4392)+E(f288(x4393,x4391),f288(x4393,x4392)) % 168.22/168.07 [440]~E(x4401,x4402)+E(f272(x4401,x4403,x4404,x4405),f272(x4402,x4403,x4404,x4405)) % 168.22/168.07 [441]~E(x4411,x4412)+E(f272(x4413,x4411,x4414,x4415),f272(x4413,x4412,x4414,x4415)) % 168.22/168.07 [442]~E(x4421,x4422)+E(f272(x4423,x4424,x4421,x4425),f272(x4423,x4424,x4422,x4425)) % 168.22/168.07 [443]~E(x4431,x4432)+E(f272(x4433,x4434,x4435,x4431),f272(x4433,x4434,x4435,x4432)) % 168.22/168.07 [444]~E(x4441,x4442)+E(f182(x4441,x4443),f182(x4442,x4443)) % 168.22/168.07 [445]~E(x4451,x4452)+E(f182(x4453,x4451),f182(x4453,x4452)) % 168.22/168.07 [446]~E(x4461,x4462)+E(f11(x4461,x4463),f11(x4462,x4463)) % 168.22/168.07 [447]~E(x4471,x4472)+E(f11(x4473,x4471),f11(x4473,x4472)) % 168.22/168.07 [448]~E(x4481,x4482)+E(f700(x4481,x4483),f700(x4482,x4483)) % 168.22/168.07 [449]~E(x4491,x4492)+E(f700(x4493,x4491),f700(x4493,x4492)) % 168.22/168.07 [450]~E(x4501,x4502)+E(f775(x4501,x4503,x4504,x4505,x4506),f775(x4502,x4503,x4504,x4505,x4506)) % 168.22/168.07 [451]~E(x4511,x4512)+E(f775(x4513,x4511,x4514,x4515,x4516),f775(x4513,x4512,x4514,x4515,x4516)) % 168.22/168.07 [452]~E(x4521,x4522)+E(f775(x4523,x4524,x4521,x4525,x4526),f775(x4523,x4524,x4522,x4525,x4526)) % 168.22/168.07 [453]~E(x4531,x4532)+E(f775(x4533,x4534,x4535,x4531,x4536),f775(x4533,x4534,x4535,x4532,x4536)) % 168.22/168.07 [454]~E(x4541,x4542)+E(f775(x4543,x4544,x4545,x4546,x4541),f775(x4543,x4544,x4545,x4546,x4542)) % 168.22/168.07 [455]~E(x4551,x4552)+E(f738(x4551,x4553,x4554,x4555,x4556),f738(x4552,x4553,x4554,x4555,x4556)) % 168.22/168.07 [456]~E(x4561,x4562)+E(f738(x4563,x4561,x4564,x4565,x4566),f738(x4563,x4562,x4564,x4565,x4566)) % 168.22/168.07 [457]~E(x4571,x4572)+E(f738(x4573,x4574,x4571,x4575,x4576),f738(x4573,x4574,x4572,x4575,x4576)) % 168.22/168.07 [458]~E(x4581,x4582)+E(f738(x4583,x4584,x4585,x4581,x4586),f738(x4583,x4584,x4585,x4582,x4586)) % 168.22/168.07 [459]~E(x4591,x4592)+E(f738(x4593,x4594,x4595,x4596,x4591),f738(x4593,x4594,x4595,x4596,x4592)) % 168.22/168.07 [460]~E(x4601,x4602)+E(f99(x4601,x4603),f99(x4602,x4603)) % 168.22/168.07 [461]~E(x4611,x4612)+E(f99(x4613,x4611),f99(x4613,x4612)) % 168.22/168.07 [462]~E(x4621,x4622)+E(f172(x4621,x4623),f172(x4622,x4623)) % 168.22/168.07 [463]~E(x4631,x4632)+E(f172(x4633,x4631),f172(x4633,x4632)) % 168.22/168.07 [464]~E(x4641,x4642)+E(f147(x4641,x4643),f147(x4642,x4643)) % 168.22/168.07 [465]~E(x4651,x4652)+E(f147(x4653,x4651),f147(x4653,x4652)) % 168.22/168.07 [466]~E(x4661,x4662)+E(f422(x4661,x4663,x4664,x4665),f422(x4662,x4663,x4664,x4665)) % 168.22/168.07 [467]~E(x4671,x4672)+E(f422(x4673,x4671,x4674,x4675),f422(x4673,x4672,x4674,x4675)) % 168.22/168.07 [468]~E(x4681,x4682)+E(f422(x4683,x4684,x4681,x4685),f422(x4683,x4684,x4682,x4685)) % 168.22/168.07 [469]~E(x4691,x4692)+E(f422(x4693,x4694,x4695,x4691),f422(x4693,x4694,x4695,x4692)) % 168.22/168.07 [470]~E(x4701,x4702)+E(f15(x4701,x4703),f15(x4702,x4703)) % 168.22/168.07 [471]~E(x4711,x4712)+E(f15(x4713,x4711),f15(x4713,x4712)) % 168.22/168.07 [472]~E(x4721,x4722)+E(f606(x4721,x4723,x4724,x4725),f606(x4722,x4723,x4724,x4725)) % 168.22/168.07 [473]~E(x4731,x4732)+E(f606(x4733,x4731,x4734,x4735),f606(x4733,x4732,x4734,x4735)) % 168.22/168.07 [474]~E(x4741,x4742)+E(f606(x4743,x4744,x4741,x4745),f606(x4743,x4744,x4742,x4745)) % 168.22/168.07 [475]~E(x4751,x4752)+E(f606(x4753,x4754,x4755,x4751),f606(x4753,x4754,x4755,x4752)) % 168.22/168.07 [476]~E(x4761,x4762)+E(f620(x4761,x4763,x4764,x4765,x4766),f620(x4762,x4763,x4764,x4765,x4766)) % 168.22/168.07 [477]~E(x4771,x4772)+E(f620(x4773,x4771,x4774,x4775,x4776),f620(x4773,x4772,x4774,x4775,x4776)) % 168.22/168.07 [478]~E(x4781,x4782)+E(f620(x4783,x4784,x4781,x4785,x4786),f620(x4783,x4784,x4782,x4785,x4786)) % 168.22/168.07 [479]~E(x4791,x4792)+E(f620(x4793,x4794,x4795,x4791,x4796),f620(x4793,x4794,x4795,x4792,x4796)) % 168.22/168.07 [480]~E(x4801,x4802)+E(f620(x4803,x4804,x4805,x4806,x4801),f620(x4803,x4804,x4805,x4806,x4802)) % 168.22/168.07 [481]~E(x4811,x4812)+E(f522(x4811,x4813,x4814),f522(x4812,x4813,x4814)) % 168.22/168.07 [482]~E(x4821,x4822)+E(f522(x4823,x4821,x4824),f522(x4823,x4822,x4824)) % 168.22/168.07 [483]~E(x4831,x4832)+E(f522(x4833,x4834,x4831),f522(x4833,x4834,x4832)) % 168.22/168.07 [484]~E(x4841,x4842)+E(f297(x4841,x4843),f297(x4842,x4843)) % 168.22/168.07 [485]~E(x4851,x4852)+E(f297(x4853,x4851),f297(x4853,x4852)) % 168.22/168.07 [486]~E(x4861,x4862)+E(f787(x4861,x4863,x4864),f787(x4862,x4863,x4864)) % 168.22/168.07 [487]~E(x4871,x4872)+E(f787(x4873,x4871,x4874),f787(x4873,x4872,x4874)) % 168.22/168.07 [488]~E(x4881,x4882)+E(f787(x4883,x4884,x4881),f787(x4883,x4884,x4882)) % 168.22/168.07 [489]~E(x4891,x4892)+E(f154(x4891,x4893),f154(x4892,x4893)) % 168.22/168.07 [490]~E(x4901,x4902)+E(f154(x4903,x4901),f154(x4903,x4902)) % 168.22/168.07 [491]~E(x4911,x4912)+E(f58(x4911,x4913),f58(x4912,x4913)) % 168.22/168.07 [492]~E(x4921,x4922)+E(f58(x4923,x4921),f58(x4923,x4922)) % 168.22/168.07 [493]~E(x4931,x4932)+E(f50(x4931,x4933),f50(x4932,x4933)) % 168.22/168.07 [494]~E(x4941,x4942)+E(f50(x4943,x4941),f50(x4943,x4942)) % 168.22/168.07 [495]~E(x4951,x4952)+E(f53(x4951),f53(x4952)) % 168.22/168.07 [496]~E(x4961,x4962)+E(f160(x4961),f160(x4962)) % 168.22/168.07 [497]~E(x4971,x4972)+E(f129(x4971,x4973,x4974,x4975),f129(x4972,x4973,x4974,x4975)) % 168.22/168.07 [498]~E(x4981,x4982)+E(f129(x4983,x4981,x4984,x4985),f129(x4983,x4982,x4984,x4985)) % 168.22/168.07 [499]~E(x4991,x4992)+E(f129(x4993,x4994,x4991,x4995),f129(x4993,x4994,x4992,x4995)) % 168.22/168.07 [500]~E(x5001,x5002)+E(f129(x5003,x5004,x5005,x5001),f129(x5003,x5004,x5005,x5002)) % 168.22/168.07 [501]~E(x5011,x5012)+E(f136(x5011,x5013,x5014,x5015),f136(x5012,x5013,x5014,x5015)) % 168.22/168.07 [502]~E(x5021,x5022)+E(f136(x5023,x5021,x5024,x5025),f136(x5023,x5022,x5024,x5025)) % 168.22/168.07 [503]~E(x5031,x5032)+E(f136(x5033,x5034,x5031,x5035),f136(x5033,x5034,x5032,x5035)) % 168.22/168.07 [504]~E(x5041,x5042)+E(f136(x5043,x5044,x5045,x5041),f136(x5043,x5044,x5045,x5042)) % 168.22/168.07 [505]~E(x5051,x5052)+E(f220(x5051,x5053,x5054,x5055),f220(x5052,x5053,x5054,x5055)) % 168.22/168.07 [506]~E(x5061,x5062)+E(f220(x5063,x5061,x5064,x5065),f220(x5063,x5062,x5064,x5065)) % 168.22/168.07 [507]~E(x5071,x5072)+E(f220(x5073,x5074,x5071,x5075),f220(x5073,x5074,x5072,x5075)) % 168.22/168.07 [508]~E(x5081,x5082)+E(f220(x5083,x5084,x5085,x5081),f220(x5083,x5084,x5085,x5082)) % 168.22/168.07 [509]~E(x5091,x5092)+E(f181(x5091,x5093,x5094,x5095),f181(x5092,x5093,x5094,x5095)) % 168.22/168.07 [510]~E(x5101,x5102)+E(f181(x5103,x5101,x5104,x5105),f181(x5103,x5102,x5104,x5105)) % 168.22/168.07 [511]~E(x5111,x5112)+E(f181(x5113,x5114,x5111,x5115),f181(x5113,x5114,x5112,x5115)) % 168.22/168.07 [512]~E(x5121,x5122)+E(f181(x5123,x5124,x5125,x5121),f181(x5123,x5124,x5125,x5122)) % 168.22/168.07 [513]~E(x5131,x5132)+E(f74(x5131,x5133,x5134),f74(x5132,x5133,x5134)) % 168.22/168.07 [514]~E(x5141,x5142)+E(f74(x5143,x5141,x5144),f74(x5143,x5142,x5144)) % 168.22/168.07 [515]~E(x5151,x5152)+E(f74(x5153,x5154,x5151),f74(x5153,x5154,x5152)) % 168.22/168.07 [516]~E(x5161,x5162)+E(f714(x5161,x5163,x5164,x5165,x5166,x5167),f714(x5162,x5163,x5164,x5165,x5166,x5167)) % 168.22/168.07 [517]~E(x5171,x5172)+E(f714(x5173,x5171,x5174,x5175,x5176,x5177),f714(x5173,x5172,x5174,x5175,x5176,x5177)) % 168.22/168.07 [518]~E(x5181,x5182)+E(f714(x5183,x5184,x5181,x5185,x5186,x5187),f714(x5183,x5184,x5182,x5185,x5186,x5187)) % 168.22/168.07 [519]~E(x5191,x5192)+E(f714(x5193,x5194,x5195,x5191,x5196,x5197),f714(x5193,x5194,x5195,x5192,x5196,x5197)) % 168.22/168.07 [520]~E(x5201,x5202)+E(f714(x5203,x5204,x5205,x5206,x5201,x5207),f714(x5203,x5204,x5205,x5206,x5202,x5207)) % 168.22/168.07 [521]~E(x5211,x5212)+E(f714(x5213,x5214,x5215,x5216,x5217,x5211),f714(x5213,x5214,x5215,x5216,x5217,x5212)) % 168.22/168.07 [522]~E(x5221,x5222)+E(f33(x5221,x5223,x5224),f33(x5222,x5223,x5224)) % 168.22/168.07 [523]~E(x5231,x5232)+E(f33(x5233,x5231,x5234),f33(x5233,x5232,x5234)) % 168.22/168.07 [524]~E(x5241,x5242)+E(f33(x5243,x5244,x5241),f33(x5243,x5244,x5242)) % 168.22/168.07 [525]~E(x5251,x5252)+E(f179(x5251,x5253,x5254),f179(x5252,x5253,x5254)) % 168.22/168.07 [526]~E(x5261,x5262)+E(f179(x5263,x5261,x5264),f179(x5263,x5262,x5264)) % 168.22/168.07 [527]~E(x5271,x5272)+E(f179(x5273,x5274,x5271),f179(x5273,x5274,x5272)) % 168.22/168.07 [528]~E(x5281,x5282)+E(f183(x5281,x5283,x5284),f183(x5282,x5283,x5284)) % 168.22/168.07 [529]~E(x5291,x5292)+E(f183(x5293,x5291,x5294),f183(x5293,x5292,x5294)) % 168.22/168.07 [530]~E(x5301,x5302)+E(f183(x5303,x5304,x5301),f183(x5303,x5304,x5302)) % 168.22/168.07 [531]~E(x5311,x5312)+E(f68(x5311),f68(x5312)) % 168.22/168.07 [532]~E(x5321,x5322)+E(f282(x5321,x5323,x5324),f282(x5322,x5323,x5324)) % 168.22/168.07 [533]~E(x5331,x5332)+E(f282(x5333,x5331,x5334),f282(x5333,x5332,x5334)) % 168.22/168.07 [534]~E(x5341,x5342)+E(f282(x5343,x5344,x5341),f282(x5343,x5344,x5342)) % 168.22/168.07 [535]~E(x5351,x5352)+E(f103(x5351,x5353,x5354),f103(x5352,x5353,x5354)) % 168.22/168.07 [536]~E(x5361,x5362)+E(f103(x5363,x5361,x5364),f103(x5363,x5362,x5364)) % 168.22/168.07 [537]~E(x5371,x5372)+E(f103(x5373,x5374,x5371),f103(x5373,x5374,x5372)) % 168.22/168.07 [538]~E(x5381,x5382)+E(f242(x5381,x5383,x5384),f242(x5382,x5383,x5384)) % 168.22/168.07 [539]~E(x5391,x5392)+E(f242(x5393,x5391,x5394),f242(x5393,x5392,x5394)) % 168.22/168.07 [540]~E(x5401,x5402)+E(f242(x5403,x5404,x5401),f242(x5403,x5404,x5402)) % 168.22/168.07 [541]~E(x5411,x5412)+E(f767(x5411,x5413,x5414),f767(x5412,x5413,x5414)) % 168.22/168.07 [542]~E(x5421,x5422)+E(f767(x5423,x5421,x5424),f767(x5423,x5422,x5424)) % 168.22/168.07 [543]~E(x5431,x5432)+E(f767(x5433,x5434,x5431),f767(x5433,x5434,x5432)) % 168.22/168.07 [544]~E(x5441,x5442)+E(f583(x5441,x5443,x5444,x5445,x5446),f583(x5442,x5443,x5444,x5445,x5446)) % 168.22/168.07 [545]~E(x5451,x5452)+E(f583(x5453,x5451,x5454,x5455,x5456),f583(x5453,x5452,x5454,x5455,x5456)) % 168.22/168.07 [546]~E(x5461,x5462)+E(f583(x5463,x5464,x5461,x5465,x5466),f583(x5463,x5464,x5462,x5465,x5466)) % 168.22/168.07 [547]~E(x5471,x5472)+E(f583(x5473,x5474,x5475,x5471,x5476),f583(x5473,x5474,x5475,x5472,x5476)) % 168.22/168.07 [548]~E(x5481,x5482)+E(f583(x5483,x5484,x5485,x5486,x5481),f583(x5483,x5484,x5485,x5486,x5482)) % 168.22/168.07 [549]~E(x5491,x5492)+E(f104(x5491,x5493,x5494,x5495),f104(x5492,x5493,x5494,x5495)) % 168.22/168.07 [550]~E(x5501,x5502)+E(f104(x5503,x5501,x5504,x5505),f104(x5503,x5502,x5504,x5505)) % 168.22/168.07 [551]~E(x5511,x5512)+E(f104(x5513,x5514,x5511,x5515),f104(x5513,x5514,x5512,x5515)) % 168.22/168.07 [552]~E(x5521,x5522)+E(f104(x5523,x5524,x5525,x5521),f104(x5523,x5524,x5525,x5522)) % 168.22/168.07 [553]~E(x5531,x5532)+E(f75(x5531,x5533,x5534),f75(x5532,x5533,x5534)) % 168.22/168.07 [554]~E(x5541,x5542)+E(f75(x5543,x5541,x5544),f75(x5543,x5542,x5544)) % 168.22/168.07 [555]~E(x5551,x5552)+E(f75(x5553,x5554,x5551),f75(x5553,x5554,x5552)) % 168.22/168.07 [556]~E(x5561,x5562)+E(f532(x5561,x5563,x5564),f532(x5562,x5563,x5564)) % 168.22/168.07 [557]~E(x5571,x5572)+E(f532(x5573,x5571,x5574),f532(x5573,x5572,x5574)) % 168.22/168.07 [558]~E(x5581,x5582)+E(f532(x5583,x5584,x5581),f532(x5583,x5584,x5582)) % 168.22/168.07 [559]~E(x5591,x5592)+E(f637(x5591,x5593,x5594,x5595,x5596),f637(x5592,x5593,x5594,x5595,x5596)) % 168.22/168.07 [560]~E(x5601,x5602)+E(f637(x5603,x5601,x5604,x5605,x5606),f637(x5603,x5602,x5604,x5605,x5606)) % 168.22/168.07 [561]~E(x5611,x5612)+E(f637(x5613,x5614,x5611,x5615,x5616),f637(x5613,x5614,x5612,x5615,x5616)) % 168.22/168.07 [562]~E(x5621,x5622)+E(f637(x5623,x5624,x5625,x5621,x5626),f637(x5623,x5624,x5625,x5622,x5626)) % 168.22/168.07 [563]~E(x5631,x5632)+E(f637(x5633,x5634,x5635,x5636,x5631),f637(x5633,x5634,x5635,x5636,x5632)) % 168.22/168.07 [564]~E(x5641,x5642)+E(f91(x5641,x5643),f91(x5642,x5643)) % 168.22/168.07 [565]~E(x5651,x5652)+E(f91(x5653,x5651),f91(x5653,x5652)) % 168.22/168.07 [566]~E(x5661,x5662)+E(f198(x5661,x5663),f198(x5662,x5663)) % 168.22/168.07 [567]~E(x5671,x5672)+E(f198(x5673,x5671),f198(x5673,x5672)) % 168.22/168.07 [568]~E(x5681,x5682)+E(f283(x5681),f283(x5682)) % 168.22/168.07 [569]~E(x5691,x5692)+E(f553(x5691,x5693,x5694,x5695,x5696,x5697),f553(x5692,x5693,x5694,x5695,x5696,x5697)) % 168.22/168.07 [570]~E(x5701,x5702)+E(f553(x5703,x5701,x5704,x5705,x5706,x5707),f553(x5703,x5702,x5704,x5705,x5706,x5707)) % 168.22/168.07 [571]~E(x5711,x5712)+E(f553(x5713,x5714,x5711,x5715,x5716,x5717),f553(x5713,x5714,x5712,x5715,x5716,x5717)) % 168.22/168.07 [572]~E(x5721,x5722)+E(f553(x5723,x5724,x5725,x5721,x5726,x5727),f553(x5723,x5724,x5725,x5722,x5726,x5727)) % 168.22/168.07 [573]~E(x5731,x5732)+E(f553(x5733,x5734,x5735,x5736,x5731,x5737),f553(x5733,x5734,x5735,x5736,x5732,x5737)) % 168.22/168.07 [574]~E(x5741,x5742)+E(f553(x5743,x5744,x5745,x5746,x5747,x5741),f553(x5743,x5744,x5745,x5746,x5747,x5742)) % 168.22/168.07 [575]~E(x5751,x5752)+E(f537(x5751,x5753,x5754,x5755,x5756,x5757,x5758,x5759),f537(x5752,x5753,x5754,x5755,x5756,x5757,x5758,x5759)) % 168.22/168.07 [576]~E(x5761,x5762)+E(f537(x5763,x5761,x5764,x5765,x5766,x5767,x5768,x5769),f537(x5763,x5762,x5764,x5765,x5766,x5767,x5768,x5769)) % 168.22/168.07 [577]~E(x5771,x5772)+E(f537(x5773,x5774,x5771,x5775,x5776,x5777,x5778,x5779),f537(x5773,x5774,x5772,x5775,x5776,x5777,x5778,x5779)) % 168.22/168.07 [578]~E(x5781,x5782)+E(f537(x5783,x5784,x5785,x5781,x5786,x5787,x5788,x5789),f537(x5783,x5784,x5785,x5782,x5786,x5787,x5788,x5789)) % 168.22/168.07 [579]~E(x5791,x5792)+E(f537(x5793,x5794,x5795,x5796,x5791,x5797,x5798,x5799),f537(x5793,x5794,x5795,x5796,x5792,x5797,x5798,x5799)) % 168.22/168.07 [580]~E(x5801,x5802)+E(f537(x5803,x5804,x5805,x5806,x5807,x5801,x5808,x5809),f537(x5803,x5804,x5805,x5806,x5807,x5802,x5808,x5809)) % 168.22/168.07 [581]~E(x5811,x5812)+E(f537(x5813,x5814,x5815,x5816,x5817,x5818,x5811,x5819),f537(x5813,x5814,x5815,x5816,x5817,x5818,x5812,x5819)) % 168.22/168.07 [582]~E(x5821,x5822)+E(f537(x5823,x5824,x5825,x5826,x5827,x5828,x5829,x5821),f537(x5823,x5824,x5825,x5826,x5827,x5828,x5829,x5822)) % 168.22/168.07 [583]~E(x5831,x5832)+E(f64(x5831,x5833,x5834),f64(x5832,x5833,x5834)) % 168.22/168.07 [584]~E(x5841,x5842)+E(f64(x5843,x5841,x5844),f64(x5843,x5842,x5844)) % 168.22/168.07 [585]~E(x5851,x5852)+E(f64(x5853,x5854,x5851),f64(x5853,x5854,x5852)) % 168.22/168.07 [586]~E(x5861,x5862)+E(f464(x5861,x5863,x5864,x5865,x5866),f464(x5862,x5863,x5864,x5865,x5866)) % 168.22/168.07 [587]~E(x5871,x5872)+E(f464(x5873,x5871,x5874,x5875,x5876),f464(x5873,x5872,x5874,x5875,x5876)) % 168.22/168.07 [588]~E(x5881,x5882)+E(f464(x5883,x5884,x5881,x5885,x5886),f464(x5883,x5884,x5882,x5885,x5886)) % 168.22/168.07 [589]~E(x5891,x5892)+E(f464(x5893,x5894,x5895,x5891,x5896),f464(x5893,x5894,x5895,x5892,x5896)) % 168.22/168.07 [590]~E(x5901,x5902)+E(f464(x5903,x5904,x5905,x5906,x5901),f464(x5903,x5904,x5905,x5906,x5902)) % 168.22/168.07 [591]~E(x5911,x5912)+E(f557(x5911,x5913),f557(x5912,x5913)) % 168.22/168.07 [592]~E(x5921,x5922)+E(f557(x5923,x5921),f557(x5923,x5922)) % 168.22/168.07 [593]~E(x5931,x5932)+E(f247(x5931,x5933,x5934),f247(x5932,x5933,x5934)) % 168.22/168.07 [594]~E(x5941,x5942)+E(f247(x5943,x5941,x5944),f247(x5943,x5942,x5944)) % 168.22/168.07 [595]~E(x5951,x5952)+E(f247(x5953,x5954,x5951),f247(x5953,x5954,x5952)) % 168.22/168.07 [596]~E(x5961,x5962)+E(f231(x5961),f231(x5962)) % 168.22/168.07 [597]~E(x5971,x5972)+E(f205(x5971),f205(x5972)) % 168.22/168.07 [598]~E(x5981,x5982)+E(f833(x5981,x5983,x5984,x5985),f833(x5982,x5983,x5984,x5985)) % 168.22/168.07 [599]~E(x5991,x5992)+E(f833(x5993,x5991,x5994,x5995),f833(x5993,x5992,x5994,x5995)) % 168.22/168.07 [600]~E(x6001,x6002)+E(f833(x6003,x6004,x6001,x6005),f833(x6003,x6004,x6002,x6005)) % 168.22/168.07 [601]~E(x6011,x6012)+E(f833(x6013,x6014,x6015,x6011),f833(x6013,x6014,x6015,x6012)) % 168.22/168.07 [602]~E(x6021,x6022)+E(f135(x6021),f135(x6022)) % 168.22/168.07 [603]~E(x6031,x6032)+E(f130(x6031,x6033),f130(x6032,x6033)) % 168.22/168.07 [604]~E(x6041,x6042)+E(f130(x6043,x6041),f130(x6043,x6042)) % 168.22/168.07 [605]~E(x6051,x6052)+E(f426(x6051,x6053,x6054),f426(x6052,x6053,x6054)) % 168.22/168.07 [606]~E(x6061,x6062)+E(f426(x6063,x6061,x6064),f426(x6063,x6062,x6064)) % 168.22/168.07 [607]~E(x6071,x6072)+E(f426(x6073,x6074,x6071),f426(x6073,x6074,x6072)) % 168.22/168.07 [608]~E(x6081,x6082)+E(f737(x6081,x6083,x6084,x6085),f737(x6082,x6083,x6084,x6085)) % 168.22/168.07 [609]~E(x6091,x6092)+E(f737(x6093,x6091,x6094,x6095),f737(x6093,x6092,x6094,x6095)) % 168.22/168.07 [610]~E(x6101,x6102)+E(f737(x6103,x6104,x6101,x6105),f737(x6103,x6104,x6102,x6105)) % 168.22/168.07 [611]~E(x6111,x6112)+E(f737(x6113,x6114,x6115,x6111),f737(x6113,x6114,x6115,x6112)) % 168.22/168.07 [612]~E(x6121,x6122)+E(f396(x6121,x6123,x6124,x6125,x6126),f396(x6122,x6123,x6124,x6125,x6126)) % 168.22/168.07 [613]~E(x6131,x6132)+E(f396(x6133,x6131,x6134,x6135,x6136),f396(x6133,x6132,x6134,x6135,x6136)) % 168.22/168.07 [614]~E(x6141,x6142)+E(f396(x6143,x6144,x6141,x6145,x6146),f396(x6143,x6144,x6142,x6145,x6146)) % 168.22/168.07 [615]~E(x6151,x6152)+E(f396(x6153,x6154,x6155,x6151,x6156),f396(x6153,x6154,x6155,x6152,x6156)) % 168.22/168.07 [616]~E(x6161,x6162)+E(f396(x6163,x6164,x6165,x6166,x6161),f396(x6163,x6164,x6165,x6166,x6162)) % 168.22/168.07 [617]~E(x6171,x6172)+E(f471(x6171,x6173,x6174),f471(x6172,x6173,x6174)) % 168.22/168.07 [618]~E(x6181,x6182)+E(f471(x6183,x6181,x6184),f471(x6183,x6182,x6184)) % 168.22/168.07 [619]~E(x6191,x6192)+E(f471(x6193,x6194,x6191),f471(x6193,x6194,x6192)) % 168.22/168.07 [620]~E(x6201,x6202)+E(f815(x6201,x6203,x6204,x6205),f815(x6202,x6203,x6204,x6205)) % 168.22/168.07 [621]~E(x6211,x6212)+E(f815(x6213,x6211,x6214,x6215),f815(x6213,x6212,x6214,x6215)) % 168.22/168.07 [622]~E(x6221,x6222)+E(f815(x6223,x6224,x6221,x6225),f815(x6223,x6224,x6222,x6225)) % 168.22/168.07 [623]~E(x6231,x6232)+E(f815(x6233,x6234,x6235,x6231),f815(x6233,x6234,x6235,x6232)) % 168.22/168.07 [624]~E(x6241,x6242)+E(f56(x6241,x6243),f56(x6242,x6243)) % 168.22/168.07 [625]~E(x6251,x6252)+E(f56(x6253,x6251),f56(x6253,x6252)) % 168.22/168.07 [626]~E(x6261,x6262)+E(f141(x6261,x6263),f141(x6262,x6263)) % 168.22/168.07 [627]~E(x6271,x6272)+E(f141(x6273,x6271),f141(x6273,x6272)) % 168.22/168.07 [628]~E(x6281,x6282)+E(f832(x6281,x6283,x6284,x6285),f832(x6282,x6283,x6284,x6285)) % 168.22/168.07 [629]~E(x6291,x6292)+E(f832(x6293,x6291,x6294,x6295),f832(x6293,x6292,x6294,x6295)) % 168.22/168.07 [630]~E(x6301,x6302)+E(f832(x6303,x6304,x6301,x6305),f832(x6303,x6304,x6302,x6305)) % 168.22/168.07 [631]~E(x6311,x6312)+E(f832(x6313,x6314,x6315,x6311),f832(x6313,x6314,x6315,x6312)) % 168.22/168.07 [632]~E(x6321,x6322)+E(f632(x6321,x6323,x6324),f632(x6322,x6323,x6324)) % 168.22/168.07 [633]~E(x6331,x6332)+E(f632(x6333,x6331,x6334),f632(x6333,x6332,x6334)) % 168.22/168.07 [634]~E(x6341,x6342)+E(f632(x6343,x6344,x6341),f632(x6343,x6344,x6342)) % 168.22/168.07 [635]~E(x6351,x6352)+E(f625(x6351,x6353,x6354,x6355),f625(x6352,x6353,x6354,x6355)) % 168.22/168.07 [636]~E(x6361,x6362)+E(f625(x6363,x6361,x6364,x6365),f625(x6363,x6362,x6364,x6365)) % 168.22/168.07 [637]~E(x6371,x6372)+E(f625(x6373,x6374,x6371,x6375),f625(x6373,x6374,x6372,x6375)) % 168.22/168.07 [638]~E(x6381,x6382)+E(f625(x6383,x6384,x6385,x6381),f625(x6383,x6384,x6385,x6382)) % 168.22/168.07 [639]~E(x6391,x6392)+E(f95(x6391,x6393),f95(x6392,x6393)) % 168.22/168.07 [640]~E(x6401,x6402)+E(f95(x6403,x6401),f95(x6403,x6402)) % 168.22/168.07 [641]~E(x6411,x6412)+E(f829(x6411,x6413,x6414),f829(x6412,x6413,x6414)) % 168.22/168.07 [642]~E(x6421,x6422)+E(f829(x6423,x6421,x6424),f829(x6423,x6422,x6424)) % 168.22/168.07 [643]~E(x6431,x6432)+E(f829(x6433,x6434,x6431),f829(x6433,x6434,x6432)) % 168.22/168.07 [644]~E(x6441,x6442)+E(f633(x6441,x6443,x6444,x6445),f633(x6442,x6443,x6444,x6445)) % 168.22/168.07 [645]~E(x6451,x6452)+E(f633(x6453,x6451,x6454,x6455),f633(x6453,x6452,x6454,x6455)) % 168.22/168.07 [646]~E(x6461,x6462)+E(f633(x6463,x6464,x6461,x6465),f633(x6463,x6464,x6462,x6465)) % 168.22/168.07 [647]~E(x6471,x6472)+E(f633(x6473,x6474,x6475,x6471),f633(x6473,x6474,x6475,x6472)) % 168.22/168.07 [648]~E(x6481,x6482)+E(f558(x6481,x6483),f558(x6482,x6483)) % 168.22/168.07 [649]~E(x6491,x6492)+E(f558(x6493,x6491),f558(x6493,x6492)) % 168.22/168.07 [650]~E(x6501,x6502)+E(f216(x6501,x6503,x6504,x6505),f216(x6502,x6503,x6504,x6505)) % 168.22/168.07 [651]~E(x6511,x6512)+E(f216(x6513,x6511,x6514,x6515),f216(x6513,x6512,x6514,x6515)) % 168.22/168.07 [652]~E(x6521,x6522)+E(f216(x6523,x6524,x6521,x6525),f216(x6523,x6524,x6522,x6525)) % 168.22/168.07 [653]~E(x6531,x6532)+E(f216(x6533,x6534,x6535,x6531),f216(x6533,x6534,x6535,x6532)) % 168.22/168.07 [654]~E(x6541,x6542)+E(f407(x6541,x6543,x6544),f407(x6542,x6543,x6544)) % 168.22/168.07 [655]~E(x6551,x6552)+E(f407(x6553,x6551,x6554),f407(x6553,x6552,x6554)) % 168.22/168.07 [656]~E(x6561,x6562)+E(f407(x6563,x6564,x6561),f407(x6563,x6564,x6562)) % 168.22/168.07 [657]~E(x6571,x6572)+E(f106(x6571,x6573,x6574,x6575),f106(x6572,x6573,x6574,x6575)) % 168.22/168.07 [658]~E(x6581,x6582)+E(f106(x6583,x6581,x6584,x6585),f106(x6583,x6582,x6584,x6585)) % 168.22/168.07 [659]~E(x6591,x6592)+E(f106(x6593,x6594,x6591,x6595),f106(x6593,x6594,x6592,x6595)) % 168.22/168.07 [660]~E(x6601,x6602)+E(f106(x6603,x6604,x6605,x6601),f106(x6603,x6604,x6605,x6602)) % 168.22/168.07 [661]~E(x6611,x6612)+E(f442(x6611,x6613,x6614,x6615),f442(x6612,x6613,x6614,x6615)) % 168.22/168.07 [662]~E(x6621,x6622)+E(f442(x6623,x6621,x6624,x6625),f442(x6623,x6622,x6624,x6625)) % 168.22/168.07 [663]~E(x6631,x6632)+E(f442(x6633,x6634,x6631,x6635),f442(x6633,x6634,x6632,x6635)) % 168.22/168.07 [664]~E(x6641,x6642)+E(f442(x6643,x6644,x6645,x6641),f442(x6643,x6644,x6645,x6642)) % 168.22/168.07 [665]~E(x6651,x6652)+E(f261(x6651),f261(x6652)) % 168.22/168.07 [666]~E(x6661,x6662)+E(f168(x6661,x6663,x6664),f168(x6662,x6663,x6664)) % 168.22/168.07 [667]~E(x6671,x6672)+E(f168(x6673,x6671,x6674),f168(x6673,x6672,x6674)) % 168.22/168.07 [668]~E(x6681,x6682)+E(f168(x6683,x6684,x6681),f168(x6683,x6684,x6682)) % 168.22/168.07 [669]~E(x6691,x6692)+E(f228(x6691,x6693),f228(x6692,x6693)) % 168.22/168.07 [670]~E(x6701,x6702)+E(f228(x6703,x6701),f228(x6703,x6702)) % 168.22/168.07 [671]~E(x6711,x6712)+E(f414(x6711,x6713),f414(x6712,x6713)) % 168.22/168.07 [672]~E(x6721,x6722)+E(f414(x6723,x6721),f414(x6723,x6722)) % 168.22/168.07 [673]~E(x6731,x6732)+E(f398(x6731,x6733,x6734),f398(x6732,x6733,x6734)) % 168.22/168.07 [674]~E(x6741,x6742)+E(f398(x6743,x6741,x6744),f398(x6743,x6742,x6744)) % 168.22/168.07 [675]~E(x6751,x6752)+E(f398(x6753,x6754,x6751),f398(x6753,x6754,x6752)) % 168.22/168.07 [676]~E(x6761,x6762)+E(f218(x6761,x6763),f218(x6762,x6763)) % 168.22/168.07 [677]~E(x6771,x6772)+E(f218(x6773,x6771),f218(x6773,x6772)) % 168.22/168.07 [678]~E(x6781,x6782)+E(f518(x6781),f518(x6782)) % 168.22/168.07 [679]~E(x6791,x6792)+E(f152(x6791,x6793),f152(x6792,x6793)) % 168.22/168.07 [680]~E(x6801,x6802)+E(f152(x6803,x6801),f152(x6803,x6802)) % 168.22/168.07 [681]~E(x6811,x6812)+E(f268(x6811,x6813),f268(x6812,x6813)) % 168.22/168.07 [682]~E(x6821,x6822)+E(f268(x6823,x6821),f268(x6823,x6822)) % 168.22/168.07 [683]~E(x6831,x6832)+E(f139(x6831,x6833),f139(x6832,x6833)) % 168.22/168.07 [684]~E(x6841,x6842)+E(f139(x6843,x6841),f139(x6843,x6842)) % 168.22/168.07 [685]~E(x6851,x6852)+E(f235(x6851,x6853),f235(x6852,x6853)) % 168.22/168.07 [686]~E(x6861,x6862)+E(f235(x6863,x6861),f235(x6863,x6862)) % 168.22/168.07 [687]~E(x6871,x6872)+E(f504(x6871,x6873,x6874,x6875,x6876,x6877,x6878),f504(x6872,x6873,x6874,x6875,x6876,x6877,x6878)) % 168.22/168.07 [688]~E(x6881,x6882)+E(f504(x6883,x6881,x6884,x6885,x6886,x6887,x6888),f504(x6883,x6882,x6884,x6885,x6886,x6887,x6888)) % 168.22/168.07 [689]~E(x6891,x6892)+E(f504(x6893,x6894,x6891,x6895,x6896,x6897,x6898),f504(x6893,x6894,x6892,x6895,x6896,x6897,x6898)) % 168.22/168.07 [690]~E(x6901,x6902)+E(f504(x6903,x6904,x6905,x6901,x6906,x6907,x6908),f504(x6903,x6904,x6905,x6902,x6906,x6907,x6908)) % 168.22/168.07 [691]~E(x6911,x6912)+E(f504(x6913,x6914,x6915,x6916,x6911,x6917,x6918),f504(x6913,x6914,x6915,x6916,x6912,x6917,x6918)) % 168.22/168.07 [692]~E(x6921,x6922)+E(f504(x6923,x6924,x6925,x6926,x6927,x6921,x6928),f504(x6923,x6924,x6925,x6926,x6927,x6922,x6928)) % 168.22/168.07 [693]~E(x6931,x6932)+E(f504(x6933,x6934,x6935,x6936,x6937,x6938,x6931),f504(x6933,x6934,x6935,x6936,x6937,x6938,x6932)) % 168.22/168.07 [694]~E(x6941,x6942)+E(f478(x6941,x6943,x6944,x6945,x6946,x6947),f478(x6942,x6943,x6944,x6945,x6946,x6947)) % 168.22/168.07 [695]~E(x6951,x6952)+E(f478(x6953,x6951,x6954,x6955,x6956,x6957),f478(x6953,x6952,x6954,x6955,x6956,x6957)) % 168.22/168.07 [696]~E(x6961,x6962)+E(f478(x6963,x6964,x6961,x6965,x6966,x6967),f478(x6963,x6964,x6962,x6965,x6966,x6967)) % 168.22/168.07 [697]~E(x6971,x6972)+E(f478(x6973,x6974,x6975,x6971,x6976,x6977),f478(x6973,x6974,x6975,x6972,x6976,x6977)) % 168.22/168.07 [698]~E(x6981,x6982)+E(f478(x6983,x6984,x6985,x6986,x6981,x6987),f478(x6983,x6984,x6985,x6986,x6982,x6987)) % 168.22/168.07 [699]~E(x6991,x6992)+E(f478(x6993,x6994,x6995,x6996,x6997,x6991),f478(x6993,x6994,x6995,x6996,x6997,x6992)) % 168.22/168.07 [700]~E(x7001,x7002)+E(f241(x7001,x7003),f241(x7002,x7003)) % 168.22/168.07 [701]~E(x7011,x7012)+E(f241(x7013,x7011),f241(x7013,x7012)) % 168.22/168.07 [702]~E(x7021,x7022)+E(f254(x7021,x7023),f254(x7022,x7023)) % 168.22/168.07 [703]~E(x7031,x7032)+E(f254(x7033,x7031),f254(x7033,x7032)) % 168.22/168.07 [704]~E(x7041,x7042)+E(f618(x7041,x7043,x7044,x7045,x7046),f618(x7042,x7043,x7044,x7045,x7046)) % 168.22/168.07 [705]~E(x7051,x7052)+E(f618(x7053,x7051,x7054,x7055,x7056),f618(x7053,x7052,x7054,x7055,x7056)) % 168.22/168.07 [706]~E(x7061,x7062)+E(f618(x7063,x7064,x7061,x7065,x7066),f618(x7063,x7064,x7062,x7065,x7066)) % 168.22/168.07 [707]~E(x7071,x7072)+E(f618(x7073,x7074,x7075,x7071,x7076),f618(x7073,x7074,x7075,x7072,x7076)) % 168.22/168.07 [708]~E(x7081,x7082)+E(f618(x7083,x7084,x7085,x7086,x7081),f618(x7083,x7084,x7085,x7086,x7082)) % 168.22/168.07 [709]~E(x7091,x7092)+E(f484(x7091,x7093,x7094,x7095,x7096),f484(x7092,x7093,x7094,x7095,x7096)) % 168.22/168.07 [710]~E(x7101,x7102)+E(f484(x7103,x7101,x7104,x7105,x7106),f484(x7103,x7102,x7104,x7105,x7106)) % 168.22/168.07 [711]~E(x7111,x7112)+E(f484(x7113,x7114,x7111,x7115,x7116),f484(x7113,x7114,x7112,x7115,x7116)) % 168.22/168.07 [712]~E(x7121,x7122)+E(f484(x7123,x7124,x7125,x7121,x7126),f484(x7123,x7124,x7125,x7122,x7126)) % 168.22/168.07 [713]~E(x7131,x7132)+E(f484(x7133,x7134,x7135,x7136,x7131),f484(x7133,x7134,x7135,x7136,x7132)) % 168.22/168.07 [714]~E(x7141,x7142)+E(f730(x7141,x7143,x7144,x7145,x7146,x7147,x7148),f730(x7142,x7143,x7144,x7145,x7146,x7147,x7148)) % 168.22/168.07 [715]~E(x7151,x7152)+E(f730(x7153,x7151,x7154,x7155,x7156,x7157,x7158),f730(x7153,x7152,x7154,x7155,x7156,x7157,x7158)) % 168.22/168.07 [716]~E(x7161,x7162)+E(f730(x7163,x7164,x7161,x7165,x7166,x7167,x7168),f730(x7163,x7164,x7162,x7165,x7166,x7167,x7168)) % 168.22/168.07 [717]~E(x7171,x7172)+E(f730(x7173,x7174,x7175,x7171,x7176,x7177,x7178),f730(x7173,x7174,x7175,x7172,x7176,x7177,x7178)) % 168.22/168.07 [718]~E(x7181,x7182)+E(f730(x7183,x7184,x7185,x7186,x7181,x7187,x7188),f730(x7183,x7184,x7185,x7186,x7182,x7187,x7188)) % 168.22/168.07 [719]~E(x7191,x7192)+E(f730(x7193,x7194,x7195,x7196,x7197,x7191,x7198),f730(x7193,x7194,x7195,x7196,x7197,x7192,x7198)) % 168.22/168.07 [720]~E(x7201,x7202)+E(f730(x7203,x7204,x7205,x7206,x7207,x7208,x7201),f730(x7203,x7204,x7205,x7206,x7207,x7208,x7202)) % 168.22/168.07 [721]~E(x7211,x7212)+E(f196(x7211,x7213),f196(x7212,x7213)) % 168.22/168.07 [722]~E(x7221,x7222)+E(f196(x7223,x7221),f196(x7223,x7222)) % 168.22/168.07 [723]~E(x7231,x7232)+E(f97(x7231),f97(x7232)) % 168.22/168.07 [724]~E(x7241,x7242)+E(f577(x7241,x7243,x7244),f577(x7242,x7243,x7244)) % 168.22/168.07 [725]~E(x7251,x7252)+E(f577(x7253,x7251,x7254),f577(x7253,x7252,x7254)) % 168.22/168.07 [726]~E(x7261,x7262)+E(f577(x7263,x7264,x7261),f577(x7263,x7264,x7262)) % 168.22/168.07 [727]~E(x7271,x7272)+E(f761(x7271,x7273,x7274,x7275,x7276),f761(x7272,x7273,x7274,x7275,x7276)) % 168.22/168.07 [728]~E(x7281,x7282)+E(f761(x7283,x7281,x7284,x7285,x7286),f761(x7283,x7282,x7284,x7285,x7286)) % 168.22/168.07 [729]~E(x7291,x7292)+E(f761(x7293,x7294,x7291,x7295,x7296),f761(x7293,x7294,x7292,x7295,x7296)) % 168.22/168.07 [730]~E(x7301,x7302)+E(f761(x7303,x7304,x7305,x7301,x7306),f761(x7303,x7304,x7305,x7302,x7306)) % 168.22/168.07 [731]~E(x7311,x7312)+E(f761(x7313,x7314,x7315,x7316,x7311),f761(x7313,x7314,x7315,x7316,x7312)) % 168.22/168.07 [732]~E(x7321,x7322)+E(f456(x7321,x7323,x7324,x7325,x7326),f456(x7322,x7323,x7324,x7325,x7326)) % 168.22/168.07 [733]~E(x7331,x7332)+E(f456(x7333,x7331,x7334,x7335,x7336),f456(x7333,x7332,x7334,x7335,x7336)) % 168.22/168.07 [734]~E(x7341,x7342)+E(f456(x7343,x7344,x7341,x7345,x7346),f456(x7343,x7344,x7342,x7345,x7346)) % 168.22/168.07 [735]~E(x7351,x7352)+E(f456(x7353,x7354,x7355,x7351,x7356),f456(x7353,x7354,x7355,x7352,x7356)) % 168.22/168.07 [736]~E(x7361,x7362)+E(f456(x7363,x7364,x7365,x7366,x7361),f456(x7363,x7364,x7365,x7366,x7362)) % 168.22/168.07 [737]~E(x7371,x7372)+E(f252(x7371,x7373),f252(x7372,x7373)) % 168.22/168.07 [738]~E(x7381,x7382)+E(f252(x7383,x7381),f252(x7383,x7382)) % 168.22/168.07 [739]~E(x7391,x7392)+E(f326(x7391,x7393,x7394),f326(x7392,x7393,x7394)) % 168.22/168.07 [740]~E(x7401,x7402)+E(f326(x7403,x7401,x7404),f326(x7403,x7402,x7404)) % 168.22/168.07 [741]~E(x7411,x7412)+E(f326(x7413,x7414,x7411),f326(x7413,x7414,x7412)) % 168.22/168.07 [742]~E(x7421,x7422)+E(f663(x7421,x7423),f663(x7422,x7423)) % 168.22/168.07 [743]~E(x7431,x7432)+E(f663(x7433,x7431),f663(x7433,x7432)) % 168.22/168.07 [744]~E(x7441,x7442)+E(f727(x7441,x7443,x7444,x7445,x7446),f727(x7442,x7443,x7444,x7445,x7446)) % 168.22/168.07 [745]~E(x7451,x7452)+E(f727(x7453,x7451,x7454,x7455,x7456),f727(x7453,x7452,x7454,x7455,x7456)) % 168.22/168.07 [746]~E(x7461,x7462)+E(f727(x7463,x7464,x7461,x7465,x7466),f727(x7463,x7464,x7462,x7465,x7466)) % 168.22/168.07 [747]~E(x7471,x7472)+E(f727(x7473,x7474,x7475,x7471,x7476),f727(x7473,x7474,x7475,x7472,x7476)) % 168.22/168.07 [748]~E(x7481,x7482)+E(f727(x7483,x7484,x7485,x7486,x7481),f727(x7483,x7484,x7485,x7486,x7482)) % 168.22/168.07 [749]~E(x7491,x7492)+E(f382(x7491,x7493),f382(x7492,x7493)) % 168.22/168.07 [750]~E(x7501,x7502)+E(f382(x7503,x7501),f382(x7503,x7502)) % 168.22/168.07 [751]~E(x7511,x7512)+E(f164(x7511,x7513,x7514),f164(x7512,x7513,x7514)) % 168.22/168.07 [752]~E(x7521,x7522)+E(f164(x7523,x7521,x7524),f164(x7523,x7522,x7524)) % 168.22/168.07 [753]~E(x7531,x7532)+E(f164(x7533,x7534,x7531),f164(x7533,x7534,x7532)) % 168.22/168.07 [754]~E(x7541,x7542)+E(f604(x7541,x7543,x7544,x7545),f604(x7542,x7543,x7544,x7545)) % 168.22/168.07 [755]~E(x7551,x7552)+E(f604(x7553,x7551,x7554,x7555),f604(x7553,x7552,x7554,x7555)) % 168.22/168.07 [756]~E(x7561,x7562)+E(f604(x7563,x7564,x7561,x7565),f604(x7563,x7564,x7562,x7565)) % 168.22/168.07 [757]~E(x7571,x7572)+E(f604(x7573,x7574,x7575,x7571),f604(x7573,x7574,x7575,x7572)) % 168.22/168.07 [758]~E(x7581,x7582)+E(f751(x7581,x7583,x7584,x7585,x7586),f751(x7582,x7583,x7584,x7585,x7586)) % 168.22/168.07 [759]~E(x7591,x7592)+E(f751(x7593,x7591,x7594,x7595,x7596),f751(x7593,x7592,x7594,x7595,x7596)) % 168.22/168.07 [760]~E(x7601,x7602)+E(f751(x7603,x7604,x7601,x7605,x7606),f751(x7603,x7604,x7602,x7605,x7606)) % 168.22/168.07 [761]~E(x7611,x7612)+E(f751(x7613,x7614,x7615,x7611,x7616),f751(x7613,x7614,x7615,x7612,x7616)) % 168.22/168.07 [762]~E(x7621,x7622)+E(f751(x7623,x7624,x7625,x7626,x7621),f751(x7623,x7624,x7625,x7626,x7622)) % 168.22/168.07 [763]~E(x7631,x7632)+E(f784(x7631,x7633,x7634),f784(x7632,x7633,x7634)) % 168.22/168.07 [764]~E(x7641,x7642)+E(f784(x7643,x7641,x7644),f784(x7643,x7642,x7644)) % 168.22/168.07 [765]~E(x7651,x7652)+E(f784(x7653,x7654,x7651),f784(x7653,x7654,x7652)) % 168.22/168.07 [766]~E(x7661,x7662)+E(f685(x7661,x7663),f685(x7662,x7663)) % 168.22/168.07 [767]~E(x7671,x7672)+E(f685(x7673,x7671),f685(x7673,x7672)) % 168.22/168.07 [768]~E(x7681,x7682)+E(f699(x7681,x7683),f699(x7682,x7683)) % 168.22/168.07 [769]~E(x7691,x7692)+E(f699(x7693,x7691),f699(x7693,x7692)) % 168.22/168.07 [770]~E(x7701,x7702)+E(f689(x7701,x7703,x7704),f689(x7702,x7703,x7704)) % 168.22/168.07 [771]~E(x7711,x7712)+E(f689(x7713,x7711,x7714),f689(x7713,x7712,x7714)) % 168.22/168.07 [772]~E(x7721,x7722)+E(f689(x7723,x7724,x7721),f689(x7723,x7724,x7722)) % 168.22/168.07 [773]~E(x7731,x7732)+E(f710(x7731,x7733,x7734,x7735,x7736,x7737),f710(x7732,x7733,x7734,x7735,x7736,x7737)) % 168.22/168.07 [774]~E(x7741,x7742)+E(f710(x7743,x7741,x7744,x7745,x7746,x7747),f710(x7743,x7742,x7744,x7745,x7746,x7747)) % 168.22/168.07 [775]~E(x7751,x7752)+E(f710(x7753,x7754,x7751,x7755,x7756,x7757),f710(x7753,x7754,x7752,x7755,x7756,x7757)) % 168.22/168.07 [776]~E(x7761,x7762)+E(f710(x7763,x7764,x7765,x7761,x7766,x7767),f710(x7763,x7764,x7765,x7762,x7766,x7767)) % 168.22/168.07 [777]~E(x7771,x7772)+E(f710(x7773,x7774,x7775,x7776,x7771,x7777),f710(x7773,x7774,x7775,x7776,x7772,x7777)) % 168.22/168.07 [778]~E(x7781,x7782)+E(f710(x7783,x7784,x7785,x7786,x7787,x7781),f710(x7783,x7784,x7785,x7786,x7787,x7782)) % 168.22/168.07 [779]~E(x7791,x7792)+E(f811(x7791,x7793,x7794,x7795),f811(x7792,x7793,x7794,x7795)) % 168.22/168.07 [780]~E(x7801,x7802)+E(f811(x7803,x7801,x7804,x7805),f811(x7803,x7802,x7804,x7805)) % 168.22/168.07 [781]~E(x7811,x7812)+E(f811(x7813,x7814,x7811,x7815),f811(x7813,x7814,x7812,x7815)) % 168.22/168.07 [782]~E(x7821,x7822)+E(f811(x7823,x7824,x7825,x7821),f811(x7823,x7824,x7825,x7822)) % 168.22/168.07 [783]~E(x7831,x7832)+E(f665(x7831,x7833,x7834),f665(x7832,x7833,x7834)) % 168.22/168.07 [784]~E(x7841,x7842)+E(f665(x7843,x7841,x7844),f665(x7843,x7842,x7844)) % 168.22/168.07 [785]~E(x7851,x7852)+E(f665(x7853,x7854,x7851),f665(x7853,x7854,x7852)) % 168.22/168.07 [786]~E(x7861,x7862)+E(f412(x7861,x7863,x7864,x7865,x7866),f412(x7862,x7863,x7864,x7865,x7866)) % 168.22/168.07 [787]~E(x7871,x7872)+E(f412(x7873,x7871,x7874,x7875,x7876),f412(x7873,x7872,x7874,x7875,x7876)) % 168.22/168.07 [788]~E(x7881,x7882)+E(f412(x7883,x7884,x7881,x7885,x7886),f412(x7883,x7884,x7882,x7885,x7886)) % 168.22/168.07 [789]~E(x7891,x7892)+E(f412(x7893,x7894,x7895,x7891,x7896),f412(x7893,x7894,x7895,x7892,x7896)) % 168.22/168.07 [790]~E(x7901,x7902)+E(f412(x7903,x7904,x7905,x7906,x7901),f412(x7903,x7904,x7905,x7906,x7902)) % 168.22/168.07 [791]~E(x7911,x7912)+E(f548(x7911,x7913),f548(x7912,x7913)) % 168.22/168.07 [792]~E(x7921,x7922)+E(f548(x7923,x7921),f548(x7923,x7922)) % 168.22/168.07 [793]~E(x7931,x7932)+E(f155(x7931,x7933),f155(x7932,x7933)) % 168.22/168.07 [794]~E(x7941,x7942)+E(f155(x7943,x7941),f155(x7943,x7942)) % 168.22/168.07 [795]~E(x7951,x7952)+E(f495(x7951,x7953,x7954,x7955),f495(x7952,x7953,x7954,x7955)) % 168.22/168.07 [796]~E(x7961,x7962)+E(f495(x7963,x7961,x7964,x7965),f495(x7963,x7962,x7964,x7965)) % 168.22/168.07 [797]~E(x7971,x7972)+E(f495(x7973,x7974,x7971,x7975),f495(x7973,x7974,x7972,x7975)) % 168.22/168.07 [798]~E(x7981,x7982)+E(f495(x7983,x7984,x7985,x7981),f495(x7983,x7984,x7985,x7982)) % 168.22/168.07 [799]~E(x7991,x7992)+E(f481(x7991,x7993,x7994),f481(x7992,x7993,x7994)) % 168.22/168.07 [800]~E(x8001,x8002)+E(f481(x8003,x8001,x8004),f481(x8003,x8002,x8004)) % 168.22/168.07 [801]~E(x8011,x8012)+E(f481(x8013,x8014,x8011),f481(x8013,x8014,x8012)) % 168.22/168.07 [802]~E(x8021,x8022)+E(f678(x8021,x8023,x8024),f678(x8022,x8023,x8024)) % 168.22/168.07 [803]~E(x8031,x8032)+E(f678(x8033,x8031,x8034),f678(x8033,x8032,x8034)) % 168.22/168.07 [804]~E(x8041,x8042)+E(f678(x8043,x8044,x8041),f678(x8043,x8044,x8042)) % 168.22/168.07 [805]~E(x8051,x8052)+E(f796(x8051,x8053,x8054,x8055),f796(x8052,x8053,x8054,x8055)) % 168.22/168.07 [806]~E(x8061,x8062)+E(f796(x8063,x8061,x8064,x8065),f796(x8063,x8062,x8064,x8065)) % 168.22/168.07 [807]~E(x8071,x8072)+E(f796(x8073,x8074,x8071,x8075),f796(x8073,x8074,x8072,x8075)) % 168.22/168.07 [808]~E(x8081,x8082)+E(f796(x8083,x8084,x8085,x8081),f796(x8083,x8084,x8085,x8082)) % 168.22/168.07 [809]~E(x8091,x8092)+E(f675(x8091,x8093,x8094),f675(x8092,x8093,x8094)) % 168.22/168.07 [810]~E(x8101,x8102)+E(f675(x8103,x8101,x8104),f675(x8103,x8102,x8104)) % 168.22/168.07 [811]~E(x8111,x8112)+E(f675(x8113,x8114,x8111),f675(x8113,x8114,x8112)) % 168.22/168.07 [812]~E(x8121,x8122)+E(f275(x8121,x8123,x8124,x8125),f275(x8122,x8123,x8124,x8125)) % 168.22/168.07 [813]~E(x8131,x8132)+E(f275(x8133,x8131,x8134,x8135),f275(x8133,x8132,x8134,x8135)) % 168.22/168.07 [814]~E(x8141,x8142)+E(f275(x8143,x8144,x8141,x8145),f275(x8143,x8144,x8142,x8145)) % 168.22/168.07 [815]~E(x8151,x8152)+E(f275(x8153,x8154,x8155,x8151),f275(x8153,x8154,x8155,x8152)) % 168.22/168.07 [816]~E(x8161,x8162)+E(f277(x8161),f277(x8162)) % 168.22/168.07 [817]~E(x8171,x8172)+E(f285(x8171),f285(x8172)) % 168.22/168.07 [818]~E(x8181,x8182)+E(f137(x8181,x8183),f137(x8182,x8183)) % 168.22/168.07 [819]~E(x8191,x8192)+E(f137(x8193,x8191),f137(x8193,x8192)) % 168.22/168.07 [820]~E(x8201,x8202)+E(f209(x8201,x8203),f209(x8202,x8203)) % 168.22/168.07 [821]~E(x8211,x8212)+E(f209(x8213,x8211),f209(x8213,x8212)) % 168.22/168.07 [822]~E(x8221,x8222)+E(f693(x8221,x8223,x8224,x8225,x8226),f693(x8222,x8223,x8224,x8225,x8226)) % 168.22/168.07 [823]~E(x8231,x8232)+E(f693(x8233,x8231,x8234,x8235,x8236),f693(x8233,x8232,x8234,x8235,x8236)) % 168.22/168.07 [824]~E(x8241,x8242)+E(f693(x8243,x8244,x8241,x8245,x8246),f693(x8243,x8244,x8242,x8245,x8246)) % 168.22/168.07 [825]~E(x8251,x8252)+E(f693(x8253,x8254,x8255,x8251,x8256),f693(x8253,x8254,x8255,x8252,x8256)) % 168.22/168.07 [826]~E(x8261,x8262)+E(f693(x8263,x8264,x8265,x8266,x8261),f693(x8263,x8264,x8265,x8266,x8262)) % 168.22/168.07 [827]~E(x8271,x8272)+E(f381(x8271,x8273),f381(x8272,x8273)) % 168.22/168.07 [828]~E(x8281,x8282)+E(f381(x8283,x8281),f381(x8283,x8282)) % 168.22/168.07 [829]~E(x8291,x8292)+E(f395(x8291,x8293,x8294,x8295,x8296),f395(x8292,x8293,x8294,x8295,x8296)) % 168.22/168.07 [830]~E(x8301,x8302)+E(f395(x8303,x8301,x8304,x8305,x8306),f395(x8303,x8302,x8304,x8305,x8306)) % 168.22/168.07 [831]~E(x8311,x8312)+E(f395(x8313,x8314,x8311,x8315,x8316),f395(x8313,x8314,x8312,x8315,x8316)) % 168.22/168.07 [832]~E(x8321,x8322)+E(f395(x8323,x8324,x8325,x8321,x8326),f395(x8323,x8324,x8325,x8322,x8326)) % 168.22/168.07 [833]~E(x8331,x8332)+E(f395(x8333,x8334,x8335,x8336,x8331),f395(x8333,x8334,x8335,x8336,x8332)) % 168.22/168.07 [834]~E(x8341,x8342)+E(f372(x8341,x8343),f372(x8342,x8343)) % 168.22/168.07 [835]~E(x8351,x8352)+E(f372(x8353,x8351),f372(x8353,x8352)) % 168.22/168.07 [836]~E(x8361,x8362)+E(f525(x8361,x8363,x8364,x8365),f525(x8362,x8363,x8364,x8365)) % 168.22/168.07 [837]~E(x8371,x8372)+E(f525(x8373,x8371,x8374,x8375),f525(x8373,x8372,x8374,x8375)) % 168.22/168.07 [838]~E(x8381,x8382)+E(f525(x8383,x8384,x8381,x8385),f525(x8383,x8384,x8382,x8385)) % 168.22/168.07 [839]~E(x8391,x8392)+E(f525(x8393,x8394,x8395,x8391),f525(x8393,x8394,x8395,x8392)) % 168.22/168.07 [840]~E(x8401,x8402)+E(f722(x8401,x8403,x8404),f722(x8402,x8403,x8404)) % 168.22/168.07 [841]~E(x8411,x8412)+E(f722(x8413,x8411,x8414),f722(x8413,x8412,x8414)) % 168.22/168.07 [842]~E(x8421,x8422)+E(f722(x8423,x8424,x8421),f722(x8423,x8424,x8422)) % 168.22/168.07 [843]~E(x8431,x8432)+E(f269(x8431,x8433,x8434),f269(x8432,x8433,x8434)) % 168.22/168.07 [844]~E(x8441,x8442)+E(f269(x8443,x8441,x8444),f269(x8443,x8442,x8444)) % 168.22/168.07 [845]~E(x8451,x8452)+E(f269(x8453,x8454,x8451),f269(x8453,x8454,x8452)) % 168.22/168.07 [846]~E(x8461,x8462)+E(f161(x8461,x8463,x8464),f161(x8462,x8463,x8464)) % 168.22/168.07 [847]~E(x8471,x8472)+E(f161(x8473,x8471,x8474),f161(x8473,x8472,x8474)) % 168.22/168.07 [848]~E(x8481,x8482)+E(f161(x8483,x8484,x8481),f161(x8483,x8484,x8482)) % 168.22/168.07 [849]~E(x8491,x8492)+E(f62(x8491,x8493),f62(x8492,x8493)) % 168.22/168.07 [850]~E(x8501,x8502)+E(f62(x8503,x8501),f62(x8503,x8502)) % 168.22/168.07 [851]~E(x8511,x8512)+E(f551(x8511,x8513,x8514,x8515),f551(x8512,x8513,x8514,x8515)) % 168.22/168.07 [852]~E(x8521,x8522)+E(f551(x8523,x8521,x8524,x8525),f551(x8523,x8522,x8524,x8525)) % 168.22/168.07 [853]~E(x8531,x8532)+E(f551(x8533,x8534,x8531,x8535),f551(x8533,x8534,x8532,x8535)) % 168.22/168.07 [854]~E(x8541,x8542)+E(f551(x8543,x8544,x8545,x8541),f551(x8543,x8544,x8545,x8542)) % 168.22/168.07 [855]~E(x8551,x8552)+E(f350(x8551,x8553,x8554),f350(x8552,x8553,x8554)) % 168.22/168.07 [856]~E(x8561,x8562)+E(f350(x8563,x8561,x8564),f350(x8563,x8562,x8564)) % 168.22/168.07 [857]~E(x8571,x8572)+E(f350(x8573,x8574,x8571),f350(x8573,x8574,x8572)) % 168.22/168.07 [858]~E(x8581,x8582)+E(f691(x8581,x8583),f691(x8582,x8583)) % 168.22/168.07 [859]~E(x8591,x8592)+E(f691(x8593,x8591),f691(x8593,x8592)) % 168.22/168.07 [860]~E(x8601,x8602)+E(f267(x8601,x8603),f267(x8602,x8603)) % 168.22/168.07 [861]~E(x8611,x8612)+E(f267(x8613,x8611),f267(x8613,x8612)) % 168.22/168.07 [862]~E(x8621,x8622)+E(f774(x8621,x8623,x8624,x8625,x8626),f774(x8622,x8623,x8624,x8625,x8626)) % 168.22/168.07 [863]~E(x8631,x8632)+E(f774(x8633,x8631,x8634,x8635,x8636),f774(x8633,x8632,x8634,x8635,x8636)) % 168.22/168.07 [864]~E(x8641,x8642)+E(f774(x8643,x8644,x8641,x8645,x8646),f774(x8643,x8644,x8642,x8645,x8646)) % 168.22/168.07 [865]~E(x8651,x8652)+E(f774(x8653,x8654,x8655,x8651,x8656),f774(x8653,x8654,x8655,x8652,x8656)) % 168.22/168.07 [866]~E(x8661,x8662)+E(f774(x8663,x8664,x8665,x8666,x8661),f774(x8663,x8664,x8665,x8666,x8662)) % 168.22/168.07 [867]~E(x8671,x8672)+E(f138(x8671,x8673),f138(x8672,x8673)) % 168.22/168.07 [868]~E(x8681,x8682)+E(f138(x8683,x8681),f138(x8683,x8682)) % 168.22/168.07 [869]~E(x8691,x8692)+E(f549(x8691,x8693),f549(x8692,x8693)) % 168.22/168.07 [870]~E(x8701,x8702)+E(f549(x8703,x8701),f549(x8703,x8702)) % 168.22/168.07 [871]~E(x8711,x8712)+E(f386(x8711,x8713,x8714),f386(x8712,x8713,x8714)) % 168.22/168.07 [872]~E(x8721,x8722)+E(f386(x8723,x8721,x8724),f386(x8723,x8722,x8724)) % 168.22/168.07 [873]~E(x8731,x8732)+E(f386(x8733,x8734,x8731),f386(x8733,x8734,x8732)) % 168.22/168.07 [874]~E(x8741,x8742)+E(f797(x8741,x8743,x8744,x8745),f797(x8742,x8743,x8744,x8745)) % 168.22/168.07 [875]~E(x8751,x8752)+E(f797(x8753,x8751,x8754,x8755),f797(x8753,x8752,x8754,x8755)) % 168.22/168.07 [876]~E(x8761,x8762)+E(f797(x8763,x8764,x8761,x8765),f797(x8763,x8764,x8762,x8765)) % 168.22/168.07 [877]~E(x8771,x8772)+E(f797(x8773,x8774,x8775,x8771),f797(x8773,x8774,x8775,x8772)) % 168.22/168.07 [878]~E(x8781,x8782)+E(f310(x8781,x8783,x8784,x8785),f310(x8782,x8783,x8784,x8785)) % 168.22/168.07 [879]~E(x8791,x8792)+E(f310(x8793,x8791,x8794,x8795),f310(x8793,x8792,x8794,x8795)) % 168.22/168.07 [880]~E(x8801,x8802)+E(f310(x8803,x8804,x8801,x8805),f310(x8803,x8804,x8802,x8805)) % 168.22/168.07 [881]~E(x8811,x8812)+E(f310(x8813,x8814,x8815,x8811),f310(x8813,x8814,x8815,x8812)) % 168.22/168.07 [882]~E(x8821,x8822)+E(f527(x8821,x8823,x8824,x8825,x8826,x8827),f527(x8822,x8823,x8824,x8825,x8826,x8827)) % 168.22/168.07 [883]~E(x8831,x8832)+E(f527(x8833,x8831,x8834,x8835,x8836,x8837),f527(x8833,x8832,x8834,x8835,x8836,x8837)) % 168.22/168.07 [884]~E(x8841,x8842)+E(f527(x8843,x8844,x8841,x8845,x8846,x8847),f527(x8843,x8844,x8842,x8845,x8846,x8847)) % 168.22/168.07 [885]~E(x8851,x8852)+E(f527(x8853,x8854,x8855,x8851,x8856,x8857),f527(x8853,x8854,x8855,x8852,x8856,x8857)) % 168.22/168.07 [886]~E(x8861,x8862)+E(f527(x8863,x8864,x8865,x8866,x8861,x8867),f527(x8863,x8864,x8865,x8866,x8862,x8867)) % 168.22/168.07 [887]~E(x8871,x8872)+E(f527(x8873,x8874,x8875,x8876,x8877,x8871),f527(x8873,x8874,x8875,x8876,x8877,x8872)) % 168.22/168.07 [888]~E(x8881,x8882)+E(f631(x8881,x8883,x8884,x8885,x8886),f631(x8882,x8883,x8884,x8885,x8886)) % 168.22/168.07 [889]~E(x8891,x8892)+E(f631(x8893,x8891,x8894,x8895,x8896),f631(x8893,x8892,x8894,x8895,x8896)) % 168.22/168.07 [890]~E(x8901,x8902)+E(f631(x8903,x8904,x8901,x8905,x8906),f631(x8903,x8904,x8902,x8905,x8906)) % 168.22/168.07 [891]~E(x8911,x8912)+E(f631(x8913,x8914,x8915,x8911,x8916),f631(x8913,x8914,x8915,x8912,x8916)) % 168.22/168.07 [892]~E(x8921,x8922)+E(f631(x8923,x8924,x8925,x8926,x8921),f631(x8923,x8924,x8925,x8926,x8922)) % 168.22/168.07 [893]~E(x8931,x8932)+E(f724(x8931,x8933,x8934,x8935,x8936),f724(x8932,x8933,x8934,x8935,x8936)) % 168.22/168.07 [894]~E(x8941,x8942)+E(f724(x8943,x8941,x8944,x8945,x8946),f724(x8943,x8942,x8944,x8945,x8946)) % 168.22/168.07 [895]~E(x8951,x8952)+E(f724(x8953,x8954,x8951,x8955,x8956),f724(x8953,x8954,x8952,x8955,x8956)) % 168.22/168.07 [896]~E(x8961,x8962)+E(f724(x8963,x8964,x8965,x8961,x8966),f724(x8963,x8964,x8965,x8962,x8966)) % 168.22/168.07 [897]~E(x8971,x8972)+E(f724(x8973,x8974,x8975,x8976,x8971),f724(x8973,x8974,x8975,x8976,x8972)) % 168.22/168.07 [898]~E(x8981,x8982)+E(f760(x8981,x8983,x8984,x8985,x8986),f760(x8982,x8983,x8984,x8985,x8986)) % 168.22/168.07 [899]~E(x8991,x8992)+E(f760(x8993,x8991,x8994,x8995,x8996),f760(x8993,x8992,x8994,x8995,x8996)) % 168.22/168.07 [900]~E(x9001,x9002)+E(f760(x9003,x9004,x9001,x9005,x9006),f760(x9003,x9004,x9002,x9005,x9006)) % 168.22/168.07 [901]~E(x9011,x9012)+E(f760(x9013,x9014,x9015,x9011,x9016),f760(x9013,x9014,x9015,x9012,x9016)) % 168.22/168.07 [902]~E(x9021,x9022)+E(f760(x9023,x9024,x9025,x9026,x9021),f760(x9023,x9024,x9025,x9026,x9022)) % 168.22/168.07 [903]~E(x9031,x9032)+E(f804(x9031,x9033,x9034,x9035),f804(x9032,x9033,x9034,x9035)) % 168.22/168.07 [904]~E(x9041,x9042)+E(f804(x9043,x9041,x9044,x9045),f804(x9043,x9042,x9044,x9045)) % 168.22/168.07 [905]~E(x9051,x9052)+E(f804(x9053,x9054,x9051,x9055),f804(x9053,x9054,x9052,x9055)) % 168.22/168.07 [906]~E(x9061,x9062)+E(f804(x9063,x9064,x9065,x9061),f804(x9063,x9064,x9065,x9062)) % 168.22/168.07 [907]~E(x9071,x9072)+E(f805(x9071,x9073,x9074,x9075),f805(x9072,x9073,x9074,x9075)) % 168.22/168.07 [908]~E(x9081,x9082)+E(f805(x9083,x9081,x9084,x9085),f805(x9083,x9082,x9084,x9085)) % 168.22/168.07 [909]~E(x9091,x9092)+E(f805(x9093,x9094,x9091,x9095),f805(x9093,x9094,x9092,x9095)) % 168.22/168.07 [910]~E(x9101,x9102)+E(f805(x9103,x9104,x9105,x9101),f805(x9103,x9104,x9105,x9102)) % 168.22/168.07 [911]~E(x9111,x9112)+E(f825(x9111,x9113,x9114,x9115,x9116,x9117,x9118),f825(x9112,x9113,x9114,x9115,x9116,x9117,x9118)) % 168.22/168.07 [912]~E(x9121,x9122)+E(f825(x9123,x9121,x9124,x9125,x9126,x9127,x9128),f825(x9123,x9122,x9124,x9125,x9126,x9127,x9128)) % 168.22/168.07 [913]~E(x9131,x9132)+E(f825(x9133,x9134,x9131,x9135,x9136,x9137,x9138),f825(x9133,x9134,x9132,x9135,x9136,x9137,x9138)) % 168.22/168.07 [914]~E(x9141,x9142)+E(f825(x9143,x9144,x9145,x9141,x9146,x9147,x9148),f825(x9143,x9144,x9145,x9142,x9146,x9147,x9148)) % 168.22/168.07 [915]~E(x9151,x9152)+E(f825(x9153,x9154,x9155,x9156,x9151,x9157,x9158),f825(x9153,x9154,x9155,x9156,x9152,x9157,x9158)) % 168.22/168.07 [916]~E(x9161,x9162)+E(f825(x9163,x9164,x9165,x9166,x9167,x9161,x9168),f825(x9163,x9164,x9165,x9166,x9167,x9162,x9168)) % 168.22/168.07 [917]~E(x9171,x9172)+E(f825(x9173,x9174,x9175,x9176,x9177,x9178,x9171),f825(x9173,x9174,x9175,x9176,x9177,x9178,x9172)) % 168.22/168.07 [918]~E(x9181,x9182)+E(f429(x9181,x9183,x9184,x9185),f429(x9182,x9183,x9184,x9185)) % 168.22/168.07 [919]~E(x9191,x9192)+E(f429(x9193,x9191,x9194,x9195),f429(x9193,x9192,x9194,x9195)) % 168.22/168.07 [920]~E(x9201,x9202)+E(f429(x9203,x9204,x9201,x9205),f429(x9203,x9204,x9202,x9205)) % 168.22/168.07 [921]~E(x9211,x9212)+E(f429(x9213,x9214,x9215,x9211),f429(x9213,x9214,x9215,x9212)) % 168.22/168.07 [922]~E(x9221,x9222)+E(f671(x9221,x9223,x9224,x9225,x9226,x9227,x9228,x9229),f671(x9222,x9223,x9224,x9225,x9226,x9227,x9228,x9229)) % 168.22/168.07 [923]~E(x9231,x9232)+E(f671(x9233,x9231,x9234,x9235,x9236,x9237,x9238,x9239),f671(x9233,x9232,x9234,x9235,x9236,x9237,x9238,x9239)) % 168.22/168.07 [924]~E(x9241,x9242)+E(f671(x9243,x9244,x9241,x9245,x9246,x9247,x9248,x9249),f671(x9243,x9244,x9242,x9245,x9246,x9247,x9248,x9249)) % 168.22/168.07 [925]~E(x9251,x9252)+E(f671(x9253,x9254,x9255,x9251,x9256,x9257,x9258,x9259),f671(x9253,x9254,x9255,x9252,x9256,x9257,x9258,x9259)) % 168.22/168.07 [926]~E(x9261,x9262)+E(f671(x9263,x9264,x9265,x9266,x9261,x9267,x9268,x9269),f671(x9263,x9264,x9265,x9266,x9262,x9267,x9268,x9269)) % 168.22/168.07 [927]~E(x9271,x9272)+E(f671(x9273,x9274,x9275,x9276,x9277,x9271,x9278,x9279),f671(x9273,x9274,x9275,x9276,x9277,x9272,x9278,x9279)) % 168.22/168.07 [928]~E(x9281,x9282)+E(f671(x9283,x9284,x9285,x9286,x9287,x9288,x9281,x9289),f671(x9283,x9284,x9285,x9286,x9287,x9288,x9282,x9289)) % 168.22/168.07 [929]~E(x9291,x9292)+E(f671(x9293,x9294,x9295,x9296,x9297,x9298,x9299,x9291),f671(x9293,x9294,x9295,x9296,x9297,x9298,x9299,x9292)) % 168.22/168.07 [930]~E(x9301,x9302)+E(f795(x9301,x9303,x9304,x9305),f795(x9302,x9303,x9304,x9305)) % 168.22/168.07 [931]~E(x9311,x9312)+E(f795(x9313,x9311,x9314,x9315),f795(x9313,x9312,x9314,x9315)) % 168.22/168.07 [932]~E(x9321,x9322)+E(f795(x9323,x9324,x9321,x9325),f795(x9323,x9324,x9322,x9325)) % 168.22/168.07 [933]~E(x9331,x9332)+E(f795(x9333,x9334,x9335,x9331),f795(x9333,x9334,x9335,x9332)) % 168.22/168.07 [934]~E(x9341,x9342)+E(f240(x9341,x9343,x9344),f240(x9342,x9343,x9344)) % 168.22/168.07 [935]~E(x9351,x9352)+E(f240(x9353,x9351,x9354),f240(x9353,x9352,x9354)) % 168.22/168.07 [936]~E(x9361,x9362)+E(f240(x9363,x9364,x9361),f240(x9363,x9364,x9362)) % 168.22/168.07 [937]~E(x9371,x9372)+E(f253(x9371),f253(x9372)) % 168.22/168.07 [938]~E(x9381,x9382)+E(f690(x9381,x9383,x9384),f690(x9382,x9383,x9384)) % 168.22/168.07 [939]~E(x9391,x9392)+E(f690(x9393,x9391,x9394),f690(x9393,x9392,x9394)) % 168.22/168.07 [940]~E(x9401,x9402)+E(f690(x9403,x9404,x9401),f690(x9403,x9404,x9402)) % 168.22/168.07 [941]~E(x9411,x9412)+E(f644(x9411,x9413),f644(x9412,x9413)) % 168.22/168.07 [942]~E(x9421,x9422)+E(f644(x9423,x9421),f644(x9423,x9422)) % 168.22/168.07 [943]~E(x9431,x9432)+E(f342(x9431,x9433,x9434),f342(x9432,x9433,x9434)) % 168.22/168.07 [944]~E(x9441,x9442)+E(f342(x9443,x9441,x9444),f342(x9443,x9442,x9444)) % 168.22/168.07 [945]~E(x9451,x9452)+E(f342(x9453,x9454,x9451),f342(x9453,x9454,x9452)) % 168.22/168.07 [946]~E(x9461,x9462)+E(f749(x9461,x9463,x9464,x9465,x9466,x9467,x9468,x9469),f749(x9462,x9463,x9464,x9465,x9466,x9467,x9468,x9469)) % 168.22/168.07 [947]~E(x9471,x9472)+E(f749(x9473,x9471,x9474,x9475,x9476,x9477,x9478,x9479),f749(x9473,x9472,x9474,x9475,x9476,x9477,x9478,x9479)) % 168.22/168.07 [948]~E(x9481,x9482)+E(f749(x9483,x9484,x9481,x9485,x9486,x9487,x9488,x9489),f749(x9483,x9484,x9482,x9485,x9486,x9487,x9488,x9489)) % 168.22/168.07 [949]~E(x9491,x9492)+E(f749(x9493,x9494,x9495,x9491,x9496,x9497,x9498,x9499),f749(x9493,x9494,x9495,x9492,x9496,x9497,x9498,x9499)) % 168.22/168.07 [950]~E(x9501,x9502)+E(f749(x9503,x9504,x9505,x9506,x9501,x9507,x9508,x9509),f749(x9503,x9504,x9505,x9506,x9502,x9507,x9508,x9509)) % 168.22/168.07 [951]~E(x9511,x9512)+E(f749(x9513,x9514,x9515,x9516,x9517,x9511,x9518,x9519),f749(x9513,x9514,x9515,x9516,x9517,x9512,x9518,x9519)) % 168.22/168.07 [952]~E(x9521,x9522)+E(f749(x9523,x9524,x9525,x9526,x9527,x9528,x9521,x9529),f749(x9523,x9524,x9525,x9526,x9527,x9528,x9522,x9529)) % 168.22/168.07 [953]~E(x9531,x9532)+E(f749(x9533,x9534,x9535,x9536,x9537,x9538,x9539,x9531),f749(x9533,x9534,x9535,x9536,x9537,x9538,x9539,x9532)) % 168.22/168.07 [954]~E(x9541,x9542)+E(f603(x9541,x9543,x9544,x9545),f603(x9542,x9543,x9544,x9545)) % 168.22/168.07 [955]~E(x9551,x9552)+E(f603(x9553,x9551,x9554,x9555),f603(x9553,x9552,x9554,x9555)) % 168.22/168.07 [956]~E(x9561,x9562)+E(f603(x9563,x9564,x9561,x9565),f603(x9563,x9564,x9562,x9565)) % 168.22/168.07 [957]~E(x9571,x9572)+E(f603(x9573,x9574,x9575,x9571),f603(x9573,x9574,x9575,x9572)) % 168.22/168.07 [958]~E(x9581,x9582)+E(f404(x9581,x9583,x9584),f404(x9582,x9583,x9584)) % 168.22/168.07 [959]~E(x9591,x9592)+E(f404(x9593,x9591,x9594),f404(x9593,x9592,x9594)) % 168.22/168.07 [960]~E(x9601,x9602)+E(f404(x9603,x9604,x9601),f404(x9603,x9604,x9602)) % 168.22/168.07 [961]~E(x9611,x9612)+E(f744(x9611,x9613,x9614,x9615,x9616,x9617),f744(x9612,x9613,x9614,x9615,x9616,x9617)) % 168.22/168.07 [962]~E(x9621,x9622)+E(f744(x9623,x9621,x9624,x9625,x9626,x9627),f744(x9623,x9622,x9624,x9625,x9626,x9627)) % 168.22/168.07 [963]~E(x9631,x9632)+E(f744(x9633,x9634,x9631,x9635,x9636,x9637),f744(x9633,x9634,x9632,x9635,x9636,x9637)) % 168.22/168.07 [964]~E(x9641,x9642)+E(f744(x9643,x9644,x9645,x9641,x9646,x9647),f744(x9643,x9644,x9645,x9642,x9646,x9647)) % 168.22/168.07 [965]~E(x9651,x9652)+E(f744(x9653,x9654,x9655,x9656,x9651,x9657),f744(x9653,x9654,x9655,x9656,x9652,x9657)) % 168.22/168.07 [966]~E(x9661,x9662)+E(f744(x9663,x9664,x9665,x9666,x9667,x9661),f744(x9663,x9664,x9665,x9666,x9667,x9662)) % 168.22/168.07 [967]~E(x9671,x9672)+E(f575(x9671,x9673),f575(x9672,x9673)) % 168.22/168.07 [968]~E(x9681,x9682)+E(f575(x9683,x9681),f575(x9683,x9682)) % 168.22/168.07 [969]~E(x9691,x9692)+E(f817(x9691),f817(x9692)) % 168.22/168.07 [970]~E(x9701,x9702)+E(f460(x9701,x9703,x9704),f460(x9702,x9703,x9704)) % 168.22/168.07 [971]~E(x9711,x9712)+E(f460(x9713,x9711,x9714),f460(x9713,x9712,x9714)) % 168.22/168.07 [972]~E(x9721,x9722)+E(f460(x9723,x9724,x9721),f460(x9723,x9724,x9722)) % 168.22/168.07 [973]~E(x9731,x9732)+E(f587(x9731,x9733,x9734,x9735,x9736),f587(x9732,x9733,x9734,x9735,x9736)) % 168.22/168.07 [974]~E(x9741,x9742)+E(f587(x9743,x9741,x9744,x9745,x9746),f587(x9743,x9742,x9744,x9745,x9746)) % 168.22/168.07 [975]~E(x9751,x9752)+E(f587(x9753,x9754,x9751,x9755,x9756),f587(x9753,x9754,x9752,x9755,x9756)) % 168.22/168.07 [976]~E(x9761,x9762)+E(f587(x9763,x9764,x9765,x9761,x9766),f587(x9763,x9764,x9765,x9762,x9766)) % 168.22/168.07 [977]~E(x9771,x9772)+E(f587(x9773,x9774,x9775,x9776,x9771),f587(x9773,x9774,x9775,x9776,x9772)) % 168.22/168.07 [978]~E(x9781,x9782)+E(f544(x9781,x9783,x9784,x9785,x9786,x9787,x9788),f544(x9782,x9783,x9784,x9785,x9786,x9787,x9788)) % 168.22/168.07 [979]~E(x9791,x9792)+E(f544(x9793,x9791,x9794,x9795,x9796,x9797,x9798),f544(x9793,x9792,x9794,x9795,x9796,x9797,x9798)) % 168.22/168.07 [980]~E(x9801,x9802)+E(f544(x9803,x9804,x9801,x9805,x9806,x9807,x9808),f544(x9803,x9804,x9802,x9805,x9806,x9807,x9808)) % 168.22/168.07 [981]~E(x9811,x9812)+E(f544(x9813,x9814,x9815,x9811,x9816,x9817,x9818),f544(x9813,x9814,x9815,x9812,x9816,x9817,x9818)) % 168.22/168.07 [982]~E(x9821,x9822)+E(f544(x9823,x9824,x9825,x9826,x9821,x9827,x9828),f544(x9823,x9824,x9825,x9826,x9822,x9827,x9828)) % 168.22/168.07 [983]~E(x9831,x9832)+E(f544(x9833,x9834,x9835,x9836,x9837,x9831,x9838),f544(x9833,x9834,x9835,x9836,x9837,x9832,x9838)) % 168.22/168.07 [984]~E(x9841,x9842)+E(f544(x9843,x9844,x9845,x9846,x9847,x9848,x9841),f544(x9843,x9844,x9845,x9846,x9847,x9848,x9842)) % 168.22/168.07 [985]~E(x9851,x9852)+E(f688(x9851,x9853,x9854),f688(x9852,x9853,x9854)) % 168.22/168.07 [986]~E(x9861,x9862)+E(f688(x9863,x9861,x9864),f688(x9863,x9862,x9864)) % 168.22/168.07 [987]~E(x9871,x9872)+E(f688(x9873,x9874,x9871),f688(x9873,x9874,x9872)) % 168.22/168.07 [988]~E(x9881,x9882)+E(f793(x9881,x9883,x9884,x9885),f793(x9882,x9883,x9884,x9885)) % 168.22/168.07 [989]~E(x9891,x9892)+E(f793(x9893,x9891,x9894,x9895),f793(x9893,x9892,x9894,x9895)) % 168.22/168.07 [990]~E(x9901,x9902)+E(f793(x9903,x9904,x9901,x9905),f793(x9903,x9904,x9902,x9905)) % 168.22/168.07 [991]~E(x9911,x9912)+E(f793(x9913,x9914,x9915,x9911),f793(x9913,x9914,x9915,x9912)) % 168.22/168.07 [992]~E(x9921,x9922)+E(f659(x9921,x9923,x9924),f659(x9922,x9923,x9924)) % 168.22/168.07 [993]~E(x9931,x9932)+E(f659(x9933,x9931,x9934),f659(x9933,x9932,x9934)) % 168.22/168.07 [994]~E(x9941,x9942)+E(f659(x9943,x9944,x9941),f659(x9943,x9944,x9942)) % 168.22/168.07 [995]~E(x9951,x9952)+E(f567(x9951,x9953,x9954,x9955),f567(x9952,x9953,x9954,x9955)) % 168.22/168.07 [996]~E(x9961,x9962)+E(f567(x9963,x9961,x9964,x9965),f567(x9963,x9962,x9964,x9965)) % 168.22/168.07 [997]~E(x9971,x9972)+E(f567(x9973,x9974,x9971,x9975),f567(x9973,x9974,x9972,x9975)) % 168.22/168.07 [998]~E(x9981,x9982)+E(f567(x9983,x9984,x9985,x9981),f567(x9983,x9984,x9985,x9982)) % 168.22/168.07 [999]~E(x9991,x9992)+E(f621(x9991,x9993,x9994,x9995),f621(x9992,x9993,x9994,x9995)) % 168.22/168.07 [1000]~E(x10001,x10002)+E(f621(x10003,x10001,x10004,x10005),f621(x10003,x10002,x10004,x10005)) % 168.22/168.07 [1001]~E(x10011,x10012)+E(f621(x10013,x10014,x10011,x10015),f621(x10013,x10014,x10012,x10015)) % 168.22/168.07 [1002]~E(x10021,x10022)+E(f621(x10023,x10024,x10025,x10021),f621(x10023,x10024,x10025,x10022)) % 168.22/168.07 [1003]~E(x10031,x10032)+E(f476(x10031,x10033,x10034,x10035,x10036),f476(x10032,x10033,x10034,x10035,x10036)) % 168.22/168.07 [1004]~E(x10041,x10042)+E(f476(x10043,x10041,x10044,x10045,x10046),f476(x10043,x10042,x10044,x10045,x10046)) % 168.22/168.07 [1005]~E(x10051,x10052)+E(f476(x10053,x10054,x10051,x10055,x10056),f476(x10053,x10054,x10052,x10055,x10056)) % 168.22/168.07 [1006]~E(x10061,x10062)+E(f476(x10063,x10064,x10065,x10061,x10066),f476(x10063,x10064,x10065,x10062,x10066)) % 168.22/168.07 [1007]~E(x10071,x10072)+E(f476(x10073,x10074,x10075,x10076,x10071),f476(x10073,x10074,x10075,x10076,x10072)) % 168.22/168.07 [1008]~E(x10081,x10082)+E(f355(x10081,x10083,x10084,x10085,x10086),f355(x10082,x10083,x10084,x10085,x10086)) % 168.22/168.07 [1009]~E(x10091,x10092)+E(f355(x10093,x10091,x10094,x10095,x10096),f355(x10093,x10092,x10094,x10095,x10096)) % 168.22/168.07 [1010]~E(x10101,x10102)+E(f355(x10103,x10104,x10101,x10105,x10106),f355(x10103,x10104,x10102,x10105,x10106)) % 168.22/168.07 [1011]~E(x10111,x10112)+E(f355(x10113,x10114,x10115,x10111,x10116),f355(x10113,x10114,x10115,x10112,x10116)) % 168.22/168.07 [1012]~E(x10121,x10122)+E(f355(x10123,x10124,x10125,x10126,x10121),f355(x10123,x10124,x10125,x10126,x10122)) % 168.22/168.07 [1013]~E(x10131,x10132)+E(f410(x10131,x10133,x10134,x10135,x10136),f410(x10132,x10133,x10134,x10135,x10136)) % 168.22/168.07 [1014]~E(x10141,x10142)+E(f410(x10143,x10141,x10144,x10145,x10146),f410(x10143,x10142,x10144,x10145,x10146)) % 168.22/168.07 [1015]~E(x10151,x10152)+E(f410(x10153,x10154,x10151,x10155,x10156),f410(x10153,x10154,x10152,x10155,x10156)) % 168.22/168.07 [1016]~E(x10161,x10162)+E(f410(x10163,x10164,x10165,x10161,x10166),f410(x10163,x10164,x10165,x10162,x10166)) % 168.22/168.07 [1017]~E(x10171,x10172)+E(f410(x10173,x10174,x10175,x10176,x10171),f410(x10173,x10174,x10175,x10176,x10172)) % 168.22/168.07 [1018]~E(x10181,x10182)+E(f366(x10181,x10183,x10184,x10185),f366(x10182,x10183,x10184,x10185)) % 168.22/168.07 [1019]~E(x10191,x10192)+E(f366(x10193,x10191,x10194,x10195),f366(x10193,x10192,x10194,x10195)) % 168.22/168.07 [1020]~E(x10201,x10202)+E(f366(x10203,x10204,x10201,x10205),f366(x10203,x10204,x10202,x10205)) % 168.22/168.07 [1021]~E(x10211,x10212)+E(f366(x10213,x10214,x10215,x10211),f366(x10213,x10214,x10215,x10212)) % 168.22/168.07 [1022]~E(x10221,x10222)+E(f428(x10221,x10223,x10224,x10225),f428(x10222,x10223,x10224,x10225)) % 168.22/168.07 [1023]~E(x10231,x10232)+E(f428(x10233,x10231,x10234,x10235),f428(x10233,x10232,x10234,x10235)) % 168.22/168.07 [1024]~E(x10241,x10242)+E(f428(x10243,x10244,x10241,x10245),f428(x10243,x10244,x10242,x10245)) % 168.22/168.07 [1025]~E(x10251,x10252)+E(f428(x10253,x10254,x10255,x10251),f428(x10253,x10254,x10255,x10252)) % 168.22/168.07 [1026]~E(x10261,x10262)+E(f430(x10261,x10263,x10264,x10265),f430(x10262,x10263,x10264,x10265)) % 168.22/168.07 [1027]~E(x10271,x10272)+E(f430(x10273,x10271,x10274,x10275),f430(x10273,x10272,x10274,x10275)) % 168.22/168.07 [1028]~E(x10281,x10282)+E(f430(x10283,x10284,x10281,x10285),f430(x10283,x10284,x10282,x10285)) % 168.22/168.07 [1029]~E(x10291,x10292)+E(f430(x10293,x10294,x10295,x10291),f430(x10293,x10294,x10295,x10292)) % 168.22/168.07 [1030]~E(x10301,x10302)+E(f554(x10301,x10303,x10304,x10305),f554(x10302,x10303,x10304,x10305)) % 168.22/168.07 [1031]~E(x10311,x10312)+E(f554(x10313,x10311,x10314,x10315),f554(x10313,x10312,x10314,x10315)) % 168.22/168.07 [1032]~E(x10321,x10322)+E(f554(x10323,x10324,x10321,x10325),f554(x10323,x10324,x10322,x10325)) % 168.22/168.07 [1033]~E(x10331,x10332)+E(f554(x10333,x10334,x10335,x10331),f554(x10333,x10334,x10335,x10332)) % 168.22/168.07 [1034]~E(x10341,x10342)+E(f588(x10341,x10343,x10344,x10345),f588(x10342,x10343,x10344,x10345)) % 168.22/168.07 [1035]~E(x10351,x10352)+E(f588(x10353,x10351,x10354,x10355),f588(x10353,x10352,x10354,x10355)) % 168.22/168.07 [1036]~E(x10361,x10362)+E(f588(x10363,x10364,x10361,x10365),f588(x10363,x10364,x10362,x10365)) % 168.22/168.07 [1037]~E(x10371,x10372)+E(f588(x10373,x10374,x10375,x10371),f588(x10373,x10374,x10375,x10372)) % 168.22/168.07 [1038]~E(x10381,x10382)+E(f591(x10381,x10383,x10384,x10385,x10386),f591(x10382,x10383,x10384,x10385,x10386)) % 168.22/168.07 [1039]~E(x10391,x10392)+E(f591(x10393,x10391,x10394,x10395,x10396),f591(x10393,x10392,x10394,x10395,x10396)) % 168.22/168.07 [1040]~E(x10401,x10402)+E(f591(x10403,x10404,x10401,x10405,x10406),f591(x10403,x10404,x10402,x10405,x10406)) % 168.22/168.07 [1041]~E(x10411,x10412)+E(f591(x10413,x10414,x10415,x10411,x10416),f591(x10413,x10414,x10415,x10412,x10416)) % 168.22/168.07 [1042]~E(x10421,x10422)+E(f591(x10423,x10424,x10425,x10426,x10421),f591(x10423,x10424,x10425,x10426,x10422)) % 168.22/168.07 [1043]~E(x10431,x10432)+E(f594(x10431,x10433,x10434),f594(x10432,x10433,x10434)) % 168.22/168.07 [1044]~E(x10441,x10442)+E(f594(x10443,x10441,x10444),f594(x10443,x10442,x10444)) % 168.22/168.07 [1045]~E(x10451,x10452)+E(f594(x10453,x10454,x10451),f594(x10453,x10454,x10452)) % 168.22/168.07 [1046]~E(x10461,x10462)+E(f473(x10461,x10463,x10464,x10465,x10466),f473(x10462,x10463,x10464,x10465,x10466)) % 168.22/168.07 [1047]~E(x10471,x10472)+E(f473(x10473,x10471,x10474,x10475,x10476),f473(x10473,x10472,x10474,x10475,x10476)) % 168.22/168.07 [1048]~E(x10481,x10482)+E(f473(x10483,x10484,x10481,x10485,x10486),f473(x10483,x10484,x10482,x10485,x10486)) % 168.22/168.07 [1049]~E(x10491,x10492)+E(f473(x10493,x10494,x10495,x10491,x10496),f473(x10493,x10494,x10495,x10492,x10496)) % 168.22/168.07 [1050]~E(x10501,x10502)+E(f473(x10503,x10504,x10505,x10506,x10501),f473(x10503,x10504,x10505,x10506,x10502)) % 168.22/168.07 [1051]~E(x10511,x10512)+E(f792(x10511,x10513,x10514,x10515,x10516),f792(x10512,x10513,x10514,x10515,x10516)) % 168.22/168.07 [1052]~E(x10521,x10522)+E(f792(x10523,x10521,x10524,x10525,x10526),f792(x10523,x10522,x10524,x10525,x10526)) % 168.22/168.07 [1053]~E(x10531,x10532)+E(f792(x10533,x10534,x10531,x10535,x10536),f792(x10533,x10534,x10532,x10535,x10536)) % 168.22/168.07 [1054]~E(x10541,x10542)+E(f792(x10543,x10544,x10545,x10541,x10546),f792(x10543,x10544,x10545,x10542,x10546)) % 168.22/168.07 [1055]~E(x10551,x10552)+E(f792(x10553,x10554,x10555,x10556,x10551),f792(x10553,x10554,x10555,x10556,x10552)) % 168.22/168.07 [1056]~E(x10561,x10562)+E(f534(x10561,x10563,x10564,x10565,x10566),f534(x10562,x10563,x10564,x10565,x10566)) % 168.22/168.07 [1057]~E(x10571,x10572)+E(f534(x10573,x10571,x10574,x10575,x10576),f534(x10573,x10572,x10574,x10575,x10576)) % 168.22/168.07 [1058]~E(x10581,x10582)+E(f534(x10583,x10584,x10581,x10585,x10586),f534(x10583,x10584,x10582,x10585,x10586)) % 168.22/168.07 [1059]~E(x10591,x10592)+E(f534(x10593,x10594,x10595,x10591,x10596),f534(x10593,x10594,x10595,x10592,x10596)) % 168.22/168.07 [1060]~E(x10601,x10602)+E(f534(x10603,x10604,x10605,x10606,x10601),f534(x10603,x10604,x10605,x10606,x10602)) % 168.22/168.07 [1061]~E(x10611,x10612)+E(f489(x10611,x10613,x10614),f489(x10612,x10613,x10614)) % 168.22/168.07 [1062]~E(x10621,x10622)+E(f489(x10623,x10621,x10624),f489(x10623,x10622,x10624)) % 168.22/168.07 [1063]~E(x10631,x10632)+E(f489(x10633,x10634,x10631),f489(x10633,x10634,x10632)) % 168.22/168.07 [1064]~E(x10641,x10642)+E(f249(x10641,x10643,x10644,x10645),f249(x10642,x10643,x10644,x10645)) % 168.22/168.07 [1065]~E(x10651,x10652)+E(f249(x10653,x10651,x10654,x10655),f249(x10653,x10652,x10654,x10655)) % 168.22/168.07 [1066]~E(x10661,x10662)+E(f249(x10663,x10664,x10661,x10665),f249(x10663,x10664,x10662,x10665)) % 168.22/168.07 [1067]~E(x10671,x10672)+E(f249(x10673,x10674,x10675,x10671),f249(x10673,x10674,x10675,x10672)) % 168.22/168.07 [1068]~E(x10681,x10682)+E(f409(x10681,x10683,x10684),f409(x10682,x10683,x10684)) % 168.22/168.07 [1069]~E(x10691,x10692)+E(f409(x10693,x10691,x10694),f409(x10693,x10692,x10694)) % 168.22/168.07 [1070]~E(x10701,x10702)+E(f409(x10703,x10704,x10701),f409(x10703,x10704,x10702)) % 168.22/168.07 [1071]~E(x10711,x10712)+E(f440(x10711,x10713,x10714,x10715),f440(x10712,x10713,x10714,x10715)) % 168.22/168.07 [1072]~E(x10721,x10722)+E(f440(x10723,x10721,x10724,x10725),f440(x10723,x10722,x10724,x10725)) % 168.22/168.07 [1073]~E(x10731,x10732)+E(f440(x10733,x10734,x10731,x10735),f440(x10733,x10734,x10732,x10735)) % 168.22/168.07 [1074]~E(x10741,x10742)+E(f440(x10743,x10744,x10745,x10741),f440(x10743,x10744,x10745,x10742)) % 168.22/168.07 [1075]~E(x10751,x10752)+E(f628(x10751,x10753,x10754),f628(x10752,x10753,x10754)) % 168.22/168.07 [1076]~E(x10761,x10762)+E(f628(x10763,x10761,x10764),f628(x10763,x10762,x10764)) % 168.22/168.07 [1077]~E(x10771,x10772)+E(f628(x10773,x10774,x10771),f628(x10773,x10774,x10772)) % 168.22/168.07 [1078]~E(x10781,x10782)+E(f650(x10781,x10783),f650(x10782,x10783)) % 168.22/168.07 [1079]~E(x10791,x10792)+E(f650(x10793,x10791),f650(x10793,x10792)) % 168.22/168.07 [1080]~E(x10801,x10802)+E(f636(x10801,x10803,x10804,x10805,x10806),f636(x10802,x10803,x10804,x10805,x10806)) % 168.22/168.07 [1081]~E(x10811,x10812)+E(f636(x10813,x10811,x10814,x10815,x10816),f636(x10813,x10812,x10814,x10815,x10816)) % 168.22/168.07 [1082]~E(x10821,x10822)+E(f636(x10823,x10824,x10821,x10825,x10826),f636(x10823,x10824,x10822,x10825,x10826)) % 168.22/168.07 [1083]~E(x10831,x10832)+E(f636(x10833,x10834,x10835,x10831,x10836),f636(x10833,x10834,x10835,x10832,x10836)) % 168.22/168.07 [1084]~E(x10841,x10842)+E(f636(x10843,x10844,x10845,x10846,x10841),f636(x10843,x10844,x10845,x10846,x10842)) % 168.22/168.07 [1085]~E(x10851,x10852)+E(f692(x10851,x10853,x10854,x10855),f692(x10852,x10853,x10854,x10855)) % 168.22/168.07 [1086]~E(x10861,x10862)+E(f692(x10863,x10861,x10864,x10865),f692(x10863,x10862,x10864,x10865)) % 168.22/168.07 [1087]~E(x10871,x10872)+E(f692(x10873,x10874,x10871,x10875),f692(x10873,x10874,x10872,x10875)) % 168.22/168.07 [1088]~E(x10881,x10882)+E(f692(x10883,x10884,x10885,x10881),f692(x10883,x10884,x10885,x10882)) % 168.22/168.07 [1089]~E(x10891,x10892)+E(f374(x10891,x10893),f374(x10892,x10893)) % 168.22/168.07 [1090]~E(x10901,x10902)+E(f374(x10903,x10901),f374(x10903,x10902)) % 168.22/168.07 [1091]~E(x10911,x10912)+E(f538(x10911,x10913,x10914,x10915,x10916,x10917,x10918,x10919),f538(x10912,x10913,x10914,x10915,x10916,x10917,x10918,x10919)) % 168.22/168.07 [1092]~E(x10921,x10922)+E(f538(x10923,x10921,x10924,x10925,x10926,x10927,x10928,x10929),f538(x10923,x10922,x10924,x10925,x10926,x10927,x10928,x10929)) % 168.22/168.07 [1093]~E(x10931,x10932)+E(f538(x10933,x10934,x10931,x10935,x10936,x10937,x10938,x10939),f538(x10933,x10934,x10932,x10935,x10936,x10937,x10938,x10939)) % 168.22/168.07 [1094]~E(x10941,x10942)+E(f538(x10943,x10944,x10945,x10941,x10946,x10947,x10948,x10949),f538(x10943,x10944,x10945,x10942,x10946,x10947,x10948,x10949)) % 168.22/168.07 [1095]~E(x10951,x10952)+E(f538(x10953,x10954,x10955,x10956,x10951,x10957,x10958,x10959),f538(x10953,x10954,x10955,x10956,x10952,x10957,x10958,x10959)) % 168.22/168.07 [1096]~E(x10961,x10962)+E(f538(x10963,x10964,x10965,x10966,x10967,x10961,x10968,x10969),f538(x10963,x10964,x10965,x10966,x10967,x10962,x10968,x10969)) % 168.22/168.07 [1097]~E(x10971,x10972)+E(f538(x10973,x10974,x10975,x10976,x10977,x10978,x10971,x10979),f538(x10973,x10974,x10975,x10976,x10977,x10978,x10972,x10979)) % 168.22/168.07 [1098]~E(x10981,x10982)+E(f538(x10983,x10984,x10985,x10986,x10987,x10988,x10989,x10981),f538(x10983,x10984,x10985,x10986,x10987,x10988,x10989,x10982)) % 168.22/168.07 [1099]~E(x10991,x10992)+E(f348(x10991,x10993,x10994,x10995),f348(x10992,x10993,x10994,x10995)) % 168.22/168.07 [1100]~E(x11001,x11002)+E(f348(x11003,x11001,x11004,x11005),f348(x11003,x11002,x11004,x11005)) % 168.22/168.07 [1101]~E(x11011,x11012)+E(f348(x11013,x11014,x11011,x11015),f348(x11013,x11014,x11012,x11015)) % 168.22/168.07 [1102]~E(x11021,x11022)+E(f348(x11023,x11024,x11025,x11021),f348(x11023,x11024,x11025,x11022)) % 168.22/168.07 [1103]~E(x11031,x11032)+E(f477(x11031,x11033,x11034,x11035,x11036,x11037),f477(x11032,x11033,x11034,x11035,x11036,x11037)) % 168.22/168.07 [1104]~E(x11041,x11042)+E(f477(x11043,x11041,x11044,x11045,x11046,x11047),f477(x11043,x11042,x11044,x11045,x11046,x11047)) % 168.22/168.07 [1105]~E(x11051,x11052)+E(f477(x11053,x11054,x11051,x11055,x11056,x11057),f477(x11053,x11054,x11052,x11055,x11056,x11057)) % 168.22/168.07 [1106]~E(x11061,x11062)+E(f477(x11063,x11064,x11065,x11061,x11066,x11067),f477(x11063,x11064,x11065,x11062,x11066,x11067)) % 168.22/168.07 [1107]~E(x11071,x11072)+E(f477(x11073,x11074,x11075,x11076,x11071,x11077),f477(x11073,x11074,x11075,x11076,x11072,x11077)) % 168.22/168.07 [1108]~E(x11081,x11082)+E(f477(x11083,x11084,x11085,x11086,x11087,x11081),f477(x11083,x11084,x11085,x11086,x11087,x11082)) % 168.22/168.07 [1109]~E(x11091,x11092)+E(f677(x11091,x11093,x11094),f677(x11092,x11093,x11094)) % 168.22/168.07 [1110]~E(x11101,x11102)+E(f677(x11103,x11101,x11104),f677(x11103,x11102,x11104)) % 168.22/168.07 [1111]~E(x11111,x11112)+E(f677(x11113,x11114,x11111),f677(x11113,x11114,x11112)) % 168.22/168.07 [1112]~E(x11121,x11122)+E(f468(x11121,x11123,x11124,x11125),f468(x11122,x11123,x11124,x11125)) % 168.22/168.07 [1113]~E(x11131,x11132)+E(f468(x11133,x11131,x11134,x11135),f468(x11133,x11132,x11134,x11135)) % 168.22/168.07 [1114]~E(x11141,x11142)+E(f468(x11143,x11144,x11141,x11145),f468(x11143,x11144,x11142,x11145)) % 168.22/168.07 [1115]~E(x11151,x11152)+E(f468(x11153,x11154,x11155,x11151),f468(x11153,x11154,x11155,x11152)) % 168.22/168.07 [1116]~E(x11161,x11162)+E(f37(x11161,x11163,x11164,x11165,x11166,x11167,x11168,x11169,x111610,x111611),f37(x11162,x11163,x11164,x11165,x11166,x11167,x11168,x11169,x111610,x111611)) % 168.22/168.07 [1117]~E(x11171,x11172)+E(f37(x11173,x11171,x11174,x11175,x11176,x11177,x11178,x11179,x111710,x111711),f37(x11173,x11172,x11174,x11175,x11176,x11177,x11178,x11179,x111710,x111711)) % 168.22/168.07 [1118]~E(x11181,x11182)+E(f37(x11183,x11184,x11181,x11185,x11186,x11187,x11188,x11189,x111810,x111811),f37(x11183,x11184,x11182,x11185,x11186,x11187,x11188,x11189,x111810,x111811)) % 168.22/168.07 [1119]~E(x11191,x11192)+E(f37(x11193,x11194,x11195,x11191,x11196,x11197,x11198,x11199,x111910,x111911),f37(x11193,x11194,x11195,x11192,x11196,x11197,x11198,x11199,x111910,x111911)) % 168.22/168.07 [1120]~E(x11201,x11202)+E(f37(x11203,x11204,x11205,x11206,x11201,x11207,x11208,x11209,x112010,x112011),f37(x11203,x11204,x11205,x11206,x11202,x11207,x11208,x11209,x112010,x112011)) % 168.22/168.07 [1121]~E(x11211,x11212)+E(f37(x11213,x11214,x11215,x11216,x11217,x11211,x11218,x11219,x112110,x112111),f37(x11213,x11214,x11215,x11216,x11217,x11212,x11218,x11219,x112110,x112111)) % 168.22/168.07 [1122]~E(x11221,x11222)+E(f37(x11223,x11224,x11225,x11226,x11227,x11228,x11221,x11229,x112210,x112211),f37(x11223,x11224,x11225,x11226,x11227,x11228,x11222,x11229,x112210,x112211)) % 168.22/168.07 [1123]~E(x11231,x11232)+E(f37(x11233,x11234,x11235,x11236,x11237,x11238,x11239,x11231,x112310,x112311),f37(x11233,x11234,x11235,x11236,x11237,x11238,x11239,x11232,x112310,x112311)) % 168.22/168.07 [1124]~E(x11241,x11242)+E(f37(x11243,x11244,x11245,x11246,x11247,x11248,x11249,x112410,x11241,x112411),f37(x11243,x11244,x11245,x11246,x11247,x11248,x11249,x112410,x11242,x112411)) % 168.22/168.07 [1125]~E(x11251,x11252)+E(f37(x11253,x11254,x11255,x11256,x11257,x11258,x11259,x112510,x112511,x11251),f37(x11253,x11254,x11255,x11256,x11257,x11258,x11259,x112510,x112511,x11252)) % 168.22/168.07 [1126]~E(x11261,x11262)+E(f391(x11261,x11263,x11264),f391(x11262,x11263,x11264)) % 168.22/168.07 [1127]~E(x11271,x11272)+E(f391(x11273,x11271,x11274),f391(x11273,x11272,x11274)) % 168.22/168.07 [1128]~E(x11281,x11282)+E(f391(x11283,x11284,x11281),f391(x11283,x11284,x11282)) % 168.22/168.07 [1129]~E(x11291,x11292)+E(f619(x11291,x11293,x11294,x11295,x11296),f619(x11292,x11293,x11294,x11295,x11296)) % 168.22/168.07 [1130]~E(x11301,x11302)+E(f619(x11303,x11301,x11304,x11305,x11306),f619(x11303,x11302,x11304,x11305,x11306)) % 168.22/168.07 [1131]~E(x11311,x11312)+E(f619(x11313,x11314,x11311,x11315,x11316),f619(x11313,x11314,x11312,x11315,x11316)) % 168.22/168.07 [1132]~E(x11321,x11322)+E(f619(x11323,x11324,x11325,x11321,x11326),f619(x11323,x11324,x11325,x11322,x11326)) % 168.22/168.07 [1133]~E(x11331,x11332)+E(f619(x11333,x11334,x11335,x11336,x11331),f619(x11333,x11334,x11335,x11336,x11332)) % 168.22/168.07 [1134]~E(x11341,x11342)+E(f780(x11341,x11343,x11344),f780(x11342,x11343,x11344)) % 168.22/168.07 [1135]~E(x11351,x11352)+E(f780(x11353,x11351,x11354),f780(x11353,x11352,x11354)) % 168.22/168.07 [1136]~E(x11361,x11362)+E(f780(x11363,x11364,x11361),f780(x11363,x11364,x11362)) % 168.22/168.07 [1137]~E(x11371,x11372)+E(f134(x11371,x11373,x11374),f134(x11372,x11373,x11374)) % 168.22/168.07 [1138]~E(x11381,x11382)+E(f134(x11383,x11381,x11384),f134(x11383,x11382,x11384)) % 168.22/168.07 [1139]~E(x11391,x11392)+E(f134(x11393,x11394,x11391),f134(x11393,x11394,x11392)) % 168.22/168.07 [1140]~E(x11401,x11402)+E(f808(x11401,x11403,x11404),f808(x11402,x11403,x11404)) % 168.22/168.07 [1141]~E(x11411,x11412)+E(f808(x11413,x11411,x11414),f808(x11413,x11412,x11414)) % 168.22/168.07 [1142]~E(x11421,x11422)+E(f808(x11423,x11424,x11421),f808(x11423,x11424,x11422)) % 168.22/168.07 [1143]~E(x11431,x11432)+E(f144(x11431,x11433,x11434,x11435,x11436),f144(x11432,x11433,x11434,x11435,x11436)) % 168.22/168.07 [1144]~E(x11441,x11442)+E(f144(x11443,x11441,x11444,x11445,x11446),f144(x11443,x11442,x11444,x11445,x11446)) % 168.22/168.07 [1145]~E(x11451,x11452)+E(f144(x11453,x11454,x11451,x11455,x11456),f144(x11453,x11454,x11452,x11455,x11456)) % 168.22/168.07 [1146]~E(x11461,x11462)+E(f144(x11463,x11464,x11465,x11461,x11466),f144(x11463,x11464,x11465,x11462,x11466)) % 168.22/168.07 [1147]~E(x11471,x11472)+E(f144(x11473,x11474,x11475,x11476,x11471),f144(x11473,x11474,x11475,x11476,x11472)) % 168.22/168.07 [1148]~E(x11481,x11482)+E(f720(x11481,x11483,x11484),f720(x11482,x11483,x11484)) % 168.22/168.07 [1149]~E(x11491,x11492)+E(f720(x11493,x11491,x11494),f720(x11493,x11492,x11494)) % 168.22/168.07 [1150]~E(x11501,x11502)+E(f720(x11503,x11504,x11501),f720(x11503,x11504,x11502)) % 168.22/168.07 [1151]~E(x11511,x11512)+E(f779(x11511,x11513,x11514,x11515,x11516),f779(x11512,x11513,x11514,x11515,x11516)) % 168.22/168.07 [1152]~E(x11521,x11522)+E(f779(x11523,x11521,x11524,x11525,x11526),f779(x11523,x11522,x11524,x11525,x11526)) % 168.22/168.07 [1153]~E(x11531,x11532)+E(f779(x11533,x11534,x11531,x11535,x11536),f779(x11533,x11534,x11532,x11535,x11536)) % 168.22/168.07 [1154]~E(x11541,x11542)+E(f779(x11543,x11544,x11545,x11541,x11546),f779(x11543,x11544,x11545,x11542,x11546)) % 168.22/168.07 [1155]~E(x11551,x11552)+E(f779(x11553,x11554,x11555,x11556,x11551),f779(x11553,x11554,x11555,x11556,x11552)) % 168.22/168.07 [1156]~E(x11561,x11562)+E(f462(x11561,x11563,x11564,x11565),f462(x11562,x11563,x11564,x11565)) % 168.22/168.07 [1157]~E(x11571,x11572)+E(f462(x11573,x11571,x11574,x11575),f462(x11573,x11572,x11574,x11575)) % 168.22/168.07 [1158]~E(x11581,x11582)+E(f462(x11583,x11584,x11581,x11585),f462(x11583,x11584,x11582,x11585)) % 168.22/168.07 [1159]~E(x11591,x11592)+E(f462(x11593,x11594,x11595,x11591),f462(x11593,x11594,x11595,x11592)) % 168.22/168.07 [1160]~E(x11601,x11602)+E(f185(x11601),f185(x11602)) % 168.22/168.07 [1161]~E(x11611,x11612)+E(f734(x11611,x11613,x11614),f734(x11612,x11613,x11614)) % 168.22/168.07 [1162]~E(x11621,x11622)+E(f734(x11623,x11621,x11624),f734(x11623,x11622,x11624)) % 168.22/168.07 [1163]~E(x11631,x11632)+E(f734(x11633,x11634,x11631),f734(x11633,x11634,x11632)) % 168.22/168.07 [1164]~E(x11641,x11642)+E(f354(x11641,x11643,x11644,x11645),f354(x11642,x11643,x11644,x11645)) % 168.22/168.07 [1165]~E(x11651,x11652)+E(f354(x11653,x11651,x11654,x11655),f354(x11653,x11652,x11654,x11655)) % 168.22/168.07 [1166]~E(x11661,x11662)+E(f354(x11663,x11664,x11661,x11665),f354(x11663,x11664,x11662,x11665)) % 168.22/168.07 [1167]~E(x11671,x11672)+E(f354(x11673,x11674,x11675,x11671),f354(x11673,x11674,x11675,x11672)) % 168.22/168.07 [1168]~E(x11681,x11682)+E(f584(x11681,x11683,x11684),f584(x11682,x11683,x11684)) % 168.22/168.07 [1169]~E(x11691,x11692)+E(f584(x11693,x11691,x11694),f584(x11693,x11692,x11694)) % 168.22/168.07 [1170]~E(x11701,x11702)+E(f584(x11703,x11704,x11701),f584(x11703,x11704,x11702)) % 168.22/168.07 [1171]~E(x11711,x11712)+E(f728(x11711,x11713,x11714,x11715,x11716,x11717,x11718),f728(x11712,x11713,x11714,x11715,x11716,x11717,x11718)) % 168.22/168.07 [1172]~E(x11721,x11722)+E(f728(x11723,x11721,x11724,x11725,x11726,x11727,x11728),f728(x11723,x11722,x11724,x11725,x11726,x11727,x11728)) % 168.22/168.07 [1173]~E(x11731,x11732)+E(f728(x11733,x11734,x11731,x11735,x11736,x11737,x11738),f728(x11733,x11734,x11732,x11735,x11736,x11737,x11738)) % 168.22/168.07 [1174]~E(x11741,x11742)+E(f728(x11743,x11744,x11745,x11741,x11746,x11747,x11748),f728(x11743,x11744,x11745,x11742,x11746,x11747,x11748)) % 168.22/168.07 [1175]~E(x11751,x11752)+E(f728(x11753,x11754,x11755,x11756,x11751,x11757,x11758),f728(x11753,x11754,x11755,x11756,x11752,x11757,x11758)) % 168.22/168.07 [1176]~E(x11761,x11762)+E(f728(x11763,x11764,x11765,x11766,x11767,x11761,x11768),f728(x11763,x11764,x11765,x11766,x11767,x11762,x11768)) % 168.22/168.07 [1177]~E(x11771,x11772)+E(f728(x11773,x11774,x11775,x11776,x11777,x11778,x11771),f728(x11773,x11774,x11775,x11776,x11777,x11778,x11772)) % 168.22/168.07 [1178]~E(x11781,x11782)+E(f600(x11781,x11783,x11784,x11785,x11786),f600(x11782,x11783,x11784,x11785,x11786)) % 168.22/168.07 [1179]~E(x11791,x11792)+E(f600(x11793,x11791,x11794,x11795,x11796),f600(x11793,x11792,x11794,x11795,x11796)) % 168.22/168.07 [1180]~E(x11801,x11802)+E(f600(x11803,x11804,x11801,x11805,x11806),f600(x11803,x11804,x11802,x11805,x11806)) % 168.22/168.07 [1181]~E(x11811,x11812)+E(f600(x11813,x11814,x11815,x11811,x11816),f600(x11813,x11814,x11815,x11812,x11816)) % 168.22/168.07 [1182]~E(x11821,x11822)+E(f600(x11823,x11824,x11825,x11826,x11821),f600(x11823,x11824,x11825,x11826,x11822)) % 168.22/168.07 [1183]~E(x11831,x11832)+E(f823(x11831,x11833),f823(x11832,x11833)) % 168.22/168.07 [1184]~E(x11841,x11842)+E(f823(x11843,x11841),f823(x11843,x11842)) % 168.22/168.07 [1185]~E(x11851,x11852)+E(f611(x11851,x11853,x11854,x11855,x11856,x11857),f611(x11852,x11853,x11854,x11855,x11856,x11857)) % 168.22/168.07 [1186]~E(x11861,x11862)+E(f611(x11863,x11861,x11864,x11865,x11866,x11867),f611(x11863,x11862,x11864,x11865,x11866,x11867)) % 168.22/168.07 [1187]~E(x11871,x11872)+E(f611(x11873,x11874,x11871,x11875,x11876,x11877),f611(x11873,x11874,x11872,x11875,x11876,x11877)) % 168.22/168.07 [1188]~E(x11881,x11882)+E(f611(x11883,x11884,x11885,x11881,x11886,x11887),f611(x11883,x11884,x11885,x11882,x11886,x11887)) % 168.22/168.07 [1189]~E(x11891,x11892)+E(f611(x11893,x11894,x11895,x11896,x11891,x11897),f611(x11893,x11894,x11895,x11896,x11892,x11897)) % 168.22/168.07 [1190]~E(x11901,x11902)+E(f611(x11903,x11904,x11905,x11906,x11907,x11901),f611(x11903,x11904,x11905,x11906,x11907,x11902)) % 168.22/168.07 [1191]~E(x11911,x11912)+E(f413(x11911,x11913,x11914,x11915,x11916),f413(x11912,x11913,x11914,x11915,x11916)) % 168.22/168.07 [1192]~E(x11921,x11922)+E(f413(x11923,x11921,x11924,x11925,x11926),f413(x11923,x11922,x11924,x11925,x11926)) % 168.22/168.07 [1193]~E(x11931,x11932)+E(f413(x11933,x11934,x11931,x11935,x11936),f413(x11933,x11934,x11932,x11935,x11936)) % 168.22/168.07 [1194]~E(x11941,x11942)+E(f413(x11943,x11944,x11945,x11941,x11946),f413(x11943,x11944,x11945,x11942,x11946)) % 168.22/168.07 [1195]~E(x11951,x11952)+E(f413(x11953,x11954,x11955,x11956,x11951),f413(x11953,x11954,x11955,x11956,x11952)) % 168.22/168.07 [1196]~E(x11961,x11962)+E(f605(x11961,x11963,x11964,x11965),f605(x11962,x11963,x11964,x11965)) % 168.22/168.07 [1197]~E(x11971,x11972)+E(f605(x11973,x11971,x11974,x11975),f605(x11973,x11972,x11974,x11975)) % 168.22/168.07 [1198]~E(x11981,x11982)+E(f605(x11983,x11984,x11981,x11985),f605(x11983,x11984,x11982,x11985)) % 168.22/168.07 [1199]~E(x11991,x11992)+E(f605(x11993,x11994,x11995,x11991),f605(x11993,x11994,x11995,x11992)) % 168.22/168.07 [1200]~E(x12001,x12002)+E(f624(x12001,x12003,x12004,x12005),f624(x12002,x12003,x12004,x12005)) % 168.22/168.07 [1201]~E(x12011,x12012)+E(f624(x12013,x12011,x12014,x12015),f624(x12013,x12012,x12014,x12015)) % 168.22/168.07 [1202]~E(x12021,x12022)+E(f624(x12023,x12024,x12021,x12025),f624(x12023,x12024,x12022,x12025)) % 168.22/168.07 [1203]~E(x12031,x12032)+E(f624(x12033,x12034,x12035,x12031),f624(x12033,x12034,x12035,x12032)) % 168.22/168.07 [1204]~E(x12041,x12042)+E(f684(x12041,x12043),f684(x12042,x12043)) % 168.22/168.07 [1205]~E(x12051,x12052)+E(f684(x12053,x12051),f684(x12053,x12052)) % 168.22/168.07 [1206]~E(x12061,x12062)+E(f157(x12061,x12063,x12064,x12065),f157(x12062,x12063,x12064,x12065)) % 168.22/168.07 [1207]~E(x12071,x12072)+E(f157(x12073,x12071,x12074,x12075),f157(x12073,x12072,x12074,x12075)) % 168.22/168.07 [1208]~E(x12081,x12082)+E(f157(x12083,x12084,x12081,x12085),f157(x12083,x12084,x12082,x12085)) % 168.22/168.07 [1209]~E(x12091,x12092)+E(f157(x12093,x12094,x12095,x12091),f157(x12093,x12094,x12095,x12092)) % 168.22/168.07 [1210]~E(x12101,x12102)+E(f447(x12101,x12103,x12104,x12105),f447(x12102,x12103,x12104,x12105)) % 168.22/168.07 [1211]~E(x12111,x12112)+E(f447(x12113,x12111,x12114,x12115),f447(x12113,x12112,x12114,x12115)) % 168.22/168.07 [1212]~E(x12121,x12122)+E(f447(x12123,x12124,x12121,x12125),f447(x12123,x12124,x12122,x12125)) % 168.22/168.07 [1213]~E(x12131,x12132)+E(f447(x12133,x12134,x12135,x12131),f447(x12133,x12134,x12135,x12132)) % 168.22/168.07 [1214]~E(x12141,x12142)+E(f781(x12141,x12143,x12144),f781(x12142,x12143,x12144)) % 168.22/168.07 [1215]~E(x12151,x12152)+E(f781(x12153,x12151,x12154),f781(x12153,x12152,x12154)) % 168.22/168.07 [1216]~E(x12161,x12162)+E(f781(x12163,x12164,x12161),f781(x12163,x12164,x12162)) % 168.22/168.07 [1217]~E(x12171,x12172)+E(f763(x12171,x12173,x12174,x12175,x12176,x12177),f763(x12172,x12173,x12174,x12175,x12176,x12177)) % 168.22/168.07 [1218]~E(x12181,x12182)+E(f763(x12183,x12181,x12184,x12185,x12186,x12187),f763(x12183,x12182,x12184,x12185,x12186,x12187)) % 168.22/168.07 [1219]~E(x12191,x12192)+E(f763(x12193,x12194,x12191,x12195,x12196,x12197),f763(x12193,x12194,x12192,x12195,x12196,x12197)) % 168.22/168.07 [1220]~E(x12201,x12202)+E(f763(x12203,x12204,x12205,x12201,x12206,x12207),f763(x12203,x12204,x12205,x12202,x12206,x12207)) % 168.22/168.07 [1221]~E(x12211,x12212)+E(f763(x12213,x12214,x12215,x12216,x12211,x12217),f763(x12213,x12214,x12215,x12216,x12212,x12217)) % 168.22/168.07 [1222]~E(x12221,x12222)+E(f763(x12223,x12224,x12225,x12226,x12227,x12221),f763(x12223,x12224,x12225,x12226,x12227,x12222)) % 168.22/168.07 [1223]~E(x12231,x12232)+E(f820(x12231),f820(x12232)) % 168.22/168.07 [1224]~E(x12241,x12242)+E(f716(x12241,x12243,x12244,x12245),f716(x12242,x12243,x12244,x12245)) % 168.22/168.07 [1225]~E(x12251,x12252)+E(f716(x12253,x12251,x12254,x12255),f716(x12253,x12252,x12254,x12255)) % 168.22/168.07 [1226]~E(x12261,x12262)+E(f716(x12263,x12264,x12261,x12265),f716(x12263,x12264,x12262,x12265)) % 168.22/168.07 [1227]~E(x12271,x12272)+E(f716(x12273,x12274,x12275,x12271),f716(x12273,x12274,x12275,x12272)) % 168.22/168.07 [1228]~E(x12281,x12282)+E(f213(x12281,x12283,x12284,x12285,x12286),f213(x12282,x12283,x12284,x12285,x12286)) % 168.22/168.07 [1229]~E(x12291,x12292)+E(f213(x12293,x12291,x12294,x12295,x12296),f213(x12293,x12292,x12294,x12295,x12296)) % 168.22/168.07 [1230]~E(x12301,x12302)+E(f213(x12303,x12304,x12301,x12305,x12306),f213(x12303,x12304,x12302,x12305,x12306)) % 168.22/168.07 [1231]~E(x12311,x12312)+E(f213(x12313,x12314,x12315,x12311,x12316),f213(x12313,x12314,x12315,x12312,x12316)) % 168.22/168.07 [1232]~E(x12321,x12322)+E(f213(x12323,x12324,x12325,x12326,x12321),f213(x12323,x12324,x12325,x12326,x12322)) % 168.22/168.07 [1233]~E(x12331,x12332)+E(f706(x12331,x12333,x12334,x12335,x12336,x12337,x12338,x12339),f706(x12332,x12333,x12334,x12335,x12336,x12337,x12338,x12339)) % 168.22/168.07 [1234]~E(x12341,x12342)+E(f706(x12343,x12341,x12344,x12345,x12346,x12347,x12348,x12349),f706(x12343,x12342,x12344,x12345,x12346,x12347,x12348,x12349)) % 168.22/168.07 [1235]~E(x12351,x12352)+E(f706(x12353,x12354,x12351,x12355,x12356,x12357,x12358,x12359),f706(x12353,x12354,x12352,x12355,x12356,x12357,x12358,x12359)) % 168.22/168.07 [1236]~E(x12361,x12362)+E(f706(x12363,x12364,x12365,x12361,x12366,x12367,x12368,x12369),f706(x12363,x12364,x12365,x12362,x12366,x12367,x12368,x12369)) % 168.22/168.07 [1237]~E(x12371,x12372)+E(f706(x12373,x12374,x12375,x12376,x12371,x12377,x12378,x12379),f706(x12373,x12374,x12375,x12376,x12372,x12377,x12378,x12379)) % 168.22/168.07 [1238]~E(x12381,x12382)+E(f706(x12383,x12384,x12385,x12386,x12387,x12381,x12388,x12389),f706(x12383,x12384,x12385,x12386,x12387,x12382,x12388,x12389)) % 168.22/168.07 [1239]~E(x12391,x12392)+E(f706(x12393,x12394,x12395,x12396,x12397,x12398,x12391,x12399),f706(x12393,x12394,x12395,x12396,x12397,x12398,x12392,x12399)) % 168.22/168.07 [1240]~E(x12401,x12402)+E(f706(x12403,x12404,x12405,x12406,x12407,x12408,x12409,x12401),f706(x12403,x12404,x12405,x12406,x12407,x12408,x12409,x12402)) % 168.22/168.07 [1241]~E(x12411,x12412)+E(f291(x12411,x12413,x12414),f291(x12412,x12413,x12414)) % 168.22/168.07 [1242]~E(x12421,x12422)+E(f291(x12423,x12421,x12424),f291(x12423,x12422,x12424)) % 168.22/168.07 [1243]~E(x12431,x12432)+E(f291(x12433,x12434,x12431),f291(x12433,x12434,x12432)) % 168.22/168.07 [1244]~E(x12441,x12442)+E(f523(x12441,x12443,x12444,x12445),f523(x12442,x12443,x12444,x12445)) % 168.22/168.07 [1245]~E(x12451,x12452)+E(f523(x12453,x12451,x12454,x12455),f523(x12453,x12452,x12454,x12455)) % 168.22/168.07 [1246]~E(x12461,x12462)+E(f523(x12463,x12464,x12461,x12465),f523(x12463,x12464,x12462,x12465)) % 168.22/168.07 [1247]~E(x12471,x12472)+E(f523(x12473,x12474,x12475,x12471),f523(x12473,x12474,x12475,x12472)) % 168.22/168.07 [1248]~E(x12481,x12482)+E(f444(x12481,x12483),f444(x12482,x12483)) % 168.22/168.07 [1249]~E(x12491,x12492)+E(f444(x12493,x12491),f444(x12493,x12492)) % 168.22/168.07 [1250]~E(x12501,x12502)+E(f300(x12501,x12503,x12504,x12505),f300(x12502,x12503,x12504,x12505)) % 168.22/168.07 [1251]~E(x12511,x12512)+E(f300(x12513,x12511,x12514,x12515),f300(x12513,x12512,x12514,x12515)) % 168.22/168.07 [1252]~E(x12521,x12522)+E(f300(x12523,x12524,x12521,x12525),f300(x12523,x12524,x12522,x12525)) % 168.22/168.07 [1253]~E(x12531,x12532)+E(f300(x12533,x12534,x12535,x12531),f300(x12533,x12534,x12535,x12532)) % 168.22/168.07 [1254]~E(x12541,x12542)+E(f777(x12541,x12543,x12544,x12545,x12546),f777(x12542,x12543,x12544,x12545,x12546)) % 168.22/168.07 [1255]~E(x12551,x12552)+E(f777(x12553,x12551,x12554,x12555,x12556),f777(x12553,x12552,x12554,x12555,x12556)) % 168.22/168.07 [1256]~E(x12561,x12562)+E(f777(x12563,x12564,x12561,x12565,x12566),f777(x12563,x12564,x12562,x12565,x12566)) % 168.22/168.07 [1257]~E(x12571,x12572)+E(f777(x12573,x12574,x12575,x12571,x12576),f777(x12573,x12574,x12575,x12572,x12576)) % 168.22/168.07 [1258]~E(x12581,x12582)+E(f777(x12583,x12584,x12585,x12586,x12581),f777(x12583,x12584,x12585,x12586,x12582)) % 168.22/168.07 [1259]~E(x12591,x12592)+E(f357(x12591,x12593,x12594,x12595,x12596,x12597,x12598,x12599,x125910),f357(x12592,x12593,x12594,x12595,x12596,x12597,x12598,x12599,x125910)) % 168.22/168.07 [1260]~E(x12601,x12602)+E(f357(x12603,x12601,x12604,x12605,x12606,x12607,x12608,x12609,x126010),f357(x12603,x12602,x12604,x12605,x12606,x12607,x12608,x12609,x126010)) % 168.22/168.07 [1261]~E(x12611,x12612)+E(f357(x12613,x12614,x12611,x12615,x12616,x12617,x12618,x12619,x126110),f357(x12613,x12614,x12612,x12615,x12616,x12617,x12618,x12619,x126110)) % 168.22/168.07 [1262]~E(x12621,x12622)+E(f357(x12623,x12624,x12625,x12621,x12626,x12627,x12628,x12629,x126210),f357(x12623,x12624,x12625,x12622,x12626,x12627,x12628,x12629,x126210)) % 168.22/168.07 [1263]~E(x12631,x12632)+E(f357(x12633,x12634,x12635,x12636,x12631,x12637,x12638,x12639,x126310),f357(x12633,x12634,x12635,x12636,x12632,x12637,x12638,x12639,x126310)) % 168.22/168.07 [1264]~E(x12641,x12642)+E(f357(x12643,x12644,x12645,x12646,x12647,x12641,x12648,x12649,x126410),f357(x12643,x12644,x12645,x12646,x12647,x12642,x12648,x12649,x126410)) % 168.22/168.07 [1265]~E(x12651,x12652)+E(f357(x12653,x12654,x12655,x12656,x12657,x12658,x12651,x12659,x126510),f357(x12653,x12654,x12655,x12656,x12657,x12658,x12652,x12659,x126510)) % 168.22/168.07 [1266]~E(x12661,x12662)+E(f357(x12663,x12664,x12665,x12666,x12667,x12668,x12669,x12661,x126610),f357(x12663,x12664,x12665,x12666,x12667,x12668,x12669,x12662,x126610)) % 168.22/168.07 [1267]~E(x12671,x12672)+E(f357(x12673,x12674,x12675,x12676,x12677,x12678,x12679,x126710,x12671),f357(x12673,x12674,x12675,x12676,x12677,x12678,x12679,x126710,x12672)) % 168.22/168.07 [1268]~E(x12681,x12682)+E(f660(x12681,x12683,x12684),f660(x12682,x12683,x12684)) % 168.22/168.07 [1269]~E(x12691,x12692)+E(f660(x12693,x12691,x12694),f660(x12693,x12692,x12694)) % 168.22/168.07 [1270]~E(x12701,x12702)+E(f660(x12703,x12704,x12701),f660(x12703,x12704,x12702)) % 168.22/168.07 [1271]~E(x12711,x12712)+E(f441(x12711,x12713,x12714,x12715),f441(x12712,x12713,x12714,x12715)) % 168.22/168.07 [1272]~E(x12721,x12722)+E(f441(x12723,x12721,x12724,x12725),f441(x12723,x12722,x12724,x12725)) % 168.22/168.07 [1273]~E(x12731,x12732)+E(f441(x12733,x12734,x12731,x12735),f441(x12733,x12734,x12732,x12735)) % 168.22/168.07 [1274]~E(x12741,x12742)+E(f441(x12743,x12744,x12745,x12741),f441(x12743,x12744,x12745,x12742)) % 168.22/168.07 [1275]~E(x12751,x12752)+E(f539(x12751,x12753,x12754),f539(x12752,x12753,x12754)) % 168.22/168.07 [1276]~E(x12761,x12762)+E(f539(x12763,x12761,x12764),f539(x12763,x12762,x12764)) % 168.22/168.07 [1277]~E(x12771,x12772)+E(f539(x12773,x12774,x12771),f539(x12773,x12774,x12772)) % 168.22/168.07 [1278]~E(x12781,x12782)+E(f597(x12781,x12783,x12784),f597(x12782,x12783,x12784)) % 168.22/168.07 [1279]~E(x12791,x12792)+E(f597(x12793,x12791,x12794),f597(x12793,x12792,x12794)) % 168.22/168.07 [1280]~E(x12801,x12802)+E(f597(x12803,x12804,x12801),f597(x12803,x12804,x12802)) % 168.22/168.07 [1281]~E(x12811,x12812)+E(f415(x12811,x12813,x12814,x12815),f415(x12812,x12813,x12814,x12815)) % 168.22/168.07 [1282]~E(x12821,x12822)+E(f415(x12823,x12821,x12824,x12825),f415(x12823,x12822,x12824,x12825)) % 168.22/168.07 [1283]~E(x12831,x12832)+E(f415(x12833,x12834,x12831,x12835),f415(x12833,x12834,x12832,x12835)) % 168.22/168.07 [1284]~E(x12841,x12842)+E(f415(x12843,x12844,x12845,x12841),f415(x12843,x12844,x12845,x12842)) % 168.22/168.07 [1285]~E(x12851,x12852)+E(f411(x12851,x12853,x12854,x12855,x12856),f411(x12852,x12853,x12854,x12855,x12856)) % 168.22/168.07 [1286]~E(x12861,x12862)+E(f411(x12863,x12861,x12864,x12865,x12866),f411(x12863,x12862,x12864,x12865,x12866)) % 168.22/168.07 [1287]~E(x12871,x12872)+E(f411(x12873,x12874,x12871,x12875,x12876),f411(x12873,x12874,x12872,x12875,x12876)) % 168.22/168.07 [1288]~E(x12881,x12882)+E(f411(x12883,x12884,x12885,x12881,x12886),f411(x12883,x12884,x12885,x12882,x12886)) % 168.22/168.07 [1289]~E(x12891,x12892)+E(f411(x12893,x12894,x12895,x12896,x12891),f411(x12893,x12894,x12895,x12896,x12892)) % 168.22/168.07 [1290]~E(x12901,x12902)+E(f788(x12901,x12903,x12904,x12905,x12906),f788(x12902,x12903,x12904,x12905,x12906)) % 168.22/168.07 [1291]~E(x12911,x12912)+E(f788(x12913,x12911,x12914,x12915,x12916),f788(x12913,x12912,x12914,x12915,x12916)) % 168.22/168.07 [1292]~E(x12921,x12922)+E(f788(x12923,x12924,x12921,x12925,x12926),f788(x12923,x12924,x12922,x12925,x12926)) % 168.22/168.07 [1293]~E(x12931,x12932)+E(f788(x12933,x12934,x12935,x12931,x12936),f788(x12933,x12934,x12935,x12932,x12936)) % 168.22/168.07 [1294]~E(x12941,x12942)+E(f788(x12943,x12944,x12945,x12946,x12941),f788(x12943,x12944,x12945,x12946,x12942)) % 168.22/168.07 [1295]~E(x12951,x12952)+E(f329(x12951,x12953,x12954),f329(x12952,x12953,x12954)) % 168.22/168.07 [1296]~E(x12961,x12962)+E(f329(x12963,x12961,x12964),f329(x12963,x12962,x12964)) % 168.22/168.07 [1297]~E(x12971,x12972)+E(f329(x12973,x12974,x12971),f329(x12973,x12974,x12972)) % 168.22/168.07 [1298]~E(x12981,x12982)+E(f208(x12981,x12983,x12984,x12985),f208(x12982,x12983,x12984,x12985)) % 168.22/168.07 [1299]~E(x12991,x12992)+E(f208(x12993,x12991,x12994,x12995),f208(x12993,x12992,x12994,x12995)) % 168.22/168.07 [1300]~E(x13001,x13002)+E(f208(x13003,x13004,x13001,x13005),f208(x13003,x13004,x13002,x13005)) % 168.22/168.07 [1301]~E(x13011,x13012)+E(f208(x13013,x13014,x13015,x13011),f208(x13013,x13014,x13015,x13012)) % 168.22/168.07 [1302]~E(x13021,x13022)+E(f745(x13021,x13023,x13024),f745(x13022,x13023,x13024)) % 168.22/168.07 [1303]~E(x13031,x13032)+E(f745(x13033,x13031,x13034),f745(x13033,x13032,x13034)) % 168.22/168.07 [1304]~E(x13041,x13042)+E(f745(x13043,x13044,x13041),f745(x13043,x13044,x13042)) % 168.22/168.07 [1305]~E(x13051,x13052)+E(f328(x13051,x13053,x13054),f328(x13052,x13053,x13054)) % 168.22/168.07 [1306]~E(x13061,x13062)+E(f328(x13063,x13061,x13064),f328(x13063,x13062,x13064)) % 168.22/168.07 [1307]~E(x13071,x13072)+E(f328(x13073,x13074,x13071),f328(x13073,x13074,x13072)) % 168.22/168.07 [1308]~E(x13081,x13082)+E(f483(x13081,x13083,x13084,x13085),f483(x13082,x13083,x13084,x13085)) % 168.22/168.07 [1309]~E(x13091,x13092)+E(f483(x13093,x13091,x13094,x13095),f483(x13093,x13092,x13094,x13095)) % 168.22/168.07 [1310]~E(x13101,x13102)+E(f483(x13103,x13104,x13101,x13105),f483(x13103,x13104,x13102,x13105)) % 168.22/168.07 [1311]~E(x13111,x13112)+E(f483(x13113,x13114,x13115,x13111),f483(x13113,x13114,x13115,x13112)) % 168.22/168.07 [1312]~E(x13121,x13122)+E(f494(x13121,x13123,x13124,x13125,x13126),f494(x13122,x13123,x13124,x13125,x13126)) % 168.22/168.07 [1313]~E(x13131,x13132)+E(f494(x13133,x13131,x13134,x13135,x13136),f494(x13133,x13132,x13134,x13135,x13136)) % 168.22/168.07 [1314]~E(x13141,x13142)+E(f494(x13143,x13144,x13141,x13145,x13146),f494(x13143,x13144,x13142,x13145,x13146)) % 168.22/168.07 [1315]~E(x13151,x13152)+E(f494(x13153,x13154,x13155,x13151,x13156),f494(x13153,x13154,x13155,x13152,x13156)) % 168.22/168.07 [1316]~E(x13161,x13162)+E(f494(x13163,x13164,x13165,x13166,x13161),f494(x13163,x13164,x13165,x13166,x13162)) % 168.22/168.07 [1317]~E(x13171,x13172)+E(f271(x13171,x13173,x13174),f271(x13172,x13173,x13174)) % 168.22/168.07 [1318]~E(x13181,x13182)+E(f271(x13183,x13181,x13184),f271(x13183,x13182,x13184)) % 168.22/168.07 [1319]~E(x13191,x13192)+E(f271(x13193,x13194,x13191),f271(x13193,x13194,x13192)) % 168.22/168.07 [1320]~E(x13201,x13202)+E(f634(x13201,x13203,x13204,x13205),f634(x13202,x13203,x13204,x13205)) % 168.22/168.07 [1321]~E(x13211,x13212)+E(f634(x13213,x13211,x13214,x13215),f634(x13213,x13212,x13214,x13215)) % 168.22/168.07 [1322]~E(x13221,x13222)+E(f634(x13223,x13224,x13221,x13225),f634(x13223,x13224,x13222,x13225)) % 168.22/168.07 [1323]~E(x13231,x13232)+E(f634(x13233,x13234,x13235,x13231),f634(x13233,x13234,x13235,x13232)) % 168.22/168.07 [1324]~E(x13241,x13242)+E(f322(x13241),f322(x13242)) % 168.22/168.07 [1325]~E(x13251,x13252)+E(f69(x13251,x13253,x13254,x13255),f69(x13252,x13253,x13254,x13255)) % 168.22/168.07 [1326]~E(x13261,x13262)+E(f69(x13263,x13261,x13264,x13265),f69(x13263,x13262,x13264,x13265)) % 168.22/168.07 [1327]~E(x13271,x13272)+E(f69(x13273,x13274,x13271,x13275),f69(x13273,x13274,x13272,x13275)) % 168.22/168.07 [1328]~E(x13281,x13282)+E(f69(x13283,x13284,x13285,x13281),f69(x13283,x13284,x13285,x13282)) % 168.22/168.07 [1329]~E(x13291,x13292)+E(f802(x13291),f802(x13292)) % 168.22/168.07 [1330]~E(x13301,x13302)+E(f330(x13301,x13303,x13304),f330(x13302,x13303,x13304)) % 168.22/168.07 [1331]~E(x13311,x13312)+E(f330(x13313,x13311,x13314),f330(x13313,x13312,x13314)) % 168.22/168.07 [1332]~E(x13321,x13322)+E(f330(x13323,x13324,x13321),f330(x13323,x13324,x13322)) % 168.22/168.07 [1333]~E(x13331,x13332)+E(f376(x13331,x13333,x13334,x13335),f376(x13332,x13333,x13334,x13335)) % 168.22/168.07 [1334]~E(x13341,x13342)+E(f376(x13343,x13341,x13344,x13345),f376(x13343,x13342,x13344,x13345)) % 168.22/168.07 [1335]~E(x13351,x13352)+E(f376(x13353,x13354,x13351,x13355),f376(x13353,x13354,x13352,x13355)) % 168.22/168.07 [1336]~E(x13361,x13362)+E(f376(x13363,x13364,x13365,x13361),f376(x13363,x13364,x13365,x13362)) % 168.22/168.07 [1337]~E(x13371,x13372)+E(f711(x13371,x13373,x13374,x13375,x13376,x13377),f711(x13372,x13373,x13374,x13375,x13376,x13377)) % 168.22/168.07 [1338]~E(x13381,x13382)+E(f711(x13383,x13381,x13384,x13385,x13386,x13387),f711(x13383,x13382,x13384,x13385,x13386,x13387)) % 168.22/168.07 [1339]~E(x13391,x13392)+E(f711(x13393,x13394,x13391,x13395,x13396,x13397),f711(x13393,x13394,x13392,x13395,x13396,x13397)) % 168.22/168.07 [1340]~E(x13401,x13402)+E(f711(x13403,x13404,x13405,x13401,x13406,x13407),f711(x13403,x13404,x13405,x13402,x13406,x13407)) % 168.22/168.07 [1341]~E(x13411,x13412)+E(f711(x13413,x13414,x13415,x13416,x13411,x13417),f711(x13413,x13414,x13415,x13416,x13412,x13417)) % 168.22/168.07 [1342]~E(x13421,x13422)+E(f711(x13423,x13424,x13425,x13426,x13427,x13421),f711(x13423,x13424,x13425,x13426,x13427,x13422)) % 168.22/168.07 [1343]~E(x13431,x13432)+E(f657(x13431,x13433),f657(x13432,x13433)) % 168.22/168.07 [1344]~E(x13441,x13442)+E(f657(x13443,x13441),f657(x13443,x13442)) % 168.22/168.07 [1345]~E(x13451,x13452)+E(f501(x13451,x13453,x13454),f501(x13452,x13453,x13454)) % 168.22/168.07 [1346]~E(x13461,x13462)+E(f501(x13463,x13461,x13464),f501(x13463,x13462,x13464)) % 168.22/168.07 [1347]~E(x13471,x13472)+E(f501(x13473,x13474,x13471),f501(x13473,x13474,x13472)) % 168.22/168.07 [1348]~E(x13481,x13482)+E(f488(x13481,x13483,x13484,x13485,x13486),f488(x13482,x13483,x13484,x13485,x13486)) % 168.22/168.07 [1349]~E(x13491,x13492)+E(f488(x13493,x13491,x13494,x13495,x13496),f488(x13493,x13492,x13494,x13495,x13496)) % 168.22/168.07 [1350]~E(x13501,x13502)+E(f488(x13503,x13504,x13501,x13505,x13506),f488(x13503,x13504,x13502,x13505,x13506)) % 168.22/168.07 [1351]~E(x13511,x13512)+E(f488(x13513,x13514,x13515,x13511,x13516),f488(x13513,x13514,x13515,x13512,x13516)) % 168.22/168.07 [1352]~E(x13521,x13522)+E(f488(x13523,x13524,x13525,x13526,x13521),f488(x13523,x13524,x13525,x13526,x13522)) % 168.22/168.07 [1353]~E(x13531,x13532)+E(f446(x13531,x13533),f446(x13532,x13533)) % 168.22/168.07 [1354]~E(x13541,x13542)+E(f446(x13543,x13541),f446(x13543,x13542)) % 168.22/168.07 [1355]~E(x13551,x13552)+E(f586(x13551,x13553,x13554,x13555,x13556),f586(x13552,x13553,x13554,x13555,x13556)) % 168.22/168.07 [1356]~E(x13561,x13562)+E(f586(x13563,x13561,x13564,x13565,x13566),f586(x13563,x13562,x13564,x13565,x13566)) % 168.22/168.07 [1357]~E(x13571,x13572)+E(f586(x13573,x13574,x13571,x13575,x13576),f586(x13573,x13574,x13572,x13575,x13576)) % 168.22/168.07 [1358]~E(x13581,x13582)+E(f586(x13583,x13584,x13585,x13581,x13586),f586(x13583,x13584,x13585,x13582,x13586)) % 168.22/168.07 [1359]~E(x13591,x13592)+E(f586(x13593,x13594,x13595,x13596,x13591),f586(x13593,x13594,x13595,x13596,x13592)) % 168.22/168.07 [1360]~E(x13601,x13602)+E(f158(x13601,x13603,x13604,x13605),f158(x13602,x13603,x13604,x13605)) % 168.22/168.07 [1361]~E(x13611,x13612)+E(f158(x13613,x13611,x13614,x13615),f158(x13613,x13612,x13614,x13615)) % 168.22/168.07 [1362]~E(x13621,x13622)+E(f158(x13623,x13624,x13621,x13625),f158(x13623,x13624,x13622,x13625)) % 168.22/168.07 [1363]~E(x13631,x13632)+E(f158(x13633,x13634,x13635,x13631),f158(x13633,x13634,x13635,x13632)) % 168.22/168.07 [1364]~E(x13641,x13642)+E(f419(x13641,x13643,x13644,x13645),f419(x13642,x13643,x13644,x13645)) % 168.22/168.07 [1365]~E(x13651,x13652)+E(f419(x13653,x13651,x13654,x13655),f419(x13653,x13652,x13654,x13655)) % 168.22/168.07 [1366]~E(x13661,x13662)+E(f419(x13663,x13664,x13661,x13665),f419(x13663,x13664,x13662,x13665)) % 168.22/168.07 [1367]~E(x13671,x13672)+E(f419(x13673,x13674,x13675,x13671),f419(x13673,x13674,x13675,x13672)) % 168.22/168.07 [1368]~E(x13681,x13682)+E(f435(x13681,x13683),f435(x13682,x13683)) % 168.22/168.07 [1369]~E(x13691,x13692)+E(f435(x13693,x13691),f435(x13693,x13692)) % 168.22/168.07 [1370]~E(x13701,x13702)+E(f613(x13701,x13703),f613(x13702,x13703)) % 168.22/168.07 [1371]~E(x13711,x13712)+E(f613(x13713,x13711),f613(x13713,x13712)) % 168.22/168.07 [1372]~E(x13721,x13722)+E(f541(x13721,x13723,x13724,x13725,x13726),f541(x13722,x13723,x13724,x13725,x13726)) % 168.22/168.07 [1373]~E(x13731,x13732)+E(f541(x13733,x13731,x13734,x13735,x13736),f541(x13733,x13732,x13734,x13735,x13736)) % 168.22/168.07 [1374]~E(x13741,x13742)+E(f541(x13743,x13744,x13741,x13745,x13746),f541(x13743,x13744,x13742,x13745,x13746)) % 168.22/168.07 [1375]~E(x13751,x13752)+E(f541(x13753,x13754,x13755,x13751,x13756),f541(x13753,x13754,x13755,x13752,x13756)) % 168.22/168.07 [1376]~E(x13761,x13762)+E(f541(x13763,x13764,x13765,x13766,x13761),f541(x13763,x13764,x13765,x13766,x13762)) % 168.22/168.07 [1377]~E(x13771,x13772)+E(f752(x13771,x13773,x13774),f752(x13772,x13773,x13774)) % 168.22/168.07 [1378]~E(x13781,x13782)+E(f752(x13783,x13781,x13784),f752(x13783,x13782,x13784)) % 168.22/168.07 [1379]~E(x13791,x13792)+E(f752(x13793,x13794,x13791),f752(x13793,x13794,x13792)) % 168.22/168.07 [1380]~E(x13801,x13802)+E(f753(x13801,x13803,x13804),f753(x13802,x13803,x13804)) % 168.22/168.07 [1381]~E(x13811,x13812)+E(f753(x13813,x13811,x13814),f753(x13813,x13812,x13814)) % 168.22/168.07 [1382]~E(x13821,x13822)+E(f753(x13823,x13824,x13821),f753(x13823,x13824,x13822)) % 168.22/168.07 [1383]~E(x13831,x13832)+E(f566(x13831,x13833,x13834),f566(x13832,x13833,x13834)) % 168.22/168.07 [1384]~E(x13841,x13842)+E(f566(x13843,x13841,x13844),f566(x13843,x13842,x13844)) % 168.22/168.07 [1385]~E(x13851,x13852)+E(f566(x13853,x13854,x13851),f566(x13853,x13854,x13852)) % 168.22/168.07 [1386]~E(x13861,x13862)+E(f750(x13861,x13863,x13864),f750(x13862,x13863,x13864)) % 168.22/168.07 [1387]~E(x13871,x13872)+E(f750(x13873,x13871,x13874),f750(x13873,x13872,x13874)) % 168.22/168.07 [1388]~E(x13881,x13882)+E(f750(x13883,x13884,x13881),f750(x13883,x13884,x13882)) % 168.22/168.07 [1389]~E(x13891,x13892)+E(f349(x13891,x13893,x13894),f349(x13892,x13893,x13894)) % 168.22/168.07 [1390]~E(x13901,x13902)+E(f349(x13903,x13901,x13904),f349(x13903,x13902,x13904)) % 168.22/168.07 [1391]~E(x13911,x13912)+E(f349(x13913,x13914,x13911),f349(x13913,x13914,x13912)) % 168.22/168.07 [1392]~E(x13921,x13922)+E(f390(x13921,x13923,x13924),f390(x13922,x13923,x13924)) % 168.22/168.07 [1393]~E(x13931,x13932)+E(f390(x13933,x13931,x13934),f390(x13933,x13932,x13934)) % 168.22/168.07 [1394]~E(x13941,x13942)+E(f390(x13943,x13944,x13941),f390(x13943,x13944,x13942)) % 168.22/168.07 [1395]~E(x13951,x13952)+E(f327(x13951,x13953,x13954),f327(x13952,x13953,x13954)) % 168.22/168.07 [1396]~E(x13961,x13962)+E(f327(x13963,x13961,x13964),f327(x13963,x13962,x13964)) % 168.22/168.07 [1397]~E(x13971,x13972)+E(f327(x13973,x13974,x13971),f327(x13973,x13974,x13972)) % 168.22/168.07 [1398]~E(x13981,x13982)+E(f712(x13981,x13983,x13984,x13985,x13986,x13987),f712(x13982,x13983,x13984,x13985,x13986,x13987)) % 168.22/168.07 [1399]~E(x13991,x13992)+E(f712(x13993,x13991,x13994,x13995,x13996,x13997),f712(x13993,x13992,x13994,x13995,x13996,x13997)) % 168.22/168.07 [1400]~E(x14001,x14002)+E(f712(x14003,x14004,x14001,x14005,x14006,x14007),f712(x14003,x14004,x14002,x14005,x14006,x14007)) % 168.22/168.07 [1401]~E(x14011,x14012)+E(f712(x14013,x14014,x14015,x14011,x14016,x14017),f712(x14013,x14014,x14015,x14012,x14016,x14017)) % 168.22/168.07 [1402]~E(x14021,x14022)+E(f712(x14023,x14024,x14025,x14026,x14021,x14027),f712(x14023,x14024,x14025,x14026,x14022,x14027)) % 168.22/168.07 [1403]~E(x14031,x14032)+E(f712(x14033,x14034,x14035,x14036,x14037,x14031),f712(x14033,x14034,x14035,x14036,x14037,x14032)) % 168.22/168.07 [1404]~E(x14041,x14042)+E(f508(x14041,x14043,x14044,x14045),f508(x14042,x14043,x14044,x14045)) % 168.22/168.07 [1405]~E(x14051,x14052)+E(f508(x14053,x14051,x14054,x14055),f508(x14053,x14052,x14054,x14055)) % 168.22/168.07 [1406]~E(x14061,x14062)+E(f508(x14063,x14064,x14061,x14065),f508(x14063,x14064,x14062,x14065)) % 168.22/168.07 [1407]~E(x14071,x14072)+E(f508(x14073,x14074,x14075,x14071),f508(x14073,x14074,x14075,x14072)) % 168.22/168.07 [1408]~E(x14081,x14082)+E(f368(x14081,x14083),f368(x14082,x14083)) % 168.22/168.07 [1409]~E(x14091,x14092)+E(f368(x14093,x14091),f368(x14093,x14092)) % 168.22/168.07 [1410]~E(x14101,x14102)+E(f649(x14101,x14103),f649(x14102,x14103)) % 168.22/168.07 [1411]~E(x14111,x14112)+E(f649(x14113,x14111),f649(x14113,x14112)) % 168.22/168.07 [1412]~E(x14121,x14122)+E(f359(x14121,x14123),f359(x14122,x14123)) % 168.22/168.07 [1413]~E(x14131,x14132)+E(f359(x14133,x14131),f359(x14133,x14132)) % 168.22/168.07 [1414]~E(x14141,x14142)+E(f596(x14141,x14143),f596(x14142,x14143)) % 168.22/168.07 [1415]~E(x14151,x14152)+E(f596(x14153,x14151),f596(x14153,x14152)) % 168.22/168.07 [1416]~E(x14161,x14162)+E(f361(x14161,x14163),f361(x14162,x14163)) % 168.22/168.07 [1417]~E(x14171,x14172)+E(f361(x14173,x14171),f361(x14173,x14172)) % 168.22/168.07 [1418]~E(x14181,x14182)+E(f683(x14181,x14183,x14184,x14185,x14186),f683(x14182,x14183,x14184,x14185,x14186)) % 168.22/168.07 [1419]~E(x14191,x14192)+E(f683(x14193,x14191,x14194,x14195,x14196),f683(x14193,x14192,x14194,x14195,x14196)) % 168.22/168.07 [1420]~E(x14201,x14202)+E(f683(x14203,x14204,x14201,x14205,x14206),f683(x14203,x14204,x14202,x14205,x14206)) % 168.22/168.07 [1421]~E(x14211,x14212)+E(f683(x14213,x14214,x14215,x14211,x14216),f683(x14213,x14214,x14215,x14212,x14216)) % 168.22/168.07 [1422]~E(x14221,x14222)+E(f683(x14223,x14224,x14225,x14226,x14221),f683(x14223,x14224,x14225,x14226,x14222)) % 168.22/168.07 [1423]~E(x14231,x14232)+E(f839(x14231,x14233),f839(x14232,x14233)) % 168.22/168.07 [1424]~E(x14241,x14242)+E(f839(x14243,x14241),f839(x14243,x14242)) % 168.22/168.07 [1425]~E(x14251,x14252)+E(f417(x14251,x14253,x14254,x14255),f417(x14252,x14253,x14254,x14255)) % 168.22/168.07 [1426]~E(x14261,x14262)+E(f417(x14263,x14261,x14264,x14265),f417(x14263,x14262,x14264,x14265)) % 168.22/168.07 [1427]~E(x14271,x14272)+E(f417(x14273,x14274,x14271,x14275),f417(x14273,x14274,x14272,x14275)) % 168.22/168.07 [1428]~E(x14281,x14282)+E(f417(x14283,x14284,x14285,x14281),f417(x14283,x14284,x14285,x14282)) % 168.22/168.07 [1429]~E(x14291,x14292)+E(f517(x14291,x14293,x14294),f517(x14292,x14293,x14294)) % 168.22/168.07 [1430]~E(x14301,x14302)+E(f517(x14303,x14301,x14304),f517(x14303,x14302,x14304)) % 168.22/168.07 [1431]~E(x14311,x14312)+E(f517(x14313,x14314,x14311),f517(x14313,x14314,x14312)) % 168.22/168.07 [1432]~E(x14321,x14322)+E(f423(x14321,x14323,x14324),f423(x14322,x14323,x14324)) % 168.22/168.07 [1433]~E(x14331,x14332)+E(f423(x14333,x14331,x14334),f423(x14333,x14332,x14334)) % 168.22/168.07 [1434]~E(x14341,x14342)+E(f423(x14343,x14344,x14341),f423(x14343,x14344,x14342)) % 168.22/168.07 [1435]~E(x14351,x14352)+E(f526(x14351,x14353,x14354,x14355,x14356,x14357),f526(x14352,x14353,x14354,x14355,x14356,x14357)) % 168.22/168.07 [1436]~E(x14361,x14362)+E(f526(x14363,x14361,x14364,x14365,x14366,x14367),f526(x14363,x14362,x14364,x14365,x14366,x14367)) % 168.22/168.07 [1437]~E(x14371,x14372)+E(f526(x14373,x14374,x14371,x14375,x14376,x14377),f526(x14373,x14374,x14372,x14375,x14376,x14377)) % 168.22/168.07 [1438]~E(x14381,x14382)+E(f526(x14383,x14384,x14385,x14381,x14386,x14387),f526(x14383,x14384,x14385,x14382,x14386,x14387)) % 168.22/168.07 [1439]~E(x14391,x14392)+E(f526(x14393,x14394,x14395,x14396,x14391,x14397),f526(x14393,x14394,x14395,x14396,x14392,x14397)) % 168.22/168.07 [1440]~E(x14401,x14402)+E(f526(x14403,x14404,x14405,x14406,x14407,x14401),f526(x14403,x14404,x14405,x14406,x14407,x14402)) % 168.22/168.07 [1441]~E(x14411,x14412)+E(f445(x14411,x14413,x14414,x14415),f445(x14412,x14413,x14414,x14415)) % 168.22/168.07 [1442]~E(x14421,x14422)+E(f445(x14423,x14421,x14424,x14425),f445(x14423,x14422,x14424,x14425)) % 168.22/168.07 [1443]~E(x14431,x14432)+E(f445(x14433,x14434,x14431,x14435),f445(x14433,x14434,x14432,x14435)) % 168.22/168.07 [1444]~E(x14441,x14442)+E(f445(x14443,x14444,x14445,x14441),f445(x14443,x14444,x14445,x14442)) % 168.22/168.07 [1445]~E(x14451,x14452)+E(f841(x14451,x14453,x14454,x14455,x14456),f841(x14452,x14453,x14454,x14455,x14456)) % 168.22/168.07 [1446]~E(x14461,x14462)+E(f841(x14463,x14461,x14464,x14465,x14466),f841(x14463,x14462,x14464,x14465,x14466)) % 168.22/168.07 [1447]~E(x14471,x14472)+E(f841(x14473,x14474,x14471,x14475,x14476),f841(x14473,x14474,x14472,x14475,x14476)) % 168.22/168.07 [1448]~E(x14481,x14482)+E(f841(x14483,x14484,x14485,x14481,x14486),f841(x14483,x14484,x14485,x14482,x14486)) % 168.22/168.07 [1449]~E(x14491,x14492)+E(f841(x14493,x14494,x14495,x14496,x14491),f841(x14493,x14494,x14495,x14496,x14492)) % 168.22/168.07 [1450]~E(x14501,x14502)+E(f559(x14501,x14503,x14504),f559(x14502,x14503,x14504)) % 168.22/168.07 [1451]~E(x14511,x14512)+E(f559(x14513,x14511,x14514),f559(x14513,x14512,x14514)) % 168.22/168.07 [1452]~E(x14521,x14522)+E(f559(x14523,x14524,x14521),f559(x14523,x14524,x14522)) % 168.22/168.07 [1453]~E(x14531,x14532)+E(f658(x14531,x14533,x14534),f658(x14532,x14533,x14534)) % 168.22/168.07 [1454]~E(x14541,x14542)+E(f658(x14543,x14541,x14544),f658(x14543,x14542,x14544)) % 168.22/168.07 [1455]~E(x14551,x14552)+E(f658(x14553,x14554,x14551),f658(x14553,x14554,x14552)) % 168.22/168.07 [1456]~E(x14561,x14562)+E(f433(x14561),f433(x14562)) % 168.22/168.07 [1457]~E(x14571,x14572)+E(f758(x14571,x14573,x14574,x14575,x14576),f758(x14572,x14573,x14574,x14575,x14576)) % 168.22/168.07 [1458]~E(x14581,x14582)+E(f758(x14583,x14581,x14584,x14585,x14586),f758(x14583,x14582,x14584,x14585,x14586)) % 168.22/168.07 [1459]~E(x14591,x14592)+E(f758(x14593,x14594,x14591,x14595,x14596),f758(x14593,x14594,x14592,x14595,x14596)) % 168.22/168.07 [1460]~E(x14601,x14602)+E(f758(x14603,x14604,x14605,x14601,x14606),f758(x14603,x14604,x14605,x14602,x14606)) % 168.22/168.07 [1461]~E(x14611,x14612)+E(f758(x14613,x14614,x14615,x14616,x14611),f758(x14613,x14614,x14615,x14616,x14612)) % 168.22/168.07 [1462]~E(x14621,x14622)+E(f258(x14621,x14623,x14624),f258(x14622,x14623,x14624)) % 168.22/168.07 [1463]~E(x14631,x14632)+E(f258(x14633,x14631,x14634),f258(x14633,x14632,x14634)) % 168.22/168.07 [1464]~E(x14641,x14642)+E(f258(x14643,x14644,x14641),f258(x14643,x14644,x14642)) % 168.22/168.07 [1465]~E(x14651,x14652)+E(f260(x14651,x14653,x14654,x14655),f260(x14652,x14653,x14654,x14655)) % 168.22/168.07 [1466]~E(x14661,x14662)+E(f260(x14663,x14661,x14664,x14665),f260(x14663,x14662,x14664,x14665)) % 168.22/168.07 [1467]~E(x14671,x14672)+E(f260(x14673,x14674,x14671,x14675),f260(x14673,x14674,x14672,x14675)) % 168.22/168.07 [1468]~E(x14681,x14682)+E(f260(x14683,x14684,x14685,x14681),f260(x14683,x14684,x14685,x14682)) % 168.22/168.07 [1469]~E(x14691,x14692)+E(f679(x14691,x14693,x14694,x14695),f679(x14692,x14693,x14694,x14695)) % 168.22/168.07 [1470]~E(x14701,x14702)+E(f679(x14703,x14701,x14704,x14705),f679(x14703,x14702,x14704,x14705)) % 168.22/168.07 [1471]~E(x14711,x14712)+E(f679(x14713,x14714,x14711,x14715),f679(x14713,x14714,x14712,x14715)) % 168.22/168.07 [1472]~E(x14721,x14722)+E(f679(x14723,x14724,x14725,x14721),f679(x14723,x14724,x14725,x14722)) % 168.22/168.07 [1473]~E(x14731,x14732)+E(f697(x14731,x14733,x14734,x14735),f697(x14732,x14733,x14734,x14735)) % 168.22/168.07 [1474]~E(x14741,x14742)+E(f697(x14743,x14741,x14744,x14745),f697(x14743,x14742,x14744,x14745)) % 168.22/168.07 [1475]~E(x14751,x14752)+E(f697(x14753,x14754,x14751,x14755),f697(x14753,x14754,x14752,x14755)) % 168.22/168.07 [1476]~E(x14761,x14762)+E(f697(x14763,x14764,x14765,x14761),f697(x14763,x14764,x14765,x14762)) % 168.22/168.07 [1477]~E(x14771,x14772)+E(f789(x14771,x14773,x14774),f789(x14772,x14773,x14774)) % 168.22/168.07 [1478]~E(x14781,x14782)+E(f789(x14783,x14781,x14784),f789(x14783,x14782,x14784)) % 168.22/168.07 [1479]~E(x14791,x14792)+E(f789(x14793,x14794,x14791),f789(x14793,x14794,x14792)) % 168.22/168.07 [1480]~E(x14801,x14802)+E(f215(x14801,x14803,x14804,x14805),f215(x14802,x14803,x14804,x14805)) % 168.22/168.07 [1481]~E(x14811,x14812)+E(f215(x14813,x14811,x14814,x14815),f215(x14813,x14812,x14814,x14815)) % 168.22/168.07 [1482]~E(x14821,x14822)+E(f215(x14823,x14824,x14821,x14825),f215(x14823,x14824,x14822,x14825)) % 168.22/168.07 [1483]~E(x14831,x14832)+E(f215(x14833,x14834,x14835,x14831),f215(x14833,x14834,x14835,x14832)) % 168.22/168.07 [1484]~E(x14841,x14842)+E(f344(x14841,x14843,x14844,x14845),f344(x14842,x14843,x14844,x14845)) % 168.22/168.07 [1485]~E(x14851,x14852)+E(f344(x14853,x14851,x14854,x14855),f344(x14853,x14852,x14854,x14855)) % 168.22/168.07 [1486]~E(x14861,x14862)+E(f344(x14863,x14864,x14861,x14865),f344(x14863,x14864,x14862,x14865)) % 168.22/168.07 [1487]~E(x14871,x14872)+E(f344(x14873,x14874,x14875,x14871),f344(x14873,x14874,x14875,x14872)) % 168.22/168.07 [1488]~E(x14881,x14882)+E(f701(x14881,x14883,x14884,x14885,x14886),f701(x14882,x14883,x14884,x14885,x14886)) % 168.22/168.07 [1489]~E(x14891,x14892)+E(f701(x14893,x14891,x14894,x14895,x14896),f701(x14893,x14892,x14894,x14895,x14896)) % 168.22/168.07 [1490]~E(x14901,x14902)+E(f701(x14903,x14904,x14901,x14905,x14906),f701(x14903,x14904,x14902,x14905,x14906)) % 168.22/168.07 [1491]~E(x14911,x14912)+E(f701(x14913,x14914,x14915,x14911,x14916),f701(x14913,x14914,x14915,x14912,x14916)) % 168.22/168.07 [1492]~E(x14921,x14922)+E(f701(x14923,x14924,x14925,x14926,x14921),f701(x14923,x14924,x14925,x14926,x14922)) % 168.22/168.07 [1493]~E(x14931,x14932)+E(f595(x14931,x14933,x14934),f595(x14932,x14933,x14934)) % 168.22/168.07 [1494]~E(x14941,x14942)+E(f595(x14943,x14941,x14944),f595(x14943,x14942,x14944)) % 168.22/168.07 [1495]~E(x14951,x14952)+E(f595(x14953,x14954,x14951),f595(x14953,x14954,x14952)) % 168.22/168.07 [1496]~E(x14961,x14962)+E(f571(x14961,x14963,x14964),f571(x14962,x14963,x14964)) % 168.22/168.07 [1497]~E(x14971,x14972)+E(f571(x14973,x14971,x14974),f571(x14973,x14972,x14974)) % 168.22/168.07 [1498]~E(x14981,x14982)+E(f571(x14983,x14984,x14981),f571(x14983,x14984,x14982)) % 168.22/168.07 [1499]~E(x14991,x14992)+E(f219(x14991,x14993,x14994),f219(x14992,x14993,x14994)) % 168.22/168.07 [1500]~E(x15001,x15002)+E(f219(x15003,x15001,x15004),f219(x15003,x15002,x15004)) % 168.22/168.07 [1501]~E(x15011,x15012)+E(f219(x15013,x15014,x15011),f219(x15013,x15014,x15012)) % 168.22/168.07 [1502]~E(x15021,x15022)+E(f335(x15021,x15023,x15024),f335(x15022,x15023,x15024)) % 168.22/168.07 [1503]~E(x15031,x15032)+E(f335(x15033,x15031,x15034),f335(x15033,x15032,x15034)) % 168.22/168.07 [1504]~E(x15041,x15042)+E(f335(x15043,x15044,x15041),f335(x15043,x15044,x15042)) % 168.22/168.07 [1505]~E(x15051,x15052)+E(f622(x15051,x15053),f622(x15052,x15053)) % 168.22/168.07 [1506]~E(x15061,x15062)+E(f622(x15063,x15061),f622(x15063,x15062)) % 168.22/168.07 [1507]~E(x15071,x15072)+E(f599(x15071,x15073,x15074,x15075),f599(x15072,x15073,x15074,x15075)) % 168.22/168.07 [1508]~E(x15081,x15082)+E(f599(x15083,x15081,x15084,x15085),f599(x15083,x15082,x15084,x15085)) % 168.22/168.07 [1509]~E(x15091,x15092)+E(f599(x15093,x15094,x15091,x15095),f599(x15093,x15094,x15092,x15095)) % 168.22/168.07 [1510]~E(x15101,x15102)+E(f599(x15103,x15104,x15105,x15101),f599(x15103,x15104,x15105,x15102)) % 168.22/168.07 [1511]~E(x15111,x15112)+E(f709(x15111,x15113,x15114,x15115,x15116),f709(x15112,x15113,x15114,x15115,x15116)) % 168.22/168.07 [1512]~E(x15121,x15122)+E(f709(x15123,x15121,x15124,x15125,x15126),f709(x15123,x15122,x15124,x15125,x15126)) % 168.22/168.07 [1513]~E(x15131,x15132)+E(f709(x15133,x15134,x15131,x15135,x15136),f709(x15133,x15134,x15132,x15135,x15136)) % 168.22/168.07 [1514]~E(x15141,x15142)+E(f709(x15143,x15144,x15145,x15141,x15146),f709(x15143,x15144,x15145,x15142,x15146)) % 168.22/168.07 [1515]~E(x15151,x15152)+E(f709(x15153,x15154,x15155,x15156,x15151),f709(x15153,x15154,x15155,x15156,x15152)) % 168.22/168.07 [1516]~E(x15161,x15162)+E(f458(x15161,x15163,x15164),f458(x15162,x15163,x15164)) % 168.22/168.07 [1517]~E(x15171,x15172)+E(f458(x15173,x15171,x15174),f458(x15173,x15172,x15174)) % 168.22/168.07 [1518]~E(x15181,x15182)+E(f458(x15183,x15184,x15181),f458(x15183,x15184,x15182)) % 168.22/168.07 [1519]~E(x15191,x15192)+E(f830(x15191,x15193,x15194),f830(x15192,x15193,x15194)) % 168.22/168.07 [1520]~E(x15201,x15202)+E(f830(x15203,x15201,x15204),f830(x15203,x15202,x15204)) % 168.22/168.07 [1521]~E(x15211,x15212)+E(f830(x15213,x15214,x15211),f830(x15213,x15214,x15212)) % 168.22/168.07 [1522]~E(x15221,x15222)+E(f358(x15221),f358(x15222)) % 168.22/168.07 [1523]~E(x15231,x15232)+E(f673(x15231,x15233,x15234),f673(x15232,x15233,x15234)) % 168.22/168.07 [1524]~E(x15241,x15242)+E(f673(x15243,x15241,x15244),f673(x15243,x15242,x15244)) % 168.22/168.07 [1525]~E(x15251,x15252)+E(f673(x15253,x15254,x15251),f673(x15253,x15254,x15252)) % 168.22/168.07 [1526]~E(x15261,x15262)+E(f347(x15261,x15263,x15264,x15265),f347(x15262,x15263,x15264,x15265)) % 168.22/168.07 [1527]~E(x15271,x15272)+E(f347(x15273,x15271,x15274,x15275),f347(x15273,x15272,x15274,x15275)) % 168.22/168.07 [1528]~E(x15281,x15282)+E(f347(x15283,x15284,x15281,x15285),f347(x15283,x15284,x15282,x15285)) % 168.22/168.07 [1529]~E(x15291,x15292)+E(f347(x15293,x15294,x15295,x15291),f347(x15293,x15294,x15295,x15292)) % 168.22/168.07 [1530]~E(x15301,x15302)+E(f809(x15301,x15303,x15304),f809(x15302,x15303,x15304)) % 168.22/168.07 [1531]~E(x15311,x15312)+E(f809(x15313,x15311,x15314),f809(x15313,x15312,x15314)) % 168.22/168.07 [1532]~E(x15321,x15322)+E(f809(x15323,x15324,x15321),f809(x15323,x15324,x15322)) % 168.22/168.07 [1533]~E(x15331,x15332)+E(f497(x15331,x15333,x15334,x15335,x15336,x15337,x15338),f497(x15332,x15333,x15334,x15335,x15336,x15337,x15338)) % 168.22/168.07 [1534]~E(x15341,x15342)+E(f497(x15343,x15341,x15344,x15345,x15346,x15347,x15348),f497(x15343,x15342,x15344,x15345,x15346,x15347,x15348)) % 168.22/168.07 [1535]~E(x15351,x15352)+E(f497(x15353,x15354,x15351,x15355,x15356,x15357,x15358),f497(x15353,x15354,x15352,x15355,x15356,x15357,x15358)) % 168.22/168.07 [1536]~E(x15361,x15362)+E(f497(x15363,x15364,x15365,x15361,x15366,x15367,x15368),f497(x15363,x15364,x15365,x15362,x15366,x15367,x15368)) % 168.22/168.07 [1537]~E(x15371,x15372)+E(f497(x15373,x15374,x15375,x15376,x15371,x15377,x15378),f497(x15373,x15374,x15375,x15376,x15372,x15377,x15378)) % 168.22/168.07 [1538]~E(x15381,x15382)+E(f497(x15383,x15384,x15385,x15386,x15387,x15381,x15388),f497(x15383,x15384,x15385,x15386,x15387,x15382,x15388)) % 168.22/168.07 [1539]~E(x15391,x15392)+E(f497(x15393,x15394,x15395,x15396,x15397,x15398,x15391),f497(x15393,x15394,x15395,x15396,x15397,x15398,x15392)) % 168.22/168.07 [1540]~E(x15401,x15402)+E(f345(x15401,x15403,x15404),f345(x15402,x15403,x15404)) % 168.22/168.07 [1541]~E(x15411,x15412)+E(f345(x15413,x15411,x15414),f345(x15413,x15412,x15414)) % 168.22/168.07 [1542]~E(x15421,x15422)+E(f345(x15423,x15424,x15421),f345(x15423,x15424,x15422)) % 168.22/168.07 [1543]~E(x15431,x15432)+E(f251(x15431,x15433,x15434,x15435,x15436),f251(x15432,x15433,x15434,x15435,x15436)) % 168.22/168.07 [1544]~E(x15441,x15442)+E(f251(x15443,x15441,x15444,x15445,x15446),f251(x15443,x15442,x15444,x15445,x15446)) % 168.22/168.07 [1545]~E(x15451,x15452)+E(f251(x15453,x15454,x15451,x15455,x15456),f251(x15453,x15454,x15452,x15455,x15456)) % 168.22/168.07 [1546]~E(x15461,x15462)+E(f251(x15463,x15464,x15465,x15461,x15466),f251(x15463,x15464,x15465,x15462,x15466)) % 168.22/168.07 [1547]~E(x15471,x15472)+E(f251(x15473,x15474,x15475,x15476,x15471),f251(x15473,x15474,x15475,x15476,x15472)) % 168.22/168.07 [1548]~E(x15481,x15482)+E(f818(x15481),f818(x15482)) % 168.22/168.07 [1549]~E(x15491,x15492)+E(f740(x15491,x15493,x15494),f740(x15492,x15493,x15494)) % 168.22/168.07 [1550]~E(x15501,x15502)+E(f740(x15503,x15501,x15504),f740(x15503,x15502,x15504)) % 168.22/168.07 [1551]~E(x15511,x15512)+E(f740(x15513,x15514,x15511),f740(x15513,x15514,x15512)) % 168.22/168.07 [1552]~E(x15521,x15522)+E(f174(x15521),f174(x15522)) % 168.22/168.07 [1553]~E(x15531,x15532)+E(f438(x15531,x15533),f438(x15532,x15533)) % 168.22/168.07 [1554]~E(x15541,x15542)+E(f438(x15543,x15541),f438(x15543,x15542)) % 168.22/168.07 [1555]~E(x15551,x15552)+E(f574(x15551),f574(x15552)) % 168.22/168.07 [1556]~E(x15561,x15562)+E(f294(x15561),f294(x15562)) % 168.22/168.07 [1557]~E(x15571,x15572)+E(f421(x15571,x15573),f421(x15572,x15573)) % 168.22/168.07 [1558]~E(x15581,x15582)+E(f421(x15583,x15581),f421(x15583,x15582)) % 168.22/168.07 [1559]~E(x15591,x15592)+E(f602(x15591,x15593,x15594,x15595),f602(x15592,x15593,x15594,x15595)) % 168.22/168.07 [1560]~E(x15601,x15602)+E(f602(x15603,x15601,x15604,x15605),f602(x15603,x15602,x15604,x15605)) % 168.22/168.07 [1561]~E(x15611,x15612)+E(f602(x15613,x15614,x15611,x15615),f602(x15613,x15614,x15612,x15615)) % 168.22/168.07 [1562]~E(x15621,x15622)+E(f602(x15623,x15624,x15625,x15621),f602(x15623,x15624,x15625,x15622)) % 168.22/168.07 [1563]~E(x15631,x15632)+E(f465(x15631,x15633,x15634,x15635,x15636),f465(x15632,x15633,x15634,x15635,x15636)) % 168.22/168.07 [1564]~E(x15641,x15642)+E(f465(x15643,x15641,x15644,x15645,x15646),f465(x15643,x15642,x15644,x15645,x15646)) % 168.22/168.07 [1565]~E(x15651,x15652)+E(f465(x15653,x15654,x15651,x15655,x15656),f465(x15653,x15654,x15652,x15655,x15656)) % 168.22/168.07 [1566]~E(x15661,x15662)+E(f465(x15663,x15664,x15665,x15661,x15666),f465(x15663,x15664,x15665,x15662,x15666)) % 168.22/168.07 [1567]~E(x15671,x15672)+E(f465(x15673,x15674,x15675,x15676,x15671),f465(x15673,x15674,x15675,x15676,x15672)) % 168.22/168.07 [1568]~E(x15681,x15682)+E(f755(x15681,x15683,x15684,x15685,x15686,x15687),f755(x15682,x15683,x15684,x15685,x15686,x15687)) % 168.22/168.07 [1569]~E(x15691,x15692)+E(f755(x15693,x15691,x15694,x15695,x15696,x15697),f755(x15693,x15692,x15694,x15695,x15696,x15697)) % 168.22/168.07 [1570]~E(x15701,x15702)+E(f755(x15703,x15704,x15701,x15705,x15706,x15707),f755(x15703,x15704,x15702,x15705,x15706,x15707)) % 168.22/168.07 [1571]~E(x15711,x15712)+E(f755(x15713,x15714,x15715,x15711,x15716,x15717),f755(x15713,x15714,x15715,x15712,x15716,x15717)) % 168.22/168.07 [1572]~E(x15721,x15722)+E(f755(x15723,x15724,x15725,x15726,x15721,x15727),f755(x15723,x15724,x15725,x15726,x15722,x15727)) % 168.22/168.07 [1573]~E(x15731,x15732)+E(f755(x15733,x15734,x15735,x15736,x15737,x15731),f755(x15733,x15734,x15735,x15736,x15737,x15732)) % 168.22/168.07 [1574]~E(x15741,x15742)+E(f455(x15741,x15743,x15744,x15745,x15746),f455(x15742,x15743,x15744,x15745,x15746)) % 168.22/168.07 [1575]~E(x15751,x15752)+E(f455(x15753,x15751,x15754,x15755,x15756),f455(x15753,x15752,x15754,x15755,x15756)) % 168.22/168.07 [1576]~E(x15761,x15762)+E(f455(x15763,x15764,x15761,x15765,x15766),f455(x15763,x15764,x15762,x15765,x15766)) % 168.22/168.07 [1577]~E(x15771,x15772)+E(f455(x15773,x15774,x15775,x15771,x15776),f455(x15773,x15774,x15775,x15772,x15776)) % 168.22/168.07 [1578]~E(x15781,x15782)+E(f455(x15783,x15784,x15785,x15786,x15781),f455(x15783,x15784,x15785,x15786,x15782)) % 168.22/168.07 [1579]~E(x15791,x15792)+E(f616(x15791,x15793,x15794),f616(x15792,x15793,x15794)) % 168.22/168.07 [1580]~E(x15801,x15802)+E(f616(x15803,x15801,x15804),f616(x15803,x15802,x15804)) % 168.22/168.07 [1581]~E(x15811,x15812)+E(f616(x15813,x15814,x15811),f616(x15813,x15814,x15812)) % 168.22/168.07 [1582]~E(x15821,x15822)+E(f834(x15821,x15823,x15824,x15825,x15826,x15827),f834(x15822,x15823,x15824,x15825,x15826,x15827)) % 168.22/168.07 [1583]~E(x15831,x15832)+E(f834(x15833,x15831,x15834,x15835,x15836,x15837),f834(x15833,x15832,x15834,x15835,x15836,x15837)) % 168.22/168.07 [1584]~E(x15841,x15842)+E(f834(x15843,x15844,x15841,x15845,x15846,x15847),f834(x15843,x15844,x15842,x15845,x15846,x15847)) % 168.22/168.07 [1585]~E(x15851,x15852)+E(f834(x15853,x15854,x15855,x15851,x15856,x15857),f834(x15853,x15854,x15855,x15852,x15856,x15857)) % 168.22/168.07 [1586]~E(x15861,x15862)+E(f834(x15863,x15864,x15865,x15866,x15861,x15867),f834(x15863,x15864,x15865,x15866,x15862,x15867)) % 168.22/168.07 [1587]~E(x15871,x15872)+E(f834(x15873,x15874,x15875,x15876,x15877,x15871),f834(x15873,x15874,x15875,x15876,x15877,x15872)) % 168.22/168.07 [1588]~E(x15881,x15882)+E(f654(x15881,x15883),f654(x15882,x15883)) % 168.22/168.07 [1589]~E(x15891,x15892)+E(f654(x15893,x15891),f654(x15893,x15892)) % 168.22/168.07 [1590]~E(x15901,x15902)+E(f373(x15901,x15903),f373(x15902,x15903)) % 168.22/168.07 [1591]~E(x15911,x15912)+E(f373(x15913,x15911),f373(x15913,x15912)) % 168.22/168.07 [1592]~E(x15921,x15922)+E(f207(x15921,x15923),f207(x15922,x15923)) % 168.22/168.07 [1593]~E(x15931,x15932)+E(f207(x15933,x15931),f207(x15933,x15932)) % 168.22/168.07 [1594]~E(x15941,x15942)+E(f387(x15941,x15943,x15944,x15945),f387(x15942,x15943,x15944,x15945)) % 168.22/168.07 [1595]~E(x15951,x15952)+E(f387(x15953,x15951,x15954,x15955),f387(x15953,x15952,x15954,x15955)) % 168.22/168.07 [1596]~E(x15961,x15962)+E(f387(x15963,x15964,x15961,x15965),f387(x15963,x15964,x15962,x15965)) % 168.22/168.07 [1597]~E(x15971,x15972)+E(f387(x15973,x15974,x15975,x15971),f387(x15973,x15974,x15975,x15972)) % 168.22/168.07 [1598]~E(x15981,x15982)+E(f452(x15981,x15983,x15984),f452(x15982,x15983,x15984)) % 168.22/168.07 [1599]~E(x15991,x15992)+E(f452(x15993,x15991,x15994),f452(x15993,x15992,x15994)) % 168.22/168.07 [1600]~E(x16001,x16002)+E(f452(x16003,x16004,x16001),f452(x16003,x16004,x16002)) % 168.22/168.07 [1601]~E(x16011,x16012)+E(f363(x16011,x16013),f363(x16012,x16013)) % 168.22/168.07 [1602]~E(x16021,x16022)+E(f363(x16023,x16021),f363(x16023,x16022)) % 168.22/168.07 [1603]~E(x16031,x16032)+E(f507(x16031,x16033,x16034,x16035,x16036),f507(x16032,x16033,x16034,x16035,x16036)) % 168.22/168.07 [1604]~E(x16041,x16042)+E(f507(x16043,x16041,x16044,x16045,x16046),f507(x16043,x16042,x16044,x16045,x16046)) % 168.22/168.07 [1605]~E(x16051,x16052)+E(f507(x16053,x16054,x16051,x16055,x16056),f507(x16053,x16054,x16052,x16055,x16056)) % 168.22/168.07 [1606]~E(x16061,x16062)+E(f507(x16063,x16064,x16065,x16061,x16066),f507(x16063,x16064,x16065,x16062,x16066)) % 168.22/168.07 [1607]~E(x16071,x16072)+E(f507(x16073,x16074,x16075,x16076,x16071),f507(x16073,x16074,x16075,x16076,x16072)) % 168.22/168.07 [1608]~E(x16081,x16082)+E(f810(x16081,x16083,x16084,x16085),f810(x16082,x16083,x16084,x16085)) % 168.22/168.07 [1609]~E(x16091,x16092)+E(f810(x16093,x16091,x16094,x16095),f810(x16093,x16092,x16094,x16095)) % 168.22/168.07 [1610]~E(x16101,x16102)+E(f810(x16103,x16104,x16101,x16105),f810(x16103,x16104,x16102,x16105)) % 168.22/168.07 [1611]~E(x16111,x16112)+E(f810(x16113,x16114,x16115,x16111),f810(x16113,x16114,x16115,x16112)) % 168.22/168.07 [1612]~E(x16121,x16122)+E(f556(x16121,x16123,x16124,x16125,x16126),f556(x16122,x16123,x16124,x16125,x16126)) % 168.22/168.07 [1613]~E(x16131,x16132)+E(f556(x16133,x16131,x16134,x16135,x16136),f556(x16133,x16132,x16134,x16135,x16136)) % 168.22/168.07 [1614]~E(x16141,x16142)+E(f556(x16143,x16144,x16141,x16145,x16146),f556(x16143,x16144,x16142,x16145,x16146)) % 168.22/168.07 [1615]~E(x16151,x16152)+E(f556(x16153,x16154,x16155,x16151,x16156),f556(x16153,x16154,x16155,x16152,x16156)) % 168.22/168.07 [1616]~E(x16161,x16162)+E(f556(x16163,x16164,x16165,x16166,x16161),f556(x16163,x16164,x16165,x16166,x16162)) % 168.22/168.07 [1617]~E(x16171,x16172)+E(f651(x16171,x16173,x16174),f651(x16172,x16173,x16174)) % 168.22/168.07 [1618]~E(x16181,x16182)+E(f651(x16183,x16181,x16184),f651(x16183,x16182,x16184)) % 168.22/168.07 [1619]~E(x16191,x16192)+E(f651(x16193,x16194,x16191),f651(x16193,x16194,x16192)) % 168.22/168.07 [1620]~E(x16201,x16202)+E(f696(x16201,x16203,x16204,x16205),f696(x16202,x16203,x16204,x16205)) % 168.22/168.07 [1621]~E(x16211,x16212)+E(f696(x16213,x16211,x16214,x16215),f696(x16213,x16212,x16214,x16215)) % 168.22/168.07 [1622]~E(x16221,x16222)+E(f696(x16223,x16224,x16221,x16225),f696(x16223,x16224,x16222,x16225)) % 168.22/168.07 [1623]~E(x16231,x16232)+E(f696(x16233,x16234,x16235,x16231),f696(x16233,x16234,x16235,x16232)) % 168.22/168.07 [1624]~E(x16241,x16242)+E(f405(x16241,x16243,x16244),f405(x16242,x16243,x16244)) % 168.22/168.07 [1625]~E(x16251,x16252)+E(f405(x16253,x16251,x16254),f405(x16253,x16252,x16254)) % 168.22/168.07 [1626]~E(x16261,x16262)+E(f405(x16263,x16264,x16261),f405(x16263,x16264,x16262)) % 168.22/168.07 [1627]~E(x16271,x16272)+E(f195(x16271,x16273),f195(x16272,x16273)) % 168.22/168.07 [1628]~E(x16281,x16282)+E(f195(x16283,x16281),f195(x16283,x16282)) % 168.22/168.07 [1629]~E(x16291,x16292)+E(f520(x16291),f520(x16292)) % 168.22/168.07 [1630]~E(x16301,x16302)+E(f565(x16301,x16303,x16304),f565(x16302,x16303,x16304)) % 168.22/168.07 [1631]~E(x16311,x16312)+E(f565(x16313,x16311,x16314),f565(x16313,x16312,x16314)) % 168.22/168.07 [1632]~E(x16321,x16322)+E(f565(x16323,x16324,x16321),f565(x16323,x16324,x16322)) % 168.22/168.07 [1633]~E(x16331,x16332)+E(f800(x16331),f800(x16332)) % 168.22/168.07 [1634]~E(x16341,x16342)+E(f707(x16341,x16343,x16344),f707(x16342,x16343,x16344)) % 168.22/168.07 [1635]~E(x16351,x16352)+E(f707(x16353,x16351,x16354),f707(x16353,x16352,x16354)) % 168.22/168.07 [1636]~E(x16361,x16362)+E(f707(x16363,x16364,x16361),f707(x16363,x16364,x16362)) % 168.22/168.07 [1637]~E(x16371,x16372)+E(f773(x16371,x16373,x16374,x16375,x16376),f773(x16372,x16373,x16374,x16375,x16376)) % 168.22/168.07 [1638]~E(x16381,x16382)+E(f773(x16383,x16381,x16384,x16385,x16386),f773(x16383,x16382,x16384,x16385,x16386)) % 168.22/168.07 [1639]~E(x16391,x16392)+E(f773(x16393,x16394,x16391,x16395,x16396),f773(x16393,x16394,x16392,x16395,x16396)) % 168.22/168.07 [1640]~E(x16401,x16402)+E(f773(x16403,x16404,x16405,x16401,x16406),f773(x16403,x16404,x16405,x16402,x16406)) % 168.22/168.07 [1641]~E(x16411,x16412)+E(f773(x16413,x16414,x16415,x16416,x16411),f773(x16413,x16414,x16415,x16416,x16412)) % 168.22/168.07 [1642]~E(x16421,x16422)+E(f827(x16421,x16423),f827(x16422,x16423)) % 168.22/168.07 [1643]~E(x16431,x16432)+E(f827(x16433,x16431),f827(x16433,x16432)) % 168.22/168.07 [1644]~E(x16441,x16442)+E(f630(x16441,x16443,x16444),f630(x16442,x16443,x16444)) % 168.22/168.07 [1645]~E(x16451,x16452)+E(f630(x16453,x16451,x16454),f630(x16453,x16452,x16454)) % 168.22/168.07 [1646]~E(x16461,x16462)+E(f630(x16463,x16464,x16461),f630(x16463,x16464,x16462)) % 168.22/168.07 [1647]~E(x16471,x16472)+E(f776(x16471,x16473,x16474,x16475,x16476),f776(x16472,x16473,x16474,x16475,x16476)) % 168.22/168.07 [1648]~E(x16481,x16482)+E(f776(x16483,x16481,x16484,x16485,x16486),f776(x16483,x16482,x16484,x16485,x16486)) % 168.22/168.07 [1649]~E(x16491,x16492)+E(f776(x16493,x16494,x16491,x16495,x16496),f776(x16493,x16494,x16492,x16495,x16496)) % 168.22/168.07 [1650]~E(x16501,x16502)+E(f776(x16503,x16504,x16505,x16501,x16506),f776(x16503,x16504,x16505,x16502,x16506)) % 168.22/168.07 [1651]~E(x16511,x16512)+E(f776(x16513,x16514,x16515,x16516,x16511),f776(x16513,x16514,x16515,x16516,x16512)) % 168.22/168.07 [1652]~E(x16521,x16522)+E(f757(x16521,x16523),f757(x16522,x16523)) % 168.22/168.07 [1653]~E(x16531,x16532)+E(f757(x16533,x16531),f757(x16533,x16532)) % 168.22/168.07 [1654]~E(x16541,x16542)+E(f323(x16541,x16543),f323(x16542,x16543)) % 168.22/168.07 [1655]~E(x16551,x16552)+E(f323(x16553,x16551),f323(x16553,x16552)) % 168.22/168.07 [1656]~E(x16561,x16562)+E(f511(x16561,x16563,x16564,x16565,x16566),f511(x16562,x16563,x16564,x16565,x16566)) % 168.22/168.07 [1657]~E(x16571,x16572)+E(f511(x16573,x16571,x16574,x16575,x16576),f511(x16573,x16572,x16574,x16575,x16576)) % 168.22/168.07 [1658]~E(x16581,x16582)+E(f511(x16583,x16584,x16581,x16585,x16586),f511(x16583,x16584,x16582,x16585,x16586)) % 168.22/168.07 [1659]~E(x16591,x16592)+E(f511(x16593,x16594,x16595,x16591,x16596),f511(x16593,x16594,x16595,x16592,x16596)) % 168.22/168.07 [1660]~E(x16601,x16602)+E(f511(x16603,x16604,x16605,x16606,x16601),f511(x16603,x16604,x16605,x16606,x16602)) % 168.22/168.07 [1661]~E(x16611,x16612)+E(f356(x16611,x16613),f356(x16612,x16613)) % 168.22/168.07 [1662]~E(x16621,x16622)+E(f356(x16623,x16621),f356(x16623,x16622)) % 168.22/168.07 [1663]~E(x16631,x16632)+E(f593(x16631,x16633,x16634,x16635,x16636),f593(x16632,x16633,x16634,x16635,x16636)) % 168.22/168.07 [1664]~E(x16641,x16642)+E(f593(x16643,x16641,x16644,x16645,x16646),f593(x16643,x16642,x16644,x16645,x16646)) % 168.22/168.07 [1665]~E(x16651,x16652)+E(f593(x16653,x16654,x16651,x16655,x16656),f593(x16653,x16654,x16652,x16655,x16656)) % 168.22/168.07 [1666]~E(x16661,x16662)+E(f593(x16663,x16664,x16665,x16661,x16666),f593(x16663,x16664,x16665,x16662,x16666)) % 168.22/168.07 [1667]~E(x16671,x16672)+E(f593(x16673,x16674,x16675,x16676,x16671),f593(x16673,x16674,x16675,x16676,x16672)) % 168.22/168.07 [1668]~E(x16681,x16682)+E(f726(x16681,x16683,x16684,x16685,x16686),f726(x16682,x16683,x16684,x16685,x16686)) % 168.22/168.07 [1669]~E(x16691,x16692)+E(f726(x16693,x16691,x16694,x16695,x16696),f726(x16693,x16692,x16694,x16695,x16696)) % 168.22/168.07 [1670]~E(x16701,x16702)+E(f726(x16703,x16704,x16701,x16705,x16706),f726(x16703,x16704,x16702,x16705,x16706)) % 168.22/168.07 [1671]~E(x16711,x16712)+E(f726(x16713,x16714,x16715,x16711,x16716),f726(x16713,x16714,x16715,x16712,x16716)) % 168.22/168.07 [1672]~E(x16721,x16722)+E(f726(x16723,x16724,x16725,x16726,x16721),f726(x16723,x16724,x16725,x16726,x16722)) % 168.22/168.07 [1673]~E(x16731,x16732)+E(f190(x16731,x16733,x16734,x16735),f190(x16732,x16733,x16734,x16735)) % 168.22/168.07 [1674]~E(x16741,x16742)+E(f190(x16743,x16741,x16744,x16745),f190(x16743,x16742,x16744,x16745)) % 168.22/168.07 [1675]~E(x16751,x16752)+E(f190(x16753,x16754,x16751,x16755),f190(x16753,x16754,x16752,x16755)) % 168.22/168.07 [1676]~E(x16761,x16762)+E(f190(x16763,x16764,x16765,x16761),f190(x16763,x16764,x16765,x16762)) % 168.22/168.07 [1677]~E(x16771,x16772)+E(f339(x16771,x16773,x16774),f339(x16772,x16773,x16774)) % 168.22/168.07 [1678]~E(x16781,x16782)+E(f339(x16783,x16781,x16784),f339(x16783,x16782,x16784)) % 168.22/168.07 [1679]~E(x16791,x16792)+E(f339(x16793,x16794,x16791),f339(x16793,x16794,x16792)) % 168.22/168.07 [1680]~E(x16801,x16802)+E(f623(x16801,x16803,x16804,x16805),f623(x16802,x16803,x16804,x16805)) % 168.22/168.07 [1681]~E(x16811,x16812)+E(f623(x16813,x16811,x16814,x16815),f623(x16813,x16812,x16814,x16815)) % 168.22/168.07 [1682]~E(x16821,x16822)+E(f623(x16823,x16824,x16821,x16825),f623(x16823,x16824,x16822,x16825)) % 168.22/168.07 [1683]~E(x16831,x16832)+E(f623(x16833,x16834,x16835,x16831),f623(x16833,x16834,x16835,x16832)) % 168.22/168.07 [1684]~E(x16841,x16842)+E(f493(x16841,x16843,x16844,x16845,x16846),f493(x16842,x16843,x16844,x16845,x16846)) % 168.22/168.07 [1685]~E(x16851,x16852)+E(f493(x16853,x16851,x16854,x16855,x16856),f493(x16853,x16852,x16854,x16855,x16856)) % 168.22/168.07 [1686]~E(x16861,x16862)+E(f493(x16863,x16864,x16861,x16865,x16866),f493(x16863,x16864,x16862,x16865,x16866)) % 168.22/168.07 [1687]~E(x16871,x16872)+E(f493(x16873,x16874,x16875,x16871,x16876),f493(x16873,x16874,x16875,x16872,x16876)) % 168.22/168.07 [1688]~E(x16881,x16882)+E(f493(x16883,x16884,x16885,x16886,x16881),f493(x16883,x16884,x16885,x16886,x16882)) % 168.22/168.07 [1689]~E(x16891,x16892)+E(f721(x16891,x16893),f721(x16892,x16893)) % 168.22/168.07 [1690]~E(x16901,x16902)+E(f721(x16903,x16901),f721(x16903,x16902)) % 168.22/168.07 [1691]~E(x16911,x16912)+E(f243(x16911,x16913,x16914),f243(x16912,x16913,x16914)) % 168.22/168.07 [1692]~E(x16921,x16922)+E(f243(x16923,x16921,x16924),f243(x16923,x16922,x16924)) % 168.22/168.07 [1693]~E(x16931,x16932)+E(f243(x16933,x16934,x16931),f243(x16933,x16934,x16932)) % 168.22/168.07 [1694]~E(x16941,x16942)+E(f725(x16941,x16943,x16944,x16945,x16946,x16947),f725(x16942,x16943,x16944,x16945,x16946,x16947)) % 168.22/168.07 [1695]~E(x16951,x16952)+E(f725(x16953,x16951,x16954,x16955,x16956,x16957),f725(x16953,x16952,x16954,x16955,x16956,x16957)) % 168.22/168.07 [1696]~E(x16961,x16962)+E(f725(x16963,x16964,x16961,x16965,x16966,x16967),f725(x16963,x16964,x16962,x16965,x16966,x16967)) % 168.22/168.07 [1697]~E(x16971,x16972)+E(f725(x16973,x16974,x16975,x16971,x16976,x16977),f725(x16973,x16974,x16975,x16972,x16976,x16977)) % 168.22/168.07 [1698]~E(x16981,x16982)+E(f725(x16983,x16984,x16985,x16986,x16981,x16987),f725(x16983,x16984,x16985,x16986,x16982,x16987)) % 168.22/168.07 [1699]~E(x16991,x16992)+E(f725(x16993,x16994,x16995,x16996,x16997,x16991),f725(x16993,x16994,x16995,x16996,x16997,x16992)) % 168.22/168.07 [1700]~E(x17001,x17002)+E(f406(x17001,x17003,x17004),f406(x17002,x17003,x17004)) % 168.22/168.07 [1701]~E(x17011,x17012)+E(f406(x17013,x17011,x17014),f406(x17013,x17012,x17014)) % 168.22/168.07 [1702]~E(x17021,x17022)+E(f406(x17023,x17024,x17021),f406(x17023,x17024,x17022)) % 168.22/168.07 [1703]~E(x17031,x17032)+E(f461(x17031,x17033,x17034,x17035),f461(x17032,x17033,x17034,x17035)) % 168.22/168.07 [1704]~E(x17041,x17042)+E(f461(x17043,x17041,x17044,x17045),f461(x17043,x17042,x17044,x17045)) % 168.22/168.07 [1705]~E(x17051,x17052)+E(f461(x17053,x17054,x17051,x17055),f461(x17053,x17054,x17052,x17055)) % 168.22/168.07 [1706]~E(x17061,x17062)+E(f461(x17063,x17064,x17065,x17061),f461(x17063,x17064,x17065,x17062)) % 168.22/168.07 [1707]~E(x17071,x17072)+E(f83(x17071,x17073),f83(x17072,x17073)) % 168.22/168.07 [1708]~E(x17081,x17082)+E(f83(x17083,x17081),f83(x17083,x17082)) % 168.22/168.07 [1709]~E(x17091,x17092)+E(f214(x17091,x17093,x17094,x17095,x17096),f214(x17092,x17093,x17094,x17095,x17096)) % 168.22/168.07 [1710]~E(x17101,x17102)+E(f214(x17103,x17101,x17104,x17105,x17106),f214(x17103,x17102,x17104,x17105,x17106)) % 168.22/168.07 [1711]~E(x17111,x17112)+E(f214(x17113,x17114,x17111,x17115,x17116),f214(x17113,x17114,x17112,x17115,x17116)) % 168.22/168.07 [1712]~E(x17121,x17122)+E(f214(x17123,x17124,x17125,x17121,x17126),f214(x17123,x17124,x17125,x17122,x17126)) % 168.22/168.07 [1713]~E(x17131,x17132)+E(f214(x17133,x17134,x17135,x17136,x17131),f214(x17133,x17134,x17135,x17136,x17132)) % 168.22/168.07 [1714]~E(x17141,x17142)+E(f418(x17141,x17143,x17144,x17145),f418(x17142,x17143,x17144,x17145)) % 168.22/168.07 [1715]~E(x17151,x17152)+E(f418(x17153,x17151,x17154,x17155),f418(x17153,x17152,x17154,x17155)) % 168.22/168.07 [1716]~E(x17161,x17162)+E(f418(x17163,x17164,x17161,x17165),f418(x17163,x17164,x17162,x17165)) % 168.22/168.07 [1717]~E(x17171,x17172)+E(f418(x17173,x17174,x17175,x17171),f418(x17173,x17174,x17175,x17172)) % 168.22/168.07 [1718]~E(x17181,x17182)+E(f490(x17181,x17183,x17184,x17185),f490(x17182,x17183,x17184,x17185)) % 168.22/168.07 [1719]~E(x17191,x17192)+E(f490(x17193,x17191,x17194,x17195),f490(x17193,x17192,x17194,x17195)) % 168.22/168.07 [1720]~E(x17201,x17202)+E(f490(x17203,x17204,x17201,x17205),f490(x17203,x17204,x17202,x17205)) % 168.22/168.07 [1721]~E(x17211,x17212)+E(f490(x17213,x17214,x17215,x17211),f490(x17213,x17214,x17215,x17212)) % 168.22/168.07 [1722]~E(x17221,x17222)+E(f479(x17221,x17223,x17224,x17225,x17226,x17227,x17228,x17229),f479(x17222,x17223,x17224,x17225,x17226,x17227,x17228,x17229)) % 168.22/168.07 [1723]~E(x17231,x17232)+E(f479(x17233,x17231,x17234,x17235,x17236,x17237,x17238,x17239),f479(x17233,x17232,x17234,x17235,x17236,x17237,x17238,x17239)) % 168.22/168.07 [1724]~E(x17241,x17242)+E(f479(x17243,x17244,x17241,x17245,x17246,x17247,x17248,x17249),f479(x17243,x17244,x17242,x17245,x17246,x17247,x17248,x17249)) % 168.22/168.07 [1725]~E(x17251,x17252)+E(f479(x17253,x17254,x17255,x17251,x17256,x17257,x17258,x17259),f479(x17253,x17254,x17255,x17252,x17256,x17257,x17258,x17259)) % 168.22/168.07 [1726]~E(x17261,x17262)+E(f479(x17263,x17264,x17265,x17266,x17261,x17267,x17268,x17269),f479(x17263,x17264,x17265,x17266,x17262,x17267,x17268,x17269)) % 168.22/168.07 [1727]~E(x17271,x17272)+E(f479(x17273,x17274,x17275,x17276,x17277,x17271,x17278,x17279),f479(x17273,x17274,x17275,x17276,x17277,x17272,x17278,x17279)) % 168.22/168.07 [1728]~E(x17281,x17282)+E(f479(x17283,x17284,x17285,x17286,x17287,x17288,x17281,x17289),f479(x17283,x17284,x17285,x17286,x17287,x17288,x17282,x17289)) % 168.22/168.07 [1729]~E(x17291,x17292)+E(f479(x17293,x17294,x17295,x17296,x17297,x17298,x17299,x17291),f479(x17293,x17294,x17295,x17296,x17297,x17298,x17299,x17292)) % 168.22/168.07 [1730]~E(x17301,x17302)+E(f733(x17301,x17303,x17304,x17305,x17306,x17307,x17308),f733(x17302,x17303,x17304,x17305,x17306,x17307,x17308)) % 168.22/168.07 [1731]~E(x17311,x17312)+E(f733(x17313,x17311,x17314,x17315,x17316,x17317,x17318),f733(x17313,x17312,x17314,x17315,x17316,x17317,x17318)) % 168.22/168.07 [1732]~E(x17321,x17322)+E(f733(x17323,x17324,x17321,x17325,x17326,x17327,x17328),f733(x17323,x17324,x17322,x17325,x17326,x17327,x17328)) % 168.22/168.07 [1733]~E(x17331,x17332)+E(f733(x17333,x17334,x17335,x17331,x17336,x17337,x17338),f733(x17333,x17334,x17335,x17332,x17336,x17337,x17338)) % 168.22/168.07 [1734]~E(x17341,x17342)+E(f733(x17343,x17344,x17345,x17346,x17341,x17347,x17348),f733(x17343,x17344,x17345,x17346,x17342,x17347,x17348)) % 168.22/168.07 [1735]~E(x17351,x17352)+E(f733(x17353,x17354,x17355,x17356,x17357,x17351,x17358),f733(x17353,x17354,x17355,x17356,x17357,x17352,x17358)) % 168.22/168.07 [1736]~E(x17361,x17362)+E(f733(x17363,x17364,x17365,x17366,x17367,x17368,x17361),f733(x17363,x17364,x17365,x17366,x17367,x17368,x17362)) % 168.22/168.07 [1737]~E(x17371,x17372)+E(f424(x17371,x17373,x17374),f424(x17372,x17373,x17374)) % 168.22/168.07 [1738]~E(x17381,x17382)+E(f424(x17383,x17381,x17384),f424(x17383,x17382,x17384)) % 168.22/168.07 [1739]~E(x17391,x17392)+E(f424(x17393,x17394,x17391),f424(x17393,x17394,x17392)) % 168.22/168.07 [1740]~E(x17401,x17402)+E(f44(x17401,x17403,x17404,x17405),f44(x17402,x17403,x17404,x17405)) % 168.22/168.07 [1741]~E(x17411,x17412)+E(f44(x17413,x17411,x17414,x17415),f44(x17413,x17412,x17414,x17415)) % 168.22/168.07 [1742]~E(x17421,x17422)+E(f44(x17423,x17424,x17421,x17425),f44(x17423,x17424,x17422,x17425)) % 168.22/168.07 [1743]~E(x17431,x17432)+E(f44(x17433,x17434,x17435,x17431),f44(x17433,x17434,x17435,x17432)) % 168.22/168.07 [1744]~E(x17441,x17442)+E(f585(x17441,x17443,x17444),f585(x17442,x17443,x17444)) % 168.22/168.07 [1745]~E(x17451,x17452)+E(f585(x17453,x17451,x17454),f585(x17453,x17452,x17454)) % 168.22/168.07 [1746]~E(x17461,x17462)+E(f585(x17463,x17464,x17461),f585(x17463,x17464,x17462)) % 168.22/168.07 [1747]~E(x17471,x17472)+E(f550(x17471,x17473),f550(x17472,x17473)) % 168.22/168.07 [1748]~E(x17481,x17482)+E(f550(x17483,x17481),f550(x17483,x17482)) % 168.22/168.07 [1749]~E(x17491,x17492)+E(f206(x17491,x17493),f206(x17492,x17493)) % 168.22/168.07 [1750]~E(x17501,x17502)+E(f206(x17503,x17501),f206(x17503,x17502)) % 168.22/168.07 [1751]~E(x17511,x17512)+E(f592(x17511,x17513,x17514,x17515,x17516),f592(x17512,x17513,x17514,x17515,x17516)) % 168.22/168.07 [1752]~E(x17521,x17522)+E(f592(x17523,x17521,x17524,x17525,x17526),f592(x17523,x17522,x17524,x17525,x17526)) % 168.22/168.07 [1753]~E(x17531,x17532)+E(f592(x17533,x17534,x17531,x17535,x17536),f592(x17533,x17534,x17532,x17535,x17536)) % 168.22/168.07 [1754]~E(x17541,x17542)+E(f592(x17543,x17544,x17545,x17541,x17546),f592(x17543,x17544,x17545,x17542,x17546)) % 168.22/168.07 [1755]~E(x17551,x17552)+E(f592(x17553,x17554,x17555,x17556,x17551),f592(x17553,x17554,x17555,x17556,x17552)) % 168.22/168.07 [1756]~E(x17561,x17562)+E(f794(x17561,x17563,x17564,x17565),f794(x17562,x17563,x17564,x17565)) % 168.22/168.07 [1757]~E(x17571,x17572)+E(f794(x17573,x17571,x17574,x17575),f794(x17573,x17572,x17574,x17575)) % 168.22/168.07 [1758]~E(x17581,x17582)+E(f794(x17583,x17584,x17581,x17585),f794(x17583,x17584,x17582,x17585)) % 168.22/168.07 [1759]~E(x17591,x17592)+E(f794(x17593,x17594,x17595,x17591),f794(x17593,x17594,x17595,x17592)) % 168.22/168.07 [1760]~E(x17601,x17602)+E(f742(x17601,x17603,x17604),f742(x17602,x17603,x17604)) % 168.22/168.07 [1761]~E(x17611,x17612)+E(f742(x17613,x17611,x17614),f742(x17613,x17612,x17614)) % 168.22/168.07 [1762]~E(x17621,x17622)+E(f742(x17623,x17624,x17621),f742(x17623,x17624,x17622)) % 168.22/168.07 [1763]~E(x17631,x17632)+E(f670(x17631,x17633,x17634,x17635),f670(x17632,x17633,x17634,x17635)) % 168.22/168.07 [1764]~E(x17641,x17642)+E(f670(x17643,x17641,x17644,x17645),f670(x17643,x17642,x17644,x17645)) % 168.22/168.07 [1765]~E(x17651,x17652)+E(f670(x17653,x17654,x17651,x17655),f670(x17653,x17654,x17652,x17655)) % 168.22/168.07 [1766]~E(x17661,x17662)+E(f670(x17663,x17664,x17665,x17661),f670(x17663,x17664,x17665,x17662)) % 168.22/168.07 [1767]~E(x17671,x17672)+E(f450(x17671,x17673,x17674,x17675),f450(x17672,x17673,x17674,x17675)) % 168.22/168.07 [1768]~E(x17681,x17682)+E(f450(x17683,x17681,x17684,x17685),f450(x17683,x17682,x17684,x17685)) % 168.22/168.07 [1769]~E(x17691,x17692)+E(f450(x17693,x17694,x17691,x17695),f450(x17693,x17694,x17692,x17695)) % 168.22/168.07 [1770]~E(x17701,x17702)+E(f450(x17703,x17704,x17705,x17701),f450(x17703,x17704,x17705,x17702)) % 168.22/168.07 [1771]~E(x17711,x17712)+E(f609(x17711,x17713),f609(x17712,x17713)) % 168.22/168.07 [1772]~E(x17721,x17722)+E(f609(x17723,x17721),f609(x17723,x17722)) % 168.22/168.07 [1773]~E(x17731,x17732)+E(f337(x17731,x17733,x17734),f337(x17732,x17733,x17734)) % 168.22/168.07 [1774]~E(x17741,x17742)+E(f337(x17743,x17741,x17744),f337(x17743,x17742,x17744)) % 168.22/168.07 [1775]~E(x17751,x17752)+E(f337(x17753,x17754,x17751),f337(x17753,x17754,x17752)) % 168.22/168.07 [1776]~E(x17761,x17762)+E(f379(x17761,x17763,x17764,x17765),f379(x17762,x17763,x17764,x17765)) % 168.22/168.07 [1777]~E(x17771,x17772)+E(f379(x17773,x17771,x17774,x17775),f379(x17773,x17772,x17774,x17775)) % 168.22/168.07 [1778]~E(x17781,x17782)+E(f379(x17783,x17784,x17781,x17785),f379(x17783,x17784,x17782,x17785)) % 168.22/168.07 [1779]~E(x17791,x17792)+E(f379(x17793,x17794,x17795,x17791),f379(x17793,x17794,x17795,x17792)) % 168.22/168.07 [1780]~E(x17801,x17802)+E(f334(x17801,x17803),f334(x17802,x17803)) % 168.22/168.07 [1781]~E(x17811,x17812)+E(f334(x17813,x17811),f334(x17813,x17812)) % 168.22/168.07 [1782]~E(x17821,x17822)+E(f239(x17821,x17823,x17824),f239(x17822,x17823,x17824)) % 168.22/168.07 [1783]~E(x17831,x17832)+E(f239(x17833,x17831,x17834),f239(x17833,x17832,x17834)) % 168.22/168.07 [1784]~E(x17841,x17842)+E(f239(x17843,x17844,x17841),f239(x17843,x17844,x17842)) % 168.22/168.07 [1785]~E(x17851,x17852)+E(f580(x17851,x17853,x17854),f580(x17852,x17853,x17854)) % 168.22/168.07 [1786]~E(x17861,x17862)+E(f580(x17863,x17861,x17864),f580(x17863,x17862,x17864)) % 168.22/168.07 [1787]~E(x17871,x17872)+E(f580(x17873,x17874,x17871),f580(x17873,x17874,x17872)) % 168.22/168.07 [1788]~E(x17881,x17882)+E(f694(x17881,x17883,x17884,x17885,x17886),f694(x17882,x17883,x17884,x17885,x17886)) % 168.22/168.07 [1789]~E(x17891,x17892)+E(f694(x17893,x17891,x17894,x17895,x17896),f694(x17893,x17892,x17894,x17895,x17896)) % 168.22/168.07 [1790]~E(x17901,x17902)+E(f694(x17903,x17904,x17901,x17905,x17906),f694(x17903,x17904,x17902,x17905,x17906)) % 168.22/168.07 [1791]~E(x17911,x17912)+E(f694(x17913,x17914,x17915,x17911,x17916),f694(x17913,x17914,x17915,x17912,x17916)) % 168.22/168.07 [1792]~E(x17921,x17922)+E(f694(x17923,x17924,x17925,x17926,x17921),f694(x17923,x17924,x17925,x17926,x17922)) % 168.22/168.07 [1793]~E(x17931,x17932)+E(f718(x17931,x17933,x17934,x17935,x17936),f718(x17932,x17933,x17934,x17935,x17936)) % 168.22/168.07 [1794]~E(x17941,x17942)+E(f718(x17943,x17941,x17944,x17945,x17946),f718(x17943,x17942,x17944,x17945,x17946)) % 168.22/168.07 [1795]~E(x17951,x17952)+E(f718(x17953,x17954,x17951,x17955,x17956),f718(x17953,x17954,x17952,x17955,x17956)) % 168.22/168.07 [1796]~E(x17961,x17962)+E(f718(x17963,x17964,x17965,x17961,x17966),f718(x17963,x17964,x17965,x17962,x17966)) % 168.22/168.07 [1797]~E(x17971,x17972)+E(f718(x17973,x17974,x17975,x17976,x17971),f718(x17973,x17974,x17975,x17976,x17972)) % 168.22/168.07 [1798]~E(x17981,x17982)+E(f614(x17981,x17983,x17984),f614(x17982,x17983,x17984)) % 168.22/168.07 [1799]~E(x17991,x17992)+E(f614(x17993,x17991,x17994),f614(x17993,x17992,x17994)) % 168.22/168.07 [1800]~E(x18001,x18002)+E(f614(x18003,x18004,x18001),f614(x18003,x18004,x18002)) % 168.22/168.07 [1801]~E(x18011,x18012)+E(f568(x18011,x18013,x18014,x18015,x18016,x18017),f568(x18012,x18013,x18014,x18015,x18016,x18017)) % 168.22/168.07 [1802]~E(x18021,x18022)+E(f568(x18023,x18021,x18024,x18025,x18026,x18027),f568(x18023,x18022,x18024,x18025,x18026,x18027)) % 168.22/168.07 [1803]~E(x18031,x18032)+E(f568(x18033,x18034,x18031,x18035,x18036,x18037),f568(x18033,x18034,x18032,x18035,x18036,x18037)) % 168.22/168.07 [1804]~E(x18041,x18042)+E(f568(x18043,x18044,x18045,x18041,x18046,x18047),f568(x18043,x18044,x18045,x18042,x18046,x18047)) % 168.22/168.07 [1805]~E(x18051,x18052)+E(f568(x18053,x18054,x18055,x18056,x18051,x18057),f568(x18053,x18054,x18055,x18056,x18052,x18057)) % 168.22/168.07 [1806]~E(x18061,x18062)+E(f568(x18063,x18064,x18065,x18066,x18067,x18061),f568(x18063,x18064,x18065,x18066,x18067,x18062)) % 168.22/168.07 [1807]~E(x18071,x18072)+E(f377(x18071,x18073,x18074,x18075),f377(x18072,x18073,x18074,x18075)) % 168.22/168.07 [1808]~E(x18081,x18082)+E(f377(x18083,x18081,x18084,x18085),f377(x18083,x18082,x18084,x18085)) % 168.22/168.07 [1809]~E(x18091,x18092)+E(f377(x18093,x18094,x18091,x18095),f377(x18093,x18094,x18092,x18095)) % 168.22/168.07 [1810]~E(x18101,x18102)+E(f377(x18103,x18104,x18105,x18101),f377(x18103,x18104,x18105,x18102)) % 168.22/168.07 [1811]~E(x18111,x18112)+E(f664(x18111,x18113,x18114),f664(x18112,x18113,x18114)) % 168.22/168.07 [1812]~E(x18121,x18122)+E(f664(x18123,x18121,x18124),f664(x18123,x18122,x18124)) % 168.22/168.07 [1813]~E(x18131,x18132)+E(f664(x18133,x18134,x18131),f664(x18133,x18134,x18132)) % 168.22/168.07 [1814]~E(x18141,x18142)+E(f836(x18141),f836(x18142)) % 168.22/168.07 [1815]~E(x18151,x18152)+E(f686(x18151,x18153),f686(x18152,x18153)) % 168.22/168.07 [1816]~E(x18161,x18162)+E(f686(x18163,x18161),f686(x18163,x18162)) % 168.22/168.07 [1817]~E(x18171,x18172)+E(f702(x18171,x18173,x18174),f702(x18172,x18173,x18174)) % 168.22/168.07 [1818]~E(x18181,x18182)+E(f702(x18183,x18181,x18184),f702(x18183,x18182,x18184)) % 168.22/168.07 [1819]~E(x18191,x18192)+E(f702(x18193,x18194,x18191),f702(x18193,x18194,x18192)) % 168.22/168.07 [1820]~E(x18201,x18202)+E(f806(x18201,x18203),f806(x18202,x18203)) % 168.22/168.07 [1821]~E(x18211,x18212)+E(f806(x18213,x18211),f806(x18213,x18212)) % 168.22/168.07 [1822]~E(x18221,x18222)+E(f270(x18221,x18223,x18224),f270(x18222,x18223,x18224)) % 168.22/168.07 [1823]~E(x18231,x18232)+E(f270(x18233,x18231,x18234),f270(x18233,x18232,x18234)) % 168.22/168.07 [1824]~E(x18241,x18242)+E(f270(x18243,x18244,x18241),f270(x18243,x18244,x18242)) % 168.22/168.07 [1825]~E(x18251,x18252)+E(f399(x18251,x18253,x18254),f399(x18252,x18253,x18254)) % 168.22/168.07 [1826]~E(x18261,x18262)+E(f399(x18263,x18261,x18264),f399(x18263,x18262,x18264)) % 168.22/168.07 [1827]~E(x18271,x18272)+E(f399(x18273,x18274,x18271),f399(x18273,x18274,x18272)) % 168.22/168.07 [1828]~E(x18281,x18282)+E(f427(x18281,x18283,x18284,x18285),f427(x18282,x18283,x18284,x18285)) % 168.22/168.07 [1829]~E(x18291,x18292)+E(f427(x18293,x18291,x18294,x18295),f427(x18293,x18292,x18294,x18295)) % 168.22/168.07 [1830]~E(x18301,x18302)+E(f427(x18303,x18304,x18301,x18305),f427(x18303,x18304,x18302,x18305)) % 168.22/168.07 [1831]~E(x18311,x18312)+E(f427(x18313,x18314,x18315,x18311),f427(x18313,x18314,x18315,x18312)) % 168.22/168.07 [1832]~E(x18321,x18322)+E(f453(x18321,x18323),f453(x18322,x18323)) % 168.22/168.07 [1833]~E(x18331,x18332)+E(f453(x18333,x18331),f453(x18333,x18332)) % 168.22/168.07 [1834]~E(x18341,x18342)+E(f703(x18341,x18343,x18344),f703(x18342,x18343,x18344)) % 168.22/168.07 [1835]~E(x18351,x18352)+E(f703(x18353,x18351,x18354),f703(x18353,x18352,x18354)) % 168.22/168.07 [1836]~E(x18361,x18362)+E(f703(x18363,x18364,x18361),f703(x18363,x18364,x18362)) % 168.22/168.07 [1837]~E(x18371,x18372)+E(f256(x18371,x18373),f256(x18372,x18373)) % 168.22/168.07 [1838]~E(x18381,x18382)+E(f256(x18383,x18381),f256(x18383,x18382)) % 168.22/168.07 [1839]~E(x18391,x18392)+E(f676(x18391,x18393,x18394),f676(x18392,x18393,x18394)) % 168.22/168.07 [1840]~E(x18401,x18402)+E(f676(x18403,x18401,x18404),f676(x18403,x18402,x18404)) % 168.22/168.07 [1841]~E(x18411,x18412)+E(f676(x18413,x18414,x18411),f676(x18413,x18414,x18412)) % 168.22/168.07 [1842]~E(x18421,x18422)+E(f552(x18421,x18423,x18424,x18425,x18426,x18427),f552(x18422,x18423,x18424,x18425,x18426,x18427)) % 168.22/168.07 [1843]~E(x18431,x18432)+E(f552(x18433,x18431,x18434,x18435,x18436,x18437),f552(x18433,x18432,x18434,x18435,x18436,x18437)) % 168.22/168.07 [1844]~E(x18441,x18442)+E(f552(x18443,x18444,x18441,x18445,x18446,x18447),f552(x18443,x18444,x18442,x18445,x18446,x18447)) % 168.22/168.07 [1845]~E(x18451,x18452)+E(f552(x18453,x18454,x18455,x18451,x18456,x18457),f552(x18453,x18454,x18455,x18452,x18456,x18457)) % 168.22/168.07 [1846]~E(x18461,x18462)+E(f552(x18463,x18464,x18465,x18466,x18461,x18467),f552(x18463,x18464,x18465,x18466,x18462,x18467)) % 168.22/168.07 [1847]~E(x18471,x18472)+E(f552(x18473,x18474,x18475,x18476,x18477,x18471),f552(x18473,x18474,x18475,x18476,x18477,x18472)) % 168.22/168.07 [1848]~E(x18481,x18482)+E(f607(x18481,x18483,x18484),f607(x18482,x18483,x18484)) % 168.22/168.07 [1849]~E(x18491,x18492)+E(f607(x18493,x18491,x18494),f607(x18493,x18492,x18494)) % 168.22/168.07 [1850]~E(x18501,x18502)+E(f607(x18503,x18504,x18501),f607(x18503,x18504,x18502)) % 168.22/168.07 [1851]~E(x18511,x18512)+E(f612(x18511,x18513),f612(x18512,x18513)) % 168.22/168.07 [1852]~E(x18521,x18522)+E(f612(x18523,x18521),f612(x18523,x18522)) % 168.22/168.07 [1853]~E(x18531,x18532)+E(f681(x18531,x18533,x18534,x18535),f681(x18532,x18533,x18534,x18535)) % 168.22/168.07 [1854]~E(x18541,x18542)+E(f681(x18543,x18541,x18544,x18545),f681(x18543,x18542,x18544,x18545)) % 168.22/168.07 [1855]~E(x18551,x18552)+E(f681(x18553,x18554,x18551,x18555),f681(x18553,x18554,x18552,x18555)) % 168.22/168.07 [1856]~E(x18561,x18562)+E(f681(x18563,x18564,x18565,x18561),f681(x18563,x18564,x18565,x18562)) % 168.22/168.07 [1857]~E(x18571,x18572)+E(f394(x18571,x18573,x18574),f394(x18572,x18573,x18574)) % 168.22/168.07 [1858]~E(x18581,x18582)+E(f394(x18583,x18581,x18584),f394(x18583,x18582,x18584)) % 168.22/168.07 [1859]~E(x18591,x18592)+E(f394(x18593,x18594,x18591),f394(x18593,x18594,x18592)) % 168.22/168.07 [1860]~E(x18601,x18602)+E(f369(x18601,x18603),f369(x18602,x18603)) % 168.22/168.07 [1861]~E(x18611,x18612)+E(f369(x18613,x18611),f369(x18613,x18612)) % 168.22/168.07 [1862]~E(x18621,x18622)+E(f713(x18621,x18623,x18624,x18625,x18626,x18627),f713(x18622,x18623,x18624,x18625,x18626,x18627)) % 168.22/168.07 [1863]~E(x18631,x18632)+E(f713(x18633,x18631,x18634,x18635,x18636,x18637),f713(x18633,x18632,x18634,x18635,x18636,x18637)) % 168.22/168.07 [1864]~E(x18641,x18642)+E(f713(x18643,x18644,x18641,x18645,x18646,x18647),f713(x18643,x18644,x18642,x18645,x18646,x18647)) % 168.22/168.07 [1865]~E(x18651,x18652)+E(f713(x18653,x18654,x18655,x18651,x18656,x18657),f713(x18653,x18654,x18655,x18652,x18656,x18657)) % 168.22/168.07 [1866]~E(x18661,x18662)+E(f713(x18663,x18664,x18665,x18666,x18661,x18667),f713(x18663,x18664,x18665,x18666,x18662,x18667)) % 168.22/168.07 [1867]~E(x18671,x18672)+E(f713(x18673,x18674,x18675,x18676,x18677,x18671),f713(x18673,x18674,x18675,x18676,x18677,x18672)) % 168.22/168.07 [1868]~E(x18681,x18682)+E(f425(x18681,x18683,x18684),f425(x18682,x18683,x18684)) % 168.22/168.07 [1869]~E(x18691,x18692)+E(f425(x18693,x18691,x18694),f425(x18693,x18692,x18694)) % 168.22/168.07 [1870]~E(x18701,x18702)+E(f425(x18703,x18704,x18701),f425(x18703,x18704,x18702)) % 168.22/168.07 [1871]~E(x18711,x18712)+E(f449(x18711,x18713,x18714,x18715),f449(x18712,x18713,x18714,x18715)) % 168.22/168.07 [1872]~E(x18721,x18722)+E(f449(x18723,x18721,x18724,x18725),f449(x18723,x18722,x18724,x18725)) % 168.22/168.07 [1873]~E(x18731,x18732)+E(f449(x18733,x18734,x18731,x18735),f449(x18733,x18734,x18732,x18735)) % 168.22/168.07 [1874]~E(x18741,x18742)+E(f449(x18743,x18744,x18745,x18741),f449(x18743,x18744,x18745,x18742)) % 168.22/168.07 [1875]~E(x18751,x18752)+E(f510(x18751,x18753,x18754,x18755,x18756),f510(x18752,x18753,x18754,x18755,x18756)) % 168.22/168.07 [1876]~E(x18761,x18762)+E(f510(x18763,x18761,x18764,x18765,x18766),f510(x18763,x18762,x18764,x18765,x18766)) % 168.22/168.07 [1877]~E(x18771,x18772)+E(f510(x18773,x18774,x18771,x18775,x18776),f510(x18773,x18774,x18772,x18775,x18776)) % 168.22/168.07 [1878]~E(x18781,x18782)+E(f510(x18783,x18784,x18785,x18781,x18786),f510(x18783,x18784,x18785,x18782,x18786)) % 168.22/168.07 [1879]~E(x18791,x18792)+E(f510(x18793,x18794,x18795,x18796,x18791),f510(x18793,x18794,x18795,x18796,x18792)) % 168.22/168.07 [1880]~E(x18801,x18802)+E(f576(x18801,x18803,x18804),f576(x18802,x18803,x18804)) % 168.22/168.07 [1881]~E(x18811,x18812)+E(f576(x18813,x18811,x18814),f576(x18813,x18812,x18814)) % 168.22/168.07 [1882]~E(x18821,x18822)+E(f576(x18823,x18824,x18821),f576(x18823,x18824,x18822)) % 168.22/168.07 [1883]~E(x18831,x18832)+E(f828(x18831,x18833,x18834),f828(x18832,x18833,x18834)) % 168.22/168.07 [1884]~E(x18841,x18842)+E(f828(x18843,x18841,x18844),f828(x18843,x18842,x18844)) % 168.22/168.07 [1885]~E(x18851,x18852)+E(f828(x18853,x18854,x18851),f828(x18853,x18854,x18852)) % 168.22/168.07 [1886]~E(x18861,x18862)+E(f276(x18861,x18863,x18864,x18865,x18866),f276(x18862,x18863,x18864,x18865,x18866)) % 168.22/168.07 [1887]~E(x18871,x18872)+E(f276(x18873,x18871,x18874,x18875,x18876),f276(x18873,x18872,x18874,x18875,x18876)) % 168.22/168.07 [1888]~E(x18881,x18882)+E(f276(x18883,x18884,x18881,x18885,x18886),f276(x18883,x18884,x18882,x18885,x18886)) % 168.22/168.07 [1889]~E(x18891,x18892)+E(f276(x18893,x18894,x18895,x18891,x18896),f276(x18893,x18894,x18895,x18892,x18896)) % 168.22/168.07 [1890]~E(x18901,x18902)+E(f276(x18903,x18904,x18905,x18906,x18901),f276(x18903,x18904,x18905,x18906,x18902)) % 168.22/168.07 [1891]~E(x18911,x18912)+E(f393(x18911,x18913,x18914,x18915,x18916),f393(x18912,x18913,x18914,x18915,x18916)) % 168.22/168.07 [1892]~E(x18921,x18922)+E(f393(x18923,x18921,x18924,x18925,x18926),f393(x18923,x18922,x18924,x18925,x18926)) % 168.22/168.07 [1893]~E(x18931,x18932)+E(f393(x18933,x18934,x18931,x18935,x18936),f393(x18933,x18934,x18932,x18935,x18936)) % 168.22/168.07 [1894]~E(x18941,x18942)+E(f393(x18943,x18944,x18945,x18941,x18946),f393(x18943,x18944,x18945,x18942,x18946)) % 168.22/168.07 [1895]~E(x18951,x18952)+E(f393(x18953,x18954,x18955,x18956,x18951),f393(x18953,x18954,x18955,x18956,x18952)) % 168.22/168.07 [1896]~E(x18961,x18962)+E(f674(x18961,x18963,x18964),f674(x18962,x18963,x18964)) % 168.22/168.07 [1897]~E(x18971,x18972)+E(f674(x18973,x18971,x18974),f674(x18973,x18972,x18974)) % 168.22/168.07 [1898]~E(x18981,x18982)+E(f674(x18983,x18984,x18981),f674(x18983,x18984,x18982)) % 168.22/168.07 [1899]~E(x18991,x18992)+E(f741(x18991,x18993,x18994),f741(x18992,x18993,x18994)) % 168.22/168.07 [1900]~E(x19001,x19002)+E(f741(x19003,x19001,x19004),f741(x19003,x19002,x19004)) % 168.22/168.07 [1901]~E(x19011,x19012)+E(f741(x19013,x19014,x19011),f741(x19013,x19014,x19012)) % 168.22/168.07 [1902]~E(x19021,x19022)+E(f687(x19021,x19023,x19024),f687(x19022,x19023,x19024)) % 168.22/168.07 [1903]~E(x19031,x19032)+E(f687(x19033,x19031,x19034),f687(x19033,x19032,x19034)) % 168.22/168.07 [1904]~E(x19041,x19042)+E(f687(x19043,x19044,x19041),f687(x19043,x19044,x19042)) % 168.22/168.07 [1905]~E(x19051,x19052)+E(f487(x19051,x19053,x19054,x19055,x19056),f487(x19052,x19053,x19054,x19055,x19056)) % 168.22/168.07 [1906]~E(x19061,x19062)+E(f487(x19063,x19061,x19064,x19065,x19066),f487(x19063,x19062,x19064,x19065,x19066)) % 168.22/168.07 [1907]~E(x19071,x19072)+E(f487(x19073,x19074,x19071,x19075,x19076),f487(x19073,x19074,x19072,x19075,x19076)) % 168.22/168.07 [1908]~E(x19081,x19082)+E(f487(x19083,x19084,x19085,x19081,x19086),f487(x19083,x19084,x19085,x19082,x19086)) % 168.22/168.07 [1909]~E(x19091,x19092)+E(f487(x19093,x19094,x19095,x19096,x19091),f487(x19093,x19094,x19095,x19096,x19092)) % 168.22/168.07 [1910]~E(x19101,x19102)+E(f475(x19101,x19103,x19104,x19105,x19106),f475(x19102,x19103,x19104,x19105,x19106)) % 168.22/168.07 [1911]~E(x19111,x19112)+E(f475(x19113,x19111,x19114,x19115,x19116),f475(x19113,x19112,x19114,x19115,x19116)) % 168.22/168.07 [1912]~E(x19121,x19122)+E(f475(x19123,x19124,x19121,x19125,x19126),f475(x19123,x19124,x19122,x19125,x19126)) % 168.22/168.07 [1913]~E(x19131,x19132)+E(f475(x19133,x19134,x19135,x19131,x19136),f475(x19133,x19134,x19135,x19132,x19136)) % 168.22/168.07 [1914]~E(x19141,x19142)+E(f475(x19143,x19144,x19145,x19146,x19141),f475(x19143,x19144,x19145,x19146,x19142)) % 168.22/168.07 [1915]~E(x19151,x19152)+E(f723(x19151,x19153,x19154,x19155,x19156),f723(x19152,x19153,x19154,x19155,x19156)) % 168.22/168.07 [1916]~E(x19161,x19162)+E(f723(x19163,x19161,x19164,x19165,x19166),f723(x19163,x19162,x19164,x19165,x19166)) % 168.22/168.07 [1917]~E(x19171,x19172)+E(f723(x19173,x19174,x19171,x19175,x19176),f723(x19173,x19174,x19172,x19175,x19176)) % 168.22/168.07 [1918]~E(x19181,x19182)+E(f723(x19183,x19184,x19185,x19181,x19186),f723(x19183,x19184,x19185,x19182,x19186)) % 168.22/168.07 [1919]~E(x19191,x19192)+E(f723(x19193,x19194,x19195,x19196,x19191),f723(x19193,x19194,x19195,x19196,x19192)) % 168.22/168.07 [1920]~E(x19201,x19202)+E(f661(x19201,x19203,x19204),f661(x19202,x19203,x19204)) % 168.22/168.07 [1921]~E(x19211,x19212)+E(f661(x19213,x19211,x19214),f661(x19213,x19212,x19214)) % 168.22/168.07 [1922]~E(x19221,x19222)+E(f661(x19223,x19224,x19221),f661(x19223,x19224,x19222)) % 168.22/168.07 [1923]~E(x19231,x19232)+E(f156(x19231,x19233),f156(x19232,x19233)) % 168.22/168.07 [1924]~E(x19241,x19242)+E(f156(x19243,x19241),f156(x19243,x19242)) % 168.22/168.07 [1925]~E(x19251,x19252)+E(f380(x19251,x19253),f380(x19252,x19253)) % 168.22/168.07 [1926]~E(x19261,x19262)+E(f380(x19263,x19261),f380(x19263,x19262)) % 168.22/168.07 [1927]~E(x19271,x19272)+E(f443(x19271,x19273),f443(x19272,x19273)) % 168.22/168.07 [1928]~E(x19281,x19282)+E(f443(x19283,x19281),f443(x19283,x19282)) % 168.22/168.07 [1929]~E(x19291,x19292)+E(f545(x19291,x19293),f545(x19292,x19293)) % 168.22/168.07 [1930]~E(x19301,x19302)+E(f545(x19303,x19301),f545(x19303,x19302)) % 168.22/168.07 [1931]~E(x19311,x19312)+E(f401(x19311,x19313,x19314),f401(x19312,x19313,x19314)) % 168.22/168.07 [1932]~E(x19321,x19322)+E(f401(x19323,x19321,x19324),f401(x19323,x19322,x19324)) % 168.22/168.07 [1933]~E(x19331,x19332)+E(f401(x19333,x19334,x19331),f401(x19333,x19334,x19332)) % 168.22/168.07 [1934]~E(x19341,x19342)+E(f353(x19341,x19343,x19344),f353(x19342,x19343,x19344)) % 168.22/168.07 [1935]~E(x19351,x19352)+E(f353(x19353,x19351,x19354),f353(x19353,x19352,x19354)) % 168.22/168.07 [1936]~E(x19361,x19362)+E(f353(x19363,x19364,x19361),f353(x19363,x19364,x19362)) % 168.22/168.07 [1937]~E(x19371,x19372)+E(f439(x19371,x19373,x19374,x19375),f439(x19372,x19373,x19374,x19375)) % 168.22/168.07 [1938]~E(x19381,x19382)+E(f439(x19383,x19381,x19384,x19385),f439(x19383,x19382,x19384,x19385)) % 168.22/168.07 [1939]~E(x19391,x19392)+E(f439(x19393,x19394,x19391,x19395),f439(x19393,x19394,x19392,x19395)) % 168.22/168.07 [1940]~E(x19401,x19402)+E(f439(x19403,x19404,x19405,x19401),f439(x19403,x19404,x19405,x19402)) % 168.22/168.07 [1941]~E(x19411,x19412)+E(f512(x19411,x19413,x19414,x19415,x19416),f512(x19412,x19413,x19414,x19415,x19416)) % 168.22/168.07 [1942]~E(x19421,x19422)+E(f512(x19423,x19421,x19424,x19425,x19426),f512(x19423,x19422,x19424,x19425,x19426)) % 168.22/168.07 [1943]~E(x19431,x19432)+E(f512(x19433,x19434,x19431,x19435,x19436),f512(x19433,x19434,x19432,x19435,x19436)) % 168.22/168.07 [1944]~E(x19441,x19442)+E(f512(x19443,x19444,x19445,x19441,x19446),f512(x19443,x19444,x19445,x19442,x19446)) % 168.22/168.07 [1945]~E(x19451,x19452)+E(f512(x19453,x19454,x19455,x19456,x19451),f512(x19453,x19454,x19455,x19456,x19452)) % 168.22/168.07 [1946]~E(x19461,x19462)+E(f729(x19461,x19463,x19464,x19465,x19466,x19467),f729(x19462,x19463,x19464,x19465,x19466,x19467)) % 168.22/168.07 [1947]~E(x19471,x19472)+E(f729(x19473,x19471,x19474,x19475,x19476,x19477),f729(x19473,x19472,x19474,x19475,x19476,x19477)) % 168.22/168.07 [1948]~E(x19481,x19482)+E(f729(x19483,x19484,x19481,x19485,x19486,x19487),f729(x19483,x19484,x19482,x19485,x19486,x19487)) % 168.22/168.07 [1949]~E(x19491,x19492)+E(f729(x19493,x19494,x19495,x19491,x19496,x19497),f729(x19493,x19494,x19495,x19492,x19496,x19497)) % 168.22/168.07 [1950]~E(x19501,x19502)+E(f729(x19503,x19504,x19505,x19506,x19501,x19507),f729(x19503,x19504,x19505,x19506,x19502,x19507)) % 168.22/168.07 [1951]~E(x19511,x19512)+E(f729(x19513,x19514,x19515,x19516,x19517,x19511),f729(x19513,x19514,x19515,x19516,x19517,x19512)) % 168.22/168.07 [1952]~E(x19521,x19522)+E(f63(x19521,x19523),f63(x19522,x19523)) % 168.22/168.07 [1953]~E(x19531,x19532)+E(f63(x19533,x19531),f63(x19533,x19532)) % 168.22/168.07 [1954]~E(x19541,x19542)+E(f336(x19541,x19543,x19544),f336(x19542,x19543,x19544)) % 168.22/168.07 [1955]~E(x19551,x19552)+E(f336(x19553,x19551,x19554),f336(x19553,x19552,x19554)) % 168.22/168.07 [1956]~E(x19561,x19562)+E(f336(x19563,x19564,x19561),f336(x19563,x19564,x19562)) % 168.22/168.07 [1957]~E(x19571,x19572)+E(f770(x19571,x19573,x19574,x19575),f770(x19572,x19573,x19574,x19575)) % 168.22/168.07 [1958]~E(x19581,x19582)+E(f770(x19583,x19581,x19584,x19585),f770(x19583,x19582,x19584,x19585)) % 168.22/168.07 [1959]~E(x19591,x19592)+E(f770(x19593,x19594,x19591,x19595),f770(x19593,x19594,x19592,x19595)) % 168.22/168.07 [1960]~E(x19601,x19602)+E(f770(x19603,x19604,x19605,x19601),f770(x19603,x19604,x19605,x19602)) % 168.22/168.07 [1961]~E(x19611,x19612)+E(f803(x19611,x19613),f803(x19612,x19613)) % 168.22/168.07 [1962]~E(x19621,x19622)+E(f803(x19623,x19621),f803(x19623,x19622)) % 168.22/168.07 [1963]~E(x19631,x19632)+E(f408(x19631,x19633,x19634),f408(x19632,x19633,x19634)) % 168.22/168.07 [1964]~E(x19641,x19642)+E(f408(x19643,x19641,x19644),f408(x19643,x19642,x19644)) % 168.22/168.07 [1965]~E(x19651,x19652)+E(f408(x19653,x19654,x19651),f408(x19653,x19654,x19652)) % 168.22/168.07 [1966]~E(x19661,x19662)+E(f332(x19661,x19663,x19664),f332(x19662,x19663,x19664)) % 168.22/168.07 [1967]~E(x19671,x19672)+E(f332(x19673,x19671,x19674),f332(x19673,x19672,x19674)) % 168.22/168.07 [1968]~E(x19681,x19682)+E(f332(x19683,x19684,x19681),f332(x19683,x19684,x19682)) % 168.22/168.07 [1969]~E(x19691,x19692)+E(f695(x19691,x19693,x19694),f695(x19692,x19693,x19694)) % 168.22/168.07 [1970]~E(x19701,x19702)+E(f695(x19703,x19701,x19704),f695(x19703,x19702,x19704)) % 168.22/168.07 [1971]~E(x19711,x19712)+E(f695(x19713,x19714,x19711),f695(x19713,x19714,x19712)) % 168.22/168.07 [1972]~E(x19721,x19722)+E(f302(x19721,x19723,x19724,x19725,x19726),f302(x19722,x19723,x19724,x19725,x19726)) % 168.22/168.07 [1973]~E(x19731,x19732)+E(f302(x19733,x19731,x19734,x19735,x19736),f302(x19733,x19732,x19734,x19735,x19736)) % 168.22/168.07 [1974]~E(x19741,x19742)+E(f302(x19743,x19744,x19741,x19745,x19746),f302(x19743,x19744,x19742,x19745,x19746)) % 168.22/168.07 [1975]~E(x19751,x19752)+E(f302(x19753,x19754,x19755,x19751,x19756),f302(x19753,x19754,x19755,x19752,x19756)) % 168.22/168.07 [1976]~E(x19761,x19762)+E(f302(x19763,x19764,x19765,x19766,x19761),f302(x19763,x19764,x19765,x19766,x19762)) % 168.22/168.07 [1977]~E(x19771,x19772)+E(f467(x19771,x19773,x19774,x19775,x19776,x19777),f467(x19772,x19773,x19774,x19775,x19776,x19777)) % 168.22/168.07 [1978]~E(x19781,x19782)+E(f467(x19783,x19781,x19784,x19785,x19786,x19787),f467(x19783,x19782,x19784,x19785,x19786,x19787)) % 168.22/168.07 [1979]~E(x19791,x19792)+E(f467(x19793,x19794,x19791,x19795,x19796,x19797),f467(x19793,x19794,x19792,x19795,x19796,x19797)) % 168.22/168.07 [1980]~E(x19801,x19802)+E(f467(x19803,x19804,x19805,x19801,x19806,x19807),f467(x19803,x19804,x19805,x19802,x19806,x19807)) % 168.22/168.07 [1981]~E(x19811,x19812)+E(f467(x19813,x19814,x19815,x19816,x19811,x19817),f467(x19813,x19814,x19815,x19816,x19812,x19817)) % 168.22/168.07 [1982]~E(x19821,x19822)+E(f467(x19823,x19824,x19825,x19826,x19827,x19821),f467(x19823,x19824,x19825,x19826,x19827,x19822)) % 168.22/168.07 [1983]~E(x19831,x19832)+E(f420(x19831,x19833,x19834,x19835),f420(x19832,x19833,x19834,x19835)) % 168.22/168.07 [1984]~E(x19841,x19842)+E(f420(x19843,x19841,x19844,x19845),f420(x19843,x19842,x19844,x19845)) % 168.22/168.07 [1985]~E(x19851,x19852)+E(f420(x19853,x19854,x19851,x19855),f420(x19853,x19854,x19852,x19855)) % 168.22/168.07 [1986]~E(x19861,x19862)+E(f420(x19863,x19864,x19865,x19861),f420(x19863,x19864,x19865,x19862)) % 168.22/168.07 [1987]~E(x19871,x19872)+E(f432(x19871,x19873,x19874,x19875),f432(x19872,x19873,x19874,x19875)) % 168.22/168.07 [1988]~E(x19881,x19882)+E(f432(x19883,x19881,x19884,x19885),f432(x19883,x19882,x19884,x19885)) % 168.22/168.07 [1989]~E(x19891,x19892)+E(f432(x19893,x19894,x19891,x19895),f432(x19893,x19894,x19892,x19895)) % 168.22/168.07 [1990]~E(x19901,x19902)+E(f432(x19903,x19904,x19905,x19901),f432(x19903,x19904,x19905,x19902)) % 168.22/168.07 [1991]~E(x19911,x19912)+E(f731(x19911,x19913,x19914),f731(x19912,x19913,x19914)) % 168.22/168.07 [1992]~E(x19921,x19922)+E(f731(x19923,x19921,x19924),f731(x19923,x19922,x19924)) % 168.22/168.07 [1993]~E(x19931,x19932)+E(f731(x19933,x19934,x19931),f731(x19933,x19934,x19932)) % 168.22/168.07 [1994]~E(x19941,x19942)+E(f531(x19941,x19943,x19944),f531(x19942,x19943,x19944)) % 168.22/168.07 [1995]~E(x19951,x19952)+E(f531(x19953,x19951,x19954),f531(x19953,x19952,x19954)) % 168.22/168.07 [1996]~E(x19961,x19962)+E(f531(x19963,x19964,x19961),f531(x19963,x19964,x19962)) % 168.22/168.07 [1997]~E(x19971,x19972)+E(f662(x19971,x19973,x19974,x19975,x19976),f662(x19972,x19973,x19974,x19975,x19976)) % 168.22/168.07 [1998]~E(x19981,x19982)+E(f662(x19983,x19981,x19984,x19985,x19986),f662(x19983,x19982,x19984,x19985,x19986)) % 168.22/168.07 [1999]~E(x19991,x19992)+E(f662(x19993,x19994,x19991,x19995,x19996),f662(x19993,x19994,x19992,x19995,x19996)) % 168.22/168.07 [2000]~E(x20001,x20002)+E(f662(x20003,x20004,x20005,x20001,x20006),f662(x20003,x20004,x20005,x20002,x20006)) % 168.22/168.07 [2001]~E(x20011,x20012)+E(f662(x20013,x20014,x20015,x20016,x20011),f662(x20013,x20014,x20015,x20016,x20012)) % 168.22/168.07 [2002]~E(x20021,x20022)+E(f542(x20021,x20023),f542(x20022,x20023)) % 168.22/168.07 [2003]~E(x20031,x20032)+E(f542(x20033,x20031),f542(x20033,x20032)) % 168.22/168.07 [2004]~E(x20041,x20042)+E(f469(x20041,x20043,x20044,x20045),f469(x20042,x20043,x20044,x20045)) % 168.22/168.07 [2005]~E(x20051,x20052)+E(f469(x20053,x20051,x20054,x20055),f469(x20053,x20052,x20054,x20055)) % 168.22/168.07 [2006]~E(x20061,x20062)+E(f469(x20063,x20064,x20061,x20065),f469(x20063,x20064,x20062,x20065)) % 168.22/168.07 [2007]~E(x20071,x20072)+E(f469(x20073,x20074,x20075,x20071),f469(x20073,x20074,x20075,x20072)) % 168.22/168.07 [2008]~E(x20081,x20082)+E(f472(x20081,x20083,x20084,x20085,x20086),f472(x20082,x20083,x20084,x20085,x20086)) % 168.22/168.07 [2009]~E(x20091,x20092)+E(f472(x20093,x20091,x20094,x20095,x20096),f472(x20093,x20092,x20094,x20095,x20096)) % 168.22/168.07 [2010]~E(x20101,x20102)+E(f472(x20103,x20104,x20101,x20105,x20106),f472(x20103,x20104,x20102,x20105,x20106)) % 168.22/168.07 [2011]~E(x20111,x20112)+E(f472(x20113,x20114,x20115,x20111,x20116),f472(x20113,x20114,x20115,x20112,x20116)) % 168.22/168.07 [2012]~E(x20121,x20122)+E(f472(x20123,x20124,x20125,x20126,x20121),f472(x20123,x20124,x20125,x20126,x20122)) % 168.22/168.07 [2013]~E(x20131,x20132)+E(f486(x20131,x20133,x20134,x20135,x20136),f486(x20132,x20133,x20134,x20135,x20136)) % 168.22/168.07 [2014]~E(x20141,x20142)+E(f486(x20143,x20141,x20144,x20145,x20146),f486(x20143,x20142,x20144,x20145,x20146)) % 168.22/168.07 [2015]~E(x20151,x20152)+E(f486(x20153,x20154,x20151,x20155,x20156),f486(x20153,x20154,x20152,x20155,x20156)) % 168.22/168.07 [2016]~E(x20161,x20162)+E(f486(x20163,x20164,x20165,x20161,x20166),f486(x20163,x20164,x20165,x20162,x20166)) % 168.22/168.07 [2017]~E(x20171,x20172)+E(f486(x20173,x20174,x20175,x20176,x20171),f486(x20173,x20174,x20175,x20176,x20172)) % 168.22/168.07 [2018]~E(x20181,x20182)+E(f503(x20181,x20183,x20184,x20185),f503(x20182,x20183,x20184,x20185)) % 168.22/168.07 [2019]~E(x20191,x20192)+E(f503(x20193,x20191,x20194,x20195),f503(x20193,x20192,x20194,x20195)) % 168.22/168.07 [2020]~E(x20201,x20202)+E(f503(x20203,x20204,x20201,x20205),f503(x20203,x20204,x20202,x20205)) % 168.22/168.07 [2021]~E(x20211,x20212)+E(f503(x20213,x20214,x20215,x20211),f503(x20213,x20214,x20215,x20212)) % 168.22/168.07 [2022]~E(x20221,x20222)+E(f403(x20221,x20223,x20224),f403(x20222,x20223,x20224)) % 168.22/168.07 [2023]~E(x20231,x20232)+E(f403(x20233,x20231,x20234),f403(x20233,x20232,x20234)) % 168.22/168.07 [2024]~E(x20241,x20242)+E(f403(x20243,x20244,x20241),f403(x20243,x20244,x20242)) % 168.22/168.07 [2025]~E(x20251,x20252)+E(f304(x20251,x20253,x20254,x20255,x20256,x20257),f304(x20252,x20253,x20254,x20255,x20256,x20257)) % 168.22/168.07 [2026]~E(x20261,x20262)+E(f304(x20263,x20261,x20264,x20265,x20266,x20267),f304(x20263,x20262,x20264,x20265,x20266,x20267)) % 168.22/168.07 [2027]~E(x20271,x20272)+E(f304(x20273,x20274,x20271,x20275,x20276,x20277),f304(x20273,x20274,x20272,x20275,x20276,x20277)) % 168.22/168.07 [2028]~E(x20281,x20282)+E(f304(x20283,x20284,x20285,x20281,x20286,x20287),f304(x20283,x20284,x20285,x20282,x20286,x20287)) % 168.22/168.07 [2029]~E(x20291,x20292)+E(f304(x20293,x20294,x20295,x20296,x20291,x20297),f304(x20293,x20294,x20295,x20296,x20292,x20297)) % 168.22/168.07 [2030]~E(x20301,x20302)+E(f304(x20303,x20304,x20305,x20306,x20307,x20301),f304(x20303,x20304,x20305,x20306,x20307,x20302)) % 168.22/168.07 [2031]~E(x20311,x20312)+E(f648(x20311,x20313,x20314),f648(x20312,x20313,x20314)) % 168.22/168.07 [2032]~E(x20321,x20322)+E(f648(x20323,x20321,x20324),f648(x20323,x20322,x20324)) % 168.22/168.07 [2033]~E(x20331,x20332)+E(f648(x20333,x20334,x20331),f648(x20333,x20334,x20332)) % 168.22/168.07 [2034]~E(x20341,x20342)+E(f365(x20341,x20343,x20344),f365(x20342,x20343,x20344)) % 168.22/168.07 [2035]~E(x20351,x20352)+E(f365(x20353,x20351,x20354),f365(x20353,x20352,x20354)) % 168.22/168.07 [2036]~E(x20361,x20362)+E(f365(x20363,x20364,x20361),f365(x20363,x20364,x20362)) % 168.22/168.07 [2037]~E(x20371,x20372)+E(f498(x20371,x20373,x20374,x20375,x20376,x20377,x20378),f498(x20372,x20373,x20374,x20375,x20376,x20377,x20378)) % 168.22/168.07 [2038]~E(x20381,x20382)+E(f498(x20383,x20381,x20384,x20385,x20386,x20387,x20388),f498(x20383,x20382,x20384,x20385,x20386,x20387,x20388)) % 168.22/168.07 [2039]~E(x20391,x20392)+E(f498(x20393,x20394,x20391,x20395,x20396,x20397,x20398),f498(x20393,x20394,x20392,x20395,x20396,x20397,x20398)) % 168.22/168.07 [2040]~E(x20401,x20402)+E(f498(x20403,x20404,x20405,x20401,x20406,x20407,x20408),f498(x20403,x20404,x20405,x20402,x20406,x20407,x20408)) % 168.22/168.07 [2041]~E(x20411,x20412)+E(f498(x20413,x20414,x20415,x20416,x20411,x20417,x20418),f498(x20413,x20414,x20415,x20416,x20412,x20417,x20418)) % 168.22/168.07 [2042]~E(x20421,x20422)+E(f498(x20423,x20424,x20425,x20426,x20427,x20421,x20428),f498(x20423,x20424,x20425,x20426,x20427,x20422,x20428)) % 168.22/168.07 [2043]~E(x20431,x20432)+E(f498(x20433,x20434,x20435,x20436,x20437,x20438,x20431),f498(x20433,x20434,x20435,x20436,x20437,x20438,x20432)) % 168.22/168.07 [2044]~E(x20441,x20442)+E(f835(x20441,x20443,x20444),f835(x20442,x20443,x20444)) % 168.22/168.07 [2045]~E(x20451,x20452)+E(f835(x20453,x20451,x20454),f835(x20453,x20452,x20454)) % 168.22/168.07 [2046]~E(x20461,x20462)+E(f835(x20463,x20464,x20461),f835(x20463,x20464,x20462)) % 168.22/168.07 [2047]~E(x20471,x20472)+E(f831(x20471,x20473,x20474),f831(x20472,x20473,x20474)) % 168.22/168.07 [2048]~E(x20481,x20482)+E(f831(x20483,x20481,x20484),f831(x20483,x20482,x20484)) % 168.22/168.07 [2049]~E(x20491,x20492)+E(f831(x20493,x20494,x20491),f831(x20493,x20494,x20492)) % 168.22/168.07 [2050]~E(x20501,x20502)+E(f536(x20501,x20503,x20504,x20505,x20506,x20507),f536(x20502,x20503,x20504,x20505,x20506,x20507)) % 168.22/168.07 [2051]~E(x20511,x20512)+E(f536(x20513,x20511,x20514,x20515,x20516,x20517),f536(x20513,x20512,x20514,x20515,x20516,x20517)) % 168.22/168.07 [2052]~E(x20521,x20522)+E(f536(x20523,x20524,x20521,x20525,x20526,x20527),f536(x20523,x20524,x20522,x20525,x20526,x20527)) % 168.22/168.07 [2053]~E(x20531,x20532)+E(f536(x20533,x20534,x20535,x20531,x20536,x20537),f536(x20533,x20534,x20535,x20532,x20536,x20537)) % 168.22/168.07 [2054]~E(x20541,x20542)+E(f536(x20543,x20544,x20545,x20546,x20541,x20547),f536(x20543,x20544,x20545,x20546,x20542,x20547)) % 168.22/168.07 [2055]~E(x20551,x20552)+E(f536(x20553,x20554,x20555,x20556,x20557,x20551),f536(x20553,x20554,x20555,x20556,x20557,x20552)) % 168.22/168.07 [2056]~E(x20561,x20562)+E(f748(x20561,x20563),f748(x20562,x20563)) % 168.22/168.07 [2057]~E(x20571,x20572)+E(f748(x20573,x20571),f748(x20573,x20572)) % 168.22/168.07 [2058]~E(x20581,x20582)+E(f759(x20581,x20583,x20584,x20585,x20586),f759(x20582,x20583,x20584,x20585,x20586)) % 168.22/168.07 [2059]~E(x20591,x20592)+E(f759(x20593,x20591,x20594,x20595,x20596),f759(x20593,x20592,x20594,x20595,x20596)) % 168.22/168.07 [2060]~E(x20601,x20602)+E(f759(x20603,x20604,x20601,x20605,x20606),f759(x20603,x20604,x20602,x20605,x20606)) % 168.22/168.07 [2061]~E(x20611,x20612)+E(f759(x20613,x20614,x20615,x20611,x20616),f759(x20613,x20614,x20615,x20612,x20616)) % 168.22/168.07 [2062]~E(x20621,x20622)+E(f759(x20623,x20624,x20625,x20626,x20621),f759(x20623,x20624,x20625,x20626,x20622)) % 168.22/168.07 [2063]~E(x20631,x20632)+E(f448(x20631,x20633,x20634,x20635),f448(x20632,x20633,x20634,x20635)) % 168.22/168.07 [2064]~E(x20641,x20642)+E(f448(x20643,x20641,x20644,x20645),f448(x20643,x20642,x20644,x20645)) % 168.22/168.07 [2065]~E(x20651,x20652)+E(f448(x20653,x20654,x20651,x20655),f448(x20653,x20654,x20652,x20655)) % 168.22/168.07 [2066]~E(x20661,x20662)+E(f448(x20663,x20664,x20665,x20661),f448(x20663,x20664,x20665,x20662)) % 168.22/168.07 [2067]~E(x20671,x20672)+E(f384(x20671,x20673),f384(x20672,x20673)) % 168.22/168.07 [2068]~E(x20681,x20682)+E(f384(x20683,x20681),f384(x20683,x20682)) % 168.22/168.07 [2069]~E(x20691,x20692)+E(f352(x20691,x20693,x20694),f352(x20692,x20693,x20694)) % 168.22/168.07 [2070]~E(x20701,x20702)+E(f352(x20703,x20701,x20704),f352(x20703,x20702,x20704)) % 168.22/168.07 [2071]~E(x20711,x20712)+E(f352(x20713,x20714,x20711),f352(x20713,x20714,x20712)) % 168.22/168.07 [2072]~E(x20721,x20722)+E(f77(x20721,x20723,x20724),f77(x20722,x20723,x20724)) % 168.22/168.07 [2073]~E(x20731,x20732)+E(f77(x20733,x20731,x20734),f77(x20733,x20732,x20734)) % 168.22/168.07 [2074]~E(x20741,x20742)+E(f77(x20743,x20744,x20741),f77(x20743,x20744,x20742)) % 168.22/168.07 [2075]~E(x20751,x20752)+E(f321(x20751,x20753,x20754,x20755),f321(x20752,x20753,x20754,x20755)) % 168.22/168.07 [2076]~E(x20761,x20762)+E(f321(x20763,x20761,x20764,x20765),f321(x20763,x20762,x20764,x20765)) % 168.22/168.07 [2077]~E(x20771,x20772)+E(f321(x20773,x20774,x20771,x20775),f321(x20773,x20774,x20772,x20775)) % 168.22/168.07 [2078]~E(x20781,x20782)+E(f321(x20783,x20784,x20785,x20781),f321(x20783,x20784,x20785,x20782)) % 168.22/168.07 [2079]~E(x20791,x20792)+E(f762(x20791,x20793,x20794,x20795,x20796),f762(x20792,x20793,x20794,x20795,x20796)) % 168.22/168.07 [2080]~E(x20801,x20802)+E(f762(x20803,x20801,x20804,x20805,x20806),f762(x20803,x20802,x20804,x20805,x20806)) % 168.22/168.07 [2081]~E(x20811,x20812)+E(f762(x20813,x20814,x20811,x20815,x20816),f762(x20813,x20814,x20812,x20815,x20816)) % 168.22/168.07 [2082]~E(x20821,x20822)+E(f762(x20823,x20824,x20825,x20821,x20826),f762(x20823,x20824,x20825,x20822,x20826)) % 168.22/168.07 [2083]~E(x20831,x20832)+E(f762(x20833,x20834,x20835,x20836,x20831),f762(x20833,x20834,x20835,x20836,x20832)) % 168.22/168.07 [2084]~E(x20841,x20842)+E(f292(x20841,x20843,x20844),f292(x20842,x20843,x20844)) % 168.22/168.07 [2085]~E(x20851,x20852)+E(f292(x20853,x20851,x20854),f292(x20853,x20852,x20854)) % 168.22/168.07 [2086]~E(x20861,x20862)+E(f292(x20863,x20864,x20861),f292(x20863,x20864,x20862)) % 168.22/168.07 [2087]~E(x20871,x20872)+E(f641(x20871,x20873,x20874),f641(x20872,x20873,x20874)) % 168.22/168.07 [2088]~E(x20881,x20882)+E(f641(x20883,x20881,x20884),f641(x20883,x20882,x20884)) % 168.22/168.07 [2089]~E(x20891,x20892)+E(f641(x20893,x20894,x20891),f641(x20893,x20894,x20892)) % 168.22/168.07 [2090]~E(x20901,x20902)+E(f562(x20901,x20903,x20904,x20905),f562(x20902,x20903,x20904,x20905)) % 168.22/168.07 [2091]~E(x20911,x20912)+E(f562(x20913,x20911,x20914,x20915),f562(x20913,x20912,x20914,x20915)) % 168.22/168.07 [2092]~E(x20921,x20922)+E(f562(x20923,x20924,x20921,x20925),f562(x20923,x20924,x20922,x20925)) % 168.22/168.07 [2093]~E(x20931,x20932)+E(f562(x20933,x20934,x20935,x20931),f562(x20933,x20934,x20935,x20932)) % 168.22/168.07 [2094]~E(x20941,x20942)+E(f579(x20941,x20943,x20944,x20945,x20946,x20947),f579(x20942,x20943,x20944,x20945,x20946,x20947)) % 168.22/168.07 [2095]~E(x20951,x20952)+E(f579(x20953,x20951,x20954,x20955,x20956,x20957),f579(x20953,x20952,x20954,x20955,x20956,x20957)) % 168.22/168.07 [2096]~E(x20961,x20962)+E(f579(x20963,x20964,x20961,x20965,x20966,x20967),f579(x20963,x20964,x20962,x20965,x20966,x20967)) % 168.22/168.07 [2097]~E(x20971,x20972)+E(f579(x20973,x20974,x20975,x20971,x20976,x20977),f579(x20973,x20974,x20975,x20972,x20976,x20977)) % 168.22/168.07 [2098]~E(x20981,x20982)+E(f579(x20983,x20984,x20985,x20986,x20981,x20987),f579(x20983,x20984,x20985,x20986,x20982,x20987)) % 168.22/168.07 [2099]~E(x20991,x20992)+E(f579(x20993,x20994,x20995,x20996,x20997,x20991),f579(x20993,x20994,x20995,x20996,x20997,x20992)) % 168.22/168.07 [2100]~E(x21001,x21002)+E(f528(x21001,x21003,x21004,x21005,x21006,x21007),f528(x21002,x21003,x21004,x21005,x21006,x21007)) % 168.22/168.07 [2101]~E(x21011,x21012)+E(f528(x21013,x21011,x21014,x21015,x21016,x21017),f528(x21013,x21012,x21014,x21015,x21016,x21017)) % 168.22/168.07 [2102]~E(x21021,x21022)+E(f528(x21023,x21024,x21021,x21025,x21026,x21027),f528(x21023,x21024,x21022,x21025,x21026,x21027)) % 168.22/168.07 [2103]~E(x21031,x21032)+E(f528(x21033,x21034,x21035,x21031,x21036,x21037),f528(x21033,x21034,x21035,x21032,x21036,x21037)) % 168.22/168.07 [2104]~E(x21041,x21042)+E(f528(x21043,x21044,x21045,x21046,x21041,x21047),f528(x21043,x21044,x21045,x21046,x21042,x21047)) % 168.22/168.07 [2105]~E(x21051,x21052)+E(f528(x21053,x21054,x21055,x21056,x21057,x21051),f528(x21053,x21054,x21055,x21056,x21057,x21052)) % 168.22/168.07 [2106]~E(x21061,x21062)+E(f397(x21061,x21063,x21064,x21065,x21066),f397(x21062,x21063,x21064,x21065,x21066)) % 168.22/168.07 [2107]~E(x21071,x21072)+E(f397(x21073,x21071,x21074,x21075,x21076),f397(x21073,x21072,x21074,x21075,x21076)) % 168.22/168.07 [2108]~E(x21081,x21082)+E(f397(x21083,x21084,x21081,x21085,x21086),f397(x21083,x21084,x21082,x21085,x21086)) % 168.22/168.07 [2109]~E(x21091,x21092)+E(f397(x21093,x21094,x21095,x21091,x21096),f397(x21093,x21094,x21095,x21092,x21096)) % 168.22/168.07 [2110]~E(x21101,x21102)+E(f397(x21103,x21104,x21105,x21106,x21101),f397(x21103,x21104,x21105,x21106,x21102)) % 168.22/168.07 [2111]~E(x21111,x21112)+E(f343(x21111,x21113,x21114),f343(x21112,x21113,x21114)) % 168.22/168.07 [2112]~E(x21121,x21122)+E(f343(x21123,x21121,x21124),f343(x21123,x21122,x21124)) % 168.22/168.07 [2113]~E(x21131,x21132)+E(f343(x21133,x21134,x21131),f343(x21133,x21134,x21132)) % 168.22/168.07 [2114]~E(x21141,x21142)+E(f719(x21141,x21143,x21144),f719(x21142,x21143,x21144)) % 168.22/168.07 [2115]~E(x21151,x21152)+E(f719(x21153,x21151,x21154),f719(x21153,x21152,x21154)) % 168.22/168.07 [2116]~E(x21161,x21162)+E(f719(x21163,x21164,x21161),f719(x21163,x21164,x21162)) % 168.22/168.07 [2117]~E(x21171,x21172)+E(f85(x21171,x21173,x21174,x21175,x21176),f85(x21172,x21173,x21174,x21175,x21176)) % 168.22/168.07 [2118]~E(x21181,x21182)+E(f85(x21183,x21181,x21184,x21185,x21186),f85(x21183,x21182,x21184,x21185,x21186)) % 168.22/168.07 [2119]~E(x21191,x21192)+E(f85(x21193,x21194,x21191,x21195,x21196),f85(x21193,x21194,x21192,x21195,x21196)) % 168.22/168.07 [2120]~E(x21201,x21202)+E(f85(x21203,x21204,x21205,x21201,x21206),f85(x21203,x21204,x21205,x21202,x21206)) % 168.22/168.07 [2121]~E(x21211,x21212)+E(f85(x21213,x21214,x21215,x21216,x21211),f85(x21213,x21214,x21215,x21216,x21212)) % 168.22/168.07 [2122]~E(x21221,x21222)+E(f814(x21221,x21223),f814(x21222,x21223)) % 168.22/168.07 [2123]~E(x21231,x21232)+E(f814(x21233,x21231),f814(x21233,x21232)) % 168.22/168.07 [2124]~E(x21241,x21242)+E(f431(x21241,x21243,x21244,x21245),f431(x21242,x21243,x21244,x21245)) % 168.22/168.07 [2125]~E(x21251,x21252)+E(f431(x21253,x21251,x21254,x21255),f431(x21253,x21252,x21254,x21255)) % 168.22/168.07 [2126]~E(x21261,x21262)+E(f431(x21263,x21264,x21261,x21265),f431(x21263,x21264,x21262,x21265)) % 168.22/168.07 [2127]~E(x21271,x21272)+E(f431(x21273,x21274,x21275,x21271),f431(x21273,x21274,x21275,x21272)) % 168.22/168.07 [2128]~E(x21281,x21282)+E(f647(x21281,x21283,x21284),f647(x21282,x21283,x21284)) % 168.22/168.07 [2129]~E(x21291,x21292)+E(f647(x21293,x21291,x21294),f647(x21293,x21292,x21294)) % 168.22/168.07 [2130]~E(x21301,x21302)+E(f647(x21303,x21304,x21301),f647(x21303,x21304,x21302)) % 168.22/168.07 [2131]~E(x21311,x21312)+E(f564(x21311,x21313,x21314,x21315),f564(x21312,x21313,x21314,x21315)) % 168.22/168.07 [2132]~E(x21321,x21322)+E(f564(x21323,x21321,x21324,x21325),f564(x21323,x21322,x21324,x21325)) % 168.22/168.07 [2133]~E(x21331,x21332)+E(f564(x21333,x21334,x21331,x21335),f564(x21333,x21334,x21332,x21335)) % 168.22/168.07 [2134]~E(x21341,x21342)+E(f564(x21343,x21344,x21345,x21341),f564(x21343,x21344,x21345,x21342)) % 168.22/168.07 [2135]~E(x21351,x21352)+E(f638(x21351,x21353,x21354,x21355,x21356),f638(x21352,x21353,x21354,x21355,x21356)) % 168.22/168.07 [2136]~E(x21361,x21362)+E(f638(x21363,x21361,x21364,x21365,x21366),f638(x21363,x21362,x21364,x21365,x21366)) % 168.22/168.07 [2137]~E(x21371,x21372)+E(f638(x21373,x21374,x21371,x21375,x21376),f638(x21373,x21374,x21372,x21375,x21376)) % 168.22/168.07 [2138]~E(x21381,x21382)+E(f638(x21383,x21384,x21385,x21381,x21386),f638(x21383,x21384,x21385,x21382,x21386)) % 168.22/168.07 [2139]~E(x21391,x21392)+E(f638(x21393,x21394,x21395,x21396,x21391),f638(x21393,x21394,x21395,x21396,x21392)) % 168.22/168.07 [2140]~E(x21401,x21402)+E(f227(x21401,x21403),f227(x21402,x21403)) % 168.22/168.07 [2141]~E(x21411,x21412)+E(f227(x21413,x21411),f227(x21413,x21412)) % 168.22/168.07 [2142]~E(x21421,x21422)+E(f704(x21421,x21423,x21424,x21425),f704(x21422,x21423,x21424,x21425)) % 168.22/168.07 [2143]~E(x21431,x21432)+E(f704(x21433,x21431,x21434,x21435),f704(x21433,x21432,x21434,x21435)) % 168.22/168.07 [2144]~E(x21441,x21442)+E(f704(x21443,x21444,x21441,x21445),f704(x21443,x21444,x21442,x21445)) % 168.22/168.07 [2145]~E(x21451,x21452)+E(f704(x21453,x21454,x21455,x21451),f704(x21453,x21454,x21455,x21452)) % 168.22/168.07 [2146]~E(x21461,x21462)+E(f717(x21461,x21463,x21464,x21465),f717(x21462,x21463,x21464,x21465)) % 168.22/168.07 [2147]~E(x21471,x21472)+E(f717(x21473,x21471,x21474,x21475),f717(x21473,x21472,x21474,x21475)) % 168.22/168.07 [2148]~E(x21481,x21482)+E(f717(x21483,x21484,x21481,x21485),f717(x21483,x21484,x21482,x21485)) % 168.22/168.07 [2149]~E(x21491,x21492)+E(f717(x21493,x21494,x21495,x21491),f717(x21493,x21494,x21495,x21492)) % 168.22/168.07 [2150]~E(x21501,x21502)+E(f105(x21501,x21503,x21504),f105(x21502,x21503,x21504)) % 168.22/168.07 [2151]~E(x21511,x21512)+E(f105(x21513,x21511,x21514),f105(x21513,x21512,x21514)) % 168.22/168.07 [2152]~E(x21521,x21522)+E(f105(x21523,x21524,x21521),f105(x21523,x21524,x21522)) % 168.22/168.07 [2153]~E(x21531,x21532)+E(f346(x21531,x21533,x21534),f346(x21532,x21533,x21534)) % 168.22/168.07 [2154]~E(x21541,x21542)+E(f346(x21543,x21541,x21544),f346(x21543,x21542,x21544)) % 168.22/168.07 [2155]~E(x21551,x21552)+E(f346(x21553,x21554,x21551),f346(x21553,x21554,x21552)) % 168.22/168.07 [2156]~E(x21561,x21562)+E(f524(x21561,x21563,x21564,x21565),f524(x21562,x21563,x21564,x21565)) % 168.22/168.07 [2157]~E(x21571,x21572)+E(f524(x21573,x21571,x21574,x21575),f524(x21573,x21572,x21574,x21575)) % 168.22/168.07 [2158]~E(x21581,x21582)+E(f524(x21583,x21584,x21581,x21585),f524(x21583,x21584,x21582,x21585)) % 168.22/168.07 [2159]~E(x21591,x21592)+E(f524(x21593,x21594,x21595,x21591),f524(x21593,x21594,x21595,x21592)) % 168.22/168.07 [2160]~E(x21601,x21602)+E(f301(x21601,x21603,x21604,x21605),f301(x21602,x21603,x21604,x21605)) % 168.22/168.07 [2161]~E(x21611,x21612)+E(f301(x21613,x21611,x21614,x21615),f301(x21613,x21612,x21614,x21615)) % 168.22/168.07 [2162]~E(x21621,x21622)+E(f301(x21623,x21624,x21621,x21625),f301(x21623,x21624,x21622,x21625)) % 168.22/168.07 [2163]~E(x21631,x21632)+E(f301(x21633,x21634,x21635,x21631),f301(x21633,x21634,x21635,x21632)) % 168.22/168.07 [2164]~E(x21641,x21642)+E(f540(x21641,x21643,x21644,x21645,x21646),f540(x21642,x21643,x21644,x21645,x21646)) % 168.22/168.07 [2165]~E(x21651,x21652)+E(f540(x21653,x21651,x21654,x21655,x21656),f540(x21653,x21652,x21654,x21655,x21656)) % 168.22/168.07 [2166]~E(x21661,x21662)+E(f540(x21663,x21664,x21661,x21665,x21666),f540(x21663,x21664,x21662,x21665,x21666)) % 168.22/168.07 [2167]~E(x21671,x21672)+E(f540(x21673,x21674,x21675,x21671,x21676),f540(x21673,x21674,x21675,x21672,x21676)) % 168.22/168.07 [2168]~E(x21681,x21682)+E(f540(x21683,x21684,x21685,x21686,x21681),f540(x21683,x21684,x21685,x21686,x21682)) % 168.22/168.07 [2169]~E(x21691,x21692)+E(f293(x21691,x21693,x21694),f293(x21692,x21693,x21694)) % 168.22/168.07 [2170]~E(x21701,x21702)+E(f293(x21703,x21701,x21704),f293(x21703,x21702,x21704)) % 168.22/168.07 [2171]~E(x21711,x21712)+E(f293(x21713,x21714,x21711),f293(x21713,x21714,x21712)) % 168.22/168.07 [2172]~E(x21721,x21722)+E(f747(x21721,x21723,x21724,x21725,x21726,x21727,x21728,x21729),f747(x21722,x21723,x21724,x21725,x21726,x21727,x21728,x21729)) % 168.22/168.07 [2173]~E(x21731,x21732)+E(f747(x21733,x21731,x21734,x21735,x21736,x21737,x21738,x21739),f747(x21733,x21732,x21734,x21735,x21736,x21737,x21738,x21739)) % 168.22/168.07 [2174]~E(x21741,x21742)+E(f747(x21743,x21744,x21741,x21745,x21746,x21747,x21748,x21749),f747(x21743,x21744,x21742,x21745,x21746,x21747,x21748,x21749)) % 168.22/168.07 [2175]~E(x21751,x21752)+E(f747(x21753,x21754,x21755,x21751,x21756,x21757,x21758,x21759),f747(x21753,x21754,x21755,x21752,x21756,x21757,x21758,x21759)) % 168.22/168.07 [2176]~E(x21761,x21762)+E(f747(x21763,x21764,x21765,x21766,x21761,x21767,x21768,x21769),f747(x21763,x21764,x21765,x21766,x21762,x21767,x21768,x21769)) % 168.22/168.07 [2177]~E(x21771,x21772)+E(f747(x21773,x21774,x21775,x21776,x21777,x21771,x21778,x21779),f747(x21773,x21774,x21775,x21776,x21777,x21772,x21778,x21779)) % 168.22/168.07 [2178]~E(x21781,x21782)+E(f747(x21783,x21784,x21785,x21786,x21787,x21788,x21781,x21789),f747(x21783,x21784,x21785,x21786,x21787,x21788,x21782,x21789)) % 168.22/168.07 [2179]~E(x21791,x21792)+E(f747(x21793,x21794,x21795,x21796,x21797,x21798,x21799,x21791),f747(x21793,x21794,x21795,x21796,x21797,x21798,x21799,x21792)) % 168.22/168.07 [2180]~E(x21801,x21802)+E(f311(x21801,x21803,x21804),f311(x21802,x21803,x21804)) % 168.22/168.07 [2181]~E(x21811,x21812)+E(f311(x21813,x21811,x21814),f311(x21813,x21812,x21814)) % 168.22/168.07 [2182]~E(x21821,x21822)+E(f311(x21823,x21824,x21821),f311(x21823,x21824,x21822)) % 168.22/168.07 [2183]~E(x21831,x21832)+E(f598(x21831,x21833,x21834),f598(x21832,x21833,x21834)) % 168.22/168.07 [2184]~E(x21841,x21842)+E(f598(x21843,x21841,x21844),f598(x21843,x21842,x21844)) % 168.22/168.07 [2185]~E(x21851,x21852)+E(f598(x21853,x21854,x21851),f598(x21853,x21854,x21852)) % 168.22/168.07 [2186]~E(x21861,x21862)+E(f543(x21861,x21863,x21864,x21865,x21866),f543(x21862,x21863,x21864,x21865,x21866)) % 168.22/168.07 [2187]~E(x21871,x21872)+E(f543(x21873,x21871,x21874,x21875,x21876),f543(x21873,x21872,x21874,x21875,x21876)) % 168.22/168.07 [2188]~E(x21881,x21882)+E(f543(x21883,x21884,x21881,x21885,x21886),f543(x21883,x21884,x21882,x21885,x21886)) % 168.22/168.07 [2189]~E(x21891,x21892)+E(f543(x21893,x21894,x21895,x21891,x21896),f543(x21893,x21894,x21895,x21892,x21896)) % 168.22/168.07 [2190]~E(x21901,x21902)+E(f543(x21903,x21904,x21905,x21906,x21901),f543(x21903,x21904,x21905,x21906,x21902)) % 168.22/168.07 [2191]~E(x21911,x21912)+E(f812(x21911),f812(x21912)) % 168.22/168.07 [2192]~E(x21921,x21922)+E(f325(x21921,x21923),f325(x21922,x21923)) % 168.22/168.07 [2193]~E(x21931,x21932)+E(f325(x21933,x21931),f325(x21933,x21932)) % 168.22/168.07 [2194]~E(x21941,x21942)+E(f491(x21941,x21943,x21944,x21945),f491(x21942,x21943,x21944,x21945)) % 168.22/168.07 [2195]~E(x21951,x21952)+E(f491(x21953,x21951,x21954,x21955),f491(x21953,x21952,x21954,x21955)) % 168.22/168.07 [2196]~E(x21961,x21962)+E(f491(x21963,x21964,x21961,x21965),f491(x21963,x21964,x21962,x21965)) % 168.22/168.07 [2197]~E(x21971,x21972)+E(f491(x21973,x21974,x21975,x21971),f491(x21973,x21974,x21975,x21972)) % 168.22/168.07 [2198]~E(x21981,x21982)+E(f617(x21981,x21983,x21984,x21985,x21986),f617(x21982,x21983,x21984,x21985,x21986)) % 168.22/168.07 [2199]~E(x21991,x21992)+E(f617(x21993,x21991,x21994,x21995,x21996),f617(x21993,x21992,x21994,x21995,x21996)) % 168.22/168.07 [2200]~E(x22001,x22002)+E(f617(x22003,x22004,x22001,x22005,x22006),f617(x22003,x22004,x22002,x22005,x22006)) % 168.22/168.07 [2201]~E(x22011,x22012)+E(f617(x22013,x22014,x22015,x22011,x22016),f617(x22013,x22014,x22015,x22012,x22016)) % 168.22/168.07 [2202]~E(x22021,x22022)+E(f617(x22023,x22024,x22025,x22026,x22021),f617(x22023,x22024,x22025,x22026,x22022)) % 168.22/168.07 [2203]~E(x22031,x22032)+E(f569(x22031,x22033),f569(x22032,x22033)) % 168.22/168.07 [2204]~E(x22041,x22042)+E(f569(x22043,x22041),f569(x22043,x22042)) % 168.22/168.07 [2205]~E(x22051,x22052)+E(f107(x22051,x22053,x22054,x22055),f107(x22052,x22053,x22054,x22055)) % 168.22/168.07 [2206]~E(x22061,x22062)+E(f107(x22063,x22061,x22064,x22065),f107(x22063,x22062,x22064,x22065)) % 168.22/168.07 [2207]~E(x22071,x22072)+E(f107(x22073,x22074,x22071,x22075),f107(x22073,x22074,x22072,x22075)) % 168.22/168.07 [2208]~E(x22081,x22082)+E(f107(x22083,x22084,x22085,x22081),f107(x22083,x22084,x22085,x22082)) % 168.22/168.07 [2209]~E(x22091,x22092)+E(f362(x22091),f362(x22092)) % 168.22/168.07 [2210]~E(x22101,x22102)+E(f434(x22101,x22103),f434(x22102,x22103)) % 168.22/168.07 [2211]~E(x22111,x22112)+E(f434(x22113,x22111),f434(x22113,x22112)) % 168.22/168.07 [2212]~E(x22121,x22122)+E(f496(x22121,x22123,x22124,x22125,x22126),f496(x22122,x22123,x22124,x22125,x22126)) % 168.22/168.07 [2213]~E(x22131,x22132)+E(f496(x22133,x22131,x22134,x22135,x22136),f496(x22133,x22132,x22134,x22135,x22136)) % 168.22/168.07 [2214]~E(x22141,x22142)+E(f496(x22143,x22144,x22141,x22145,x22146),f496(x22143,x22144,x22142,x22145,x22146)) % 168.22/168.07 [2215]~E(x22151,x22152)+E(f496(x22153,x22154,x22155,x22151,x22156),f496(x22153,x22154,x22155,x22152,x22156)) % 168.22/168.07 [2216]~E(x22161,x22162)+E(f496(x22163,x22164,x22165,x22166,x22161),f496(x22163,x22164,x22165,x22166,x22162)) % 168.22/168.07 [2217]~E(x22171,x22172)+E(f768(x22171,x22173,x22174),f768(x22172,x22173,x22174)) % 168.22/168.07 [2218]~E(x22181,x22182)+E(f768(x22183,x22181,x22184),f768(x22183,x22182,x22184)) % 168.22/168.07 [2219]~E(x22191,x22192)+E(f768(x22193,x22194,x22191),f768(x22193,x22194,x22192)) % 168.22/168.07 [2220]~E(x22201,x22202)+E(f519(x22201),f519(x22202)) % 168.22/168.07 [2221]~E(x22211,x22212)+E(f715(x22211,x22213,x22214),f715(x22212,x22213,x22214)) % 168.22/168.07 [2222]~E(x22221,x22222)+E(f715(x22223,x22221,x22224),f715(x22223,x22222,x22224)) % 168.22/168.07 [2223]~E(x22231,x22232)+E(f715(x22233,x22234,x22231),f715(x22233,x22234,x22232)) % 168.22/168.07 [2224]~E(x22241,x22242)+E(f705(x22241,x22243,x22244,x22245,x22246,x22247),f705(x22242,x22243,x22244,x22245,x22246,x22247)) % 168.22/168.07 [2225]~E(x22251,x22252)+E(f705(x22253,x22251,x22254,x22255,x22256,x22257),f705(x22253,x22252,x22254,x22255,x22256,x22257)) % 168.22/168.07 [2226]~E(x22261,x22262)+E(f705(x22263,x22264,x22261,x22265,x22266,x22267),f705(x22263,x22264,x22262,x22265,x22266,x22267)) % 168.22/168.07 [2227]~E(x22271,x22272)+E(f705(x22273,x22274,x22275,x22271,x22276,x22277),f705(x22273,x22274,x22275,x22272,x22276,x22277)) % 168.22/168.07 [2228]~E(x22281,x22282)+E(f705(x22283,x22284,x22285,x22286,x22281,x22287),f705(x22283,x22284,x22285,x22286,x22282,x22287)) % 168.22/168.07 [2229]~E(x22291,x22292)+E(f705(x22293,x22294,x22295,x22296,x22297,x22291),f705(x22293,x22294,x22295,x22296,x22297,x22292)) % 168.22/168.07 [2230]~E(x22301,x22302)+E(f746(x22301,x22303,x22304,x22305,x22306,x22307,x22308),f746(x22302,x22303,x22304,x22305,x22306,x22307,x22308)) % 168.22/168.07 [2231]~E(x22311,x22312)+E(f746(x22313,x22311,x22314,x22315,x22316,x22317,x22318),f746(x22313,x22312,x22314,x22315,x22316,x22317,x22318)) % 168.22/168.07 [2232]~E(x22321,x22322)+E(f746(x22323,x22324,x22321,x22325,x22326,x22327,x22328),f746(x22323,x22324,x22322,x22325,x22326,x22327,x22328)) % 168.22/168.07 [2233]~E(x22331,x22332)+E(f746(x22333,x22334,x22335,x22331,x22336,x22337,x22338),f746(x22333,x22334,x22335,x22332,x22336,x22337,x22338)) % 168.22/168.07 [2234]~E(x22341,x22342)+E(f746(x22343,x22344,x22345,x22346,x22341,x22347,x22348),f746(x22343,x22344,x22345,x22346,x22342,x22347,x22348)) % 168.22/168.07 [2235]~E(x22351,x22352)+E(f746(x22353,x22354,x22355,x22356,x22357,x22351,x22358),f746(x22353,x22354,x22355,x22356,x22357,x22352,x22358)) % 168.22/168.07 [2236]~E(x22361,x22362)+E(f746(x22363,x22364,x22365,x22366,x22367,x22368,x22361),f746(x22363,x22364,x22365,x22366,x22367,x22368,x22362)) % 168.22/168.07 [2237]~E(x22371,x22372)+E(f790(x22371,x22373,x22374,x22375),f790(x22372,x22373,x22374,x22375)) % 168.22/168.07 [2238]~E(x22381,x22382)+E(f790(x22383,x22381,x22384,x22385),f790(x22383,x22382,x22384,x22385)) % 168.22/168.07 [2239]~E(x22391,x22392)+E(f790(x22393,x22394,x22391,x22395),f790(x22393,x22394,x22392,x22395)) % 168.22/168.07 [2240]~E(x22401,x22402)+E(f790(x22403,x22404,x22405,x22401),f790(x22403,x22404,x22405,x22402)) % 168.22/168.07 [2241]~E(x22411,x22412)+E(f470(x22411,x22413,x22414,x22415,x22416),f470(x22412,x22413,x22414,x22415,x22416)) % 168.22/168.07 [2242]~E(x22421,x22422)+E(f470(x22423,x22421,x22424,x22425,x22426),f470(x22423,x22422,x22424,x22425,x22426)) % 168.22/168.07 [2243]~E(x22431,x22432)+E(f470(x22433,x22434,x22431,x22435,x22436),f470(x22433,x22434,x22432,x22435,x22436)) % 168.22/168.07 [2244]~E(x22441,x22442)+E(f470(x22443,x22444,x22445,x22441,x22446),f470(x22443,x22444,x22445,x22442,x22446)) % 168.22/168.07 [2245]~E(x22451,x22452)+E(f470(x22453,x22454,x22455,x22456,x22451),f470(x22453,x22454,x22455,x22456,x22452)) % 168.22/168.07 [2246]~E(x22461,x22462)+E(f643(x22461,x22463),f643(x22462,x22463)) % 168.22/168.07 [2247]~E(x22471,x22472)+E(f643(x22473,x22471),f643(x22473,x22472)) % 168.22/168.07 [2248]~E(x22481,x22482)+E(f672(x22481,x22483),f672(x22482,x22483)) % 168.22/168.07 [2249]~E(x22491,x22492)+E(f672(x22493,x22491),f672(x22493,x22492)) % 168.22/168.07 [2250]~E(x22501,x22502)+E(f169(x22501,x22503,x22504),f169(x22502,x22503,x22504)) % 168.22/168.07 [2251]~E(x22511,x22512)+E(f169(x22513,x22511,x22514),f169(x22513,x22512,x22514)) % 168.22/168.07 [2252]~E(x22521,x22522)+E(f169(x22523,x22524,x22521),f169(x22523,x22524,x22522)) % 168.22/168.07 [2253]~E(x22531,x22532)+E(f505(x22531,x22533,x22534,x22535,x22536,x22537,x22538),f505(x22532,x22533,x22534,x22535,x22536,x22537,x22538)) % 168.22/168.07 [2254]~E(x22541,x22542)+E(f505(x22543,x22541,x22544,x22545,x22546,x22547,x22548),f505(x22543,x22542,x22544,x22545,x22546,x22547,x22548)) % 168.22/168.07 [2255]~E(x22551,x22552)+E(f505(x22553,x22554,x22551,x22555,x22556,x22557,x22558),f505(x22553,x22554,x22552,x22555,x22556,x22557,x22558)) % 168.22/168.07 [2256]~E(x22561,x22562)+E(f505(x22563,x22564,x22565,x22561,x22566,x22567,x22568),f505(x22563,x22564,x22565,x22562,x22566,x22567,x22568)) % 168.22/168.07 [2257]~E(x22571,x22572)+E(f505(x22573,x22574,x22575,x22576,x22571,x22577,x22578),f505(x22573,x22574,x22575,x22576,x22572,x22577,x22578)) % 168.22/168.07 [2258]~E(x22581,x22582)+E(f505(x22583,x22584,x22585,x22586,x22587,x22581,x22588),f505(x22583,x22584,x22585,x22586,x22587,x22582,x22588)) % 168.22/168.07 [2259]~E(x22591,x22592)+E(f505(x22593,x22594,x22595,x22596,x22597,x22598,x22591),f505(x22593,x22594,x22595,x22596,x22597,x22598,x22592)) % 168.22/168.07 [2260]~E(x22601,x22602)+E(f799(x22601),f799(x22602)) % 168.22/168.07 [2261]~E(x22611,x22612)+E(f682(x22611,x22613,x22614,x22615),f682(x22612,x22613,x22614,x22615)) % 168.22/168.07 [2262]~E(x22621,x22622)+E(f682(x22623,x22621,x22624,x22625),f682(x22623,x22622,x22624,x22625)) % 168.22/168.07 [2263]~E(x22631,x22632)+E(f682(x22633,x22634,x22631,x22635),f682(x22633,x22634,x22632,x22635)) % 168.22/168.07 [2264]~E(x22641,x22642)+E(f682(x22643,x22644,x22645,x22641),f682(x22643,x22644,x22645,x22642)) % 168.22/168.07 [2265]~E(x22651,x22652)+E(f801(x22651),f801(x22652)) % 168.22/168.07 [2266]~E(x22661,x22662)+E(f383(x22661,x22663),f383(x22662,x22663)) % 168.22/168.07 [2267]~E(x22671,x22672)+E(f383(x22673,x22671),f383(x22673,x22672)) % 168.22/168.07 [2268]~E(x22681,x22682)+E(f578(x22681,x22683,x22684,x22685),f578(x22682,x22683,x22684,x22685)) % 168.22/168.07 [2269]~E(x22691,x22692)+E(f578(x22693,x22691,x22694,x22695),f578(x22693,x22692,x22694,x22695)) % 168.22/168.07 [2270]~E(x22701,x22702)+E(f578(x22703,x22704,x22701,x22705),f578(x22703,x22704,x22702,x22705)) % 168.22/168.07 [2271]~E(x22711,x22712)+E(f578(x22713,x22714,x22715,x22711),f578(x22713,x22714,x22715,x22712)) % 168.22/168.07 [2272]~E(x22721,x22722)+E(f492(x22721,x22723,x22724,x22725,x22726),f492(x22722,x22723,x22724,x22725,x22726)) % 168.22/168.07 [2273]~E(x22731,x22732)+E(f492(x22733,x22731,x22734,x22735,x22736),f492(x22733,x22732,x22734,x22735,x22736)) % 168.22/168.07 [2274]~E(x22741,x22742)+E(f492(x22743,x22744,x22741,x22745,x22746),f492(x22743,x22744,x22742,x22745,x22746)) % 168.22/168.07 [2275]~E(x22751,x22752)+E(f492(x22753,x22754,x22755,x22751,x22756),f492(x22753,x22754,x22755,x22752,x22756)) % 168.22/168.07 [2276]~E(x22761,x22762)+E(f492(x22763,x22764,x22765,x22766,x22761),f492(x22763,x22764,x22765,x22766,x22762)) % 168.22/168.07 [2277]~E(x22771,x22772)+E(f392(x22771,x22773,x22774),f392(x22772,x22773,x22774)) % 168.22/168.07 [2278]~E(x22781,x22782)+E(f392(x22783,x22781,x22784),f392(x22783,x22782,x22784)) % 168.22/168.07 [2279]~E(x22791,x22792)+E(f392(x22793,x22794,x22791),f392(x22793,x22794,x22792)) % 168.22/168.07 [2280]~E(x22801,x22802)+E(f367(x22801,x22803,x22804,x22805),f367(x22802,x22803,x22804,x22805)) % 168.22/168.07 [2281]~E(x22811,x22812)+E(f367(x22813,x22811,x22814,x22815),f367(x22813,x22812,x22814,x22815)) % 168.22/168.07 [2282]~E(x22821,x22822)+E(f367(x22823,x22824,x22821,x22825),f367(x22823,x22824,x22822,x22825)) % 168.22/168.07 [2283]~E(x22831,x22832)+E(f367(x22833,x22834,x22835,x22831),f367(x22833,x22834,x22835,x22832)) % 168.22/168.07 [2284]~E(x22841,x22842)+E(f756(x22841,x22843,x22844),f756(x22842,x22843,x22844)) % 168.22/168.07 [2285]~E(x22851,x22852)+E(f756(x22853,x22851,x22854),f756(x22853,x22852,x22854)) % 168.22/168.07 [2286]~E(x22861,x22862)+E(f756(x22863,x22864,x22861),f756(x22863,x22864,x22862)) % 168.22/168.07 [2287]~E(x22871,x22872)+E(f128(x22871),f128(x22872)) % 168.22/168.07 [2288]~E(x22881,x22882)+E(f639(x22881,x22883,x22884,x22885,x22886,x22887,x22888),f639(x22882,x22883,x22884,x22885,x22886,x22887,x22888)) % 168.22/168.07 [2289]~E(x22891,x22892)+E(f639(x22893,x22891,x22894,x22895,x22896,x22897,x22898),f639(x22893,x22892,x22894,x22895,x22896,x22897,x22898)) % 168.22/168.07 [2290]~E(x22901,x22902)+E(f639(x22903,x22904,x22901,x22905,x22906,x22907,x22908),f639(x22903,x22904,x22902,x22905,x22906,x22907,x22908)) % 168.22/168.07 [2291]~E(x22911,x22912)+E(f639(x22913,x22914,x22915,x22911,x22916,x22917,x22918),f639(x22913,x22914,x22915,x22912,x22916,x22917,x22918)) % 168.22/168.07 [2292]~E(x22921,x22922)+E(f639(x22923,x22924,x22925,x22926,x22921,x22927,x22928),f639(x22923,x22924,x22925,x22926,x22922,x22927,x22928)) % 168.22/168.07 [2293]~E(x22931,x22932)+E(f639(x22933,x22934,x22935,x22936,x22937,x22931,x22938),f639(x22933,x22934,x22935,x22936,x22937,x22932,x22938)) % 168.22/168.07 [2294]~E(x22941,x22942)+E(f639(x22943,x22944,x22945,x22946,x22947,x22948,x22941),f639(x22943,x22944,x22945,x22946,x22947,x22948,x22942)) % 168.22/168.07 [2295]~E(x22951,x22952)+E(f555(x22951,x22953,x22954,x22955),f555(x22952,x22953,x22954,x22955)) % 168.22/168.07 [2296]~E(x22961,x22962)+E(f555(x22963,x22961,x22964,x22965),f555(x22963,x22962,x22964,x22965)) % 168.22/168.07 [2297]~E(x22971,x22972)+E(f555(x22973,x22974,x22971,x22975),f555(x22973,x22974,x22972,x22975)) % 168.22/168.07 [2298]~E(x22981,x22982)+E(f555(x22983,x22984,x22985,x22981),f555(x22983,x22984,x22985,x22982)) % 168.22/168.07 [2299]~E(x22991,x22992)+E(f783(x22991,x22993,x22994),f783(x22992,x22993,x22994)) % 168.22/168.07 [2300]~E(x23001,x23002)+E(f783(x23003,x23001,x23004),f783(x23003,x23002,x23004)) % 168.22/168.07 [2301]~E(x23011,x23012)+E(f783(x23013,x23014,x23011),f783(x23013,x23014,x23012)) % 168.22/168.07 [2302]~E(x23021,x23022)+E(f514(x23021,x23023,x23024),f514(x23022,x23023,x23024)) % 168.22/168.07 [2303]~E(x23031,x23032)+E(f514(x23033,x23031,x23034),f514(x23033,x23032,x23034)) % 168.22/168.07 [2304]~E(x23041,x23042)+E(f514(x23043,x23044,x23041),f514(x23043,x23044,x23042)) % 168.22/168.07 [2305]~E(x23051,x23052)+E(f629(x23051,x23053,x23054),f629(x23052,x23053,x23054)) % 168.22/168.07 [2306]~E(x23061,x23062)+E(f629(x23063,x23061,x23064),f629(x23063,x23062,x23064)) % 168.22/168.07 [2307]~E(x23071,x23072)+E(f629(x23073,x23074,x23071),f629(x23073,x23074,x23072)) % 168.22/168.07 [2308]~E(x23081,x23082)+E(f324(x23081,x23083),f324(x23082,x23083)) % 168.22/168.07 [2309]~E(x23091,x23092)+E(f324(x23093,x23091),f324(x23093,x23092)) % 168.22/168.07 [2310]~E(x23101,x23102)+E(f666(x23101,x23103,x23104,x23105),f666(x23102,x23103,x23104,x23105)) % 168.22/168.07 [2311]~E(x23111,x23112)+E(f666(x23113,x23111,x23114,x23115),f666(x23113,x23112,x23114,x23115)) % 168.22/168.07 [2312]~E(x23121,x23122)+E(f666(x23123,x23124,x23121,x23125),f666(x23123,x23124,x23122,x23125)) % 168.22/168.07 [2313]~E(x23131,x23132)+E(f666(x23133,x23134,x23135,x23131),f666(x23133,x23134,x23135,x23132)) % 168.22/168.07 [2314]~E(x23141,x23142)+E(f257(x23141,x23143,x23144,x23145),f257(x23142,x23143,x23144,x23145)) % 168.22/168.07 [2315]~E(x23151,x23152)+E(f257(x23153,x23151,x23154,x23155),f257(x23153,x23152,x23154,x23155)) % 168.22/168.07 [2316]~E(x23161,x23162)+E(f257(x23163,x23164,x23161,x23165),f257(x23163,x23164,x23162,x23165)) % 168.22/168.07 [2317]~E(x23171,x23172)+E(f257(x23173,x23174,x23175,x23171),f257(x23173,x23174,x23175,x23172)) % 168.22/168.07 [2318]~E(x23181,x23182)+E(f743(x23181,x23183,x23184),f743(x23182,x23183,x23184)) % 168.22/168.07 [2319]~E(x23191,x23192)+E(f743(x23193,x23191,x23194),f743(x23193,x23192,x23194)) % 168.22/168.07 [2320]~E(x23201,x23202)+E(f743(x23203,x23204,x23201),f743(x23203,x23204,x23202)) % 168.22/168.07 [2321]~E(x23211,x23212)+E(f474(x23211,x23213,x23214,x23215),f474(x23212,x23213,x23214,x23215)) % 168.22/168.07 [2322]~E(x23221,x23222)+E(f474(x23223,x23221,x23224,x23225),f474(x23223,x23222,x23224,x23225)) % 168.22/168.07 [2323]~E(x23231,x23232)+E(f474(x23233,x23234,x23231,x23235),f474(x23233,x23234,x23232,x23235)) % 168.22/168.07 [2324]~E(x23241,x23242)+E(f474(x23243,x23244,x23245,x23241),f474(x23243,x23244,x23245,x23242)) % 168.22/168.07 [2325]~E(x23251,x23252)+E(f454(x23251,x23253,x23254,x23255,x23256),f454(x23252,x23253,x23254,x23255,x23256)) % 168.22/168.07 [2326]~E(x23261,x23262)+E(f454(x23263,x23261,x23264,x23265,x23266),f454(x23263,x23262,x23264,x23265,x23266)) % 168.22/168.07 [2327]~E(x23271,x23272)+E(f454(x23273,x23274,x23271,x23275,x23276),f454(x23273,x23274,x23272,x23275,x23276)) % 168.22/168.07 [2328]~E(x23281,x23282)+E(f454(x23283,x23284,x23285,x23281,x23286),f454(x23283,x23284,x23285,x23282,x23286)) % 168.22/168.07 [2329]~E(x23291,x23292)+E(f454(x23293,x23294,x23295,x23296,x23291),f454(x23293,x23294,x23295,x23296,x23292)) % 168.22/168.07 [2330]~E(x23301,x23302)+E(f824(x23301,x23303,x23304),f824(x23302,x23303,x23304)) % 168.22/168.07 [2331]~E(x23311,x23312)+E(f824(x23313,x23311,x23314),f824(x23313,x23312,x23314)) % 168.22/168.07 [2332]~E(x23321,x23322)+E(f824(x23323,x23324,x23321),f824(x23323,x23324,x23322)) % 168.22/168.07 [2333]~E(x23331,x23332)+E(f451(x23331,x23333,x23334),f451(x23332,x23333,x23334)) % 168.22/168.07 [2334]~E(x23341,x23342)+E(f451(x23343,x23341,x23344),f451(x23343,x23342,x23344)) % 168.22/168.07 [2335]~E(x23351,x23352)+E(f451(x23353,x23354,x23351),f451(x23353,x23354,x23352)) % 168.22/168.07 [2336]~E(x23361,x23362)+E(f570(x23361),f570(x23362)) % 168.22/168.07 [2337]~E(x23371,x23372)+E(f769(x23371,x23373),f769(x23372,x23373)) % 168.22/168.07 [2338]~E(x23381,x23382)+E(f769(x23383,x23381),f769(x23383,x23382)) % 168.22/168.07 [2339]~E(x23391,x23392)+E(f515(x23391,x23393,x23394),f515(x23392,x23393,x23394)) % 168.22/168.07 [2340]~E(x23401,x23402)+E(f515(x23403,x23401,x23404),f515(x23403,x23402,x23404)) % 168.22/168.07 [2341]~E(x23411,x23412)+E(f515(x23413,x23414,x23411),f515(x23413,x23414,x23412)) % 168.22/168.07 [2342]~E(x23421,x23422)+E(f807(x23421,x23423),f807(x23422,x23423)) % 168.22/168.07 [2343]~E(x23431,x23432)+E(f807(x23433,x23431),f807(x23433,x23432)) % 168.22/168.07 [2344]~E(x23441,x23442)+E(f389(x23441,x23443,x23444),f389(x23442,x23443,x23444)) % 168.22/168.07 [2345]~E(x23451,x23452)+E(f389(x23453,x23451,x23454),f389(x23453,x23452,x23454)) % 168.22/168.07 [2346]~E(x23461,x23462)+E(f389(x23463,x23464,x23461),f389(x23463,x23464,x23462)) % 168.22/168.07 [2347]~E(x23471,x23472)+E(f351(x23471,x23473,x23474),f351(x23472,x23473,x23474)) % 168.22/168.07 [2348]~E(x23481,x23482)+E(f351(x23483,x23481,x23484),f351(x23483,x23482,x23484)) % 168.22/168.07 [2349]~E(x23491,x23492)+E(f351(x23493,x23494,x23491),f351(x23493,x23494,x23492)) % 168.22/168.07 [2350]~E(x23501,x23502)+E(f840(x23501,x23503,x23504,x23505),f840(x23502,x23503,x23504,x23505)) % 168.22/168.07 [2351]~E(x23511,x23512)+E(f840(x23513,x23511,x23514,x23515),f840(x23513,x23512,x23514,x23515)) % 168.22/168.07 [2352]~E(x23521,x23522)+E(f840(x23523,x23524,x23521,x23525),f840(x23523,x23524,x23522,x23525)) % 168.22/168.07 [2353]~E(x23531,x23532)+E(f840(x23533,x23534,x23535,x23531),f840(x23533,x23534,x23535,x23532)) % 168.22/168.07 [2354]~E(x23541,x23542)+E(f385(x23541,x23543),f385(x23542,x23543)) % 168.22/168.07 [2355]~E(x23551,x23552)+E(f385(x23553,x23551),f385(x23553,x23552)) % 168.22/168.07 [2356]~E(x23561,x23562)+E(f732(x23561,x23563,x23564,x23565),f732(x23562,x23563,x23564,x23565)) % 168.22/168.07 [2357]~E(x23571,x23572)+E(f732(x23573,x23571,x23574,x23575),f732(x23573,x23572,x23574,x23575)) % 168.22/168.07 [2358]~E(x23581,x23582)+E(f732(x23583,x23584,x23581,x23585),f732(x23583,x23584,x23582,x23585)) % 168.22/168.07 [2359]~E(x23591,x23592)+E(f732(x23593,x23594,x23595,x23591),f732(x23593,x23594,x23595,x23592)) % 168.22/168.07 [2360]~E(x23601,x23602)+E(f826(x23601,x23603,x23604),f826(x23602,x23603,x23604)) % 168.22/168.07 [2361]~E(x23611,x23612)+E(f826(x23613,x23611,x23614),f826(x23613,x23612,x23614)) % 168.22/168.07 [2362]~E(x23621,x23622)+E(f826(x23623,x23624,x23621),f826(x23623,x23624,x23622)) % 168.22/168.07 [2363]~E(x23631,x23632)+E(f668(x23631,x23633),f668(x23632,x23633)) % 168.22/168.07 [2364]~E(x23641,x23642)+E(f668(x23643,x23641),f668(x23643,x23642)) % 168.22/168.07 [2365]~E(x23651,x23652)+E(f43(x23651,x23653,x23654,x23655),f43(x23652,x23653,x23654,x23655)) % 168.22/168.07 [2366]~E(x23661,x23662)+E(f43(x23663,x23661,x23664,x23665),f43(x23663,x23662,x23664,x23665)) % 168.22/168.07 [2367]~E(x23671,x23672)+E(f43(x23673,x23674,x23671,x23675),f43(x23673,x23674,x23672,x23675)) % 168.22/168.07 [2368]~E(x23681,x23682)+E(f43(x23683,x23684,x23685,x23681),f43(x23683,x23684,x23685,x23682)) % 168.22/168.07 [2369]~E(x23691,x23692)+E(f102(x23691),f102(x23692)) % 168.22/168.07 [2370]~E(x23701,x23702)+E(f627(x23701,x23703,x23704),f627(x23702,x23703,x23704)) % 168.22/168.07 [2371]~E(x23711,x23712)+E(f627(x23713,x23711,x23714),f627(x23713,x23712,x23714)) % 168.22/168.07 [2372]~E(x23721,x23722)+E(f627(x23723,x23724,x23721),f627(x23723,x23724,x23722)) % 168.22/168.07 [2373]~E(x23731,x23732)+E(f608(x23731,x23733),f608(x23732,x23733)) % 168.22/168.07 [2374]~E(x23741,x23742)+E(f608(x23743,x23741),f608(x23743,x23742)) % 168.22/168.07 [2375]~E(x23751,x23752)+E(f822(x23751,x23753,x23754),f822(x23752,x23753,x23754)) % 168.22/168.07 [2376]~E(x23761,x23762)+E(f822(x23763,x23761,x23764),f822(x23763,x23762,x23764)) % 168.22/168.07 [2377]~E(x23771,x23772)+E(f822(x23773,x23774,x23771),f822(x23773,x23774,x23772)) % 168.22/168.07 [2378]~E(x23781,x23782)+E(f655(x23781,x23783),f655(x23782,x23783)) % 168.22/168.07 [2379]~E(x23791,x23792)+E(f655(x23793,x23791),f655(x23793,x23792)) % 168.22/168.07 [2380]~E(x23801,x23802)+E(f791(x23801,x23803,x23804,x23805,x23806),f791(x23802,x23803,x23804,x23805,x23806)) % 168.22/168.07 [2381]~E(x23811,x23812)+E(f791(x23813,x23811,x23814,x23815,x23816),f791(x23813,x23812,x23814,x23815,x23816)) % 168.22/168.07 [2382]~E(x23821,x23822)+E(f791(x23823,x23824,x23821,x23825,x23826),f791(x23823,x23824,x23822,x23825,x23826)) % 168.22/168.07 [2383]~E(x23831,x23832)+E(f791(x23833,x23834,x23835,x23831,x23836),f791(x23833,x23834,x23835,x23832,x23836)) % 168.22/168.07 [2384]~E(x23841,x23842)+E(f791(x23843,x23844,x23845,x23846,x23841),f791(x23843,x23844,x23845,x23846,x23842)) % 168.22/168.07 [2385]~E(x23851,x23852)+E(f590(x23851,x23853,x23854,x23855,x23856),f590(x23852,x23853,x23854,x23855,x23856)) % 168.22/168.07 [2386]~E(x23861,x23862)+E(f590(x23863,x23861,x23864,x23865,x23866),f590(x23863,x23862,x23864,x23865,x23866)) % 168.22/168.07 [2387]~E(x23871,x23872)+E(f590(x23873,x23874,x23871,x23875,x23876),f590(x23873,x23874,x23872,x23875,x23876)) % 168.22/168.07 [2388]~E(x23881,x23882)+E(f590(x23883,x23884,x23885,x23881,x23886),f590(x23883,x23884,x23885,x23882,x23886)) % 168.22/168.07 [2389]~E(x23891,x23892)+E(f590(x23893,x23894,x23895,x23896,x23891),f590(x23893,x23894,x23895,x23896,x23892)) % 168.22/168.07 [2390]~E(x23901,x23902)+E(f140(x23901,x23903),f140(x23902,x23903)) % 168.22/168.07 [2391]~E(x23911,x23912)+E(f140(x23913,x23911),f140(x23913,x23912)) % 168.22/168.07 [2392]~E(x23921,x23922)+E(f250(x23921,x23923,x23924,x23925,x23926),f250(x23922,x23923,x23924,x23925,x23926)) % 168.22/168.07 [2393]~E(x23931,x23932)+E(f250(x23933,x23931,x23934,x23935,x23936),f250(x23933,x23932,x23934,x23935,x23936)) % 168.22/168.07 [2394]~E(x23941,x23942)+E(f250(x23943,x23944,x23941,x23945,x23946),f250(x23943,x23944,x23942,x23945,x23946)) % 168.22/168.07 [2395]~E(x23951,x23952)+E(f250(x23953,x23954,x23955,x23951,x23956),f250(x23953,x23954,x23955,x23952,x23956)) % 168.22/168.07 [2396]~E(x23961,x23962)+E(f250(x23963,x23964,x23965,x23966,x23961),f250(x23963,x23964,x23965,x23966,x23962)) % 168.22/168.07 [2397]~E(x23971,x23972)+E(f338(x23971,x23973),f338(x23972,x23973)) % 168.22/168.07 [2398]~E(x23981,x23982)+E(f338(x23983,x23981),f338(x23983,x23982)) % 168.22/168.07 [2399]~E(x23991,x23992)+E(f561(x23991,x23993,x23994,x23995),f561(x23992,x23993,x23994,x23995)) % 168.22/168.07 [2400]~E(x24001,x24002)+E(f561(x24003,x24001,x24004,x24005),f561(x24003,x24002,x24004,x24005)) % 168.22/168.07 [2401]~E(x24011,x24012)+E(f561(x24013,x24014,x24011,x24015),f561(x24013,x24014,x24012,x24015)) % 168.22/168.07 [2402]~E(x24021,x24022)+E(f561(x24023,x24024,x24025,x24021),f561(x24023,x24024,x24025,x24022)) % 168.22/168.07 [2403]~E(x24031,x24032)+E(f667(x24031,x24033),f667(x24032,x24033)) % 168.22/168.07 [2404]~E(x24041,x24042)+E(f667(x24043,x24041),f667(x24043,x24042)) % 168.22/168.07 [2405]~E(x24051,x24052)+E(f546(x24051,x24053),f546(x24052,x24053)) % 168.22/168.07 [2406]~E(x24061,x24062)+E(f546(x24063,x24061),f546(x24063,x24062)) % 168.22/168.07 [2407]~E(x24071,x24072)+E(f560(x24071,x24073,x24074,x24075),f560(x24072,x24073,x24074,x24075)) % 168.22/168.07 [2408]~E(x24081,x24082)+E(f560(x24083,x24081,x24084,x24085),f560(x24083,x24082,x24084,x24085)) % 168.22/168.07 [2409]~E(x24091,x24092)+E(f560(x24093,x24094,x24091,x24095),f560(x24093,x24094,x24092,x24095)) % 168.22/168.07 [2410]~E(x24101,x24102)+E(f560(x24103,x24104,x24105,x24101),f560(x24103,x24104,x24105,x24102)) % 168.22/168.07 [2411]~E(x24111,x24112)+E(f482(x24111,x24113,x24114),f482(x24112,x24113,x24114)) % 168.22/168.07 [2412]~E(x24121,x24122)+E(f482(x24123,x24121,x24124),f482(x24123,x24122,x24124)) % 168.22/168.07 [2413]~E(x24131,x24132)+E(f482(x24133,x24134,x24131),f482(x24133,x24134,x24132)) % 168.22/168.07 [2414]~E(x24141,x24142)+E(f563(x24141,x24143,x24144,x24145),f563(x24142,x24143,x24144,x24145)) % 168.22/168.07 [2415]~E(x24151,x24152)+E(f563(x24153,x24151,x24154,x24155),f563(x24153,x24152,x24154,x24155)) % 168.22/168.07 [2416]~E(x24161,x24162)+E(f563(x24163,x24164,x24161,x24165),f563(x24163,x24164,x24162,x24165)) % 168.22/168.07 [2417]~E(x24171,x24172)+E(f563(x24173,x24174,x24175,x24171),f563(x24173,x24174,x24175,x24172)) % 168.22/168.07 [2418]~E(x24181,x24182)+E(f388(x24181,x24183,x24184),f388(x24182,x24183,x24184)) % 168.22/168.07 [2419]~E(x24191,x24192)+E(f388(x24193,x24191,x24194),f388(x24193,x24192,x24194)) % 168.22/168.07 [2420]~E(x24201,x24202)+E(f388(x24203,x24204,x24201),f388(x24203,x24204,x24202)) % 168.22/168.07 [2421]~E(x24211,x24212)+E(f378(x24211,x24213,x24214),f378(x24212,x24213,x24214)) % 168.22/168.07 [2422]~E(x24221,x24222)+E(f378(x24223,x24221,x24224),f378(x24223,x24222,x24224)) % 168.22/168.07 [2423]~E(x24231,x24232)+E(f378(x24233,x24234,x24231),f378(x24233,x24234,x24232)) % 168.22/168.07 [2424]~E(x24241,x24242)+E(f101(x24241,x24243,x24244),f101(x24242,x24243,x24244)) % 168.22/168.07 [2425]~E(x24251,x24252)+E(f101(x24253,x24251,x24254),f101(x24253,x24252,x24254)) % 168.22/168.07 [2426]~E(x24261,x24262)+E(f101(x24263,x24264,x24261),f101(x24263,x24264,x24262)) % 168.22/168.07 [2427]~E(x24271,x24272)+E(f212(x24271,x24273,x24274,x24275,x24276),f212(x24272,x24273,x24274,x24275,x24276)) % 168.22/168.07 [2428]~E(x24281,x24282)+E(f212(x24283,x24281,x24284,x24285,x24286),f212(x24283,x24282,x24284,x24285,x24286)) % 168.22/168.07 [2429]~E(x24291,x24292)+E(f212(x24293,x24294,x24291,x24295,x24296),f212(x24293,x24294,x24292,x24295,x24296)) % 168.22/168.07 [2430]~E(x24301,x24302)+E(f212(x24303,x24304,x24305,x24301,x24306),f212(x24303,x24304,x24305,x24302,x24306)) % 168.22/168.07 [2431]~E(x24311,x24312)+E(f212(x24313,x24314,x24315,x24316,x24311),f212(x24313,x24314,x24315,x24316,x24312)) % 168.22/168.07 [2432]~E(x24321,x24322)+E(f299(x24321,x24323,x24324),f299(x24322,x24323,x24324)) % 168.22/168.07 [2433]~E(x24331,x24332)+E(f299(x24333,x24331,x24334),f299(x24333,x24332,x24334)) % 168.22/168.07 [2434]~E(x24341,x24342)+E(f299(x24343,x24344,x24341),f299(x24343,x24344,x24342)) % 168.22/168.07 [2435]~E(x24351,x24352)+E(f340(x24351,x24353,x24354),f340(x24352,x24353,x24354)) % 168.22/168.07 [2436]~E(x24361,x24362)+E(f340(x24363,x24361,x24364),f340(x24363,x24362,x24364)) % 168.22/168.07 [2437]~E(x24371,x24372)+E(f340(x24373,x24374,x24371),f340(x24373,x24374,x24372)) % 168.22/168.07 [2438]~E(x24381,x24382)+E(f331(x24381,x24383,x24384),f331(x24382,x24383,x24384)) % 168.22/168.07 [2439]~E(x24391,x24392)+E(f331(x24393,x24391,x24394),f331(x24393,x24392,x24394)) % 168.22/168.07 [2440]~E(x24401,x24402)+E(f331(x24403,x24404,x24401),f331(x24403,x24404,x24402)) % 168.22/168.07 [2441]~E(x24411,x24412)+E(f645(x24411,x24413,x24414),f645(x24412,x24413,x24414)) % 168.22/168.07 [2442]~E(x24421,x24422)+E(f645(x24423,x24421,x24424),f645(x24423,x24422,x24424)) % 168.22/168.07 [2443]~E(x24431,x24432)+E(f645(x24433,x24434,x24431),f645(x24433,x24434,x24432)) % 168.22/168.07 [2444]~E(x24441,x24442)+E(f221(x24441,x24443,x24444,x24445,x24446),f221(x24442,x24443,x24444,x24445,x24446)) % 168.22/168.07 [2445]~E(x24451,x24452)+E(f221(x24453,x24451,x24454,x24455,x24456),f221(x24453,x24452,x24454,x24455,x24456)) % 168.22/168.07 [2446]~E(x24461,x24462)+E(f221(x24463,x24464,x24461,x24465,x24466),f221(x24463,x24464,x24462,x24465,x24466)) % 168.22/168.07 [2447]~E(x24471,x24472)+E(f221(x24473,x24474,x24475,x24471,x24476),f221(x24473,x24474,x24475,x24472,x24476)) % 168.22/168.07 [2448]~E(x24481,x24482)+E(f221(x24483,x24484,x24485,x24486,x24481),f221(x24483,x24484,x24485,x24486,x24482)) % 168.22/168.07 [2449]~E(x24491,x24492)+E(f646(x24491,x24493,x24494),f646(x24492,x24493,x24494)) % 168.22/168.07 [2450]~E(x24501,x24502)+E(f646(x24503,x24501,x24504),f646(x24503,x24502,x24504)) % 168.22/168.07 [2451]~E(x24511,x24512)+E(f646(x24513,x24514,x24511),f646(x24513,x24514,x24512)) % 168.22/168.07 [2452]~E(x24521,x24522)+E(f771(x24521,x24523,x24524,x24525),f771(x24522,x24523,x24524,x24525)) % 168.22/168.07 [2453]~E(x24531,x24532)+E(f771(x24533,x24531,x24534,x24535),f771(x24533,x24532,x24534,x24535)) % 168.22/168.07 [2454]~E(x24541,x24542)+E(f771(x24543,x24544,x24541,x24545),f771(x24543,x24544,x24542,x24545)) % 168.22/168.07 [2455]~E(x24551,x24552)+E(f771(x24553,x24554,x24555,x24551),f771(x24553,x24554,x24555,x24552)) % 168.22/168.07 [2456]~E(x24561,x24562)+E(f680(x24561,x24563,x24564),f680(x24562,x24563,x24564)) % 168.22/168.07 [2457]~E(x24571,x24572)+E(f680(x24573,x24571,x24574),f680(x24573,x24572,x24574)) % 168.22/168.07 [2458]~E(x24581,x24582)+E(f680(x24583,x24584,x24581),f680(x24583,x24584,x24582)) % 168.22/168.07 [2459]~E(x24591,x24592)+E(f764(x24591),f764(x24592)) % 168.22/168.07 [2460]~E(x24601,x24602)+E(f437(x24601,x24603,x24604),f437(x24602,x24603,x24604)) % 168.22/168.07 [2461]~E(x24611,x24612)+E(f437(x24613,x24611,x24614),f437(x24613,x24612,x24614)) % 168.22/168.07 [2462]~E(x24621,x24622)+E(f437(x24623,x24624,x24621),f437(x24623,x24624,x24622)) % 168.22/168.07 [2463]~E(x24631,x24632)+E(f273(x24631,x24633,x24634,x24635,x24636),f273(x24632,x24633,x24634,x24635,x24636)) % 168.22/168.07 [2464]~E(x24641,x24642)+E(f273(x24643,x24641,x24644,x24645,x24646),f273(x24643,x24642,x24644,x24645,x24646)) % 168.22/168.07 [2465]~E(x24651,x24652)+E(f273(x24653,x24654,x24651,x24655,x24656),f273(x24653,x24654,x24652,x24655,x24656)) % 168.22/168.07 [2466]~E(x24661,x24662)+E(f273(x24663,x24664,x24665,x24661,x24666),f273(x24663,x24664,x24665,x24662,x24666)) % 168.22/168.07 [2467]~E(x24671,x24672)+E(f273(x24673,x24674,x24675,x24676,x24671),f273(x24673,x24674,x24675,x24676,x24672)) % 168.22/168.07 [2468]~E(x24681,x24682)+E(f375(x24681,x24683),f375(x24682,x24683)) % 168.22/168.07 [2469]~E(x24691,x24692)+E(f375(x24693,x24691),f375(x24693,x24692)) % 168.22/168.07 [2470]~E(x24701,x24702)+E(f572(x24701,x24703,x24704,x24705),f572(x24702,x24703,x24704,x24705)) % 168.22/168.07 [2471]~E(x24711,x24712)+E(f572(x24713,x24711,x24714,x24715),f572(x24713,x24712,x24714,x24715)) % 168.22/168.07 [2472]~E(x24721,x24722)+E(f572(x24723,x24724,x24721,x24725),f572(x24723,x24724,x24722,x24725)) % 168.22/168.07 [2473]~E(x24731,x24732)+E(f572(x24733,x24734,x24735,x24731),f572(x24733,x24734,x24735,x24732)) % 168.22/168.07 [2474]~E(x24741,x24742)+E(f341(x24741,x24743,x24744),f341(x24742,x24743,x24744)) % 168.22/168.07 [2475]~E(x24751,x24752)+E(f341(x24753,x24751,x24754),f341(x24753,x24752,x24754)) % 168.22/168.07 [2476]~E(x24761,x24762)+E(f341(x24763,x24764,x24761),f341(x24763,x24764,x24762)) % 168.22/168.07 [2477]~E(x24771,x24772)+E(f782(x24771,x24773,x24774),f782(x24772,x24773,x24774)) % 168.22/168.07 [2478]~E(x24781,x24782)+E(f782(x24783,x24781,x24784),f782(x24783,x24782,x24784)) % 168.22/168.07 [2479]~E(x24791,x24792)+E(f782(x24793,x24794,x24791),f782(x24793,x24794,x24792)) % 168.22/168.07 [2480]~E(x24801,x24802)+E(f669(x24801,x24803,x24804),f669(x24802,x24803,x24804)) % 168.22/168.07 [2481]~E(x24811,x24812)+E(f669(x24813,x24811,x24814),f669(x24813,x24812,x24814)) % 168.22/168.07 [2482]~E(x24821,x24822)+E(f669(x24823,x24824,x24821),f669(x24823,x24824,x24822)) % 168.22/168.07 [2483]~E(x24831,x24832)+E(f819(x24831),f819(x24832)) % 168.22/168.07 [2484]~E(x24841,x24842)+E(f739(x24841,x24843,x24844),f739(x24842,x24843,x24844)) % 168.22/168.07 [2485]~E(x24851,x24852)+E(f739(x24853,x24851,x24854),f739(x24853,x24852,x24854)) % 168.22/168.07 [2486]~E(x24861,x24862)+E(f739(x24863,x24864,x24861),f739(x24863,x24864,x24862)) % 168.22/168.07 [2487]~E(x24871,x24872)+E(f816(x24871,x24873,x24874,x24875),f816(x24872,x24873,x24874,x24875)) % 168.22/168.07 [2488]~E(x24881,x24882)+E(f816(x24883,x24881,x24884,x24885),f816(x24883,x24882,x24884,x24885)) % 168.22/168.07 [2489]~E(x24891,x24892)+E(f816(x24893,x24894,x24891,x24895),f816(x24893,x24894,x24892,x24895)) % 168.22/168.07 [2490]~E(x24901,x24902)+E(f816(x24903,x24904,x24905,x24901),f816(x24903,x24904,x24905,x24902)) % 168.22/168.07 [2491]~E(x24911,x24912)+E(f535(x24911,x24913,x24914,x24915,x24916),f535(x24912,x24913,x24914,x24915,x24916)) % 168.22/168.07 [2492]~E(x24921,x24922)+E(f535(x24923,x24921,x24924,x24925,x24926),f535(x24923,x24922,x24924,x24925,x24926)) % 168.22/168.07 [2493]~E(x24931,x24932)+E(f535(x24933,x24934,x24931,x24935,x24936),f535(x24933,x24934,x24932,x24935,x24936)) % 168.22/168.07 [2494]~E(x24941,x24942)+E(f535(x24943,x24944,x24945,x24941,x24946),f535(x24943,x24944,x24945,x24942,x24946)) % 168.22/168.07 [2495]~E(x24951,x24952)+E(f535(x24953,x24954,x24955,x24956,x24951),f535(x24953,x24954,x24955,x24956,x24952)) % 168.22/168.07 [2496]~E(x24961,x24962)+E(f635(x24961,x24963,x24964,x24965,x24966),f635(x24962,x24963,x24964,x24965,x24966)) % 168.22/168.07 [2497]~E(x24971,x24972)+E(f635(x24973,x24971,x24974,x24975,x24976),f635(x24973,x24972,x24974,x24975,x24976)) % 168.22/168.07 [2498]~E(x24981,x24982)+E(f635(x24983,x24984,x24981,x24985,x24986),f635(x24983,x24984,x24982,x24985,x24986)) % 168.22/168.07 [2499]~E(x24991,x24992)+E(f635(x24993,x24994,x24995,x24991,x24996),f635(x24993,x24994,x24995,x24992,x24996)) % 168.22/168.07 [2500]~E(x25001,x25002)+E(f635(x25003,x25004,x25005,x25006,x25001),f635(x25003,x25004,x25005,x25006,x25002)) % 168.22/168.07 [2501]~E(x25011,x25012)+E(f530(x25011,x25013),f530(x25012,x25013)) % 168.22/168.07 [2502]~E(x25021,x25022)+E(f530(x25023,x25021),f530(x25023,x25022)) % 168.22/168.07 [2503]~E(x25031,x25032)+E(f485(x25031,x25033,x25034,x25035,x25036),f485(x25032,x25033,x25034,x25035,x25036)) % 168.22/168.07 [2504]~E(x25041,x25042)+E(f485(x25043,x25041,x25044,x25045,x25046),f485(x25043,x25042,x25044,x25045,x25046)) % 168.22/168.07 [2505]~E(x25051,x25052)+E(f485(x25053,x25054,x25051,x25055,x25056),f485(x25053,x25054,x25052,x25055,x25056)) % 168.22/168.07 [2506]~E(x25061,x25062)+E(f485(x25063,x25064,x25065,x25061,x25066),f485(x25063,x25064,x25065,x25062,x25066)) % 168.22/168.07 [2507]~E(x25071,x25072)+E(f485(x25073,x25074,x25075,x25076,x25071),f485(x25073,x25074,x25075,x25076,x25072)) % 168.22/168.07 [2508]~E(x25081,x25082)+E(f838(x25081),f838(x25082)) % 168.22/168.07 [2509]~E(x25091,x25092)+E(f656(x25091,x25093),f656(x25092,x25093)) % 168.22/168.07 [2510]~E(x25101,x25102)+E(f656(x25103,x25101),f656(x25103,x25102)) % 168.22/168.07 [2511]~E(x25111,x25112)+E(f457(x25111,x25113,x25114,x25115,x25116),f457(x25112,x25113,x25114,x25115,x25116)) % 168.22/168.07 [2512]~E(x25121,x25122)+E(f457(x25123,x25121,x25124,x25125,x25126),f457(x25123,x25122,x25124,x25125,x25126)) % 168.22/168.07 [2513]~E(x25131,x25132)+E(f457(x25133,x25134,x25131,x25135,x25136),f457(x25133,x25134,x25132,x25135,x25136)) % 168.22/168.07 [2514]~E(x25141,x25142)+E(f457(x25143,x25144,x25145,x25141,x25146),f457(x25143,x25144,x25145,x25142,x25146)) % 168.22/168.07 [2515]~E(x25151,x25152)+E(f457(x25153,x25154,x25155,x25156,x25151),f457(x25153,x25154,x25155,x25156,x25152)) % 168.22/168.07 [2516]~E(x25161,x25162)+E(f17(x25161,x25163,x25164,x25165),f17(x25162,x25163,x25164,x25165)) % 168.22/168.07 [2517]~E(x25171,x25172)+E(f17(x25173,x25171,x25174,x25175),f17(x25173,x25172,x25174,x25175)) % 168.22/168.07 [2518]~E(x25181,x25182)+E(f17(x25183,x25184,x25181,x25185),f17(x25183,x25184,x25182,x25185)) % 168.22/168.07 [2519]~E(x25191,x25192)+E(f17(x25193,x25194,x25195,x25191),f17(x25193,x25194,x25195,x25192)) % 168.22/168.07 [2520]~E(x25201,x25202)+E(f509(x25201,x25203,x25204,x25205),f509(x25202,x25203,x25204,x25205)) % 168.22/168.07 [2521]~E(x25211,x25212)+E(f509(x25213,x25211,x25214,x25215),f509(x25213,x25212,x25214,x25215)) % 168.22/168.07 [2522]~E(x25221,x25222)+E(f509(x25223,x25224,x25221,x25225),f509(x25223,x25224,x25222,x25225)) % 168.22/168.07 [2523]~E(x25231,x25232)+E(f509(x25233,x25234,x25235,x25231),f509(x25233,x25234,x25235,x25232)) % 168.22/168.07 [2524]~E(x25241,x25242)+E(f370(x25241,x25243),f370(x25242,x25243)) % 168.22/168.07 [2525]~E(x25251,x25252)+E(f370(x25253,x25251),f370(x25253,x25252)) % 168.22/168.07 [2526]~E(x25261,x25262)+E(f798(x25261,x25263),f798(x25262,x25263)) % 168.22/168.07 [2527]~E(x25271,x25272)+E(f798(x25273,x25271),f798(x25273,x25272)) % 168.22/168.07 [2528]~E(x25281,x25282)+E(f813(x25281,x25283),f813(x25282,x25283)) % 168.22/168.07 [2529]~E(x25291,x25292)+E(f813(x25293,x25291),f813(x25293,x25292)) % 168.22/168.07 [2530]~E(x25301,x25302)+E(f296(x25301,x25303,x25304),f296(x25302,x25303,x25304)) % 168.22/168.07 [2531]~E(x25311,x25312)+E(f296(x25313,x25311,x25314),f296(x25313,x25312,x25314)) % 168.22/168.07 [2532]~E(x25321,x25322)+E(f296(x25323,x25324,x25321),f296(x25323,x25324,x25322)) % 168.22/168.07 [2533]~E(x25331,x25332)+E(f821(x25331),f821(x25332)) % 168.22/168.07 [2534]~E(x25341,x25342)+E(f547(x25341,x25343),f547(x25342,x25343)) % 168.22/168.07 [2535]~E(x25351,x25352)+E(f547(x25353,x25351),f547(x25353,x25352)) % 168.22/168.07 [2536]~E(x25361,x25362)+E(f582(x25361,x25363,x25364,x25365),f582(x25362,x25363,x25364,x25365)) % 168.22/168.07 [2537]~E(x25371,x25372)+E(f582(x25373,x25371,x25374,x25375),f582(x25373,x25372,x25374,x25375)) % 168.22/168.07 [2538]~E(x25381,x25382)+E(f582(x25383,x25384,x25381,x25385),f582(x25383,x25384,x25382,x25385)) % 168.22/168.07 [2539]~E(x25391,x25392)+E(f582(x25393,x25394,x25395,x25391),f582(x25393,x25394,x25395,x25392)) % 168.22/168.07 [2540]~E(x25401,x25402)+E(f837(x25401),f837(x25402)) % 168.22/168.07 [2541]~E(x25411,x25412)+E(f521(x25411),f521(x25412)) % 168.22/168.07 [2542]~P1(x25421)+P1(x25422)+~E(x25421,x25422) % 168.22/168.07 [2543]~P4(x25431)+P4(x25432)+~E(x25431,x25432) % 168.22/168.07 [2544]~P22(x25441)+P22(x25442)+~E(x25441,x25442) % 168.22/168.07 [2545]~P23(x25451)+P23(x25452)+~E(x25451,x25452) % 168.22/168.07 [2546]P139(x25462,x25463,x25464)+~E(x25461,x25462)+~P139(x25461,x25463,x25464) % 168.22/168.07 [2547]P139(x25473,x25472,x25474)+~E(x25471,x25472)+~P139(x25473,x25471,x25474) % 168.22/168.07 [2548]P139(x25483,x25484,x25482)+~E(x25481,x25482)+~P139(x25483,x25484,x25481) % 168.22/168.07 [2549]P29(x25492,x25493)+~E(x25491,x25492)+~P29(x25491,x25493) % 168.22/168.07 [2550]P29(x25503,x25502)+~E(x25501,x25502)+~P29(x25503,x25501) % 168.22/168.07 [2551]~P24(x25511)+P24(x25512)+~E(x25511,x25512) % 168.22/168.07 [2552]~P112(x25521)+P112(x25522)+~E(x25521,x25522) % 168.22/168.07 [2553]~P55(x25531)+P55(x25532)+~E(x25531,x25532) % 168.22/168.07 [2554]~P62(x25541)+P62(x25542)+~E(x25541,x25542) % 168.22/168.07 [2555]P138(x25552,x25553,x25554)+~E(x25551,x25552)+~P138(x25551,x25553,x25554) % 168.22/168.07 [2556]P138(x25563,x25562,x25564)+~E(x25561,x25562)+~P138(x25563,x25561,x25564) % 168.22/168.07 [2557]P138(x25573,x25574,x25572)+~E(x25571,x25572)+~P138(x25573,x25574,x25571) % 168.22/168.07 [2558]P49(x25582,x25583,x25584)+~E(x25581,x25582)+~P49(x25581,x25583,x25584) % 168.22/168.07 [2559]P49(x25593,x25592,x25594)+~E(x25591,x25592)+~P49(x25593,x25591,x25594) % 168.22/168.07 [2560]P49(x25603,x25604,x25602)+~E(x25601,x25602)+~P49(x25603,x25604,x25601) % 168.22/168.07 [2561]~P63(x25611)+P63(x25612)+~E(x25611,x25612) % 168.22/168.07 [2562]~P61(x25621)+P61(x25622)+~E(x25621,x25622) % 168.22/168.07 [2563]~P60(x25631)+P60(x25632)+~E(x25631,x25632) % 168.22/168.07 [2564]~P66(x25641)+P66(x25642)+~E(x25641,x25642) % 168.22/168.07 [2565]~P103(x25651)+P103(x25652)+~E(x25651,x25652) % 168.22/168.07 [2566]~P90(x25661)+P90(x25662)+~E(x25661,x25662) % 168.22/168.07 [2567]~P67(x25671)+P67(x25672)+~E(x25671,x25672) % 168.22/168.07 [2568]P54(x25682,x25683)+~E(x25681,x25682)+~P54(x25681,x25683) % 168.22/168.07 [2569]P54(x25693,x25692)+~E(x25691,x25692)+~P54(x25693,x25691) % 168.22/168.07 [2570]P31(x25702,x25703)+~E(x25701,x25702)+~P31(x25701,x25703) % 168.22/168.07 [2571]P31(x25713,x25712)+~E(x25711,x25712)+~P31(x25713,x25711) % 168.22/168.07 [2572]~P68(x25721)+P68(x25722)+~E(x25721,x25722) % 168.22/168.07 [2573]~P84(x25731)+P84(x25732)+~E(x25731,x25732) % 168.22/168.07 [2574]~P110(x25741)+P110(x25742)+~E(x25741,x25742) % 168.22/168.07 [2575]~P25(x25751)+P25(x25752)+~E(x25751,x25752) % 168.22/168.07 [2576]~P109(x25761)+P109(x25762)+~E(x25761,x25762) % 168.22/168.07 [2577]P37(x25772,x25773)+~E(x25771,x25772)+~P37(x25771,x25773) % 168.22/168.07 [2578]P37(x25783,x25782)+~E(x25781,x25782)+~P37(x25783,x25781) % 168.22/168.07 [2579]~P113(x25791)+P113(x25792)+~E(x25791,x25792) % 168.22/168.07 [2580]~P121(x25801)+P121(x25802)+~E(x25801,x25802) % 168.22/168.07 [2581]~P88(x25811)+P88(x25812)+~E(x25811,x25812) % 168.22/168.07 [2582]~P85(x25821)+P85(x25822)+~E(x25821,x25822) % 168.22/168.07 [2583]~P39(x25831)+P39(x25832)+~E(x25831,x25832) % 168.22/168.07 [2584]~P118(x25841)+P118(x25842)+~E(x25841,x25842) % 168.22/168.07 [2585]~P69(x25851)+P69(x25852)+~E(x25851,x25852) % 168.22/168.07 [2586]~P71(x25861)+P71(x25862)+~E(x25861,x25862) % 168.22/168.07 [2587]~P93(x25871)+P93(x25872)+~E(x25871,x25872) % 168.22/168.07 [2588]~P58(x25881)+P58(x25882)+~E(x25881,x25882) % 168.22/168.07 [2589]P51(x25892,x25893,x25894,x25895,x25896)+~E(x25891,x25892)+~P51(x25891,x25893,x25894,x25895,x25896) % 168.22/168.07 [2590]P51(x25903,x25902,x25904,x25905,x25906)+~E(x25901,x25902)+~P51(x25903,x25901,x25904,x25905,x25906) % 168.22/168.07 [2591]P51(x25913,x25914,x25912,x25915,x25916)+~E(x25911,x25912)+~P51(x25913,x25914,x25911,x25915,x25916) % 168.22/168.07 [2592]P51(x25923,x25924,x25925,x25922,x25926)+~E(x25921,x25922)+~P51(x25923,x25924,x25925,x25921,x25926) % 168.22/168.07 [2593]P51(x25933,x25934,x25935,x25936,x25932)+~E(x25931,x25932)+~P51(x25933,x25934,x25935,x25936,x25931) % 168.22/168.07 [2594]~P73(x25941)+P73(x25942)+~E(x25941,x25942) % 168.22/168.07 [2595]~P111(x25951)+P111(x25952)+~E(x25951,x25952) % 168.22/168.07 [2596]~P86(x25961)+P86(x25962)+~E(x25961,x25962) % 168.22/168.07 [2597]~P100(x25971)+P100(x25972)+~E(x25971,x25972) % 168.22/168.07 [2598]~P87(x25981)+P87(x25982)+~E(x25981,x25982) % 168.22/168.07 [2599]~P101(x25991)+P101(x25992)+~E(x25991,x25992) % 168.22/168.07 [2600]~P78(x26001)+P78(x26002)+~E(x26001,x26002) % 168.22/168.07 [2601]P50(x26012,x26013,x26014)+~E(x26011,x26012)+~P50(x26011,x26013,x26014) % 168.22/168.07 [2602]P50(x26023,x26022,x26024)+~E(x26021,x26022)+~P50(x26023,x26021,x26024) % 168.22/168.07 [2603]P50(x26033,x26034,x26032)+~E(x26031,x26032)+~P50(x26033,x26034,x26031) % 168.22/168.07 [2604]P52(x26042,x26043)+~E(x26041,x26042)+~P52(x26041,x26043) % 168.22/168.07 [2605]P52(x26053,x26052)+~E(x26051,x26052)+~P52(x26053,x26051) % 168.22/168.07 [2606]~P74(x26061)+P74(x26062)+~E(x26061,x26062) % 168.22/168.07 [2607]P19(x26072,x26073,x26074,x26075)+~E(x26071,x26072)+~P19(x26071,x26073,x26074,x26075) % 168.22/168.07 [2608]P19(x26083,x26082,x26084,x26085)+~E(x26081,x26082)+~P19(x26083,x26081,x26084,x26085) % 168.22/168.07 [2609]P19(x26093,x26094,x26092,x26095)+~E(x26091,x26092)+~P19(x26093,x26094,x26091,x26095) % 168.22/168.07 [2610]P19(x26103,x26104,x26105,x26102)+~E(x26101,x26102)+~P19(x26103,x26104,x26105,x26101) % 168.22/168.07 [2611]~P36(x26111)+P36(x26112)+~E(x26111,x26112) % 168.22/168.07 [2612]~P102(x26121)+P102(x26122)+~E(x26121,x26122) % 168.22/168.07 [2613]~P79(x26131)+P79(x26132)+~E(x26131,x26132) % 168.22/168.07 [2614]P35(x26142,x26143,x26144,x26145,x26146)+~E(x26141,x26142)+~P35(x26141,x26143,x26144,x26145,x26146) % 168.22/168.07 [2615]P35(x26153,x26152,x26154,x26155,x26156)+~E(x26151,x26152)+~P35(x26153,x26151,x26154,x26155,x26156) % 168.22/168.07 [2616]P35(x26163,x26164,x26162,x26165,x26166)+~E(x26161,x26162)+~P35(x26163,x26164,x26161,x26165,x26166) % 168.22/168.07 [2617]P35(x26173,x26174,x26175,x26172,x26176)+~E(x26171,x26172)+~P35(x26173,x26174,x26175,x26171,x26176) % 168.22/168.07 [2618]P35(x26183,x26184,x26185,x26186,x26182)+~E(x26181,x26182)+~P35(x26183,x26184,x26185,x26186,x26181) % 168.22/168.07 [2619]P14(x26192,x26193,x26194,x26195)+~E(x26191,x26192)+~P14(x26191,x26193,x26194,x26195) % 168.22/168.07 [2620]P14(x26203,x26202,x26204,x26205)+~E(x26201,x26202)+~P14(x26203,x26201,x26204,x26205) % 168.22/168.07 [2621]P14(x26213,x26214,x26212,x26215)+~E(x26211,x26212)+~P14(x26213,x26214,x26211,x26215) % 168.22/168.07 [2622]P14(x26223,x26224,x26225,x26222)+~E(x26221,x26222)+~P14(x26223,x26224,x26225,x26221) % 168.22/168.07 [2623]~P104(x26231)+P104(x26232)+~E(x26231,x26232) % 168.22/168.07 [2624]P33(x26242,x26243,x26244,x26245)+~E(x26241,x26242)+~P33(x26241,x26243,x26244,x26245) % 168.22/168.07 [2625]P33(x26253,x26252,x26254,x26255)+~E(x26251,x26252)+~P33(x26253,x26251,x26254,x26255) % 168.22/168.07 [2626]P33(x26263,x26264,x26262,x26265)+~E(x26261,x26262)+~P33(x26263,x26264,x26261,x26265) % 168.22/168.07 [2627]P33(x26273,x26274,x26275,x26272)+~E(x26271,x26272)+~P33(x26273,x26274,x26275,x26271) % 168.22/168.07 [2628]~P92(x26281)+P92(x26282)+~E(x26281,x26282) % 168.22/168.07 [2629]~P70(x26291)+P70(x26292)+~E(x26291,x26292) % 168.22/168.07 [2630]~P133(x26301)+P133(x26302)+~E(x26301,x26302) % 168.22/168.07 [2631]~P59(x26311)+P59(x26312)+~E(x26311,x26312) % 168.22/168.07 [2632]~P64(x26321)+P64(x26322)+~E(x26321,x26322) % 168.22/168.07 [2633]P32(x26332,x26333,x26334,x26335)+~E(x26331,x26332)+~P32(x26331,x26333,x26334,x26335) % 168.22/168.07 [2634]P32(x26343,x26342,x26344,x26345)+~E(x26341,x26342)+~P32(x26343,x26341,x26344,x26345) % 168.22/168.07 [2635]P32(x26353,x26354,x26352,x26355)+~E(x26351,x26352)+~P32(x26353,x26354,x26351,x26355) % 168.22/168.07 [2636]P32(x26363,x26364,x26365,x26362)+~E(x26361,x26362)+~P32(x26363,x26364,x26365,x26361) % 168.22/168.07 [2637]~P76(x26371)+P76(x26372)+~E(x26371,x26372) % 168.22/168.07 [2638]~P115(x26381)+P115(x26382)+~E(x26381,x26382) % 168.22/168.07 [2639]~P65(x26391)+P65(x26392)+~E(x26391,x26392) % 168.22/168.07 [2640]~P77(x26401)+P77(x26402)+~E(x26401,x26402) % 168.22/168.07 [2641]~P57(x26411)+P57(x26412)+~E(x26411,x26412) % 168.22/168.07 [2642]~P98(x26421)+P98(x26422)+~E(x26421,x26422) % 168.22/168.07 [2643]P18(x26432,x26433,x26434)+~E(x26431,x26432)+~P18(x26431,x26433,x26434) % 168.22/168.07 [2644]P18(x26443,x26442,x26444)+~E(x26441,x26442)+~P18(x26443,x26441,x26444) % 168.22/168.07 [2645]P18(x26453,x26454,x26452)+~E(x26451,x26452)+~P18(x26453,x26454,x26451) % 168.22/168.07 [2646]~P80(x26461)+P80(x26462)+~E(x26461,x26462) % 168.22/168.07 [2647]~P119(x26471)+P119(x26472)+~E(x26471,x26472) % 168.22/168.07 [2648]P34(x26482,x26483,x26484)+~E(x26481,x26482)+~P34(x26481,x26483,x26484) % 168.22/168.07 [2649]P34(x26493,x26492,x26494)+~E(x26491,x26492)+~P34(x26493,x26491,x26494) % 168.22/168.07 [2650]P34(x26503,x26504,x26502)+~E(x26501,x26502)+~P34(x26503,x26504,x26501) % 168.22/168.07 [2651]~P27(x26511)+P27(x26512)+~E(x26511,x26512) % 168.22/168.07 [2652]P10(x26522,x26523,x26524,x26525,x26526,x26527)+~E(x26521,x26522)+~P10(x26521,x26523,x26524,x26525,x26526,x26527) % 168.22/168.07 [2653]P10(x26533,x26532,x26534,x26535,x26536,x26537)+~E(x26531,x26532)+~P10(x26533,x26531,x26534,x26535,x26536,x26537) % 168.22/168.07 [2654]P10(x26543,x26544,x26542,x26545,x26546,x26547)+~E(x26541,x26542)+~P10(x26543,x26544,x26541,x26545,x26546,x26547) % 168.22/168.07 [2655]P10(x26553,x26554,x26555,x26552,x26556,x26557)+~E(x26551,x26552)+~P10(x26553,x26554,x26555,x26551,x26556,x26557) % 168.22/168.07 [2656]P10(x26563,x26564,x26565,x26566,x26562,x26567)+~E(x26561,x26562)+~P10(x26563,x26564,x26565,x26566,x26561,x26567) % 168.22/168.07 [2657]P10(x26573,x26574,x26575,x26576,x26577,x26572)+~E(x26571,x26572)+~P10(x26573,x26574,x26575,x26576,x26577,x26571) % 168.22/168.07 [2658]P20(x26582,x26583)+~E(x26581,x26582)+~P20(x26581,x26583) % 168.22/168.07 [2659]P20(x26593,x26592)+~E(x26591,x26592)+~P20(x26593,x26591) % 168.22/168.07 [2660]~P136(x26601)+P136(x26602)+~E(x26601,x26602) % 168.22/168.07 [2661]~P97(x26611)+P97(x26612)+~E(x26611,x26612) % 168.22/168.07 [2662]P7(x26622,x26623,x26624)+~E(x26621,x26622)+~P7(x26621,x26623,x26624) % 168.22/168.07 [2663]P7(x26633,x26632,x26634)+~E(x26631,x26632)+~P7(x26633,x26631,x26634) % 168.22/168.07 [2664]P7(x26643,x26644,x26642)+~E(x26641,x26642)+~P7(x26643,x26644,x26641) % 168.22/168.07 [2665]~P135(x26651)+P135(x26652)+~E(x26651,x26652) % 168.22/168.07 [2666]P6(x26662,x26663,x26664)+~E(x26661,x26662)+~P6(x26661,x26663,x26664) % 168.22/168.07 [2667]P6(x26673,x26672,x26674)+~E(x26671,x26672)+~P6(x26673,x26671,x26674) % 168.22/168.07 [2668]P6(x26683,x26684,x26682)+~E(x26681,x26682)+~P6(x26683,x26684,x26681) % 168.22/168.07 [2669]~P96(x26691)+P96(x26692)+~E(x26691,x26692) % 168.22/168.07 [2670]~P128(x26701)+P128(x26702)+~E(x26701,x26702) % 168.22/168.07 [2671]P11(x26712,x26713,x26714)+~E(x26711,x26712)+~P11(x26711,x26713,x26714) % 168.22/168.07 [2672]P11(x26723,x26722,x26724)+~E(x26721,x26722)+~P11(x26723,x26721,x26724) % 168.22/168.07 [2673]P11(x26733,x26734,x26732)+~E(x26731,x26732)+~P11(x26733,x26734,x26731) % 168.22/168.07 [2674]~P130(x26741)+P130(x26742)+~E(x26741,x26742) % 168.22/168.07 [2675]P5(x26752,x26753)+~E(x26751,x26752)+~P5(x26751,x26753) % 168.22/168.07 [2676]P5(x26763,x26762)+~E(x26761,x26762)+~P5(x26763,x26761) % 168.22/168.07 [2677]~P94(x26771)+P94(x26772)+~E(x26771,x26772) % 168.22/168.07 [2678]~P81(x26781)+P81(x26782)+~E(x26781,x26782) % 168.22/168.07 [2679]~P124(x26791)+P124(x26792)+~E(x26791,x26792) % 168.22/168.07 [2680]P12(x26802,x26803,x26804)+~E(x26801,x26802)+~P12(x26801,x26803,x26804) % 168.22/168.07 [2681]P12(x26813,x26812,x26814)+~E(x26811,x26812)+~P12(x26813,x26811,x26814) % 168.22/168.07 [2682]P12(x26823,x26824,x26822)+~E(x26821,x26822)+~P12(x26823,x26824,x26821) % 168.22/168.07 [2683]~P82(x26831)+P82(x26832)+~E(x26831,x26832) % 168.22/168.07 [2684]~P120(x26841)+P120(x26842)+~E(x26841,x26842) % 168.22/168.07 [2685]~P105(x26851)+P105(x26852)+~E(x26851,x26852) % 168.22/168.07 [2686]~P91(x26861)+P91(x26862)+~E(x26861,x26862) % 168.22/168.07 [2687]~P127(x26871)+P127(x26872)+~E(x26871,x26872) % 168.22/168.07 [2688]~P99(x26881)+P99(x26882)+~E(x26881,x26882) % 168.22/168.07 [2689]P38(x26892,x26893)+~E(x26891,x26892)+~P38(x26891,x26893) % 168.22/168.07 [2690]P38(x26903,x26902)+~E(x26901,x26902)+~P38(x26903,x26901) % 168.22/168.07 [2691]P3(x26912,x26913,x26914,x26915,x26916)+~E(x26911,x26912)+~P3(x26911,x26913,x26914,x26915,x26916) % 168.22/168.07 [2692]P3(x26923,x26922,x26924,x26925,x26926)+~E(x26921,x26922)+~P3(x26923,x26921,x26924,x26925,x26926) % 168.22/168.07 [2693]P3(x26933,x26934,x26932,x26935,x26936)+~E(x26931,x26932)+~P3(x26933,x26934,x26931,x26935,x26936) % 168.22/168.07 [2694]P3(x26943,x26944,x26945,x26942,x26946)+~E(x26941,x26942)+~P3(x26943,x26944,x26945,x26941,x26946) % 168.22/168.07 [2695]P3(x26953,x26954,x26955,x26956,x26952)+~E(x26951,x26952)+~P3(x26953,x26954,x26955,x26956,x26951) % 168.22/168.07 [2696]~P123(x26961)+P123(x26962)+~E(x26961,x26962) % 168.22/168.07 [2697]P45(x26972,x26973,x26974)+~E(x26971,x26972)+~P45(x26971,x26973,x26974) % 168.22/168.07 [2698]P45(x26983,x26982,x26984)+~E(x26981,x26982)+~P45(x26983,x26981,x26984) % 168.22/168.07 [2699]P45(x26993,x26994,x26992)+~E(x26991,x26992)+~P45(x26993,x26994,x26991) % 168.22/168.07 [2700]~P83(x27001)+P83(x27002)+~E(x27001,x27002) % 168.22/168.07 [2701]~P132(x27011)+P132(x27012)+~E(x27011,x27012) % 168.22/168.07 [2702]~P125(x27021)+P125(x27022)+~E(x27021,x27022) % 168.22/168.07 [2703]~P106(x27031)+P106(x27032)+~E(x27031,x27032) % 168.22/168.07 [2704]P53(x27042,x27043,x27044,x27045)+~E(x27041,x27042)+~P53(x27041,x27043,x27044,x27045) % 168.22/168.07 [2705]P53(x27053,x27052,x27054,x27055)+~E(x27051,x27052)+~P53(x27053,x27051,x27054,x27055) % 168.22/168.07 [2706]P53(x27063,x27064,x27062,x27065)+~E(x27061,x27062)+~P53(x27063,x27064,x27061,x27065) % 168.22/168.07 [2707]P53(x27073,x27074,x27075,x27072)+~E(x27071,x27072)+~P53(x27073,x27074,x27075,x27071) % 168.22/168.07 [2708]~P134(x27081)+P134(x27082)+~E(x27081,x27082) % 168.22/168.07 [2709]P41(x27092,x27093,x27094,x27095,x27096,x27097)+~E(x27091,x27092)+~P41(x27091,x27093,x27094,x27095,x27096,x27097) % 168.22/168.07 [2710]P41(x27103,x27102,x27104,x27105,x27106,x27107)+~E(x27101,x27102)+~P41(x27103,x27101,x27104,x27105,x27106,x27107) % 168.22/168.07 [2711]P41(x27113,x27114,x27112,x27115,x27116,x27117)+~E(x27111,x27112)+~P41(x27113,x27114,x27111,x27115,x27116,x27117) % 168.22/168.07 [2712]P41(x27123,x27124,x27125,x27122,x27126,x27127)+~E(x27121,x27122)+~P41(x27123,x27124,x27125,x27121,x27126,x27127) % 168.22/168.07 [2713]P41(x27133,x27134,x27135,x27136,x27132,x27137)+~E(x27131,x27132)+~P41(x27133,x27134,x27135,x27136,x27131,x27137) % 168.22/168.07 [2714]P41(x27143,x27144,x27145,x27146,x27147,x27142)+~E(x27141,x27142)+~P41(x27143,x27144,x27145,x27146,x27147,x27141) % 168.22/168.07 [2715]~P137(x27151)+P137(x27152)+~E(x27151,x27152) % 168.22/168.07 [2716]~P108(x27161)+P108(x27162)+~E(x27161,x27162) % 168.22/168.07 [2717]P30(x27172,x27173,x27174)+~E(x27171,x27172)+~P30(x27171,x27173,x27174) % 168.22/168.07 [2718]P30(x27183,x27182,x27184)+~E(x27181,x27182)+~P30(x27183,x27181,x27184) % 168.22/168.07 [2719]P30(x27193,x27194,x27192)+~E(x27191,x27192)+~P30(x27193,x27194,x27191) % 168.22/168.07 [2720]~P75(x27201)+P75(x27202)+~E(x27201,x27202) % 168.22/168.07 [2721]P9(x27212,x27213,x27214,x27215)+~E(x27211,x27212)+~P9(x27211,x27213,x27214,x27215) % 168.22/168.07 [2722]P9(x27223,x27222,x27224,x27225)+~E(x27221,x27222)+~P9(x27223,x27221,x27224,x27225) % 168.22/168.07 [2723]P9(x27233,x27234,x27232,x27235)+~E(x27231,x27232)+~P9(x27233,x27234,x27231,x27235) % 168.22/168.07 [2724]P9(x27243,x27244,x27245,x27242)+~E(x27241,x27242)+~P9(x27243,x27244,x27245,x27241) % 168.22/168.07 [2725]~P26(x27251)+P26(x27252)+~E(x27251,x27252) % 168.22/168.07 [2726]P21(x27262,x27263,x27264)+~E(x27261,x27262)+~P21(x27261,x27263,x27264) % 168.22/168.07 [2727]P21(x27273,x27272,x27274)+~E(x27271,x27272)+~P21(x27273,x27271,x27274) % 168.22/168.07 [2728]P21(x27283,x27284,x27282)+~E(x27281,x27282)+~P21(x27283,x27284,x27281) % 168.22/168.07 [2729]~P56(x27291)+P56(x27292)+~E(x27291,x27292) % 168.22/168.07 [2730]~P89(x27301)+P89(x27302)+~E(x27301,x27302) % 168.22/168.07 [2731]P17(x27312,x27313,x27314,x27315,x27316,x27317)+~E(x27311,x27312)+~P17(x27311,x27313,x27314,x27315,x27316,x27317) % 168.22/168.07 [2732]P17(x27323,x27322,x27324,x27325,x27326,x27327)+~E(x27321,x27322)+~P17(x27323,x27321,x27324,x27325,x27326,x27327) % 168.22/168.07 [2733]P17(x27333,x27334,x27332,x27335,x27336,x27337)+~E(x27331,x27332)+~P17(x27333,x27334,x27331,x27335,x27336,x27337) % 168.22/168.07 [2734]P17(x27343,x27344,x27345,x27342,x27346,x27347)+~E(x27341,x27342)+~P17(x27343,x27344,x27345,x27341,x27346,x27347) % 168.22/168.07 [2735]P17(x27353,x27354,x27355,x27356,x27352,x27357)+~E(x27351,x27352)+~P17(x27353,x27354,x27355,x27356,x27351,x27357) % 168.22/168.07 [2736]P17(x27363,x27364,x27365,x27366,x27367,x27362)+~E(x27361,x27362)+~P17(x27363,x27364,x27365,x27366,x27367,x27361) % 168.22/168.07 [2737]~P114(x27371)+P114(x27372)+~E(x27371,x27372) % 168.22/168.07 [2738]~P126(x27381)+P126(x27382)+~E(x27381,x27382) % 168.22/168.07 [2739]P13(x27392,x27393,x27394)+~E(x27391,x27392)+~P13(x27391,x27393,x27394) % 168.22/168.07 [2740]P13(x27403,x27402,x27404)+~E(x27401,x27402)+~P13(x27403,x27401,x27404) % 168.22/168.07 [2741]P13(x27413,x27414,x27412)+~E(x27411,x27412)+~P13(x27413,x27414,x27411) % 168.22/168.07 [2742]~P129(x27421)+P129(x27422)+~E(x27421,x27422) % 168.22/168.07 [2743]P2(x27432,x27433,x27434)+~E(x27431,x27432)+~P2(x27431,x27433,x27434) % 168.22/168.07 [2744]P2(x27443,x27442,x27444)+~E(x27441,x27442)+~P2(x27443,x27441,x27444) % 168.22/168.07 [2745]P2(x27453,x27454,x27452)+~E(x27451,x27452)+~P2(x27453,x27454,x27451) % 168.22/168.07 [2746]~P28(x27461)+P28(x27462)+~E(x27461,x27462) % 168.22/168.07 [2747]P46(x27472,x27473)+~E(x27471,x27472)+~P46(x27471,x27473) % 168.22/168.07 [2748]P46(x27483,x27482)+~E(x27481,x27482)+~P46(x27483,x27481) % 168.22/168.07 [2749]~P116(x27491)+P116(x27492)+~E(x27491,x27492) % 168.22/168.07 [2750]P44(x27502,x27503)+~E(x27501,x27502)+~P44(x27501,x27503) % 168.22/168.07 [2751]P44(x27513,x27512)+~E(x27511,x27512)+~P44(x27513,x27511) % 168.22/168.07 [2752]P42(x27522,x27523)+~E(x27521,x27522)+~P42(x27521,x27523) % 168.22/168.07 [2753]P42(x27533,x27532)+~E(x27531,x27532)+~P42(x27533,x27531) % 168.22/168.07 [2754]~P131(x27541)+P131(x27542)+~E(x27541,x27542) % 168.22/168.07 [2755]P16(x27552,x27553,x27554,x27555,x27556)+~E(x27551,x27552)+~P16(x27551,x27553,x27554,x27555,x27556) % 168.22/168.07 [2756]P16(x27563,x27562,x27564,x27565,x27566)+~E(x27561,x27562)+~P16(x27563,x27561,x27564,x27565,x27566) % 168.22/168.07 [2757]P16(x27573,x27574,x27572,x27575,x27576)+~E(x27571,x27572)+~P16(x27573,x27574,x27571,x27575,x27576) % 168.22/168.07 [2758]P16(x27583,x27584,x27585,x27582,x27586)+~E(x27581,x27582)+~P16(x27583,x27584,x27585,x27581,x27586) % 168.22/168.07 [2759]P16(x27593,x27594,x27595,x27596,x27592)+~E(x27591,x27592)+~P16(x27593,x27594,x27595,x27596,x27591) % 168.22/168.07 [2760]P47(x27602,x27603)+~E(x27601,x27602)+~P47(x27601,x27603) % 168.22/168.07 [2761]P47(x27613,x27612)+~E(x27611,x27612)+~P47(x27613,x27611) % 168.22/168.07 [2762]P48(x27622,x27623,x27624,x27625,x27626,x27627,x27628)+~E(x27621,x27622)+~P48(x27621,x27623,x27624,x27625,x27626,x27627,x27628) % 168.22/168.07 [2763]P48(x27633,x27632,x27634,x27635,x27636,x27637,x27638)+~E(x27631,x27632)+~P48(x27633,x27631,x27634,x27635,x27636,x27637,x27638) % 168.22/168.07 [2764]P48(x27643,x27644,x27642,x27645,x27646,x27647,x27648)+~E(x27641,x27642)+~P48(x27643,x27644,x27641,x27645,x27646,x27647,x27648) % 168.22/168.07 [2765]P48(x27653,x27654,x27655,x27652,x27656,x27657,x27658)+~E(x27651,x27652)+~P48(x27653,x27654,x27655,x27651,x27656,x27657,x27658) % 168.22/168.07 [2766]P48(x27663,x27664,x27665,x27666,x27662,x27667,x27668)+~E(x27661,x27662)+~P48(x27663,x27664,x27665,x27666,x27661,x27667,x27668) % 168.22/168.07 [2767]P48(x27673,x27674,x27675,x27676,x27677,x27672,x27678)+~E(x27671,x27672)+~P48(x27673,x27674,x27675,x27676,x27677,x27671,x27678) % 168.22/168.07 [2768]P48(x27683,x27684,x27685,x27686,x27687,x27688,x27682)+~E(x27681,x27682)+~P48(x27683,x27684,x27685,x27686,x27687,x27688,x27681) % 168.22/168.07 [2769]~P117(x27691)+P117(x27692)+~E(x27691,x27692) % 168.22/168.07 [2770]~P72(x27701)+P72(x27702)+~E(x27701,x27702) % 168.22/168.07 [2771]~P107(x27711)+P107(x27712)+~E(x27711,x27712) % 168.22/168.07 [2772]~P95(x27721)+P95(x27722)+~E(x27721,x27722) % 168.22/168.07 [2773]P15(x27732,x27733,x27734,x27735)+~E(x27731,x27732)+~P15(x27731,x27733,x27734,x27735) % 168.22/168.07 [2774]P15(x27743,x27742,x27744,x27745)+~E(x27741,x27742)+~P15(x27743,x27741,x27744,x27745) % 168.22/168.07 [2775]P15(x27753,x27754,x27752,x27755)+~E(x27751,x27752)+~P15(x27753,x27754,x27751,x27755) % 168.22/168.07 [2776]P15(x27763,x27764,x27765,x27762)+~E(x27761,x27762)+~P15(x27763,x27764,x27765,x27761) % 168.22/168.07 [2777]P8(x27772,x27773,x27774)+~E(x27771,x27772)+~P8(x27771,x27773,x27774) % 168.22/168.07 [2778]P8(x27783,x27782,x27784)+~E(x27781,x27782)+~P8(x27783,x27781,x27784) % 168.22/168.07 [2779]P8(x27793,x27794,x27792)+~E(x27791,x27792)+~P8(x27793,x27794,x27791) % 168.22/168.07 [2780]~P122(x27801)+P122(x27802)+~E(x27801,x27802) % 168.22/168.07 [2781]P40(x27812,x27813,x27814,x27815)+~E(x27811,x27812)+~P40(x27811,x27813,x27814,x27815) % 168.22/168.07 [2782]P40(x27823,x27822,x27824,x27825)+~E(x27821,x27822)+~P40(x27823,x27821,x27824,x27825) % 168.22/168.07 [2783]P40(x27833,x27834,x27832,x27835)+~E(x27831,x27832)+~P40(x27833,x27834,x27831,x27835) % 168.22/168.07 [2784]P40(x27843,x27844,x27845,x27842)+~E(x27841,x27842)+~P40(x27843,x27844,x27845,x27841) % 168.22/168.07 [2785]~P43(x27851)+P43(x27852)+~E(x27851,x27852) % 168.22/168.07 % 168.22/168.07 %------------------------------------------- % 168.30/168.12 cnf(10081,plain, % 168.30/168.12 (E(f37(x100811,x100812,x100813,x100814,x100815,x100816,x100817,x100818,x100819,a23),x100812)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10084,plain, % 168.30/168.12 (E(f37(x100841,x100842,x100843,x100844,x100845,x100846,x100847,x100848,x100849,a23),x100842)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10087,plain, % 168.30/168.12 (~E(f317(a124,x100871),x100871)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10090,plain, % 168.30/168.12 (~E(f317(a124,x100901),x100901)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10093,plain, % 168.30/168.12 (E(f37(x100931,x100932,x100933,x100934,x100935,x100936,x100937,x100938,x100939,a23),x100932)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10100,plain, % 168.30/168.12 (~E(f317(a124,x101001),x101001)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10111,plain, % 168.30/168.12 (~E(f317(a124,x101111),x101111)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10116,plain, % 168.30/168.12 (~P22(f317(f72(x101161,x101162,f188(f858(x101161,a842))),x101163))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(10119,plain, % 168.30/168.12 (~P22(f317(f72(x101191,x101192,f188(f858(x101191,a842))),x101193))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(10122,plain, % 168.30/168.12 (~E(f317(a124,x101221),x101221)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10125,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x101251),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(10128,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x101281),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(10145,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x101451)),x101451))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(10148,plain, % 168.30/168.12 (~E(f317(f317(f145(x101481),x101482),x101483),x101483)), % 168.30/168.12 inference(rename_variables,[],[4421])). % 168.30/168.12 cnf(10151,plain, % 168.30/168.12 (E(f317(f115(a1),x101511),f317(f114(a1),x101511))), % 168.30/168.12 inference(rename_variables,[],[3052])). % 168.30/168.12 cnf(10154,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x101541),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(10157,plain, % 168.30/168.12 (E(f37(x101571,x101572,x101573,x101574,x101575,x101576,x101577,x101578,x101579,a23),x101572)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10160,plain, % 168.30/168.12 (E(f37(x101601,x101602,x101603,x101604,x101605,x101606,x101607,x101608,x101609,a23),x101602)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10167,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x101671),x101672)),x101672))), % 168.30/168.12 inference(rename_variables,[],[4500])). % 168.30/168.12 cnf(10170,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x101701),x101702)),x101702))), % 168.30/168.12 inference(rename_variables,[],[4500])). % 168.30/168.12 cnf(10191,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x101911),x101911))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(10194,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f55(a849,x101941,x101942)),x101941))), % 168.30/168.12 inference(rename_variables,[],[3648])). % 168.30/168.12 cnf(10213,plain, % 168.30/168.12 (E(f317(f54(a849),f317(f231(a849),x102131)),x102131)), % 168.30/168.12 inference(rename_variables,[],[3086])). % 168.30/168.12 cnf(10221,plain, % 168.30/168.12 (~E(f317(a124,x102211),x102211)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10224,plain, % 168.30/168.12 (~E(f317(a124,x102241),x102241)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10227,plain, % 168.30/168.12 (~E(f317(a124,x102271),x102271)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10232,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x102321),f317(a124,x102321)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(10243,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x102431),x102431))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(10250,plain, % 168.30/168.12 (E(f37(x102501,x102502,x102503,x102504,x102505,x102506,x102507,x102508,x102509,a23),x102502)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10253,plain, % 168.30/168.12 (E(f37(x102531,x102532,x102533,x102534,x102535,x102536,x102537,x102538,x102539,a23),x102532)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10276,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x102761),x102761))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(10283,plain, % 168.30/168.12 (~E(f317(f317(f317(f81(x102831,f853(x102832)),x102833),x102834),f317(f217(x102832),x102835)),f317(f16(f853(x102832),x102831),f191(x102832)))), % 168.30/168.12 inference(rename_variables,[],[4496])). % 168.30/168.12 cnf(10308,plain, % 168.30/168.12 (~E(f317(f317(f145(x103081),x103082),x103083),x103083)), % 168.30/168.12 inference(rename_variables,[],[4421])). % 168.30/168.12 cnf(10311,plain, % 168.30/168.12 (~E(f317(a29,x103111),f36(x103112,x103113))), % 168.30/168.12 inference(rename_variables,[],[4405])). % 168.30/168.12 cnf(10324,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x103241),x103241))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(10327,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x103271),x103271))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(10330,plain, % 168.30/168.12 (~E(f317(a124,x103301),x103301)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10337,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x103371),x103371))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(10348,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x103481),f317(a124,x103481)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(10355,plain, % 168.30/168.12 (E(f317(f317(f127(x103551),f125(x103551)),x103552),x103552)), % 168.30/168.12 inference(rename_variables,[],[3139])). % 168.30/168.12 cnf(10373,plain, % 168.30/168.12 (~P22(f317(f72(x103731,x103732,f188(f858(x103731,a842))),x103733))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(10402,plain, % 168.30/168.12 (~E(f317(a29,x104021),f36(x104022,x104023))), % 168.30/168.12 inference(rename_variables,[],[4405])). % 168.30/168.12 cnf(10408,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),f2(a849)),f317(a116,f87(a1))))), % 168.30/168.12 inference(scs_inference,[],[4358,10081,10084,10093,10157,10160,10250,4386,10087,10090,10100,10111,10122,10221,10224,10227,4405,10311,2787,3021,3090,3052,3029,3119,3139,10355,4496,4421,10148,3086,3978,4505,3103,3558,3258,10232,10348,3171,4476,10125,10128,10154,4492,3630,3782,3215,3216,3189,4473,4415,3899,3186,10243,3187,3188,4472,10191,10276,3285,3710,3648,10194,4485,10145,4023,4483,4464,3164,3168,4466,4465,4499,10116,10119,4502,3669,4500,10167,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800])). % 168.30/168.12 cnf(10411,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x104111),x104111))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(10416,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x104161),x104161))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(10419,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x104191),f317(a124,x104191)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(10422,plain, % 168.30/168.12 (~P22(f317(f72(x104221,x104222,f188(f858(x104221,a842))),x104223))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(10427,plain, % 168.30/168.12 (~P22(f317(f72(x104271,x104272,f188(f858(x104271,a842))),x104273))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(10440,plain, % 168.30/168.12 (~E(f317(a124,x104401),x104401)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10458,plain, % 168.30/168.12 (P22(f317(f317(f226(a111),f317(a3,x104581)),f317(a3,f317(a124,x104581))))), % 168.30/168.12 inference(scs_inference,[],[4358,10081,10084,10093,10157,10160,10250,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,4405,10311,2787,3021,3090,3052,3029,3119,3139,10355,4496,4421,10148,3086,3978,4505,3103,3558,3258,10232,10348,10419,3643,3171,4476,10125,10128,10154,4492,3630,3782,3215,3216,3189,4473,4415,3899,3186,10243,10337,3187,3188,4472,10191,10276,10327,3285,3710,3648,10194,4485,10145,4023,4483,4464,3164,3168,4466,4465,4499,10116,10119,10373,10422,4502,3669,4500,10167,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995])). % 168.30/168.12 cnf(10463,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x104631),f317(a124,x104631)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(10466,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x104661),f317(a124,x104661)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(10469,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x104691),f317(f317(f90(a849),x104691),x104691)))), % 168.30/168.12 inference(rename_variables,[],[3466])). % 168.30/168.12 cnf(10471,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x104711),f317(f317(f90(a849),f317(a124,x104711)),f317(a124,x104711))))), % 168.30/168.12 inference(scs_inference,[],[4358,10081,10084,10093,10157,10160,10250,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,4405,10311,2787,3021,3090,3052,3029,3119,3139,10355,4496,4421,10148,3086,3978,4505,3103,3558,3258,10232,10348,10419,10463,3643,3171,4476,10125,10128,10154,4492,3630,3782,3215,3216,3189,4473,4415,3899,3186,10243,10337,3187,3188,4472,10191,10276,10327,3285,3710,3648,10194,4485,10145,4023,4483,4464,3164,3168,4466,4465,4499,10116,10119,10373,10422,3466,10469,4502,3669,4500,10167,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016])). % 168.30/168.12 cnf(10472,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x104721),f317(f317(f90(a849),x104721),x104721)))), % 168.30/168.12 inference(rename_variables,[],[3466])). % 168.30/168.12 cnf(10475,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x104751),f317(a124,f317(f317(f89(a849),x104752),x104751))))), % 168.30/168.12 inference(rename_variables,[],[3641])). % 168.30/168.12 cnf(10480,plain, % 168.30/168.12 (P22(f317(f317(f319(x104801),x104802),f233(f858(x104801,a842))))), % 168.30/168.12 inference(rename_variables,[],[3349])). % 168.30/168.12 cnf(10495,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x104951)),x104951))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(10498,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x104981)),x104981))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(10501,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x105011),x105012)),x105012))), % 168.30/168.12 inference(rename_variables,[],[4500])). % 168.30/168.12 cnf(10504,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x105041),x105042)),x105042))), % 168.30/168.12 inference(rename_variables,[],[4500])). % 168.30/168.12 cnf(10507,plain, % 168.30/168.12 (P22(f317(f233(f858(x105071,a842)),x105072))), % 168.30/168.12 inference(rename_variables,[],[3252])). % 168.30/168.12 cnf(10510,plain, % 168.30/168.12 (E(f317(f54(a849),f317(f231(a849),x105101)),x105101)), % 168.30/168.12 inference(rename_variables,[],[3086])). % 168.30/168.12 cnf(10513,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x105131),f317(a124,x105131)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(10520,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x105201),x105201))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(10525,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x105251),x105251))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(10534,plain, % 168.30/168.12 (E(f37(x105341,x105342,x105343,x105344,x105345,x105346,x105347,x105348,x105349,a23),x105342)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10537,plain, % 168.30/168.12 (P22(f317(f233(f858(x105371,a842)),x105372))), % 168.30/168.12 inference(rename_variables,[],[3252])). % 168.30/168.12 cnf(10540,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x105401),f317(f317(f90(a849),x105401),x105401)))), % 168.30/168.12 inference(rename_variables,[],[3466])). % 168.30/168.12 cnf(10544,plain, % 168.30/168.12 (E(f317(f163(x105441),f37(x105442,f317(f317(f127(x105441),f317(f163(x105441),x105443)),f317(f317(f145(x105441),x105444),f125(x105441))),x105445,x105446,x105447,x105448,x105449,x1054410,x1054411,a23)),f317(f317(f145(x105441),x105444),x105443))), % 168.30/168.12 inference(scs_inference,[],[4358,10081,10084,10093,10157,10160,10250,10253,10534,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,4405,10311,2787,3021,3090,3052,3029,3119,3139,10355,4496,4421,10148,3086,10213,3978,4505,3103,3558,3500,3258,10232,10348,10419,10463,10466,3643,3171,4476,10125,10128,10154,4492,3630,3404,3782,3215,3216,3189,4473,4415,3899,3186,10243,10337,10416,3187,3188,10324,4472,10191,10276,10327,3349,3252,10507,3285,3710,3648,10194,4485,10145,10495,4023,4483,4464,3164,3168,4466,4465,4499,10116,10119,10373,10422,4504,3466,10469,10472,4502,3669,4500,10167,10170,10501,3641,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261])). % 168.30/168.12 cnf(10545,plain, % 168.30/168.12 (E(f37(x105451,x105452,x105453,x105454,x105455,x105456,x105457,x105458,x105459,a23),x105452)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10549,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,f317(a124,f317(f317(f89(a849),x105491),x105492)))),f317(a124,x105492)))), % 168.30/168.12 inference(scs_inference,[],[4358,10081,10084,10093,10157,10160,10250,10253,10534,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,4405,10311,2787,3021,3090,3052,3029,3119,3139,10355,4496,4421,10148,3086,10213,3978,4505,3103,3558,3500,3258,10232,10348,10419,10463,10466,10513,3643,3171,4476,10125,10128,10154,4492,3630,3404,3782,3215,3216,3189,4473,4415,3899,3186,10243,10337,10416,3187,3188,10324,4472,10191,10276,10327,3349,3252,10507,3285,3710,3648,10194,4485,10145,10495,4023,4483,4464,3164,3168,4466,4465,4499,10116,10119,10373,10422,4504,3466,10469,10472,4502,3669,4500,10167,10170,10501,3641,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264])). % 168.30/168.12 cnf(10582,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x105821),x105821))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(10595,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x105951),f317(a124,x105951)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(10598,plain, % 168.30/168.12 (~P22(f317(f317(f188(f858(x105981,f858(x105982,a842))),x105983),x105984))), % 168.30/168.12 inference(rename_variables,[],[4503])). % 168.30/168.12 cnf(10601,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x106011),x106011))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(10606,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x106061),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(10619,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x106191),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(10622,plain, % 168.30/168.12 (~P22(f317(f317(f226(f858(x106221,a842)),x106222),f188(f858(x106221,a842))))), % 168.30/168.12 inference(rename_variables,[],[4497])). % 168.30/168.12 cnf(10625,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x106251),x106251))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(10628,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x106281),x106281))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(10643,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x106431),x106431))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(10652,plain, % 168.30/168.12 (~P22(f317(f317(f319(x106521),x106522),f188(f858(x106521,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10661,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x106611),x106611))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(10664,plain, % 168.30/168.12 (~P22(f317(f317(f319(x106641),x106642),f188(f858(x106641,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10667,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x106671,a842)),f317(f287(x106672,x106671,x106673),f317(f289(x106672,x106671,x106673),x106674))),x106674))), % 168.30/168.12 inference(rename_variables,[],[4087])). % 168.30/168.12 cnf(10674,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x106741,a842)),f317(f166(x106741),f317(f130(x106741,x106742),x106743))),f317(f166(x106741),x106743)))), % 168.30/168.12 inference(rename_variables,[],[3842])). % 168.30/168.12 cnf(10677,plain, % 168.30/168.12 (E(f317(f287(x106771,x106771,f5(x106771)),x106772),x106772)), % 168.30/168.12 inference(rename_variables,[],[3248])). % 168.30/168.12 cnf(10682,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f2(a849)),x106821))), % 168.30/168.12 inference(rename_variables,[],[3208])). % 168.30/168.12 cnf(10685,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x106851),x106851))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(10688,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x106881),x106881))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(10691,plain, % 168.30/168.12 (~P22(f317(f317(f188(f858(x106911,f858(x106912,a842))),x106913),x106914))), % 168.30/168.12 inference(rename_variables,[],[4503])). % 168.30/168.12 cnf(10698,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x106981),x106981))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(10709,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x107091),f317(f317(f90(a849),x107091),x107091)))), % 168.30/168.12 inference(rename_variables,[],[3466])). % 168.30/168.12 cnf(10715,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x107151),f317(a124,f317(f317(f89(a849),x107152),x107151))))), % 168.30/168.12 inference(rename_variables,[],[3641])). % 168.30/168.12 cnf(10722,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x107221),x107221))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(10725,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x107251),x107251))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(10728,plain, % 168.30/168.12 (~E(f317(a124,x107281),x107281)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10733,plain, % 168.30/168.12 (P22(f317(f317(f319(x107331),x107332),f233(f858(x107331,a842))))), % 168.30/168.12 inference(rename_variables,[],[3349])). % 168.30/168.12 cnf(10738,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x107381),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(10753,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f2(a849)),x107531))), % 168.30/168.12 inference(rename_variables,[],[3208])). % 168.30/168.12 cnf(10760,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x107601),x107601))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(10769,plain, % 168.30/168.12 (~P22(f317(f317(f319(x107691),x107692),f188(f858(x107691,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10776,plain, % 168.30/168.12 (P22(f317(f317(f319(f850(x107761)),x107762),f155(x107761,f233(f858(x107761,a842)))))), % 168.30/168.12 inference(scs_inference,[],[4358,10081,10084,10093,10157,10160,10250,10253,10534,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,4405,10311,2787,3021,3090,3052,3029,3248,3119,3139,10355,4496,4421,10148,3086,10213,3978,3832,4505,3103,3396,3558,3500,3704,3258,10232,10348,10419,10463,10466,10513,10595,3643,3171,4476,10125,10128,10154,10606,10619,4492,3630,3404,3782,3215,3216,3189,4473,4415,3941,3842,10674,3559,3899,4497,3186,10243,10337,10416,3187,10582,10625,10628,10661,10685,10722,3188,10324,10525,10601,4472,10191,10276,10327,10411,10643,10688,3349,10480,10733,4488,10652,10664,3252,10507,3285,3710,3648,10194,4485,10145,10495,10498,3208,10682,4023,4483,3718,4464,4467,3164,3168,4466,4465,4499,10116,10119,10373,10422,4504,3466,10469,10472,10540,10709,4502,4503,10598,4087,3669,4500,10167,10170,10501,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666])). % 168.30/168.12 cnf(10777,plain, % 168.30/168.12 (P22(f317(f317(f319(x107771),x107772),f233(f858(x107771,a842))))), % 168.30/168.12 inference(rename_variables,[],[3349])). % 168.30/168.12 cnf(10780,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x107801),f850(x107801))),f317(f317(f237(f850(x107801),f850(x107801)),x107802),f125(x107801))),f139(x107801,x107803)))), % 168.30/168.12 inference(rename_variables,[],[4505])). % 168.30/168.12 cnf(10786,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(x107861,x107861)),x107862),f235(x107861,f188(f858(x107861,a842)))))), % 168.30/168.12 inference(scs_inference,[],[4358,10081,10084,10093,10157,10160,10250,10253,10534,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,4405,10311,2787,3021,3090,3052,3029,3248,3119,3139,10355,4496,4421,10148,3086,10213,3978,3832,4505,3103,3396,3558,3500,3704,3258,10232,10348,10419,10463,10466,10513,10595,3643,3171,4476,10125,10128,10154,10606,10619,4492,3630,3404,3782,3215,3216,3189,4473,4415,3941,3842,10674,3559,3899,4497,3186,10243,10337,10416,3187,10582,10625,10628,10661,10685,10722,3188,10324,10525,10601,4472,10191,10276,10327,10411,10643,10688,3349,10480,10733,4488,10652,10664,10769,3252,10507,3285,3710,3648,10194,4485,10145,10495,10498,3208,10682,4023,4483,3718,4464,4467,3164,3168,4466,4465,4499,10116,10119,10373,10422,4504,3466,10469,10472,10540,10709,4502,4503,10598,4087,3669,4500,10167,10170,10501,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795])). % 168.30/168.12 cnf(10787,plain, % 168.30/168.12 (~P22(f317(f317(f319(x107871),x107872),f188(f858(x107871,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10790,plain, % 168.30/168.12 (~P22(f317(f317(f319(x107901),x107902),f188(f858(x107901,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10793,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x107931,a842)),x107932),f317(f317(f286(x107931),x107933),x107932)))), % 168.30/168.12 inference(rename_variables,[],[3637])). % 168.30/168.12 cnf(10796,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x107961),x107961))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(10799,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x107991,a842)),x107992),f317(f317(f286(x107991),x107993),x107992)))), % 168.30/168.12 inference(rename_variables,[],[3637])). % 168.30/168.12 cnf(10802,plain, % 168.30/168.12 (E(f37(x108021,x108022,x108023,x108024,x108025,x108026,x108027,x108028,x108029,a23),x108022)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10805,plain, % 168.30/168.12 (E(f37(x108051,x108052,x108053,x108054,x108055,x108056,x108057,x108058,x108059,a23),x108052)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(10816,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x108161,a842)),x108162),f317(f317(f286(x108161),x108163),x108162)))), % 168.30/168.12 inference(rename_variables,[],[3637])). % 168.30/168.12 cnf(10819,plain, % 168.30/168.12 (P32(x108191,x108192,x108193,f178(x108191,x108192,x108194,x108193))), % 168.30/168.12 inference(rename_variables,[],[3758])). % 168.30/168.12 cnf(10827,plain, % 168.30/168.12 (~P22(f317(f72(x108271,x108272,f188(f858(x108271,a842))),x108273))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(10842,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x108421),f317(a124,x108421)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(10852,plain, % 168.30/168.12 (~E(f317(f297(x108521,x108522),x108523),f317(f288(x108522,x108521),x108524))), % 168.30/168.12 inference(rename_variables,[],[4461])). % 168.30/168.12 cnf(10855,plain, % 168.30/168.12 (~P22(f317(f317(f319(x108551),x108552),f188(f858(x108551,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10858,plain, % 168.30/168.12 (P22(f317(f317(f319(f857(x108581,x108581)),f317(f317(f237(x108581,x108581),x108582),x108582)),f284(x108581,x108583)))), % 168.30/168.12 inference(rename_variables,[],[3832])). % 168.30/168.12 cnf(10861,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x108611,a842)),x108612),f233(f858(x108611,a842))))), % 168.30/168.12 inference(rename_variables,[],[3575])). % 168.30/168.12 cnf(10864,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x108641,a842)),f317(f166(x108641),f164(x108641,x108642,x108643))),f317(f166(x108641),x108643)))), % 168.30/168.12 inference(rename_variables,[],[3893])). % 168.30/168.12 cnf(10884,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x108841,a842)),f188(f858(x108841,a842))),x108842))), % 168.30/168.12 inference(rename_variables,[],[3639])). % 168.30/168.12 cnf(10898,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x108981),f850(x108981))),f317(f317(f237(f850(x108981),f850(x108981)),x108982),f125(x108981))),f141(x108981,x108983)))), % 168.30/168.12 inference(rename_variables,[],[4506])). % 168.30/168.12 cnf(10909,plain, % 168.30/168.12 (~E(f317(a124,x109091),x109091)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10912,plain, % 168.30/168.12 (~E(f317(a124,x109121),x109121)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(10914,plain, % 168.30/168.12 (P22(f317(f317(f319(f857(f850(x109141),f850(x109141))),f317(f317(f237(f850(x109141),f850(x109141)),f125(x109141)),f125(x109141))),f317(f317(f265(f850(x109141),f850(x109141),f850(x109141)),f152(x109141,x109142)),f284(f850(x109141),f152(x109141,x109142)))))), % 168.30/168.12 inference(scs_inference,[],[3758,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,4405,10311,2787,3924,3651,3021,4461,3090,3052,10151,3029,3248,3119,3139,10355,4496,3830,4421,10148,3086,10213,3978,3832,10858,4505,10780,4506,3103,3396,3558,3500,3704,3258,10232,10348,10419,10463,10466,10513,10595,3643,3171,4476,10125,10128,10154,10606,10619,10738,4492,3630,3404,3782,3215,3216,3189,4473,4415,3941,3842,10674,3893,3559,3899,3575,4497,3186,10243,10337,10416,3187,10582,10625,10628,10661,10685,10722,10760,3188,10324,10525,10601,4472,10191,10276,10327,10411,10643,10688,3349,10480,10733,10777,4488,10652,10664,10769,10787,10790,3252,10507,3285,3710,3648,10194,4485,10145,10495,10498,3208,10682,4023,4483,3718,4464,4467,3164,3168,4466,4465,4499,10116,10119,10373,10422,10427,4504,3799,3637,10793,10799,3639,3466,10469,10472,10540,10709,4502,4503,10598,4087,3669,4500,10167,10170,10501,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500])). % 168.30/168.12 cnf(10924,plain, % 168.30/168.12 (P19(x109241,x109241,f5(x109241),x109242)), % 168.30/168.12 inference(rename_variables,[],[3434])). % 168.30/168.12 cnf(10929,plain, % 168.30/168.12 (~E(f317(f287(x109291,f858(x109291,a842),x109292),x109293),f317(f285(x109291),x109293))), % 168.30/168.12 inference(rename_variables,[],[4486])). % 168.30/168.12 cnf(10934,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x109341,a842)),x109342),f233(f858(x109341,a842))))), % 168.30/168.12 inference(rename_variables,[],[3575])). % 168.30/168.12 cnf(10948,plain, % 168.30/168.12 (~P22(f317(f317(f319(x109481),x109482),f188(f858(x109481,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10951,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x109511)),x109511))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(10956,plain, % 168.30/168.12 (~P22(f317(f317(f319(x109561),x109562),f188(f858(x109561,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10969,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x109691)),x109691))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(10972,plain, % 168.30/168.12 (~P22(f317(f317(f319(x109721),x109722),f188(f858(x109721,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(10982,plain, % 168.30/168.12 (E(f317(x109821,f779(f317(x109821,x109822),f317(f217(x109823),x109822),x109821,x109824,x109823)),f317(x109821,x109822))), % 168.30/168.12 inference(scs_inference,[],[3434,3758,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,4405,10311,10402,2787,3924,3651,3021,4461,3090,3052,10151,3029,3248,3119,3139,10355,3297,4496,3830,4421,10148,4486,3298,3086,10213,3978,3832,10858,4505,10780,4506,3103,3396,3558,3500,3704,3258,10232,10348,10419,10463,10466,10513,10595,10842,3643,3171,4476,10125,10128,10154,10606,10619,10738,4492,3630,3404,3782,3215,3216,3189,4473,4415,3941,3842,10674,3893,3559,3899,3575,10861,4497,3186,10243,10337,10416,3187,10582,10625,10628,10661,10685,10722,10760,3188,10324,10525,10601,4472,10191,10276,10327,10411,10643,10688,3349,10480,10733,10777,4488,10652,10664,10769,10787,10790,10855,10948,10956,3252,10507,3285,3710,3648,10194,4485,10145,10495,10498,10951,3208,10682,4023,4483,3718,4464,4467,3164,3168,4466,4465,4499,10116,10119,10373,10422,10427,4504,3799,3637,10793,10799,3639,3466,10469,10472,10540,10709,4502,4503,10598,4087,3669,4500,10167,10170,10501,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782])). % 168.30/168.12 cnf(10991,plain, % 168.30/168.12 (P22(f317(f317(f319(f857(x109911,x109911)),f317(f317(f237(x109911,x109911),x109912),x109912)),f284(x109911,x109913)))), % 168.30/168.12 inference(rename_variables,[],[3832])). % 168.30/168.12 cnf(10996,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x109961),f850(x109961))),f317(f317(f237(f850(x109961),f850(x109961)),x109962),f125(x109961))),f139(x109961,x109963)))), % 168.30/168.12 inference(rename_variables,[],[4505])). % 168.30/168.12 cnf(10999,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x109991),f850(x109991))),f317(f317(f237(f850(x109991),f850(x109991)),x109992),f125(x109991))),f141(x109991,x109993)))), % 168.30/168.12 inference(rename_variables,[],[4506])). % 168.30/168.12 cnf(11002,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x110021),f850(x110021))),f317(f317(f237(f850(x110021),f850(x110021)),x110022),f125(x110021))),f151(x110021,x110023)))), % 168.30/168.12 inference(rename_variables,[],[4507])). % 168.30/168.12 cnf(11007,plain, % 168.30/168.12 (~P22(f317(f317(f226(f858(x110071,a842)),x110072),f188(f858(x110071,a842))))), % 168.30/168.12 inference(rename_variables,[],[4497])). % 168.30/168.12 cnf(11010,plain, % 168.30/168.12 (~P22(f317(f317(f319(x110101),x110102),f188(f858(x110101,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11015,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x110151,a842)),x110152),f233(f858(x110151,a842))))), % 168.30/168.12 inference(rename_variables,[],[3575])). % 168.30/168.12 cnf(11018,plain, % 168.30/168.12 (~P22(f317(f317(f188(f858(x110181,f858(x110182,a842))),x110183),x110184))), % 168.30/168.12 inference(rename_variables,[],[4503])). % 168.30/168.12 cnf(11027,plain, % 168.30/168.12 (~P22(f317(f317(f319(x110271),x110272),f188(f858(x110271,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11030,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(x110301,x110301)),f317(f317(f237(x110301,x110301),x110302),x110303)),f147(x110301,f125(f858(x110301,a849)))))), % 168.30/168.12 inference(rename_variables,[],[4504])). % 168.30/168.12 cnf(11033,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x110331,a842)),x110332),x110332))), % 168.30/168.12 inference(rename_variables,[],[3494])). % 168.30/168.12 cnf(11036,plain, % 168.30/168.12 (E(f303(x110361,x110362,x110363,f317(f317(f8(f856(x110361,x110363),x110362,x110361),x110364),f288(x110361,x110363)),f317(f317(f8(f856(x110361,x110363),x110362,x110363),x110364),f297(x110363,x110361))),x110364)), % 168.30/168.12 inference(rename_variables,[],[4068])). % 168.30/168.12 cnf(11042,plain, % 168.30/168.12 (~P22(f317(f317(f319(x110421),x110422),f188(f858(x110421,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11045,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x110451,a842)),f188(f858(x110451,a842))),x110452))), % 168.30/168.12 inference(rename_variables,[],[3639])). % 168.30/168.12 cnf(11048,plain, % 168.30/168.12 (P22(f317(f317(f319(f857(x110481,x110481)),f317(f317(f237(x110481,x110481),x110482),x110482)),f284(x110481,x110483)))), % 168.30/168.12 inference(rename_variables,[],[3832])). % 168.30/168.12 cnf(11054,plain, % 168.30/168.12 (P35(x110541,x110542,x110543,f317(f317(f148(x110544,x110541),x110545),f37(x110546,f125(x110544),x110547,x110548,x110549,x1105410,x1105411,x1105412,x1105413,a23)),f125(x110542))), % 168.30/168.12 inference(scs_inference,[],[3434,3758,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,4405,10311,10402,2787,3924,3651,3021,4461,3090,3052,10151,3029,4068,11036,3248,3119,3139,10355,3297,4496,3830,4421,10148,4486,3298,3086,10213,3978,3832,10858,10991,4505,10780,10996,4506,10898,4507,3103,3396,3558,3500,3704,3258,10232,10348,10419,10463,10466,10513,10595,10842,3643,3171,4476,10125,10128,10154,10606,10619,10738,4492,3630,3404,3782,3215,3216,3189,4473,4415,3941,3842,10674,3893,3559,3899,3575,10861,10934,4497,10622,3186,10243,10337,10416,3187,10582,10625,10628,10661,10685,10722,10760,3188,10324,10525,10601,4472,10191,10276,10327,10411,10643,10688,3349,10480,10733,10777,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,3252,10507,3285,3710,3648,10194,4485,10145,10495,10498,10951,3208,10682,4023,4483,3718,4464,4467,3164,3168,4466,4465,4499,10116,10119,10373,10422,10427,4504,3799,3637,10793,10799,3494,3639,10884,3466,10469,10472,10540,10709,4502,4503,10598,10691,4087,3669,4500,10167,10170,10501,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180])). % 168.30/168.12 cnf(11059,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x110591),f850(x110591))),f317(f317(f237(f850(x110591),f850(x110591)),x110592),f125(x110591))),f151(x110591,x110593)))), % 168.30/168.12 inference(rename_variables,[],[4507])). % 168.30/168.12 cnf(11062,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x110621),f850(x110621))),f317(f317(f237(f850(x110621),f850(x110621)),f125(x110621)),x110622)),f139(x110621,x110623)))), % 168.30/168.12 inference(rename_variables,[],[4508])). % 168.30/168.12 cnf(11070,plain, % 168.30/168.12 (P22(f317(f317(f319(x110701),x110702),f233(f858(x110701,a842))))), % 168.30/168.12 inference(rename_variables,[],[3349])). % 168.30/168.12 cnf(11075,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x110751,a842)),f188(f858(x110751,a842))),x110752))), % 168.30/168.12 inference(rename_variables,[],[3639])). % 168.30/168.12 cnf(11078,plain, % 168.30/168.12 (~P22(f317(f317(f319(x110781),x110782),f188(f858(x110781,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11081,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x110811,a842)),x110812),f233(f858(x110811,a842))))), % 168.30/168.12 inference(rename_variables,[],[3575])). % 168.30/168.12 cnf(11086,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x110861,a842)),f188(f858(x110861,a842))),x110862))), % 168.30/168.12 inference(rename_variables,[],[3639])). % 168.30/168.12 cnf(11099,plain, % 168.30/168.12 (P22(f317(f233(f858(x110991,a842)),x110992))), % 168.30/168.12 inference(rename_variables,[],[3252])). % 168.30/168.12 cnf(11107,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x111071),f850(x111071))),f317(f317(f237(f850(x111071),f850(x111071)),x111072),f125(x111071))),f139(x111071,x111073)))), % 168.30/168.12 inference(rename_variables,[],[4505])). % 168.30/168.12 cnf(11110,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x111101),f850(x111101))),f317(f317(f237(f850(x111101),f850(x111101)),x111102),f125(x111101))),f141(x111101,x111103)))), % 168.30/168.12 inference(rename_variables,[],[4506])). % 168.30/168.12 cnf(11113,plain, % 168.30/168.12 (~E(f317(a124,x111131),x111131)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11116,plain, % 168.30/168.12 (~P22(f317(f317(f319(x111161),x111162),f188(f858(x111161,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11121,plain, % 168.30/168.12 (P22(f317(f317(f319(f857(f850(x111211),f850(x111211))),f317(f317(f237(f850(x111211),f850(x111211)),x111212),x111212)),f152(x111211,f284(x111211,x111213))))), % 168.30/168.12 inference(rename_variables,[],[3972])). % 168.30/168.12 cnf(11126,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x111261),f850(x111261))),f317(f317(f237(f850(x111261),f850(x111261)),x111262),f125(x111261))),f139(x111261,x111263)))), % 168.30/168.12 inference(rename_variables,[],[4505])). % 168.30/168.12 cnf(11136,plain, % 168.30/168.12 (~P22(f317(f317(f319(x111361),x111362),f188(f858(x111361,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11139,plain, % 168.30/168.12 (~P22(f317(f317(f319(x111391),x111392),f188(f858(x111391,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11142,plain, % 168.30/168.12 (P22(f317(f317(f319(x111421),x111422),f233(f858(x111421,a842))))), % 168.30/168.12 inference(rename_variables,[],[3349])). % 168.30/168.12 cnf(11147,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(x111471,x111471)),f317(f317(f237(x111471,x111471),x111472),x111473)),f147(x111471,f125(f858(x111471,a849)))))), % 168.30/168.12 inference(rename_variables,[],[4504])). % 168.30/168.12 cnf(11150,plain, % 168.30/168.12 (~E(f317(f297(x111501,x111502),x111503),f317(f288(x111502,x111501),x111504))), % 168.30/168.12 inference(rename_variables,[],[4461])). % 168.30/168.12 cnf(11153,plain, % 168.30/168.12 (~E(f317(f297(x111531,x111532),x111533),f317(f288(x111532,x111531),x111534))), % 168.30/168.12 inference(rename_variables,[],[4461])). % 168.30/168.12 cnf(11156,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x111561),f850(x111561))),f317(f317(f237(f850(x111561),f850(x111561)),x111562),f125(x111561))),f139(x111561,x111563)))), % 168.30/168.12 inference(rename_variables,[],[4505])). % 168.30/168.12 cnf(11162,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x111621),f850(x111621))),f317(f317(f237(f850(x111621),f850(x111621)),x111622),f125(x111621))),f139(x111621,x111623)))), % 168.30/168.12 inference(rename_variables,[],[4505])). % 168.30/168.12 cnf(11165,plain, % 168.30/168.12 (~P22(f317(f317(f319(x111651),x111652),f188(f858(x111651,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11168,plain, % 168.30/168.12 (~P22(f317(f317(f188(f858(x111681,f858(x111682,a842))),x111683),x111684))), % 168.30/168.12 inference(rename_variables,[],[4503])). % 168.30/168.12 cnf(11171,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x111711),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(11178,plain, % 168.30/168.12 (P22(f317(f317(f319(x111781),f317(x111782,x111783)),f317(f287(x111784,x111781,x111782),f233(f858(x111784,a842)))))), % 168.30/168.12 inference(rename_variables,[],[3799])). % 168.30/168.12 cnf(11181,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(x111811,x111811)),f317(f317(f237(x111811,x111811),x111812),x111813)),f147(x111811,f125(f858(x111811,a849)))))), % 168.30/168.12 inference(rename_variables,[],[4504])). % 168.30/168.12 cnf(11188,plain, % 168.30/168.12 (E(f37(x111881,x111882,x111883,x111884,x111885,x111886,x111887,x111888,x111889,a23),x111882)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11191,plain, % 168.30/168.12 (E(f37(x111911,x111912,x111913,x111914,x111915,x111916,x111917,x111918,x111919,a23),x111912)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11194,plain, % 168.30/168.12 (~E(f317(a124,x111941),x111941)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11201,plain, % 168.30/168.12 (~E(f317(a124,x112011),x112011)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11206,plain, % 168.30/168.12 (E(f37(x112061,x112062,x112063,x112064,x112065,x112066,x112067,x112068,x112069,a23),x112062)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11207,plain, % 168.30/168.12 (E(f38(x112071,x112072,x112073,x112074,x112075,x112076,x112077,x112078,x112079,a23),x112072)), % 168.30/168.12 inference(rename_variables,[],[4359])). % 168.30/168.12 cnf(11210,plain, % 168.30/168.12 (E(f37(x112101,x112102,x112103,x112104,x112105,x112106,x112107,x112108,x112109,a23),x112102)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11211,plain, % 168.30/168.12 (E(f38(x112111,x112112,x112113,x112114,x112115,x112116,x112117,x112118,x112119,a23),x112112)), % 168.30/168.12 inference(rename_variables,[],[4359])). % 168.30/168.12 cnf(11217,plain, % 168.30/168.12 (~E(f317(a124,x112171),x112171)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11222,plain, % 168.30/168.12 (~E(f317(f317(f89(a1),x112221),x112221),a109)), % 168.30/168.12 inference(rename_variables,[],[4418])). % 168.30/168.12 cnf(11233,plain, % 168.30/168.12 (E(f317(f317(f21(a849),f2(a849)),x112331),f2(a849))), % 168.30/168.12 inference(rename_variables,[],[3104])). % 168.30/168.12 cnf(11242,plain, % 168.30/168.12 (E(f317(f317(f89(a1),f317(f317(f90(a1),x112421),f317(f48(a1,x112422),x112421))),f55(a1,x112422,x112421)),x112422)), % 168.30/168.12 inference(rename_variables,[],[3714])). % 168.30/168.12 cnf(11256,plain, % 168.30/168.12 (E(f37(x112561,x112562,x112563,x112564,x112565,x112566,x112567,x112568,x112569,a23),x112562)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11259,plain, % 168.30/168.12 (E(f37(x112591,x112592,x112593,x112594,x112595,x112596,x112597,x112598,x112599,a23),x112592)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11262,plain, % 168.30/168.12 (E(f37(x112621,x112622,x112623,x112624,x112625,x112626,x112627,x112628,x112629,a23),x112622)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11265,plain, % 168.30/168.12 (E(f37(x112651,x112652,x112653,x112654,x112655,x112656,x112657,x112658,x112659,a23),x112652)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11268,plain, % 168.30/168.12 (~E(f317(a124,x112681),x112681)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11271,plain, % 168.30/168.12 (~E(f317(a124,x112711),x112711)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11275,plain, % 168.30/168.12 (E(f37(x112751,x112752,x112753,x112754,x112755,x112756,x112757,x112758,x112759,a23),x112752)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11298,plain, % 168.30/168.12 (~P22(f317(f72(x112981,x112982,f188(f858(x112981,a842))),x112983))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(11301,plain, % 168.30/168.12 (~P22(f317(f317(f188(f858(x113011,f858(x113012,a842))),x113013),x113014))), % 168.30/168.12 inference(rename_variables,[],[4503])). % 168.30/168.12 cnf(11304,plain, % 168.30/168.12 (P22(f317(f317(f319(x113041),x113042),f233(f858(x113041,a842))))), % 168.30/168.12 inference(rename_variables,[],[3349])). % 168.30/168.12 cnf(11312,plain, % 168.30/168.12 (E(f37(x113121,x113122,x113123,x113124,x113125,x113126,x113127,x113128,x113129,a23),x113122)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11319,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x113191),x113191))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11326,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x113261),x113261))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11327,plain, % 168.30/168.12 (E(f37(x113271,x113272,x113273,x113274,x113275,x113276,x113277,x113278,x113279,a23),x113272)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11340,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x113401),x113402)),x113402))), % 168.30/168.12 inference(rename_variables,[],[4500])). % 168.30/168.12 cnf(11343,plain, % 168.30/168.12 (~P22(f317(f317(f226(a1),f317(f112(a1),x113431)),f2(a1)))), % 168.30/168.12 inference(rename_variables,[],[4492])). % 168.30/168.12 cnf(11354,plain, % 168.30/168.12 (E(f37(x113541,x113542,x113543,x113544,x113545,x113546,x113547,x113548,x113549,a23),x113542)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11357,plain, % 168.30/168.12 (E(f37(x113571,x113572,x113573,x113574,x113575,x113576,x113577,x113578,x113579,a23),x113572)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11368,plain, % 168.30/168.12 (E(f37(x113681,x113682,x113683,x113684,x113685,x113686,x113687,x113688,x113689,a23),x113682)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11373,plain, % 168.30/168.12 (E(f37(x113731,x113732,x113733,x113734,x113735,x113736,x113737,x113738,x113739,a23),x113732)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11376,plain, % 168.30/168.12 (~P22(f317(f317(f226(a1),f317(f112(a1),x113761)),f2(a1)))), % 168.30/168.12 inference(rename_variables,[],[4492])). % 168.30/168.12 cnf(11379,plain, % 168.30/168.12 (E(f37(x113791,x113792,x113793,x113794,x113795,x113796,x113797,x113798,x113799,a23),x113792)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11382,plain, % 168.30/168.12 (~E(f317(a124,x113821),x113821)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11385,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x113851),x113851))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11392,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x113921),x113921))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11413,plain, % 168.30/168.12 (~P22(f317(f317(f226(a1),f317(f112(a1),x114131)),f2(a1)))), % 168.30/168.12 inference(rename_variables,[],[4492])). % 168.30/168.12 cnf(11428,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x114281)),x114281))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11429,plain, % 168.30/168.12 (~E(f317(a124,x114291),x114291)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11435,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x114351)),x114351))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11436,plain, % 168.30/168.12 (E(f37(x114361,x114362,x114363,x114364,x114365,x114366,x114367,x114368,x114369,a23),x114362)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11443,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x114431),x114432)),x114431))), % 168.30/168.12 inference(rename_variables,[],[4501])). % 168.30/168.12 cnf(11446,plain, % 168.30/168.12 (~P22(f317(f317(f226(a1),f317(f112(a1),x114461)),f2(a1)))), % 168.30/168.12 inference(rename_variables,[],[4492])). % 168.30/168.12 cnf(11449,plain, % 168.30/168.12 (~E(f317(a124,x114491),x114491)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11462,plain, % 168.30/168.12 (P22(f317(f317(f319(x114621),x114622),f317(f317(f286(x114621),x114622),x114623)))), % 168.30/168.12 inference(rename_variables,[],[3509])). % 168.30/168.12 cnf(11463,plain, % 168.30/168.12 (~P22(f317(f317(f225(a1),f2(a1)),f317(f88(a1),f317(f112(a1),f317(a124,x114631)))))), % 168.30/168.12 inference(rename_variables,[],[4502])). % 168.30/168.12 cnf(11466,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),f317(f317(f21(a849),x114661),x114662)),f317(a124,x114661)))), % 168.30/168.12 inference(rename_variables,[],[3643])). % 168.30/168.12 cnf(11469,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f55(a849,x114691,x114692)),x114691))), % 168.30/168.12 inference(rename_variables,[],[3648])). % 168.30/168.12 cnf(11475,plain, % 168.30/168.12 (E(f317(f317(f127(x114751),x114752),f125(x114751)),x114752)), % 168.30/168.12 inference(rename_variables,[],[3120])). % 168.30/168.12 cnf(11478,plain, % 168.30/168.12 (E(f37(x114781,x114782,x114783,x114784,x114785,x114786,x114787,x114788,x114789,a23),x114782)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11481,plain, % 168.30/168.12 (E(f37(x114811,x114812,x114813,x114814,x114815,x114816,x114817,x114818,x114819,a23),x114812)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11484,plain, % 168.30/168.12 (E(f37(x114841,x114842,x114843,x114844,x114845,x114846,x114847,x114848,x114849,a23),x114842)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11493,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x114931),x114931))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11494,plain, % 168.30/168.12 (E(f37(x114941,x114942,x114943,x114944,x114945,x114946,x114947,x114948,x114949,a23),x114942)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11497,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f55(a849,x114971,x114972)),x114971))), % 168.30/168.12 inference(rename_variables,[],[3648])). % 168.30/168.12 cnf(11498,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f2(a849)),x114981))), % 168.30/168.12 inference(rename_variables,[],[3208])). % 168.30/168.12 cnf(11513,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x115131),x115131))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11516,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x115161),x115161))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11519,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x115191),x115191))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11522,plain, % 168.30/168.12 (P22(f317(f317(f319(x115221),f317(x115222,x115223)),f317(f287(x115224,x115221,x115222),f233(f858(x115224,a842)))))), % 168.30/168.12 inference(rename_variables,[],[3799])). % 168.30/168.12 cnf(11523,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x115231)),x115231))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11526,plain, % 168.30/168.12 (P22(f317(f317(f319(x115261),f317(x115262,x115263)),f317(f287(x115264,x115261,x115262),f233(f858(x115264,a842)))))), % 168.30/168.12 inference(rename_variables,[],[3799])). % 168.30/168.12 cnf(11527,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x115271),x115272)),x115272))), % 168.30/168.12 inference(rename_variables,[],[4500])). % 168.30/168.12 cnf(11532,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x115321),x115321))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11533,plain, % 168.30/168.12 (E(f37(x115331,x115332,x115333,x115334,x115335,x115336,x115337,x115338,x115339,a23),x115332)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11536,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x115361),x115362)),x115361))), % 168.30/168.12 inference(rename_variables,[],[4501])). % 168.30/168.12 cnf(11539,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x115391),x115391))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11542,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x115421),x115421))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11548,plain, % 168.30/168.12 (P22(f317(f317(f319(x115481),x115482),f233(f858(x115481,a842))))), % 168.30/168.12 inference(rename_variables,[],[3349])). % 168.30/168.12 cnf(11549,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x115491)),x115491))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11552,plain, % 168.30/168.12 (~P22(f317(f72(x115521,x115522,f188(f858(x115521,a842))),x115523))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(11555,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x115551),x115551))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11568,plain, % 168.30/168.12 (~P22(f317(f317(f319(x115681),x115682),f188(f858(x115681,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11571,plain, % 168.30/168.12 (E(f317(f317(f16(x115711,x115712),x115713),x115714),x115713)), % 168.30/168.12 inference(rename_variables,[],[3176])). % 168.30/168.12 cnf(11574,plain, % 168.30/168.12 (E(f317(f317(f16(x115741,x115742),x115743),x115744),x115743)), % 168.30/168.12 inference(rename_variables,[],[3176])). % 168.30/168.12 cnf(11583,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f317(f48(a849,x115831),x115832)),x115831))), % 168.30/168.12 inference(rename_variables,[],[3568])). % 168.30/168.12 cnf(11584,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),f2(a849)),f317(a124,x115841)))), % 168.30/168.12 inference(rename_variables,[],[3272])). % 168.30/168.12 cnf(11587,plain, % 168.30/168.12 (P22(f317(f317(f319(x115871),f317(x115872,x115873)),f317(f287(x115874,x115871,x115872),f233(f858(x115874,a842)))))), % 168.30/168.12 inference(rename_variables,[],[3799])). % 168.30/168.12 cnf(11590,plain, % 168.30/168.12 (P22(f317(f71(x115901),f317(f166(x115901),x115902)))), % 168.30/168.12 inference(rename_variables,[],[3228])). % 168.30/168.12 cnf(11593,plain, % 168.30/168.12 (P22(f317(f71(x115931),f317(f166(x115931),x115932)))), % 168.30/168.12 inference(rename_variables,[],[3228])). % 168.30/168.12 cnf(11596,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),f317(f88(a1),f317(f112(a1),x115961))),f317(f112(a1),x115962)))), % 168.30/168.12 inference(rename_variables,[],[3670])). % 168.30/168.12 cnf(11599,plain, % 168.30/168.12 (~P22(f317(f317(f319(x115991),x115992),f188(f858(x115991,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11618,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x116181),x116181))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11619,plain, % 168.30/168.12 (E(f37(x116191,x116192,x116193,x116194,x116195,x116196,x116197,x116198,x116199,a23),x116192)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11622,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x116221),x116221))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11635,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x116351),x116351))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11638,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x116381),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(11643,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x116431),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(11648,plain, % 168.30/168.12 (P22(f317(f233(f858(x116481,a842)),x116482))), % 168.30/168.12 inference(rename_variables,[],[3252])). % 168.30/168.12 cnf(11653,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f2(a849)),x116531))), % 168.30/168.12 inference(rename_variables,[],[3208])). % 168.30/168.12 cnf(11654,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x116541)),x116541))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11657,plain, % 168.30/168.12 (~P22(f317(f72(x116571,x116572,f188(f858(x116571,a842))),x116573))), % 168.30/168.12 inference(rename_variables,[],[4499])). % 168.30/168.12 cnf(11676,plain, % 168.30/168.12 (P22(f317(f317(f226(a1),f317(f88(a1),f87(a1))),f2(a1)))), % 168.30/168.12 inference(scs_inference,[],[4401,3434,3758,4431,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,4359,11207,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,4405,10311,10402,2786,2787,2798,2799,2807,2810,2814,2815,2816,2822,2832,2834,2839,2843,2844,2846,2848,2850,2857,2861,2867,2868,2870,2871,2902,2930,2932,2936,2937,2939,2959,2967,4380,3229,3924,3120,11475,3651,3021,4461,10852,11150,11153,3714,11242,3090,3052,10151,3046,3029,3034,4068,11036,3248,3119,3139,10355,3297,4496,3830,4421,10148,3176,11571,4486,3298,3085,3086,10213,10510,3355,2999,3104,11233,3978,3832,10858,10991,11048,4505,10780,10996,11107,11126,11156,4506,10898,10999,11110,4507,11002,4508,11062,4509,3103,3396,3558,4266,4267,4418,3500,3704,4103,3258,10232,10348,10419,10463,10466,10513,10595,10842,3643,11466,3171,3272,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,4492,11343,11376,11413,11446,3630,3404,3782,3215,3216,3189,4473,4415,3388,4493,3972,11121,3518,3228,11590,3941,3842,10674,3893,3559,3899,3575,10861,10934,11015,4497,10622,11007,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,3187,10582,10625,10628,10661,10685,10722,10760,3188,10324,10525,10601,10725,11385,11622,3266,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,3349,10480,10733,10777,11070,11142,11304,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,3252,10507,10537,11099,3293,3285,3710,3648,10194,11469,11497,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,3208,10682,10753,11498,3670,4023,4483,3718,4464,4467,3164,3168,4466,4465,3509,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,3907,3799,11178,11522,11526,3637,10793,10799,3494,3639,10884,11045,11075,3568,3466,10469,10472,10540,10709,4502,11463,4503,10598,10691,11018,11168,4087,3983,3669,4500,10167,10170,10501,10504,11340,4501,11443,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348])). % 168.30/168.12 cnf(11679,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x116791)),x116791))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11682,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x116821)),x116821))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11685,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x116851)),x116851))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11688,plain, % 168.30/168.12 (~P22(f317(f317(f225(a849),f317(a124,x116881)),x116881))), % 168.30/168.12 inference(rename_variables,[],[4485])). % 168.30/168.12 cnf(11691,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x116911),x116911))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11694,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x116941),x116941))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11697,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x116971),x116971))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11700,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x117001),x117001))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11718,plain, % 168.30/168.12 (E(f317(f189(f850(x117181)),f317(f162(x117181),x117182)),f317(f189(f850(x117181)),x117182))), % 168.30/168.12 inference(rename_variables,[],[3200])). % 168.30/168.12 cnf(11721,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x117211),x117211))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11727,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x117271),x117271))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11728,plain, % 168.30/168.12 (~E(f317(a124,x117281),x117281)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11730,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x117301),f317(f84(a1),x117301)))), % 168.30/168.12 inference(scs_inference,[],[4401,3434,3497,3758,4431,4382,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,4359,11207,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,4405,10311,10402,2786,2787,2798,2799,2807,2810,2814,2815,2816,2822,2832,2834,2839,2843,2844,2846,2848,2850,2857,2861,2867,2868,2870,2871,2902,2930,2932,2936,2937,2939,2959,2967,4380,3229,3924,3120,11475,3241,3651,3021,4461,10852,11150,11153,3714,11242,3090,3052,10151,3046,3029,3034,4068,11036,3200,3248,3119,3139,10355,3297,4496,3830,4421,10148,3176,11571,4486,3298,3085,3086,10213,10510,3355,2999,3104,11233,3978,3832,10858,10991,11048,4505,10780,10996,11107,11126,11156,4506,10898,10999,11110,4507,11002,4508,11062,4509,3103,3396,3558,4266,4267,4418,3500,3704,4103,3258,10232,10348,10419,10463,10466,10513,10595,10842,3643,11466,3171,3272,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,4492,11343,11376,11413,11446,3630,3404,3782,3215,3216,3189,4473,4415,3388,4493,3972,11121,3518,3228,11590,3941,3842,10674,3893,3559,3899,3575,10861,10934,11015,4497,10622,11007,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,3187,10582,10625,10628,10661,10685,10722,10760,3188,10324,10525,10601,10725,11385,11622,11635,3266,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,3349,10480,10733,10777,11070,11142,11304,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,3252,10507,10537,11099,3293,3285,3710,3648,10194,11469,11497,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,3208,10682,10753,11498,3670,4023,4483,3718,4464,4467,3164,3168,4466,4465,3509,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,3907,3799,11178,11522,11526,3637,10793,10799,3494,3639,10884,11045,11075,3568,3466,10469,10472,10540,10709,4502,11463,4503,10598,10691,11018,11168,4087,3983,3669,4500,10167,10170,10501,10504,11340,4501,11443,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348,6351,6352,6354,6356,6357,6358,6360,6362,6365,6370,6371,6373,6374,6380,6382,6387,6425,6428,6441,6443])). % 168.30/168.12 cnf(11731,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x117311),x117311))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11742,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x117421),x117421))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11745,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(f857(f850(x117451),f850(x117451)),a842)),f152(x117451,x117452)),f284(f850(x117451),f151(x117451,x117452))))), % 168.30/168.12 inference(rename_variables,[],[3898])). % 168.30/168.12 cnf(11752,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x117521),f317(a124,x117521)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(11755,plain, % 168.30/168.12 (P22(f317(f317(f319(f858(x117551,a842)),x117552),f317(f285(x117551),x117552)))), % 168.30/168.12 inference(rename_variables,[],[3559])). % 168.30/168.12 cnf(11756,plain, % 168.30/168.12 (~E(f317(a124,x117561),x117561)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11761,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x117611),x117611))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11766,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x117661),x117661))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11775,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x117751),x117751))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11776,plain, % 168.30/168.12 (~E(f317(a124,x117761),x117761)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11781,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x117811,a842)),x117812),f317(f317(f286(x117811),x117813),x117812)))), % 168.30/168.12 inference(rename_variables,[],[3637])). % 168.30/168.12 cnf(11784,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x117841),x117841))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11795,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x117951),x117951))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11796,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x117961),f317(a124,x117961)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(11799,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x117991),x117991))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(11802,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x118021),x118021))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(11805,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x118051),x118051))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(11808,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x118081),x118081))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(11811,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x118111),x118111))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11814,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118141),x118141))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11823,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118231),x118231))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11824,plain, % 168.30/168.12 (~E(f317(a124,x118241),x118241)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11827,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x118271),x118271))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11844,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x118441),x118441))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11849,plain, % 168.30/168.12 (P22(f317(f317(f225(a1),x118491),x118491))), % 168.30/168.12 inference(rename_variables,[],[3188])). % 168.30/168.12 cnf(11854,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f2(a849)),x118541))), % 168.30/168.12 inference(rename_variables,[],[3208])). % 168.30/168.12 cnf(11873,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x118731),f317(a124,x118731)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(11876,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118761),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(11879,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118791),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(11882,plain, % 168.30/168.12 (~P22(f317(f317(f319(x118821),x118822),f188(f858(x118821,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11885,plain, % 168.30/168.12 (~P22(f317(f317(f319(x118851),x118852),f188(f858(x118851,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11888,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118881),x118881))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11890,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118901),f317(f317(f113(a849),x118901),x118902)))), % 168.30/168.12 inference(scs_inference,[],[4401,3434,3497,3758,4431,4382,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,4359,11207,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,11728,11756,11776,4405,10311,10402,2786,2787,2798,2799,2807,2810,2814,2815,2816,2822,2832,2834,2839,2843,2844,2846,2848,2850,2857,2861,2867,2868,2870,2871,2902,2930,2932,2936,2937,2939,2959,2967,4380,3229,3924,3120,11475,3129,3241,3651,3965,3021,4461,10852,11150,11153,3714,11242,3090,3052,10151,3046,3029,3034,4068,11036,3200,3248,3119,3139,10355,3297,4496,3830,4421,10148,3176,11571,4486,3298,3085,3086,10213,10510,3355,2999,3104,11233,3978,3832,10858,10991,11048,4505,10780,10996,11107,11126,11156,4506,10898,10999,11110,4507,11002,4508,11062,4509,3103,3396,3558,4266,4267,4418,3500,3704,4103,3258,10232,10348,10419,10463,10466,10513,10595,10842,11752,11796,3643,11466,3171,3272,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,11876,4492,11343,11376,11413,11446,3630,3404,3782,3215,3216,3189,4473,4415,3388,4493,3972,11121,3518,3228,11590,3941,3898,3842,10674,3893,3559,3899,3575,10861,10934,11015,4497,10622,11007,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,3187,10582,10625,10628,10661,10685,10722,10760,10796,11799,11802,11805,11808,3188,10324,10525,10601,10725,11385,11622,11635,11731,11742,11761,11766,11784,11811,11827,11844,3266,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,11700,11775,11795,11814,11823,11888,3349,10480,10733,10777,11070,11142,11304,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,11599,11882,3252,10507,10537,11099,3293,3285,3710,3648,10194,11469,11497,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,11688,3208,10682,10753,11498,11653,3670,4023,4483,3679,3718,4464,4467,3164,3168,4466,4465,3687,3509,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,3907,3799,11178,11522,11526,3637,10793,10799,10816,3494,3639,10884,11045,11075,3568,3466,10469,10472,10540,10709,4502,11463,4503,10598,10691,11018,11168,4087,3983,3669,4500,10167,10170,10501,10504,11340,4501,11443,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348,6351,6352,6354,6356,6357,6358,6360,6362,6365,6370,6371,6373,6374,6380,6382,6387,6425,6428,6441,6443,6445,6446,6447,6480,6485,6487,6492,6493,6501,6505,6518,6541,6542,6544,6545,6556,6560,6573,6579,6582,6584,6633,6634,6635,6640,6643,6672,6674,6676,6678,6683,6688,6701,6710,6743,6744,6745,6759,6760,6762,6763,6781,6782,6797,6818,6819,6825,6846,6859,6861,6863,6865,6866,6867,6874,6892,6906,6907,6912,6913,6920,6921])). % 168.30/168.12 cnf(11891,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118911),x118911))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11894,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118941),x118941))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11897,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x118971),x118971))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11904,plain, % 168.30/168.12 (P22(f317(f317(f319(f858(x119041,a842)),x119042),f317(f285(x119041),x119042)))), % 168.30/168.12 inference(rename_variables,[],[3559])). % 168.30/168.12 cnf(11917,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x119171,a842)),f317(f166(x119171),f317(f130(x119171,x119172),x119173))),f317(f166(x119171),x119173)))), % 168.30/168.12 inference(rename_variables,[],[3842])). % 168.30/168.12 cnf(11922,plain, % 168.30/168.12 (~P22(f317(f317(f319(x119221),x119222),f188(f858(x119221,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11927,plain, % 168.30/168.12 (E(f317(f189(f850(x119271)),f317(f162(x119271),x119272)),f317(f189(f850(x119271)),x119272))), % 168.30/168.12 inference(rename_variables,[],[3200])). % 168.30/168.12 cnf(11934,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x119341),f317(a124,x119341)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(11937,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x119371,a842)),x119372),f233(f858(x119371,a842))))), % 168.30/168.12 inference(rename_variables,[],[3575])). % 168.30/168.12 cnf(11938,plain, % 168.30/168.12 (~E(f317(a124,x119381),x119381)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11941,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x119411,a842)),f317(f166(x119411),f317(f130(x119411,x119412),x119413))),f317(f166(x119411),x119413)))), % 168.30/168.12 inference(rename_variables,[],[3842])). % 168.30/168.12 cnf(11953,plain, % 168.30/168.12 (E(f37(x119531,x119532,x119533,x119534,x119535,x119536,x119537,x119538,x119539,a23),x119532)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(11956,plain, % 168.30/168.12 (~E(f317(a124,x119561),x119561)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(11960,plain, % 168.30/168.12 (P22(f317(f71(x119601),f188(f858(x119601,a842))))), % 168.30/168.12 inference(rename_variables,[],[3266])). % 168.30/168.12 cnf(11961,plain, % 168.30/168.12 (~P22(f317(f317(f319(x119611),x119612),f188(f858(x119611,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11966,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x119661),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(11967,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x119671),x119671))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(11972,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x119721,a842)),f317(f166(x119721),f164(x119721,x119722,x119723))),f317(f166(x119721),x119723)))), % 168.30/168.12 inference(rename_variables,[],[3893])). % 168.30/168.12 cnf(11975,plain, % 168.30/168.12 (P19(x119751,x119751,f5(x119751),x119752)), % 168.30/168.12 inference(rename_variables,[],[3434])). % 168.30/168.12 cnf(11980,plain, % 168.30/168.12 (P22(f317(f317(f319(f858(x119801,a842)),x119802),f317(f285(x119801),x119802)))), % 168.30/168.12 inference(rename_variables,[],[3559])). % 168.30/168.12 cnf(11991,plain, % 168.30/168.12 (P22(f317(f317(f194(a23),x119911),x119911))), % 168.30/168.12 inference(rename_variables,[],[3186])). % 168.30/168.12 cnf(11994,plain, % 168.30/168.12 (~P22(f317(f317(f319(x119941),x119942),f188(f858(x119941,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(11997,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x119971,a842)),x119972),f317(f317(f286(x119971),x119973),x119972)))), % 168.30/168.12 inference(rename_variables,[],[3637])). % 168.30/168.12 cnf(11998,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x119981,a842)),x119982),f233(f858(x119981,a842))))), % 168.30/168.12 inference(rename_variables,[],[3575])). % 168.30/168.12 cnf(12005,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x120051),x120051))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(12008,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x120081),x120081))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(12011,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x120111),x120111))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(12014,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x120141),x120141))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(12017,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x120171),f317(a124,x120171)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(12020,plain, % 168.30/168.12 (P22(f317(f317(f226(a849),x120201),f317(a124,x120201)))), % 168.30/168.12 inference(rename_variables,[],[3258])). % 168.30/168.12 cnf(12023,plain, % 168.30/168.12 (~E(f317(a124,x120231),x120231)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(12030,plain, % 168.30/168.12 (P22(f317(f317(f319(f858(x120301,a842)),x120302),f317(f285(x120301),x120302)))), % 168.30/168.12 inference(rename_variables,[],[3559])). % 168.30/168.12 cnf(12039,plain, % 168.30/168.12 (~E(f317(a124,x120391),x120391)), % 168.30/168.12 inference(rename_variables,[],[4386])). % 168.30/168.12 cnf(12040,plain, % 168.30/168.12 (E(f317(f287(x120401,x120401,f5(x120401)),x120402),x120402)), % 168.30/168.12 inference(rename_variables,[],[3248])). % 168.30/168.12 cnf(12043,plain, % 168.30/168.12 (P33(x120431,x120432,f125(x120431),f125(x120431))), % 168.30/168.12 inference(rename_variables,[],[3441])). % 168.30/168.12 cnf(12046,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x120461,a842)),f317(f166(x120461),f164(x120461,x120462,x120463))),f317(f166(x120461),x120463)))), % 168.30/168.12 inference(rename_variables,[],[3893])). % 168.30/168.12 cnf(12047,plain, % 168.30/168.12 (P22(f317(f71(x120471),f317(f166(x120471),x120472)))), % 168.30/168.12 inference(rename_variables,[],[3228])). % 168.30/168.12 cnf(12054,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x120541),x120541))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(12057,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x120571),x120571))), % 168.30/168.12 inference(rename_variables,[],[4472])). % 168.30/168.12 cnf(12062,plain, % 168.30/168.12 (E(f317(f189(f850(x120621)),f317(f162(x120621),x120622)),f317(f189(f850(x120621)),x120622))), % 168.30/168.12 inference(rename_variables,[],[3200])). % 168.30/168.12 cnf(12065,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f2(a849)),x120651))), % 168.30/168.12 inference(rename_variables,[],[3208])). % 168.30/168.12 cnf(12068,plain, % 168.30/168.12 (~P22(f317(f317(f188(f858(x120681,f858(x120682,a842))),x120683),x120684))), % 168.30/168.12 inference(rename_variables,[],[4503])). % 168.30/168.12 cnf(12075,plain, % 168.30/168.12 (~P22(f317(f317(f188(f858(x120751,f858(x120752,a842))),x120753),x120754))), % 168.30/168.12 inference(rename_variables,[],[4503])). % 168.30/168.12 cnf(12078,plain, % 168.30/168.12 (P29(a849,f317(f163(a849),f317(f317(f148(f850(x120781),a849),f189(f850(x120781))),f173(x120781,x120782))))), % 168.30/168.12 inference(rename_variables,[],[3752])). % 168.30/168.12 cnf(12081,plain, % 168.30/168.12 (P19(x120811,x120811,f5(x120811),x120812)), % 168.30/168.12 inference(rename_variables,[],[3434])). % 168.30/168.12 cnf(12084,plain, % 168.30/168.12 (P22(f317(f317(f319(f850(x120841)),f125(x120841)),f155(x120841,x120842)))), % 168.30/168.12 inference(rename_variables,[],[3396])). % 168.30/168.12 cnf(12089,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),x120891),x120891))), % 168.30/168.12 inference(rename_variables,[],[3187])). % 168.30/168.12 cnf(12090,plain, % 168.30/168.12 (P22(f317(f317(f225(a849),f2(a849)),x120901))), % 168.30/168.12 inference(rename_variables,[],[3208])). % 168.30/168.12 cnf(12093,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(f857(f850(x120931),f850(x120931)),a842)),f152(x120931,x120932)),f284(f850(x120931),f151(x120931,x120932))))), % 168.30/168.12 inference(rename_variables,[],[3898])). % 168.30/168.12 cnf(12099,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x120991,a842)),f317(f166(x120991),f164(x120991,x120992,x120993))),f317(f166(x120991),x120993)))), % 168.30/168.12 inference(rename_variables,[],[3893])). % 168.30/168.12 cnf(12100,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x121001,a842)),f317(f166(x121001),f317(f130(x121001,x121002),x121003))),f317(f166(x121001),x121003)))), % 168.30/168.12 inference(rename_variables,[],[3842])). % 168.30/168.12 cnf(12103,plain, % 168.30/168.12 (~P22(f317(f317(f226(f858(x121031,a842)),x121032),f188(f858(x121031,a842))))), % 168.30/168.12 inference(rename_variables,[],[4497])). % 168.30/168.12 cnf(12106,plain, % 168.30/168.12 (P19(x121061,f853(x121061),f217(x121061),x121062)), % 168.30/168.12 inference(rename_variables,[],[3442])). % 168.30/168.12 cnf(12111,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x121111,a842)),f317(f287(x121112,x121111,x121113),f317(f289(x121112,x121111,x121113),x121114))),x121114))), % 168.30/168.12 inference(rename_variables,[],[4087])). % 168.30/168.12 cnf(12114,plain, % 168.30/168.12 (P22(f317(f71(f853(x121141)),f317(f287(x121142,f853(x121141),f317(f171(x121142,x121141),x121143)),f233(f858(x121142,a842)))))), % 168.30/168.12 inference(rename_variables,[],[3907])). % 168.30/168.12 cnf(12119,plain, % 168.30/168.12 (~P22(f317(f317(f188(f858(x121191,f858(x121192,a842))),x121193),x121194))), % 168.30/168.12 inference(rename_variables,[],[4503])). % 168.30/168.12 cnf(12122,plain, % 168.30/168.12 (P22(f317(f317(f319(f850(x121221)),f125(x121221)),f155(x121221,x121222)))), % 168.30/168.12 inference(rename_variables,[],[3396])). % 168.30/168.12 cnf(12125,plain, % 168.30/168.12 (~P22(f317(f317(f319(f857(f850(x121251),f850(x121251))),f317(f317(f237(f850(x121251),f850(x121251)),x121252),f125(x121251))),f139(x121251,x121253)))), % 168.30/168.12 inference(rename_variables,[],[4505])). % 168.30/168.12 cnf(12128,plain, % 168.30/168.12 (~P22(f317(f317(f226(a849),x121281),f2(a849)))), % 168.30/168.12 inference(rename_variables,[],[4476])). % 168.30/168.12 cnf(12130,plain, % 168.30/168.12 (~P22(f317(f71(x121301),f233(f858(x121301,a842))))), % 168.30/168.12 inference(scs_inference,[],[4401,3434,10924,11975,3441,3442,3497,3758,3157,4431,3061,4382,3543,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,11619,4359,11207,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,11728,11756,11776,11824,11938,11956,12023,4405,10311,10402,2786,2787,2798,2799,2807,2810,2814,2815,2816,2822,2832,2834,2839,2840,2843,2844,2846,2848,2850,2851,2857,2861,2867,2868,2870,2871,2902,2930,2932,2936,2937,2939,2959,2967,4380,3229,3924,3120,11475,3129,3241,3651,3965,3021,4461,10852,11150,11153,3714,11242,3090,3052,10151,3046,3029,3034,4068,11036,3067,3200,11718,11927,3248,10677,3119,3139,10355,3297,4496,3830,4421,10148,3176,11571,4486,3298,3085,3086,10213,10510,3355,2999,3104,11233,3978,3832,10858,10991,11048,4505,10780,10996,11107,11126,11156,11162,4506,10898,10999,11110,4507,11002,4508,11062,4509,3103,3396,12084,12122,3558,4266,4267,4418,3500,3704,4103,3752,3382,3632,3258,10232,10348,10419,10463,10466,10513,10595,10842,11752,11796,11873,11934,12017,3643,11466,3171,3272,3463,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,11876,11879,11966,4492,11343,11376,11413,11446,3630,3404,3782,3215,3216,3189,4473,4415,3388,4493,3972,11121,3518,3228,11590,11593,3941,3898,11745,12093,3842,10674,11917,11941,3893,10864,11972,12046,3559,11755,11904,11980,12030,3899,3575,10861,10934,11015,11081,11937,4497,10622,11007,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,11727,3187,10582,10625,10628,10661,10685,10722,10760,10796,11799,11802,11805,11808,12005,12008,12011,12014,3188,10324,10525,10601,10725,11385,11622,11635,11731,11742,11761,11766,11784,11811,11827,11844,3266,11960,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,11700,11775,11795,11814,11823,11888,11891,11894,11897,11967,12054,3349,10480,10733,10777,11070,11142,11304,11548,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,11599,11882,11885,11922,11961,3252,10507,10537,11099,3293,3285,3710,3648,10194,11469,11497,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,11688,3208,10682,10753,11498,11653,11854,12065,3670,4023,4483,3679,3718,4464,4467,3164,3168,4466,4465,3687,3509,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,3907,3799,11178,11522,11526,3637,10793,10799,10816,11781,3494,11033,3639,10884,11045,11075,3568,3466,10469,10472,10540,10709,4502,11463,4503,10598,10691,11018,11168,11301,12068,12075,4087,10667,3983,3669,4500,10167,10170,10501,10504,11340,4501,11443,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348,6351,6352,6354,6356,6357,6358,6360,6362,6365,6370,6371,6373,6374,6380,6382,6387,6425,6428,6441,6443,6445,6446,6447,6480,6485,6487,6492,6493,6501,6505,6518,6541,6542,6544,6545,6556,6560,6573,6579,6582,6584,6633,6634,6635,6640,6643,6672,6674,6676,6678,6683,6688,6701,6710,6743,6744,6745,6759,6760,6762,6763,6781,6782,6797,6818,6819,6825,6846,6859,6861,6863,6865,6866,6867,6874,6892,6906,6907,6912,6913,6920,6921,6923,6925,6952,6953,6965,6972,6973,6974,6976,7005,7014,7025,7034,7047,7048,7053,7055,7056,7062,7071,7085,7119,7121,7136,7146,7187,7192,7217,7262,7295,7309,7325,7356,7357,7360,7361,7385,7408,7425,7428,7429,7439,7459,7461,7463,7465,7466,7467,7514,7518,7519,7549,7551,7552,7553,7558,7580,7599,7609,7619,7631,7632,7634,7654,7658,7663,7664,7687,7705,7753,7754,7796,7804,7826,7843,7844,7906,7907,7934,7963,7974,7976,7984,7993,7997,8031,8037,8044])). % 168.30/168.12 cnf(12131,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x121311,a842)),x121312),x121312))), % 168.30/168.12 inference(rename_variables,[],[3494])). % 168.30/168.12 cnf(12134,plain, % 168.30/168.12 (~P22(f317(f317(f319(x121341),x121342),f188(f858(x121341,a842))))), % 168.30/168.12 inference(rename_variables,[],[4488])). % 168.30/168.12 cnf(12137,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x121371,a842)),f317(f287(x121372,x121371,x121373),f317(f289(x121372,x121371,x121373),x121374))),x121374))), % 168.30/168.12 inference(rename_variables,[],[4087])). % 168.30/168.12 cnf(12138,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x121381,a842)),x121382),x121382))), % 168.30/168.12 inference(rename_variables,[],[3494])). % 168.30/168.12 cnf(12143,plain, % 168.30/168.12 (E(f37(x121431,x121432,x121433,x121434,x121435,x121436,x121437,x121438,x121439,a23),x121432)), % 168.30/168.12 inference(rename_variables,[],[4358])). % 168.30/168.12 cnf(12146,plain, % 168.30/168.12 (P22(f317(f317(f225(f858(x121461,a842)),f317(f166(x121461),f164(x121461,x121462,x121463))),f317(f166(x121461),x121463)))), % 168.30/168.12 inference(rename_variables,[],[3893])). % 168.30/168.12 cnf(12147,plain, % 168.30/168.13 (P22(f317(f71(x121471),f317(f166(x121471),x121472)))), % 168.30/168.13 inference(rename_variables,[],[3228])). % 168.30/168.13 cnf(12150,plain, % 168.30/168.13 (P22(f317(f317(f194(a23),x121501),x121501))), % 168.30/168.13 inference(rename_variables,[],[3186])). % 168.30/168.13 cnf(12153,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x121531),x121531))), % 168.30/168.13 inference(rename_variables,[],[4472])). % 168.30/168.13 cnf(12156,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x121561),x121561))), % 168.30/168.13 inference(rename_variables,[],[4472])). % 168.30/168.13 cnf(12167,plain, % 168.30/168.13 (P19(x121671,x121671,f5(x121671),x121672)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12174,plain, % 168.30/168.13 (~P22(f317(f317(f319(x121741),x121742),f188(f858(x121741,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12177,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(x121771,x121771)),f317(f317(f237(x121771,x121771),x121772),x121772)),f284(x121771,x121773)))), % 168.30/168.13 inference(rename_variables,[],[3832])). % 168.30/168.13 cnf(12180,plain, % 168.30/168.13 (~P22(f317(f317(f319(x121801),x121802),f188(f858(x121801,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12183,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(x121831,x121831)),f317(f317(f237(x121831,x121831),x121832),x121832)),f284(x121831,x121833)))), % 168.30/168.13 inference(rename_variables,[],[3832])). % 168.30/168.13 cnf(12193,plain, % 168.30/168.13 (~E(f317(f317(f145(x121931),x121932),x121933),x121933)), % 168.30/168.13 inference(rename_variables,[],[4421])). % 168.30/168.13 cnf(12196,plain, % 168.30/168.13 (P22(f317(f317(f319(x121961),x121962),f233(f858(x121961,a842))))), % 168.30/168.13 inference(rename_variables,[],[3349])). % 168.30/168.13 cnf(12197,plain, % 168.30/168.13 (~E(f317(a124,x121971),x121971)), % 168.30/168.13 inference(rename_variables,[],[4386])). % 168.30/168.13 cnf(12200,plain, % 168.30/168.13 (P22(f317(f317(f319(f850(x122001)),f125(x122001)),f155(x122001,x122002)))), % 168.30/168.13 inference(rename_variables,[],[3396])). % 168.30/168.13 cnf(12201,plain, % 168.30/168.13 (~E(f317(f317(f145(x122011),x122012),x122013),f125(x122011))), % 168.30/168.13 inference(rename_variables,[],[4430])). % 168.30/168.13 cnf(12204,plain, % 168.30/168.13 (P22(f317(f317(f319(x122041),f317(x122042,x122043)),f317(f287(x122044,x122041,x122042),f233(f858(x122044,a842)))))), % 168.30/168.13 inference(rename_variables,[],[3799])). % 168.30/168.13 cnf(12205,plain, % 168.30/168.13 (P19(x122051,x122051,f5(x122051),x122052)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12208,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x122081,a842)),f188(f858(x122081,a842))),x122082))), % 168.30/168.13 inference(rename_variables,[],[3639])). % 168.30/168.13 cnf(12209,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x122091,a842)),x122092),x122092))), % 168.30/168.13 inference(rename_variables,[],[3494])). % 168.30/168.13 cnf(12212,plain, % 168.30/168.13 (P22(f317(f317(f319(x122121),f317(x122122,x122123)),f317(f287(x122124,x122121,x122122),f233(f858(x122124,a842)))))), % 168.30/168.13 inference(rename_variables,[],[3799])). % 168.30/168.13 cnf(12213,plain, % 168.30/168.13 (P19(x122131,x122131,f5(x122131),x122132)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12216,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(f850(x122161),f850(x122161))),f317(f317(f237(f850(x122161),f850(x122161)),f125(x122161)),f125(x122161))),f152(x122161,x122162)))), % 168.30/168.13 inference(rename_variables,[],[3978])). % 168.30/168.13 cnf(12219,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x122191),x122191))), % 168.30/168.13 inference(rename_variables,[],[4472])). % 168.30/168.13 cnf(12220,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x122201),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12226,plain, % 168.30/168.13 (E(f317(f317(f127(x122261),x122262),f125(x122261)),x122262)), % 168.30/168.13 inference(rename_variables,[],[3120])). % 168.30/168.13 cnf(12227,plain, % 168.30/168.13 (~E(f317(f317(f145(x122271),x122272),x122273),x122273)), % 168.30/168.13 inference(rename_variables,[],[4421])). % 168.30/168.13 cnf(12230,plain, % 168.30/168.13 (E(f317(f317(f127(x122301),x122302),f125(x122301)),x122302)), % 168.30/168.13 inference(rename_variables,[],[3120])). % 168.30/168.13 cnf(12231,plain, % 168.30/168.13 (~E(f317(f317(f145(x122311),x122312),x122313),x122313)), % 168.30/168.13 inference(rename_variables,[],[4421])). % 168.30/168.13 cnf(12234,plain, % 168.30/168.13 (E(f317(f317(f127(x122341),x122342),f125(x122341)),x122342)), % 168.30/168.13 inference(rename_variables,[],[3120])). % 168.30/168.13 cnf(12241,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x122411,a842)),x122412),f233(f858(x122411,a842))))), % 168.30/168.13 inference(rename_variables,[],[3575])). % 168.30/168.13 cnf(12245,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x122451),x122451))), % 168.30/168.13 inference(rename_variables,[],[4472])). % 168.30/168.13 cnf(12246,plain, % 168.30/168.13 (~E(f317(a124,x122461),x122461)), % 168.30/168.13 inference(rename_variables,[],[4386])). % 168.30/168.13 cnf(12249,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x122491,a842)),f188(f858(x122491,a842))),x122492))), % 168.30/168.13 inference(rename_variables,[],[3639])). % 168.30/168.13 cnf(12252,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x122521),x122521))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12255,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x122551,a842)),x122552),x122552))), % 168.30/168.13 inference(rename_variables,[],[3494])). % 168.30/168.13 cnf(12260,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x122601,a842)),x122602),f317(f317(f286(x122601),x122603),x122602)))), % 168.30/168.13 inference(rename_variables,[],[3637])). % 168.30/168.13 cnf(12263,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x122631,a842)),x122632),x122632))), % 168.30/168.13 inference(rename_variables,[],[3494])). % 168.30/168.13 cnf(12264,plain, % 168.30/168.13 (~P22(f317(f317(f319(x122641),x122642),f188(f858(x122641,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12267,plain, % 168.30/168.13 (~P22(f317(f317(f319(x122671),x122672),f188(f858(x122671,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12274,plain, % 168.30/168.13 (P19(x122741,x122741,f5(x122741),x122742)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12277,plain, % 168.30/168.13 (E(f317(f189(f850(x122771)),f317(f162(x122771),x122772)),f317(f189(f850(x122771)),x122772))), % 168.30/168.13 inference(rename_variables,[],[3200])). % 168.30/168.13 cnf(12280,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x122801),x122801))), % 168.30/168.13 inference(rename_variables,[],[4472])). % 168.30/168.13 cnf(12281,plain, % 168.30/168.13 (P22(f317(f233(f858(x122811,a842)),x122812))), % 168.30/168.13 inference(rename_variables,[],[3252])). % 168.30/168.13 cnf(12284,plain, % 168.30/168.13 (~P22(f317(f317(f319(x122841),x122842),f188(f858(x122841,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12287,plain, % 168.30/168.13 (P22(f317(f317(f319(x122871),f317(x122872,x122873)),f317(f287(x122874,x122871,x122872),f233(f858(x122874,a842)))))), % 168.30/168.13 inference(rename_variables,[],[3799])). % 168.30/168.13 cnf(12288,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(x122881,x122881)),f317(f317(f237(x122881,x122881),x122882),x122882)),f284(x122881,x122883)))), % 168.30/168.13 inference(rename_variables,[],[3832])). % 168.30/168.13 cnf(12291,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(x122911,x122911)),f317(f317(f237(x122911,x122911),x122912),x122912)),f284(x122911,x122913)))), % 168.30/168.13 inference(rename_variables,[],[3832])). % 168.30/168.13 cnf(12294,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x122941),x122941))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12295,plain, % 168.30/168.13 (P22(f317(f233(f858(x122951,a842)),x122952))), % 168.30/168.13 inference(rename_variables,[],[3252])). % 168.30/168.13 cnf(12298,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x122981,a842)),f188(f858(x122981,a842))),x122982))), % 168.30/168.13 inference(rename_variables,[],[3639])). % 168.30/168.13 cnf(12301,plain, % 168.30/168.13 (P22(f317(f71(x123011),f317(f166(x123011),x123012)))), % 168.30/168.13 inference(rename_variables,[],[3228])). % 168.30/168.13 cnf(12308,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(x123081,x123081)),f317(f317(f237(x123081,x123081),x123082),x123082)),f317(f317(f265(x123081,x123081,x123081),f284(x123081,x123083)),f284(x123081,f284(x123081,x123083)))))), % 168.30/168.13 inference(scs_inference,[],[4401,3434,10924,11975,12081,12167,12205,12213,3441,3442,3497,3758,3157,4431,3061,4382,3543,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,11619,11953,4359,11207,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,11728,11756,11776,11824,11938,11956,12023,12039,12197,4405,10311,10402,3245,2786,2787,2798,2799,2807,2810,2814,2815,2816,2822,2832,2834,2839,2840,2843,2844,2846,2848,2850,2851,2857,2861,2867,2868,2870,2871,2902,2906,2930,2932,2936,2937,2939,2959,2967,4380,3229,3924,3120,11475,12226,12230,12234,3129,3241,3651,3965,3021,4400,4461,10852,11150,11153,3714,11242,3090,3052,10151,3046,3029,3034,4068,11036,3067,3200,11718,11927,12062,3248,10677,12040,3118,3119,3139,10355,3297,4496,3830,4421,10148,10308,12193,12227,4430,12201,3176,11571,4486,3298,3085,3086,10213,10510,3355,2999,3104,11233,3978,12216,3832,10858,10991,11048,12177,12183,12288,12291,4505,10780,10996,11107,11126,11156,11162,12125,4506,10898,10999,11110,4507,11002,4508,11062,4509,3103,3396,12084,12122,12200,3558,4266,4267,4418,11222,3500,3704,4103,3752,3382,3632,3258,10232,10348,10419,10463,10466,10513,10595,10842,11752,11796,11873,11934,12017,12020,3643,11466,3171,3272,3463,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,11876,11879,11966,12128,4492,11343,11376,11413,11446,3630,3404,3782,3215,3216,3189,4473,4415,3584,3388,4493,3972,11121,3518,3228,11590,11593,12047,12147,3941,3898,11745,12093,3842,10674,11917,11941,3893,10864,11972,12046,12099,12146,3559,11755,11904,11980,12030,3899,3575,10861,10934,11015,11081,11937,11998,4497,10622,11007,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,11727,11991,3187,10582,10625,10628,10661,10685,10722,10760,10796,11799,11802,11805,11808,12005,12008,12011,12014,12089,12252,3188,10324,10525,10601,10725,11385,11622,11635,11731,11742,11761,11766,11784,11811,11827,11844,3266,11960,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,11700,11775,11795,11814,11823,11888,11891,11894,11897,11967,12054,12057,12153,12156,12219,12245,3349,10480,10733,10777,11070,11142,11304,11548,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,11599,11882,11885,11922,11961,11994,12134,12174,12180,12264,12267,3252,10507,10537,11099,11648,12281,3293,3285,3710,3648,10194,11469,11497,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,11688,3208,10682,10753,11498,11653,11854,12065,3670,4023,4483,3679,3718,4464,4467,3164,3168,4466,4465,3687,3509,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,11181,3907,3799,11178,11522,11526,11587,12204,12212,3637,10793,10799,10816,11781,11997,3494,11033,12131,12138,12209,12255,3639,10884,11045,11075,11086,12208,12249,3568,3466,10469,10472,10540,10709,4502,11463,4503,10598,10691,11018,11168,11301,12068,12075,4087,10667,12111,3983,3669,4500,10167,10170,10501,10504,11340,4501,11443,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348,6351,6352,6354,6356,6357,6358,6360,6362,6365,6370,6371,6373,6374,6380,6382,6387,6425,6428,6441,6443,6445,6446,6447,6480,6485,6487,6492,6493,6501,6505,6518,6541,6542,6544,6545,6556,6560,6573,6579,6582,6584,6633,6634,6635,6640,6643,6672,6674,6676,6678,6683,6688,6701,6710,6743,6744,6745,6759,6760,6762,6763,6781,6782,6797,6818,6819,6825,6846,6859,6861,6863,6865,6866,6867,6874,6892,6906,6907,6912,6913,6920,6921,6923,6925,6952,6953,6965,6972,6973,6974,6976,7005,7014,7025,7034,7047,7048,7053,7055,7056,7062,7071,7085,7119,7121,7136,7146,7187,7192,7217,7262,7295,7309,7325,7356,7357,7360,7361,7385,7408,7425,7428,7429,7439,7459,7461,7463,7465,7466,7467,7514,7518,7519,7549,7551,7552,7553,7558,7580,7599,7609,7619,7631,7632,7634,7654,7658,7663,7664,7687,7705,7753,7754,7796,7804,7826,7843,7844,7906,7907,7934,7963,7974,7976,7984,7993,7997,8031,8037,8044,8058,8081,8104,8148,8178,8190,8207,8210,8245,8266,8331,8332,8336,8338,8356,8447,8448,8449,8450,8480,8507,8532,8574,8592,8647,8690,8693,8706,8713,8748,8795,8796,8813,8814,8958,8977,8987,9009,9011,9014,9018,9021,9022,9036,9054,9060,9072,9120,9139,9192,9193,9199,9235,9259,9264,9299,9306])). % 168.30/168.13 cnf(12311,plain, % 168.30/168.13 (~P22(f317(f317(f188(f858(x123111,f858(x123112,a842))),x123113),x123114))), % 168.30/168.13 inference(rename_variables,[],[4503])). % 168.30/168.13 cnf(12314,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x123141,a842)),x123142),f233(f858(x123141,a842))))), % 168.30/168.13 inference(rename_variables,[],[3575])). % 168.30/168.13 cnf(12317,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(x123171,x123171)),f317(f317(f237(x123171,x123171),x123172),x123172)),f284(x123171,x123173)))), % 168.30/168.13 inference(rename_variables,[],[3832])). % 168.30/168.13 cnf(12320,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),f317(f317(f89(a849),x123201),x123202)),x123202))), % 168.30/168.13 inference(rename_variables,[],[4500])). % 168.30/168.13 cnf(12321,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x123211),f317(a124,x123211)))), % 168.30/168.13 inference(rename_variables,[],[3258])). % 168.30/168.13 cnf(12324,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x123241,a842)),f317(f166(x123241),f317(f130(x123241,x123242),x123243))),f317(f166(x123241),x123243)))), % 168.30/168.13 inference(rename_variables,[],[3842])). % 168.30/168.13 cnf(12327,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x123271,a842)),x123272),f233(f858(x123271,a842))))), % 168.30/168.13 inference(rename_variables,[],[3575])). % 168.30/168.13 cnf(12330,plain, % 168.30/168.13 (E(f37(x123301,x123302,x123303,x123304,x123305,x123306,x123307,x123308,x123309,a23),x123302)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12341,plain, % 168.30/168.13 (~P22(f317(f317(f319(x123411),x123412),f188(f858(x123411,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12342,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(f850(x123421),f850(x123421))),f317(f317(f237(f850(x123421),f850(x123421)),f125(x123421)),f125(x123421))),f152(x123421,x123422)))), % 168.30/168.13 inference(rename_variables,[],[3978])). % 168.30/168.13 cnf(12347,plain, % 168.30/168.13 (~P22(f317(f317(f319(x123471),x123472),f188(f858(x123471,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12350,plain, % 168.30/168.13 (E(f317(f189(f850(x123501)),f317(f162(x123501),x123502)),f317(f189(f850(x123501)),x123502))), % 168.30/168.13 inference(rename_variables,[],[3200])). % 168.30/168.13 cnf(12353,plain, % 168.30/168.13 (~P22(f317(f317(f319(x123531),x123532),f188(f858(x123531,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12358,plain, % 168.30/168.13 (~P22(f317(f317(f319(x123581),x123582),f188(f858(x123581,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12365,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x123651),x123651))), % 168.30/168.13 inference(rename_variables,[],[4472])). % 168.30/168.13 cnf(12367,plain, % 168.30/168.13 (P22(f317(f317(f319(f857(f850(x123671),f850(x123671))),f317(f317(f237(f850(x123671),f850(x123671)),f317(f162(x123671),x123672)),x123672)),f152(x123671,f233(f858(f857(x123671,x123671),a842)))))), % 168.30/168.13 inference(scs_inference,[],[4401,3434,10924,11975,12081,12167,12205,12213,3441,3442,3497,3758,3157,4431,3061,4382,3543,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,11619,11953,12143,4359,11207,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,11728,11756,11776,11824,11938,11956,12023,12039,12197,4405,10311,10402,3245,2786,2787,2798,2799,2807,2810,2814,2815,2816,2822,2832,2834,2839,2840,2843,2844,2846,2848,2850,2851,2857,2861,2867,2868,2870,2871,2902,2906,2930,2932,2936,2937,2939,2959,2967,4380,3533,3229,3924,3120,11475,12226,12230,12234,3129,3241,3651,3965,3021,4400,4461,10852,11150,11153,3714,11242,3090,3052,10151,3046,3029,3034,4068,11036,3067,3200,11718,11927,12062,12277,12350,3248,10677,12040,3118,3119,3139,10355,3297,4496,3830,4421,10148,10308,12193,12227,4430,12201,3176,11571,4486,3298,3085,3086,10213,10510,3355,2999,3104,11233,3978,12216,12342,3832,10858,10991,11048,12177,12183,12288,12291,12317,4505,10780,10996,11107,11126,11156,11162,12125,4506,10898,10999,11110,4507,11002,4508,11062,4509,3103,3396,12084,12122,12200,3558,4266,4267,4418,11222,3500,3704,4103,3752,3382,3632,3258,10232,10348,10419,10463,10466,10513,10595,10842,11752,11796,11873,11934,12017,12020,3643,11466,3171,3272,3463,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,11876,11879,11966,12128,4492,11343,11376,11413,11446,3630,3404,3782,3215,3216,3189,4473,4415,3584,4118,3388,4493,3972,11121,3518,3228,11590,11593,12047,12147,3941,3898,11745,12093,3842,10674,11917,11941,12100,3893,10864,11972,12046,12099,12146,3559,11755,11904,11980,12030,3899,3575,10861,10934,11015,11081,11937,11998,12241,12314,4497,10622,11007,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,11727,11991,12150,3187,10582,10625,10628,10661,10685,10722,10760,10796,11799,11802,11805,11808,12005,12008,12011,12014,12089,12252,3188,10324,10525,10601,10725,11385,11622,11635,11731,11742,11761,11766,11784,11811,11827,11844,3266,11960,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,11700,11775,11795,11814,11823,11888,11891,11894,11897,11967,12054,12057,12153,12156,12219,12245,12280,3349,10480,10733,10777,11070,11142,11304,11548,12196,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,11599,11882,11885,11922,11961,11994,12134,12174,12180,12264,12267,12284,12341,12347,12353,3252,10507,10537,11099,11648,12281,3293,3285,3710,3648,10194,11469,11497,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,11688,3208,10682,10753,11498,11653,11854,12065,3670,4023,4483,3679,3718,4464,4467,3164,3168,4466,4465,3687,3509,4123,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,11181,3907,3799,11178,11522,11526,11587,12204,12212,3637,10793,10799,10816,11781,11997,3494,11033,12131,12138,12209,12255,3976,3639,10884,11045,11075,11086,12208,12249,3568,3466,10469,10472,10540,10709,4502,11463,4503,10598,10691,11018,11168,11301,12068,12075,12119,4087,10667,12111,3983,3669,4500,10167,10170,10501,10504,11340,11527,4501,11443,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348,6351,6352,6354,6356,6357,6358,6360,6362,6365,6370,6371,6373,6374,6380,6382,6387,6425,6428,6441,6443,6445,6446,6447,6480,6485,6487,6492,6493,6501,6505,6518,6541,6542,6544,6545,6556,6560,6573,6579,6582,6584,6633,6634,6635,6640,6643,6672,6674,6676,6678,6683,6688,6701,6710,6743,6744,6745,6759,6760,6762,6763,6781,6782,6797,6818,6819,6825,6846,6859,6861,6863,6865,6866,6867,6874,6892,6906,6907,6912,6913,6920,6921,6923,6925,6952,6953,6965,6972,6973,6974,6976,7005,7014,7025,7034,7047,7048,7053,7055,7056,7062,7071,7085,7119,7121,7136,7146,7187,7192,7217,7262,7295,7309,7325,7356,7357,7360,7361,7385,7408,7425,7428,7429,7439,7459,7461,7463,7465,7466,7467,7514,7518,7519,7549,7551,7552,7553,7558,7580,7599,7609,7619,7631,7632,7634,7654,7658,7663,7664,7687,7705,7753,7754,7796,7804,7826,7843,7844,7906,7907,7934,7963,7974,7976,7984,7993,7997,8031,8037,8044,8058,8081,8104,8148,8178,8190,8207,8210,8245,8266,8331,8332,8336,8338,8356,8447,8448,8449,8450,8480,8507,8532,8574,8592,8647,8690,8693,8706,8713,8748,8795,8796,8813,8814,8958,8977,8987,9009,9011,9014,9018,9021,9022,9036,9054,9060,9072,9120,9139,9192,9193,9199,9235,9259,9264,9299,9306,9310,9313,9314,9329,9343,9352,9363,9376,9377,9381,9383,9409,9527,9569,9611,9656,9723,9774,9775,9834])). % 168.30/168.13 cnf(12368,plain, % 168.30/168.13 (P22(f317(f317(f319(x123681),x123682),f233(f858(x123681,a842))))), % 168.30/168.13 inference(rename_variables,[],[3349])). % 168.30/168.13 cnf(12375,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x123751,a842)),x123752),x123752))), % 168.30/168.13 inference(rename_variables,[],[3494])). % 168.30/168.13 cnf(12378,plain, % 168.30/168.13 (~P22(f317(f317(f319(x123781),x123782),f188(f858(x123781,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12381,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),f2(a1)),f317(f317(f238(a1),f317(f84(a1),x123811)),x123812)))), % 168.30/168.13 inference(rename_variables,[],[3669])). % 168.30/168.13 cnf(12384,plain, % 168.30/168.13 (E(f37(x123841,x123842,x123843,x123844,x123845,x123846,x123847,x123848,x123849,a23),x123842)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12386,plain, % 168.30/168.13 (E(f37(x123861,x123862,x123863,x123864,x123865,x123866,x123867,x123868,x123869,a23),x123862)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12396,plain, % 168.30/168.13 (P49(x123961,x123961,f235(x123961,x123962))), % 168.30/168.13 inference(rename_variables,[],[3157])). % 168.30/168.13 cnf(12405,plain, % 168.30/168.13 (E(f37(x124051,x124052,x124053,x124054,x124055,x124056,x124057,x124058,x124059,a23),x124052)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12407,plain, % 168.30/168.13 (P37(x124071,f147(x124071,x124072))), % 168.30/168.13 inference(rename_variables,[],[3061])). % 168.30/168.13 cnf(12411,plain, % 168.30/168.13 (E(f37(x124111,x124112,x124113,x124114,x124115,x124116,x124117,x124118,x124119,a23),x124112)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12413,plain, % 168.30/168.13 (E(f37(x124131,x124132,x124133,x124134,x124135,x124136,x124137,x124138,x124139,a23),x124132)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12415,plain, % 168.30/168.13 (E(f37(x124151,x124152,x124153,x124154,x124155,x124156,x124157,x124158,x124159,a23),x124152)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12419,plain, % 168.30/168.13 (E(f37(x124191,x124192,x124193,x124194,x124195,x124196,x124197,x124198,x124199,a23),x124192)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12421,plain, % 168.30/168.13 (P50(x124211,f188(f858(x124211,a842)),x124212)), % 168.30/168.13 inference(rename_variables,[],[3206])). % 168.30/168.13 cnf(12425,plain, % 168.30/168.13 (P19(x124251,x124251,f5(x124251),x124252)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12427,plain, % 168.30/168.13 (P19(x124271,x124271,f5(x124271),x124272)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12437,plain, % 168.30/168.13 (P33(x124371,x124372,f125(x124371),f125(x124371))), % 168.30/168.13 inference(rename_variables,[],[3441])). % 168.30/168.13 cnf(12439,plain, % 168.30/168.13 (P33(x124391,x124392,f125(x124391),f125(x124391))), % 168.30/168.13 inference(rename_variables,[],[3441])). % 168.30/168.13 cnf(12443,plain, % 168.30/168.13 (P32(x124431,x124432,x124433,f178(x124431,x124432,x124434,x124433))), % 168.30/168.13 inference(rename_variables,[],[3758])). % 168.30/168.13 cnf(12445,plain, % 168.30/168.13 (P32(x124451,x124452,x124453,f178(x124451,x124452,x124454,x124453))), % 168.30/168.13 inference(rename_variables,[],[3758])). % 168.30/168.13 cnf(12447,plain, % 168.30/168.13 (P32(x124471,x124472,x124473,f178(x124471,x124472,x124474,x124473))), % 168.30/168.13 inference(rename_variables,[],[3758])). % 168.30/168.13 cnf(12449,plain, % 168.30/168.13 (P32(x124491,x124492,x124493,f178(x124491,x124492,x124494,x124493))), % 168.30/168.13 inference(rename_variables,[],[3758])). % 168.30/168.13 cnf(12451,plain, % 168.30/168.13 (P18(x124511,x124512,f188(f858(f848(x124511),a842)))), % 168.30/168.13 inference(rename_variables,[],[3244])). % 168.30/168.13 cnf(12456,plain, % 168.30/168.13 (E(f37(x124561,x124562,x124563,x124564,x124565,x124566,x124567,x124568,x124569,a23),x124562)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12459,plain, % 168.30/168.13 (E(f188(f858(f857(x124591,x124591),a842)),f235(x124591,f188(f858(x124591,a842))))), % 168.30/168.13 inference(rename_variables,[],[3261])). % 168.30/168.13 cnf(12461,plain, % 168.30/168.13 (P11(x124611,f858(x124611,a842),f286(x124611))), % 168.30/168.13 inference(rename_variables,[],[3161])). % 168.30/168.13 cnf(12467,plain, % 168.30/168.13 (E(f37(x124671,x124672,x124673,x124674,x124675,x124676,x124677,x124678,x124679,a23),x124672)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12469,plain, % 168.30/168.13 (P38(x124691,f191(x124691))), % 168.30/168.13 inference(rename_variables,[],[3018])). % 168.30/168.13 cnf(12473,plain, % 168.30/168.13 (P45(x124731,x124732,f235(x124731,x124732))), % 168.30/168.13 inference(rename_variables,[],[3156])). % 168.30/168.13 cnf(12475,plain, % 168.30/168.13 (P45(x124751,x124752,f235(x124751,x124752))), % 168.30/168.13 inference(rename_variables,[],[3156])). % 168.30/168.13 cnf(12479,plain, % 168.30/168.13 (P41(x124791,x124792,x124793,x124794,f188(f858(x124791,a842)),x124794)), % 168.30/168.13 inference(rename_variables,[],[4147])). % 168.30/168.13 cnf(12482,plain, % 168.30/168.13 (P41(x124821,x124822,x124823,x124824,f188(f858(x124821,a842)),x124824)), % 168.30/168.13 inference(rename_variables,[],[4147])). % 168.30/168.13 cnf(12486,plain, % 168.30/168.13 (P30(x124861,f2(a849),f317(f317(f317(f100(x124861),x124862),f317(a29,x124863)),x124864))), % 168.30/168.13 inference(rename_variables,[],[3566])). % 168.30/168.13 cnf(12496,plain, % 168.30/168.13 (E(f37(x124961,x124962,x124963,x124964,x124965,x124966,x124967,x124968,x124969,a23),x124962)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12498,plain, % 168.30/168.13 (E(f37(x124981,x124982,x124983,x124984,x124985,x124986,x124987,x124988,x124989,a23),x124982)), % 168.30/168.13 inference(rename_variables,[],[4358])). % 168.30/168.13 cnf(12511,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x125111),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12520,plain, % 168.30/168.13 (~P22(f317(f317(f226(a1),f317(f112(a1),x125201)),f317(f88(a1),f317(f112(a1),x125202))))), % 168.30/168.13 inference(rename_variables,[],[4498])). % 168.30/168.13 cnf(12530,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x125301),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12533,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x125331),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12536,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x125361,x125362)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12539,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x125391,x125392)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12542,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x125421,x125422)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12545,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x125451,x125452)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12552,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),f317(f88(a1),f317(f112(a1),x125521))),f317(f112(a1),x125522)))), % 168.30/168.13 inference(rename_variables,[],[3670])). % 168.30/168.13 cnf(12554,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),f2(a1)),f317(f115(a1),f2(a1))))), % 168.30/168.13 inference(scs_inference,[],[4401,3434,10924,11975,12081,12167,12205,12213,12274,12425,3441,12043,12437,12439,3442,12106,3497,3758,10819,12443,12445,12447,3156,12473,12475,3157,12396,4431,4147,12479,12482,3161,12461,2996,3018,12469,3061,12407,4382,3543,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,11619,11953,12143,12330,12384,12386,12405,12411,12413,12415,12419,12456,12467,12496,12498,4359,11207,3496,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,11728,11756,11776,11824,11938,11956,12023,12039,12197,4405,10311,10402,3245,3206,12421,2786,2787,2798,2799,2807,2810,2814,2815,2816,2821,2822,2832,2834,2839,2840,2843,2844,2846,2848,2850,2851,2857,2861,2867,2868,2870,2871,2878,2902,2906,2930,2932,2936,2937,2939,2959,2967,3060,4380,3533,3169,3229,3924,3141,4371,3120,11475,12226,12230,12234,3129,3241,3651,3965,3021,4400,4419,4461,10852,11150,11153,3714,11242,3244,12451,3090,3052,10151,3566,12486,3046,3865,3573,4345,3029,3008,3034,4068,11036,3067,3200,11718,11927,12062,12277,12350,3248,10677,12040,3118,3119,3139,10355,3297,4496,10283,3830,4421,10148,10308,12193,12227,4430,12201,3176,11571,4486,3298,3519,3261,12459,3085,3086,10213,10510,3355,3077,2999,3104,11233,3978,12216,12342,3832,10858,10991,11048,12177,12183,12288,12291,12317,4505,10780,10996,11107,11126,11156,11162,12125,4506,10898,10999,11110,4507,11002,4508,11062,4509,3103,3396,12084,12122,12200,3558,4266,4267,4418,11222,3500,3704,4103,3752,3382,3632,3258,10232,10348,10419,10463,10466,10513,10595,10842,11752,11796,11873,11934,12017,12020,3643,11466,3171,3272,3463,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,11876,11879,11966,12128,12220,12511,12530,4492,11343,11376,11413,11446,3630,3404,3405,12536,12539,12542,3782,3215,3216,3189,4473,4415,3584,4118,3900,3388,4493,3972,11121,3518,3228,11590,11593,12047,12147,3941,3898,11745,12093,3842,10674,11917,11941,12100,3893,10864,11972,12046,12099,12146,3559,11755,11904,11980,12030,3899,3575,10861,10934,11015,11081,11937,11998,12241,12314,12327,4497,10622,11007,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,11727,11991,12150,3187,10582,10625,10628,10661,10685,10722,10760,10796,11799,11802,11805,11808,12005,12008,12011,12014,12089,12252,3188,10324,10525,10601,10725,11385,11622,11635,11731,11742,11761,11766,11784,11811,11827,11844,3266,11960,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,11700,11775,11795,11814,11823,11888,11891,11894,11897,11967,12054,12057,12153,12156,12219,12245,12280,3349,10480,10733,10777,11070,11142,11304,11548,12196,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,11599,11882,11885,11922,11961,11994,12134,12174,12180,12264,12267,12284,12341,12347,12353,12358,3252,10507,10537,11099,11648,12281,3293,3285,3710,3648,10194,11469,11497,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,11688,3208,10682,10753,11498,11653,11854,12065,3670,11596,4023,4483,3679,3718,4464,4467,4468,3164,3168,4466,4465,3687,3509,4123,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,11181,3907,3799,11178,11522,11526,11587,12204,12212,3637,10793,10799,10816,11781,11997,3494,11033,12131,12138,12209,12255,12263,3976,3639,10884,11045,11075,11086,12208,12249,3568,11583,3466,10469,10472,10540,10709,3465,4502,11463,4498,12520,4503,10598,10691,11018,11168,11301,12068,12075,12119,12311,4087,10667,12111,3983,3669,4500,10167,10170,10501,10504,11340,11527,4501,11443,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6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% 168.30/168.13 cnf(12557,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x125571),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12558,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x125581),x125581))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12565,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x125651),f317(a124,x125651)))), % 168.30/168.13 inference(rename_variables,[],[3258])). % 168.30/168.13 cnf(12570,plain, % 168.30/168.13 (P22(f317(f317(f319(x125701),f317(x125702,x125703)),f317(f287(x125704,x125701,x125702),f233(f858(x125704,a842)))))), % 168.30/168.13 inference(rename_variables,[],[3799])). % 168.30/168.13 cnf(12571,plain, % 168.30/168.13 (~E(f317(a124,x125711),f2(a849))), % 168.30/168.13 inference(rename_variables,[],[4398])). % 168.30/168.13 cnf(12576,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x125761),x125761))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12579,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x125791,x125792)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12582,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x125821,x125822)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12585,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x125851),x125851))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12586,plain, % 168.30/168.13 (~E(f317(a124,x125861),f2(a849))), % 168.30/168.13 inference(rename_variables,[],[4398])). % 168.30/168.13 cnf(12603,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),f55(a849,x126031,x126032)),x126031))), % 168.30/168.13 inference(rename_variables,[],[3648])). % 168.30/168.13 cnf(12608,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x126081),f317(a124,x126081)))), % 168.30/168.13 inference(rename_variables,[],[3258])). % 168.30/168.13 cnf(12611,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x126111),f317(a124,x126111)))), % 168.30/168.13 inference(rename_variables,[],[3258])). % 168.30/168.13 cnf(12612,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x126121),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12621,plain, % 168.30/168.13 (~P22(f317(f317(f226(a1),f317(f112(a1),x126211)),f2(a1)))), % 168.30/168.13 inference(rename_variables,[],[4492])). % 168.30/168.13 cnf(12622,plain, % 168.30/168.13 (P22(f317(f233(f858(x126221,a842)),x126222))), % 168.30/168.13 inference(rename_variables,[],[3252])). % 168.30/168.13 cnf(12625,plain, % 168.30/168.13 (~P22(f317(f317(f226(a1),f317(f112(a1),x126251)),f2(a1)))), % 168.30/168.13 inference(rename_variables,[],[4492])). % 168.30/168.13 cnf(12626,plain, % 168.30/168.13 (P22(f317(f233(f858(x126261,a842)),x126262))), % 168.30/168.13 inference(rename_variables,[],[3252])). % 168.30/168.13 cnf(12629,plain, % 168.30/168.13 (P22(f317(f233(f858(x126291,a842)),x126292))), % 168.30/168.13 inference(rename_variables,[],[3252])). % 168.30/168.13 cnf(12646,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),f2(a849)),x126461))), % 168.30/168.13 inference(rename_variables,[],[3208])). % 168.30/168.13 cnf(12649,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x126491),f317(a124,x126491)))), % 168.30/168.13 inference(rename_variables,[],[3258])). % 168.30/168.13 cnf(12650,plain, % 168.30/168.13 (~E(f317(a124,x126501),x126501)), % 168.30/168.13 inference(rename_variables,[],[4386])). % 168.30/168.13 cnf(12653,plain, % 168.30/168.13 (~P22(f317(f317(f319(x126531),x126532),f188(f858(x126531,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12656,plain, % 168.30/168.13 (~P22(f317(f317(f319(x126561),x126562),f188(f858(x126561,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12659,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x126591),x126591))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12666,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x126661),x126661))), % 168.30/168.13 inference(rename_variables,[],[4472])). % 168.30/168.13 cnf(12667,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x126671),f317(a124,x126671)))), % 168.30/168.13 inference(rename_variables,[],[3258])). % 168.30/168.13 cnf(12670,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x126701),x126701))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12675,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x126751),x126751))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12678,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x126781),x126781))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12681,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x126811),x126811))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12684,plain, % 168.30/168.13 (E(f317(f317(f21(f858(x126841,a842)),f188(f858(x126841,a842))),x126842),f188(f858(x126841,a842)))), % 168.30/168.13 inference(rename_variables,[],[3468])). % 168.30/168.13 cnf(12685,plain, % 168.30/168.13 (P22(f317(f71(x126851),f188(f858(x126851,a842))))), % 168.30/168.13 inference(rename_variables,[],[3266])). % 168.30/168.13 cnf(12688,plain, % 168.30/168.13 (E(f317(f317(f21(f858(x126881,a842)),f188(f858(x126881,a842))),x126882),f188(f858(x126881,a842)))), % 168.30/168.13 inference(rename_variables,[],[3468])). % 168.30/168.13 cnf(12689,plain, % 168.30/168.13 (P22(f317(f71(x126891),f188(f858(x126891,a842))))), % 168.30/168.13 inference(rename_variables,[],[3266])). % 168.30/168.13 cnf(12692,plain, % 168.30/168.13 (E(f317(f317(f21(f858(x126921,a842)),f188(f858(x126921,a842))),x126922),f188(f858(x126921,a842)))), % 168.30/168.13 inference(rename_variables,[],[3468])). % 168.30/168.13 cnf(12693,plain, % 168.30/168.13 (P22(f317(f71(x126931),f188(f858(x126931,a842))))), % 168.30/168.13 inference(rename_variables,[],[3266])). % 168.30/168.13 cnf(12696,plain, % 168.30/168.13 (E(f317(f317(f21(f858(x126961,a842)),f188(f858(x126961,a842))),x126962),f188(f858(x126961,a842)))), % 168.30/168.13 inference(rename_variables,[],[3468])). % 168.30/168.13 cnf(12697,plain, % 168.30/168.13 (P22(f317(f71(x126971),f188(f858(x126971,a842))))), % 168.30/168.13 inference(rename_variables,[],[3266])). % 168.30/168.13 cnf(12701,plain, % 168.30/168.13 (E(f38(x127011,x127012,x127013,x127014,x127015,x127016,x127017,x127018,x127019,a23),x127012)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(12706,plain, % 168.30/168.13 (E(f317(f317(f21(f858(x127061,a842)),f188(f858(x127061,a842))),x127062),f188(f858(x127061,a842)))), % 168.30/168.13 inference(rename_variables,[],[3468])). % 168.30/168.13 cnf(12707,plain, % 168.30/168.13 (P22(f317(f71(x127071),f188(f858(x127071,a842))))), % 168.30/168.13 inference(rename_variables,[],[3266])). % 168.30/168.13 cnf(12711,plain, % 168.30/168.13 (P22(f317(f71(x127111),f188(f858(x127111,a842))))), % 168.30/168.13 inference(rename_variables,[],[3266])). % 168.30/168.13 cnf(12714,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x127141),x127141))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12718,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x127181),x127181))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12725,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x127251),x127251))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12738,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x127381),x127381))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12747,plain, % 168.30/168.13 (~P22(f317(f317(f319(x127471),x127472),f188(f858(x127471,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12758,plain, % 168.30/168.13 (P22(f317(f317(f319(x127581),x127582),f233(f858(x127581,a842))))), % 168.30/168.13 inference(rename_variables,[],[3349])). % 168.30/168.13 cnf(12762,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x127621,a842)),x127622),f233(f858(x127621,a842))))), % 168.30/168.13 inference(rename_variables,[],[3575])). % 168.30/168.13 cnf(12765,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x127651,a842)),f317(f166(x127651),f317(f130(x127651,x127652),x127653))),f317(f166(x127651),x127653)))), % 168.30/168.13 inference(rename_variables,[],[3842])). % 168.30/168.13 cnf(12771,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x127711),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12772,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x127721),x127721))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12776,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x127761),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12777,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x127771),x127771))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12782,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x127821,a842)),x127822),f233(f858(x127821,a842))))), % 168.30/168.13 inference(rename_variables,[],[3575])). % 168.30/168.13 cnf(12787,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x127871),x127871))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12794,plain, % 168.30/168.13 (E(f317(f317(f16(x127941,x127942),x127943),x127944),x127943)), % 168.30/168.13 inference(rename_variables,[],[3176])). % 168.30/168.13 cnf(12797,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x127971,a842)),f317(f166(x127971),f164(x127971,x127972,x127973))),f317(f166(x127971),x127973)))), % 168.30/168.13 inference(rename_variables,[],[3893])). % 168.30/168.13 cnf(12801,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x128011),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12802,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x128021),x128021))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12806,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),x128061),f2(a849)))), % 168.30/168.13 inference(rename_variables,[],[4476])). % 168.30/168.13 cnf(12807,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x128071),x128071))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12809,plain, % 168.30/168.13 (~P22(f317(f317(f225(f858(a849,a842)),f279(a849,f317(a124,x128091),f317(a124,x128091))),f279(a849,x128092,x128091)))), % 168.30/168.13 inference(scs_inference,[],[4401,3434,10924,11975,12081,12167,12205,12213,12274,12425,3441,12043,12437,12439,3442,12106,3497,3758,10819,12443,12445,12447,3156,12473,12475,3157,12396,4431,4147,12479,12482,3161,12461,2996,3018,12469,3061,12407,4382,3543,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,11619,11953,12143,12330,12384,12386,12405,12411,12413,12415,12419,12456,12467,12496,12498,4359,11207,11211,3496,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,11728,11756,11776,11824,11938,11956,12023,12039,12197,12246,4405,10311,10402,3245,3206,12421,4398,12571,2786,2787,2798,2799,2807,2810,2814,2815,2816,2821,2822,2832,2834,2839,2840,2843,2844,2846,2848,2850,2851,2857,2858,2861,2867,2868,2870,2871,2875,2878,2902,2906,2908,2917,2923,2930,2931,2932,2933,2936,2937,2939,2959,2967,3060,4380,3533,3169,3229,3924,3141,3520,3773,4371,3120,11475,12226,12230,12234,3129,3241,3651,3965,3021,4400,4419,4461,10852,11150,11153,3714,11242,3244,12451,3090,3052,10151,3566,12486,3046,3865,3573,4345,3029,3008,3034,4068,11036,3067,3200,11718,11927,12062,12277,12350,3248,10677,12040,3118,3119,3139,10355,3297,4496,10283,3830,4421,10148,10308,12193,12227,4430,12201,3176,11571,11574,4486,3298,3519,3261,12459,3085,3086,10213,10510,3355,3077,2999,3104,11233,3978,12216,12342,3832,10858,10991,11048,12177,12183,12288,12291,12317,4505,10780,10996,11107,11126,11156,11162,12125,4506,10898,10999,11110,4507,11002,4508,11062,4509,3103,3396,12084,12122,12200,3558,4266,4267,4418,11222,3500,3536,3704,4103,3468,12684,12688,12692,12696,12706,3752,12078,3382,3632,3258,10232,10348,10419,10463,10466,10513,10595,10842,11752,11796,11873,11934,12017,12020,12321,12565,12608,12611,12649,12667,3643,11466,3171,3272,3463,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,11876,11879,11966,12128,12220,12511,12530,12533,12557,12612,12771,12776,12801,4492,11343,11376,11413,11446,12621,12625,3630,3404,3405,12536,12539,12542,12545,12579,3782,3215,3216,3189,4473,3084,4415,3584,4118,3900,3388,4493,3972,11121,3518,3228,11590,11593,12047,12147,12301,3941,3898,11745,12093,3842,10674,11917,11941,12100,12324,3893,10864,11972,12046,12099,12146,3559,11755,11904,11980,12030,3862,3899,3575,10861,10934,11015,11081,11937,11998,12241,12314,12327,12762,4497,10622,11007,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,11727,11991,12150,3187,10582,10625,10628,10661,10685,10722,10760,10796,11799,11802,11805,11808,12005,12008,12011,12014,12089,12252,12294,12558,12585,12659,12670,12675,12678,12681,12714,12725,12787,3188,10324,10525,10601,10725,11385,11622,11635,11731,11742,11761,11766,11784,11811,11827,11844,11849,12576,12718,12738,12772,12777,12802,3266,11960,12685,12689,12693,12697,12707,12711,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,11700,11775,11795,11814,11823,11888,11891,11894,11897,11967,12054,12057,12153,12156,12219,12245,12280,12365,12666,3349,10480,10733,10777,11070,11142,11304,11548,12196,12368,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,11599,11882,11885,11922,11961,11994,12134,12174,12180,12264,12267,12284,12341,12347,12353,12358,12378,12653,12656,3252,10507,10537,11099,11648,12281,12295,12622,12626,12629,3293,3285,3710,3648,10194,11469,11497,12603,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,11688,3208,10682,10753,11498,11653,11854,12065,12090,3670,11596,12552,4023,3410,4483,3679,3718,4464,4467,4468,3164,3168,4466,4465,3687,3509,4123,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,11181,3907,12114,3799,11178,11522,11526,11587,12204,12212,12287,3637,10793,10799,10816,11781,11997,3494,11033,12131,12138,12209,12255,12263,3976,3639,10884,11045,11075,11086,12208,12249,3568,11583,3466,10469,10472,10540,10709,3465,4502,11463,4498,12520,4503,10598,10691,11018,11168,11301,12068,12075,12119,12311,4087,10667,12111,3983,3669,12381,4500,10167,10170,10501,10504,11340,11527,12320,4501,11443,11536,3641,10475,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348,6351,6352,6354,6356,6357,6358,6360,6362,6365,6370,6371,6373,6374,6380,6382,6387,6425,6428,6441,6443,6445,6446,6447,6480,6485,6487,6492,6493,6501,6505,6518,6541,6542,6544,6545,6556,6560,6573,6579,6582,6584,6633,6634,6635,6640,6643,6672,6674,6676,6678,6683,6688,6701,6710,6743,6744,6745,6759,6760,6762,6763,6781,6782,6797,6818,6819,6825,6846,6859,6861,6863,6865,6866,6867,6874,6892,6906,6907,6912,6913,6920,6921,6923,6925,6952,6953,6965,6972,6973,6974,6976,7005,7014,7025,7034,7047,7048,7053,7055,7056,7062,7071,7085,7119,7121,7136,7146,7187,7192,7217,7262,7295,7309,7325,7356,7357,7360,7361,7385,7408,7425,7428,7429,7439,7459,7461,7463,7465,7466,7467,7514,7518,7519,7549,7551,7552,7553,7558,7580,7599,7609,7619,7631,7632,7634,7654,7658,7663,7664,7687,7705,7753,7754,7796,7804,7826,7843,7844,7906,7907,7934,7963,7974,7976,7984,7993,7997,8031,8037,8044,8058,8081,8104,8148,8178,8190,8207,8210,8245,8266,8331,8332,8336,8338,8356,8447,8448,8449,8450,8480,8507,8532,8574,8592,8647,8690,8693,8706,8713,8748,8795,8796,8813,8814,8958,8977,8987,9009,9011,9014,9018,9021,9022,9036,9054,9060,9072,9120,9139,9192,9193,9199,9235,9259,9264,9299,9306,9310,9313,9314,9329,9343,9352,9363,9376,9377,9381,9383,9409,9527,9569,9611,9656,9723,9774,9775,9834,9903,9976,9991,9996,3,2544,2546,2547,2548,2550,2555,2556,2557,2558,2559,2560,2568,2571,2575,2577,2578,2579,2583,2585,2591,2592,2600,2601,2602,2607,2608,2609,2610,2614,2615,2617,2618,2624,2626,2627,2633,2634,2635,2636,2643,2644,2645,2651,2666,2668,2671,2673,2676,2685,2689,2690,2697,2698,2699,2709,2712,2713,2714,2717,2718,2719,2721,2723,2726,2728,2729,2746,2747,2748,2750,2751,2765,5218,5395,5396,5397,5471,5517,5546,5574,5650,5652,5658,5715,5716,5717,5718,5724,5752,5883,5924,5933,5952,5987,6020,6024,6169,6174,6209,6210,6226,6229,6231,6238,6239,6240,6241,6242,6243,6244,6245,6328,6394,6395,6479,6512,6513,6553,6554,6689,6771,6772,6776,6798,6823,6831,6833,6882,6910,6911,6928,6929,6964,7008,7009,7108,7168,7169,7170,7171,7184,7211,7267,7268,7276,7285,7286,7298,7328,7329,7330,7331,7474,7476,7477,7478,7484,7485,7695,7701,7702,7712,7752,7822,7862,7918,7939,7940,7955,8016,8118,8188,8189,8191,8228,8291,8292,8387])). % 168.30/168.13 cnf(12810,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x128101),x128101))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12813,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),x128131),x128131))), % 168.30/168.13 inference(rename_variables,[],[3187])). % 168.30/168.13 cnf(12816,plain, % 168.30/168.13 (~P22(f317(f317(f225(a849),f317(a124,x128161)),x128161))), % 168.30/168.13 inference(rename_variables,[],[4485])). % 168.30/168.13 cnf(12822,plain, % 168.30/168.13 (P22(f317(f317(f319(x128221),f317(x128222,x128223)),f317(f287(x128224,x128221,x128222),f233(f858(x128224,a842)))))), % 168.30/168.13 inference(rename_variables,[],[3799])). % 168.30/168.13 cnf(12823,plain, % 168.30/168.13 (P19(x128231,x128231,f5(x128231),x128232)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12827,plain, % 168.30/168.13 (P22(f317(f317(f319(x128271),x128272),f233(f858(x128271,a842))))), % 168.30/168.13 inference(rename_variables,[],[3349])). % 168.30/168.13 cnf(12828,plain, % 168.30/168.13 (~P22(f317(f317(f319(x128281),x128282),f188(f858(x128281,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12832,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x128321,a842)),x128322),f233(f858(x128321,a842))))), % 168.30/168.13 inference(rename_variables,[],[3575])). % 168.30/168.13 cnf(12833,plain, % 168.30/168.13 (P19(x128331,x128331,f5(x128331),x128332)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12837,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x128371,a842)),x128372),f233(f858(x128371,a842))))), % 168.30/168.13 inference(rename_variables,[],[3575])). % 168.30/168.13 cnf(12838,plain, % 168.30/168.13 (P19(x128381,x128381,f5(x128381),x128382)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12845,plain, % 168.30/168.13 (P19(x128451,x128451,f5(x128451),x128452)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12848,plain, % 168.30/168.13 (~P22(f317(f317(f226(f858(x128481,a842)),x128482),f188(f858(x128481,a842))))), % 168.30/168.13 inference(rename_variables,[],[4497])). % 168.30/168.13 cnf(12851,plain, % 168.30/168.13 (P19(x128511,x128511,f5(x128511),x128512)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12854,plain, % 168.30/168.13 (P19(x128541,x128541,f5(x128541),x128542)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12865,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x128651,a842)),f188(f858(x128651,a842))),x128652))), % 168.30/168.13 inference(rename_variables,[],[3639])). % 168.30/168.13 cnf(12869,plain, % 168.30/168.13 (E(f38(x128691,x128692,x128693,x128694,x128695,x128696,x128697,x128698,x128699,a23),x128692)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(12873,plain, % 168.30/168.13 (~P22(f317(f317(f319(x128731),x128732),f188(f858(x128731,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12876,plain, % 168.30/168.13 (~P22(f317(f317(f226(a1),f317(f112(a1),x128761)),f2(a1)))), % 168.30/168.13 inference(rename_variables,[],[4492])). % 168.30/168.13 cnf(12877,plain, % 168.30/168.13 (~E(f317(a124,x128771),x128771)), % 168.30/168.13 inference(rename_variables,[],[4386])). % 168.30/168.13 cnf(12881,plain, % 168.30/168.13 (P22(f317(f317(f319(x128811),f317(x128812,x128813)),f317(f287(x128814,x128811,x128812),f233(f858(x128814,a842)))))), % 168.30/168.13 inference(rename_variables,[],[3799])). % 168.30/168.13 cnf(12882,plain, % 168.30/168.13 (P19(x128821,x128821,f5(x128821),x128822)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12892,plain, % 168.30/168.13 (~P22(f317(f317(f319(x128921),x128922),f188(f858(x128921,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12895,plain, % 168.30/168.13 (~P22(f317(f317(f319(x128951),x128952),f188(f858(x128951,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12898,plain, % 168.30/168.13 (E(f38(x128981,x128982,x128983,x128984,x128985,x128986,x128987,x128988,x128989,a23),x128982)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(12900,plain, % 168.30/168.13 (~E(f317(a124,x129001),x129001)), % 168.30/168.13 inference(rename_variables,[],[4386])). % 168.30/168.13 cnf(12904,plain, % 168.30/168.13 (E(f317(f317(f16(x129041,x129042),x129043),x129044),x129043)), % 168.30/168.13 inference(rename_variables,[],[3176])). % 168.30/168.13 cnf(12907,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x129071),f317(a124,x129071)))), % 168.30/168.13 inference(rename_variables,[],[3258])). % 168.30/168.13 cnf(12908,plain, % 168.30/168.13 (~E(f317(a124,x129081),x129081)), % 168.30/168.13 inference(rename_variables,[],[4386])). % 168.30/168.13 cnf(12911,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x129111),f317(a124,f317(f317(f89(a849),x129112),x129111))))), % 168.30/168.13 inference(rename_variables,[],[3641])). % 168.30/168.13 cnf(12912,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),x129121),f317(a124,x129121)))), % 168.30/168.13 inference(rename_variables,[],[3258])). % 168.30/168.13 cnf(12921,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),f2(a1)),f317(f112(a1),x129211)))), % 168.30/168.13 inference(rename_variables,[],[3293])). % 168.30/168.13 cnf(12924,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),f2(a849)),x129241))), % 168.30/168.13 inference(rename_variables,[],[3208])). % 168.30/168.13 cnf(12928,plain, % 168.30/168.13 (~E(f317(a124,x129281),f2(a849))), % 168.30/168.13 inference(rename_variables,[],[4398])). % 168.30/168.13 cnf(12933,plain, % 168.30/168.13 (~P22(f317(f317(f319(x129331),x129332),f188(f858(x129331,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12936,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x129361,x129362)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12937,plain, % 168.30/168.13 (E(f317(f317(f224(a849),f317(a124,x129371)),f317(a124,x129372)),f317(a124,f317(f317(f224(a849),x129371),x129372)))), % 168.30/168.13 inference(rename_variables,[],[3367])). % 168.30/168.13 cnf(12940,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x129401,x129402)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12941,plain, % 168.30/168.13 (E(f317(f317(f223(a849),f317(a124,x129411)),f317(a124,x129412)),f317(a124,f317(f317(f223(a849),x129411),x129412)))), % 168.30/168.13 inference(rename_variables,[],[3366])). % 168.30/168.13 cnf(12944,plain, % 168.30/168.13 (P22(f317(f71(a849),f281(a849,x129441,x129442)))), % 168.30/168.13 inference(rename_variables,[],[3405])). % 168.30/168.13 cnf(12952,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x129521,a842)),f317(f166(x129521),f317(f130(x129521,x129522),x129523))),f317(f166(x129521),x129523)))), % 168.30/168.13 inference(rename_variables,[],[3842])). % 168.30/168.13 cnf(12953,plain, % 168.30/168.13 (E(f317(f317(f16(x129531,x129532),x129533),x129534),x129533)), % 168.30/168.13 inference(rename_variables,[],[3176])). % 168.30/168.13 cnf(12956,plain, % 168.30/168.13 (P22(f317(f317(f225(f858(x129561,a842)),f317(f166(x129561),f317(f317(f167(x129561),x129562),x129563))),f317(f166(x129561),x129563)))), % 168.30/168.13 inference(rename_variables,[],[3888])). % 168.30/168.13 cnf(12957,plain, % 168.30/168.13 (E(f317(f317(f16(x129571,x129572),x129573),x129574),x129573)), % 168.30/168.13 inference(rename_variables,[],[3176])). % 168.30/168.13 cnf(12961,plain, % 168.30/168.13 (E(f317(f317(f16(x129611,x129612),x129613),x129614),x129613)), % 168.30/168.13 inference(rename_variables,[],[3176])). % 168.30/168.13 cnf(12974,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),f2(a1)),f317(f112(a1),x129741)))), % 168.30/168.13 inference(rename_variables,[],[3293])). % 168.30/168.13 cnf(12977,plain, % 168.30/168.13 (~P22(f317(f317(f319(x129771),x129772),f188(f858(x129771,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(12978,plain, % 168.30/168.13 (E(f38(x129781,x129782,x129783,x129784,x129785,x129786,x129787,x129788,x129789,a23),x129782)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(12979,plain, % 168.30/168.13 (P19(x129791,x129791,f5(x129791),x129792)), % 168.30/168.13 inference(rename_variables,[],[3434])). % 168.30/168.13 cnf(12983,plain, % 168.30/168.13 (E(f38(x129831,x129832,x129833,x129834,x129835,x129836,x129837,x129838,x129839,a23),x129832)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(12989,plain, % 168.30/168.13 (E(f38(x129891,x129892,x129893,x129894,x129895,x129896,x129897,x129898,x129899,a23),x129892)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(12990,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x129901),x129901))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12993,plain, % 168.30/168.13 (E(f38(x129931,x129932,x129933,x129934,x129935,x129936,x129937,x129938,x129939,a23),x129932)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(12994,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x129941),x129941))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(12997,plain, % 168.30/168.13 (E(f38(x129971,x129972,x129973,x129974,x129975,x129976,x129977,x129978,x129979,a23),x129972)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(12998,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x129981),x129981))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(13001,plain, % 168.30/168.13 (P22(f317(f317(f225(a1),x130011),x130011))), % 168.30/168.13 inference(rename_variables,[],[3188])). % 168.30/168.13 cnf(13002,plain, % 168.30/168.13 (E(f38(x130021,x130022,x130023,x130024,x130025,x130026,x130027,x130028,x130029,a23),x130022)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(13013,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),f2(a849)),x130131))), % 168.30/168.13 inference(rename_variables,[],[3208])). % 168.30/168.13 cnf(13014,plain, % 168.30/168.13 (P22(f317(f317(f226(a849),f2(a849)),f317(a124,x130141)))), % 168.30/168.13 inference(rename_variables,[],[3272])). % 168.30/168.13 cnf(13015,plain, % 168.30/168.13 (E(f38(x130151,x130152,x130153,x130154,x130155,x130156,x130157,x130158,x130159,a23),x130152)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(13093,plain, % 168.30/168.13 (P22(f317(f317(f226(a1),f2(a1)),f317(f84(a1),f87(a1))))), % 168.30/168.13 inference(scs_inference,[],[4401,3416,3434,10924,11975,12081,12167,12205,12213,12274,12425,12427,12823,12833,12838,12845,12851,12854,12882,12979,3441,12043,12437,12439,3442,12106,3497,3758,10819,12443,12445,12447,12449,3156,12473,12475,3157,12396,4431,4147,12479,12482,3161,12461,2996,3018,12469,3061,12407,4382,3543,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,11619,11953,12143,12330,12384,12386,12405,12411,12413,12415,12419,12456,12467,12496,12498,4359,11207,11211,12701,12869,12898,12978,12983,12989,12993,12997,13002,13015,3496,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,11728,11756,11776,11824,11938,11956,12023,12039,12197,12246,12650,12877,12900,12908,4405,10311,10402,3245,3206,12421,4398,12571,12586,12928,2786,2787,2798,2799,2807,2808,2810,2811,2814,2815,2816,2821,2822,2832,2834,2839,2840,2843,2844,2846,2848,2850,2851,2855,2857,2858,2859,2861,2867,2868,2870,2871,2875,2878,2880,2890,2902,2906,2908,2917,2923,2930,2931,2932,2933,2936,2937,2939,2959,2967,3060,4380,3533,3169,3229,3924,3141,3520,3773,4371,3120,11475,12226,12230,12234,3129,3241,3651,3965,3020,3021,4400,4419,4461,10852,11150,11153,3714,11242,3244,12451,3090,3052,10151,3566,12486,3046,3865,3068,3573,4345,3029,3008,3034,4068,11036,3067,3200,11718,11927,12062,12277,12350,3248,10677,12040,3118,3119,3139,10355,3297,4496,10283,3830,4421,10148,10308,12193,12227,12231,4430,12201,3176,11571,11574,12794,12904,12953,12957,12961,4486,10929,3172,3298,3519,3288,3261,12459,3085,3086,10213,10510,4470,3355,3077,2999,3128,3104,11233,3978,12216,12342,3832,10858,10991,11048,12177,12183,12288,12291,12317,4505,10780,10996,11107,11126,11156,11162,12125,4506,10898,10999,11110,4507,11002,11059,4508,11062,4509,3103,3396,12084,12122,12200,3558,4266,4267,3379,4418,11222,3500,3536,3704,4103,3468,12684,12688,12692,12696,12706,3752,12078,3382,3632,3258,10232,10348,10419,10463,10466,10513,10595,10842,11752,11796,11873,11934,12017,12020,12321,12565,12608,12611,12649,12667,12907,12912,3643,11466,3171,3272,11584,13014,3463,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,11876,11879,11966,12128,12220,12511,12530,12533,12557,12612,12771,12776,12801,12806,4492,11343,11376,11413,11446,12621,12625,12876,3630,3404,3405,12536,12539,12542,12545,12579,12582,12936,12940,12944,3782,3366,12941,3367,12937,3215,3216,3189,4473,3084,4415,3584,4118,3900,3388,4493,3972,11121,3518,3228,11590,11593,12047,12147,12301,3941,3898,11745,12093,3842,10674,11917,11941,12100,12324,12765,12952,3888,12956,3893,10864,11972,12046,12099,12146,12797,3894,3559,11755,11904,11980,12030,3862,3899,3575,10861,10934,11015,11081,11937,11998,12241,12314,12327,12762,12782,12832,12837,4497,10622,11007,12103,12848,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,11727,11991,12150,3187,10582,10625,10628,10661,10685,10722,10760,10796,11799,11802,11805,11808,12005,12008,12011,12014,12089,12252,12294,12558,12585,12659,12670,12675,12678,12681,12714,12725,12787,12810,12813,3188,10324,10525,10601,10725,11385,11622,11635,11731,11742,11761,11766,11784,11811,11827,11844,11849,12576,12718,12738,12772,12777,12802,12807,12990,12994,12998,13001,3266,11960,12685,12689,12693,12697,12707,12711,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,11700,11775,11795,11814,11823,11888,11891,11894,11897,11967,12054,12057,12153,12156,12219,12245,12280,12365,12666,3349,10480,10733,10777,11070,11142,11304,11548,12196,12368,12758,12827,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,11599,11882,11885,11922,11961,11994,12134,12174,12180,12264,12267,12284,12341,12347,12353,12358,12378,12653,12656,12747,12828,12873,12892,12895,12933,12977,3252,10507,10537,11099,11648,12281,12295,12622,12626,12629,3293,12921,12974,3285,3710,3648,10194,11469,11497,12603,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,11688,12816,3208,10682,10753,11498,11653,11854,12065,12090,12646,12924,13013,3670,11596,12552,4023,3410,4483,3679,3718,4464,4467,4468,3164,3168,4466,4465,4204,3687,3509,11462,4123,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,11181,3907,12114,3799,11178,11522,11526,11587,12204,12212,12287,12570,12822,12881,3637,10793,10799,10816,11781,11997,12260,3494,11033,12131,12138,12209,12255,12263,12375,3976,3639,10884,11045,11075,11086,12208,12249,12298,12865,3568,11583,3466,10469,10472,10540,10709,3465,4502,11463,4498,12520,4503,10598,10691,11018,11168,11301,12068,12075,12119,12311,4087,10667,12111,12137,3983,3669,12381,4500,10167,10170,10501,10504,11340,11527,12320,4501,11443,11536,3641,10475,10715,12911,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348,6351,6352,6354,6356,6357,6358,6360,6362,6365,6370,6371,6373,6374,6380,6382,6387,6425,6428,6441,6443,6445,6446,6447,6480,6485,6487,6492,6493,6501,6505,6518,6541,6542,6544,6545,6556,6560,6573,6579,6582,6584,6633,6634,6635,6640,6643,6672,6674,6676,6678,6683,6688,6701,6710,6743,6744,6745,6759,6760,6762,6763,6781,6782,6797,6818,6819,6825,6846,6859,6861,6863,6865,6866,6867,6874,6892,6906,6907,6912,6913,6920,6921,6923,6925,6952,6953,6965,6972,6973,6974,6976,7005,7014,7025,7034,7047,7048,7053,7055,7056,7062,7071,7085,7119,7121,7136,7146,7187,7192,7217,7262,7295,7309,7325,7356,7357,7360,7361,7385,7408,7425,7428,7429,7439,7459,7461,7463,7465,7466,7467,7514,7518,7519,7549,7551,7552,7553,7558,7580,7599,7609,7619,7631,7632,7634,7654,7658,7663,7664,7687,7705,7753,7754,7796,7804,7826,7843,7844,7906,7907,7934,7963,7974,7976,7984,7993,7997,8031,8037,8044,8058,8081,8104,8148,8178,8190,8207,8210,8245,8266,8331,8332,8336,8338,8356,8447,8448,8449,8450,8480,8507,8532,8574,8592,8647,8690,8693,8706,8713,8748,8795,8796,8813,8814,8958,8977,8987,9009,9011,9014,9018,9021,9022,9036,9054,9060,9072,9120,9139,9192,9193,9199,9235,9259,9264,9299,9306,9310,9313,9314,9329,9343,9352,9363,9376,9377,9381,9383,9409,9527,9569,9611,9656,9723,9774,9775,9834,9903,9976,9991,9996,3,2544,2546,2547,2548,2550,2555,2556,2557,2558,2559,2560,2568,2571,2575,2577,2578,2579,2583,2585,2591,2592,2600,2601,2602,2607,2608,2609,2610,2614,2615,2617,2618,2624,2626,2627,2633,2634,2635,2636,2643,2644,2645,2651,2666,2668,2671,2673,2676,2685,2689,2690,2697,2698,2699,2709,2712,2713,2714,2717,2718,2719,2721,2723,2726,2728,2729,2746,2747,2748,2750,2751,2765,5218,5395,5396,5397,5471,5517,5546,5574,5650,5652,5658,5715,5716,5717,5718,5724,5752,5883,5924,5933,5952,5987,6020,6024,6169,6174,6209,6210,6226,6229,6231,6238,6239,6240,6241,6242,6243,6244,6245,6328,6394,6395,6479,6512,6513,6553,6554,6689,6771,6772,6776,6798,6823,6831,6833,6882,6910,6911,6928,6929,6964,7008,7009,7108,7168,7169,7170,7171,7184,7211,7267,7268,7276,7285,7286,7298,7328,7329,7330,7331,7474,7476,7477,7478,7484,7485,7695,7701,7702,7712,7752,7822,7862,7918,7939,7940,7955,8016,8118,8188,8189,8191,8228,8291,8292,8387,8388,8389,8390,8536,8742,8765,8766,8817,8845,8861,8917,8918,9031,9064,9087,9121,9162,9319,9350,9605,9803,9861,9864,5543,5947,6309,6310,6398,6418,6419,6822,7043,8464,8684,8873,8874,8944,8945,9209,9210,9211,9212,9412,9675,10036,10037,6379,7263,7515,7516,7555,8282,8283,8732,8749,9676,10035,4558,4589,4591,4592,4651,4661,4794,4808,4809,4839,4840,4870,4920,4980,5040,5090,5118,5154,5157,5161,5163,5164,5189,5259,5280,5411,5478,5479,5480,5600,5601])). % 168.30/168.13 cnf(13129,plain, % 168.30/168.13 (~P22(f317(f317(f226(a849),f2(a849)),f37(x131291,f2(a849),x131292,x131293,x131294,x131295,x131296,x131297,x131298,a23)))), % 168.30/168.13 inference(scs_inference,[],[4401,3416,3434,10924,11975,12081,12167,12205,12213,12274,12425,12427,12823,12833,12838,12845,12851,12854,12882,12979,3441,12043,12437,12439,3442,12106,3497,3758,10819,12443,12445,12447,12449,3156,12473,12475,3157,12396,4431,4147,12479,12482,3161,12461,2996,3018,12469,3061,12407,4382,3543,4358,10081,10084,10093,10157,10160,10250,10253,10534,10545,10802,10805,11188,11191,11206,11210,11256,11259,11262,11265,11275,11312,11327,11354,11357,11368,11373,11379,11436,11478,11481,11484,11494,11533,11619,11953,12143,12330,12384,12386,12405,12411,12413,12415,12419,12456,12467,12496,12498,4359,11207,11211,12701,12869,12898,12978,12983,12989,12993,12997,13002,13015,3496,4386,10087,10090,10100,10111,10122,10221,10224,10227,10330,10440,10728,10909,10912,11113,11194,11201,11217,11268,11271,11382,11429,11449,11728,11756,11776,11824,11938,11956,12023,12039,12197,12246,12650,12877,12900,12908,4405,10311,10402,3245,3206,12421,4398,12571,12586,12928,2786,2787,2798,2799,2807,2808,2810,2811,2814,2815,2816,2821,2822,2832,2834,2839,2840,2843,2844,2846,2848,2850,2851,2855,2857,2858,2859,2861,2867,2868,2870,2871,2875,2878,2880,2890,2902,2906,2908,2917,2923,2930,2931,2932,2933,2936,2937,2939,2959,2967,3060,4380,3533,3169,3229,3924,3141,3520,3773,4371,3120,11475,12226,12230,12234,3129,3241,3651,3965,3020,3021,4400,4419,4461,10852,11150,11153,3714,11242,3244,12451,3090,3052,10151,3566,12486,3046,3865,3068,3573,4345,3029,3008,3034,4068,11036,3067,3200,11718,11927,12062,12277,12350,3248,10677,12040,3118,3119,3139,10355,3297,4496,10283,3830,4421,10148,10308,12193,12227,12231,4430,12201,3176,11571,11574,12794,12904,12953,12957,12961,4486,10929,3172,3298,3519,3288,3261,12459,3085,3086,10213,10510,4470,3355,3077,2999,3128,3104,11233,3978,12216,12342,3832,10858,10991,11048,12177,12183,12288,12291,12317,4505,10780,10996,11107,11126,11156,11162,12125,4506,10898,10999,11110,4507,11002,11059,4508,11062,4509,3103,3396,12084,12122,12200,3558,4266,4267,3379,4418,11222,3500,3536,3704,4103,3468,12684,12688,12692,12696,12706,3752,12078,3382,3632,3258,10232,10348,10419,10463,10466,10513,10595,10842,11752,11796,11873,11934,12017,12020,12321,12565,12608,12611,12649,12667,12907,12912,3643,11466,3171,3272,11584,13014,3463,4476,10125,10128,10154,10606,10619,10738,11171,11638,11643,11876,11879,11966,12128,12220,12511,12530,12533,12557,12612,12771,12776,12801,12806,4492,11343,11376,11413,11446,12621,12625,12876,3630,3404,3405,12536,12539,12542,12545,12579,12582,12936,12940,12944,3782,3366,12941,3367,12937,3215,3216,3189,4473,3084,4415,3584,4118,3900,3388,4493,3972,11121,3518,3228,11590,11593,12047,12147,12301,3941,3898,11745,12093,3842,10674,11917,11941,12100,12324,12765,12952,3888,12956,3893,10864,11972,12046,12099,12146,12797,3894,3559,11755,11904,11980,12030,3862,3899,3575,10861,10934,11015,11081,11937,11998,12241,12314,12327,12762,12782,12832,12837,4497,10622,11007,12103,12848,3186,10243,10337,10416,10520,11319,11326,11532,11542,11555,11618,11721,11727,11991,12150,3187,10582,10625,10628,10661,10685,10722,10760,10796,11799,11802,11805,11808,12005,12008,12011,12014,12089,12252,12294,12558,12585,12659,12670,12675,12678,12681,12714,12725,12787,12810,12813,3188,10324,10525,10601,10725,11385,11622,11635,11731,11742,11761,11766,11784,11811,11827,11844,11849,12576,12718,12738,12772,12777,12802,12807,12990,12994,12998,13001,3266,11960,12685,12689,12693,12697,12707,12711,4472,10191,10276,10327,10411,10643,10688,10698,11392,11493,11513,11516,11519,11539,11691,11694,11697,11700,11775,11795,11814,11823,11888,11891,11894,11897,11967,12054,12057,12153,12156,12219,12245,12280,12365,12666,3349,10480,10733,10777,11070,11142,11304,11548,12196,12368,12758,12827,4488,10652,10664,10769,10787,10790,10855,10948,10956,10972,11010,11027,11042,11078,11116,11136,11139,11165,11568,11599,11882,11885,11922,11961,11994,12134,12174,12180,12264,12267,12284,12341,12347,12353,12358,12378,12653,12656,12747,12828,12873,12892,12895,12933,12977,3252,10507,10537,11099,11648,12281,12295,12622,12626,12629,3293,12921,12974,3285,3710,3648,10194,11469,11497,12603,4485,10145,10495,10498,10951,10969,11428,11435,11523,11549,11654,11679,11682,11685,11688,12816,3208,10682,10753,11498,11653,11854,12065,12090,12646,12924,13013,3670,11596,12552,4023,3410,4483,3679,3718,4464,4467,4468,3164,3168,4466,4465,4204,3687,3509,11462,4123,4499,10116,10119,10373,10422,10427,10827,11298,11552,11657,4504,11030,11147,11181,3907,12114,3799,11178,11522,11526,11587,12204,12212,12287,12570,12822,12881,3637,10793,10799,10816,11781,11997,12260,3494,11033,12131,12138,12209,12255,12263,12375,3976,3639,10884,11045,11075,11086,12208,12249,12298,12865,3568,11583,3466,10469,10472,10540,10709,3465,4502,11463,4498,12520,4503,10598,10691,11018,11168,11301,12068,12075,12119,12311,4087,10667,12111,12137,3983,3669,12381,4500,10167,10170,10501,10504,11340,11527,12320,4501,11443,11536,3641,10475,10715,12911,3914,4512,4520,4525,4532,4548,4597,4599,4633,4650,4659,4660,4700,4728,4733,4816,4841,4842,4878,4903,4904,4921,4922,4935,4938,4959,4966,4983,4986,4987,4992,4997,4998,5019,5043,5044,5054,5059,5065,5110,5111,5119,5129,5133,5135,5145,5147,5153,5156,5171,5178,5181,5182,5186,5220,5232,5239,5241,5242,5245,5246,5247,5254,5256,5258,5262,5263,5264,5271,5275,5276,5277,5285,5289,5294,5306,5314,5326,5328,5336,5337,5341,5345,5368,5371,5377,5387,5388,5403,5436,5442,5458,5459,5462,5483,5491,5492,5497,5498,5508,5510,5523,5527,5538,5539,5540,5542,5558,5563,5575,5576,5585,5592,5604,5607,5608,5614,5615,5616,5619,5620,5625,5662,5663,5666,5669,5670,5672,5674,5676,5681,5688,5701,5719,5720,5729,5730,5735,5739,5741,5744,5788,5800,5808,5811,5815,5823,5826,5833,5847,5853,5871,5874,5886,5918,5919,5932,5953,5972,5973,5976,5989,5991,5993,5995,6007,6010,6011,6013,6016,6017,6028,6033,6035,6040,6079,6080,6087,6096,6137,6139,6141,6143,6149,6151,6153,6159,6161,6167,6170,6178,6185,6186,6187,6193,6215,6221,6225,6261,6262,6264,6265,6266,6268,6269,6270,6271,6277,6311,6312,6319,6322,6323,6343,6363,6366,6377,6378,6384,6397,6415,6416,6417,6429,6523,6546,6590,6605,6614,6615,6616,6617,6638,6639,6646,6657,6660,6662,6664,6665,6666,6668,6682,6691,6693,6694,6706,6709,6757,6768,6770,6774,6788,6789,6827,6840,6870,6909,6961,6993,7044,7068,7077,7081,7133,7145,7191,7193,7210,7220,7221,7222,7243,7249,7250,7299,7308,7311,7326,7376,7378,7381,7423,7424,7442,7510,7530,7550,7573,7588,7602,7612,7622,7623,7653,7655,7657,7666,7704,7715,7741,7795,7824,7855,7899,7915,7931,7932,8009,8063,8080,8105,8125,8145,8150,8237,8251,8253,8258,8275,8279,8295,8298,8317,8328,8330,8346,8352,8355,8380,8394,8395,8405,8406,8412,8415,8420,8421,8422,8423,8424,8443,8444,8445,8454,8455,8469,8471,8485,8489,8491,8492,8493,8500,8504,8528,8529,8558,8571,8575,8593,8615,8616,8617,8618,8630,8631,8653,8663,8672,8673,8674,8675,8677,8697,8698,8709,8751,8757,8763,8776,8778,8782,8785,8786,8790,8799,8883,8914,8915,8916,8931,8948,8953,8979,8980,9020,9023,9049,9092,9093,9094,9109,9115,9116,9134,9147,9153,9157,9179,9180,9207,9267,9302,9303,9304,9330,9331,9347,9364,9370,9389,9411,9433,9440,9441,9442,9443,9457,9459,9464,9497,9498,9504,9543,9544,9572,9582,9592,9594,9595,9604,9618,9648,9679,9685,9745,9791,9792,9804,9805,9825,9830,9853,9858,9877,9926,10050,10066,2,8,9,4535,4536,4554,4585,4586,4588,4617,4625,4626,4637,4688,4690,4732,4761,4776,4857,4858,4871,4891,4941,4942,4945,4946,4948,4950,4962,4963,4973,4984,4985,4995,5014,5015,5031,5036,5037,5038,5039,5042,5050,5053,5060,5125,5131,5132,5139,5168,5179,5184,5200,5203,5219,5226,5227,5228,5236,5251,5252,5253,5260,5267,5268,5281,5282,5283,5284,5286,5287,5290,5291,5292,5293,5322,5323,5324,5332,5333,5334,5335,5379,5384,5386,5421,5423,5424,5426,5427,5429,5430,5432,5441,5446,5448,5449,5450,5451,5452,5453,5460,5470,5474,5475,5486,5502,5503,5506,5516,5519,5520,5521,5550,5560,5577,5578,5586,5587,5589,5591,5627,5632,5634,5689,5721,5722,5726,5731,5732,5733,5734,5740,5750,5751,5753,5754,5762,5769,5785,5814,5829,5832,5834,5843,5845,5861,5865,5868,5869,5870,5890,5902,5903,5934,5935,5955,5958,5980,5985,5986,6008,6012,6019,6027,6032,6034,6044,6045,6046,6047,6082,6097,6135,6152,6188,6189,6191,6211,6212,6214,6218,6219,6227,6236,6253,6273,6274,6278,6288,6302,6326,6331,6333,6347,6348,6351,6352,6354,6356,6357,6358,6360,6362,6365,6370,6371,6373,6374,6380,6382,6387,6425,6428,6441,6443,6445,6446,6447,6480,6485,6487,6492,6493,6501,6505,6518,6541,6542,6544,6545,6556,6560,6573,6579,6582,6584,6633,6634,6635,6640,6643,6672,6674,6676,6678,6683,6688,6701,6710,6743,6744,6745,6759,6760,6762,6763,6781,6782,6797,6818,6819,6825,6846,6859,6861,6863,6865,6866,6867,6874,6892,6906,6907,6912,6913,6920,6921,6923,6925,6952,6953,6965,6972,6973,6974,6976,7005,7014,7025,7034,7047,7048,7053,7055,7056,7062,7071,7085,7119,7121,7136,7146,7187,7192,7217,7262,7295,7309,7325,7356,7357,7360,7361,7385,7408,7425,7428,7429,7439,7459,7461,7463,7465,7466,7467,7514,7518,7519,7549,7551,7552,7553,7558,7580,7599,7609,7619,7631,7632,7634,7654,7658,7663,7664,7687,7705,7753,7754,7796,7804,7826,7843,7844,7906,7907,7934,7963,7974,7976,7984,7993,7997,8031,8037,8044,8058,8081,8104,8148,8178,8190,8207,8210,8245,8266,8331,8332,8336,8338,8356,8447,8448,8449,8450,8480,8507,8532,8574,8592,8647,8690,8693,8706,8713,8748,8795,8796,8813,8814,8958,8977,8987,9009,9011,9014,9018,9021,9022,9036,9054,9060,9072,9120,9139,9192,9193,9199,9235,9259,9264,9299,9306,9310,9313,9314,9329,9343,9352,9363,9376,9377,9381,9383,9409,9527,9569,9611,9656,9723,9774,9775,9834,9903,9976,9991,9996,3,2544,2546,2547,2548,2550,2555,2556,2557,2558,2559,2560,2568,2571,2575,2577,2578,2579,2583,2585,2591,2592,2600,2601,2602,2607,2608,2609,2610,2614,2615,2617,2618,2624,2626,2627,2633,2634,2635,2636,2643,2644,2645,2651,2666,2668,2671,2673,2676,2685,2689,2690,2697,2698,2699,2709,2712,2713,2714,2717,2718,2719,2721,2723,2726,2728,2729,2746,2747,2748,2750,2751,2765,5218,5395,5396,5397,5471,5517,5546,5574,5650,5652,5658,5715,5716,5717,5718,5724,5752,5883,5924,5933,5952,5987,6020,6024,6169,6174,6209,6210,6226,6229,6231,6238,6239,6240,6241,6242,6243,6244,6245,6328,6394,6395,6479,6512,6513,6553,6554,6689,6771,6772,6776,6798,6823,6831,6833,6882,6910,6911,6928,6929,6964,7008,7009,7108,7168,7169,7170,7171,7184,7211,7267,7268,7276,7285,7286,7298,7328,7329,7330,7331,7474,7476,7477,7478,7484,7485,7695,7701,7702,7712,7752,7822,7862,7918,7939,7940,7955,8016,8118,8188,8189,8191,8228,8291,8292,8387,8388,8389,8390,8536,8742,8765,8766,8817,8845,8861,8917,8918,9031,9064,9087,9121,9162,9319,9350,9605,9803,9861,9864,5543,5947,6309,6310,6398,6418,6419,6822,7043,8464,8684,8873,8874,8944,8945,9209,9210,9211,9212,9412,9675,10036,10037,6379,7263,7515,7516,7555,8282,8283,8732,8749,9676,10035,4558,4589,4591,4592,4651,4661,4794,4808,4809,4839,4840,4870,4920,4980,5040,5090,5118,5154,5157,5161,5163,5164,5189,5259,5280,5411,5478,5479,5480,5600,5601,5623,5624,5628,5678,5684,5693,5699,5765,5841,5908,5994,6155,6272,6426,6508,6769,6835,6877])). % 168.30/168.13 cnf(13255,plain, % 168.30/168.13 (~P22(f317(f317(f319(f857(x132551,x132551)),x132552),f235(x132551,f188(f858(x132551,a842)))))), % 168.30/168.13 inference(rename_variables,[],[10786])). % 168.30/168.13 cnf(13266,plain, % 168.30/168.13 (E(f38(x132661,x132662,x132663,x132664,x132665,x132666,x132667,x132668,x132669,a23),x132662)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(13273,plain, % 168.30/168.13 (P22(f317(f317(f225(a849),f55(a849,x132731,x132732)),x132731))), % 168.30/168.13 inference(rename_variables,[],[3648])). % 168.30/168.13 cnf(13289,plain, % 168.30/168.13 (~P22(f317(f317(f319(x132891),x132892),f188(f858(x132891,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(13305,plain, % 168.30/168.13 (E(f38(x133051,x133052,x133053,x133054,x133055,x133056,x133057,x133058,x133059,a23),x133052)), % 168.30/168.13 inference(rename_variables,[],[4359])). % 168.30/168.13 cnf(13322,plain, % 168.30/168.13 (~P22(f317(f317(f319(x133221),x133222),f188(f858(x133221,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(13327,plain, % 168.30/168.13 (E(f317(x133271,f779(f317(x133271,x133272),f317(f217(x133273),x133272),x133271,x133274,x133273)),f317(x133271,x133272))), % 168.30/168.13 inference(rename_variables,[],[10982])). % 168.30/168.13 cnf(13359,plain, % 168.30/168.13 (~P22(f317(f317(f319(x133591),x133592),f188(f858(x133591,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(13404,plain, % 168.30/168.13 (~P22(f317(f317(f319(x134041),x134042),f188(f858(x134041,a842))))), % 168.30/168.13 inference(rename_variables,[],[4488])). % 168.30/168.13 cnf(13417,plain, % 168.30/168.13 ($false), % 168.30/168.13 inference(scs_inference,[],[3978,4502,3187,4473,3832,3285,3643,4505,4488,13289,13322,13359,13404,3893,3799,4421,4486,3171,3648,13273,4358,4359,13266,13305,3128,4472,4485,4503,4500,3442,11676,13093,10408,10471,11730,12554,10458,10914,12308,10776,12367,10982,13327,10544,12809,10549,13129,12130,10786,13255,11890,11054,2957,5480,6170,8,9180,9464,5276,5833,6151,6377,8279,6616,7666,5306,8979,9441,9459,5681,6757,9443,6017,5388,6664,7932,8672,5847,7442,8405,8420,8445,8915,5118,4592,5459,8258,8751,8346,5241,6265,5699,9433,8571,6384,7133,7381,9804,5135,5264,6363,6666,8412,8785,9572,5991,9049,5666,5181,5245,6323,8422,5247,7299,8558,5918,6639,4992,4997,5608,6366,8757,4633]), % 168.30/168.13 ['proof']). % 168.30/168.13 % SZS output end Proof % 168.30/168.13 % Total time :147.580000s %------------------------------------------------------------------------------